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 | 22.7 | ||
Character | \(\chi\) | \(=\) | 45.22 |
Dual form | 45.3.k.a.43.7 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.238965 | − | 0.891829i | 0.119482 | − | 0.445914i | −0.880101 | − | 0.474787i | \(-0.842525\pi\) |
0.999583 | + | 0.0288727i | \(0.00919174\pi\) | |||||||
\(3\) | 0.613889 | + | 2.93652i | 0.204630 | + | 0.978839i | ||||
\(4\) | 2.72585 | + | 1.57377i | 0.681462 | + | 0.393442i | ||||
\(5\) | −3.51824 | + | 3.55274i | −0.703649 | + | 0.710548i | ||||
\(6\) | 2.76557 | + | 0.154241i | 0.460928 | + | 0.0257068i | ||||
\(7\) | 2.96175 | − | 11.0534i | 0.423108 | − | 1.57906i | −0.344913 | − | 0.938635i | \(-0.612091\pi\) |
0.768021 | − | 0.640425i | \(-0.221242\pi\) | |||||||
\(8\) | 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 | \(0.871181\pi\) | |||||||
\(12\) | −2.94803 | + | 8.97062i | −0.245669 | + | 0.747552i | ||||
\(13\) | −0.764853 | − | 2.85447i | −0.0588349 | − | 0.219575i | 0.930249 | − | 0.366929i | \(-0.119591\pi\) |
−0.989084 | + | 0.147354i | \(0.952924\pi\) | |||||||
\(14\) | −9.15000 | − | 5.28276i | −0.653572 | − | 0.377340i | ||||
\(15\) | −12.5925 | − | 8.15040i | −0.839500 | − | 0.543360i | ||||
\(16\) | 3.24857 | + | 5.62669i | 0.203036 | + | 0.351668i | ||||
\(17\) | −13.6850 | − | 13.6850i | −0.805003 | − | 0.805003i | 0.178870 | − | 0.983873i | \(-0.442756\pi\) |
−0.983873 | + | 0.178870i | \(0.942756\pi\) | |||||||
\(18\) | 1.24482 | + | 8.21583i | 0.0691568 | + | 0.456435i | ||||
\(19\) | 11.4465i | 0.602446i | 0.953554 | + | 0.301223i | \(0.0973948\pi\) | ||||
−0.953554 | + | 0.301223i | \(0.902605\pi\) | |||||||
\(20\) | −15.1814 | + | 4.14733i | −0.759069 | + | 0.207366i | ||||
\(21\) | 34.2768 | + | 1.91167i | 1.63223 | + | 0.0910321i | ||||
\(22\) | −2.32738 | + | 0.623621i | −0.105790 | + | 0.0283464i | ||||
\(23\) | 2.89082 | + | 10.7887i | 0.125688 | + | 0.469074i | 0.999863 | − | 0.0165366i | \(-0.00526400\pi\) |
−0.874175 | + | 0.485611i | \(0.838597\pi\) | |||||||
\(24\) | 16.5675 | + | 10.8382i | 0.690313 | + | 0.451594i | ||||
\(25\) | −0.243925 | − | 24.9988i | −0.00975701 | − | 0.999952i | ||||
\(26\) | −2.72847 | −0.104941 | ||||||||
\(27\) | −15.6496 | − | 22.0020i | −0.579615 | − | 0.814890i | ||||
\(28\) | 25.4688 | − | 25.4688i | 0.909601 | − | 0.909601i | ||||
\(29\) | 23.0262 | − | 13.2942i | 0.794005 | − | 0.458419i | −0.0473654 | − | 0.998878i | \(-0.515083\pi\) |
0.841371 | + | 0.540458i | \(0.181749\pi\) | |||||||
\(30\) | −10.2779 | + | 9.28269i | −0.342597 | + | 0.309423i | ||||
\(31\) | −21.8787 | + | 37.8950i | −0.705764 | + | 1.22242i | 0.260652 | + | 0.965433i | \(0.416063\pi\) |
−0.966415 | + | 0.256985i | \(0.917271\pi\) | |||||||
\(32\) | 31.2919 | − | 8.38463i | 0.977870 | − | 0.262020i | ||||
\(33\) | 5.83564 | − | 5.21910i | 0.176838 | − | 0.158154i | ||||
\(34\) | −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 | 0.874711 | − | 0.484646i | \(-0.161051\pi\) |
−0.484646 | + | 0.874711i | \(0.661051\pi\) | |||||||
\(38\) | 10.2083 | + | 2.73530i | 0.268639 | + | 0.0719817i | ||||
\(39\) | 7.91267 | − | 3.99833i | 0.202889 | − | 0.102521i | ||||
\(40\) | 0.160974 | + | 32.9958i | 0.00402435 | + | 0.824896i | ||||
\(41\) | −0.924605 | + | 1.60146i | −0.0225513 | + | 0.0390601i | −0.877081 | − | 0.480343i | \(-0.840512\pi\) |
0.854529 | + | 0.519403i | \(0.173846\pi\) | |||||||
\(42\) | 9.89582 | − | 30.1122i | 0.235615 | − | 0.716957i | ||||
\(43\) | −49.0742 | − | 13.1494i | −1.14126 | − | 0.305800i | −0.361803 | − | 0.932255i | \(-0.617839\pi\) |
−0.779458 | + | 0.626455i | \(0.784505\pi\) | |||||||
\(44\) | − | 8.21405i | − | 0.186683i | ||||||
\(45\) | 16.2034 | − | 41.9815i | 0.360075 | − | 0.932923i | ||||
\(46\) | 10.3125 | 0.224184 | ||||||||
\(47\) | −16.4309 | + | 61.3211i | −0.349594 | + | 1.30470i | 0.537558 | + | 0.843227i | \(0.319347\pi\) |
−0.887152 | + | 0.461477i | \(0.847320\pi\) | |||||||
\(48\) | −14.5286 | + | 12.9936i | −0.302679 | + | 0.270701i | ||||
\(49\) | −70.9709 | − | 40.9750i | −1.44838 | − | 0.836225i | ||||
\(50\) | −22.3529 | − | 5.75630i | −0.447059 | − | 0.115126i | ||||
\(51\) | 31.7853 | − | 48.5875i | 0.623241 | − | 0.952696i | ||||
\(52\) | 2.40740 | − | 8.98455i | 0.0462962 | − | 0.172780i | ||||
\(53\) | 6.43481 | − | 6.43481i | 0.121412 | − | 0.121412i | −0.643790 | − | 0.765202i | \(-0.722639\pi\) |
0.765202 | + | 0.643790i | \(0.222639\pi\) | |||||||
\(54\) | −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 | ||||
\(57\) | −33.6128 | + | 7.02686i | −0.589698 | + | 0.123278i | ||||
\(58\) | −6.35367 | − | 23.7122i | −0.109546 | − | 0.408831i | ||||
\(59\) | 49.5170 | + | 28.5886i | 0.839271 | + | 0.484553i | 0.857016 | − | 0.515289i | \(-0.172316\pi\) |
−0.0177457 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(60\) | −21.4984 | − | 42.0344i | −0.358306 | − | 0.700574i | ||||
\(61\) | 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 | ||||
\(63\) | 15.4285 | + | 101.828i | 0.244896 | + | 1.61632i | ||||
\(64\) | − | 3.92205i | − | 0.0612820i | ||||||
\(65\) | 12.8321 | + | 7.32540i | 0.197417 | + | 0.112698i | ||||
\(66\) | −3.26003 | − | 6.45157i | −0.0493944 | − | 0.0977511i | ||||
\(67\) | 31.4072 | − | 8.41554i | 0.468765 | − | 0.125605i | −0.0167016 | − | 0.999861i | \(-0.505317\pi\) |
0.485466 | + | 0.874255i | \(0.338650\pi\) | |||||||
\(68\) | −15.7663 | − | 58.8405i | −0.231857 | − | 0.865301i | ||||
\(69\) | −29.9066 | + | 15.1120i | −0.433429 | + | 0.219015i | ||||
\(70\) | 50.9602 | − | 13.9216i | 0.728003 | − | 0.198879i | ||||
\(71\) | −63.3498 | −0.892251 | −0.446126 | − | 0.894970i | \(-0.647197\pi\) | ||||
−0.446126 | + | 0.894970i | \(0.647197\pi\) | |||||||
\(72\) | −21.6561 | + | 55.3043i | −0.300779 | + | 0.768115i | ||||
\(73\) | −50.9063 | + | 50.9063i | −0.697347 | + | 0.697347i | −0.963838 | − | 0.266491i | \(-0.914136\pi\) |
0.266491 | + | 0.963838i | \(0.414136\pi\) | |||||||
\(74\) | 16.3201 | − | 9.42239i | 0.220541 | − | 0.127330i | ||||
\(75\) | 73.2597 | − | 16.0628i | 0.976796 | − | 0.214171i | ||||
\(76\) | −18.0141 | + | 31.2013i | −0.237028 | + | 0.410544i | ||||
\(77\) | −28.8458 | + | 7.72922i | −0.374621 | + | 0.100379i | ||||
\(78\) | −1.67498 | − | 8.01221i | −0.0214741 | − | 0.102721i | ||||
\(79\) | 59.5972 | − | 34.4084i | 0.754395 | − | 0.435550i | −0.0728850 | − | 0.997340i | \(-0.523221\pi\) |
0.827280 | + | 0.561790i | \(0.189887\pi\) | |||||||
\(80\) | −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 | ||||
\(83\) | 101.841 | + | 27.2882i | 1.22700 | + | 0.328773i | 0.813410 | − | 0.581691i | \(-0.197609\pi\) |
0.413589 | + | 0.910464i | \(0.364275\pi\) | |||||||
\(84\) | 90.4247 | + | 59.1546i | 1.07648 | + | 0.704222i | ||||
\(85\) | 96.7668 | − | 0.472089i | 1.13843 | − | 0.00555398i | ||||
\(86\) | −23.4540 | + | 40.6236i | −0.272721 | + | 0.472367i | ||||
\(87\) | 53.1740 | + | 59.4556i | 0.611196 | + | 0.683398i | ||||
\(88\) | −16.6351 | − | 4.45735i | −0.189035 | − | 0.0506517i | ||||
\(89\) | − | 136.887i | − | 1.53806i | −0.639213 | − | 0.769029i | \(-0.720740\pi\) | ||
0.639213 | − | 0.769029i | \(-0.279260\pi\) | |||||||
\(90\) | −33.5683 | − | 24.4828i | −0.372981 | − | 0.272031i | ||||
\(91\) | −33.8170 | −0.371615 | ||||||||
\(92\) | −9.09897 | + | 33.9578i | −0.0989019 | + | 0.369107i | ||||
\(93\) | −124.710 | − | 40.9838i | −1.34097 | − | 0.440686i | ||||
\(94\) | 50.7615 | + | 29.3072i | 0.540016 | + | 0.311778i | ||||
\(95\) | −40.6663 | − | 40.2715i | −0.428067 | − | 0.423910i | ||||
\(96\) | 43.8313 | + | 86.7419i | 0.456576 | + | 0.903561i | ||||
\(97\) | −9.45952 | + | 35.3034i | −0.0975209 | + | 0.363953i | −0.997390 | − | 0.0722080i | \(-0.976995\pi\) |
0.899869 | + | 0.436161i | \(0.143662\pi\) | |||||||
\(98\) | −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 | \(0.992101\pi\) | |||||||
\(102\) | −35.7362 | − | 39.9577i | −0.350355 | − | 0.391743i | ||||
\(103\) | −6.87754 | − | 25.6673i | −0.0667723 | − | 0.249198i | 0.924470 | − | 0.381255i | \(-0.124508\pi\) |
−0.991242 | + | 0.132058i | \(0.957842\pi\) | |||||||
\(104\) | −16.8891 | − | 9.75093i | −0.162395 | − | 0.0937589i | ||||
\(105\) | −127.386 | + | 115.051i | −1.21320 | + | 1.09572i | ||||
\(106\) | −4.20106 | − | 7.27645i | −0.0396326 | − | 0.0686457i | ||||
\(107\) | −43.8389 | − | 43.8389i | −0.409709 | − | 0.409709i | 0.471928 | − | 0.881637i | \(-0.343558\pi\) |
−0.881637 | + | 0.471928i | \(0.843558\pi\) | |||||||
\(108\) | −8.03231 | − | 84.6031i | −0.0743732 | − | 0.783362i | ||||
\(109\) | 13.1212i | 0.120378i | 0.998187 | + | 0.0601892i | \(0.0191704\pi\) | ||||
−0.998187 | + | 0.0601892i | \(0.980830\pi\) | |||||||
\(110\) | 5.97274 | − | 10.4626i | 0.0542977 | − | 0.0951149i | ||||
\(111\) | −33.5211 | + | 51.2409i | −0.301992 | + | 0.461630i | ||||
\(112\) | 71.8156 | − | 19.2429i | 0.641211 | − | 0.171812i | ||||
\(113\) | −8.41629 | − | 31.4100i | −0.0744805 | − | 0.277965i | 0.918635 | − | 0.395108i | \(-0.129293\pi\) |
−0.993115 | + | 0.117143i | \(0.962626\pi\) | |||||||
\(114\) | −1.76551 | + | 31.6560i | −0.0154869 | + | 0.277684i | ||||
\(115\) | −48.5001 | − | 27.6869i | −0.421740 | − | 0.240756i | ||||
\(116\) | 83.6877 | 0.721446 | ||||||||
\(117\) | 16.5987 | + | 20.7812i | 0.141869 | + | 0.177617i | ||||
\(118\) | 37.3290 | − | 37.3290i | 0.316347 | − | 0.316347i | ||||
\(119\) | −191.798 | + | 110.735i | −1.61175 | + | 0.930545i | ||||
\(120\) | −96.7940 | + | 20.7285i | −0.806617 | + | 0.172737i | ||||
\(121\) | 57.0948 | − | 98.8911i | 0.471858 | − | 0.817282i | ||||
\(122\) | 30.0356 | − | 8.04801i | 0.246193 | − | 0.0659673i | ||||
\(123\) | −5.27033 | − | 1.73200i | −0.0428482 | − | 0.0140813i | ||||
\(124\) | −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 | 0.138245 | − | 0.990398i | \(-0.455854\pi\) |
−0.990398 | + | 0.138245i | \(0.955854\pi\) | |||||||
\(128\) | 121.670 | + | 32.6013i | 0.950544 | + | 0.254697i | ||||
\(129\) | 8.48732 | − | 152.180i | 0.0657932 | − | 1.17969i | ||||
\(130\) | 9.59943 | − | 9.69355i | 0.0738418 | − | 0.0745658i | ||||
\(131\) | −3.28859 | + | 5.69601i | −0.0251038 | + | 0.0434810i | −0.878304 | − | 0.478102i | \(-0.841325\pi\) |
0.853201 | + | 0.521583i | \(0.174658\pi\) | |||||||
\(132\) | 24.1207 | − | 5.04252i | 0.182733 | − | 0.0382009i | ||||
\(133\) | 126.523 | + | 33.9016i | 0.951298 | + | 0.254900i | ||||
\(134\) | − | 30.0209i | − | 0.224036i | ||||||
\(135\) | 133.227 | + | 21.8096i | 0.986864 | + | 0.161552i | ||||
\(136\) | −127.719 | −0.939110 | ||||||||
\(137\) | 22.5393 | − | 84.1178i | 0.164520 | − | 0.613998i | −0.833581 | − | 0.552398i | \(-0.813713\pi\) |
0.998101 | − | 0.0616003i | \(-0.0196204\pi\) | |||||||
\(138\) | 6.33072 | + | 30.2828i | 0.0458748 | + | 0.219440i | ||||
\(139\) | −75.7500 | − | 43.7343i | −0.544964 | − | 0.314635i | 0.202124 | − | 0.979360i | \(-0.435215\pi\) |
−0.747088 | + | 0.664725i | \(0.768549\pi\) | |||||||
\(140\) | 0.878589 | + | 180.090i | 0.00627564 | + | 1.28635i | ||||
\(141\) | −190.157 | − | 10.6054i | −1.34863 | − | 0.0752156i | ||||
\(142\) | −15.1384 | + | 56.4972i | −0.106608 | + | 0.397868i | ||||
\(143\) | −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 | ||||
\(147\) | 76.7557 | − | 233.561i | 0.522148 | − | 1.58885i | ||||
\(148\) | 16.6273 | + | 62.0538i | 0.112346 | + | 0.419282i | ||||
\(149\) | 144.963 | + | 83.6946i | 0.972909 | + | 0.561709i | 0.900122 | − | 0.435638i | \(-0.143477\pi\) |
0.0727869 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(150\) | 3.18124 | − | 69.1736i | 0.0212082 | − | 0.461157i | ||||
\(151\) | 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 | ||||
\(153\) | 162.191 | + | 63.5108i | 1.06007 | + | 0.415103i | ||||
\(154\) | 27.5726i | 0.179043i | ||||||||
\(155\) | −57.6565 | − | 211.053i | −0.371977 | − | 1.36163i | ||||
\(156\) | 27.8612 | + | 1.55387i | 0.178597 | + | 0.00996068i | ||||
\(157\) | −48.3954 | + | 12.9675i | −0.308251 | + | 0.0825957i | −0.409629 | − | 0.912252i | \(-0.634342\pi\) |
0.101377 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(158\) | −16.4448 | − | 61.3729i | −0.104081 | − | 0.388436i | ||||
\(159\) | 22.8462 | + | 14.9457i | 0.143687 | + | 0.0939980i | ||||
\(160\) | −80.3040 | + | 140.671i | −0.501900 | + | 0.879194i | ||||
\(161\) | 127.814 | 0.793875 | ||||||||
\(162\) | −39.8865 | − | 63.2620i | −0.246213 | − | 0.390506i | ||||
\(163\) | −23.5188 | + | 23.5188i | −0.144287 | + | 0.144287i | −0.775560 | − | 0.631273i | \(-0.782533\pi\) |
0.631273 | + | 0.775560i | \(0.282533\pi\) | |||||||
\(164\) | −5.04066 | + | 2.91023i | −0.0307358 | + | 0.0177453i | ||||
\(165\) | −1.98910 | + | 39.0946i | −0.0120552 | + | 0.236937i | ||||
\(166\) | 48.6728 | − | 84.3037i | 0.293210 | − | 0.507854i | ||||
\(167\) | 106.889 | − | 28.6408i | 0.640052 | − | 0.171502i | 0.0758252 | − | 0.997121i | \(-0.475841\pi\) |
0.564227 | + | 0.825620i | \(0.309174\pi\) | |||||||
\(168\) | 168.869 | − | 151.027i | 1.00517 | − | 0.898973i | ||||
\(169\) | 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 | ||||
\(173\) | −65.8811 | − | 17.6528i | −0.380816 | − | 0.102039i | 0.0633327 | − | 0.997992i | \(-0.479827\pi\) |
−0.444149 | + | 0.895953i | \(0.646494\pi\) | |||||||
\(174\) | 65.7309 | − | 33.2143i | 0.377764 | − | 0.190887i | ||||
\(175\) | −277.045 | − | 71.3441i | −1.58311 | − | 0.407681i | ||||
\(176\) | 8.47772 | − | 14.6838i | 0.0481688 | − | 0.0834309i | ||||
\(177\) | −53.5531 | + | 162.958i | −0.302560 | + | 0.920665i | ||||
\(178\) | −122.080 | − | 32.7112i | −0.685843 | − | 0.183771i | ||||
\(179\) | 303.920i | 1.69788i | 0.528490 | + | 0.848939i | \(0.322758\pi\) | ||||
−0.528490 | + | 0.848939i | \(0.677242\pi\) | |||||||
\(180\) | 110.237 | − | 88.9349i | 0.612429 | − | 0.494083i | ||||
\(181\) | 172.576 | 0.953460 | 0.476730 | − | 0.879050i | \(-0.341822\pi\) | ||||
0.476730 | + | 0.879050i | \(0.341822\pi\) | |||||||
\(182\) | −8.08107 | + | 30.1589i | −0.0444015 | + | 0.165708i | ||||
\(183\) | −75.3107 | + | 67.3540i | −0.411534 | + | 0.368055i | ||||
\(184\) | 63.8337 | + | 36.8544i | 0.346922 | + | 0.200296i | ||||
\(185\) | −102.051 | + | 0.497870i | −0.551628 | + | 0.00269119i | ||||
\(186\) | −66.3519 | + | 101.427i | −0.356731 | + | 0.545304i | ||||
\(187\) | −13.0721 | + | 48.7856i | −0.0699041 | + | 0.260886i | ||||
\(188\) | −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 | \(0.562458\pi\) | |||||||
\(192\) | 11.5172 | − | 2.40770i | 0.0599852 | − | 0.0125401i | ||||
\(193\) | 9.52264 | + | 35.5390i | 0.0493401 | + | 0.184140i | 0.986198 | − | 0.165571i | \(-0.0529466\pi\) |
−0.936858 | + | 0.349711i | \(0.886280\pi\) | |||||||
\(194\) | 29.2241 | + | 16.8725i | 0.150640 | + | 0.0869719i | ||||
\(195\) | −13.6337 | + | 42.1788i | −0.0699162 | + | 0.216301i | ||||
\(196\) | −128.970 | − | 223.383i | −0.658013 | − | 1.13971i | ||||
\(197\) | −226.659 | − | 226.659i | −1.15056 | − | 1.15056i | −0.986441 | − | 0.164114i | \(-0.947524\pi\) |
−0.164114 | − | 0.986441i | \(-0.552476\pi\) | |||||||
\(198\) | 16.9439 | − | 13.5337i | 0.0855751 | − | 0.0683520i | ||||
\(199\) | − | 107.508i | − | 0.540240i | −0.962827 | − | 0.270120i | \(-0.912937\pi\) | ||
0.962827 | − | 0.270120i | \(-0.0870633\pi\) | |||||||
\(200\) | −117.792 | − | 115.515i | −0.588960 | − | 0.577577i | ||||
\(201\) | 43.9930 | + | 87.0617i | 0.218870 | + | 0.433143i | ||||
\(202\) | −86.1760 | + | 23.0908i | −0.426614 | + | 0.114311i | ||||
\(203\) | −78.7481 | − | 293.892i | −0.387922 | − | 1.44774i | ||||
\(204\) | 163.107 | − | 82.4194i | 0.799546 | − | 0.404017i | ||||
\(205\) | −2.43660 | − | 8.91922i | −0.0118858 | − | 0.0435084i | ||||
\(206\) | −24.5344 | −0.119099 | ||||||||
\(207\) | −62.7360 | − | 78.5441i | −0.303073 | − | 0.379440i | ||||
\(208\) | 13.5765 | − | 13.5765i | 0.0652718 | − | 0.0652718i | ||||
\(209\) | 25.8695 | − | 14.9358i | 0.123778 | − | 0.0714631i | ||||
\(210\) | 72.1648 | + | 141.099i | 0.343642 | + | 0.671901i | ||||
\(211\) | 45.5871 | − | 78.9591i | 0.216053 | − | 0.374214i | −0.737545 | − | 0.675298i | \(-0.764015\pi\) |
0.953598 | + | 0.301084i | \(0.0973484\pi\) | |||||||
\(212\) | 27.6672 | − | 7.41341i | 0.130506 | − | 0.0349689i | ||||
\(213\) | −38.8898 | − | 186.028i | −0.182581 | − | 0.873371i | ||||
\(214\) | −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 | ||||
\(218\) | 11.7019 | + | 3.13551i | 0.0536784 | + | 0.0143831i | ||||
\(219\) | −180.738 | − | 118.237i | −0.825289 | − | 0.539893i | ||||
\(220\) | 29.1824 | + | 28.8990i | 0.132647 | + | 0.131359i | ||||
\(221\) | −28.5965 | + | 49.5306i | −0.129396 | + | 0.224120i | ||||
\(222\) | 37.6877 | + | 42.1399i | 0.169765 | + | 0.189819i | ||||
\(223\) | 229.262 | + | 61.4305i | 1.02808 | + | 0.275473i | 0.733165 | − | 0.680051i | \(-0.238042\pi\) |
0.294914 | + | 0.955524i | \(0.404709\pi\) | |||||||
\(224\) | − | 370.715i | − | 1.65498i | ||||||
\(225\) | 92.1420 | + | 205.268i | 0.409520 | + | 0.912301i | ||||
\(226\) | −30.0236 | −0.132848 | ||||||||
\(227\) | −31.7905 | + | 118.644i | −0.140046 | + | 0.522660i | 0.859880 | + | 0.510497i | \(0.170538\pi\) |
−0.999926 | + | 0.0121631i | \(0.996128\pi\) | |||||||
\(228\) | −102.682 | − | 33.7446i | −0.450359 | − | 0.148003i | ||||
\(229\) | 285.203 | + | 164.662i | 1.24543 | + | 0.719048i | 0.970194 | − | 0.242329i | \(-0.0779114\pi\) |
0.275234 | + | 0.961377i | \(0.411245\pi\) | |||||||
\(230\) | −36.2818 | + | 36.6376i | −0.157747 | + | 0.159294i | ||||
\(231\) | −40.4051 | − | 79.9615i | −0.174914 | − | 0.346154i | ||||
\(232\) | 45.4131 | − | 169.484i | 0.195746 | − | 0.730534i | ||||
\(233\) | −227.098 | + | 227.098i | −0.974670 | + | 0.974670i | −0.999687 | − | 0.0250170i | \(-0.992036\pi\) |
0.0250170 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(234\) | 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 | ||||
\(237\) | 137.627 | + | 153.885i | 0.580705 | + | 0.649305i | ||||
\(238\) | 52.9235 | + | 197.513i | 0.222367 | + | 0.829887i | ||||
\(239\) | −123.443 | − | 71.2696i | −0.516496 | − | 0.298199i | 0.219004 | − | 0.975724i | \(-0.429719\pi\) |
−0.735500 | + | 0.677525i | \(0.763053\pi\) | |||||||
\(240\) | 4.95214 | − | 97.3312i | 0.0206339 | − | 0.405547i | ||||
\(241\) | −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 | ||||
\(243\) | 208.377 | + | 125.012i | 0.857519 | + | 0.514453i | ||||
\(244\) | 106.005i | 0.434446i | ||||||||
\(245\) | 395.266 | − | 107.981i | 1.61333 | − | 0.440738i | ||||
\(246\) | −2.80407 | + | 4.28634i | −0.0113987 | + | 0.0174242i | ||||
\(247\) | 32.6736 | − | 8.75487i | 0.132282 | − | 0.0354448i | ||||
\(248\) | 74.7380 | + | 278.926i | 0.301363 | + | 1.12470i | ||||
\(249\) | −17.6132 | + | 315.810i | −0.0707359 | + | 1.26831i | ||||
\(250\) | 99.0937 | − | 59.1622i | 0.396375 | − | 0.236649i | ||||
\(251\) | 102.580 | 0.408684 | 0.204342 | − | 0.978900i | \(-0.434494\pi\) | ||||
0.204342 | + | 0.978900i | \(0.434494\pi\) | |||||||
\(252\) | −118.198 | + | 301.848i | −0.469039 | + | 1.19781i | ||||
\(253\) | 20.6109 | − | 20.6109i | 0.0814660 | − | 0.0814660i | ||||
\(254\) | −122.378 | + | 70.6552i | −0.481805 | + | 0.278170i | ||||
\(255\) | 60.7904 | + | 283.868i | 0.238394 | + | 1.11321i | ||||
\(256\) | 65.9936 | − | 114.304i | 0.257788 | − | 0.446501i | ||||
\(257\) | −108.426 | + | 29.0526i | −0.421890 | + | 0.113045i | −0.463517 | − | 0.886088i | \(-0.653413\pi\) |
0.0416268 | + | 0.999133i | \(0.486746\pi\) | |||||||
\(258\) | −133.690 | − | 43.9348i | −0.518178 | − | 0.170290i | ||||
\(259\) | 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 | ||||
\(263\) | −143.911 | − | 38.5609i | −0.547191 | − | 0.146619i | −0.0253757 | − | 0.999678i | \(-0.508078\pi\) |
−0.521815 | + | 0.853059i | \(0.674745\pi\) | |||||||
\(264\) | 2.87701 | − | 51.5855i | 0.0108978 | − | 0.195400i | ||||
\(265\) | 0.221980 | + | 45.5005i | 0.000837659 | + | 0.171700i | ||||
\(266\) | 60.4689 | − | 104.735i | 0.227327 | − | 0.393742i | ||||
\(267\) | 401.972 | − | 84.0336i | 1.50551 | − | 0.314733i | ||||
\(268\) | 98.8554 | + | 26.4882i | 0.368864 | + | 0.0988367i | ||||
\(269\) | 31.0843i | 0.115555i | 0.998329 | + | 0.0577774i | \(0.0184014\pi\) | ||||
−0.998329 | + | 0.0577774i | \(0.981599\pi\) | |||||||
\(270\) | 51.2869 | − | 113.604i | 0.189951 | − | 0.420754i | ||||
\(271\) | 4.22458 | 0.0155889 | 0.00779444 | − | 0.999970i | \(-0.497519\pi\) | ||||
0.00779444 | + | 0.999970i | \(0.497519\pi\) | |||||||
\(272\) | 32.5447 | − | 121.458i | 0.119650 | − | 0.446538i | ||||
\(273\) | −20.7599 | − | 99.3042i | −0.0760435 | − | 0.363751i | ||||
\(274\) | −69.6325 | − | 40.2024i | −0.254133 | − | 0.146724i | ||||
\(275\) | −56.1802 | + | 33.1707i | −0.204292 | + | 0.120621i | ||||
\(276\) | −105.304 | − | 5.87296i | −0.381535 | − | 0.0212788i | ||||
\(277\) | −35.9912 | + | 134.321i | −0.129932 | + | 0.484913i | −0.999967 | − | 0.00807616i | \(-0.997429\pi\) |
0.870035 | + | 0.492990i | \(0.164096\pi\) | |||||||
\(278\) | −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 | \(-0.520018\pi\) | |||||||
\(282\) | −54.8991 | + | 167.053i | −0.194678 | + | 0.592388i | ||||
\(283\) | −37.9311 | − | 141.561i | −0.134032 | − | 0.500214i | −1.00000 | 0.000114837i | \(-0.999963\pi\) | |
0.865968 | − | 0.500099i | \(-0.166703\pi\) | |||||||
\(284\) | −172.682 | − | 99.6980i | −0.608035 | − | 0.351049i | ||||
\(285\) | 93.2933 | − | 144.140i | 0.327345 | − | 0.505753i | ||||
\(286\) | 3.56021 | + | 6.16647i | 0.0124483 | + | 0.0215611i | ||||
\(287\) | 14.9632 | + | 14.9632i | 0.0521365 | + | 0.0521365i | ||||
\(288\) | −227.812 | + | 181.961i | −0.791012 | + | 0.631811i | ||||
\(289\) | 85.5611i | 0.296059i | ||||||||
\(290\) | 106.597 | + | 60.8524i | 0.367576 | + | 0.209836i | ||||
\(291\) | −109.476 | − | 6.10568i | −0.376207 | − | 0.0209817i | ||||
\(292\) | −218.878 | + | 58.6481i | −0.749581 | + | 0.200850i | ||||
\(293\) | −88.7756 | − | 331.315i | −0.302988 | − | 1.13077i | −0.934663 | − | 0.355535i | \(-0.884299\pi\) |
0.631675 | − | 0.775234i | \(-0.282368\pi\) | |||||||
\(294\) | −189.955 | − | 124.266i | −0.646105 | − | 0.422673i | ||||
\(295\) | −275.781 | + | 75.3391i | −0.934850 | + | 0.255387i | ||||
\(296\) | 134.694 | 0.455047 | ||||||||
\(297\) | −29.3054 | + | 64.0779i | −0.0986714 | + | 0.215751i | ||||
\(298\) | 109.282 | − | 109.282i | 0.366720 | − | 0.366720i | ||||
\(299\) | 28.5850 | − | 16.5035i | 0.0956019 | − | 0.0551958i | ||||
\(300\) | 224.974 | + | 71.5091i | 0.749913 | + | 0.238364i | ||||
\(301\) | −290.692 | + | 503.493i | −0.965753 | + | 1.67273i | ||||
\(302\) | 222.556 | − | 59.6337i | 0.736941 | − | 0.197463i | ||||
\(303\) | 216.076 | − | 193.247i | 0.713123 | − | 0.637780i | ||||
\(304\) | −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 | 0.675097 | − | 0.737729i | \(-0.264102\pi\) |
−0.737729 | + | 0.675097i | \(0.764102\pi\) | |||||||
\(308\) | −90.7934 | − | 24.3280i | −0.294784 | − | 0.0789870i | ||||
\(309\) | 71.1506 | − | 35.9529i | 0.230261 | − | 0.116353i | ||||
\(310\) | −202.001 | + | 0.985487i | −0.651616 | + | 0.00317899i | ||||
\(311\) | −275.689 | + | 477.507i | −0.886459 | + | 1.53539i | −0.0424271 | + | 0.999100i | \(0.513509\pi\) |
−0.844032 | + | 0.536293i | \(0.819824\pi\) | |||||||
\(312\) | 18.2657 | − | 55.5811i | 0.0585440 | − | 0.178145i | ||||
\(313\) | −463.260 | − | 124.130i | −1.48006 | − | 0.396582i | −0.573694 | − | 0.819070i | \(-0.694490\pi\) |
−0.906368 | + | 0.422488i | \(0.861157\pi\) | |||||||
\(314\) | 46.2592i | 0.147322i | ||||||||
\(315\) | −416.049 | − | 303.442i | −1.32079 | − | 0.963308i | ||||
\(316\) | 216.604 | 0.685455 | ||||||||
\(317\) | −72.3487 | + | 270.009i | −0.228229 | + | 0.851763i | 0.752856 | + | 0.658186i | \(0.228676\pi\) |
−0.981085 | + | 0.193578i | \(0.937991\pi\) | |||||||
\(318\) | 18.7884 | − | 16.8034i | 0.0590831 | − | 0.0528409i | ||||
\(319\) | −60.0908 | − | 34.6934i | −0.188372 | − | 0.108757i | ||||
\(320\) | 13.9340 | + | 13.7987i | 0.0435438 | + | 0.0431210i | ||||
\(321\) | 101.821 | − | 155.646i | 0.317201 | − | 0.484878i | ||||
\(322\) | 30.5430 | − | 113.988i | 0.0948541 | − | 0.354000i | ||||
\(323\) | 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 | ||||
\(327\) | −38.5307 | + | 8.05498i | −0.117831 | + | 0.0246330i | ||||
\(328\) | 3.15847 | + | 11.7876i | 0.00962948 | + | 0.0359377i | ||||
\(329\) | 629.143 | + | 363.236i | 1.91229 | + | 1.10406i | ||||
\(330\) | 34.3903 | + | 11.1162i | 0.104213 | + | 0.0336853i | ||||
\(331\) | −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 | ||||
\(333\) | −171.048 | − | 66.9791i | −0.513658 | − | 0.201139i | ||||
\(334\) | − | 102.171i | − | 0.305900i | ||||||
\(335\) | −80.6001 | + | 141.190i | −0.240597 | + | 0.421462i | ||||
\(336\) | 100.594 | + | 199.075i | 0.299387 | + | 0.592485i | ||||
\(337\) | −319.193 | + | 85.5276i | −0.947161 | + | 0.253791i | −0.699157 | − | 0.714968i | \(-0.746441\pi\) |
−0.248004 | + | 0.968759i | \(0.579775\pi\) | |||||||
\(338\) | −38.2982 | − | 142.931i | −0.113308 | − | 0.422872i | ||||
\(339\) | 87.0694 | − | 43.9969i | 0.256842 | − | 0.129784i | ||||
\(340\) | 264.514 | + | 151.002i | 0.777983 | + | 0.444122i | ||||
\(341\) | 114.192 | 0.334875 | ||||||||
\(342\) | −94.0423 | + | 14.2488i | −0.274977 | + | 0.0416632i | ||||
\(343\) | −266.621 | + | 266.621i | −0.777321 | + | 0.777321i | ||||
\(344\) | −290.358 | + | 167.638i | −0.844065 | + | 0.487321i | ||||
\(345\) | 51.5295 | − | 159.418i | 0.149361 | − | 0.462081i | ||||
\(346\) | −31.4865 | + | 54.5363i | −0.0910016 | + | 0.157619i | ||||
\(347\) | 343.816 | − | 92.1251i | 0.990823 | − | 0.265490i | 0.273227 | − | 0.961950i | \(-0.411909\pi\) |
0.717596 | + | 0.696459i | \(0.245242\pi\) | |||||||
\(348\) | 51.3750 | + | 245.750i | 0.147629 | + | 0.706180i | ||||
\(349\) | −43.1516 | + | 24.9136i | −0.123644 | + | 0.0713857i | −0.560546 | − | 0.828123i | \(-0.689409\pi\) |
0.436903 | + | 0.899509i | \(0.356075\pi\) | |||||||
\(350\) | −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 | ||||
\(353\) | 606.831 | + | 162.600i | 1.71907 | + | 0.460623i | 0.977619 | − | 0.210385i | \(-0.0674718\pi\) |
0.741450 | + | 0.671008i | \(0.234138\pi\) | |||||||
\(354\) | 132.533 | + | 86.7014i | 0.374387 | + | 0.244919i | ||||
\(355\) | 222.880 | − | 225.065i | 0.627831 | − | 0.633987i | ||||
\(356\) | 215.429 | − | 373.134i | 0.605137 | − | 1.04813i | ||||
\(357\) | −442.918 | − | 495.240i | −1.24067 | − | 1.38723i | ||||
\(358\) | 271.045 | + | 72.6263i | 0.757109 | + | 0.202867i | ||||
\(359\) | 81.3046i | 0.226475i | 0.993568 | + | 0.113238i | \(0.0361221\pi\) | ||||
−0.993568 | + | 0.113238i | \(0.963878\pi\) | |||||||
\(360\) | −120.290 | − | 271.512i | −0.334140 | − | 0.754201i | ||||
\(361\) | 229.978 | 0.637059 | ||||||||
\(362\) | 41.2397 | − | 153.908i | 0.113922 | − | 0.425162i | ||||
\(363\) | 325.445 | + | 106.952i | 0.896544 | + | 0.294633i | ||||
\(364\) | −92.1799 | − | 53.2201i | −0.253241 | − | 0.146209i | ||||
\(365\) | −1.75610 | − | 359.958i | −0.00481123 | − | 0.986186i | ||||
\(366\) | 42.0717 | + | 83.2595i | 0.114950 | + | 0.227485i | ||||
\(367\) | 15.5484 | − | 58.0273i | 0.0423661 | − | 0.158113i | −0.941502 | − | 0.337007i | \(-0.890585\pi\) |
0.983868 | + | 0.178894i | \(0.0572521\pi\) | |||||||
\(368\) | −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 | ||||
\(372\) | −275.442 | − | 307.981i | −0.740436 | − | 0.827906i | ||||
\(373\) | −50.4882 | − | 188.424i | −0.135357 | − | 0.505159i | −0.999996 | − | 0.00276585i | \(-0.999120\pi\) |
0.864639 | − | 0.502393i | \(-0.167547\pi\) | |||||||
\(374\) | 40.3846 | + | 23.3161i | 0.107980 | + | 0.0623425i | ||||
\(375\) | −200.679 | + | 316.786i | −0.535143 | + | 0.844761i | ||||
\(376\) | 209.474 | + | 362.820i | 0.557112 | + | 0.964946i | ||||
\(377\) | −55.5594 | − | 55.5594i | −0.147372 | − | 0.147372i | ||||
\(378\) | 26.9625 | + | 283.992i | 0.0713294 | + | 0.751301i | ||||
\(379\) | − | 145.837i | − | 0.384795i | −0.981317 | − | 0.192398i | \(-0.938374\pi\) | ||
0.981317 | − | 0.192398i | \(-0.0616263\pi\) | |||||||
\(380\) | −47.4722 | − | 173.773i | −0.124927 | − | 0.457298i | ||||
\(381\) | 251.363 | − | 384.237i | 0.659745 | − | 1.00850i | ||||
\(382\) | 256.166 | − | 68.6394i | 0.670591 | − | 0.179684i | ||||
\(383\) | 195.458 | + | 729.460i | 0.510335 | + | 1.90459i | 0.416854 | + | 0.908973i | \(0.363133\pi\) |
0.0934803 | + | 0.995621i | \(0.470201\pi\) | |||||||
\(384\) | −21.0426 | + | 377.299i | −0.0547984 | + | 0.982549i | ||||
\(385\) | 74.0268 | − | 129.675i | 0.192277 | − | 0.336818i | ||||
\(386\) | 33.9703 | 0.0880059 | ||||||||
\(387\) | 452.088 | − | 68.4982i | 1.16819 | − | 0.176998i | ||||
\(388\) | −81.3446 | + | 81.3446i | −0.209651 | + | 0.209651i | ||||
\(389\) | −37.3613 | + | 21.5705i | −0.0960444 | + | 0.0554512i | −0.547253 | − | 0.836967i | \(-0.684326\pi\) |
0.451209 | + | 0.892419i | \(0.350993\pi\) | |||||||
\(390\) | 34.3583 | + | 22.2381i | 0.0880982 | + | 0.0570209i | ||||
\(391\) | 108.083 | − | 187.205i | 0.276427 | − | 0.478785i | ||||
\(392\) | −522.381 | + | 139.972i | −1.33260 | + | 0.357070i | ||||
\(393\) | −18.7453 | − | 6.16029i | −0.0476979 | − | 0.0156750i | ||||
\(394\) | −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 | 0.584912 | − | 0.811097i | \(-0.301129\pi\) |
−0.811097 | + | 0.584912i | \(0.801129\pi\) | |||||||
\(398\) | −95.8785 | − | 25.6906i | −0.240901 | − | 0.0645491i | ||||
\(399\) | −21.8819 | + | 392.348i | −0.0548419 | + | 0.983328i | ||||
\(400\) | 139.868 | − | 82.5829i | 0.349670 | − | 0.206457i | ||||
\(401\) | −144.777 | + | 250.762i | −0.361041 | + | 0.625341i | −0.988132 | − | 0.153604i | \(-0.950912\pi\) |
0.627092 | + | 0.778946i | \(0.284245\pi\) | |||||||
\(402\) | 88.1569 | − | 18.4295i | 0.219296 | − | 0.0458445i | ||||
\(403\) | 124.904 | + | 33.4679i | 0.309936 | + | 0.0830470i | ||||
\(404\) | − | 304.142i | − | 0.752826i | ||||||
\(405\) | 17.7422 | + | 404.611i | 0.0438080 | + | 0.999040i | ||||
\(406\) | −280.919 | −0.691919 | ||||||||
\(407\) | 13.7859 | − | 51.4498i | 0.0338721 | − | 0.126412i | ||||
\(408\) | −78.4053 | − | 375.049i | −0.192170 | − | 0.919238i | ||||
\(409\) | −178.588 | − | 103.108i | −0.436646 | − | 0.252098i | 0.265528 | − | 0.964103i | \(-0.414454\pi\) |
−0.702174 | + | 0.712006i | \(0.747787\pi\) | |||||||
\(410\) | −8.53667 | + | 0.0416472i | −0.0208212 | + | 0.000101579i | ||||
\(411\) | 260.850 | + | 14.5480i | 0.634671 | + | 0.0353967i | ||||
\(412\) | 21.6473 | − | 80.7889i | 0.0525421 | − | 0.196090i | ||||
\(413\) | 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 | ||||
\(417\) | 81.9244 | − | 249.289i | 0.196461 | − | 0.597816i | ||||
\(418\) | −7.13826 | − | 26.6403i | −0.0170772 | − | 0.0637329i | ||||
\(419\) | −621.108 | − | 358.597i | −1.48236 | − | 0.855839i | −0.482558 | − | 0.875864i | \(-0.660292\pi\) |
−0.999799 | + | 0.0200248i | \(0.993625\pi\) | |||||||
\(420\) | −528.297 | + | 113.135i | −1.25785 | + | 0.269369i | ||||
\(421\) | 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 | ||||
\(423\) | −85.5925 | − | 564.911i | −0.202346 | − | 1.33549i | ||||
\(424\) | − | 60.0544i | − | 0.141638i | ||||||
\(425\) | −338.772 | + | 345.448i | −0.797110 | + | 0.812819i | ||||
\(426\) | −175.198 | − | 9.77111i | −0.411264 | − | 0.0229369i | ||||
\(427\) | 372.264 | − | 99.7479i | 0.871814 | − | 0.233602i | ||||
\(428\) | −50.5058 | − | 188.490i | −0.118004 | − | 0.440398i | ||||
\(429\) | −19.3612 | − | 12.6658i | −0.0451309 | − | 0.0295241i | ||||
\(430\) | −61.8080 | − | 226.250i | −0.143739 | − | 0.526162i | ||||
\(431\) | −234.096 | −0.543146 | −0.271573 | − | 0.962418i | \(-0.587544\pi\) | ||||
−0.271573 | + | 0.962418i | \(0.587544\pi\) | |||||||
\(432\) | 72.9598 | − | 159.531i | 0.168888 | − | 0.369284i | ||||
\(433\) | 372.915 | − | 372.915i | 0.861236 | − | 0.861236i | −0.130245 | − | 0.991482i | \(-0.541577\pi\) |
0.991482 | + | 0.130245i | \(0.0415765\pi\) | |||||||
\(434\) | 400.380 | − | 231.159i | 0.922534 | − | 0.532625i | ||||
\(435\) | −398.309 | − | 20.2657i | −0.915654 | − | 0.0465878i | ||||
\(436\) | −20.6498 | + | 35.7665i | −0.0473619 | + | 0.0820332i | ||||
\(437\) | −123.493 | + | 33.0897i | −0.282592 | + | 0.0757202i | ||||
\(438\) | −148.637 | + | 132.933i | −0.339353 | + | 0.303500i | ||||
\(439\) | −558.854 | + | 322.654i | −1.27302 | + | 0.734976i | −0.975554 | − | 0.219758i | \(-0.929473\pi\) |
−0.297461 | + | 0.954734i | \(0.596140\pi\) | |||||||
\(440\) | 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 | ||||
\(443\) | −265.585 | − | 71.1633i | −0.599515 | − | 0.160640i | −0.0537167 | − | 0.998556i | \(-0.517107\pi\) |
−0.545798 | + | 0.837917i | \(0.683773\pi\) | |||||||
\(444\) | −172.015 | + | 86.9204i | −0.387421 | + | 0.195767i | ||||
\(445\) | 486.325 | + | 481.603i | 1.09286 | + | 1.08225i | ||||
\(446\) | 109.571 | − | 189.782i | 0.245675 | − | 0.425521i | ||||
\(447\) | −156.779 | + | 477.067i | −0.350737 | + | 1.06726i | ||||
\(448\) | −43.3520 | − | 11.6161i | −0.0967679 | − | 0.0259289i | ||||
\(449\) | 190.668i | 0.424651i | 0.977199 | + | 0.212325i | \(0.0681036\pi\) | ||||
−0.977199 | + | 0.212325i | \(0.931896\pi\) | |||||||
\(450\) | 205.082 | − | 33.1231i | 0.455739 | − | 0.0736070i | ||||
\(451\) | 4.82584 | 0.0107003 | ||||||||
\(452\) | 26.4906 | − | 98.8642i | 0.0586075 | − | 0.218726i | ||||
\(453\) | −558.033 | + | 499.076i | −1.23186 | + | 1.10171i | ||||
\(454\) | 98.2131 | + | 56.7034i | 0.216328 | + | 0.124897i | ||||
\(455\) | 118.976 | − | 120.143i | 0.261486 | − | 0.264050i | ||||
\(456\) | −124.060 | + | 189.640i | −0.272061 | + | 0.415876i | ||||
\(457\) | 80.9404 | − | 302.074i | 0.177112 | − | 0.660993i | −0.819070 | − | 0.573694i | \(-0.805510\pi\) |
0.996182 | − | 0.0872988i | \(-0.0278235\pi\) | |||||||
\(458\) | 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 | \(0.910283\pi\) | |||||||
\(462\) | −80.9673 | + | 16.9265i | −0.175254 | + | 0.0366374i | ||||
\(463\) | 74.7605 | + | 279.010i | 0.161470 | + | 0.602613i | 0.998464 | + | 0.0554018i | \(0.0176440\pi\) |
−0.836994 | + | 0.547211i | \(0.815689\pi\) | |||||||
\(464\) | 149.604 | + | 86.3740i | 0.322423 | + | 0.186151i | ||||
\(465\) | 584.366 | − | 298.872i | 1.25670 | − | 0.642736i | ||||
\(466\) | 148.264 | + | 256.801i | 0.318163 | + | 0.551075i | ||||
\(467\) | −249.664 | − | 249.664i | −0.534613 | − | 0.534613i | 0.387329 | − | 0.921942i | \(-0.373398\pi\) |
−0.921942 | + | 0.387329i | \(0.873398\pi\) | |||||||
\(468\) | 12.5407 | + | 82.7688i | 0.0267964 | + | 0.176856i | ||||
\(469\) | − | 372.082i | − | 0.793352i | ||||||
\(470\) | −282.712 | + | 77.2327i | −0.601515 | + | 0.164325i | ||||
\(471\) | −67.7888 | − | 134.153i | −0.143925 | − | 0.284827i | ||||
\(472\) | 364.470 | − | 97.6593i | 0.772181 | − | 0.206905i | ||||
\(473\) | 34.3157 | + | 128.068i | 0.0725490 | + | 0.270756i | ||||
\(474\) | 170.127 | − | 85.9666i | 0.358918 | − | 0.181364i | ||||
\(475\) | 286.148 | − | 2.79208i | 0.602417 | − | 0.00587807i | ||||
\(476\) | −697.084 | −1.46446 | ||||||||
\(477\) | −29.8632 | + | 76.2633i | −0.0626064 | + | 0.159881i | ||||
\(478\) | −93.0588 | + | 93.0588i | −0.194684 | + | 0.194684i | ||||
\(479\) | 757.971 | − | 437.615i | 1.58240 | − | 0.913600i | 0.587895 | − | 0.808938i | \(-0.299957\pi\) |
0.994508 | − | 0.104663i | \(-0.0333763\pi\) | |||||||
\(480\) | −462.381 | − | 149.458i | −0.963293 | − | 0.311370i | ||||
\(481\) | 30.1582 | − | 52.2355i | 0.0626989 | − | 0.108598i | ||||
\(482\) | −408.221 | + | 109.382i | −0.846931 | + | 0.226934i | ||||
\(483\) | 78.4636 | + | 375.328i | 0.162450 | + | 0.777077i | ||||
\(484\) | 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 | 0.414263 | − | 0.910157i | \(-0.364039\pi\) |
−0.910157 | + | 0.414263i | \(0.864039\pi\) | |||||||
\(488\) | 214.681 | + | 57.5235i | 0.439919 | + | 0.117876i | ||||
\(489\) | −83.5012 | − | 54.6253i | −0.170759 | − | 0.111708i | ||||
\(490\) | −1.84565 | − | 378.314i | −0.00376663 | − | 0.772069i | ||||
\(491\) | −14.2377 | + | 24.6604i | −0.0289973 | + | 0.0502248i | −0.880160 | − | 0.474677i | \(-0.842565\pi\) |
0.851163 | + | 0.524902i | \(0.175898\pi\) | |||||||
\(492\) | −11.6403 | − | 13.0154i | −0.0236592 | − | 0.0264542i | ||||
\(493\) | −497.045 | − | 133.183i | −1.00821 | − | 0.270148i | ||||
\(494\) | − | 31.2314i | − | 0.0632214i | ||||||
\(495\) | −116.023 | + | 18.1587i | −0.234390 | + | 0.0366842i | ||||
\(496\) | −284.298 | −0.573181 | ||||||||
\(497\) | −187.627 | + | 700.232i | −0.377518 | + | 1.40892i | ||||
\(498\) | 277.439 | + | 91.1754i | 0.557107 | + | 0.183083i | ||||
\(499\) | 409.907 | + | 236.660i | 0.821457 | + | 0.474269i | 0.850919 | − | 0.525297i | \(-0.176046\pi\) |
−0.0294615 | + | 0.999566i | \(0.509379\pi\) | |||||||
\(500\) | 107.381 | + | 378.505i | 0.214763 | + | 0.757010i | ||||
\(501\) | 149.722 | + | 296.298i | 0.298846 | + | 0.591414i | ||||
\(502\) | 24.5130 | − | 91.4836i | 0.0488306 | − | 0.182238i | ||||
\(503\) | 58.9981 | − | 58.9981i | 0.117292 | − | 0.117292i | −0.646024 | − | 0.763317i | \(-0.723570\pi\) |
0.763317 | + | 0.646024i | \(0.223570\pi\) | |||||||
\(504\) | 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 | ||||
\(507\) | 320.518 | + | 358.382i | 0.632186 | + | 0.706868i | ||||
\(508\) | −124.682 | − | 465.319i | −0.245437 | − | 0.915983i | ||||
\(509\) | −388.655 | − | 224.390i | −0.763565 | − | 0.440844i | 0.0670093 | − | 0.997752i | \(-0.478654\pi\) |
−0.830574 | + | 0.556908i | \(0.811988\pi\) | |||||||
\(510\) | 267.688 | + | 13.6198i | 0.524878 | + | 0.0267054i | ||||
\(511\) | 411.917 | + | 713.461i | 0.806100 | + | 1.39621i | ||||
\(512\) | 270.104 | + | 270.104i | 0.527546 | + | 0.527546i | ||||
\(513\) | 251.846 | − | 179.133i | 0.490927 | − | 0.349187i | ||||
\(514\) | 103.640i | 0.201634i | ||||||||
\(515\) | 115.386 | + | 65.8698i | 0.224051 | + | 0.127903i | ||||
\(516\) | 262.631 | − | 401.461i | 0.508974 | − | 0.778026i | ||||
\(517\) | 160.028 | − | 42.8794i | 0.309532 | − | 0.0829389i | ||||
\(518\) | −55.8136 | − | 208.299i | −0.107748 | − | 0.402122i | ||||
\(519\) | 11.3941 | − | 204.298i | 0.0219539 | − | 0.393638i | ||||
\(520\) | 94.0625 | − | 25.6965i | 0.180889 | − | 0.0494163i | ||||
\(521\) | −548.131 | −1.05208 | −0.526038 | − | 0.850461i | \(-0.676323\pi\) | ||||
−0.526038 | + | 0.850461i | \(0.676323\pi\) | |||||||
\(522\) | 137.886 | + | 172.630i | 0.264150 | + | 0.330709i | ||||
\(523\) | −237.559 | + | 237.559i | −0.454224 | + | 0.454224i | −0.896754 | − | 0.442530i | \(-0.854081\pi\) |
0.442530 | + | 0.896754i | \(0.354081\pi\) | |||||||
\(524\) | −17.9284 | + | 10.3510i | −0.0342145 | + | 0.0197538i | ||||
\(525\) | 39.4286 | − | 857.344i | 0.0751021 | − | 1.63304i | ||||
\(526\) | −68.7794 | + | 119.129i | −0.130759 | + | 0.226482i | ||||
\(527\) | 818.005 | − | 219.184i | 1.55219 | − | 0.415909i | ||||
\(528\) | 48.3237 | + | 15.8807i | 0.0915222 | + | 0.0300771i | ||||
\(529\) | 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 | ||||
\(533\) | 5.27851 | + | 1.41437i | 0.00990340 | + | 0.00265361i | ||||
\(534\) | 21.1136 | − | 378.571i | 0.0395385 | − | 0.708935i | ||||
\(535\) | 309.984 | − | 1.51229i | 0.579409 | − | 0.00282672i | ||||
\(536\) | 107.288 | − | 185.828i | 0.200164 | − | 0.346694i | ||||
\(537\) | −892.468 | + | 186.573i | −1.66195 | + | 0.347436i | ||||
\(538\) | 27.7218 | + | 7.42804i | 0.0515276 | + | 0.0138068i | ||||
\(539\) | 213.863i | 0.396778i | ||||||||
\(540\) | 328.832 | + | 269.117i | 0.608949 | + | 0.498366i | ||||
\(541\) | −694.204 | −1.28319 | −0.641593 | − | 0.767045i | \(-0.721726\pi\) | ||||
−0.641593 | + | 0.767045i | \(0.721726\pi\) | |||||||
\(542\) | 1.00953 | − | 3.76761i | 0.00186260 | − | 0.00695130i | ||||
\(543\) | 105.943 | + | 506.773i | 0.195106 | + | 0.933284i | ||||
\(544\) | −542.975 | − | 313.487i | −0.998115 | − | 0.576262i | ||||
\(545\) | −46.6163 | − | 46.1637i | −0.0855346 | − | 0.0847040i | ||||
\(546\) | −93.5232 | − | 5.21595i | −0.171288 | − | 0.00955302i | ||||
\(547\) | −229.183 | + | 855.323i | −0.418982 | + | 1.56366i | 0.357742 | + | 0.933820i | \(0.383547\pi\) |
−0.776724 | + | 0.629841i | \(0.783120\pi\) | |||||||
\(548\) | 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 | ||||
\(552\) | −69.0368 | + | 210.073i | −0.125067 | + | 0.380568i | ||||
\(553\) | −203.819 | − | 760.662i | −0.368569 | − | 1.37552i | ||||
\(554\) | 111.191 | + | 64.1960i | 0.200705 | + | 0.115877i | ||||
\(555\) | −64.1101 | − | 299.370i | −0.115514 | − | 0.539405i | ||||
\(556\) | −137.655 | − | 238.426i | −0.247581 | − | 0.428824i | ||||
\(557\) | 598.653 | + | 598.653i | 1.07478 | + | 1.07478i | 0.996968 | + | 0.0778138i | \(0.0247940\pi\) |
0.0778138 | + | 0.996968i | \(0.475206\pi\) | |||||||
\(558\) | −338.574 | − | 132.579i | −0.606763 | − | 0.237597i | ||||
\(559\) | 150.138i | 0.268584i | ||||||||
\(560\) | −184.300 | + | 322.844i | −0.329107 | + | 0.576506i | ||||
\(561\) | −151.285 | − | 8.43740i | −0.269670 | − | 0.0150399i | ||||
\(562\) | −448.950 | + | 120.296i | −0.798844 | + | 0.214050i | ||||
\(563\) | 80.5980 | + | 300.796i | 0.143158 | + | 0.534273i | 0.999830 | + | 0.0184123i | \(0.00586116\pi\) |
−0.856672 | + | 0.515861i | \(0.827472\pi\) | |||||||
\(564\) | −501.649 | − | 328.172i | −0.889449 | − | 0.581866i | ||||
\(565\) | 141.202 | + | 80.6072i | 0.249915 | + | 0.142668i | ||||
\(566\) | −135.312 | −0.239067 | ||||||||
\(567\) | −494.357 | − | 784.076i | −0.871882 | − | 1.38285i | ||||
\(568\) | −295.614 | + | 295.614i | −0.520447 | + | 0.520447i | ||||
\(569\) | 20.4998 | − | 11.8356i | 0.0360278 | − | 0.0208006i | −0.481878 | − | 0.876238i | \(-0.660045\pi\) |
0.517906 | + | 0.855438i | \(0.326712\pi\) | |||||||
\(570\) | −106.254 | − | 117.646i | −0.186411 | − | 0.206396i | ||||
\(571\) | 22.7049 | − | 39.3260i | 0.0397633 | − | 0.0688721i | −0.845459 | − | 0.534041i | \(-0.820673\pi\) |
0.885222 | + | 0.465169i | \(0.154006\pi\) | |||||||
\(572\) | −23.4468 | + | 6.28254i | −0.0409909 | + | 0.0109835i | ||||
\(573\) | −642.305 | + | 574.445i | −1.12095 | + | 1.00252i | ||||
\(574\) | 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 | 0.356262 | − | 0.934386i | \(-0.384051\pi\) |
−0.934386 | + | 0.356262i | \(0.884051\pi\) | |||||||
\(578\) | 76.3059 | + | 20.4461i | 0.132017 | + | 0.0353739i | ||||
\(579\) | −98.5150 | + | 49.7804i | −0.170147 | + | 0.0859765i | ||||
\(580\) | −294.434 | + | 297.321i | −0.507644 | + | 0.512622i | ||||
\(581\) | 603.256 | − | 1044.87i | 1.03831 | − | 1.79840i | ||||
\(582\) | −31.6062 | + | 96.1750i | −0.0543062 | + | 0.165249i | ||||
\(583\) | −22.9394 | − | 6.14658i | −0.0393471 | − | 0.0105430i | ||||
\(584\) | 475.096i | 0.813520i | ||||||||
\(585\) | −132.228 | − | 14.1424i | −0.226031 | − | 0.0241751i | ||||
\(586\) | −316.691 | −0.540428 | ||||||||
\(587\) | 201.489 | − | 751.967i | 0.343252 | − | 1.28103i | −0.551388 | − | 0.834249i | \(-0.685902\pi\) |
0.894641 | − | 0.446786i | \(-0.147432\pi\) | |||||||
\(588\) | 576.796 | − | 515.857i | 0.980945 | − | 0.877307i | ||||
\(589\) | −433.764 | − | 250.434i | −0.736441 | − | 0.425184i | ||||
\(590\) | 1.28773 | + | 263.953i | 0.00218258 | + | 0.447377i | ||||
\(591\) | 526.446 | − | 804.733i | 0.890771 | − | 1.36165i | ||||
\(592\) | −34.3219 | + | 128.091i | −0.0579763 | + | 0.216370i | ||||
\(593\) | −464.151 | + | 464.151i | −0.782717 | + | 0.782717i | −0.980289 | − | 0.197571i | \(-0.936695\pi\) |
0.197571 | + | 0.980289i | \(0.436695\pi\) | |||||||
\(594\) | 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 | ||||
\(597\) | 315.698 | − | 65.9978i | 0.528808 | − | 0.110549i | ||||
\(598\) | −7.88753 | − | 29.4367i | −0.0131899 | − | 0.0492252i | ||||
\(599\) | −402.592 | − | 232.437i | −0.672108 | − | 0.388042i | 0.124767 | − | 0.992186i | \(-0.460182\pi\) |
−0.796875 | + | 0.604145i | \(0.793515\pi\) | |||||||
\(600\) | 266.902 | − | 416.812i | 0.444837 | − | 0.694686i | ||||
\(601\) | −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 | ||||
\(603\) | −228.651 | + | 182.632i | −0.379190 | + | 0.302873i | ||||
\(604\) | 785.469i | 1.30045i | ||||||||
\(605\) | 150.461 | + | 550.766i | 0.248696 | + | 0.910357i | ||||
\(606\) | −120.709 | − | 238.882i | −0.199190 | − | 0.394195i | ||||
\(607\) | 81.5905 | − | 21.8621i | 0.134416 | − | 0.0360167i | −0.190984 | − | 0.981593i | \(-0.561168\pi\) |
0.325400 | + | 0.945577i | \(0.394501\pi\) | |||||||
\(608\) | 95.9744 | + | 358.181i | 0.157853 | + | 0.589114i | ||||
\(609\) | 814.676 | − | 411.662i | 1.33773 | − | 0.675964i | ||||
\(610\) | −77.0800 | + | 135.024i | −0.126361 | + | 0.221350i | ||||
\(611\) | 187.606 | 0.307048 | ||||||||
\(612\) | 342.156 | + | 428.371i | 0.559078 | + | 0.699953i | ||||
\(613\) | 463.301 | − | 463.301i | 0.755793 | − | 0.755793i | −0.219760 | − | 0.975554i | \(-0.570528\pi\) |
0.975554 | + | 0.219760i | \(0.0705276\pi\) | |||||||
\(614\) | −21.7432 | + | 12.5534i | −0.0354123 | + | 0.0204453i | ||||
\(615\) | 24.6956 | − | 12.6305i | 0.0401555 | − | 0.0205374i | ||||
\(616\) | −98.5380 | + | 170.673i | −0.159964 | + | 0.277066i | ||||
\(617\) | −650.709 | + | 174.357i | −1.05463 | + | 0.282588i | −0.744165 | − | 0.667995i | \(-0.767153\pi\) |
−0.310468 | + | 0.950584i | \(0.600486\pi\) | |||||||
\(618\) | −15.0614 | − | 72.0456i | −0.0243712 | − | 0.116579i | ||||
\(619\) | −759.400 | + | 438.440i | −1.22682 | + | 0.708303i | −0.966363 | − | 0.257183i | \(-0.917206\pi\) |
−0.260455 | + | 0.965486i | \(0.583872\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | −1513.07 | − | 405.426i | −2.42869 | − | 0.650765i | ||||
\(624\) | 48.2022 | + | 31.5333i | 0.0772472 | + | 0.0505341i | ||||
\(625\) | −624.881 | + | 12.1957i | −0.999810 | + | 0.0195131i | ||||
\(626\) | −221.405 | + | 383.485i | −0.353683 | + | 0.612597i | ||||
\(627\) | 59.7403 | + | 66.7975i | 0.0952795 | + | 0.106535i | ||||
\(628\) | −152.326 | − | 40.8157i | −0.242558 | − | 0.0649932i | ||||
\(629\) | − | 395.016i | − | 0.628007i | ||||||
\(630\) | −370.039 | + | 298.533i | −0.587364 | + | 0.473861i | ||||
\(631\) | 1077.51 | 1.70762 | 0.853812 | − | 0.520581i | \(-0.174285\pi\) | ||||
0.853812 | + | 0.520581i | \(0.174285\pi\) | |||||||
\(632\) | 117.540 | − | 438.665i | 0.185981 | − | 0.694090i | ||||
\(633\) | 259.850 | + | 85.3951i | 0.410506 | + | 0.134905i | ||||
\(634\) | 223.513 | + | 129.045i | 0.352544 | + | 0.203541i | ||||
\(635\) | 765.246 | − | 3.73335i | 1.20511 | − | 0.00587929i | ||||
\(636\) | 38.7542 | + | 76.6943i | 0.0609343 | + | 0.120589i | ||||
\(637\) | −62.6798 | + | 233.924i | −0.0983984 | + | 0.367228i | ||||
\(638\) | −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 | \(-0.340325\pi\) | |||||||
\(642\) | −114.478 | − | 128.001i | −0.178314 | − | 0.199379i | ||||
\(643\) | 287.192 | + | 1071.82i | 0.446644 | + | 1.66690i | 0.711559 | + | 0.702626i | \(0.247989\pi\) |
−0.264915 | + | 0.964272i | \(0.585344\pi\) | |||||||
\(644\) | 348.401 | + | 201.150i | 0.540996 | + | 0.312344i | ||||
\(645\) | 510.794 | + | 565.558i | 0.791929 | + | 0.876834i | ||||
\(646\) | −102.268 | − | 177.134i | −0.158310 | − | 0.274201i | ||||
\(647\) | −231.177 | − | 231.177i | −0.357306 | − | 0.357306i | 0.505513 | − | 0.862819i | \(-0.331303\pi\) |
−0.862819 | + | 0.505513i | \(0.831303\pi\) | |||||||
\(648\) | −20.8115 | − | 534.133i | −0.0321165 | − | 0.824280i | ||||
\(649\) | − | 149.214i | − | 0.229914i | ||||||
\(650\) | 0.665544 | + | 68.2086i | 0.00102391 | + | 0.104936i | ||||
\(651\) | −822.373 | + | 1257.09i | −1.26325 | + | 1.93102i | ||||
\(652\) | −101.122 | + | 27.0955i | −0.155094 | + | 0.0415574i | ||||
\(653\) | 174.987 | + | 653.059i | 0.267974 | + | 1.00009i | 0.960405 | + | 0.278607i | \(0.0898728\pi\) |
−0.692432 | + | 0.721484i | \(0.743461\pi\) | |||||||
\(654\) | −2.02383 | + | 36.2877i | −0.00309454 | + | 0.0554858i | ||||
\(655\) | −8.66637 | − | 31.7235i | −0.0132311 | − | 0.0484328i | ||||
\(656\) | −12.0146 | −0.0183149 | ||||||||
\(657\) | 236.251 | − | 603.325i | 0.359590 | − | 0.918303i | ||||
\(658\) | 474.287 | − | 474.287i | 0.720802 | − | 0.720802i | ||||
\(659\) | 138.847 | − | 80.1633i | 0.210693 | − | 0.121644i | −0.390940 | − | 0.920416i | \(-0.627850\pi\) |
0.601634 | + | 0.798772i | \(0.294517\pi\) | |||||||
\(660\) | −66.9478 | + | 103.435i | −0.101436 | + | 0.156720i | ||||
\(661\) | −471.803 | + | 817.186i | −0.713771 | + | 1.23629i | 0.249660 | + | 0.968333i | \(0.419681\pi\) |
−0.963432 | + | 0.267954i | \(0.913652\pi\) | |||||||
\(662\) | −109.122 | + | 29.2392i | −0.164837 | + | 0.0441679i | ||||
\(663\) | −163.003 | − | 53.5679i | −0.245856 | − | 0.0807962i | ||||
\(664\) | 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 | ||||
\(668\) | 336.436 | + | 90.1478i | 0.503647 | + | 0.134952i | ||||
\(669\) | −39.6505 | + | 710.943i | −0.0592683 | + | 1.06269i | ||||
\(670\) | 106.656 | + | 105.621i | 0.159189 | + | 0.157643i | ||||
\(671\) | 43.9452 | − | 76.1153i | 0.0654921 | − | 0.113436i | ||||
\(672\) | 1088.61 | − | 227.578i | 1.61996 | − | 0.338658i | ||||
\(673\) | 549.114 | + | 147.135i | 0.815919 | + | 0.218625i | 0.642562 | − | 0.766234i | \(-0.277872\pi\) |
0.173358 | + | 0.984859i | \(0.444538\pi\) | |||||||
\(674\) | 305.104i | 0.452676i | ||||||||
\(675\) | −546.208 | + | 396.588i | −0.809196 | + | 0.587538i | ||||
\(676\) | 504.446 | 0.746222 | ||||||||
\(677\) | 76.2369 | − | 284.520i | 0.112610 | − | 0.420266i | −0.886487 | − | 0.462753i | \(-0.846862\pi\) |
0.999097 | + | 0.0424873i | \(0.0135282\pi\) | |||||||
\(678\) | −18.4311 | − | 88.1647i | −0.0271846 | − | 0.130036i | ||||
\(679\) | 362.207 | + | 209.120i | 0.533441 | + | 0.307983i | ||||
\(680\) | 449.347 | − | 453.752i | 0.660804 | − | 0.667283i | ||||
\(681\) | −367.915 | − | 20.5193i | −0.540258 | − | 0.0301311i | ||||
\(682\) | 27.2880 | − | 101.840i | 0.0400117 | − | 0.149326i | ||||
\(683\) | 449.659 | − | 449.659i | 0.658359 | − | 0.658359i | −0.296632 | − | 0.954992i | \(-0.595864\pi\) |
0.954992 | + | 0.296632i | \(0.0958636\pi\) | |||||||
\(684\) | 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 | ||||
\(687\) | −308.450 | + | 938.588i | −0.448981 | + | 1.36621i | ||||
\(688\) | −85.4335 | − | 318.842i | −0.124177 | − | 0.463433i | ||||
\(689\) | −23.2897 | − | 13.4463i | −0.0338021 | − | 0.0195157i | ||||
\(690\) | −129.860 | − | 84.0508i | −0.188203 | − | 0.121813i | ||||
\(691\) | −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 | ||||
\(693\) | 210.004 | − | 167.738i | 0.303036 | − | 0.242046i | ||||
\(694\) | − | 328.639i | − | 0.473544i | ||||||
\(695\) | 421.883 | − | 115.252i | 0.607027 | − | 0.165831i | ||||
\(696\) | 525.571 | + | 29.3120i | 0.755131 | + | 0.0421150i | ||||
\(697\) | 34.5694 | − | 9.26283i | 0.0495974 | − | 0.0132896i | ||||
\(698\) | 11.9069 | + | 44.4373i | 0.0170587 | + | 0.0636638i | ||||
\(699\) | −806.291 | − | 527.465i | −1.15349 | − | 0.754599i | ||||
\(700\) | −642.903 | − | 630.478i | −0.918432 | − | 0.900682i | ||||
\(701\) | 1256.95 | 1.79308 | 0.896539 | − | 0.442964i | \(-0.146073\pi\) | ||||
0.896539 | + | 0.442964i | \(0.146073\pi\) | |||||||
\(702\) | 42.6995 | + | 60.0320i | 0.0608255 | + | 0.0855156i | ||||
\(703\) | −165.200 | + | 165.200i | −0.234993 | + | 0.234993i | ||||
\(704\) | −8.86400 | + | 5.11763i | −0.0125909 | + | 0.00726937i | ||||
\(705\) | 706.698 | − | 638.267i | 1.00241 | − | 0.905343i | ||||
\(706\) | 290.023 | − | 502.334i | 0.410797 | − | 0.711521i | ||||
\(707\) | −1068.07 | + | 286.190i | −1.51071 | + | 0.404795i | ||||
\(708\) | −402.435 | + | 359.918i | −0.568412 | + | 0.508358i | ||||
\(709\) | 631.908 | − | 364.832i | 0.891267 | − | 0.514573i | 0.0169102 | − | 0.999857i | \(-0.494617\pi\) |
0.874357 | + | 0.485284i | \(0.161284\pi\) | |||||||
\(710\) | −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 | ||||
\(713\) | −472.085 | − | 126.495i | −0.662111 | − | 0.177412i | ||||
\(714\) | −547.511 | + | 276.662i | −0.766823 | + | 0.387481i | ||||
\(715\) | −0.188118 | − | 38.5597i | −0.000263102 | − | 0.0539296i | ||||
\(716\) | −478.300 | + | 828.440i | −0.668017 | + | 1.15704i | ||||
\(717\) | 133.505 | − | 406.243i | 0.186199 | − | 0.566588i | ||||
\(718\) | 72.5097 | + | 19.4289i | 0.100988 | + | 0.0270598i | ||||
\(719\) | − | 806.713i | − | 1.12199i | −0.827818 | − | 0.560997i | \(-0.810418\pi\) | ||
0.827818 | − | 0.560997i | \(-0.189582\pi\) | |||||||
\(720\) | 288.855 | − | 45.2085i | 0.401187 | − | 0.0627896i | ||||
\(721\) | −304.082 | −0.421750 | ||||||||
\(722\) | 54.9567 | − | 205.101i | 0.0761173 | − | 0.284074i | ||||
\(723\) | 1023.57 | − | 915.424i | 1.41572 | − | 1.26615i | ||||
\(724\) | 470.417 | + | 271.595i | 0.649747 | + | 0.375131i | ||||
\(725\) | −337.955 | − | 572.384i | −0.466144 | − | 0.789495i | ||||
\(726\) | 173.153 | − | 264.684i | 0.238502 | − | 0.364578i | ||||
\(727\) | 306.191 | − | 1142.72i | 0.421171 | − | 1.57183i | −0.350974 | − | 0.936385i | \(-0.614150\pi\) |
0.772145 | − | 0.635446i | \(-0.219184\pi\) | |||||||
\(728\) | −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 | ||||
\(732\) | −311.285 | + | 65.0752i | −0.425253 | + | 0.0889006i | ||||
\(733\) | 264.670 | + | 987.760i | 0.361077 | + | 1.34756i | 0.872662 | + | 0.488325i | \(0.162392\pi\) |
−0.511585 | + | 0.859233i | \(0.670941\pi\) | |||||||
\(734\) | −48.0349 | − | 27.7330i | −0.0654426 | − | 0.0377833i | ||||
\(735\) | 559.737 | + | 1094.42i | 0.761548 | + | 1.48901i | ||||
\(736\) | 180.918 | + | 313.360i | 0.245813 | + | 0.425761i | ||||
\(737\) | −60.0009 | − | 60.0009i | −0.0814123 | − | 0.0814123i | ||||
\(738\) | −14.3083 | − | 5.60286i | −0.0193880 | − | 0.00759195i | ||||
\(739\) | 808.791i | 1.09444i | 0.836989 | + | 0.547220i | \(0.184314\pi\) | ||||
−0.836989 | + | 0.547220i | \(0.815686\pi\) | |||||||
\(740\) | −278.960 | − | 159.248i | −0.376972 | − | 0.215200i | ||||
\(741\) | 45.7668 | + | 90.5722i | 0.0617636 | + | 0.122230i | ||||
\(742\) | −92.8721 | + | 24.8850i | −0.125165 | + | 0.0335378i | ||||
\(743\) | −164.727 | − | 614.769i | −0.221705 | − | 0.827415i | −0.983698 | − | 0.179829i | \(-0.942445\pi\) |
0.761993 | − | 0.647586i | \(-0.224221\pi\) | |||||||
\(744\) | −773.190 | + | 390.699i | −1.03923 | + | 0.525133i | ||||
\(745\) | −807.362 | + | 220.559i | −1.08371 | + | 0.296052i | ||||
\(746\) | −180.107 | −0.241431 | ||||||||
\(747\) | −938.193 | + | 142.150i | −1.25595 | + | 0.190295i | ||||
\(748\) | −112.410 | + | 112.410i | −0.150280 | + | 0.150280i | ||||
\(749\) | −614.409 | + | 354.729i | −0.820306 | + | 0.473604i | ||||
\(750\) | 234.563 | + | 254.672i | 0.312751 | + | 0.339562i | ||||
\(751\) | 709.826 | − | 1229.46i | 0.945175 | − | 1.63709i | 0.189774 | − | 0.981828i | \(-0.439224\pi\) |
0.755401 | − | 0.655263i | \(-0.227442\pi\) | |||||||
\(752\) | −398.412 | + | 106.754i | −0.529803 | + | 0.141960i | ||||
\(753\) | 62.9726 | + | 301.227i | 0.0836290 | + | 0.400036i | ||||
\(754\) | −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 | 0.977964 | − | 0.208772i | \(-0.0669467\pi\) |
−0.208772 | + | 0.977964i | \(0.566947\pi\) | |||||||
\(758\) | −130.062 | − | 34.8500i | −0.171586 | − | 0.0459762i | ||||
\(759\) | 73.1771 | + | 47.8715i | 0.0964125 | + | 0.0630718i | ||||
\(760\) | −377.686 | + | 1.84259i | −0.496955 | + | 0.00242446i | ||||
\(761\) | −73.5291 | + | 127.356i | −0.0966217 | + | 0.167354i | −0.910284 | − | 0.413984i | \(-0.864137\pi\) |
0.813663 | + | 0.581337i | \(0.197470\pi\) | |||||||
\(762\) | −282.607 | − | 315.992i | −0.370875 | − | 0.414687i | ||||
\(763\) | 145.035 | + | 38.8619i | 0.190085 | + | 0.0509330i | ||||
\(764\) | 904.087i | 1.18336i | ||||||||
\(765\) | −796.264 | + | 352.775i | −1.04087 | + | 0.461144i | ||||
\(766\) | 697.261 | 0.910262 | ||||||||
\(767\) | 43.7322 | − | 163.211i | 0.0570172 | − | 0.212791i | ||||
\(768\) | 376.169 | + | 123.621i | 0.489804 | + | 0.160965i | ||||
\(769\) | −798.259 | − | 460.875i | −1.03805 | − | 0.599317i | −0.118768 | − | 0.992922i | \(-0.537894\pi\) |
−0.919280 | + | 0.393605i | \(0.871228\pi\) | |||||||
\(770\) | −97.9582 | − | 97.0070i | −0.127218 | − | 0.125983i | ||||
\(771\) | −151.875 | − | 300.559i | −0.196984 | − | 0.389830i | ||||
\(772\) | −29.9729 | + | 111.860i | −0.0388250 | + | 0.144897i | ||||
\(773\) | 646.946 | − | 646.946i | 0.836928 | − | 0.836928i | −0.151525 | − | 0.988453i | \(-0.548418\pi\) |
0.988453 | + | 0.151525i | \(0.0484185\pi\) | |||||||
\(774\) | 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 | ||||
\(777\) | 467.106 | + | 522.286i | 0.601166 | + | 0.672183i | ||||
\(778\) | 10.3092 | + | 38.4744i | 0.0132509 | + | 0.0494530i | ||||
\(779\) | −18.3311 | − | 10.5835i | −0.0235316 | − | 0.0135860i | ||||
\(780\) | −103.543 | + | 93.5167i | −0.132747 | + | 0.119893i | ||||
\(781\) | 82.6613 | + | 143.174i | 0.105840 | + | 0.183321i | ||||
\(782\) | −141.127 | − | 141.127i | −0.180469 | − | 0.180469i | ||||
\(783\) | −652.849 | − | 298.574i | −0.833779 | − | 0.381321i | ||||
\(784\) | − | 532.441i | − | 0.679134i | ||||||
\(785\) | 124.197 | − | 217.559i | 0.158212 | − | 0.277146i | ||||
\(786\) | −9.97338 | + | 15.2455i | −0.0126888 | + | 0.0193963i | ||||
\(787\) | −105.372 | + | 28.2343i | −0.133890 | + | 0.0358758i | −0.325142 | − | 0.945665i | \(-0.605412\pi\) |
0.191251 | + | 0.981541i | \(0.438745\pi\) | |||||||
\(788\) | −261.129 | − | 974.548i | −0.331382 | − | 1.23674i | ||||
\(789\) | 24.8892 | − | 446.270i | 0.0315453 | − | 0.565614i | ||||
\(790\) | 275.899 | + | 157.501i | 0.349239 | + | 0.199368i | ||||
\(791\) | −372.115 | −0.470436 | ||||||||
\(792\) | 153.248 | − | 23.2194i | 0.193495 | − | 0.0293174i | ||||
\(793\) | 70.3755 | − | 70.3755i | 0.0887459 | − | 0.0887459i | ||||
\(794\) | −101.540 | + | 58.6241i | −0.127884 | + | 0.0738339i | ||||
\(795\) | −133.477 | + | 28.5841i | −0.167895 | + | 0.0359548i | ||||
\(796\) | 169.192 | − | 293.050i | 0.212553 | − | 0.368153i | ||||
\(797\) | 863.511 | − | 231.377i | 1.08345 | − | 0.290310i | 0.327443 | − | 0.944871i | \(-0.393813\pi\) |
0.756009 | + | 0.654561i | \(0.227146\pi\) | |||||||
\(798\) | 344.678 | + | 113.272i | 0.431928 | + | 0.141945i | ||||
\(799\) | 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 | ||||
\(803\) | 181.475 | + | 48.6261i | 0.225996 | + | 0.0605556i | ||||
\(804\) | −17.0969 | + | 306.552i | −0.0212648 | + | 0.381283i | ||||
\(805\) | −449.681 | + | 454.090i | −0.558609 | + | 0.564087i | ||||
\(806\) | 59.6953 | − | 103.395i | 0.0740637 | − | 0.128282i | ||||
\(807\) | −91.2795 | + | 19.0823i | −0.113110 | + | 0.0236460i | ||||
\(808\) | −615.946 | − | 165.042i | −0.762310 | − | 0.204260i | ||||
\(809\) | 920.002i | 1.13721i | 0.822611 | + | 0.568604i | \(0.192516\pi\) | ||||
−0.822611 | + | 0.568604i | \(0.807484\pi\) | |||||||
\(810\) | 365.084 | + | 80.8648i | 0.450721 | + | 0.0998331i | ||||
\(811\) | −174.196 | −0.214792 | −0.107396 | − | 0.994216i | \(-0.534251\pi\) | ||||
−0.107396 | + | 0.994216i | \(0.534251\pi\) | |||||||
\(812\) | 247.862 | − | 925.035i | 0.305249 | − | 1.13921i | ||||
\(813\) | 2.59343 | + | 12.4056i | 0.00318995 | + | 0.0152590i | ||||
\(814\) | −42.5901 | − | 24.5894i | −0.0523220 | − | 0.0302081i | ||||
\(815\) | −0.811319 | − | 166.301i | −0.000995483 | − | 0.204050i | ||||
\(816\) | 376.643 | + | 21.0061i | 0.461573 | + | 0.0257427i | ||||
\(817\) | 150.514 | − | 561.727i | 0.184228 | − | 0.687548i | ||||
\(818\) | −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 | \(0.659686\pi\) | |||||||
\(822\) | 75.3083 | − | 229.157i | 0.0916160 | − | 0.278780i | ||||
\(823\) | −53.4313 | − | 199.408i | −0.0649226 | − | 0.242295i | 0.925837 | − | 0.377923i | \(-0.123361\pi\) |
−0.990760 | + | 0.135628i | \(0.956695\pi\) | |||||||
\(824\) | −151.866 | − | 87.6802i | −0.184304 | − | 0.106408i | ||||
\(825\) | −131.895 | − | 144.611i | −0.159872 | − | 0.175286i | ||||
\(826\) | −302.054 | − | 523.172i | −0.365682 | − | 0.633380i | ||||
\(827\) | −66.1579 | − | 66.1579i | −0.0799974 | − | 0.0799974i | 0.665976 | − | 0.745973i | \(-0.268015\pi\) |
−0.745973 | + | 0.665976i | \(0.768015\pi\) | |||||||
\(828\) | −47.3987 | − | 312.831i | −0.0572448 | − | 0.377815i | ||||
\(829\) | − | 71.1280i | − | 0.0857998i | −0.999079 | − | 0.0428999i | \(-0.986340\pi\) | ||
0.999079 | − | 0.0428999i | \(-0.0136596\pi\) | |||||||
\(830\) | 128.267 | + | 469.523i | 0.154538 | + | 0.565690i | ||||
\(831\) | −416.531 | − | 23.2306i | −0.501240 | − | 0.0279550i | ||||
\(832\) | −11.1954 | + | 2.99979i | −0.0134560 | + | 0.00360552i | ||||
\(833\) | 410.494 | + | 1531.98i | 0.492790 | + | 1.83912i | ||||
\(834\) | −202.746 | − | 132.634i | −0.243101 | − | 0.159033i | ||||
\(835\) | −274.307 | + | 480.513i | −0.328512 | + | 0.575465i | ||||
\(836\) | 94.0219 | 0.112466 | ||||||||
\(837\) | 1176.16 | − | 111.666i | 1.40521 | − | 0.133412i | ||||
\(838\) | −468.230 | + | 468.230i | −0.558747 | + | 0.558747i | ||||
\(839\) | −327.523 | + | 189.096i | −0.390373 | + | 0.225382i | −0.682322 | − | 0.731052i | \(-0.739030\pi\) |
0.291949 | + | 0.956434i | \(0.405696\pi\) | |||||||
\(840\) | −57.5596 | + | 1131.30i | −0.0685233 | + | 1.34678i | ||||
\(841\) | −67.0308 | + | 116.101i | −0.0797037 | + | 0.138051i | ||||
\(842\) | 222.175 | − | 59.5317i | 0.263866 | − | 0.0707027i | ||||
\(843\) | 1125.69 | − | 1006.76i | 1.33534 | − | 1.19426i | ||||
\(844\) | 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 | ||||
\(848\) | 57.1106 | + | 15.3028i | 0.0673475 | + | 0.0180457i | ||||
\(849\) | 392.410 | − | 198.288i | 0.462203 | − | 0.233555i | ||||
\(850\) | 227.126 | + | 384.676i | 0.267207 | + | 0.452560i | ||||
\(851\) | −113.985 | + | 197.428i | −0.133943 | + | 0.231996i | ||||
\(852\) | 186.757 | − | 568.287i | 0.219199 | − | 0.667004i | ||||
\(853\) | 629.719 | + | 168.733i | 0.738240 | + | 0.197811i | 0.608296 | − | 0.793711i | \(-0.291854\pi\) |
0.129944 | + | 0.991521i | \(0.458520\pi\) | |||||||
\(854\) | − | 355.832i | − | 0.416665i | ||||||
\(855\) | 480.541 | + | 185.472i | 0.562036 | + | 0.216926i | ||||
\(856\) | −409.137 | −0.477963 | ||||||||
\(857\) | −145.445 | + | 542.809i | −0.169714 | + | 0.633382i | 0.827677 | + | 0.561204i | \(0.189662\pi\) |
−0.997392 | + | 0.0721782i | \(0.977005\pi\) | |||||||
\(858\) | −15.9224 | + | 14.2402i | −0.0185576 | + | 0.0165969i | ||||
\(859\) | 468.778 | + | 270.649i | 0.545725 | + | 0.315075i | 0.747396 | − | 0.664379i | \(-0.231304\pi\) |
−0.201671 | + | 0.979453i | \(0.564637\pi\) | |||||||
\(860\) | 799.549 | − | 3.90070i | 0.929709 | − | 0.00453570i | ||||
\(861\) | −34.7539 | + | 53.1254i | −0.0403646 | + | 0.0617020i | ||||
\(862\) | −55.9407 | + | 208.774i | −0.0648964 | + | 0.242197i | ||||
\(863\) | 24.2188 | − | 24.2188i | 0.0280635 | − | 0.0280635i | −0.692936 | − | 0.720999i | \(-0.743683\pi\) |
0.720999 | + | 0.692936i | \(0.243683\pi\) | |||||||
\(864\) | −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 | ||||
\(867\) | −251.252 | + | 52.5250i | −0.289794 | + | 0.0605825i | ||||
\(868\) | 407.916 | + | 1522.36i | 0.469950 | + | 1.75388i | ||||
\(869\) | −155.529 | − | 89.7949i | −0.178975 | − | 0.103331i | ||||
\(870\) | −113.255 | + | 350.381i | −0.130179 | + | 0.402737i | ||||
\(871\) | −48.0438 | − | 83.2144i | −0.0551594 | − | 0.0955389i | ||||
\(872\) | 61.2285 | + | 61.2285i | 0.0702162 | + | 0.0702162i | ||||
\(873\) | −49.2768 | − | 325.227i | −0.0564454 | − | 0.372540i | ||||
\(874\) | 118.041i | 0.135059i | ||||||||
\(875\) | 1228.18 | − | 733.262i | 1.40363 | − | 0.838014i | ||||
\(876\) | −306.588 | − | 606.735i | −0.349986 | − | 0.692620i | ||||
\(877\) | −1200.73 | + | 321.735i | −1.36913 | + | 0.366858i | −0.867162 | − | 0.498025i | \(-0.834059\pi\) |
−0.501972 | + | 0.864884i | \(0.667392\pi\) | |||||||
\(878\) | 154.206 | + | 575.505i | 0.175633 | + | 0.655472i | ||||
\(879\) | 918.415 | − | 464.082i | 1.04484 | − | 0.527966i | ||||
\(880\) | 22.3412 | + | 81.7804i | 0.0253877 | + | 0.0929323i | ||||
\(881\) | 1074.75 | 1.21993 | 0.609963 | − | 0.792430i | \(-0.291184\pi\) | ||||
0.609963 | + | 0.792430i | \(0.291184\pi\) | |||||||
\(882\) | 248.298 | − | 634.091i | 0.281517 | − | 0.718924i | ||||
\(883\) | 285.903 | − | 285.903i | 0.323786 | − | 0.323786i | −0.526432 | − | 0.850217i | \(-0.676470\pi\) |
0.850217 | + | 0.526432i | \(0.176470\pi\) | |||||||
\(884\) | −155.899 | + | 90.0086i | −0.176357 | + | 0.101820i | ||||
\(885\) | −390.534 | − | 763.585i | −0.441281 | − | 0.862808i | ||||
\(886\) | −126.931 | + | 219.851i | −0.143263 | + | 0.248139i | ||||
\(887\) | 1036.58 | − | 277.751i | 1.16864 | − | 0.313135i | 0.378226 | − | 0.925713i | \(-0.376534\pi\) |
0.790410 | + | 0.612578i | \(0.209868\pi\) | |||||||
\(888\) | 82.6871 | + | 395.531i | 0.0931161 | + | 0.445418i | ||||
\(889\) | −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 | ||||
\(893\) | −701.910 | − | 188.076i | −0.786013 | − | 0.210612i | ||||
\(894\) | 387.997 | + | 253.823i | 0.434001 | + | 0.283918i | ||||
\(895\) | −1079.75 | − | 1069.27i | −1.20642 | − | 1.19471i | ||||
\(896\) | 720.711 | − | 1248.31i | 0.804365 | − | 1.39320i | ||||
\(897\) | 66.0110 | + | 73.8090i | 0.0735908 | + | 0.0822842i | ||||
\(898\) | 170.043 | + | 45.5630i | 0.189358 | + | 0.0507383i | ||||
\(899\) | 1163.43i | 1.29414i | ||||||||
\(900\) | −71.8789 | + | 704.539i | −0.0798654 | + | 0.782821i | ||||
\(901\) | −176.122 | −0.195473 | ||||||||
\(902\) | 1.15321 | − | 4.30382i | 0.00127850 | − | 0.00477142i | ||||
\(903\) | −1656.97 | − | 544.533i | −1.83496 | − | 0.603026i | ||||
\(904\) | −185.844 | − | 107.297i | −0.205580 | − | 0.118692i | ||||
\(905\) | −607.165 | + | 613.119i | −0.670901 | + | 0.677479i | ||||
\(906\) | 311.740 | + | 616.932i | 0.344084 | + | 0.680940i | ||||
\(907\) | −442.672 | + | 1652.08i | −0.488062 | + | 1.82147i | 0.0777954 | + | 0.996969i | \(0.475212\pi\) |
−0.565858 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(908\) | −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 | \(0.904927\pi\) | |||||||
\(912\) | −148.731 | − | 166.301i | −0.163083 | − | 0.182348i | ||||
\(913\) | −71.2133 | − | 265.772i | −0.0779993 | − | 0.291097i | ||||
\(914\) | −250.056 | − | 144.370i | −0.273584 | − | 0.157954i | ||||
\(915\) | 25.6700 | − | 504.527i | 0.0280546 | − | 0.551396i | ||||
\(916\) | 518.280 | + | 897.687i | 0.565808 | + | 0.980008i | ||||
\(917\) | 53.2204 | + | 53.2204i | 0.0580375 | + | 0.0580375i | ||||
\(918\) | 438.754 | + | 200.660i | 0.477945 | + | 0.218584i | ||||
\(919\) | 975.596i | 1.06158i | 0.847502 | + | 0.530792i | \(0.178105\pi\) | ||||
−0.847502 | + | 0.530792i | \(0.821895\pi\) | |||||||
\(920\) | −355.517 | + | 97.1218i | −0.386431 | + | 0.105567i | ||||
\(921\) | 44.6600 | − | 68.2681i | 0.0484908 | − | 0.0741238i | ||||
\(922\) | −196.847 | + | 52.7449i | −0.213500 | + | 0.0572071i | ||||
\(923\) | 48.4533 | + | 180.830i | 0.0524955 | + | 0.195916i | ||||
\(924\) | 15.7026 | − | 281.551i | 0.0169941 | − | 0.304709i | ||||
\(925\) | 357.272 | − | 364.313i | 0.386240 | − | 0.393852i | ||||
\(926\) | 266.694 | 0.288007 | ||||||||
\(927\) | 149.255 | + | 186.864i | 0.161009 | + | 0.201579i | ||||
\(928\) | 609.065 | − | 609.065i | 0.656320 | − | 0.656320i | ||||
\(929\) | 1121.09 | − | 647.262i | 1.20677 | − | 0.696730i | 0.244719 | − | 0.969594i | \(-0.421304\pi\) |
0.962052 | + | 0.272864i | \(0.0879711\pi\) | |||||||
\(930\) | −126.900 | − | 592.575i | −0.136452 | − | 0.637177i | ||||
\(931\) | 469.020 | − | 812.366i | 0.503780 | − | 0.872573i | ||||
\(932\) | −976.435 | + | 261.635i | −1.04768 | + | 0.280724i | ||||
\(933\) | −1571.45 | − | 516.429i | −1.68430 | − | 0.553514i | ||||
\(934\) | −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 | 0.449049 | − | 0.893507i | \(-0.351763\pi\) |
−0.893507 | + | 0.449049i | \(0.851763\pi\) | |||||||
\(938\) | −331.834 | − | 88.9145i | −0.353767 | − | 0.0947916i | ||||
\(939\) | 80.1201 | − | 1436.57i | 0.0853249 | − | 1.52990i | ||||
\(940\) | −4.87415 | − | 999.083i | −0.00518527 | − | 1.06285i | ||||
\(941\) | 6.23741 | − | 10.8035i | 0.00662849 | − | 0.0114809i | −0.862692 | − | 0.505729i | \(-0.831223\pi\) |
0.869321 | + | 0.494249i | \(0.164557\pi\) | |||||||
\(942\) | −135.841 | + | 28.3980i | −0.144205 | + | 0.0301465i | ||||
\(943\) | −19.9506 | − | 5.34574i | −0.0211565 | − | 0.00566886i | ||||
\(944\) | 371.489i | 0.393526i | ||||||||
\(945\) | 635.655 | − | 1408.02i | 0.672651 | − | 1.48996i | ||||
\(946\) | 122.415 | 0.129403 | ||||||||
\(947\) | −307.908 | + | 1149.13i | −0.325140 | + | 1.21344i | 0.589031 | + | 0.808111i | \(0.299510\pi\) |
−0.914171 | + | 0.405329i | \(0.867157\pi\) | |||||||
\(948\) | 132.971 | + | 636.061i | 0.140264 | + | 0.670950i | ||||
\(949\) | 184.246 | + | 106.375i | 0.194148 | + | 0.112091i | ||||
\(950\) | 65.8893 | − | 255.862i | 0.0693571 | − | 0.269329i | ||||
\(951\) | −837.300 | − | 46.6977i | −0.880442 | − | 0.0491038i | ||||
\(952\) | −378.272 | + | 1411.73i | −0.397345 | + | 1.48291i | ||||
\(953\) | −943.370 | + | 943.370i | −0.989895 | + | 0.989895i | −0.999949 | − | 0.0100546i | \(-0.996799\pi\) |
0.0100546 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 64.9888 | − | 197.756i | 0.0679089 | − | 0.206641i | ||||
\(958\) | −209.149 | − | 780.555i | −0.218318 | − | 0.814775i | ||||
\(959\) | −863.033 | − | 498.272i | −0.899930 | − | 0.519575i | ||||
\(960\) | −31.9662 | + | 49.3883i | −0.0332982 | + | 0.0514462i | ||||
\(961\) | −476.853 | − | 825.933i | −0.496204 | − | 0.859451i | ||||
\(962\) | −39.3784 | − | 39.3784i | −0.0409339 | − | 0.0409339i | ||||
\(963\) | 519.564 | + | 203.451i | 0.539526 | + | 0.211268i | ||||
\(964\) | − | 1440.74i | − | 1.49454i | ||||||
\(965\) | −159.764 | − | 91.2033i | −0.165558 | − | 0.0945112i | ||||
\(966\) | 353.478 | + | 19.7141i | 0.365920 | + | 0.0204080i | ||||
\(967\) | 266.681 | − | 71.4571i | 0.275782 | − | 0.0738956i | −0.118277 | − | 0.992981i | \(-0.537737\pi\) |
0.394059 | + | 0.919085i | \(0.371070\pi\) | |||||||
\(968\) | −195.037 | − | 727.888i | −0.201484 | − | 0.751950i | ||||
\(969\) | 556.155 | + | 363.829i | 0.573948 | + | 0.375469i | ||||
\(970\) | −162.761 | + | 44.4639i | −0.167795 | + | 0.0458391i | ||||
\(971\) | −311.097 | −0.320388 | −0.160194 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160194 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(972\) | 371.264 | + | 668.701i | 0.381959 | + | 0.687964i | ||||
\(973\) | −707.766 | + | 707.766i | −0.727406 | + | 0.727406i | ||||
\(974\) | −273.087 | + | 157.667i | −0.280377 | + | 0.161876i | ||||
\(975\) | −101.884 | − | 196.832i | −0.104496 | − | 0.201879i | ||||
\(976\) | −109.407 | + | 189.499i | −0.112098 | + | 0.194159i | ||||
\(977\) | 608.490 | − | 163.044i | 0.622815 | − | 0.166883i | 0.0664079 | − | 0.997793i | \(-0.478846\pi\) |
0.556407 | + | 0.830910i | \(0.312179\pi\) | |||||||
\(978\) | −68.6703 | + | 61.4152i | −0.0702150 | + | 0.0627967i | ||||
\(979\) | −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 | ||||
\(983\) | 305.307 | + | 81.8068i | 0.310587 | + | 0.0832216i | 0.410746 | − | 0.911750i | \(-0.365268\pi\) |
−0.100159 | + | 0.994971i | \(0.531935\pi\) | |||||||
\(984\) | −32.6754 | + | 16.5112i | −0.0332068 | + | 0.0167796i | ||||
\(985\) | 1602.70 | − | 7.81899i | 1.62711 | − | 0.00793806i | ||||
\(986\) | −237.553 | + | 411.453i | −0.240926 | + | 0.417295i | ||||
\(987\) | −680.425 | + | 2070.48i | −0.689387 | + | 2.09775i | ||||
\(988\) | 102.841 | + | 27.5563i | 0.104091 | + | 0.0278910i | ||||
\(989\) | − | 567.460i | − | 0.573771i | ||||||
\(990\) | −11.5310 | + | 107.812i | −0.0116474 | + | 0.108901i | ||||
\(991\) | −1401.99 | −1.41472 | −0.707362 | − | 0.706852i | \(-0.750115\pi\) | ||||
−0.707362 | + | 0.706852i | \(0.750115\pi\) | |||||||
\(992\) | −366.889 | + | 1369.25i | −0.369848 | + | 1.38029i | ||||
\(993\) | 273.611 | − | 244.703i | 0.275539 | − | 0.246428i | ||||
\(994\) | 579.651 | + | 334.662i | 0.583150 | + | 0.336682i | ||||
\(995\) | 381.947 | + | 378.238i | 0.383866 | + | 0.380139i | ||||
\(996\) | −545.022 | + | 833.130i | −0.547211 | + | 0.836475i | ||||
\(997\) | 349.692 | − | 1305.07i | 0.350745 | − | 1.30900i | −0.535011 | − | 0.844845i | \(-0.679693\pi\) |
0.885756 | − | 0.464152i | \(-0.153641\pi\) | |||||||
\(998\) | 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.22.7 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.37.4 | 40 | |||
5.2 | odd | 4 | 225.3.o.b.193.7 | 40 | |||
5.3 | odd | 4 | inner | 45.3.k.a.13.4 | yes | 40 | |
5.4 | even | 2 | 225.3.o.b.157.4 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.127.7 | 40 | |||
9.4 | even | 3 | 405.3.g.h.82.7 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.82.4 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.7.4 | ✓ | 40 | |
15.8 | even | 4 | 135.3.l.a.118.7 | 40 | |||
45.7 | odd | 12 | 225.3.o.b.43.4 | 40 | |||
45.13 | odd | 12 | 405.3.g.h.163.7 | 20 | |||
45.23 | even | 12 | 405.3.g.g.163.4 | 20 | |||
45.34 | even | 6 | 225.3.o.b.7.7 | 40 | |||
45.38 | even | 12 | 135.3.l.a.73.4 | 40 | |||
45.43 | odd | 12 | inner | 45.3.k.a.43.7 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.4 | ✓ | 40 | 9.7 | even | 3 | inner | |
45.3.k.a.13.4 | yes | 40 | 5.3 | odd | 4 | inner | |
45.3.k.a.22.7 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.43.7 | yes | 40 | 45.43 | odd | 12 | inner | |
135.3.l.a.37.4 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.73.4 | 40 | 45.38 | even | 12 | |||
135.3.l.a.118.7 | 40 | 15.8 | even | 4 | |||
135.3.l.a.127.7 | 40 | 9.2 | odd | 6 | |||
225.3.o.b.7.7 | 40 | 45.34 | even | 6 | |||
225.3.o.b.43.4 | 40 | 45.7 | odd | 12 | |||
225.3.o.b.157.4 | 40 | 5.4 | even | 2 | |||
225.3.o.b.193.7 | 40 | 5.2 | odd | 4 | |||
405.3.g.g.82.4 | 20 | 9.5 | odd | 6 | |||
405.3.g.g.163.4 | 20 | 45.23 | even | 12 | |||
405.3.g.h.82.7 | 20 | 9.4 | even | 3 | |||
405.3.g.h.163.7 | 20 | 45.13 | odd | 12 |