Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.k (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 13.4 | ||
Character | \(\chi\) | \(=\) | 45.13 |
Dual form | 45.3.k.a.7.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.891829 | − | 0.238965i | −0.445914 | − | 0.119482i | 0.0288727 | − | 0.999583i | \(-0.490808\pi\) |
−0.474787 | + | 0.880101i | \(0.657475\pi\) | |||||||
\(3\) | −2.93652 | + | 0.613889i | −0.978839 | + | 0.204630i | ||||
\(4\) | −2.72585 | − | 1.57377i | −0.681462 | − | 0.393442i | ||||
\(5\) | −1.31764 | + | 4.82326i | −0.263528 | + | 0.964652i | ||||
\(6\) | 2.76557 | + | 0.154241i | 0.460928 | + | 0.0257068i | ||||
\(7\) | −11.0534 | − | 2.96175i | −1.57906 | − | 0.423108i | −0.640425 | − | 0.768021i | \(-0.721242\pi\) |
−0.938635 | + | 0.344913i | \(0.887909\pi\) | |||||||
\(8\) | 4.66637 | + | 4.66637i | 0.583296 | + | 0.583296i | ||||
\(9\) | 8.24628 | − | 3.60539i | 0.916253 | − | 0.400599i | ||||
\(10\) | 2.32770 | − | 3.98665i | 0.232770 | − | 0.398665i | ||||
\(11\) | −1.30484 | − | 2.26005i | −0.118622 | − | 0.205459i | 0.800600 | − | 0.599199i | \(-0.204514\pi\) |
−0.919222 | + | 0.393740i | \(0.871181\pi\) | |||||||
\(12\) | 8.97062 | + | 2.94803i | 0.747552 | + | 0.245669i | ||||
\(13\) | 2.85447 | − | 0.764853i | 0.219575 | − | 0.0588349i | −0.147354 | − | 0.989084i | \(-0.547076\pi\) |
0.366929 | + | 0.930249i | \(0.380409\pi\) | |||||||
\(14\) | 9.15000 | + | 5.28276i | 0.653572 | + | 0.377340i | ||||
\(15\) | 0.908333 | − | 14.9725i | 0.0605555 | − | 0.998165i | ||||
\(16\) | 3.24857 | + | 5.62669i | 0.203036 | + | 0.351668i | ||||
\(17\) | −13.6850 | + | 13.6850i | −0.805003 | + | 0.805003i | −0.983873 | − | 0.178870i | \(-0.942756\pi\) |
0.178870 | + | 0.983873i | \(0.442756\pi\) | |||||||
\(18\) | −8.21583 | + | 1.24482i | −0.456435 | + | 0.0691568i | ||||
\(19\) | − | 11.4465i | − | 0.602446i | −0.953554 | − | 0.301223i | \(-0.902605\pi\) | ||
0.953554 | − | 0.301223i | \(-0.0973948\pi\) | |||||||
\(20\) | 11.1824 | − | 11.0738i | 0.559119 | − | 0.553690i | ||||
\(21\) | 34.2768 | + | 1.91167i | 1.63223 | + | 0.0910321i | ||||
\(22\) | 0.623621 | + | 2.32738i | 0.0283464 | + | 0.105790i | ||||
\(23\) | −10.7887 | + | 2.89082i | −0.469074 | + | 0.125688i | −0.485611 | − | 0.874175i | \(-0.661403\pi\) |
0.0165366 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(24\) | −16.5675 | − | 10.8382i | −0.690313 | − | 0.451594i | ||||
\(25\) | −21.5276 | − | 12.7107i | −0.861106 | − | 0.508426i | ||||
\(26\) | −2.72847 | −0.104941 | ||||||||
\(27\) | −22.0020 | + | 15.6496i | −0.814890 | + | 0.579615i | ||||
\(28\) | 25.4688 | + | 25.4688i | 0.909601 | + | 0.909601i | ||||
\(29\) | −23.0262 | + | 13.2942i | −0.794005 | + | 0.458419i | −0.841371 | − | 0.540458i | \(-0.818251\pi\) |
0.0473654 | + | 0.998878i | \(0.484917\pi\) | |||||||
\(30\) | −4.38797 | + | 13.1358i | −0.146266 | + | 0.437861i | ||||
\(31\) | −21.8787 | + | 37.8950i | −0.705764 | + | 1.22242i | 0.260652 | + | 0.965433i | \(0.416063\pi\) |
−0.966415 | + | 0.256985i | \(0.917271\pi\) | |||||||
\(32\) | −8.38463 | − | 31.2919i | −0.262020 | − | 0.977870i | ||||
\(33\) | 5.21910 | + | 5.83564i | 0.158154 | + | 0.176838i | ||||
\(34\) | 15.4750 | − | 8.93448i | 0.455146 | − | 0.262779i | ||||
\(35\) | 28.8498 | − | 49.4110i | 0.824279 | − | 1.41174i | ||||
\(36\) | −28.1522 | − | 3.14999i | −0.782004 | − | 0.0874996i | ||||
\(37\) | 14.4324 | − | 14.4324i | 0.390065 | − | 0.390065i | −0.484646 | − | 0.874711i | \(-0.661051\pi\) |
0.874711 | + | 0.484646i | \(0.161051\pi\) | |||||||
\(38\) | −2.73530 | + | 10.2083i | −0.0719817 | + | 0.268639i | ||||
\(39\) | −7.91267 | + | 3.99833i | −0.202889 | + | 0.102521i | ||||
\(40\) | −28.6557 | + | 16.3585i | −0.716393 | + | 0.408963i | ||||
\(41\) | −0.924605 | + | 1.60146i | −0.0225513 | + | 0.0390601i | −0.877081 | − | 0.480343i | \(-0.840512\pi\) |
0.854529 | + | 0.519403i | \(0.173846\pi\) | |||||||
\(42\) | −30.1122 | − | 9.89582i | −0.716957 | − | 0.235615i | ||||
\(43\) | 13.1494 | − | 49.0742i | 0.305800 | − | 1.14126i | −0.626455 | − | 0.779458i | \(-0.715495\pi\) |
0.932255 | − | 0.361803i | \(-0.117839\pi\) | |||||||
\(44\) | 8.21405i | 0.186683i | ||||||||
\(45\) | 6.52410 | + | 44.5246i | 0.144980 | + | 0.989435i | ||||
\(46\) | 10.3125 | 0.224184 | ||||||||
\(47\) | 61.3211 | + | 16.4309i | 1.30470 | + | 0.349594i | 0.843227 | − | 0.537558i | \(-0.180653\pi\) |
0.461477 | + | 0.887152i | \(0.347320\pi\) | |||||||
\(48\) | −12.9936 | − | 14.5286i | −0.270701 | − | 0.302679i | ||||
\(49\) | 70.9709 | + | 40.9750i | 1.44838 | + | 0.836225i | ||||
\(50\) | 16.1616 | + | 16.4801i | 0.323231 | + | 0.329601i | ||||
\(51\) | 31.7853 | − | 48.5875i | 0.623241 | − | 0.952696i | ||||
\(52\) | −8.98455 | − | 2.40740i | −0.172780 | − | 0.0462962i | ||||
\(53\) | 6.43481 | + | 6.43481i | 0.121412 | + | 0.121412i | 0.765202 | − | 0.643790i | \(-0.222639\pi\) |
−0.643790 | + | 0.765202i | \(0.722639\pi\) | |||||||
\(54\) | 23.3618 | − | 8.69905i | 0.432625 | − | 0.161094i | ||||
\(55\) | 12.6201 | − | 3.31564i | 0.229456 | − | 0.0602844i | ||||
\(56\) | −37.7587 | − | 65.4000i | −0.674262 | − | 1.16786i | ||||
\(57\) | 7.02686 | + | 33.6128i | 0.123278 | + | 0.589698i | ||||
\(58\) | 23.7122 | − | 6.35367i | 0.408831 | − | 0.109546i | ||||
\(59\) | −49.5170 | − | 28.5886i | −0.839271 | − | 0.484553i | 0.0177457 | − | 0.999843i | \(-0.494351\pi\) |
−0.857016 | + | 0.515289i | \(0.827684\pi\) | |||||||
\(60\) | −26.0392 | + | 39.3832i | −0.433986 | + | 0.656386i | ||||
\(61\) | 16.8393 | + | 29.1666i | 0.276055 | + | 0.478141i | 0.970401 | − | 0.241501i | \(-0.0776396\pi\) |
−0.694346 | + | 0.719641i | \(0.744306\pi\) | |||||||
\(62\) | 28.5676 | − | 28.5676i | 0.460768 | − | 0.460768i | ||||
\(63\) | −101.828 | + | 15.4285i | −1.61632 | + | 0.244896i | ||||
\(64\) | 3.92205i | 0.0612820i | ||||||||
\(65\) | −0.0720848 | + | 14.7757i | −0.00110900 | + | 0.227318i | ||||
\(66\) | −3.26003 | − | 6.45157i | −0.0493944 | − | 0.0977511i | ||||
\(67\) | −8.41554 | − | 31.4072i | −0.125605 | − | 0.468765i | 0.874255 | − | 0.485466i | \(-0.161350\pi\) |
−0.999861 | + | 0.0167016i | \(0.994683\pi\) | |||||||
\(68\) | 58.8405 | − | 15.7663i | 0.865301 | − | 0.231857i | ||||
\(69\) | 29.9066 | − | 15.1120i | 0.433429 | − | 0.219015i | ||||
\(70\) | −37.5365 | + | 37.1720i | −0.536236 | + | 0.531029i | ||||
\(71\) | −63.3498 | −0.892251 | −0.446126 | − | 0.894970i | \(-0.647197\pi\) | ||||
−0.446126 | + | 0.894970i | \(0.647197\pi\) | |||||||
\(72\) | 55.3043 | + | 21.6561i | 0.768115 | + | 0.300779i | ||||
\(73\) | −50.9063 | − | 50.9063i | −0.697347 | − | 0.697347i | 0.266491 | − | 0.963838i | \(-0.414136\pi\) |
−0.963838 | + | 0.266491i | \(0.914136\pi\) | |||||||
\(74\) | −16.3201 | + | 9.42239i | −0.220541 | + | 0.127330i | ||||
\(75\) | 71.0192 | + | 24.1095i | 0.946923 | + | 0.321460i | ||||
\(76\) | −18.0141 | + | 31.2013i | −0.237028 | + | 0.410544i | ||||
\(77\) | 7.72922 | + | 28.8458i | 0.100379 | + | 0.374621i | ||||
\(78\) | 8.01221 | − | 1.67498i | 0.102721 | − | 0.0214741i | ||||
\(79\) | −59.5972 | + | 34.4084i | −0.754395 | + | 0.435550i | −0.827280 | − | 0.561790i | \(-0.810113\pi\) |
0.0728850 | + | 0.997340i | \(0.476779\pi\) | |||||||
\(80\) | −31.4194 | + | 8.25473i | −0.392743 | + | 0.103184i | ||||
\(81\) | 55.0023 | − | 59.4622i | 0.679040 | − | 0.734101i | ||||
\(82\) | 1.20728 | − | 1.20728i | 0.0147230 | − | 0.0147230i | ||||
\(83\) | −27.2882 | + | 101.841i | −0.328773 | + | 1.22700i | 0.581691 | + | 0.813410i | \(0.302391\pi\) |
−0.910464 | + | 0.413589i | \(0.864275\pi\) | |||||||
\(84\) | −90.4247 | − | 59.1546i | −1.07648 | − | 0.704222i | ||||
\(85\) | −47.9745 | − | 84.0385i | −0.564406 | − | 0.988688i | ||||
\(86\) | −23.4540 | + | 40.6236i | −0.272721 | + | 0.472367i | ||||
\(87\) | 59.4556 | − | 53.1740i | 0.683398 | − | 0.611196i | ||||
\(88\) | 4.45735 | − | 16.6351i | 0.0506517 | − | 0.189035i | ||||
\(89\) | 136.887i | 1.53806i | 0.639213 | + | 0.769029i | \(0.279260\pi\) | ||||
−0.639213 | + | 0.769029i | \(0.720740\pi\) | |||||||
\(90\) | 4.82142 | − | 41.2673i | 0.0535713 | − | 0.458526i | ||||
\(91\) | −33.8170 | −0.371615 | ||||||||
\(92\) | 33.9578 | + | 9.09897i | 0.369107 | + | 0.0989019i | ||||
\(93\) | 40.9838 | − | 124.710i | 0.440686 | − | 1.34097i | ||||
\(94\) | −50.7615 | − | 29.3072i | −0.540016 | − | 0.311778i | ||||
\(95\) | 55.2093 | + | 15.0823i | 0.581150 | + | 0.158762i | ||||
\(96\) | 43.8313 | + | 86.7419i | 0.456576 | + | 0.903561i | ||||
\(97\) | 35.3034 | + | 9.45952i | 0.363953 | + | 0.0975209i | 0.436161 | − | 0.899869i | \(-0.356338\pi\) |
−0.0722080 | + | 0.997390i | \(0.523005\pi\) | |||||||
\(98\) | −53.5023 | − | 53.5023i | −0.545941 | − | 0.545941i | ||||
\(99\) | −18.9084 | − | 13.9325i | −0.190994 | − | 0.140732i | ||||
\(100\) | 38.6774 | + | 68.5268i | 0.386774 | + | 0.685268i | ||||
\(101\) | −48.3142 | − | 83.6827i | −0.478359 | − | 0.828541i | 0.521334 | − | 0.853353i | \(-0.325435\pi\) |
−0.999692 | + | 0.0248116i | \(0.992101\pi\) | |||||||
\(102\) | −39.9577 | + | 35.7362i | −0.391743 | + | 0.350355i | ||||
\(103\) | 25.6673 | − | 6.87754i | 0.249198 | − | 0.0667723i | −0.132058 | − | 0.991242i | \(-0.542158\pi\) |
0.381255 | + | 0.924470i | \(0.375492\pi\) | |||||||
\(104\) | 16.8891 | + | 9.75093i | 0.162395 | + | 0.0937589i | ||||
\(105\) | −54.3850 | + | 162.807i | −0.517952 | + | 1.55054i | ||||
\(106\) | −4.20106 | − | 7.27645i | −0.0396326 | − | 0.0686457i | ||||
\(107\) | −43.8389 | + | 43.8389i | −0.409709 | + | 0.409709i | −0.881637 | − | 0.471928i | \(-0.843558\pi\) |
0.471928 | + | 0.881637i | \(0.343558\pi\) | |||||||
\(108\) | 84.6031 | − | 8.03231i | 0.783362 | − | 0.0743732i | ||||
\(109\) | − | 13.1212i | − | 0.120378i | −0.998187 | − | 0.0601892i | \(-0.980830\pi\) | ||
0.998187 | − | 0.0601892i | \(-0.0191704\pi\) | |||||||
\(110\) | −12.0473 | − | 0.0587742i | −0.109521 | − | 0.000534311i | ||||
\(111\) | −33.5211 | + | 51.2409i | −0.301992 | + | 0.461630i | ||||
\(112\) | −19.2429 | − | 71.8156i | −0.171812 | − | 0.641211i | ||||
\(113\) | 31.4100 | − | 8.41629i | 0.277965 | − | 0.0744805i | −0.117143 | − | 0.993115i | \(-0.537374\pi\) |
0.395108 | + | 0.918635i | \(0.370707\pi\) | |||||||
\(114\) | 1.76551 | − | 31.6560i | 0.0154869 | − | 0.277684i | ||||
\(115\) | 0.272450 | − | 55.8458i | 0.00236913 | − | 0.485615i | ||||
\(116\) | 83.6877 | 0.721446 | ||||||||
\(117\) | 20.7812 | − | 16.5987i | 0.177617 | − | 0.141869i | ||||
\(118\) | 37.3290 | + | 37.3290i | 0.316347 | + | 0.316347i | ||||
\(119\) | 191.798 | − | 110.735i | 1.61175 | − | 0.930545i | ||||
\(120\) | 74.1057 | − | 65.6285i | 0.617548 | − | 0.546904i | ||||
\(121\) | 57.0948 | − | 98.8911i | 0.471858 | − | 0.817282i | ||||
\(122\) | −8.04801 | − | 30.0356i | −0.0659673 | − | 0.246193i | ||||
\(123\) | 1.73200 | − | 5.27033i | 0.0140813 | − | 0.0428482i | ||||
\(124\) | 119.276 | − | 68.8639i | 0.961902 | − | 0.555354i | ||||
\(125\) | 89.6725 | − | 87.0853i | 0.717380 | − | 0.696682i | ||||
\(126\) | 94.4999 | + | 10.5737i | 0.749999 | + | 0.0839185i | ||||
\(127\) | −108.223 | + | 108.223i | −0.852153 | + | 0.852153i | −0.990398 | − | 0.138245i | \(-0.955854\pi\) |
0.138245 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(128\) | −32.6013 | + | 121.670i | −0.254697 | + | 0.950544i | ||||
\(129\) | −8.48732 | + | 152.180i | −0.0657932 | + | 1.17969i | ||||
\(130\) | 3.59515 | − | 13.1601i | 0.0276550 | − | 0.101232i | ||||
\(131\) | −3.28859 | + | 5.69601i | −0.0251038 | + | 0.0434810i | −0.878304 | − | 0.478102i | \(-0.841325\pi\) |
0.853201 | + | 0.521583i | \(0.174658\pi\) | |||||||
\(132\) | −5.04252 | − | 24.1207i | −0.0382009 | − | 0.182733i | ||||
\(133\) | −33.9016 | + | 126.523i | −0.254900 | + | 0.951298i | ||||
\(134\) | 30.0209i | 0.224036i | ||||||||
\(135\) | −46.4913 | − | 126.742i | −0.344380 | − | 0.938830i | ||||
\(136\) | −127.719 | −0.939110 | ||||||||
\(137\) | −84.1178 | − | 22.5393i | −0.613998 | − | 0.164520i | −0.0616003 | − | 0.998101i | \(-0.519620\pi\) |
−0.552398 | + | 0.833581i | \(0.686287\pi\) | |||||||
\(138\) | −30.2828 | + | 6.33072i | −0.219440 | + | 0.0458748i | ||||
\(139\) | 75.7500 | + | 43.7343i | 0.544964 | + | 0.314635i | 0.747088 | − | 0.664725i | \(-0.231451\pi\) |
−0.202124 | + | 0.979360i | \(0.564785\pi\) | |||||||
\(140\) | −156.401 | + | 89.2839i | −1.11715 | + | 0.637742i | ||||
\(141\) | −190.157 | − | 10.6054i | −1.34863 | − | 0.0752156i | ||||
\(142\) | 56.4972 | + | 15.1384i | 0.397868 | + | 0.106608i | ||||
\(143\) | −5.45322 | − | 5.45322i | −0.0381344 | − | 0.0381344i | ||||
\(144\) | 47.0750 | + | 34.6869i | 0.326910 | + | 0.240881i | ||||
\(145\) | −33.7809 | − | 128.578i | −0.232972 | − | 0.886745i | ||||
\(146\) | 33.2349 | + | 57.5646i | 0.227636 | + | 0.394278i | ||||
\(147\) | −233.561 | − | 76.7557i | −1.58885 | − | 0.522148i | ||||
\(148\) | −62.0538 | + | 16.6273i | −0.419282 | + | 0.112346i | ||||
\(149\) | −144.963 | − | 83.6946i | −0.972909 | − | 0.561709i | −0.0727869 | − | 0.997348i | \(-0.523189\pi\) |
−0.900122 | + | 0.435638i | \(0.856523\pi\) | |||||||
\(150\) | −57.5757 | − | 38.4726i | −0.383838 | − | 0.256484i | ||||
\(151\) | 124.775 | + | 216.117i | 0.826325 | + | 1.43124i | 0.900902 | + | 0.434022i | \(0.142906\pi\) |
−0.0745766 | + | 0.997215i | \(0.523761\pi\) | |||||||
\(152\) | 53.4135 | − | 53.4135i | 0.351404 | − | 0.351404i | ||||
\(153\) | −63.5108 | + | 162.191i | −0.415103 | + | 1.06007i | ||||
\(154\) | − | 27.5726i | − | 0.179043i | ||||||
\(155\) | −153.949 | − | 155.458i | −0.993219 | − | 1.00296i | ||||
\(156\) | 27.8612 | + | 1.55387i | 0.178597 | + | 0.00996068i | ||||
\(157\) | 12.9675 | + | 48.3954i | 0.0825957 | + | 0.308251i | 0.994848 | − | 0.101377i | \(-0.0323250\pi\) |
−0.912252 | + | 0.409629i | \(0.865658\pi\) | |||||||
\(158\) | 61.3729 | − | 16.4448i | 0.388436 | − | 0.104081i | ||||
\(159\) | −22.8462 | − | 14.9457i | −0.143687 | − | 0.0939980i | ||||
\(160\) | 161.977 | + | 0.790223i | 1.01235 | + | 0.00493889i | ||||
\(161\) | 127.814 | 0.793875 | ||||||||
\(162\) | −63.2620 | + | 39.8865i | −0.390506 | + | 0.246213i | ||||
\(163\) | −23.5188 | − | 23.5188i | −0.144287 | − | 0.144287i | 0.631273 | − | 0.775560i | \(-0.282533\pi\) |
−0.775560 | + | 0.631273i | \(0.782533\pi\) | |||||||
\(164\) | 5.04066 | − | 2.91023i | 0.0307358 | − | 0.0177453i | ||||
\(165\) | −35.0237 | + | 17.4838i | −0.212265 | + | 0.105962i | ||||
\(166\) | 48.6728 | − | 84.3037i | 0.293210 | − | 0.507854i | ||||
\(167\) | −28.6408 | − | 106.889i | −0.171502 | − | 0.640052i | −0.997121 | − | 0.0758252i | \(-0.975841\pi\) |
0.825620 | − | 0.564227i | \(-0.190826\pi\) | |||||||
\(168\) | 151.027 | + | 168.869i | 0.898973 | + | 1.00517i | ||||
\(169\) | −138.795 | + | 80.1335i | −0.821274 | + | 0.474163i | ||||
\(170\) | 22.7028 | + | 86.4122i | 0.133546 | + | 0.508307i | ||||
\(171\) | −41.2690 | − | 94.3908i | −0.241339 | − | 0.551993i | ||||
\(172\) | −113.075 | + | 113.075i | −0.657411 | + | 0.657411i | ||||
\(173\) | 17.6528 | − | 65.8811i | 0.102039 | − | 0.380816i | −0.895953 | − | 0.444149i | \(-0.853506\pi\) |
0.997992 | + | 0.0633327i | \(0.0201729\pi\) | |||||||
\(174\) | −65.7309 | + | 33.2143i | −0.377764 | + | 0.190887i | ||||
\(175\) | 200.308 | + | 204.256i | 1.14462 | + | 1.16718i | ||||
\(176\) | 8.47772 | − | 14.6838i | 0.0481688 | − | 0.0834309i | ||||
\(177\) | 162.958 | + | 53.5531i | 0.920665 | + | 0.302560i | ||||
\(178\) | 32.7112 | − | 122.080i | 0.183771 | − | 0.685843i | ||||
\(179\) | − | 303.920i | − | 1.69788i | −0.528490 | − | 0.848939i | \(-0.677242\pi\) | ||
0.528490 | − | 0.848939i | \(-0.322758\pi\) | |||||||
\(180\) | 52.2876 | − | 131.635i | 0.290487 | − | 0.731303i | ||||
\(181\) | 172.576 | 0.953460 | 0.476730 | − | 0.879050i | \(-0.341822\pi\) | ||||
0.476730 | + | 0.879050i | \(0.341822\pi\) | |||||||
\(182\) | 30.1589 | + | 8.08107i | 0.165708 | + | 0.0444015i | ||||
\(183\) | −67.3540 | − | 75.3107i | −0.368055 | − | 0.411534i | ||||
\(184\) | −63.8337 | − | 36.8544i | −0.346922 | − | 0.200296i | ||||
\(185\) | 50.5945 | + | 88.6279i | 0.273484 | + | 0.479070i | ||||
\(186\) | −66.3519 | + | 101.427i | −0.356731 | + | 0.545304i | ||||
\(187\) | 48.7856 | + | 13.0721i | 0.260886 | + | 0.0699041i | ||||
\(188\) | −141.293 | − | 141.293i | −0.751561 | − | 0.751561i | ||||
\(189\) | 289.548 | − | 107.817i | 1.53200 | − | 0.570460i | ||||
\(190\) | −45.6331 | − | 26.6439i | −0.240174 | − | 0.140231i | ||||
\(191\) | 143.618 | + | 248.754i | 0.751927 | + | 1.30238i | 0.946887 | + | 0.321565i | \(0.104209\pi\) |
−0.194960 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(192\) | −2.40770 | − | 11.5172i | −0.0125401 | − | 0.0599852i | ||||
\(193\) | −35.5390 | + | 9.52264i | −0.184140 | + | 0.0493401i | −0.349711 | − | 0.936858i | \(-0.613720\pi\) |
0.165571 | + | 0.986198i | \(0.447053\pi\) | |||||||
\(194\) | −29.2241 | − | 16.8725i | −0.150640 | − | 0.0869719i | ||||
\(195\) | −8.85893 | − | 43.4332i | −0.0454304 | − | 0.222734i | ||||
\(196\) | −128.970 | − | 223.383i | −0.658013 | − | 1.13971i | ||||
\(197\) | −226.659 | + | 226.659i | −1.15056 | + | 1.15056i | −0.164114 | + | 0.986441i | \(0.552476\pi\) |
−0.986441 | + | 0.164114i | \(0.947524\pi\) | |||||||
\(198\) | 13.5337 | + | 16.9439i | 0.0683520 | + | 0.0855751i | ||||
\(199\) | 107.508i | 0.540240i | 0.962827 | + | 0.270120i | \(0.0870633\pi\) | ||||
−0.962827 | + | 0.270120i | \(0.912937\pi\) | |||||||
\(200\) | −41.1433 | − | 159.769i | −0.205717 | − | 0.798843i | ||||
\(201\) | 43.9930 | + | 87.0617i | 0.218870 | + | 0.433143i | ||||
\(202\) | 23.0908 | + | 86.1760i | 0.114311 | + | 0.426614i | ||||
\(203\) | 293.892 | − | 78.7481i | 1.44774 | − | 0.387922i | ||||
\(204\) | −163.107 | + | 82.4194i | −0.799546 | + | 0.404017i | ||||
\(205\) | −6.50597 | − | 6.56976i | −0.0317364 | − | 0.0320476i | ||||
\(206\) | −24.5344 | −0.119099 | ||||||||
\(207\) | −78.5441 | + | 62.7360i | −0.379440 | + | 0.303073i | ||||
\(208\) | 13.5765 | + | 13.5765i | 0.0652718 | + | 0.0652718i | ||||
\(209\) | −25.8695 | + | 14.9358i | −0.123778 | + | 0.0714631i | ||||
\(210\) | 87.4072 | − | 132.200i | 0.416225 | − | 0.629522i | ||||
\(211\) | 45.5871 | − | 78.9591i | 0.216053 | − | 0.374214i | −0.737545 | − | 0.675298i | \(-0.764015\pi\) |
0.953598 | + | 0.301084i | \(0.0973484\pi\) | |||||||
\(212\) | −7.41341 | − | 27.6672i | −0.0349689 | − | 0.130506i | ||||
\(213\) | 186.028 | − | 38.8898i | 0.873371 | − | 0.182581i | ||||
\(214\) | 49.5727 | − | 28.6208i | 0.231648 | − | 0.133742i | ||||
\(215\) | 219.371 | + | 128.085i | 1.02033 | + | 0.595745i | ||||
\(216\) | −175.697 | − | 29.6428i | −0.813410 | − | 0.137235i | ||||
\(217\) | 354.070 | − | 354.070i | 1.63166 | − | 1.63166i | ||||
\(218\) | −3.13551 | + | 11.7019i | −0.0143831 | + | 0.0536784i | ||||
\(219\) | 180.738 | + | 118.237i | 0.825289 | + | 0.539893i | ||||
\(220\) | −39.6185 | − | 10.8232i | −0.180084 | − | 0.0491963i | ||||
\(221\) | −28.5965 | + | 49.5306i | −0.129396 | + | 0.224120i | ||||
\(222\) | 42.1399 | − | 37.6877i | 0.189819 | − | 0.169765i | ||||
\(223\) | −61.4305 | + | 229.262i | −0.275473 | + | 1.02808i | 0.680051 | + | 0.733165i | \(0.261958\pi\) |
−0.955524 | + | 0.294914i | \(0.904709\pi\) | |||||||
\(224\) | 370.715i | 1.65498i | ||||||||
\(225\) | −223.350 | − | 27.2000i | −0.992666 | − | 0.120889i | ||||
\(226\) | −30.0236 | −0.132848 | ||||||||
\(227\) | 118.644 | + | 31.7905i | 0.522660 | + | 0.140046i | 0.510497 | − | 0.859880i | \(-0.329462\pi\) |
0.0121631 | + | 0.999926i | \(0.496128\pi\) | |||||||
\(228\) | 33.7446 | − | 102.682i | 0.148003 | − | 0.450359i | ||||
\(229\) | −285.203 | − | 164.662i | −1.24543 | − | 0.719048i | −0.275234 | − | 0.961377i | \(-0.588755\pi\) |
−0.970194 | + | 0.242329i | \(0.922089\pi\) | |||||||
\(230\) | −13.5881 | + | 49.7397i | −0.0590789 | + | 0.216260i | ||||
\(231\) | −40.4051 | − | 79.9615i | −0.174914 | − | 0.346154i | ||||
\(232\) | −169.484 | − | 45.4131i | −0.730534 | − | 0.195746i | ||||
\(233\) | −227.098 | − | 227.098i | −0.974670 | − | 0.974670i | 0.0250170 | − | 0.999687i | \(-0.492036\pi\) |
−0.999687 | + | 0.0250170i | \(0.992036\pi\) | |||||||
\(234\) | −22.4997 | + | 9.83722i | −0.0961528 | + | 0.0420394i | ||||
\(235\) | −160.050 | + | 274.117i | −0.681063 | + | 1.16646i | ||||
\(236\) | 89.9838 | + | 155.856i | 0.381287 | + | 0.660409i | ||||
\(237\) | 153.885 | − | 137.627i | 0.649305 | − | 0.580705i | ||||
\(238\) | −197.513 | + | 52.9235i | −0.829887 | + | 0.222367i | ||||
\(239\) | 123.443 | + | 71.2696i | 0.516496 | + | 0.298199i | 0.735500 | − | 0.677525i | \(-0.236947\pi\) |
−0.219004 | + | 0.975724i | \(0.570281\pi\) | |||||||
\(240\) | 87.1962 | − | 43.5282i | 0.363318 | − | 0.181368i | ||||
\(241\) | −228.867 | − | 396.410i | −0.949656 | − | 1.64485i | −0.746148 | − | 0.665780i | \(-0.768099\pi\) |
−0.203509 | − | 0.979073i | \(-0.565234\pi\) | |||||||
\(242\) | −74.5503 | + | 74.5503i | −0.308059 | + | 0.308059i | ||||
\(243\) | −125.012 | + | 208.377i | −0.514453 | + | 0.857519i | ||||
\(244\) | − | 106.005i | − | 0.434446i | ||||||
\(245\) | −291.147 | + | 288.320i | −1.18836 | + | 1.17682i | ||||
\(246\) | −2.80407 | + | 4.28634i | −0.0113987 | + | 0.0174242i | ||||
\(247\) | −8.75487 | − | 32.6736i | −0.0354448 | − | 0.132282i | ||||
\(248\) | −278.926 | + | 74.7380i | −1.12470 | + | 0.301363i | ||||
\(249\) | 17.6132 | − | 315.810i | 0.0707359 | − | 1.26831i | ||||
\(250\) | −100.783 | + | 56.2366i | −0.403131 | + | 0.224946i | ||||
\(251\) | 102.580 | 0.408684 | 0.204342 | − | 0.978900i | \(-0.434494\pi\) | ||||
0.204342 | + | 0.978900i | \(0.434494\pi\) | |||||||
\(252\) | 301.848 | + | 118.198i | 1.19781 | + | 0.469039i | ||||
\(253\) | 20.6109 | + | 20.6109i | 0.0814660 | + | 0.0814660i | ||||
\(254\) | 122.378 | − | 70.6552i | 0.481805 | − | 0.278170i | ||||
\(255\) | 192.468 | + | 217.330i | 0.754778 | + | 0.852273i | ||||
\(256\) | 65.9936 | − | 114.304i | 0.257788 | − | 0.446501i | ||||
\(257\) | 29.0526 | + | 108.426i | 0.113045 | + | 0.421890i | 0.999133 | − | 0.0416268i | \(-0.0132541\pi\) |
−0.886088 | + | 0.463517i | \(0.846587\pi\) | |||||||
\(258\) | 43.9348 | − | 133.690i | 0.170290 | − | 0.518178i | ||||
\(259\) | −202.273 | + | 116.782i | −0.780975 | + | 0.450896i | ||||
\(260\) | 23.4499 | − | 40.1627i | 0.0901921 | − | 0.154472i | ||||
\(261\) | −141.949 | + | 192.646i | −0.543868 | + | 0.738106i | ||||
\(262\) | 4.29401 | − | 4.29401i | 0.0163893 | − | 0.0163893i | ||||
\(263\) | 38.5609 | − | 143.911i | 0.146619 | − | 0.547191i | −0.853059 | − | 0.521815i | \(-0.825255\pi\) |
0.999678 | − | 0.0253757i | \(-0.00807820\pi\) | |||||||
\(264\) | −2.87701 | + | 51.5855i | −0.0108978 | + | 0.195400i | ||||
\(265\) | −39.5156 | + | 22.5580i | −0.149115 | + | 0.0851245i | ||||
\(266\) | 60.4689 | − | 104.735i | 0.227327 | − | 0.393742i | ||||
\(267\) | −84.0336 | − | 401.972i | −0.314733 | − | 1.50551i | ||||
\(268\) | −26.4882 | + | 98.8554i | −0.0988367 | + | 0.368864i | ||||
\(269\) | − | 31.0843i | − | 0.115555i | −0.998329 | − | 0.0577774i | \(-0.981599\pi\) | ||
0.998329 | − | 0.0577774i | \(-0.0184014\pi\) | |||||||
\(270\) | 11.1754 | + | 124.142i | 0.0413902 | + | 0.459785i | ||||
\(271\) | 4.22458 | 0.0155889 | 0.00779444 | − | 0.999970i | \(-0.497519\pi\) | ||||
0.00779444 | + | 0.999970i | \(0.497519\pi\) | |||||||
\(272\) | −121.458 | − | 32.5447i | −0.446538 | − | 0.119650i | ||||
\(273\) | 99.3042 | − | 20.7599i | 0.363751 | − | 0.0760435i | ||||
\(274\) | 69.6325 | + | 40.2024i | 0.254133 | + | 0.146724i | ||||
\(275\) | −0.636566 | + | 65.2388i | −0.00231479 | + | 0.237232i | ||||
\(276\) | −105.304 | − | 5.87296i | −0.381535 | − | 0.0212788i | ||||
\(277\) | 134.321 | + | 35.9912i | 0.484913 | + | 0.129932i | 0.492990 | − | 0.870035i | \(-0.335904\pi\) |
−0.00807616 | + | 0.999967i | \(0.502571\pi\) | |||||||
\(278\) | −57.1051 | − | 57.1051i | −0.205414 | − | 0.205414i | ||||
\(279\) | −43.7914 | + | 391.374i | −0.156958 | + | 1.40277i | ||||
\(280\) | 365.193 | − | 95.9462i | 1.30426 | − | 0.342665i | ||||
\(281\) | −251.702 | − | 435.961i | −0.895737 | − | 1.55146i | −0.832890 | − | 0.553439i | \(-0.813315\pi\) |
−0.0628471 | − | 0.998023i | \(-0.520018\pi\) | |||||||
\(282\) | 167.053 | + | 54.8991i | 0.592388 | + | 0.194678i | ||||
\(283\) | 141.561 | − | 37.9311i | 0.500214 | − | 0.134032i | 0.000114837 | − | 1.00000i | \(-0.499963\pi\) |
0.500099 | + | 0.865968i | \(0.333297\pi\) | |||||||
\(284\) | 172.682 | + | 99.6980i | 0.608035 | + | 0.351049i | ||||
\(285\) | −171.382 | − | 10.3972i | −0.601340 | − | 0.0364814i | ||||
\(286\) | 3.56021 | + | 6.16647i | 0.0124483 | + | 0.0215611i | ||||
\(287\) | 14.9632 | − | 14.9632i | 0.0521365 | − | 0.0521365i | ||||
\(288\) | −181.961 | − | 227.812i | −0.631811 | − | 0.791012i | ||||
\(289\) | − | 85.5611i | − | 0.296059i | ||||||
\(290\) | −0.598812 | + | 122.742i | −0.00206487 | + | 0.423248i | ||||
\(291\) | −109.476 | − | 6.10568i | −0.376207 | − | 0.0209817i | ||||
\(292\) | 58.6481 | + | 218.878i | 0.200850 | + | 0.749581i | ||||
\(293\) | 331.315 | − | 88.7756i | 1.13077 | − | 0.302988i | 0.355535 | − | 0.934663i | \(-0.384299\pi\) |
0.775234 | + | 0.631675i | \(0.217632\pi\) | |||||||
\(294\) | 189.955 | + | 124.266i | 0.646105 | + | 0.422673i | ||||
\(295\) | 203.136 | − | 201.164i | 0.688596 | − | 0.681910i | ||||
\(296\) | 134.694 | 0.455047 | ||||||||
\(297\) | 64.0779 | + | 29.3054i | 0.215751 | + | 0.0986714i | ||||
\(298\) | 109.282 | + | 109.282i | 0.366720 | + | 0.366720i | ||||
\(299\) | −28.5850 | + | 16.5035i | −0.0956019 | + | 0.0551958i | ||||
\(300\) | −155.645 | − | 177.487i | −0.518816 | − | 0.591622i | ||||
\(301\) | −290.692 | + | 503.493i | −0.965753 | + | 1.67273i | ||||
\(302\) | −59.6337 | − | 222.556i | −0.197463 | − | 0.736941i | ||||
\(303\) | 193.247 | + | 216.076i | 0.637780 | + | 0.713123i | ||||
\(304\) | 64.4057 | − | 37.1847i | 0.211861 | − | 0.122318i | ||||
\(305\) | −162.866 | + | 42.7894i | −0.533987 | + | 0.140293i | ||||
\(306\) | 95.3986 | − | 129.470i | 0.311760 | − | 0.423103i | ||||
\(307\) | −19.2282 | + | 19.2282i | −0.0626327 | + | 0.0626327i | −0.737729 | − | 0.675097i | \(-0.764102\pi\) |
0.675097 | + | 0.737729i | \(0.264102\pi\) | |||||||
\(308\) | 24.3280 | − | 90.7934i | 0.0789870 | − | 0.294784i | ||||
\(309\) | −71.1506 | + | 35.9529i | −0.230261 | + | 0.116353i | ||||
\(310\) | 100.147 | + | 175.431i | 0.323055 | + | 0.565906i | ||||
\(311\) | −275.689 | + | 477.507i | −0.886459 | + | 1.53539i | −0.0424271 | + | 0.999100i | \(0.513509\pi\) |
−0.844032 | + | 0.536293i | \(0.819824\pi\) | |||||||
\(312\) | −55.5811 | − | 18.2657i | −0.178145 | − | 0.0585440i | ||||
\(313\) | 124.130 | − | 463.260i | 0.396582 | − | 1.48006i | −0.422488 | − | 0.906368i | \(-0.638843\pi\) |
0.819070 | − | 0.573694i | \(-0.194490\pi\) | |||||||
\(314\) | − | 46.2592i | − | 0.147322i | ||||||
\(315\) | 59.7572 | − | 511.471i | 0.189705 | − | 1.62372i | ||||
\(316\) | 216.604 | 0.685455 | ||||||||
\(317\) | 270.009 | + | 72.3487i | 0.851763 | + | 0.228229i | 0.658186 | − | 0.752856i | \(-0.271324\pi\) |
0.193578 | + | 0.981085i | \(0.437991\pi\) | |||||||
\(318\) | 16.8034 | + | 18.7884i | 0.0528409 | + | 0.0590831i | ||||
\(319\) | 60.0908 | + | 34.6934i | 0.188372 | + | 0.108757i | ||||
\(320\) | −18.9170 | − | 5.16785i | −0.0591157 | − | 0.0161495i | ||||
\(321\) | 101.821 | − | 155.646i | 0.317201 | − | 0.484878i | ||||
\(322\) | −113.988 | − | 30.5430i | −0.354000 | − | 0.0948541i | ||||
\(323\) | 156.646 | + | 156.646i | 0.484971 | + | 0.484971i | ||||
\(324\) | −243.508 | + | 75.5239i | −0.751566 | + | 0.233099i | ||||
\(325\) | −71.1718 | − | 19.8167i | −0.218990 | − | 0.0609744i | ||||
\(326\) | 15.3545 | + | 26.5949i | 0.0470998 | + | 0.0815793i | ||||
\(327\) | 8.05498 | + | 38.5307i | 0.0246330 | + | 0.117831i | ||||
\(328\) | −11.7876 | + | 3.15847i | −0.0359377 | + | 0.00962948i | ||||
\(329\) | −629.143 | − | 363.236i | −1.91229 | − | 1.10406i | ||||
\(330\) | 35.4131 | − | 7.22310i | 0.107313 | − | 0.0218882i | ||||
\(331\) | −61.1788 | − | 105.965i | −0.184830 | − | 0.320136i | 0.758689 | − | 0.651453i | \(-0.225840\pi\) |
−0.943519 | + | 0.331317i | \(0.892507\pi\) | |||||||
\(332\) | 234.657 | − | 234.657i | 0.706800 | − | 0.706800i | ||||
\(333\) | 66.9791 | − | 171.048i | 0.201139 | − | 0.513658i | ||||
\(334\) | 102.171i | 0.305900i | ||||||||
\(335\) | 162.574 | + | 0.793137i | 0.485295 | + | 0.00236757i | ||||
\(336\) | 100.594 | + | 199.075i | 0.299387 | + | 0.592485i | ||||
\(337\) | 85.5276 | + | 319.193i | 0.253791 | + | 0.947161i | 0.968759 | + | 0.248004i | \(0.0797746\pi\) |
−0.714968 | + | 0.699157i | \(0.753559\pi\) | |||||||
\(338\) | 142.931 | − | 38.2982i | 0.422872 | − | 0.113308i | ||||
\(339\) | −87.0694 | + | 43.9969i | −0.256842 | + | 0.129784i | ||||
\(340\) | −1.48592 | + | 304.577i | −0.00437034 | + | 0.895815i | ||||
\(341\) | 114.192 | 0.334875 | ||||||||
\(342\) | 14.2488 | + | 94.0423i | 0.0416632 | + | 0.274977i | ||||
\(343\) | −266.621 | − | 266.621i | −0.777321 | − | 0.777321i | ||||
\(344\) | 290.358 | − | 167.638i | 0.844065 | − | 0.487321i | ||||
\(345\) | 33.4830 | + | 164.159i | 0.0970523 | + | 0.475824i | ||||
\(346\) | −31.4865 | + | 54.5363i | −0.0910016 | + | 0.157619i | ||||
\(347\) | −92.1251 | − | 343.816i | −0.265490 | − | 0.990823i | −0.961950 | − | 0.273227i | \(-0.911909\pi\) |
0.696459 | − | 0.717596i | \(-0.254758\pi\) | |||||||
\(348\) | −245.750 | + | 51.3750i | −0.706180 | + | 0.147629i | ||||
\(349\) | 43.1516 | − | 24.9136i | 0.123644 | − | 0.0713857i | −0.436903 | − | 0.899509i | \(-0.643925\pi\) |
0.560546 | + | 0.828123i | \(0.310591\pi\) | |||||||
\(350\) | −129.831 | − | 230.028i | −0.370945 | − | 0.657222i | ||||
\(351\) | −50.8345 | + | 61.4997i | −0.144828 | + | 0.175213i | ||||
\(352\) | −59.7804 | + | 59.7804i | −0.169831 | + | 0.169831i | ||||
\(353\) | −162.600 | + | 606.831i | −0.460623 | + | 1.71907i | 0.210385 | + | 0.977619i | \(0.432528\pi\) |
−0.671008 | + | 0.741450i | \(0.734138\pi\) | |||||||
\(354\) | −132.533 | − | 86.7014i | −0.374387 | − | 0.244919i | ||||
\(355\) | 83.4724 | − | 305.553i | 0.235133 | − | 0.860712i | ||||
\(356\) | 215.429 | − | 373.134i | 0.605137 | − | 1.04813i | ||||
\(357\) | −495.240 | + | 442.918i | −1.38723 | + | 1.24067i | ||||
\(358\) | −72.6263 | + | 271.045i | −0.202867 | + | 0.757109i | ||||
\(359\) | − | 81.3046i | − | 0.226475i | −0.993568 | − | 0.113238i | \(-0.963878\pi\) | ||
0.993568 | − | 0.113238i | \(-0.0361221\pi\) | |||||||
\(360\) | −177.324 | + | 238.212i | −0.492567 | + | 0.661700i | ||||
\(361\) | 229.978 | 0.637059 | ||||||||
\(362\) | −153.908 | − | 41.2397i | −0.425162 | − | 0.113922i | ||||
\(363\) | −106.952 | + | 325.445i | −0.294633 | + | 0.896544i | ||||
\(364\) | 92.1799 | + | 53.2201i | 0.253241 | + | 0.146209i | ||||
\(365\) | 312.611 | − | 178.458i | 0.856468 | − | 0.488926i | ||||
\(366\) | 42.0717 | + | 83.2595i | 0.114950 | + | 0.227485i | ||||
\(367\) | −58.0273 | − | 15.5484i | −0.158113 | − | 0.0423661i | 0.178894 | − | 0.983868i | \(-0.442748\pi\) |
−0.337007 | + | 0.941502i | \(0.609415\pi\) | |||||||
\(368\) | −51.3136 | − | 51.3136i | −0.139439 | − | 0.139439i | ||||
\(369\) | −1.85065 | + | 16.5397i | −0.00501531 | + | 0.0448230i | ||||
\(370\) | −23.9426 | − | 91.1312i | −0.0647098 | − | 0.246301i | ||||
\(371\) | −52.0684 | − | 90.1851i | −0.140346 | − | 0.243086i | ||||
\(372\) | −307.981 | + | 275.442i | −0.827906 | + | 0.740436i | ||||
\(373\) | 188.424 | − | 50.4882i | 0.505159 | − | 0.135357i | 0.00276585 | − | 0.999996i | \(-0.499120\pi\) |
0.502393 | + | 0.864639i | \(0.332453\pi\) | |||||||
\(374\) | −40.3846 | − | 23.3161i | −0.107980 | − | 0.0623425i | ||||
\(375\) | −209.864 | + | 310.777i | −0.559638 | + | 0.828737i | ||||
\(376\) | 209.474 | + | 362.820i | 0.557112 | + | 0.964946i | ||||
\(377\) | −55.5594 | + | 55.5594i | −0.147372 | + | 0.147372i | ||||
\(378\) | −283.992 | + | 26.9625i | −0.751301 | + | 0.0713294i | ||||
\(379\) | 145.837i | 0.384795i | 0.981317 | + | 0.192398i | \(0.0616263\pi\) | ||||
−0.981317 | + | 0.192398i | \(0.938374\pi\) | |||||||
\(380\) | −126.756 | − | 127.999i | −0.333568 | − | 0.336839i | ||||
\(381\) | 251.363 | − | 384.237i | 0.659745 | − | 1.00850i | ||||
\(382\) | −68.6394 | − | 256.166i | −0.179684 | − | 0.670591i | ||||
\(383\) | −729.460 | + | 195.458i | −1.90459 | + | 0.510335i | −0.908973 | + | 0.416854i | \(0.863133\pi\) |
−0.995621 | + | 0.0934803i | \(0.970201\pi\) | |||||||
\(384\) | 21.0426 | − | 377.299i | 0.0547984 | − | 0.982549i | ||||
\(385\) | −149.315 | − | 0.728453i | −0.387832 | − | 0.00189209i | ||||
\(386\) | 33.9703 | 0.0880059 | ||||||||
\(387\) | −68.4982 | − | 452.088i | −0.176998 | − | 1.16819i | ||||
\(388\) | −81.3446 | − | 81.3446i | −0.209651 | − | 0.209651i | ||||
\(389\) | 37.3613 | − | 21.5705i | 0.0960444 | − | 0.0554512i | −0.451209 | − | 0.892419i | \(-0.649007\pi\) |
0.547253 | + | 0.836967i | \(0.315674\pi\) | |||||||
\(390\) | −2.47836 | + | 40.8520i | −0.00635477 | + | 0.104749i | ||||
\(391\) | 108.083 | − | 187.205i | 0.276427 | − | 0.478785i | ||||
\(392\) | 139.972 | + | 522.381i | 0.357070 | + | 1.33260i | ||||
\(393\) | 6.16029 | − | 18.7453i | 0.0156750 | − | 0.0476979i | ||||
\(394\) | 256.305 | − | 147.978i | 0.650520 | − | 0.375578i | ||||
\(395\) | −87.4331 | − | 332.791i | −0.221350 | − | 0.842508i | ||||
\(396\) | 29.6149 | + | 67.7354i | 0.0747851 | + | 0.171049i | ||||
\(397\) | −89.7953 | + | 89.7953i | −0.226185 | + | 0.226185i | −0.811097 | − | 0.584912i | \(-0.801129\pi\) |
0.584912 | + | 0.811097i | \(0.301129\pi\) | |||||||
\(398\) | 25.6906 | − | 95.8785i | 0.0645491 | − | 0.240901i | ||||
\(399\) | 21.8819 | − | 392.348i | 0.0548419 | − | 0.983328i | ||||
\(400\) | 1.58482 | − | 162.421i | 0.00396204 | − | 0.406052i | ||||
\(401\) | −144.777 | + | 250.762i | −0.361041 | + | 0.625341i | −0.988132 | − | 0.153604i | \(-0.950912\pi\) |
0.627092 | + | 0.778946i | \(0.284245\pi\) | |||||||
\(402\) | −18.4295 | − | 88.1569i | −0.0458445 | − | 0.219296i | ||||
\(403\) | −33.4679 | + | 124.904i | −0.0830470 | + | 0.309936i | ||||
\(404\) | 304.142i | 0.752826i | ||||||||
\(405\) | 214.328 | + | 343.640i | 0.529205 | + | 0.848494i | ||||
\(406\) | −280.919 | −0.691919 | ||||||||
\(407\) | −51.4498 | − | 13.7859i | −0.126412 | − | 0.0338721i | ||||
\(408\) | 375.049 | − | 78.4053i | 0.919238 | − | 0.192170i | ||||
\(409\) | 178.588 | + | 103.108i | 0.436646 | + | 0.252098i | 0.702174 | − | 0.712006i | \(-0.252213\pi\) |
−0.265528 | + | 0.964103i | \(0.585546\pi\) | |||||||
\(410\) | 4.23227 | + | 7.41380i | 0.0103226 | + | 0.0180824i | ||||
\(411\) | 260.850 | + | 14.5480i | 0.634671 | + | 0.0353967i | ||||
\(412\) | −80.7889 | − | 21.6473i | −0.196090 | − | 0.0525421i | ||||
\(413\) | 462.659 | + | 462.659i | 1.12024 | + | 1.12024i | ||||
\(414\) | 85.0396 | − | 37.1805i | 0.205410 | − | 0.0898081i | ||||
\(415\) | −455.249 | − | 265.808i | −1.09699 | − | 0.640501i | ||||
\(416\) | −47.8673 | − | 82.9087i | −0.115066 | − | 0.199300i | ||||
\(417\) | −249.289 | − | 81.9244i | −0.597816 | − | 0.196461i | ||||
\(418\) | 26.6403 | − | 7.13826i | 0.0637329 | − | 0.0170772i | ||||
\(419\) | 621.108 | + | 358.597i | 1.48236 | + | 0.855839i | 0.999799 | − | 0.0200248i | \(-0.00637453\pi\) |
0.482558 | + | 0.875864i | \(0.339708\pi\) | |||||||
\(420\) | 404.465 | − | 358.197i | 0.963013 | − | 0.852850i | ||||
\(421\) | 124.562 | + | 215.747i | 0.295871 | + | 0.512463i | 0.975187 | − | 0.221382i | \(-0.0710569\pi\) |
−0.679316 | + | 0.733846i | \(0.737724\pi\) | |||||||
\(422\) | −59.5243 | + | 59.5243i | −0.141053 | + | 0.141053i | ||||
\(423\) | 564.911 | − | 85.5925i | 1.33549 | − | 0.202346i | ||||
\(424\) | 60.0544i | 0.141638i | ||||||||
\(425\) | 468.553 | − | 120.661i | 1.10248 | − | 0.283908i | ||||
\(426\) | −175.198 | − | 9.77111i | −0.411264 | − | 0.0229369i | ||||
\(427\) | −99.7479 | − | 372.264i | −0.233602 | − | 0.871814i | ||||
\(428\) | 188.490 | − | 50.5058i | 0.440398 | − | 0.118004i | ||||
\(429\) | 19.3612 | + | 12.6658i | 0.0451309 | + | 0.0295241i | ||||
\(430\) | −165.034 | − | 166.652i | −0.383800 | − | 0.387563i | ||||
\(431\) | −234.096 | −0.543146 | −0.271573 | − | 0.962418i | \(-0.587544\pi\) | ||||
−0.271573 | + | 0.962418i | \(0.587544\pi\) | |||||||
\(432\) | −159.531 | − | 72.9598i | −0.369284 | − | 0.168888i | ||||
\(433\) | 372.915 | + | 372.915i | 0.861236 | + | 0.861236i | 0.991482 | − | 0.130245i | \(-0.0415765\pi\) |
−0.130245 | + | 0.991482i | \(0.541577\pi\) | |||||||
\(434\) | −400.380 | + | 231.159i | −0.922534 | + | 0.532625i | ||||
\(435\) | 178.131 | + | 356.834i | 0.409497 | + | 0.820308i | ||||
\(436\) | −20.6498 | + | 35.7665i | −0.0473619 | + | 0.0820332i | ||||
\(437\) | 33.0897 | + | 123.493i | 0.0757202 | + | 0.282592i | ||||
\(438\) | −132.933 | − | 148.637i | −0.303500 | − | 0.339353i | ||||
\(439\) | 558.854 | − | 322.654i | 1.27302 | − | 0.734976i | 0.297461 | − | 0.954734i | \(-0.403860\pi\) |
0.975554 | + | 0.219758i | \(0.0705269\pi\) | |||||||
\(440\) | 74.3620 | + | 43.4180i | 0.169005 | + | 0.0986773i | ||||
\(441\) | 732.977 | + | 82.0138i | 1.66208 | + | 0.185972i | ||||
\(442\) | 37.3393 | − | 37.3393i | 0.0844780 | − | 0.0844780i | ||||
\(443\) | 71.1633 | − | 265.585i | 0.160640 | − | 0.599515i | −0.837917 | − | 0.545798i | \(-0.816227\pi\) |
0.998556 | − | 0.0537167i | \(-0.0171068\pi\) | |||||||
\(444\) | 172.015 | − | 86.9204i | 0.387421 | − | 0.195767i | ||||
\(445\) | −660.242 | − | 180.368i | −1.48369 | − | 0.405322i | ||||
\(446\) | 109.571 | − | 189.782i | 0.245675 | − | 0.425521i | ||||
\(447\) | 477.067 | + | 156.779i | 1.06726 | + | 0.350737i | ||||
\(448\) | 11.6161 | − | 43.3520i | 0.0259289 | − | 0.0967679i | ||||
\(449\) | − | 190.668i | − | 0.424651i | −0.977199 | − | 0.212325i | \(-0.931896\pi\) | ||
0.977199 | − | 0.212325i | \(-0.0681036\pi\) | |||||||
\(450\) | 192.690 | + | 77.6305i | 0.428200 | + | 0.172512i | ||||
\(451\) | 4.82584 | 0.0107003 | ||||||||
\(452\) | −98.8642 | − | 26.4906i | −0.218726 | − | 0.0586075i | ||||
\(453\) | −499.076 | − | 558.033i | −1.10171 | − | 1.23186i | ||||
\(454\) | −98.2131 | − | 56.7034i | −0.216328 | − | 0.124897i | ||||
\(455\) | 44.5586 | − | 163.108i | 0.0979311 | − | 0.358479i | ||||
\(456\) | −124.060 | + | 189.640i | −0.272061 | + | 0.415876i | ||||
\(457\) | −302.074 | − | 80.9404i | −0.660993 | − | 0.177112i | −0.0872988 | − | 0.996182i | \(-0.527823\pi\) |
−0.573694 | + | 0.819070i | \(0.694490\pi\) | |||||||
\(458\) | 215.004 | + | 215.004i | 0.469441 | + | 0.469441i | ||||
\(459\) | 86.9334 | − | 515.265i | 0.189397 | − | 1.12258i | ||||
\(460\) | −88.6310 | + | 151.798i | −0.192676 | + | 0.329996i | ||||
\(461\) | −110.361 | − | 191.151i | −0.239395 | − | 0.414645i | 0.721146 | − | 0.692784i | \(-0.243616\pi\) |
−0.960541 | + | 0.278139i | \(0.910283\pi\) | |||||||
\(462\) | 16.9265 | + | 80.9673i | 0.0366374 | + | 0.175254i | ||||
\(463\) | −279.010 | + | 74.7605i | −0.602613 | + | 0.161470i | −0.547211 | − | 0.836994i | \(-0.684311\pi\) |
−0.0554018 | + | 0.998464i | \(0.517644\pi\) | |||||||
\(464\) | −149.604 | − | 86.3740i | −0.322423 | − | 0.186151i | ||||
\(465\) | 547.508 | + | 361.999i | 1.17744 | + | 0.778493i | ||||
\(466\) | 148.264 | + | 256.801i | 0.318163 | + | 0.551075i | ||||
\(467\) | −249.664 | + | 249.664i | −0.534613 | + | 0.534613i | −0.921942 | − | 0.387329i | \(-0.873398\pi\) |
0.387329 | + | 0.921942i | \(0.373398\pi\) | |||||||
\(468\) | −82.7688 | + | 12.5407i | −0.176856 | + | 0.0267964i | ||||
\(469\) | 372.082i | 0.793352i | ||||||||
\(470\) | 208.241 | − | 206.219i | 0.443067 | − | 0.438765i | ||||
\(471\) | −67.7888 | − | 134.153i | −0.143925 | − | 0.284827i | ||||
\(472\) | −97.6593 | − | 364.470i | −0.206905 | − | 0.772181i | ||||
\(473\) | −128.068 | + | 34.3157i | −0.270756 | + | 0.0725490i | ||||
\(474\) | −170.127 | + | 85.9666i | −0.358918 | + | 0.181364i | ||||
\(475\) | −145.492 | + | 246.416i | −0.306299 | + | 0.518770i | ||||
\(476\) | −697.084 | −1.46446 | ||||||||
\(477\) | 76.2633 | + | 29.8632i | 0.159881 | + | 0.0626064i | ||||
\(478\) | −93.0588 | − | 93.0588i | −0.194684 | − | 0.194684i | ||||
\(479\) | −757.971 | + | 437.615i | −1.58240 | + | 0.913600i | −0.587895 | + | 0.808938i | \(0.700043\pi\) |
−0.994508 | + | 0.104663i | \(0.966624\pi\) | |||||||
\(480\) | −476.132 | + | 97.1152i | −0.991943 | + | 0.202323i | ||||
\(481\) | 30.1582 | − | 52.2355i | 0.0626989 | − | 0.108598i | ||||
\(482\) | 109.382 | + | 408.221i | 0.226934 | + | 0.846931i | ||||
\(483\) | −375.328 | + | 78.4636i | −0.777077 | + | 0.162450i | ||||
\(484\) | −311.263 | + | 179.708i | −0.643106 | + | 0.371298i | ||||
\(485\) | −92.1430 | + | 157.813i | −0.189986 | + | 0.325388i | ||||
\(486\) | 161.284 | − | 155.963i | 0.331860 | − | 0.320912i | ||||
\(487\) | −241.500 | + | 241.500i | −0.495894 | + | 0.495894i | −0.910157 | − | 0.414263i | \(-0.864039\pi\) |
0.414263 | + | 0.910157i | \(0.364039\pi\) | |||||||
\(488\) | −57.5235 | + | 214.681i | −0.117876 | + | 0.439919i | ||||
\(489\) | 83.5012 | + | 54.6253i | 0.170759 | + | 0.111708i | ||||
\(490\) | 328.552 | − | 187.558i | 0.670514 | − | 0.382772i | ||||
\(491\) | −14.2377 | + | 24.6604i | −0.0289973 | + | 0.0502248i | −0.880160 | − | 0.474677i | \(-0.842565\pi\) |
0.851163 | + | 0.524902i | \(0.175898\pi\) | |||||||
\(492\) | −13.0154 | + | 11.6403i | −0.0264542 | + | 0.0236592i | ||||
\(493\) | 133.183 | − | 497.045i | 0.270148 | − | 1.00821i | ||||
\(494\) | 31.2314i | 0.0632214i | ||||||||
\(495\) | 92.1146 | − | 72.8421i | 0.186090 | − | 0.147156i | ||||
\(496\) | −284.298 | −0.573181 | ||||||||
\(497\) | 700.232 | + | 187.627i | 1.40892 | + | 0.377518i | ||||
\(498\) | −91.1754 | + | 277.439i | −0.183083 | + | 0.557107i | ||||
\(499\) | −409.907 | − | 236.660i | −0.821457 | − | 0.474269i | 0.0294615 | − | 0.999566i | \(-0.490621\pi\) |
−0.850919 | + | 0.525297i | \(0.823954\pi\) | |||||||
\(500\) | −381.486 | + | 96.2575i | −0.762971 | + | 0.192515i | ||||
\(501\) | 149.722 | + | 296.298i | 0.298846 | + | 0.591414i | ||||
\(502\) | −91.4836 | − | 24.5130i | −0.182238 | − | 0.0488306i | ||||
\(503\) | 58.9981 | + | 58.9981i | 0.117292 | + | 0.117292i | 0.763317 | − | 0.646024i | \(-0.223570\pi\) |
−0.646024 | + | 0.763317i | \(0.723570\pi\) | |||||||
\(504\) | −547.161 | − | 403.172i | −1.08564 | − | 0.799944i | ||||
\(505\) | 467.284 | − | 122.768i | 0.925315 | − | 0.243105i | ||||
\(506\) | −13.4561 | − | 23.3067i | −0.0265931 | − | 0.0460606i | ||||
\(507\) | 358.382 | − | 320.518i | 0.706868 | − | 0.632186i | ||||
\(508\) | 465.319 | − | 124.682i | 0.915983 | − | 0.245437i | ||||
\(509\) | 388.655 | + | 224.390i | 0.763565 | + | 0.440844i | 0.830574 | − | 0.556908i | \(-0.188012\pi\) |
−0.0670093 | + | 0.997752i | \(0.521346\pi\) | |||||||
\(510\) | −119.715 | − | 239.814i | −0.234735 | − | 0.470223i | ||||
\(511\) | 411.917 | + | 713.461i | 0.806100 | + | 1.39621i | ||||
\(512\) | 270.104 | − | 270.104i | 0.527546 | − | 0.527546i | ||||
\(513\) | 179.133 | + | 251.846i | 0.349187 | + | 0.490927i | ||||
\(514\) | − | 103.640i | − | 0.201634i | ||||||
\(515\) | −0.648185 | + | 132.862i | −0.00125861 | + | 0.257985i | ||||
\(516\) | 262.631 | − | 401.461i | 0.508974 | − | 0.778026i | ||||
\(517\) | −42.8794 | − | 160.028i | −0.0829389 | − | 0.309532i | ||||
\(518\) | 208.299 | − | 55.8136i | 0.402122 | − | 0.107748i | ||||
\(519\) | −11.3941 | + | 204.298i | −0.0219539 | + | 0.393638i | ||||
\(520\) | −69.2850 | + | 68.6123i | −0.133240 | + | 0.131947i | ||||
\(521\) | −548.131 | −1.05208 | −0.526038 | − | 0.850461i | \(-0.676323\pi\) | ||||
−0.526038 | + | 0.850461i | \(0.676323\pi\) | |||||||
\(522\) | 172.630 | − | 137.886i | 0.330709 | − | 0.264150i | ||||
\(523\) | −237.559 | − | 237.559i | −0.454224 | − | 0.454224i | 0.442530 | − | 0.896754i | \(-0.354081\pi\) |
−0.896754 | + | 0.442530i | \(0.854081\pi\) | |||||||
\(524\) | 17.9284 | − | 10.3510i | 0.0342145 | − | 0.0197538i | ||||
\(525\) | −713.599 | − | 476.834i | −1.35924 | − | 0.908255i | ||||
\(526\) | −68.7794 | + | 119.129i | −0.130759 | + | 0.226482i | ||||
\(527\) | −219.184 | − | 818.005i | −0.415909 | − | 1.55219i | ||||
\(528\) | −15.8807 | + | 48.3237i | −0.0300771 | + | 0.0915222i | ||||
\(529\) | −350.088 | + | 202.124i | −0.661793 | + | 0.382086i | ||||
\(530\) | 40.6317 | − | 10.6750i | 0.0766635 | − | 0.0201416i | ||||
\(531\) | −511.404 | − | 57.2217i | −0.963096 | − | 0.107762i | ||||
\(532\) | 291.528 | − | 291.528i | 0.547985 | − | 0.547985i | ||||
\(533\) | −1.41437 | + | 5.27851i | −0.00265361 | + | 0.00990340i | ||||
\(534\) | −21.1136 | + | 378.571i | −0.0395385 | + | 0.708935i | ||||
\(535\) | −153.682 | − | 269.210i | −0.287257 | − | 0.503196i | ||||
\(536\) | 107.288 | − | 185.828i | 0.200164 | − | 0.346694i | ||||
\(537\) | 186.573 | + | 892.468i | 0.347436 | + | 1.66195i | ||||
\(538\) | −7.42804 | + | 27.7218i | −0.0138068 | + | 0.0515276i | ||||
\(539\) | − | 213.863i | − | 0.396778i | ||||||
\(540\) | −72.7346 | + | 418.646i | −0.134694 | + | 0.775271i | ||||
\(541\) | −694.204 | −1.28319 | −0.641593 | − | 0.767045i | \(-0.721726\pi\) | ||||
−0.641593 | + | 0.767045i | \(0.721726\pi\) | |||||||
\(542\) | −3.76761 | − | 1.00953i | −0.00695130 | − | 0.00186260i | ||||
\(543\) | −506.773 | + | 105.943i | −0.933284 | + | 0.195106i | ||||
\(544\) | 542.975 | + | 313.487i | 0.998115 | + | 0.576262i | ||||
\(545\) | 63.2871 | + | 17.2891i | 0.116123 | + | 0.0317231i | ||||
\(546\) | −93.5232 | − | 5.21595i | −0.171288 | − | 0.00955302i | ||||
\(547\) | 855.323 | + | 229.183i | 1.56366 | + | 0.418982i | 0.933820 | − | 0.357742i | \(-0.116453\pi\) |
0.629841 | + | 0.776724i | \(0.283120\pi\) | |||||||
\(548\) | 193.821 | + | 193.821i | 0.353687 | + | 0.353687i | ||||
\(549\) | 244.019 | + | 179.803i | 0.444479 | + | 0.327511i | ||||
\(550\) | 16.1575 | − | 58.0297i | 0.0293772 | − | 0.105509i | ||||
\(551\) | 152.171 | + | 263.568i | 0.276173 | + | 0.478345i | ||||
\(552\) | 210.073 | + | 69.0368i | 0.380568 | + | 0.125067i | ||||
\(553\) | 760.662 | − | 203.819i | 1.37552 | − | 0.368569i | ||||
\(554\) | −111.191 | − | 64.1960i | −0.200705 | − | 0.115877i | ||||
\(555\) | −202.979 | − | 229.198i | −0.365728 | − | 0.412970i | ||||
\(556\) | −137.655 | − | 238.426i | −0.247581 | − | 0.428824i | ||||
\(557\) | 598.653 | − | 598.653i | 1.07478 | − | 1.07478i | 0.0778138 | − | 0.996968i | \(-0.475206\pi\) |
0.996968 | − | 0.0778138i | \(-0.0247940\pi\) | |||||||
\(558\) | 132.579 | − | 338.574i | 0.237597 | − | 0.606763i | ||||
\(559\) | − | 150.138i | − | 0.268584i | ||||||
\(560\) | 371.741 | + | 1.81358i | 0.663822 | + | 0.00323854i | ||||
\(561\) | −151.285 | − | 8.43740i | −0.269670 | − | 0.0150399i | ||||
\(562\) | 120.296 | + | 448.950i | 0.214050 | + | 0.798844i | ||||
\(563\) | −300.796 | + | 80.5980i | −0.534273 | + | 0.143158i | −0.515861 | − | 0.856672i | \(-0.672528\pi\) |
−0.0184123 | + | 0.999830i | \(0.505861\pi\) | |||||||
\(564\) | 501.649 | + | 328.172i | 0.889449 | + | 0.581866i | ||||
\(565\) | −0.793207 | + | 162.588i | −0.00140391 | + | 0.287767i | ||||
\(566\) | −135.312 | −0.239067 | ||||||||
\(567\) | −784.076 | + | 494.357i | −1.38285 | + | 0.871882i | ||||
\(568\) | −295.614 | − | 295.614i | −0.520447 | − | 0.520447i | ||||
\(569\) | −20.4998 | + | 11.8356i | −0.0360278 | + | 0.0208006i | −0.517906 | − | 0.855438i | \(-0.673288\pi\) |
0.481878 | + | 0.876238i | \(0.339955\pi\) | |||||||
\(570\) | 150.359 | + | 50.2268i | 0.263787 | + | 0.0881172i | ||||
\(571\) | 22.7049 | − | 39.3260i | 0.0397633 | − | 0.0688721i | −0.845459 | − | 0.534041i | \(-0.820673\pi\) |
0.885222 | + | 0.465169i | \(0.154006\pi\) | |||||||
\(572\) | 6.28254 | + | 23.4468i | 0.0109835 | + | 0.0409909i | ||||
\(573\) | −574.445 | − | 642.305i | −1.00252 | − | 1.12095i | ||||
\(574\) | −16.9203 | + | 9.76892i | −0.0294778 | + | 0.0170190i | ||||
\(575\) | 269.000 | + | 74.8988i | 0.467825 | + | 0.130259i | ||||
\(576\) | 14.1405 | + | 32.3423i | 0.0245495 | + | 0.0561498i | ||||
\(577\) | −333.577 | + | 333.577i | −0.578124 | + | 0.578124i | −0.934386 | − | 0.356262i | \(-0.884051\pi\) |
0.356262 | + | 0.934386i | \(0.384051\pi\) | |||||||
\(578\) | −20.4461 | + | 76.3059i | −0.0353739 | + | 0.132017i | ||||
\(579\) | 98.5150 | − | 49.7804i | 0.170147 | − | 0.0859765i | ||||
\(580\) | −110.270 | + | 403.647i | −0.190121 | + | 0.695944i | ||||
\(581\) | 603.256 | − | 1044.87i | 1.03831 | − | 1.79840i | ||||
\(582\) | 96.1750 | + | 31.6062i | 0.165249 | + | 0.0543062i | ||||
\(583\) | 6.14658 | − | 22.9394i | 0.0105430 | − | 0.0393471i | ||||
\(584\) | − | 475.096i | − | 0.813520i | ||||||
\(585\) | 52.6776 | + | 122.104i | 0.0900472 | + | 0.208725i | ||||
\(586\) | −316.691 | −0.540428 | ||||||||
\(587\) | −751.967 | − | 201.489i | −1.28103 | − | 0.343252i | −0.446786 | − | 0.894641i | \(-0.647432\pi\) |
−0.834249 | + | 0.551388i | \(0.814098\pi\) | |||||||
\(588\) | 515.857 | + | 576.796i | 0.877307 | + | 0.980945i | ||||
\(589\) | 433.764 | + | 250.434i | 0.736441 | + | 0.425184i | ||||
\(590\) | −229.233 | + | 130.861i | −0.388531 | + | 0.221798i | ||||
\(591\) | 526.446 | − | 804.733i | 0.890771 | − | 1.36165i | ||||
\(592\) | 128.091 | + | 34.3219i | 0.216370 | + | 0.0579763i | ||||
\(593\) | −464.151 | − | 464.151i | −0.782717 | − | 0.782717i | 0.197571 | − | 0.980289i | \(-0.436695\pi\) |
−0.980289 | + | 0.197571i | \(0.936695\pi\) | |||||||
\(594\) | −50.1436 | − | 41.4478i | −0.0844168 | − | 0.0697774i | ||||
\(595\) | 281.381 | + | 1071.00i | 0.472910 | + | 1.80000i | ||||
\(596\) | 263.432 | + | 456.278i | 0.442000 | + | 0.765567i | ||||
\(597\) | −65.9978 | − | 315.698i | −0.110549 | − | 0.528808i | ||||
\(598\) | 29.4367 | − | 7.88753i | 0.0492252 | − | 0.0131899i | ||||
\(599\) | 402.592 | + | 232.437i | 0.672108 | + | 0.388042i | 0.796875 | − | 0.604145i | \(-0.206485\pi\) |
−0.124767 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(600\) | 218.898 | + | 443.906i | 0.364831 | + | 0.739843i | ||||
\(601\) | −305.138 | − | 528.514i | −0.507717 | − | 0.879392i | −0.999960 | − | 0.00893383i | \(-0.997156\pi\) |
0.492243 | − | 0.870458i | \(-0.336177\pi\) | |||||||
\(602\) | 379.564 | − | 379.564i | 0.630505 | − | 0.630505i | ||||
\(603\) | −182.632 | − | 228.651i | −0.302873 | − | 0.379190i | ||||
\(604\) | − | 785.469i | − | 1.30045i | ||||||
\(605\) | 401.747 | + | 405.686i | 0.664044 | + | 0.670555i | ||||
\(606\) | −120.709 | − | 238.882i | −0.199190 | − | 0.394195i | ||||
\(607\) | −21.8621 | − | 81.5905i | −0.0360167 | − | 0.134416i | 0.945577 | − | 0.325400i | \(-0.105499\pi\) |
−0.981593 | + | 0.190984i | \(0.938832\pi\) | |||||||
\(608\) | −358.181 | + | 95.9744i | −0.589114 | + | 0.157853i | ||||
\(609\) | −814.676 | + | 411.662i | −1.33773 | + | 0.675964i | ||||
\(610\) | 155.474 | + | 0.758498i | 0.254875 | + | 0.00124344i | ||||
\(611\) | 187.606 | 0.307048 | ||||||||
\(612\) | 428.371 | − | 342.156i | 0.699953 | − | 0.559078i | ||||
\(613\) | 463.301 | + | 463.301i | 0.755793 | + | 0.755793i | 0.975554 | − | 0.219760i | \(-0.0705276\pi\) |
−0.219760 | + | 0.975554i | \(0.570528\pi\) | |||||||
\(614\) | 21.7432 | − | 12.5534i | 0.0354123 | − | 0.0204453i | ||||
\(615\) | 23.1380 | + | 15.2983i | 0.0376228 | + | 0.0248753i | ||||
\(616\) | −98.5380 | + | 170.673i | −0.159964 | + | 0.277066i | ||||
\(617\) | 174.357 | + | 650.709i | 0.282588 | + | 1.05463i | 0.950584 | + | 0.310468i | \(0.100486\pi\) |
−0.667995 | + | 0.744165i | \(0.732847\pi\) | |||||||
\(618\) | 72.0456 | − | 15.0614i | 0.116579 | − | 0.0243712i | ||||
\(619\) | 759.400 | − | 438.440i | 1.22682 | − | 0.708303i | 0.260455 | − | 0.965486i | \(-0.416128\pi\) |
0.966363 | + | 0.257183i | \(0.0827942\pi\) | |||||||
\(620\) | 174.986 | + | 666.036i | 0.282235 | + | 1.07425i | ||||
\(621\) | 192.133 | − | 232.443i | 0.309393 | − | 0.374304i | ||||
\(622\) | 359.975 | − | 359.975i | 0.578737 | − | 0.578737i | ||||
\(623\) | 405.426 | − | 1513.07i | 0.650765 | − | 2.42869i | ||||
\(624\) | −48.2022 | − | 31.5333i | −0.0772472 | − | 0.0505341i | ||||
\(625\) | 301.879 | + | 547.261i | 0.483006 | + | 0.875617i | ||||
\(626\) | −221.405 | + | 383.485i | −0.353683 | + | 0.612597i | ||||
\(627\) | 66.7975 | − | 59.7403i | 0.106535 | − | 0.0952795i | ||||
\(628\) | 40.8157 | − | 152.326i | 0.0649932 | − | 0.242558i | ||||
\(629\) | 395.016i | 0.628007i | ||||||||
\(630\) | −175.517 | + | 441.865i | −0.278598 | + | 0.701373i | ||||
\(631\) | 1077.51 | 1.70762 | 0.853812 | − | 0.520581i | \(-0.174285\pi\) | ||||
0.853812 | + | 0.520581i | \(0.174285\pi\) | |||||||
\(632\) | −438.665 | − | 117.540i | −0.694090 | − | 0.185981i | ||||
\(633\) | −85.3951 | + | 259.850i | −0.134905 | + | 0.410506i | ||||
\(634\) | −223.513 | − | 129.045i | −0.352544 | − | 0.203541i | ||||
\(635\) | −379.390 | − | 664.589i | −0.597464 | − | 1.04660i | ||||
\(636\) | 38.7542 | + | 76.6943i | 0.0609343 | + | 0.120589i | ||||
\(637\) | 233.924 | + | 62.6798i | 0.367228 | + | 0.0983984i | ||||
\(638\) | −45.3002 | − | 45.3002i | −0.0710034 | − | 0.0710034i | ||||
\(639\) | −522.400 | + | 228.401i | −0.817528 | + | 0.357435i | ||||
\(640\) | −543.887 | − | 317.561i | −0.849824 | − | 0.496190i | ||||
\(641\) | −332.614 | − | 576.105i | −0.518899 | − | 0.898759i | −0.999759 | − | 0.0219617i | \(-0.993009\pi\) |
0.480860 | − | 0.876797i | \(-0.340325\pi\) | |||||||
\(642\) | −128.001 | + | 114.478i | −0.199379 | + | 0.178314i | ||||
\(643\) | −1071.82 | + | 287.192i | −1.66690 | + | 0.446644i | −0.964272 | − | 0.264915i | \(-0.914656\pi\) |
−0.702626 | + | 0.711559i | \(0.747989\pi\) | |||||||
\(644\) | −348.401 | − | 201.150i | −0.540996 | − | 0.312344i | ||||
\(645\) | −722.818 | − | 241.455i | −1.12065 | − | 0.374348i | ||||
\(646\) | −102.268 | − | 177.134i | −0.158310 | − | 0.274201i | ||||
\(647\) | −231.177 | + | 231.177i | −0.357306 | + | 0.357306i | −0.862819 | − | 0.505513i | \(-0.831303\pi\) |
0.505513 | + | 0.862819i | \(0.331303\pi\) | |||||||
\(648\) | 534.133 | − | 20.8115i | 0.824280 | − | 0.0321165i | ||||
\(649\) | 149.214i | 0.229914i | ||||||||
\(650\) | 58.7376 | + | 34.6807i | 0.0903655 | + | 0.0533549i | ||||
\(651\) | −822.373 | + | 1257.09i | −1.26325 | + | 1.93102i | ||||
\(652\) | 27.0955 | + | 101.122i | 0.0415574 | + | 0.155094i | ||||
\(653\) | −653.059 | + | 174.987i | −1.00009 | + | 0.267974i | −0.721484 | − | 0.692432i | \(-0.756539\pi\) |
−0.278607 | + | 0.960405i | \(0.589873\pi\) | |||||||
\(654\) | 2.02383 | − | 36.2877i | 0.00309454 | − | 0.0554858i | ||||
\(655\) | −23.1401 | − | 23.3670i | −0.0353285 | − | 0.0356748i | ||||
\(656\) | −12.0146 | −0.0183149 | ||||||||
\(657\) | −603.325 | − | 236.251i | −0.918303 | − | 0.359590i | ||||
\(658\) | 474.287 | + | 474.287i | 0.720802 | + | 0.720802i | ||||
\(659\) | −138.847 | + | 80.1633i | −0.210693 | + | 0.121644i | −0.601634 | − | 0.798772i | \(-0.705483\pi\) |
0.390940 | + | 0.920416i | \(0.372150\pi\) | |||||||
\(660\) | 122.985 | + | 7.46109i | 0.186340 | + | 0.0113047i | ||||
\(661\) | −471.803 | + | 817.186i | −0.713771 | + | 1.23629i | 0.249660 | + | 0.968333i | \(0.419681\pi\) |
−0.963432 | + | 0.267954i | \(0.913652\pi\) | |||||||
\(662\) | 29.2392 | + | 109.122i | 0.0441679 | + | 0.164837i | ||||
\(663\) | 53.5679 | − | 163.003i | 0.0807962 | − | 0.245856i | ||||
\(664\) | −602.564 | + | 347.891i | −0.907476 | + | 0.523931i | ||||
\(665\) | −565.581 | − | 330.228i | −0.850498 | − | 0.496583i | ||||
\(666\) | −100.608 | + | 136.540i | −0.151064 | + | 0.205015i | ||||
\(667\) | 209.991 | − | 209.991i | 0.314829 | − | 0.314829i | ||||
\(668\) | −90.1478 | + | 336.436i | −0.134952 | + | 0.503647i | ||||
\(669\) | 39.6505 | − | 710.943i | 0.0592683 | − | 1.06269i | ||||
\(670\) | −144.799 | − | 39.5568i | −0.216117 | − | 0.0590400i | ||||
\(671\) | 43.9452 | − | 76.1153i | 0.0654921 | − | 0.113436i | ||||
\(672\) | −227.578 | − | 1088.61i | −0.338658 | − | 1.61996i | ||||
\(673\) | −147.135 | + | 549.114i | −0.218625 | + | 0.815919i | 0.766234 | + | 0.642562i | \(0.222128\pi\) |
−0.984859 | + | 0.173358i | \(0.944538\pi\) | |||||||
\(674\) | − | 305.104i | − | 0.452676i | ||||||
\(675\) | 672.569 | − | 57.2388i | 0.996398 | − | 0.0847983i | ||||
\(676\) | 504.446 | 0.746222 | ||||||||
\(677\) | −284.520 | − | 76.2369i | −0.420266 | − | 0.112610i | 0.0424873 | − | 0.999097i | \(-0.486472\pi\) |
−0.462753 | + | 0.886487i | \(0.653138\pi\) | |||||||
\(678\) | 88.1647 | − | 18.4311i | 0.130036 | − | 0.0271846i | ||||
\(679\) | −362.207 | − | 209.120i | −0.533441 | − | 0.307983i | ||||
\(680\) | 168.288 | − | 616.022i | 0.247482 | − | 0.905914i | ||||
\(681\) | −367.915 | − | 20.5193i | −0.540258 | − | 0.0301311i | ||||
\(682\) | −101.840 | − | 27.2880i | −0.149326 | − | 0.0400117i | ||||
\(683\) | 449.659 | + | 449.659i | 0.658359 | + | 0.658359i | 0.954992 | − | 0.296632i | \(-0.0958636\pi\) |
−0.296632 | + | 0.954992i | \(0.595864\pi\) | |||||||
\(684\) | −36.0562 | + | 322.243i | −0.0527138 | + | 0.471115i | ||||
\(685\) | 219.550 | − | 376.023i | 0.320511 | − | 0.548939i | ||||
\(686\) | 174.067 | + | 301.493i | 0.253742 | + | 0.439495i | ||||
\(687\) | 938.588 | + | 308.450i | 1.36621 | + | 0.448981i | ||||
\(688\) | 318.842 | − | 85.4335i | 0.463433 | − | 0.124177i | ||||
\(689\) | 23.2897 | + | 13.4463i | 0.0338021 | + | 0.0195157i | ||||
\(690\) | 9.36716 | − | 154.403i | 0.0135756 | − | 0.223773i | ||||
\(691\) | −465.762 | − | 806.723i | −0.674040 | − | 1.16747i | −0.976748 | − | 0.214388i | \(-0.931224\pi\) |
0.302708 | − | 0.953083i | \(-0.402109\pi\) | |||||||
\(692\) | −151.800 | + | 151.800i | −0.219365 | + | 0.219365i | ||||
\(693\) | 167.738 | + | 210.004i | 0.242046 | + | 0.303036i | ||||
\(694\) | 328.639i | 0.473544i | ||||||||
\(695\) | −310.753 | + | 307.736i | −0.447127 | + | 0.442785i | ||||
\(696\) | 525.571 | + | 29.3120i | 0.755131 | + | 0.0421150i | ||||
\(697\) | −9.26283 | − | 34.5694i | −0.0132896 | − | 0.0495974i | ||||
\(698\) | −44.4373 | + | 11.9069i | −0.0636638 | + | 0.0170587i | ||||
\(699\) | 806.291 | + | 527.465i | 1.15349 | + | 0.754599i | ||||
\(700\) | −224.558 | − | 872.009i | −0.320798 | − | 1.24573i | ||||
\(701\) | 1256.95 | 1.79308 | 0.896539 | − | 0.442964i | \(-0.146073\pi\) | ||||
0.896539 | + | 0.442964i | \(0.146073\pi\) | |||||||
\(702\) | 60.0320 | − | 42.6995i | 0.0855156 | − | 0.0608255i | ||||
\(703\) | −165.200 | − | 165.200i | −0.234993 | − | 0.234993i | ||||
\(704\) | 8.86400 | − | 5.11763i | 0.0125909 | − | 0.00726937i | ||||
\(705\) | 301.712 | − | 903.204i | 0.427960 | − | 1.28114i | ||||
\(706\) | 290.023 | − | 502.334i | 0.410797 | − | 0.711521i | ||||
\(707\) | 286.190 | + | 1068.07i | 0.404795 | + | 1.51071i | ||||
\(708\) | −359.918 | − | 402.435i | −0.508358 | − | 0.568412i | ||||
\(709\) | −631.908 | + | 364.832i | −0.891267 | + | 0.514573i | −0.874357 | − | 0.485284i | \(-0.838716\pi\) |
−0.0169102 | + | 0.999857i | \(0.505383\pi\) | |||||||
\(710\) | −147.459 | + | 252.554i | −0.207689 | + | 0.355709i | ||||
\(711\) | −367.399 | + | 498.613i | −0.516736 | + | 0.701284i | ||||
\(712\) | −638.766 | + | 638.766i | −0.897144 | + | 0.897144i | ||||
\(713\) | 126.495 | − | 472.085i | 0.177412 | − | 0.662111i | ||||
\(714\) | 547.511 | − | 276.662i | 0.766823 | − | 0.387481i | ||||
\(715\) | 33.4877 | − | 19.1169i | 0.0468360 | − | 0.0267369i | ||||
\(716\) | −478.300 | + | 828.440i | −0.668017 | + | 1.15704i | ||||
\(717\) | −406.243 | − | 133.505i | −0.566588 | − | 0.186199i | ||||
\(718\) | −19.4289 | + | 72.5097i | −0.0270598 | + | 0.100988i | ||||
\(719\) | 806.713i | 1.12199i | 0.827818 | + | 0.560997i | \(0.189582\pi\) | ||||
−0.827818 | + | 0.560997i | \(0.810418\pi\) | |||||||
\(720\) | −229.332 | + | 181.350i | −0.318516 | + | 0.251875i | ||||
\(721\) | −304.082 | −0.421750 | ||||||||
\(722\) | −205.101 | − | 54.9567i | −0.284074 | − | 0.0761173i | ||||
\(723\) | 915.424 | + | 1023.57i | 1.26615 | + | 1.41572i | ||||
\(724\) | −470.417 | − | 271.595i | −0.649747 | − | 0.375131i | ||||
\(725\) | 664.676 | + | 6.48556i | 0.916795 | + | 0.00894561i | ||||
\(726\) | 173.153 | − | 264.684i | 0.238502 | − | 0.364578i | ||||
\(727\) | −1142.72 | − | 306.191i | −1.57183 | − | 0.421171i | −0.635446 | − | 0.772145i | \(-0.719184\pi\) |
−0.936385 | + | 0.350974i | \(0.885850\pi\) | |||||||
\(728\) | −157.802 | − | 157.802i | −0.216762 | − | 0.216762i | ||||
\(729\) | 239.180 | − | 688.647i | 0.328093 | − | 0.944645i | ||||
\(730\) | −321.440 | + | 84.4511i | −0.440329 | + | 0.115686i | ||||
\(731\) | 491.633 | + | 851.533i | 0.672548 | + | 1.16489i | ||||
\(732\) | 65.0752 | + | 311.285i | 0.0889006 | + | 0.425253i | ||||
\(733\) | −987.760 | + | 264.670i | −1.34756 | + | 0.361077i | −0.859233 | − | 0.511585i | \(-0.829059\pi\) |
−0.488325 | + | 0.872662i | \(0.662392\pi\) | |||||||
\(734\) | 48.0349 | + | 27.7330i | 0.0654426 | + | 0.0377833i | ||||
\(735\) | 677.963 | − | 1025.39i | 0.922398 | − | 1.39509i | ||||
\(736\) | 180.918 | + | 313.360i | 0.245813 | + | 0.425761i | ||||
\(737\) | −60.0009 | + | 60.0009i | −0.0814123 | + | 0.0814123i | ||||
\(738\) | 5.60286 | − | 14.3083i | 0.00759195 | − | 0.0193880i | ||||
\(739\) | − | 808.791i | − | 1.09444i | −0.836989 | − | 0.547220i | \(-0.815686\pi\) | ||
0.836989 | − | 0.547220i | \(-0.184314\pi\) | |||||||
\(740\) | 1.56706 | − | 321.210i | 0.00211765 | − | 0.434068i | ||||
\(741\) | 45.7668 | + | 90.5722i | 0.0617636 | + | 0.122230i | ||||
\(742\) | 24.8850 | + | 92.8721i | 0.0335378 | + | 0.125165i | ||||
\(743\) | 614.769 | − | 164.727i | 0.827415 | − | 0.221705i | 0.179829 | − | 0.983698i | \(-0.442445\pi\) |
0.647586 | + | 0.761993i | \(0.275779\pi\) | |||||||
\(744\) | 773.190 | − | 390.699i | 1.03923 | − | 0.525133i | ||||
\(745\) | 594.691 | − | 588.916i | 0.798243 | − | 0.790492i | ||||
\(746\) | −180.107 | −0.241431 | ||||||||
\(747\) | 142.150 | + | 938.193i | 0.190295 | + | 1.25595i | ||||
\(748\) | −112.410 | − | 112.410i | −0.150280 | − | 0.150280i | ||||
\(749\) | 614.409 | − | 354.729i | 0.820306 | − | 0.473604i | ||||
\(750\) | 261.428 | − | 227.009i | 0.348570 | − | 0.302679i | ||||
\(751\) | 709.826 | − | 1229.46i | 0.945175 | − | 1.63709i | 0.189774 | − | 0.981828i | \(-0.439224\pi\) |
0.755401 | − | 0.655263i | \(-0.227442\pi\) | |||||||
\(752\) | 106.754 | + | 398.412i | 0.141960 | + | 0.529803i | ||||
\(753\) | −301.227 | + | 62.9726i | −0.400036 | + | 0.0836290i | ||||
\(754\) | 62.8262 | − | 36.2727i | 0.0833239 | − | 0.0481071i | ||||
\(755\) | −1206.80 | + | 317.058i | −1.59841 | + | 0.419945i | ||||
\(756\) | −958.943 | − | 161.789i | −1.26844 | − | 0.214007i | ||||
\(757\) | 582.278 | − | 582.278i | 0.769192 | − | 0.769192i | −0.208772 | − | 0.977964i | \(-0.566947\pi\) |
0.977964 | + | 0.208772i | \(0.0669467\pi\) | |||||||
\(758\) | 34.8500 | − | 130.062i | 0.0459762 | − | 0.171586i | ||||
\(759\) | −73.1771 | − | 47.8715i | −0.0964125 | − | 0.0630718i | ||||
\(760\) | 187.247 | + | 328.007i | 0.246378 | + | 0.431588i | ||||
\(761\) | −73.5291 | + | 127.356i | −0.0966217 | + | 0.167354i | −0.910284 | − | 0.413984i | \(-0.864137\pi\) |
0.813663 | + | 0.581337i | \(0.197470\pi\) | |||||||
\(762\) | −315.992 | + | 282.607i | −0.414687 | + | 0.370875i | ||||
\(763\) | −38.8619 | + | 145.035i | −0.0509330 | + | 0.190085i | ||||
\(764\) | − | 904.087i | − | 1.18336i | ||||||
\(765\) | −698.603 | − | 520.038i | −0.913207 | − | 0.679788i | ||||
\(766\) | 697.261 | 0.910262 | ||||||||
\(767\) | −163.211 | − | 43.7322i | −0.212791 | − | 0.0570172i | ||||
\(768\) | −123.621 | + | 376.169i | −0.160965 | + | 0.489804i | ||||
\(769\) | 798.259 | + | 460.875i | 1.03805 | + | 0.599317i | 0.919280 | − | 0.393605i | \(-0.128772\pi\) |
0.118768 | + | 0.992922i | \(0.462106\pi\) | |||||||
\(770\) | 132.990 | + | 36.3308i | 0.172714 | + | 0.0471828i | ||||
\(771\) | −151.875 | − | 300.559i | −0.196984 | − | 0.389830i | ||||
\(772\) | 111.860 | + | 29.9729i | 0.144897 | + | 0.0388250i | ||||
\(773\) | 646.946 | + | 646.946i | 0.836928 | + | 0.836928i | 0.988453 | − | 0.151525i | \(-0.0484185\pi\) |
−0.151525 | + | 0.988453i | \(0.548418\pi\) | |||||||
\(774\) | −46.9445 | + | 419.554i | −0.0606518 | + | 0.542060i | ||||
\(775\) | 952.666 | − | 537.697i | 1.22925 | − | 0.693803i | ||||
\(776\) | 120.597 | + | 208.880i | 0.155409 | + | 0.269176i | ||||
\(777\) | 522.286 | − | 467.106i | 0.672183 | − | 0.601166i | ||||
\(778\) | −38.4744 | + | 10.3092i | −0.0494530 | + | 0.0132509i | ||||
\(779\) | 18.3311 | + | 10.5835i | 0.0235316 | + | 0.0135860i | ||||
\(780\) | −44.2057 | + | 132.334i | −0.0566740 | + | 0.169659i | ||||
\(781\) | 82.6613 | + | 143.174i | 0.105840 | + | 0.183321i | ||||
\(782\) | −141.127 | + | 141.127i | −0.180469 | + | 0.180469i | ||||
\(783\) | 298.574 | − | 652.849i | 0.381321 | − | 0.833779i | ||||
\(784\) | 532.441i | 0.679134i | ||||||||
\(785\) | −250.510 | − | 1.22215i | −0.319121 | − | 0.00155687i | ||||
\(786\) | −9.97338 | + | 15.2455i | −0.0126888 | + | 0.0193963i | ||||
\(787\) | 28.2343 | + | 105.372i | 0.0358758 | + | 0.133890i | 0.981541 | − | 0.191251i | \(-0.0612546\pi\) |
−0.945665 | + | 0.325142i | \(0.894588\pi\) | |||||||
\(788\) | 974.548 | − | 261.129i | 1.23674 | − | 0.331382i | ||||
\(789\) | −24.8892 | + | 446.270i | −0.0315453 | + | 0.565614i | ||||
\(790\) | −1.54987 | + | 317.686i | −0.00196186 | + | 0.402134i | ||||
\(791\) | −372.115 | −0.470436 | ||||||||
\(792\) | −23.2194 | − | 153.248i | −0.0293174 | − | 0.193495i | ||||
\(793\) | 70.3755 | + | 70.3755i | 0.0887459 | + | 0.0887459i | ||||
\(794\) | 101.540 | − | 58.6241i | 0.127884 | − | 0.0738339i | ||||
\(795\) | 102.190 | − | 90.5001i | 0.128541 | − | 0.113837i | ||||
\(796\) | 169.192 | − | 293.050i | 0.212553 | − | 0.368153i | ||||
\(797\) | −231.377 | − | 863.511i | −0.290310 | − | 1.08345i | −0.944871 | − | 0.327443i | \(-0.893813\pi\) |
0.654561 | − | 0.756009i | \(-0.272854\pi\) | |||||||
\(798\) | −113.272 | + | 344.678i | −0.141945 | + | 0.431928i | ||||
\(799\) | −1064.04 | + | 614.324i | −1.33171 | + | 0.768866i | ||||
\(800\) | −217.239 | + | 780.214i | −0.271548 | + | 0.975267i | ||||
\(801\) | 493.532 | + | 1128.81i | 0.616145 | + | 1.40925i | ||||
\(802\) | 189.040 | − | 189.040i | 0.235711 | − | 0.235711i | ||||
\(803\) | −48.6261 | + | 181.475i | −0.0605556 | + | 0.225996i | ||||
\(804\) | 17.0969 | − | 306.552i | 0.0212648 | − | 0.381283i | ||||
\(805\) | −168.413 | + | 616.480i | −0.209209 | + | 0.765813i | ||||
\(806\) | 59.6953 | − | 103.395i | 0.0740637 | − | 0.128282i | ||||
\(807\) | 19.0823 | + | 91.2795i | 0.0236460 | + | 0.113110i | ||||
\(808\) | 165.042 | − | 615.946i | 0.204260 | − | 0.762310i | ||||
\(809\) | − | 920.002i | − | 1.13721i | −0.822611 | − | 0.568604i | \(-0.807484\pi\) | ||
0.822611 | − | 0.568604i | \(-0.192516\pi\) | |||||||
\(810\) | −109.026 | − | 357.685i | −0.134600 | − | 0.441586i | ||||
\(811\) | −174.196 | −0.214792 | −0.107396 | − | 0.994216i | \(-0.534251\pi\) | ||||
−0.107396 | + | 0.994216i | \(0.534251\pi\) | |||||||
\(812\) | −925.035 | − | 247.862i | −1.13921 | − | 0.305249i | ||||
\(813\) | −12.4056 | + | 2.59343i | −0.0152590 | + | 0.00318995i | ||||
\(814\) | 42.5901 | + | 24.5894i | 0.0523220 | + | 0.0302081i | ||||
\(815\) | 144.426 | − | 82.4477i | 0.177210 | − | 0.101163i | ||||
\(816\) | 376.643 | + | 21.0061i | 0.461573 | + | 0.0257427i | ||||
\(817\) | −561.727 | − | 150.514i | −0.687548 | − | 0.184228i | ||||
\(818\) | −134.631 | − | 134.631i | −0.164585 | − | 0.164585i | ||||
\(819\) | −278.864 | + | 121.923i | −0.340494 | + | 0.148869i | ||||
\(820\) | 7.39500 | + | 28.1471i | 0.00901829 | + | 0.0343257i | ||||
\(821\) | 425.992 | + | 737.840i | 0.518869 | + | 0.898708i | 0.999760 | + | 0.0219274i | \(0.00698027\pi\) |
−0.480890 | + | 0.876781i | \(0.659686\pi\) | |||||||
\(822\) | −229.157 | − | 75.3083i | −0.278780 | − | 0.0916160i | ||||
\(823\) | 199.408 | − | 53.4313i | 0.242295 | − | 0.0649226i | −0.135628 | − | 0.990760i | \(-0.543305\pi\) |
0.377923 | + | 0.925837i | \(0.376639\pi\) | |||||||
\(824\) | 151.866 | + | 87.6802i | 0.184304 | + | 0.106408i | ||||
\(825\) | −38.1801 | − | 191.966i | −0.0462789 | − | 0.232686i | ||||
\(826\) | −302.054 | − | 523.172i | −0.365682 | − | 0.633380i | ||||
\(827\) | −66.1579 | + | 66.1579i | −0.0799974 | + | 0.0799974i | −0.745973 | − | 0.665976i | \(-0.768015\pi\) |
0.665976 | + | 0.745973i | \(0.268015\pi\) | |||||||
\(828\) | 312.831 | − | 47.3987i | 0.377815 | − | 0.0572448i | ||||
\(829\) | 71.1280i | 0.0857998i | 0.999079 | + | 0.0428999i | \(0.0136596\pi\) | ||||
−0.999079 | + | 0.0428999i | \(0.986340\pi\) | |||||||
\(830\) | 342.485 | + | 345.843i | 0.412633 | + | 0.416679i | ||||
\(831\) | −416.531 | − | 23.2306i | −0.501240 | − | 0.0279550i | ||||
\(832\) | 2.99979 | + | 11.1954i | 0.00360552 | + | 0.0134560i | ||||
\(833\) | −1531.98 | + | 410.494i | −1.83912 | + | 0.492790i | ||||
\(834\) | 202.746 | + | 132.634i | 0.243101 | + | 0.159033i | ||||
\(835\) | 553.290 | + | 2.69929i | 0.662623 | + | 0.00323269i | ||||
\(836\) | 94.0219 | 0.112466 | ||||||||
\(837\) | −111.666 | − | 1176.16i | −0.133412 | − | 1.40521i | ||||
\(838\) | −468.230 | − | 468.230i | −0.558747 | − | 0.558747i | ||||
\(839\) | 327.523 | − | 189.096i | 0.390373 | − | 0.225382i | −0.291949 | − | 0.956434i | \(-0.594304\pi\) |
0.682322 | + | 0.731052i | \(0.260970\pi\) | |||||||
\(840\) | −1013.50 | + | 505.936i | −1.20654 | + | 0.602305i | ||||
\(841\) | −67.0308 | + | 116.101i | −0.0797037 | + | 0.138051i | ||||
\(842\) | −59.5317 | − | 222.175i | −0.0707027 | − | 0.263866i | ||||
\(843\) | 1006.76 | + | 1125.69i | 1.19426 | + | 1.33534i | ||||
\(844\) | −248.527 | + | 143.487i | −0.294463 | + | 0.170008i | ||||
\(845\) | −203.622 | − | 775.033i | −0.240973 | − | 0.917199i | ||||
\(846\) | −524.257 | − | 58.6599i | −0.619690 | − | 0.0693380i | ||||
\(847\) | −923.984 | + | 923.984i | −1.09089 | + | 1.09089i | ||||
\(848\) | −15.3028 | + | 57.1106i | −0.0180457 | + | 0.0673475i | ||||
\(849\) | −392.410 | + | 198.288i | −0.462203 | + | 0.233555i | ||||
\(850\) | −446.702 | − | 4.35869i | −0.525532 | − | 0.00512787i | ||||
\(851\) | −113.985 | + | 197.428i | −0.133943 | + | 0.231996i | ||||
\(852\) | −568.287 | − | 186.757i | −0.667004 | − | 0.219199i | ||||
\(853\) | −168.733 | + | 629.719i | −0.197811 | + | 0.738240i | 0.793711 | + | 0.608296i | \(0.208146\pi\) |
−0.991521 | + | 0.129944i | \(0.958520\pi\) | |||||||
\(854\) | 355.832i | 0.416665i | ||||||||
\(855\) | 509.649 | − | 74.6780i | 0.596081 | − | 0.0873426i | ||||
\(856\) | −409.137 | −0.477963 | ||||||||
\(857\) | 542.809 | + | 145.445i | 0.633382 | + | 0.169714i | 0.561204 | − | 0.827677i | \(-0.310338\pi\) |
0.0721782 | + | 0.997392i | \(0.477005\pi\) | |||||||
\(858\) | −14.2402 | − | 15.9224i | −0.0165969 | − | 0.0185576i | ||||
\(859\) | −468.778 | − | 270.649i | −0.545725 | − | 0.315075i | 0.201671 | − | 0.979453i | \(-0.435363\pi\) |
−0.747396 | + | 0.664379i | \(0.768696\pi\) | |||||||
\(860\) | −396.397 | − | 694.380i | −0.460926 | − | 0.807419i | ||||
\(861\) | −34.7539 | + | 53.1254i | −0.0403646 | + | 0.0617020i | ||||
\(862\) | 208.774 | + | 55.9407i | 0.242197 | + | 0.0648964i | ||||
\(863\) | 24.2188 | + | 24.2188i | 0.0280635 | + | 0.0280635i | 0.720999 | − | 0.692936i | \(-0.243683\pi\) |
−0.692936 | + | 0.720999i | \(0.743683\pi\) | |||||||
\(864\) | 674.184 | + | 557.269i | 0.780306 | + | 0.644987i | ||||
\(865\) | 294.502 | + | 171.952i | 0.340464 | + | 0.198788i | ||||
\(866\) | −243.463 | − | 421.690i | −0.281135 | − | 0.486940i | ||||
\(867\) | 52.5250 | + | 251.252i | 0.0605825 | + | 0.289794i | ||||
\(868\) | −1522.36 | + | 407.916i | −1.75388 | + | 0.469950i | ||||
\(869\) | 155.529 | + | 89.7949i | 0.178975 | + | 0.103331i | ||||
\(870\) | −73.5916 | − | 360.802i | −0.0845880 | − | 0.414715i | ||||
\(871\) | −48.0438 | − | 83.2144i | −0.0551594 | − | 0.0955389i | ||||
\(872\) | 61.2285 | − | 61.2285i | 0.0702162 | − | 0.0702162i | ||||
\(873\) | 325.227 | − | 49.2768i | 0.372540 | − | 0.0564454i | ||||
\(874\) | − | 118.041i | − | 0.135059i | ||||||
\(875\) | −1249.11 | + | 697.002i | −1.42756 | + | 0.796574i | ||||
\(876\) | −306.588 | − | 606.735i | −0.349986 | − | 0.692620i | ||||
\(877\) | 321.735 | + | 1200.73i | 0.366858 | + | 1.36913i | 0.864884 | + | 0.501972i | \(0.167392\pi\) |
−0.498025 | + | 0.867162i | \(0.665941\pi\) | |||||||
\(878\) | −575.505 | + | 154.206i | −0.655472 | + | 0.175633i | ||||
\(879\) | −918.415 | + | 464.082i | −1.04484 | + | 0.527966i | ||||
\(880\) | 59.6533 | + | 60.2382i | 0.0677879 | + | 0.0684525i | ||||
\(881\) | 1074.75 | 1.21993 | 0.609963 | − | 0.792430i | \(-0.291184\pi\) | ||||
0.609963 | + | 0.792430i | \(0.291184\pi\) | |||||||
\(882\) | −634.091 | − | 248.298i | −0.718924 | − | 0.281517i | ||||
\(883\) | 285.903 | + | 285.903i | 0.323786 | + | 0.323786i | 0.850217 | − | 0.526432i | \(-0.176470\pi\) |
−0.526432 | + | 0.850217i | \(0.676470\pi\) | |||||||
\(884\) | 155.899 | − | 90.0086i | 0.176357 | − | 0.101820i | ||||
\(885\) | −473.020 | + | 715.423i | −0.534486 | + | 0.808388i | ||||
\(886\) | −126.931 | + | 219.851i | −0.143263 | + | 0.248139i | ||||
\(887\) | −277.751 | − | 1036.58i | −0.313135 | − | 1.16864i | −0.925713 | − | 0.378226i | \(-0.876534\pi\) |
0.612578 | − | 0.790410i | \(-0.290132\pi\) | |||||||
\(888\) | −395.531 | + | 82.6871i | −0.445418 | + | 0.0931161i | ||||
\(889\) | 1516.77 | − | 875.708i | 1.70615 | − | 0.985048i | ||||
\(890\) | 545.722 | + | 318.632i | 0.613170 | + | 0.358014i | ||||
\(891\) | −206.156 | − | 46.7192i | −0.231376 | − | 0.0524345i | ||||
\(892\) | 528.255 | − | 528.255i | 0.592214 | − | 0.592214i | ||||
\(893\) | 188.076 | − | 701.910i | 0.210612 | − | 0.786013i | ||||
\(894\) | −387.997 | − | 253.823i | −0.434001 | − | 0.283918i | ||||
\(895\) | 1465.89 | + | 400.458i | 1.63786 | + | 0.447439i | ||||
\(896\) | 720.711 | − | 1248.31i | 0.804365 | − | 1.39320i | ||||
\(897\) | 73.8090 | − | 66.0110i | 0.0822842 | − | 0.0735908i | ||||
\(898\) | −45.5630 | + | 170.043i | −0.0507383 | + | 0.189358i | ||||
\(899\) | − | 1163.43i | − | 1.29414i | ||||||
\(900\) | 566.011 | + | 425.644i | 0.628901 | + | 0.472938i | ||||
\(901\) | −176.122 | −0.195473 | ||||||||
\(902\) | −4.30382 | − | 1.15321i | −0.00477142 | − | 0.00127850i | ||||
\(903\) | 544.533 | − | 1656.97i | 0.603026 | − | 1.83496i | ||||
\(904\) | 185.844 | + | 107.297i | 0.205580 | + | 0.118692i | ||||
\(905\) | −227.394 | + | 832.380i | −0.251264 | + | 0.919757i | ||||
\(906\) | 311.740 | + | 616.932i | 0.344084 | + | 0.680940i | ||||
\(907\) | 1652.08 | + | 442.672i | 1.82147 | + | 0.488062i | 0.996969 | − | 0.0777954i | \(-0.0247881\pi\) |
0.824503 | + | 0.565858i | \(0.191455\pi\) | |||||||
\(908\) | −273.374 | − | 273.374i | −0.301073 | − | 0.301073i | ||||
\(909\) | −700.122 | − | 515.879i | −0.770211 | − | 0.567524i | ||||
\(910\) | −78.7157 | + | 134.816i | −0.0865008 | + | 0.148150i | ||||
\(911\) | −203.177 | − | 351.913i | −0.223026 | − | 0.386293i | 0.732699 | − | 0.680553i | \(-0.238260\pi\) |
−0.955726 | + | 0.294260i | \(0.904927\pi\) | |||||||
\(912\) | −166.301 | + | 148.731i | −0.182348 | + | 0.163083i | ||||
\(913\) | 265.772 | − | 71.2133i | 0.291097 | − | 0.0779993i | ||||
\(914\) | 250.056 | + | 144.370i | 0.273584 | + | 0.157954i | ||||
\(915\) | 451.991 | − | 225.633i | 0.493980 | − | 0.246594i | ||||
\(916\) | 518.280 | + | 897.687i | 0.565808 | + | 0.980008i | ||||
\(917\) | 53.2204 | − | 53.2204i | 0.0580375 | − | 0.0580375i | ||||
\(918\) | −200.660 | + | 438.754i | −0.218584 | + | 0.477945i | ||||
\(919\) | − | 975.596i | − | 1.06158i | −0.847502 | − | 0.530792i | \(-0.821895\pi\) | ||
0.847502 | − | 0.530792i | \(-0.178105\pi\) | |||||||
\(920\) | 261.868 | − | 259.326i | 0.284639 | − | 0.281876i | ||||
\(921\) | 44.6600 | − | 68.2681i | 0.0484908 | − | 0.0741238i | ||||
\(922\) | 52.7449 | + | 196.847i | 0.0572071 | + | 0.213500i | ||||
\(923\) | −180.830 | + | 48.4533i | −0.195916 | + | 0.0524955i | ||||
\(924\) | −15.7026 | + | 281.551i | −0.0169941 | + | 0.304709i | ||||
\(925\) | −494.141 | + | 127.250i | −0.534206 | + | 0.137568i | ||||
\(926\) | 266.694 | 0.288007 | ||||||||
\(927\) | 186.864 | − | 149.255i | 0.201579 | − | 0.161009i | ||||
\(928\) | 609.065 | + | 609.065i | 0.656320 | + | 0.656320i | ||||
\(929\) | −1121.09 | + | 647.262i | −1.20677 | + | 0.696730i | −0.962052 | − | 0.272864i | \(-0.912029\pi\) |
−0.244719 | + | 0.969594i | \(0.578696\pi\) | |||||||
\(930\) | −401.779 | − | 453.676i | −0.432020 | − | 0.487824i | ||||
\(931\) | 469.020 | − | 812.366i | 0.503780 | − | 0.872573i | ||||
\(932\) | 261.635 | + | 976.435i | 0.280724 | + | 1.04768i | ||||
\(933\) | 516.429 | − | 1571.45i | 0.553514 | − | 1.68430i | ||||
\(934\) | 282.319 | − | 162.997i | 0.302269 | − | 0.174515i | ||||
\(935\) | −127.332 | + | 218.081i | −0.136184 | + | 0.233242i | ||||
\(936\) | 174.428 | + | 19.5170i | 0.186355 | + | 0.0208515i | ||||
\(937\) | −416.458 | + | 416.458i | −0.444459 | + | 0.444459i | −0.893507 | − | 0.449049i | \(-0.851763\pi\) |
0.449049 | + | 0.893507i | \(0.351763\pi\) | |||||||
\(938\) | 88.9145 | − | 331.834i | 0.0947916 | − | 0.353767i | ||||
\(939\) | −80.1201 | + | 1436.57i | −0.0853249 | + | 1.52990i | ||||
\(940\) | 867.669 | − | 495.321i | 0.923052 | − | 0.526937i | ||||
\(941\) | 6.23741 | − | 10.8035i | 0.00662849 | − | 0.0114809i | −0.862692 | − | 0.505729i | \(-0.831223\pi\) |
0.869321 | + | 0.494249i | \(0.164557\pi\) | |||||||
\(942\) | 28.3980 | + | 135.841i | 0.0301465 | + | 0.144205i | ||||
\(943\) | 5.34574 | − | 19.9506i | 0.00566886 | − | 0.0211565i | ||||
\(944\) | − | 371.489i | − | 0.393526i | ||||||
\(945\) | 138.509 | + | 1538.63i | 0.146570 | + | 1.62818i | ||||
\(946\) | 122.415 | 0.129403 | ||||||||
\(947\) | 1149.13 | + | 307.908i | 1.21344 | + | 0.325140i | 0.808111 | − | 0.589031i | \(-0.200490\pi\) |
0.405329 | + | 0.914171i | \(0.367157\pi\) | |||||||
\(948\) | −636.061 | + | 132.971i | −0.670950 | + | 0.140264i | ||||
\(949\) | −184.246 | − | 106.375i | −0.194148 | − | 0.112091i | ||||
\(950\) | 188.639 | − | 184.993i | 0.198567 | − | 0.194729i | ||||
\(951\) | −837.300 | − | 46.6977i | −0.880442 | − | 0.0491038i | ||||
\(952\) | 1411.73 | + | 378.272i | 1.48291 | + | 0.397345i | ||||
\(953\) | −943.370 | − | 943.370i | −0.989895 | − | 0.989895i | 0.0100546 | − | 0.999949i | \(-0.496799\pi\) |
−0.999949 | + | 0.0100546i | \(0.996799\pi\) | |||||||
\(954\) | −60.8776 | − | 44.8572i | −0.0638130 | − | 0.0470201i | ||||
\(955\) | −1389.04 | + | 364.939i | −1.45449 | + | 0.382135i | ||||
\(956\) | −224.324 | − | 388.540i | −0.234648 | − | 0.406423i | ||||
\(957\) | −197.756 | − | 64.9888i | −0.206641 | − | 0.0679089i | ||||
\(958\) | 780.555 | − | 209.149i | 0.814775 | − | 0.218318i | ||||
\(959\) | 863.033 | + | 498.272i | 0.899930 | + | 0.519575i | ||||
\(960\) | 58.7227 | + | 3.56252i | 0.0611695 | + | 0.00371096i | ||||
\(961\) | −476.853 | − | 825.933i | −0.496204 | − | 0.859451i | ||||
\(962\) | −39.3784 | + | 39.3784i | −0.0409339 | + | 0.0409339i | ||||
\(963\) | −203.451 | + | 519.564i | −0.211268 | + | 0.539526i | ||||
\(964\) | 1440.74i | 1.49454i | ||||||||
\(965\) | 0.897477 | − | 183.961i | 0.000930028 | − | 0.190633i | ||||
\(966\) | 353.478 | + | 19.7141i | 0.365920 | + | 0.0204080i | ||||
\(967\) | −71.4571 | − | 266.681i | −0.0738956 | − | 0.275782i | 0.919085 | − | 0.394059i | \(-0.128930\pi\) |
−0.992981 | + | 0.118277i | \(0.962263\pi\) | |||||||
\(968\) | 727.888 | − | 195.037i | 0.751950 | − | 0.201484i | ||||
\(969\) | −556.155 | − | 363.829i | −0.573948 | − | 0.375469i | ||||
\(970\) | 119.888 | − | 118.723i | 0.123595 | − | 0.122395i | ||||
\(971\) | −311.097 | −0.320388 | −0.160194 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160194 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(972\) | 668.701 | − | 371.264i | 0.687964 | − | 0.381959i | ||||
\(973\) | −707.766 | − | 707.766i | −0.727406 | − | 0.727406i | ||||
\(974\) | 273.087 | − | 157.667i | 0.280377 | − | 0.161876i | ||||
\(975\) | 221.163 | + | 14.5005i | 0.226833 | + | 0.0148723i | ||||
\(976\) | −109.407 | + | 189.499i | −0.112098 | + | 0.194159i | ||||
\(977\) | −163.044 | − | 608.490i | −0.166883 | − | 0.622815i | −0.997793 | − | 0.0664079i | \(-0.978846\pi\) |
0.830910 | − | 0.556407i | \(-0.187821\pi\) | |||||||
\(978\) | −61.4152 | − | 68.6703i | −0.0627967 | − | 0.0702150i | ||||
\(979\) | 309.371 | − | 178.616i | 0.316008 | − | 0.182447i | ||||
\(980\) | 1247.37 | − | 327.719i | 1.27283 | − | 0.334407i | ||||
\(981\) | −47.3072 | − | 108.201i | −0.0482235 | − | 0.110297i | ||||
\(982\) | 18.5905 | − | 18.5905i | 0.0189313 | − | 0.0189313i | ||||
\(983\) | −81.8068 | + | 305.307i | −0.0832216 | + | 0.310587i | −0.994971 | − | 0.100159i | \(-0.968065\pi\) |
0.911750 | + | 0.410746i | \(0.134732\pi\) | |||||||
\(984\) | 32.6754 | − | 16.5112i | 0.0332068 | − | 0.0167796i | ||||
\(985\) | −794.581 | − | 1391.89i | −0.806681 | − | 1.41309i | ||||
\(986\) | −237.553 | + | 411.453i | −0.240926 | + | 0.417295i | ||||
\(987\) | 2070.48 | + | 680.425i | 2.09775 | + | 0.689387i | ||||
\(988\) | −27.5563 | + | 102.841i | −0.0278910 | + | 0.104091i | ||||
\(989\) | 567.460i | 0.573771i | ||||||||
\(990\) | −99.5572 | + | 42.9505i | −0.100563 | + | 0.0433844i | ||||
\(991\) | −1401.99 | −1.41472 | −0.707362 | − | 0.706852i | \(-0.750115\pi\) | ||||
−0.707362 | + | 0.706852i | \(0.750115\pi\) | |||||||
\(992\) | 1369.25 | + | 366.889i | 1.38029 | + | 0.369848i | ||||
\(993\) | 244.703 | + | 273.611i | 0.246428 | + | 0.275539i | ||||
\(994\) | −579.651 | − | 334.662i | −0.583150 | − | 0.336682i | ||||
\(995\) | −518.538 | − | 141.657i | −0.521143 | − | 0.142368i | ||||
\(996\) | −545.022 | + | 833.130i | −0.547211 | + | 0.836475i | ||||
\(997\) | −1305.07 | − | 349.692i | −1.30900 | − | 0.350745i | −0.464152 | − | 0.885756i | \(-0.653641\pi\) |
−0.844845 | + | 0.535011i | \(0.820307\pi\) | |||||||
\(998\) | 309.014 | + | 309.014i | 0.309633 | + | 0.309633i | ||||
\(999\) | −91.6809 | + | 543.404i | −0.0917727 | + | 0.543947i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 45.3.k.a.13.4 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.118.7 | 40 | |||
5.2 | odd | 4 | inner | 45.3.k.a.22.7 | yes | 40 | |
5.3 | odd | 4 | 225.3.o.b.157.4 | 40 | |||
5.4 | even | 2 | 225.3.o.b.193.7 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.73.4 | 40 | |||
9.4 | even | 3 | 405.3.g.h.163.7 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.163.4 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.43.7 | yes | 40 | |
15.2 | even | 4 | 135.3.l.a.37.4 | 40 | |||
45.2 | even | 12 | 135.3.l.a.127.7 | 40 | |||
45.7 | odd | 12 | inner | 45.3.k.a.7.4 | ✓ | 40 | |
45.22 | odd | 12 | 405.3.g.h.82.7 | 20 | |||
45.32 | even | 12 | 405.3.g.g.82.4 | 20 | |||
45.34 | even | 6 | 225.3.o.b.43.4 | 40 | |||
45.43 | odd | 12 | 225.3.o.b.7.7 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.4 | ✓ | 40 | 45.7 | odd | 12 | inner | |
45.3.k.a.13.4 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.22.7 | yes | 40 | 5.2 | odd | 4 | inner | |
45.3.k.a.43.7 | yes | 40 | 9.7 | even | 3 | inner | |
135.3.l.a.37.4 | 40 | 15.2 | even | 4 | |||
135.3.l.a.73.4 | 40 | 9.2 | odd | 6 | |||
135.3.l.a.118.7 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.127.7 | 40 | 45.2 | even | 12 | |||
225.3.o.b.7.7 | 40 | 45.43 | odd | 12 | |||
225.3.o.b.43.4 | 40 | 45.34 | even | 6 | |||
225.3.o.b.157.4 | 40 | 5.3 | odd | 4 | |||
225.3.o.b.193.7 | 40 | 5.4 | even | 2 | |||
405.3.g.g.82.4 | 20 | 45.32 | even | 12 | |||
405.3.g.g.163.4 | 20 | 9.5 | odd | 6 | |||
405.3.g.h.82.7 | 20 | 45.22 | odd | 12 | |||
405.3.g.h.163.7 | 20 | 9.4 | even | 3 |