Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,3,Mod(2,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.f (of order \(20\), degree \(8\), 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: | \(0.681200660901\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 8.4 | ||
Character | \(\chi\) | \(=\) | 25.8 |
Dual form | 25.3.f.a.22.4 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70026 | + | 1.37585i | 1.35013 | + | 0.687927i | 0.971371 | − | 0.237568i | \(-0.0763501\pi\) |
0.378761 | + | 0.925494i | \(0.376350\pi\) | |||||||
\(3\) | −4.42692 | − | 0.701156i | −1.47564 | − | 0.233719i | −0.633822 | − | 0.773479i | \(-0.718515\pi\) |
−0.841819 | + | 0.539760i | \(0.818515\pi\) | |||||||
\(4\) | 3.04732 | + | 4.19427i | 0.761829 | + | 1.04857i | ||||
\(5\) | 1.95091 | − | 4.60369i | 0.390182 | − | 0.920738i | ||||
\(6\) | −10.9892 | − | 7.98410i | −1.83153 | − | 1.33068i | ||||
\(7\) | −4.77540 | + | 4.77540i | −0.682200 | + | 0.682200i | −0.960496 | − | 0.278295i | \(-0.910231\pi\) |
0.278295 | + | 0.960496i | \(0.410231\pi\) | |||||||
\(8\) | 0.561510 | + | 3.54523i | 0.0701887 | + | 0.443154i | ||||
\(9\) | 10.5465 | + | 3.42677i | 1.17184 | + | 0.380753i | ||||
\(10\) | 11.6020 | − | 9.74701i | 1.16020 | − | 0.974701i | ||||
\(11\) | 3.84423 | + | 11.8313i | 0.349476 | + | 1.07558i | 0.959144 | + | 0.282919i | \(0.0913027\pi\) |
−0.609668 | + | 0.792657i | \(0.708697\pi\) | |||||||
\(12\) | −10.5494 | − | 20.7044i | −0.879116 | − | 1.72536i | ||||
\(13\) | −1.05261 | + | 0.536333i | −0.0809703 | + | 0.0412564i | −0.494007 | − | 0.869458i | \(-0.664468\pi\) |
0.413036 | + | 0.910714i | \(0.364468\pi\) | |||||||
\(14\) | −19.4651 | + | 6.32459i | −1.39036 | + | 0.451757i | ||||
\(15\) | −11.8644 | + | 19.0123i | −0.790963 | + | 1.26749i | ||||
\(16\) | 3.04678 | − | 9.37702i | 0.190424 | − | 0.586064i | ||||
\(17\) | −4.59461 | + | 0.727715i | −0.270271 | + | 0.0428067i | −0.290099 | − | 0.956997i | \(-0.593688\pi\) |
0.0198278 | + | 0.999803i | \(0.493688\pi\) | |||||||
\(18\) | 23.7637 | + | 23.7637i | 1.32020 | + | 1.32020i | ||||
\(19\) | 12.8564 | − | 17.6953i | 0.676652 | − | 0.931332i | −0.323235 | − | 0.946319i | \(-0.604771\pi\) |
0.999888 | + | 0.0149865i | \(0.00477052\pi\) | |||||||
\(20\) | 25.2542 | − | 5.84624i | 1.26271 | − | 0.292312i | ||||
\(21\) | 24.4886 | − | 17.7920i | 1.16613 | − | 0.847240i | ||||
\(22\) | −5.89773 | + | 37.2368i | −0.268079 | + | 1.69258i | ||||
\(23\) | −4.03970 | + | 7.92835i | −0.175639 | + | 0.344711i | −0.961997 | − | 0.273060i | \(-0.911964\pi\) |
0.786358 | + | 0.617771i | \(0.211964\pi\) | |||||||
\(24\) | − | 16.0882i | − | 0.670341i | ||||||
\(25\) | −17.3879 | − | 17.9628i | −0.695515 | − | 0.718511i | ||||
\(26\) | −3.58025 | −0.137702 | ||||||||
\(27\) | −8.34369 | − | 4.25132i | −0.309025 | − | 0.157456i | ||||
\(28\) | −34.5815 | − | 5.47717i | −1.23505 | − | 0.195613i | ||||
\(29\) | 5.42781 | + | 7.47074i | 0.187166 | + | 0.257612i | 0.892280 | − | 0.451482i | \(-0.149104\pi\) |
−0.705114 | + | 0.709094i | \(0.749104\pi\) | |||||||
\(30\) | −58.1952 | + | 35.0145i | −1.93984 | + | 1.16715i | ||||
\(31\) | −25.3215 | − | 18.3971i | −0.816821 | − | 0.593456i | 0.0989788 | − | 0.995090i | \(-0.468442\pi\) |
−0.915800 | + | 0.401634i | \(0.868442\pi\) | |||||||
\(32\) | 31.2809 | − | 31.2809i | 0.977529 | − | 0.977529i | ||||
\(33\) | −8.72252 | − | 55.0718i | −0.264319 | − | 1.66884i | ||||
\(34\) | −13.4079 | − | 4.35649i | −0.394350 | − | 0.128132i | ||||
\(35\) | 12.6681 | + | 31.3008i | 0.361945 | + | 0.894310i | ||||
\(36\) | 17.7658 | + | 54.6774i | 0.493494 | + | 1.51882i | ||||
\(37\) | 6.47182 | + | 12.7017i | 0.174914 | + | 0.343288i | 0.961774 | − | 0.273843i | \(-0.0882948\pi\) |
−0.786860 | + | 0.617131i | \(0.788295\pi\) | |||||||
\(38\) | 59.0618 | − | 30.0935i | 1.55426 | − | 0.791934i | ||||
\(39\) | 5.03589 | − | 1.63626i | 0.129125 | − | 0.0419554i | ||||
\(40\) | 17.4166 | + | 4.33142i | 0.435415 | + | 0.108286i | ||||
\(41\) | −16.8825 | + | 51.9589i | −0.411767 | + | 1.26729i | 0.503343 | + | 0.864086i | \(0.332103\pi\) |
−0.915111 | + | 0.403203i | \(0.867897\pi\) | |||||||
\(42\) | 90.6050 | − | 14.3504i | 2.15726 | − | 0.341677i | ||||
\(43\) | −36.1728 | − | 36.1728i | −0.841228 | − | 0.841228i | 0.147791 | − | 0.989019i | \(-0.452784\pi\) |
−0.989019 | + | 0.147791i | \(0.952784\pi\) | |||||||
\(44\) | −37.9092 | + | 52.1775i | −0.861573 | + | 1.18585i | ||||
\(45\) | 36.3511 | − | 41.8676i | 0.807803 | − | 0.930390i | ||||
\(46\) | −21.8165 | + | 15.8506i | −0.474272 | + | 0.344579i | ||||
\(47\) | −0.703158 | + | 4.43956i | −0.0149608 | + | 0.0944588i | −0.994039 | − | 0.109026i | \(-0.965227\pi\) |
0.979078 | + | 0.203485i | \(0.0652268\pi\) | |||||||
\(48\) | −20.0626 | + | 39.3751i | −0.417971 | + | 0.820314i | ||||
\(49\) | 3.39110i | 0.0692062i | ||||||||
\(50\) | −22.2377 | − | 72.4274i | −0.444755 | − | 1.44855i | ||||
\(51\) | 20.8502 | 0.408828 | ||||||||
\(52\) | −5.45717 | − | 2.78057i | −0.104946 | − | 0.0534725i | ||||
\(53\) | 69.2402 | + | 10.9666i | 1.30642 | + | 0.206916i | 0.770547 | − | 0.637383i | \(-0.219983\pi\) |
0.535872 | + | 0.844299i | \(0.319983\pi\) | |||||||
\(54\) | −16.6810 | − | 22.9594i | −0.308907 | − | 0.425174i | ||||
\(55\) | 61.9675 | + | 5.38424i | 1.12668 | + | 0.0978953i | ||||
\(56\) | −19.6113 | − | 14.2485i | −0.350202 | − | 0.254437i | ||||
\(57\) | −69.3215 | + | 69.3215i | −1.21617 | + | 1.21617i | ||||
\(58\) | 4.37788 | + | 27.6409i | 0.0754807 | + | 0.476567i | ||||
\(59\) | −67.9339 | − | 22.0730i | −1.15142 | − | 0.374119i | −0.329743 | − | 0.944071i | \(-0.606962\pi\) |
−0.821678 | + | 0.569951i | \(0.806962\pi\) | |||||||
\(60\) | −115.897 | + | 8.17375i | −1.93162 | + | 0.136229i | ||||
\(61\) | 15.0860 | + | 46.4300i | 0.247312 | + | 0.761148i | 0.995248 | + | 0.0973769i | \(0.0310452\pi\) |
−0.747936 | + | 0.663771i | \(0.768955\pi\) | |||||||
\(62\) | −43.0629 | − | 84.5157i | −0.694563 | − | 1.36316i | ||||
\(63\) | −66.7281 | + | 33.9997i | −1.05918 | + | 0.539677i | ||||
\(64\) | 89.9967 | − | 29.2417i | 1.40620 | − | 0.456902i | ||||
\(65\) | 0.415555 | + | 5.89224i | 0.00639315 | + | 0.0906499i | ||||
\(66\) | 52.2176 | − | 160.709i | 0.791176 | − | 2.43499i | ||||
\(67\) | 79.5063 | − | 12.5926i | 1.18666 | − | 0.187949i | 0.468268 | − | 0.883586i | \(-0.344878\pi\) |
0.718393 | + | 0.695638i | \(0.244878\pi\) | |||||||
\(68\) | −17.0535 | − | 17.0535i | −0.250786 | − | 0.250786i | ||||
\(69\) | 23.4424 | − | 32.2657i | 0.339745 | − | 0.467620i | ||||
\(70\) | −8.85824 | + | 101.950i | −0.126546 | + | 1.45643i | ||||
\(71\) | −34.9284 | + | 25.3769i | −0.491949 | + | 0.357422i | −0.805933 | − | 0.592006i | \(-0.798336\pi\) |
0.313985 | + | 0.949428i | \(0.398336\pi\) | |||||||
\(72\) | −6.22673 | + | 39.3140i | −0.0864824 | + | 0.546028i | ||||
\(73\) | 27.3286 | − | 53.6354i | 0.374364 | − | 0.734731i | −0.624566 | − | 0.780972i | \(-0.714724\pi\) |
0.998930 | + | 0.0462407i | \(0.0147241\pi\) | |||||||
\(74\) | 43.2021i | 0.583813i | ||||||||
\(75\) | 64.3801 | + | 91.7115i | 0.858402 | + | 1.22282i | ||||
\(76\) | 113.396 | 1.49206 | ||||||||
\(77\) | −74.8571 | − | 38.1416i | −0.972170 | − | 0.495345i | ||||
\(78\) | 15.8495 | + | 2.51031i | 0.203199 | + | 0.0321835i | ||||
\(79\) | −27.4839 | − | 37.8283i | −0.347898 | − | 0.478840i | 0.598830 | − | 0.800876i | \(-0.295633\pi\) |
−0.946727 | + | 0.322037i | \(0.895633\pi\) | |||||||
\(80\) | −37.2249 | − | 32.3202i | −0.465311 | − | 0.404002i | ||||
\(81\) | −46.7867 | − | 33.9925i | −0.577613 | − | 0.419660i | ||||
\(82\) | −117.075 | + | 117.075i | −1.42774 | + | 1.42774i | ||||
\(83\) | 17.1166 | + | 108.070i | 0.206224 | + | 1.30205i | 0.845874 | + | 0.533382i | \(0.179079\pi\) |
−0.639650 | + | 0.768666i | \(0.720921\pi\) | |||||||
\(84\) | 149.249 | + | 48.4940i | 1.77678 | + | 0.577309i | ||||
\(85\) | −5.61351 | + | 22.5719i | −0.0660413 | + | 0.265551i | ||||
\(86\) | −47.9077 | − | 147.445i | −0.557066 | − | 1.71447i | ||||
\(87\) | −18.7904 | − | 36.8782i | −0.215981 | − | 0.423887i | ||||
\(88\) | −39.7862 | + | 20.2721i | −0.452116 | + | 0.230365i | ||||
\(89\) | 63.0322 | − | 20.4804i | 0.708227 | − | 0.230117i | 0.0673154 | − | 0.997732i | \(-0.478557\pi\) |
0.640911 | + | 0.767615i | \(0.278557\pi\) | |||||||
\(90\) | 155.761 | − | 63.0397i | 1.73068 | − | 0.700441i | ||||
\(91\) | 2.46544 | − | 7.58786i | 0.0270928 | − | 0.0833830i | ||||
\(92\) | −45.5639 | + | 7.21661i | −0.495259 | + | 0.0784414i | ||||
\(93\) | 99.1969 | + | 99.1969i | 1.06663 | + | 1.06663i | ||||
\(94\) | −8.00690 | + | 11.0206i | −0.0851798 | + | 0.117240i | ||||
\(95\) | −56.3820 | − | 93.7088i | −0.593495 | − | 0.986409i | ||||
\(96\) | −160.411 | + | 116.546i | −1.67095 | + | 1.21402i | ||||
\(97\) | 8.99168 | − | 56.7712i | 0.0926977 | − | 0.585270i | −0.896993 | − | 0.442046i | \(-0.854253\pi\) |
0.989690 | − | 0.143225i | \(-0.0457471\pi\) | |||||||
\(98\) | −4.66566 | + | 9.15688i | −0.0476088 | + | 0.0934375i | ||||
\(99\) | 137.953i | 1.39346i | ||||||||
\(100\) | 22.3544 | − | 127.668i | 0.223544 | − | 1.27668i | ||||
\(101\) | −4.10343 | −0.0406280 | −0.0203140 | − | 0.999794i | \(-0.506467\pi\) | ||||
−0.0203140 | + | 0.999794i | \(0.506467\pi\) | |||||||
\(102\) | 56.3011 | + | 28.6869i | 0.551972 | + | 0.281244i | ||||
\(103\) | −93.2854 | − | 14.7750i | −0.905683 | − | 0.143446i | −0.313818 | − | 0.949483i | \(-0.601608\pi\) |
−0.591865 | + | 0.806037i | \(0.701608\pi\) | |||||||
\(104\) | −2.49248 | − | 3.43060i | −0.0239661 | − | 0.0329866i | ||||
\(105\) | −34.1338 | − | 147.449i | −0.325084 | − | 1.40427i | ||||
\(106\) | 171.878 | + | 124.877i | 1.62149 | + | 1.17808i | ||||
\(107\) | 142.289 | − | 142.289i | 1.32980 | − | 1.32980i | 0.424266 | − | 0.905538i | \(-0.360532\pi\) |
0.905538 | − | 0.424266i | \(-0.139468\pi\) | |||||||
\(108\) | −7.59466 | − | 47.9508i | −0.0703209 | − | 0.443989i | ||||
\(109\) | −129.134 | − | 41.9581i | −1.18471 | − | 0.384936i | −0.350597 | − | 0.936526i | \(-0.614021\pi\) |
−0.834115 | + | 0.551590i | \(0.814021\pi\) | |||||||
\(110\) | 159.921 | + | 99.7971i | 1.45383 | + | 0.907246i | ||||
\(111\) | −19.7444 | − | 60.7671i | −0.177878 | − | 0.547451i | ||||
\(112\) | 30.2294 | + | 59.3286i | 0.269906 | + | 0.529720i | ||||
\(113\) | −82.9619 | + | 42.2712i | −0.734176 | + | 0.374081i | −0.780758 | − | 0.624833i | \(-0.785167\pi\) |
0.0465823 | + | 0.998914i | \(0.485167\pi\) | |||||||
\(114\) | −282.562 | + | 91.8101i | −2.47862 | + | 0.805352i | ||||
\(115\) | 28.6186 | + | 34.0650i | 0.248857 | + | 0.296218i | ||||
\(116\) | −14.7941 | + | 45.5314i | −0.127535 | + | 0.392512i | ||||
\(117\) | −12.9393 | + | 2.04938i | −0.110592 | + | 0.0175161i | ||||
\(118\) | −153.070 | − | 153.070i | −1.29720 | − | 1.29720i | ||||
\(119\) | 18.4660 | − | 25.4162i | 0.155176 | − | 0.213582i | ||||
\(120\) | −74.0649 | − | 31.3866i | −0.617208 | − | 0.261555i | ||||
\(121\) | −27.3112 | + | 19.8428i | −0.225713 | + | 0.163990i | ||||
\(122\) | −23.1447 | + | 146.130i | −0.189710 | + | 1.19778i | ||||
\(123\) | 111.169 | − | 218.181i | 0.903810 | − | 1.77383i | ||||
\(124\) | − | 162.267i | − | 1.30860i | ||||||
\(125\) | −116.617 | + | 45.0046i | −0.932938 | + | 0.360037i | ||||
\(126\) | −226.962 | −1.80129 | ||||||||
\(127\) | −43.9744 | − | 22.4061i | −0.346255 | − | 0.176426i | 0.272210 | − | 0.962238i | \(-0.412245\pi\) |
−0.618465 | + | 0.785812i | \(0.712245\pi\) | |||||||
\(128\) | 108.474 | + | 17.1806i | 0.847454 | + | 0.134224i | ||||
\(129\) | 134.771 | + | 185.497i | 1.04474 | + | 1.43796i | ||||
\(130\) | −6.98475 | + | 16.4824i | −0.0537289 | + | 0.126787i | ||||
\(131\) | 109.772 | + | 79.7539i | 0.837953 | + | 0.608809i | 0.921798 | − | 0.387670i | \(-0.126720\pi\) |
−0.0838450 | + | 0.996479i | \(0.526720\pi\) | |||||||
\(132\) | 204.406 | − | 204.406i | 1.54853 | − | 1.54853i | ||||
\(133\) | 23.1078 | + | 145.897i | 0.173743 | + | 1.09697i | ||||
\(134\) | 232.014 | + | 75.3858i | 1.73144 | + | 0.562580i | ||||
\(135\) | −35.8496 | + | 30.1178i | −0.265552 | + | 0.223095i | ||||
\(136\) | −5.15983 | − | 15.8803i | −0.0379400 | − | 0.116767i | ||||
\(137\) | 84.2247 | + | 165.300i | 0.614779 | + | 1.20657i | 0.963087 | + | 0.269192i | \(0.0867565\pi\) |
−0.348308 | + | 0.937380i | \(0.613243\pi\) | |||||||
\(138\) | 107.694 | − | 54.8727i | 0.780389 | − | 0.397628i | ||||
\(139\) | 122.872 | − | 39.9236i | 0.883973 | − | 0.287220i | 0.168367 | − | 0.985724i | \(-0.446151\pi\) |
0.715606 | + | 0.698504i | \(0.246151\pi\) | |||||||
\(140\) | −92.6806 | + | 148.517i | −0.662004 | + | 1.06083i | ||||
\(141\) | 6.22565 | − | 19.1606i | 0.0441535 | − | 0.135891i | ||||
\(142\) | −129.231 | + | 20.4681i | −0.910076 | + | 0.144142i | ||||
\(143\) | −10.3920 | − | 10.3920i | −0.0726715 | − | 0.0726715i | ||||
\(144\) | 64.2658 | − | 88.4543i | 0.446291 | − | 0.614266i | ||||
\(145\) | 44.9822 | − | 10.4132i | 0.310222 | − | 0.0718151i | ||||
\(146\) | 147.589 | − | 107.230i | 1.01088 | − | 0.734449i | ||||
\(147\) | 2.37769 | − | 15.0122i | 0.0161748 | − | 0.102123i | ||||
\(148\) | −33.5525 | + | 65.8506i | −0.226706 | + | 0.444936i | ||||
\(149\) | − | 232.485i | − | 1.56030i | −0.625592 | − | 0.780150i | \(-0.715143\pi\) | ||
0.625592 | − | 0.780150i | \(-0.284857\pi\) | |||||||
\(150\) | 47.6618 | + | 336.223i | 0.317745 | + | 2.24149i | ||||
\(151\) | 172.702 | 1.14372 | 0.571861 | − | 0.820351i | \(-0.306222\pi\) | ||||
0.571861 | + | 0.820351i | \(0.306222\pi\) | |||||||
\(152\) | 69.9530 | + | 35.6428i | 0.460217 | + | 0.234492i | ||||
\(153\) | −50.9509 | − | 8.06982i | −0.333012 | − | 0.0527439i | ||||
\(154\) | −149.657 | − | 205.985i | −0.971797 | − | 1.33756i | ||||
\(155\) | −134.095 | + | 80.6810i | −0.865126 | + | 0.520522i | ||||
\(156\) | 22.2089 | + | 16.1357i | 0.142365 | + | 0.103434i | ||||
\(157\) | −154.466 | + | 154.466i | −0.983858 | + | 0.983858i | −0.999872 | − | 0.0160139i | \(-0.994902\pi\) |
0.0160139 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(158\) | −22.1675 | − | 139.960i | −0.140301 | − | 0.885825i | ||||
\(159\) | −298.832 | − | 97.0963i | −1.87945 | − | 0.610669i | ||||
\(160\) | −82.9813 | − | 205.034i | −0.518633 | − | 1.28146i | ||||
\(161\) | −18.5699 | − | 57.1522i | −0.115341 | − | 0.354983i | ||||
\(162\) | −79.5677 | − | 156.160i | −0.491158 | − | 0.963953i | ||||
\(163\) | 32.1939 | − | 16.4036i | 0.197508 | − | 0.100636i | −0.352439 | − | 0.935835i | \(-0.614648\pi\) |
0.549948 | + | 0.835199i | \(0.314648\pi\) | |||||||
\(164\) | −269.376 | + | 87.5254i | −1.64253 | + | 0.533692i | ||||
\(165\) | −270.550 | − | 67.2845i | −1.63970 | − | 0.407785i | ||||
\(166\) | −102.469 | + | 315.368i | −0.617284 | + | 1.89980i | ||||
\(167\) | −11.3916 | + | 1.80425i | −0.0682130 | + | 0.0108039i | −0.190448 | − | 0.981697i | \(-0.560994\pi\) |
0.122235 | + | 0.992501i | \(0.460994\pi\) | |||||||
\(168\) | 76.8275 | + | 76.8275i | 0.457306 | + | 0.457306i | ||||
\(169\) | −98.5154 | + | 135.595i | −0.582931 | + | 0.802336i | ||||
\(170\) | −46.2135 | + | 53.2266i | −0.271844 | + | 0.313098i | ||||
\(171\) | 196.228 | − | 142.568i | 1.14753 | − | 0.833731i | ||||
\(172\) | 41.4886 | − | 261.948i | 0.241213 | − | 1.52296i | ||||
\(173\) | −44.0149 | + | 86.3841i | −0.254421 | + | 0.499330i | −0.982523 | − | 0.186139i | \(-0.940403\pi\) |
0.728102 | + | 0.685469i | \(0.240403\pi\) | |||||||
\(174\) | − | 125.434i | − | 0.720883i | ||||||
\(175\) | 168.814 | + | 2.74537i | 0.964649 | + | 0.0156878i | ||||
\(176\) | 122.655 | 0.696904 | ||||||||
\(177\) | 285.261 | + | 145.348i | 1.61165 | + | 0.821175i | ||||
\(178\) | 198.382 | + | 31.4206i | 1.11450 | + | 0.176520i | ||||
\(179\) | 119.212 | + | 164.081i | 0.665987 | + | 0.916653i | 0.999661 | − | 0.0260360i | \(-0.00828846\pi\) |
−0.333674 | + | 0.942689i | \(0.608288\pi\) | |||||||
\(180\) | 286.377 | + | 24.8828i | 1.59098 | + | 0.138238i | ||||
\(181\) | −245.629 | − | 178.460i | −1.35707 | − | 0.985966i | −0.998625 | − | 0.0524129i | \(-0.983309\pi\) |
−0.358440 | − | 0.933553i | \(-0.616691\pi\) | |||||||
\(182\) | 17.0971 | − | 17.0971i | 0.0939403 | − | 0.0939403i | ||||
\(183\) | −34.2300 | − | 216.120i | −0.187049 | − | 1.18098i | ||||
\(184\) | −30.3762 | − | 9.86982i | −0.165088 | − | 0.0536403i | ||||
\(185\) | 71.1005 | − | 5.01441i | 0.384327 | − | 0.0271049i | ||||
\(186\) | 131.378 | + | 404.338i | 0.706331 | + | 2.17386i | ||||
\(187\) | −26.2726 | − | 51.5628i | −0.140495 | − | 0.275737i | ||||
\(188\) | −20.7635 | + | 10.5795i | −0.110444 | + | 0.0562740i | ||||
\(189\) | 60.1462 | − | 19.5427i | 0.318234 | − | 0.103400i | ||||
\(190\) | −23.3167 | − | 330.612i | −0.122719 | − | 1.74006i | ||||
\(191\) | 28.3111 | − | 87.1326i | 0.148226 | − | 0.456192i | −0.849186 | − | 0.528094i | \(-0.822907\pi\) |
0.997412 | + | 0.0719021i | \(0.0229069\pi\) | |||||||
\(192\) | −418.912 | + | 66.3491i | −2.18183 | + | 0.345568i | ||||
\(193\) | 129.347 | + | 129.347i | 0.670189 | + | 0.670189i | 0.957760 | − | 0.287570i | \(-0.0928475\pi\) |
−0.287570 | + | 0.957760i | \(0.592847\pi\) | |||||||
\(194\) | 102.389 | − | 140.926i | 0.527777 | − | 0.726423i | ||||
\(195\) | 2.29175 | − | 26.3759i | 0.0117526 | − | 0.135261i | ||||
\(196\) | −14.2232 | + | 10.3338i | −0.0725673 | + | 0.0527233i | ||||
\(197\) | 19.2400 | − | 121.476i | 0.0976648 | − | 0.616631i | −0.889501 | − | 0.456933i | \(-0.848948\pi\) |
0.987166 | − | 0.159698i | \(-0.0510521\pi\) | |||||||
\(198\) | −189.803 | + | 372.509i | −0.958600 | + | 1.88136i | ||||
\(199\) | 390.191i | 1.96076i | 0.197114 | + | 0.980381i | \(0.436843\pi\) | ||||
−0.197114 | + | 0.980381i | \(0.563157\pi\) | |||||||
\(200\) | 53.9188 | − | 71.7304i | 0.269594 | − | 0.358652i | ||||
\(201\) | −360.798 | −1.79501 | ||||||||
\(202\) | −11.0803 | − | 5.64572i | −0.0548532 | − | 0.0279491i | ||||
\(203\) | −61.5958 | − | 9.75581i | −0.303427 | − | 0.0480582i | ||||
\(204\) | 63.5372 | + | 87.4515i | 0.311457 | + | 0.428684i | ||||
\(205\) | 206.266 | + | 179.089i | 1.00618 | + | 0.873604i | ||||
\(206\) | −231.567 | − | 168.243i | −1.12411 | − | 0.816715i | ||||
\(207\) | −69.7734 | + | 69.7734i | −0.337070 | + | 0.337070i | ||||
\(208\) | 1.82213 | + | 11.5045i | 0.00876023 | + | 0.0553099i | ||||
\(209\) | 258.782 | + | 84.0834i | 1.23819 | + | 0.402313i | ||||
\(210\) | 110.698 | − | 445.114i | 0.527131 | − | 2.11959i | ||||
\(211\) | −34.5087 | − | 106.207i | −0.163548 | − | 0.503350i | 0.835378 | − | 0.549676i | \(-0.185249\pi\) |
−0.998926 | + | 0.0463257i | \(0.985249\pi\) | |||||||
\(212\) | 165.000 | + | 323.831i | 0.778302 | + | 1.52750i | ||||
\(213\) | 172.418 | − | 87.8515i | 0.809476 | − | 0.412449i | ||||
\(214\) | 579.987 | − | 188.449i | 2.71022 | − | 0.880603i | ||||
\(215\) | −237.098 | + | 95.9583i | −1.10278 | + | 0.446318i | ||||
\(216\) | 10.3869 | − | 31.9675i | 0.0480873 | − | 0.147998i | ||||
\(217\) | 208.774 | − | 33.0665i | 0.962091 | − | 0.152380i | ||||
\(218\) | −290.967 | − | 290.967i | −1.33471 | − | 1.33471i | ||||
\(219\) | −158.588 | + | 218.278i | −0.724148 | + | 0.996704i | ||||
\(220\) | 166.252 | + | 276.316i | 0.755689 | + | 1.25598i | ||||
\(221\) | 4.44605 | − | 3.23024i | 0.0201179 | − | 0.0146165i | ||||
\(222\) | 30.2914 | − | 191.253i | 0.136448 | − | 0.861498i | ||||
\(223\) | −20.5207 | + | 40.2741i | −0.0920209 | + | 0.180601i | −0.932429 | − | 0.361352i | \(-0.882315\pi\) |
0.840408 | + | 0.541954i | \(0.182315\pi\) | |||||||
\(224\) | 298.758i | 1.33374i | ||||||||
\(225\) | −121.827 | − | 249.029i | −0.541455 | − | 1.10680i | ||||
\(226\) | −282.178 | −1.24858 | ||||||||
\(227\) | −107.017 | − | 54.5277i | −0.471439 | − | 0.240210i | 0.202096 | − | 0.979366i | \(-0.435225\pi\) |
−0.673535 | + | 0.739156i | \(0.735225\pi\) | |||||||
\(228\) | −501.997 | − | 79.5085i | −2.20174 | − | 0.348722i | ||||
\(229\) | −71.1775 | − | 97.9675i | −0.310819 | − | 0.427806i | 0.624817 | − | 0.780771i | \(-0.285173\pi\) |
−0.935636 | + | 0.352965i | \(0.885173\pi\) | |||||||
\(230\) | 30.4092 | + | 131.360i | 0.132214 | + | 0.571128i | ||||
\(231\) | 304.643 | + | 221.336i | 1.31880 | + | 0.958166i | ||||
\(232\) | −23.4377 | + | 23.4377i | −0.101025 | + | 0.101025i | ||||
\(233\) | −30.8904 | − | 195.034i | −0.132577 | − | 0.837056i | −0.960918 | − | 0.276833i | \(-0.910715\pi\) |
0.828341 | − | 0.560224i | \(-0.189285\pi\) | |||||||
\(234\) | −37.7592 | − | 12.2687i | −0.161364 | − | 0.0524304i | ||||
\(235\) | 19.0666 | + | 11.8983i | 0.0811343 | + | 0.0506311i | ||||
\(236\) | −114.436 | − | 352.196i | −0.484896 | − | 1.49236i | ||||
\(237\) | 95.1456 | + | 186.734i | 0.401458 | + | 0.787906i | ||||
\(238\) | 84.8320 | − | 43.2241i | 0.356437 | − | 0.181614i | ||||
\(239\) | −105.011 | + | 34.1201i | −0.439375 | + | 0.142762i | −0.520347 | − | 0.853955i | \(-0.674198\pi\) |
0.0809720 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(240\) | 142.130 | + | 169.179i | 0.592209 | + | 0.704914i | ||||
\(241\) | 21.0011 | − | 64.6348i | 0.0871416 | − | 0.268194i | −0.897985 | − | 0.440027i | \(-0.854969\pi\) |
0.985126 | + | 0.171833i | \(0.0549689\pi\) | |||||||
\(242\) | −101.048 | + | 16.0045i | −0.417555 | + | 0.0661342i | ||||
\(243\) | 242.881 | + | 242.881i | 0.999511 | + | 0.999511i | ||||
\(244\) | −148.768 | + | 204.762i | −0.609706 | + | 0.839188i | ||||
\(245\) | 15.6116 | + | 6.61574i | 0.0637207 | + | 0.0270030i | ||||
\(246\) | 600.369 | − | 436.194i | 2.44053 | − | 1.77315i | ||||
\(247\) | −4.04223 | + | 25.5216i | −0.0163653 | + | 0.103326i | ||||
\(248\) | 51.0038 | − | 100.101i | 0.205661 | − | 0.403632i | ||||
\(249\) | − | 490.419i | − | 1.96955i | ||||||
\(250\) | −376.817 | − | 38.9240i | −1.50727 | − | 0.155696i | ||||
\(251\) | −184.575 | −0.735358 | −0.367679 | − | 0.929953i | \(-0.619847\pi\) | ||||
−0.367679 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(252\) | −345.945 | − | 176.268i | −1.37280 | − | 0.699476i | ||||
\(253\) | −109.332 | − | 17.3166i | −0.432144 | − | 0.0684449i | ||||
\(254\) | −87.9151 | − | 121.005i | −0.346122 | − | 0.476396i | ||||
\(255\) | 40.6770 | − | 95.9879i | 0.159517 | − | 0.376423i | ||||
\(256\) | −36.9523 | − | 26.8474i | −0.144345 | − | 0.104873i | ||||
\(257\) | 110.251 | − | 110.251i | 0.428992 | − | 0.428992i | −0.459293 | − | 0.888285i | \(-0.651897\pi\) |
0.888285 | + | 0.459293i | \(0.151897\pi\) | |||||||
\(258\) | 108.702 | + | 686.317i | 0.421325 | + | 2.66014i | ||||
\(259\) | −91.5611 | − | 29.7500i | −0.353518 | − | 0.114865i | ||||
\(260\) | −23.4473 | + | 19.6985i | −0.0901820 | + | 0.0757633i | ||||
\(261\) | 31.6440 | + | 97.3903i | 0.121241 | + | 0.373143i | ||||
\(262\) | 186.683 | + | 366.387i | 0.712532 | + | 1.39842i | ||||
\(263\) | −295.330 | + | 150.478i | −1.12293 | + | 0.572160i | −0.913977 | − | 0.405766i | \(-0.867005\pi\) |
−0.208950 | + | 0.977926i | \(0.567005\pi\) | |||||||
\(264\) | 190.345 | − | 61.8467i | 0.721002 | − | 0.234268i | ||||
\(265\) | 185.568 | − | 297.365i | 0.700257 | − | 1.12213i | ||||
\(266\) | −138.335 | + | 425.752i | −0.520058 | + | 1.60057i | ||||
\(267\) | −293.399 | + | 46.4698i | −1.09887 | + | 0.174044i | ||||
\(268\) | 295.097 | + | 295.097i | 1.10111 | + | 1.10111i | ||||
\(269\) | 306.607 | − | 422.008i | 1.13980 | − | 1.56880i | 0.371857 | − | 0.928290i | \(-0.378721\pi\) |
0.767946 | − | 0.640515i | \(-0.221279\pi\) | |||||||
\(270\) | −138.241 | + | 32.0022i | −0.512003 | + | 0.118527i | ||||
\(271\) | 33.2207 | − | 24.1363i | 0.122586 | − | 0.0890638i | −0.524803 | − | 0.851224i | \(-0.675861\pi\) |
0.647389 | + | 0.762160i | \(0.275861\pi\) | |||||||
\(272\) | −7.17496 | + | 45.3009i | −0.0263785 | + | 0.166547i | ||||
\(273\) | −16.2346 | + | 31.8622i | −0.0594674 | + | 0.116711i | ||||
\(274\) | 562.236i | 2.05195i | ||||||||
\(275\) | 145.681 | − | 274.775i | 0.529747 | − | 0.999182i | ||||
\(276\) | 206.768 | 0.749159 | ||||||||
\(277\) | −471.855 | − | 240.422i | −1.70345 | − | 0.867950i | −0.985040 | − | 0.172327i | \(-0.944872\pi\) |
−0.718407 | − | 0.695623i | \(-0.755128\pi\) | |||||||
\(278\) | 386.717 | + | 61.2499i | 1.39107 | + | 0.220323i | ||||
\(279\) | −204.011 | − | 280.797i | −0.731221 | − | 1.00644i | ||||
\(280\) | −103.855 | + | 62.4870i | −0.370912 | + | 0.223168i | ||||
\(281\) | 130.914 | + | 95.1145i | 0.465886 | + | 0.338486i | 0.795836 | − | 0.605513i | \(-0.207032\pi\) |
−0.329950 | + | 0.943998i | \(0.607032\pi\) | |||||||
\(282\) | 43.1731 | − | 43.1731i | 0.153096 | − | 0.153096i | ||||
\(283\) | −50.0186 | − | 315.805i | −0.176744 | − | 1.11592i | −0.903362 | − | 0.428878i | \(-0.858909\pi\) |
0.726618 | − | 0.687042i | \(-0.241091\pi\) | |||||||
\(284\) | −212.875 | − | 69.1674i | −0.749561 | − | 0.243547i | ||||
\(285\) | 183.894 | + | 454.374i | 0.645243 | + | 1.59430i | ||||
\(286\) | −13.7633 | − | 42.3591i | −0.0481235 | − | 0.148109i | ||||
\(287\) | −167.504 | − | 328.745i | −0.583637 | − | 1.14545i | ||||
\(288\) | 437.098 | − | 222.712i | 1.51770 | − | 0.773307i | ||||
\(289\) | −254.274 | + | 82.6188i | −0.879842 | + | 0.285878i | ||||
\(290\) | 135.791 | + | 33.7705i | 0.468244 | + | 0.116450i | ||||
\(291\) | −79.6109 | + | 245.017i | −0.273577 | + | 0.841984i | ||||
\(292\) | 308.240 | − | 48.8204i | 1.05562 | − | 0.167193i | ||||
\(293\) | 252.694 | + | 252.694i | 0.862436 | + | 0.862436i | 0.991621 | − | 0.129184i | \(-0.0412359\pi\) |
−0.129184 | + | 0.991621i | \(0.541236\pi\) | |||||||
\(294\) | 27.0749 | − | 37.2654i | 0.0920916 | − | 0.126753i | ||||
\(295\) | −234.150 | + | 269.684i | −0.793730 | + | 0.914182i | ||||
\(296\) | −41.3964 | + | 30.0762i | −0.139853 | + | 0.101609i | ||||
\(297\) | 18.2237 | − | 115.060i | 0.0613593 | − | 0.387407i | ||||
\(298\) | 319.865 | − | 627.770i | 1.07337 | − | 2.10661i | ||||
\(299\) | − | 10.5121i | − | 0.0351576i | ||||||
\(300\) | −188.476 | + | 549.501i | −0.628254 | + | 1.83167i | ||||
\(301\) | 345.479 | 1.14777 | ||||||||
\(302\) | 466.341 | + | 237.613i | 1.54417 | + | 0.786796i | ||||
\(303\) | 18.1656 | + | 2.87714i | 0.0599524 | + | 0.00949552i | ||||
\(304\) | −126.759 | − | 174.468i | −0.416969 | − | 0.573909i | ||||
\(305\) | 243.181 | + | 21.1295i | 0.797315 | + | 0.0692772i | ||||
\(306\) | −126.478 | − | 91.8916i | −0.413327 | − | 0.300299i | ||||
\(307\) | 260.783 | − | 260.783i | 0.849457 | − | 0.849457i | −0.140609 | − | 0.990065i | \(-0.544906\pi\) |
0.990065 | + | 0.140609i | \(0.0449060\pi\) | |||||||
\(308\) | −68.1370 | − | 430.200i | −0.221224 | − | 1.39675i | ||||
\(309\) | 402.608 | + | 130.815i | 1.30294 | + | 0.423350i | ||||
\(310\) | −473.096 | + | 33.3655i | −1.52612 | + | 0.107630i | ||||
\(311\) | 117.574 | + | 361.855i | 0.378051 | + | 1.16352i | 0.941397 | + | 0.337300i | \(0.109514\pi\) |
−0.563347 | + | 0.826221i | \(0.690486\pi\) | |||||||
\(312\) | 8.62862 | + | 16.9346i | 0.0276558 | + | 0.0542777i | ||||
\(313\) | −365.880 | + | 186.425i | −1.16895 | + | 0.595607i | −0.927139 | − | 0.374717i | \(-0.877740\pi\) |
−0.241806 | + | 0.970325i | \(0.577740\pi\) | |||||||
\(314\) | −629.620 | + | 204.576i | −2.00516 | + | 0.651516i | ||||
\(315\) | 26.3432 | + | 373.526i | 0.0836291 | + | 1.18580i | ||||
\(316\) | 74.9102 | − | 230.550i | 0.237058 | − | 0.729588i | ||||
\(317\) | −171.773 | + | 27.2062i | −0.541872 | + | 0.0858241i | −0.421370 | − | 0.906889i | \(-0.638450\pi\) |
−0.120502 | + | 0.992713i | \(0.538450\pi\) | |||||||
\(318\) | −673.335 | − | 673.335i | −2.11740 | − | 2.11740i | ||||
\(319\) | −67.5231 | + | 92.9375i | −0.211671 | + | 0.291340i | ||||
\(320\) | 40.9560 | − | 471.365i | 0.127988 | − | 1.47301i | ||||
\(321\) | −729.669 | + | 530.136i | −2.27311 | + | 1.65151i | ||||
\(322\) | 28.4895 | − | 179.876i | 0.0884767 | − | 0.558620i | ||||
\(323\) | −46.1930 | + | 90.6588i | −0.143012 | + | 0.280677i | ||||
\(324\) | − | 299.822i | − | 0.925376i | ||||||
\(325\) | 27.9368 | + | 9.58216i | 0.0859592 | + | 0.0294836i | ||||
\(326\) | 109.501 | 0.335892 | ||||||||
\(327\) | 542.246 | + | 276.288i | 1.65824 | + | 0.844917i | ||||
\(328\) | −193.686 | − | 30.6768i | −0.590506 | − | 0.0935269i | ||||
\(329\) | −17.8428 | − | 24.5585i | −0.0542335 | − | 0.0746460i | ||||
\(330\) | −637.984 | − | 553.924i | −1.93328 | − | 1.67856i | ||||
\(331\) | 31.9665 | + | 23.2250i | 0.0965755 | + | 0.0701662i | 0.635025 | − | 0.772492i | \(-0.280990\pi\) |
−0.538450 | + | 0.842658i | \(0.680990\pi\) | |||||||
\(332\) | −401.115 | + | 401.115i | −1.20818 | + | 1.20818i | ||||
\(333\) | 24.7295 | + | 156.136i | 0.0742628 | + | 0.468877i | ||||
\(334\) | −33.2426 | − | 10.8012i | −0.0995289 | − | 0.0323389i | ||||
\(335\) | 97.1376 | − | 390.589i | 0.289963 | − | 1.16594i | ||||
\(336\) | −92.2248 | − | 283.839i | −0.274479 | − | 0.844758i | ||||
\(337\) | 53.9081 | + | 105.801i | 0.159965 | + | 0.313948i | 0.957052 | − | 0.289915i | \(-0.0936271\pi\) |
−0.797088 | + | 0.603864i | \(0.793627\pi\) | |||||||
\(338\) | −452.576 | + | 230.599i | −1.33898 | + | 0.682246i | ||||
\(339\) | 396.905 | − | 128.962i | 1.17081 | − | 0.380419i | ||||
\(340\) | −111.779 | + | 45.2390i | −0.328760 | + | 0.133056i | ||||
\(341\) | 120.321 | − | 370.309i | 0.352847 | − | 1.08595i | ||||
\(342\) | 726.021 | − | 114.990i | 2.12287 | − | 0.336229i | ||||
\(343\) | −250.188 | − | 250.188i | −0.729413 | − | 0.729413i | ||||
\(344\) | 107.930 | − | 148.552i | 0.313749 | − | 0.431838i | ||||
\(345\) | −102.807 | − | 170.869i | −0.297992 | − | 0.495273i | ||||
\(346\) | −237.704 | + | 172.702i | −0.687005 | + | 0.499138i | ||||
\(347\) | −67.0138 | + | 423.108i | −0.193123 | + | 1.21933i | 0.680507 | + | 0.732742i | \(0.261760\pi\) |
−0.873630 | + | 0.486591i | \(0.838240\pi\) | |||||||
\(348\) | 97.4168 | − | 191.191i | 0.279933 | − | 0.549400i | ||||
\(349\) | − | 111.740i | − | 0.320171i | −0.987103 | − | 0.160085i | \(-0.948823\pi\) | ||
0.987103 | − | 0.160085i | \(-0.0511769\pi\) | |||||||
\(350\) | 452.064 | + | 239.676i | 1.29161 | + | 0.684789i | ||||
\(351\) | 11.0628 | 0.0315180 | ||||||||
\(352\) | 490.346 | + | 249.844i | 1.39303 | + | 0.709784i | ||||
\(353\) | 329.586 | + | 52.2014i | 0.933673 | + | 0.147879i | 0.604694 | − | 0.796458i | \(-0.293295\pi\) |
0.328979 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(354\) | 570.304 | + | 784.956i | 1.61103 | + | 2.21739i | ||||
\(355\) | 48.6853 | + | 210.307i | 0.137142 | + | 0.592415i | ||||
\(356\) | 277.979 | + | 201.964i | 0.780840 | + | 0.567314i | ||||
\(357\) | −99.5682 | + | 99.5682i | −0.278902 | + | 0.278902i | ||||
\(358\) | 96.1519 | + | 607.079i | 0.268581 | + | 1.69575i | ||||
\(359\) | −111.358 | − | 36.1824i | −0.310189 | − | 0.100787i | 0.149786 | − | 0.988718i | \(-0.452142\pi\) |
−0.459975 | + | 0.887932i | \(0.652142\pi\) | |||||||
\(360\) | 168.842 | + | 105.364i | 0.469005 | + | 0.292678i | ||||
\(361\) | −36.2820 | − | 111.664i | −0.100504 | − | 0.309320i | ||||
\(362\) | −417.728 | − | 819.838i | −1.15395 | − | 2.26475i | ||||
\(363\) | 134.818 | − | 68.6930i | 0.371398 | − | 0.189237i | ||||
\(364\) | 39.3385 | − | 12.7819i | 0.108073 | − | 0.0351150i | ||||
\(365\) | −193.605 | − | 230.450i | −0.530424 | − | 0.631370i | ||||
\(366\) | 204.919 | − | 630.676i | 0.559889 | − | 1.72316i | ||||
\(367\) | 153.553 | − | 24.3204i | 0.418401 | − | 0.0662682i | 0.0563153 | − | 0.998413i | \(-0.482065\pi\) |
0.362086 | + | 0.932145i | \(0.382065\pi\) | |||||||
\(368\) | 62.0362 | + | 62.0362i | 0.168577 | + | 0.168577i | ||||
\(369\) | −356.102 | + | 490.133i | −0.965047 | + | 1.32827i | ||||
\(370\) | 198.889 | + | 84.2836i | 0.537538 | + | 0.227794i | ||||
\(371\) | −383.019 | + | 278.280i | −1.03240 | + | 0.750081i | ||||
\(372\) | −113.774 | + | 718.343i | −0.305845 | + | 1.93103i | ||||
\(373\) | 160.733 | − | 315.456i | 0.430919 | − | 0.845725i | −0.568811 | − | 0.822468i | \(-0.692596\pi\) |
0.999730 | − | 0.0232570i | \(-0.00740360\pi\) | |||||||
\(374\) | − | 175.381i | − | 0.468932i | ||||||
\(375\) | 547.811 | − | 117.465i | 1.46083 | − | 0.313240i | ||||
\(376\) | −16.1341 | −0.0429099 | ||||||||
\(377\) | −9.72020 | − | 4.95269i | −0.0257830 | − | 0.0131371i | ||||
\(378\) | 189.299 | + | 29.9819i | 0.500790 | + | 0.0793173i | ||||
\(379\) | 210.869 | + | 290.236i | 0.556382 | + | 0.765794i | 0.990861 | − | 0.134888i | \(-0.0430674\pi\) |
−0.434479 | + | 0.900682i | \(0.643067\pi\) | |||||||
\(380\) | 221.226 | − | 522.042i | 0.582175 | − | 1.37379i | ||||
\(381\) | 178.961 | + | 130.023i | 0.469714 | + | 0.341267i | ||||
\(382\) | 196.329 | − | 196.329i | 0.513951 | − | 0.513951i | ||||
\(383\) | −8.47845 | − | 53.5308i | −0.0221370 | − | 0.139767i | 0.974144 | − | 0.225926i | \(-0.0725408\pi\) |
−0.996281 | + | 0.0861588i | \(0.972541\pi\) | |||||||
\(384\) | −468.160 | − | 152.115i | −1.21917 | − | 0.396132i | ||||
\(385\) | −321.632 | + | 270.208i | −0.835407 | + | 0.701838i | ||||
\(386\) | 171.308 | + | 527.232i | 0.443803 | + | 1.36589i | ||||
\(387\) | −257.541 | − | 505.453i | −0.665482 | − | 1.30608i | ||||
\(388\) | 265.514 | − | 135.286i | 0.684315 | − | 0.348676i | ||||
\(389\) | −340.490 | + | 110.632i | −0.875296 | + | 0.284401i | −0.712003 | − | 0.702176i | \(-0.752212\pi\) |
−0.163294 | + | 0.986578i | \(0.552212\pi\) | |||||||
\(390\) | 42.4777 | − | 68.0687i | 0.108917 | − | 0.174535i | ||||
\(391\) | 12.7912 | − | 39.3674i | 0.0327142 | − | 0.100684i | ||||
\(392\) | −12.0222 | + | 1.90414i | −0.0306690 | + | 0.00485749i | ||||
\(393\) | −430.032 | − | 430.032i | −1.09423 | − | 1.09423i | ||||
\(394\) | 219.087 | − | 301.547i | 0.556057 | − | 0.765347i | ||||
\(395\) | −227.769 | + | 52.7275i | −0.576629 | + | 0.133487i | ||||
\(396\) | −578.611 | + | 420.386i | −1.46114 | + | 1.06158i | ||||
\(397\) | −8.95869 | + | 56.5629i | −0.0225660 | + | 0.142476i | −0.996399 | − | 0.0847891i | \(-0.972978\pi\) |
0.973833 | + | 0.227265i | \(0.0729784\pi\) | |||||||
\(398\) | −536.846 | + | 1053.62i | −1.34886 | + | 2.64729i | ||||
\(399\) | − | 662.075i | − | 1.65934i | ||||||
\(400\) | −221.414 | + | 108.318i | −0.553536 | + | 0.270795i | ||||
\(401\) | 410.265 | 1.02310 | 0.511552 | − | 0.859252i | \(-0.329071\pi\) | ||||
0.511552 | + | 0.859252i | \(0.329071\pi\) | |||||||
\(402\) | −974.249 | − | 496.405i | −2.42351 | − | 1.23484i | ||||
\(403\) | 36.5207 | + | 5.78431i | 0.0906221 | + | 0.0143531i | ||||
\(404\) | −12.5044 | − | 17.2109i | −0.0309516 | − | 0.0426012i | ||||
\(405\) | −247.768 | + | 149.075i | −0.611772 | + | 0.368086i | ||||
\(406\) | −152.902 | − | 111.090i | −0.376607 | − | 0.273621i | ||||
\(407\) | −125.398 | + | 125.398i | −0.308104 | + | 0.308104i | ||||
\(408\) | 11.7076 | + | 73.9189i | 0.0286951 | + | 0.181174i | ||||
\(409\) | 230.995 | + | 75.0548i | 0.564780 | + | 0.183508i | 0.577471 | − | 0.816411i | \(-0.304040\pi\) |
−0.0126910 | + | 0.999919i | \(0.504040\pi\) | |||||||
\(410\) | 310.573 | + | 767.379i | 0.757496 | + | 1.87166i | ||||
\(411\) | −256.955 | − | 790.827i | −0.625195 | − | 1.92415i | ||||
\(412\) | −222.300 | − | 436.288i | −0.539563 | − | 1.05895i | ||||
\(413\) | 429.819 | − | 219.004i | 1.04072 | − | 0.530275i | ||||
\(414\) | −284.405 | + | 92.4087i | −0.686968 | + | 0.223209i | ||||
\(415\) | 530.914 | + | 132.036i | 1.27931 | + | 0.318158i | ||||
\(416\) | −16.1497 | + | 49.7037i | −0.0388215 | + | 0.119480i | ||||
\(417\) | −571.939 | + | 90.5862i | −1.37156 | + | 0.217233i | ||||
\(418\) | 583.094 | + | 583.094i | 1.39496 | + | 1.39496i | ||||
\(419\) | 27.4988 | − | 37.8489i | 0.0656296 | − | 0.0903314i | −0.774940 | − | 0.632034i | \(-0.782220\pi\) |
0.840570 | + | 0.541703i | \(0.182220\pi\) | |||||||
\(420\) | 514.423 | − | 592.489i | 1.22482 | − | 1.41069i | ||||
\(421\) | 516.008 | − | 374.902i | 1.22567 | − | 0.890503i | 0.229114 | − | 0.973400i | \(-0.426417\pi\) |
0.996558 | + | 0.0828969i | \(0.0264172\pi\) | |||||||
\(422\) | 52.9425 | − | 334.266i | 0.125456 | − | 0.792099i | ||||
\(423\) | −22.6292 | + | 44.4124i | −0.0534970 | + | 0.104994i | ||||
\(424\) | 251.630i | 0.593468i | ||||||||
\(425\) | 92.9623 | + | 69.8785i | 0.218735 | + | 0.164420i | ||||
\(426\) | 586.446 | 1.37663 | ||||||||
\(427\) | −293.764 | − | 149.680i | −0.687972 | − | 0.350539i | ||||
\(428\) | 1030.40 | + | 163.199i | 2.40747 | + | 0.381306i | ||||
\(429\) | 38.7183 | + | 53.2911i | 0.0902524 | + | 0.124222i | ||||
\(430\) | −772.253 | − | 67.0996i | −1.79594 | − | 0.156046i | ||||
\(431\) | −126.852 | − | 92.1635i | −0.294321 | − | 0.213836i | 0.430819 | − | 0.902438i | \(-0.358225\pi\) |
−0.725140 | + | 0.688602i | \(0.758225\pi\) | |||||||
\(432\) | −65.2861 | + | 65.2861i | −0.151125 | + | 0.151125i | ||||
\(433\) | 20.5870 | + | 129.981i | 0.0475451 | + | 0.300188i | 0.999990 | − | 0.00452353i | \(-0.00143989\pi\) |
−0.952445 | + | 0.304712i | \(0.901440\pi\) | |||||||
\(434\) | 609.239 | + | 197.954i | 1.40378 | + | 0.456115i | ||||
\(435\) | −206.434 | + | 14.5589i | −0.474561 | + | 0.0334687i | ||||
\(436\) | −217.528 | − | 669.481i | −0.498916 | − | 1.53551i | ||||
\(437\) | 88.3587 | + | 173.414i | 0.202194 | + | 0.396828i | ||||
\(438\) | −728.549 | + | 371.214i | −1.66335 | + | 0.847521i | ||||
\(439\) | 648.563 | − | 210.731i | 1.47736 | − | 0.480025i | 0.544040 | − | 0.839059i | \(-0.316894\pi\) |
0.933324 | + | 0.359034i | \(0.116894\pi\) | |||||||
\(440\) | 15.7070 | + | 222.713i | 0.0356977 | + | 0.506165i | ||||
\(441\) | −11.6205 | + | 35.7644i | −0.0263504 | + | 0.0810983i | ||||
\(442\) | 16.4499 | − | 2.60540i | 0.0372169 | − | 0.00589457i | ||||
\(443\) | 3.05272 | + | 3.05272i | 0.00689102 | + | 0.00689102i | 0.710544 | − | 0.703653i | \(-0.248449\pi\) |
−0.703653 | + | 0.710544i | \(0.748449\pi\) | |||||||
\(444\) | 194.706 | − | 267.990i | 0.438527 | − | 0.603581i | ||||
\(445\) | 28.6849 | − | 330.136i | 0.0644604 | − | 0.741878i | ||||
\(446\) | −110.822 | + | 80.5172i | −0.248481 | + | 0.180532i | ||||
\(447\) | −163.008 | + | 1029.19i | −0.364671 | + | 2.30244i | ||||
\(448\) | −290.130 | + | 569.411i | −0.647611 | + | 1.27101i | ||||
\(449\) | − | 68.8584i | − | 0.153359i | −0.997056 | − | 0.0766797i | \(-0.975568\pi\) | ||
0.997056 | − | 0.0766797i | \(-0.0244319\pi\) | |||||||
\(450\) | 13.6617 | − | 840.061i | 0.0303593 | − | 1.86680i | ||||
\(451\) | −679.643 | −1.50697 | ||||||||
\(452\) | −430.108 | − | 219.151i | −0.951566 | − | 0.484847i | ||||
\(453\) | −764.538 | − | 121.091i | −1.68772 | − | 0.267309i | ||||
\(454\) | −213.951 | − | 294.479i | −0.471258 | − | 0.648631i | ||||
\(455\) | −30.1223 | − | 26.1534i | −0.0662028 | − | 0.0574799i | ||||
\(456\) | −284.685 | − | 206.836i | −0.624310 | − | 0.453588i | ||||
\(457\) | −133.432 | + | 133.432i | −0.291974 | + | 0.291974i | −0.837860 | − | 0.545886i | \(-0.816193\pi\) |
0.545886 | + | 0.837860i | \(0.316193\pi\) | |||||||
\(458\) | −57.4093 | − | 362.468i | −0.125348 | − | 0.791415i | ||||
\(459\) | 41.4297 | + | 13.4613i | 0.0902608 | + | 0.0293275i | ||||
\(460\) | −55.6681 | + | 223.841i | −0.121018 | + | 0.486610i | ||||
\(461\) | 141.436 | + | 435.294i | 0.306802 | + | 0.944239i | 0.978999 | + | 0.203866i | \(0.0653508\pi\) |
−0.672197 | + | 0.740372i | \(0.734649\pi\) | |||||||
\(462\) | 518.091 | + | 1016.81i | 1.12141 | + | 2.20089i | ||||
\(463\) | −210.502 | + | 107.256i | −0.454649 | + | 0.231655i | −0.666291 | − | 0.745692i | \(-0.732119\pi\) |
0.211642 | + | 0.977347i | \(0.432119\pi\) | |||||||
\(464\) | 86.5907 | − | 28.1350i | 0.186618 | − | 0.0606358i | ||||
\(465\) | 650.196 | − | 263.147i | 1.39827 | − | 0.565908i | ||||
\(466\) | 184.926 | − | 569.144i | 0.396837 | − | 1.22134i | ||||
\(467\) | 375.182 | − | 59.4229i | 0.803387 | − | 0.127244i | 0.258781 | − | 0.965936i | \(-0.416679\pi\) |
0.544606 | + | 0.838692i | \(0.316679\pi\) | |||||||
\(468\) | −48.0258 | − | 48.0258i | −0.102619 | − | 0.102619i | ||||
\(469\) | −319.540 | + | 439.809i | −0.681322 | + | 0.937759i | ||||
\(470\) | 35.1144 | + | 58.3614i | 0.0747115 | + | 0.124173i | ||||
\(471\) | 792.112 | − | 575.503i | 1.68177 | − | 1.22188i | ||||
\(472\) | 40.1086 | − | 253.236i | 0.0849758 | − | 0.536516i | ||||
\(473\) | 288.916 | − | 567.029i | 0.610816 | − | 1.19879i | ||||
\(474\) | 635.137i | 1.33995i | ||||||||
\(475\) | −541.403 | + | 76.7474i | −1.13979 | + | 0.161573i | ||||
\(476\) | 162.874 | 0.342173 | ||||||||
\(477\) | 692.663 | + | 352.930i | 1.45212 | + | 0.739894i | ||||
\(478\) | −330.501 | − | 52.3462i | −0.691425 | − | 0.109511i | ||||
\(479\) | −136.238 | − | 187.515i | −0.284421 | − | 0.391472i | 0.642771 | − | 0.766058i | \(-0.277785\pi\) |
−0.927192 | + | 0.374587i | \(0.877785\pi\) | |||||||
\(480\) | 223.591 | + | 965.853i | 0.465815 | + | 2.01219i | ||||
\(481\) | −13.6247 | − | 9.89889i | −0.0283257 | − | 0.0205798i | ||||
\(482\) | 145.637 | − | 145.637i | 0.302151 | − | 0.302151i | ||||
\(483\) | 42.1348 | + | 266.029i | 0.0872357 | + | 0.550784i | ||||
\(484\) | −166.452 | − | 54.0835i | −0.343909 | − | 0.111743i | ||||
\(485\) | −243.815 | − | 152.151i | −0.502711 | − | 0.313712i | ||||
\(486\) | 321.675 | + | 990.013i | 0.661882 | + | 2.03706i | ||||
\(487\) | 65.2171 | + | 127.996i | 0.133916 | + | 0.262825i | 0.948220 | − | 0.317613i | \(-0.102881\pi\) |
−0.814304 | + | 0.580438i | \(0.802881\pi\) | |||||||
\(488\) | −156.134 | + | 79.5544i | −0.319947 | + | 0.163021i | ||||
\(489\) | −154.021 | + | 50.0446i | −0.314972 | + | 0.102341i | ||||
\(490\) | 33.0531 | + | 39.3435i | 0.0674553 | + | 0.0802929i | ||||
\(491\) | −37.0190 | + | 113.933i | −0.0753951 | + | 0.232042i | −0.981651 | − | 0.190688i | \(-0.938928\pi\) |
0.906256 | + | 0.422730i | \(0.138928\pi\) | |||||||
\(492\) | 1253.87 | − | 198.594i | 2.54852 | − | 0.403647i | ||||
\(493\) | −30.3752 | − | 30.3752i | −0.0616131 | − | 0.0616131i | ||||
\(494\) | −46.0291 | + | 63.3536i | −0.0931764 | + | 0.128246i | ||||
\(495\) | 635.091 | + | 269.134i | 1.28301 | + | 0.543704i | ||||
\(496\) | −249.659 | + | 181.388i | −0.503345 | + | 0.365701i | ||||
\(497\) | 45.6119 | − | 287.982i | 0.0917743 | − | 0.579440i | ||||
\(498\) | 674.745 | − | 1324.26i | 1.35491 | − | 2.65916i | ||||
\(499\) | 274.256i | 0.549612i | 0.961500 | + | 0.274806i | \(0.0886136\pi\) | ||||
−0.961500 | + | 0.274806i | \(0.911386\pi\) | |||||||
\(500\) | −544.131 | − | 351.981i | −1.08826 | − | 0.703962i | ||||
\(501\) | 51.6947 | 0.103183 | ||||||||
\(502\) | −498.401 | − | 253.948i | −0.992831 | − | 0.505872i | ||||
\(503\) | −379.704 | − | 60.1392i | −0.754879 | − | 0.119561i | −0.232878 | − | 0.972506i | \(-0.574814\pi\) |
−0.522001 | + | 0.852945i | \(0.674814\pi\) | |||||||
\(504\) | −158.005 | − | 217.475i | −0.313502 | − | 0.431499i | ||||
\(505\) | −8.00543 | + | 18.8909i | −0.0158523 | + | 0.0374077i | ||||
\(506\) | −271.402 | − | 197.185i | −0.536367 | − | 0.389693i | ||||
\(507\) | 531.193 | − | 531.193i | 1.04772 | − | 1.04772i | ||||
\(508\) | −40.0267 | − | 252.719i | −0.0787928 | − | 0.497478i | ||||
\(509\) | 21.4135 | + | 6.95766i | 0.0420697 | + | 0.0136693i | 0.329976 | − | 0.943989i | \(-0.392959\pi\) |
−0.287907 | + | 0.957659i | \(0.592959\pi\) | |||||||
\(510\) | 241.904 | − | 203.227i | 0.474321 | − | 0.398485i | ||||
\(511\) | 125.625 | + | 386.635i | 0.245842 | + | 0.756625i | ||||
\(512\) | −262.283 | − | 514.760i | −0.512272 | − | 1.00539i | ||||
\(513\) | −182.498 | + | 92.9875i | −0.355747 | + | 0.181262i | ||||
\(514\) | 449.396 | − | 146.018i | 0.874312 | − | 0.284081i | ||||
\(515\) | −250.011 | + | 400.632i | −0.485458 | + | 0.777927i | ||||
\(516\) | −367.333 | + | 1130.54i | −0.711886 | + | 2.19096i | ||||
\(517\) | −55.2290 | + | 8.74742i | −0.106826 | + | 0.0169196i | ||||
\(518\) | −206.308 | − | 206.308i | −0.398277 | − | 0.398277i | ||||
\(519\) | 255.419 | − | 351.554i | 0.492137 | − | 0.677369i | ||||
\(520\) | −20.6560 | + | 4.78179i | −0.0397231 | + | 0.00919575i | ||||
\(521\) | −189.989 | + | 138.035i | −0.364663 | + | 0.264943i | −0.754994 | − | 0.655731i | \(-0.772360\pi\) |
0.390332 | + | 0.920674i | \(0.372360\pi\) | |||||||
\(522\) | −48.5475 | + | 306.517i | −0.0930029 | + | 0.587197i | ||||
\(523\) | 27.0755 | − | 53.1387i | 0.0517696 | − | 0.101604i | −0.863672 | − | 0.504054i | \(-0.831841\pi\) |
0.915442 | + | 0.402450i | \(0.131841\pi\) | |||||||
\(524\) | 703.448i | 1.34246i | ||||||||
\(525\) | −745.400 | − | 130.518i | −1.41981 | − | 0.248606i | ||||
\(526\) | −1004.50 | −1.90970 | ||||||||
\(527\) | 129.730 | + | 66.1008i | 0.246167 | + | 0.125428i | ||||
\(528\) | −542.985 | − | 86.0004i | −1.02838 | − | 0.162880i | ||||
\(529\) | 264.399 | + | 363.914i | 0.499809 | + | 0.687928i | ||||
\(530\) | 910.214 | − | 547.651i | 1.71739 | − | 1.03330i | ||||
\(531\) | −640.827 | − | 465.588i | −1.20683 | − | 0.876813i | ||||
\(532\) | −541.513 | + | 541.513i | −1.01788 | + | 1.01788i | ||||
\(533\) | −10.0966 | − | 63.7472i | −0.0189429 | − | 0.119601i | ||||
\(534\) | −856.189 | − | 278.193i | −1.60335 | − | 0.520960i | ||||
\(535\) | −377.461 | − | 932.647i | −0.705534 | − | 1.74327i | ||||
\(536\) | 89.2871 | + | 274.797i | 0.166580 | + | 0.512682i | ||||
\(537\) | −412.695 | − | 809.959i | −0.768519 | − | 1.50830i | ||||
\(538\) | 1408.54 | − | 717.688i | 2.61811 | − | 1.33399i | ||||
\(539\) | −40.1213 | + | 13.0362i | −0.0744365 | + | 0.0241859i | ||||
\(540\) | −235.567 | − | 58.5843i | −0.436235 | − | 0.108490i | ||||
\(541\) | −127.378 | + | 392.030i | −0.235450 | + | 0.724640i | 0.761612 | + | 0.648034i | \(0.224408\pi\) |
−0.997061 | + | 0.0766062i | \(0.975592\pi\) | |||||||
\(542\) | 122.913 | − | 19.4675i | 0.226776 | − | 0.0359178i | ||||
\(543\) | 962.252 | + | 962.252i | 1.77210 | + | 1.77210i | ||||
\(544\) | −120.960 | + | 166.487i | −0.222353 | + | 0.306043i | ||||
\(545\) | −445.090 | + | 512.635i | −0.816679 | + | 0.940614i | ||||
\(546\) | −87.6754 | + | 63.6999i | −0.160578 | + | 0.116667i | ||||
\(547\) | 64.7443 | − | 408.779i | 0.118362 | − | 0.747311i | −0.855100 | − | 0.518463i | \(-0.826504\pi\) |
0.973462 | − | 0.228848i | \(-0.0734958\pi\) | |||||||
\(548\) | −436.655 | + | 856.984i | −0.796816 | + | 1.56384i | ||||
\(549\) | 541.372i | 0.986106i | ||||||||
\(550\) | 771.426 | − | 541.530i | 1.40259 | − | 0.984600i | ||||
\(551\) | 201.979 | 0.366569 | ||||||||
\(552\) | 127.553 | + | 64.9914i | 0.231074 | + | 0.117738i | ||||
\(553\) | 311.892 | + | 49.3989i | 0.564000 | + | 0.0893289i | ||||
\(554\) | −943.347 | − | 1298.41i | −1.70279 | − | 2.34369i | ||||
\(555\) | −318.272 | − | 27.6541i | −0.573464 | − | 0.0498272i | ||||
\(556\) | 541.881 | + | 393.699i | 0.974606 | + | 0.708092i | ||||
\(557\) | −364.882 | + | 364.882i | −0.655084 | + | 0.655084i | −0.954213 | − | 0.299129i | \(-0.903304\pi\) |
0.299129 | + | 0.954213i | \(0.403304\pi\) | |||||||
\(558\) | −164.548 | − | 1038.91i | −0.294889 | − | 1.86185i | ||||
\(559\) | 57.4767 | + | 18.6753i | 0.102820 | + | 0.0334084i | ||||
\(560\) | 332.105 | − | 23.4220i | 0.593045 | − | 0.0418250i | ||||
\(561\) | 80.1531 | + | 246.686i | 0.142875 | + | 0.439725i | ||||
\(562\) | 222.638 | + | 436.953i | 0.396154 | + | 0.777496i | ||||
\(563\) | 453.798 | − | 231.222i | 0.806036 | − | 0.410696i | −0.00187651 | − | 0.999998i | \(-0.500597\pi\) |
0.807913 | + | 0.589302i | \(0.200597\pi\) | |||||||
\(564\) | 99.3362 | − | 32.2763i | 0.176128 | − | 0.0572274i | ||||
\(565\) | 32.7520 | + | 464.398i | 0.0579682 | + | 0.821943i | ||||
\(566\) | 299.438 | − | 921.576i | 0.529043 | − | 1.62823i | ||||
\(567\) | 385.753 | − | 61.0972i | 0.680340 | − | 0.107755i | ||||
\(568\) | −109.580 | − | 109.580i | −0.192922 | − | 0.192922i | ||||
\(569\) | −282.994 | + | 389.508i | −0.497353 | + | 0.684548i | −0.981723 | − | 0.190315i | \(-0.939049\pi\) |
0.484370 | + | 0.874863i | \(0.339049\pi\) | |||||||
\(570\) | −128.589 | + | 1479.94i | −0.225596 | + | 2.59639i | ||||
\(571\) | 501.209 | − | 364.150i | 0.877775 | − | 0.637741i | −0.0548871 | − | 0.998493i | \(-0.517480\pi\) |
0.932662 | + | 0.360752i | \(0.117480\pi\) | |||||||
\(572\) | 11.9192 | − | 75.2548i | 0.0208377 | − | 0.131564i | ||||
\(573\) | −186.425 | + | 365.879i | −0.325349 | + | 0.638532i | ||||
\(574\) | − | 1118.16i | − | 1.94801i | ||||||
\(575\) | 212.657 | − | 65.2931i | 0.369838 | − | 0.113553i | ||||
\(576\) | 1049.36 | 1.82180 | ||||||||
\(577\) | 296.742 | + | 151.197i | 0.514284 | + | 0.262041i | 0.691815 | − | 0.722074i | \(-0.256811\pi\) |
−0.177532 | + | 0.984115i | \(0.556811\pi\) | |||||||
\(578\) | −800.280 | − | 126.752i | −1.38457 | − | 0.219294i | ||||
\(579\) | −481.915 | − | 663.299i | −0.832323 | − | 1.14559i | ||||
\(580\) | 180.751 | + | 156.935i | 0.311639 | + | 0.270578i | ||||
\(581\) | −597.816 | − | 434.339i | −1.02894 | − | 0.747571i | ||||
\(582\) | −552.078 | + | 552.078i | −0.948588 | + | 0.948588i | ||||
\(583\) | 136.426 | + | 861.362i | 0.234007 | + | 1.47746i | ||||
\(584\) | 205.495 | + | 66.7694i | 0.351875 | + | 0.114331i | ||||
\(585\) | −15.8087 | + | 63.5667i | −0.0270235 | + | 0.108661i | ||||
\(586\) | 334.671 | + | 1030.01i | 0.571110 | + | 1.75770i | ||||
\(587\) | 313.341 | + | 614.967i | 0.533801 | + | 1.04764i | 0.987666 | + | 0.156573i | \(0.0500448\pi\) |
−0.453865 | + | 0.891070i | \(0.649955\pi\) | |||||||
\(588\) | 70.2106 | − | 35.7741i | 0.119406 | − | 0.0608403i | ||||
\(589\) | −651.086 | + | 211.551i | −1.10541 | + | 0.359169i | ||||
\(590\) | −1003.31 | + | 406.061i | −1.70053 | + | 0.688238i | ||||
\(591\) | −170.348 | + | 524.276i | −0.288236 | + | 0.887100i | ||||
\(592\) | 138.822 | − | 21.9872i | 0.234497 | − | 0.0371406i | ||||
\(593\) | −236.882 | − | 236.882i | −0.399464 | − | 0.399464i | 0.478580 | − | 0.878044i | \(-0.341152\pi\) |
−0.878044 | + | 0.478580i | \(0.841152\pi\) | |||||||
\(594\) | 207.515 | − | 285.619i | 0.349351 | − | 0.480841i | ||||
\(595\) | −80.9829 | − | 134.596i | −0.136106 | − | 0.226212i | ||||
\(596\) | 975.104 | − | 708.454i | 1.63608 | − | 1.18868i | ||||
\(597\) | 273.585 | − | 1727.35i | 0.458266 | − | 2.89338i | ||||
\(598\) | 14.4631 | − | 28.3855i | 0.0241858 | − | 0.0474674i | ||||
\(599\) | − | 120.628i | − | 0.201382i | −0.994918 | − | 0.100691i | \(-0.967895\pi\) | ||
0.994918 | − | 0.100691i | \(-0.0321053\pi\) | |||||||
\(600\) | −288.988 | + | 279.739i | −0.481647 | + | 0.466232i | ||||
\(601\) | 1122.78 | 1.86819 | 0.934095 | − | 0.357025i | \(-0.116209\pi\) | ||||
0.934095 | + | 0.357025i | \(0.116209\pi\) | |||||||
\(602\) | 932.885 | + | 475.329i | 1.54964 | + | 0.789583i | ||||
\(603\) | 881.667 | + | 139.642i | 1.46213 | + | 0.231579i | ||||
\(604\) | 526.277 | + | 724.358i | 0.871320 | + | 1.19927i | ||||
\(605\) | 38.0681 | + | 164.444i | 0.0629225 | + | 0.271808i | ||||
\(606\) | 45.0933 | + | 32.7622i | 0.0744114 | + | 0.0540630i | ||||
\(607\) | 125.125 | − | 125.125i | 0.206136 | − | 0.206136i | −0.596487 | − | 0.802623i | \(-0.703437\pi\) |
0.802623 | + | 0.596487i | \(0.203437\pi\) | |||||||
\(608\) | −151.366 | − | 955.686i | −0.248957 | − | 1.57185i | ||||
\(609\) | 265.839 | + | 86.3765i | 0.436518 | + | 0.141833i | ||||
\(610\) | 627.582 | + | 391.637i | 1.02882 | + | 0.642027i | ||||
\(611\) | −1.64093 | − | 5.05027i | −0.00268565 | − | 0.00826558i | ||||
\(612\) | −121.416 | − | 238.293i | −0.198393 | − | 0.389368i | ||||
\(613\) | −249.961 | + | 127.362i | −0.407767 | + | 0.207768i | −0.645829 | − | 0.763482i | \(-0.723488\pi\) |
0.238062 | + | 0.971250i | \(0.423488\pi\) | |||||||
\(614\) | 1062.98 | − | 345.384i | 1.73124 | − | 0.562515i | ||||
\(615\) | −787.555 | − | 937.437i | −1.28058 | − | 1.52429i | ||||
\(616\) | 93.1878 | − | 286.803i | 0.151279 | − | 0.465589i | ||||
\(617\) | −74.7801 | + | 11.8440i | −0.121200 | + | 0.0191961i | −0.216740 | − | 0.976229i | \(-0.569542\pi\) |
0.0955399 | + | 0.995426i | \(0.469542\pi\) | |||||||
\(618\) | 907.165 | + | 907.165i | 1.46790 | + | 1.46790i | ||||
\(619\) | 131.262 | − | 180.667i | 0.212055 | − | 0.291868i | −0.689719 | − | 0.724078i | \(-0.742266\pi\) |
0.901773 | + | 0.432209i | \(0.142266\pi\) | |||||||
\(620\) | −747.026 | − | 316.568i | −1.20488 | − | 0.510594i | ||||
\(621\) | 67.4119 | − | 48.9776i | 0.108554 | − | 0.0788690i | ||||
\(622\) | −180.379 | + | 1138.87i | −0.289998 | + | 1.83098i | ||||
\(623\) | −203.202 | + | 398.806i | −0.326167 | + | 0.640138i | ||||
\(624\) | − | 52.2070i | − | 0.0836650i | ||||||
\(625\) | −20.3230 | + | 624.669i | −0.0325168 | + | 0.999471i | ||||
\(626\) | −1244.47 | −1.98796 | ||||||||
\(627\) | −1086.65 | − | 553.677i | −1.73310 | − | 0.883058i | ||||
\(628\) | −1118.58 | − | 177.165i | −1.78117 | − | 0.282110i | ||||
\(629\) | −38.9787 | − | 53.6496i | −0.0619693 | − | 0.0852934i | ||||
\(630\) | −442.783 | + | 1044.86i | −0.702830 | + | 1.65851i | ||||
\(631\) | −292.773 | − | 212.712i | −0.463982 | − | 0.337103i | 0.331109 | − | 0.943592i | \(-0.392577\pi\) |
−0.795091 | + | 0.606490i | \(0.792577\pi\) | |||||||
\(632\) | 118.678 | − | 118.678i | 0.187781 | − | 0.187781i | ||||
\(633\) | 78.2999 | + | 494.366i | 0.123696 | + | 0.780989i | ||||
\(634\) | −501.265 | − | 162.871i | −0.790639 | − | 0.256894i | ||||
\(635\) | −188.941 | + | 158.732i | −0.297545 | + | 0.249972i | ||||
\(636\) | −503.386 | − | 1549.26i | −0.791488 | − | 2.43595i | ||||
\(637\) | −1.81876 | − | 3.56952i | −0.00285520 | − | 0.00560364i | ||||
\(638\) | −310.199 | + | 158.054i | −0.486205 | + | 0.247734i | ||||
\(639\) | −455.334 | + | 147.947i | −0.712572 | + | 0.231529i | ||||
\(640\) | 290.718 | − | 465.863i | 0.454246 | − | 0.727911i | ||||
\(641\) | 282.130 | − | 868.306i | 0.440140 | − | 1.35461i | −0.447587 | − | 0.894241i | \(-0.647716\pi\) |
0.887727 | − | 0.460371i | \(-0.152284\pi\) | |||||||
\(642\) | −2699.69 | + | 427.589i | −4.20512 | + | 0.666026i | ||||
\(643\) | −520.582 | − | 520.582i | −0.809615 | − | 0.809615i | 0.174960 | − | 0.984575i | \(-0.444020\pi\) |
−0.984575 | + | 0.174960i | \(0.944020\pi\) | |||||||
\(644\) | 183.124 | − | 252.048i | 0.284353 | − | 0.391379i | ||||
\(645\) | 1116.90 | − | 258.557i | 1.73162 | − | 0.400864i | ||||
\(646\) | −249.467 | + | 181.248i | −0.386171 | + | 0.280570i | ||||
\(647\) | −167.501 | + | 1057.56i | −0.258888 | + | 1.63456i | 0.425159 | + | 0.905118i | \(0.360218\pi\) |
−0.684048 | + | 0.729437i | \(0.739782\pi\) | |||||||
\(648\) | 94.2401 | − | 184.957i | 0.145432 | − | 0.285427i | ||||
\(649\) | − | 888.602i | − | 1.36919i | ||||||
\(650\) | 62.2530 | + | 64.3113i | 0.0957738 | + | 0.0989404i | ||||
\(651\) | −947.410 | −1.45532 | ||||||||
\(652\) | 166.906 | + | 85.0429i | 0.255991 | + | 0.130434i | ||||
\(653\) | 357.048 | + | 56.5509i | 0.546781 | + | 0.0866016i | 0.423713 | − | 0.905797i | \(-0.360727\pi\) |
0.123068 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(654\) | 1084.08 | + | 1492.10i | 1.65761 | + | 2.28150i | ||||
\(655\) | 581.317 | − | 349.762i | 0.887508 | − | 0.533989i | ||||
\(656\) | 435.782 | + | 316.614i | 0.664302 | + | 0.482644i | ||||
\(657\) | 472.018 | − | 472.018i | 0.718444 | − | 0.718444i | ||||
\(658\) | −14.3914 | − | 90.8637i | −0.0218714 | − | 0.138091i | ||||
\(659\) | 438.078 | + | 142.340i | 0.664762 | + | 0.215994i | 0.621912 | − | 0.783087i | \(-0.286356\pi\) |
0.0428503 | + | 0.999082i | \(0.486356\pi\) | |||||||
\(660\) | −542.243 | − | 1339.80i | −0.821580 | − | 2.03000i | ||||
\(661\) | 42.7285 | + | 131.505i | 0.0646422 | + | 0.198948i | 0.978161 | − | 0.207848i | \(-0.0666459\pi\) |
−0.913519 | + | 0.406796i | \(0.866646\pi\) | |||||||
\(662\) | 54.3638 | + | 106.695i | 0.0821205 | + | 0.161171i | ||||
\(663\) | −21.9472 | + | 11.1827i | −0.0331029 | + | 0.0168668i | ||||
\(664\) | −373.522 | + | 121.365i | −0.562533 | + | 0.182778i | ||||
\(665\) | 716.744 | + | 178.251i | 1.07781 | + | 0.268046i | ||||
\(666\) | −148.044 | + | 455.633i | −0.222288 | + | 0.684133i | ||||
\(667\) | −81.1574 | + | 12.8541i | −0.121675 | + | 0.0192715i | ||||
\(668\) | −42.2812 | − | 42.2812i | −0.0632952 | − | 0.0632952i | ||||
\(669\) | 119.082 | − | 163.902i | 0.178000 | − | 0.244996i | ||||
\(670\) | 799.691 | − | 921.047i | 1.19357 | − | 1.37470i | ||||
\(671\) | −491.335 | + | 356.976i | −0.732243 | + | 0.532006i | ||||
\(672\) | 209.476 | − | 1322.58i | 0.311720 | − | 1.96812i | ||||
\(673\) | −274.452 | + | 538.642i | −0.407803 | + | 0.800359i | −0.999985 | − | 0.00544506i | \(-0.998267\pi\) |
0.592182 | + | 0.805804i | \(0.298267\pi\) | |||||||
\(674\) | 359.859i | 0.533916i | ||||||||
\(675\) | 68.7135 | + | 223.797i | 0.101798 | + | 0.331552i | ||||
\(676\) | −868.928 | −1.28540 | ||||||||
\(677\) | 222.931 | + | 113.589i | 0.329293 | + | 0.167783i | 0.610819 | − | 0.791771i | \(-0.290840\pi\) |
−0.281526 | + | 0.959554i | \(0.590840\pi\) | |||||||
\(678\) | 1249.18 | + | 197.851i | 1.84245 | + | 0.291815i | ||||
\(679\) | 228.166 | + | 314.044i | 0.336033 | + | 0.462510i | ||||
\(680\) | −83.1745 | − | 7.22687i | −0.122315 | − | 0.0106278i | ||||
\(681\) | 435.522 | + | 316.425i | 0.639533 | + | 0.464648i | ||||
\(682\) | 834.390 | − | 834.390i | 1.22345 | − | 1.22345i | ||||
\(683\) | −59.7898 | − | 377.498i | −0.0875400 | − | 0.552706i | −0.992009 | − | 0.126167i | \(-0.959733\pi\) |
0.904469 | − | 0.426539i | \(-0.140267\pi\) | |||||||
\(684\) | 1195.94 | + | 388.584i | 1.74845 | + | 0.568105i | ||||
\(685\) | 925.306 | − | 65.2579i | 1.35081 | − | 0.0952671i | ||||
\(686\) | −331.352 | − | 1019.80i | −0.483021 | − | 1.48659i | ||||
\(687\) | 246.407 | + | 483.601i | 0.358671 | + | 0.703932i | ||||
\(688\) | −449.404 | + | 228.983i | −0.653203 | + | 0.332824i | ||||
\(689\) | −78.7649 | + | 25.5923i | −0.114318 | + | 0.0371441i | ||||
\(690\) | −42.5158 | − | 602.840i | −0.0616170 | − | 0.873681i | ||||
\(691\) | −328.195 | + | 1010.08i | −0.474957 | + | 1.46177i | 0.371059 | + | 0.928609i | \(0.378995\pi\) |
−0.846016 | + | 0.533158i | \(0.821005\pi\) | |||||||
\(692\) | −496.445 | + | 78.6292i | −0.717406 | + | 0.113626i | ||||
\(693\) | −658.780 | − | 658.780i | −0.950620 | − | 0.950620i | ||||
\(694\) | −763.090 | + | 1050.30i | −1.09955 | + | 1.51341i | ||||
\(695\) | 55.9171 | − | 643.553i | 0.0804562 | − | 0.925975i | ||||
\(696\) | 120.191 | − | 87.3236i | 0.172688 | − | 0.125465i | ||||
\(697\) | 39.7571 | − | 251.016i | 0.0570403 | − | 0.360138i | ||||
\(698\) | 153.737 | − | 301.726i | 0.220254 | − | 0.432273i | ||||
\(699\) | 885.060i | 1.26618i | ||||||||
\(700\) | 502.913 | + | 716.416i | 0.718448 | + | 1.02345i | ||||
\(701\) | −709.732 | −1.01246 | −0.506228 | − | 0.862400i | \(-0.668961\pi\) | ||||
−0.506228 | + | 0.862400i | \(0.668961\pi\) | |||||||
\(702\) | 29.8725 | + | 15.2208i | 0.0425534 | + | 0.0216820i | ||||
\(703\) | 307.964 | + | 48.7768i | 0.438072 | + | 0.0693837i | ||||
\(704\) | 691.937 | + | 952.369i | 0.982865 | + | 1.35280i | ||||
\(705\) | −76.0636 | − | 66.0416i | −0.107892 | − | 0.0936760i | ||||
\(706\) | 818.149 | + | 594.420i | 1.15885 | + | 0.841955i | ||||
\(707\) | 19.5955 | − | 19.5955i | 0.0277164 | − | 0.0277164i | ||||
\(708\) | 259.653 | + | 1639.38i | 0.366741 | + | 2.31551i | ||||
\(709\) | −1304.06 | − | 423.715i | −1.83930 | − | 0.597624i | −0.998407 | − | 0.0564168i | \(-0.982032\pi\) |
−0.840889 | − | 0.541207i | \(-0.817968\pi\) | |||||||
\(710\) | −157.889 | + | 634.870i | −0.222379 | + | 0.894182i | ||||
\(711\) | −160.230 | − | 493.139i | −0.225359 | − | 0.693585i | ||||
\(712\) | 108.001 | + | 211.964i | 0.151687 | + | 0.297702i | ||||
\(713\) | 248.150 | − | 126.439i | 0.348036 | − | 0.177333i | ||||
\(714\) | −405.852 | + | 131.869i | −0.568420 | + | 0.184691i | ||||
\(715\) | −68.1156 | + | 27.5677i | −0.0952666 | + | 0.0385563i | ||||
\(716\) | −324.924 | + | 1000.01i | −0.453804 | + | 1.39666i | ||||
\(717\) | 488.798 | − | 77.4180i | 0.681727 | − | 0.107975i | ||||
\(718\) | −250.914 | − | 250.914i | −0.349463 | − | 0.349463i | ||||
\(719\) | 182.262 | − | 250.863i | 0.253494 | − | 0.348905i | −0.663237 | − | 0.748409i | \(-0.730818\pi\) |
0.916731 | + | 0.399505i | \(0.130818\pi\) | |||||||
\(720\) | −281.839 | − | 468.427i | −0.391443 | − | 0.650592i | ||||
\(721\) | 516.031 | − | 374.919i | 0.715716 | − | 0.519998i | ||||
\(722\) | 55.6630 | − | 351.442i | 0.0770956 | − | 0.486762i | ||||
\(723\) | −138.289 | + | 271.408i | −0.191272 | + | 0.375392i | ||||
\(724\) | − | 1574.06i | − | 2.17411i | ||||||
\(725\) | 39.8172 | − | 227.399i | 0.0549202 | − | 0.313654i | ||||
\(726\) | 458.555 | 0.631618 | ||||||||
\(727\) | −573.466 | − | 292.196i | −0.788812 | − | 0.401920i | 0.0126843 | − | 0.999920i | \(-0.495962\pi\) |
−0.801496 | + | 0.598000i | \(0.795962\pi\) | |||||||
\(728\) | 28.2851 | + | 4.47992i | 0.0388531 | + | 0.00615373i | ||||
\(729\) | −598.987 | − | 824.434i | −0.821655 | − | 1.13091i | ||||
\(730\) | −205.719 | − | 888.649i | −0.281806 | − | 1.21733i | ||||
\(731\) | 192.523 | + | 139.876i | 0.263370 | + | 0.191349i | ||||
\(732\) | 802.155 | − | 802.155i | 1.09584 | − | 1.09584i | ||||
\(733\) | −157.542 | − | 994.681i | −0.214928 | − | 1.35700i | −0.825214 | − | 0.564820i | \(-0.808946\pi\) |
0.610287 | − | 0.792181i | \(-0.291054\pi\) | |||||||
\(734\) | 448.096 | + | 145.595i | 0.610484 | + | 0.198358i | ||||
\(735\) | −64.4726 | − | 40.2335i | −0.0877178 | − | 0.0547395i | ||||
\(736\) | 121.641 | + | 374.372i | 0.165273 | + | 0.508657i | ||||
\(737\) | 454.627 | + | 892.257i | 0.616862 | + | 1.21066i | ||||
\(738\) | −1635.92 | + | 833.544i | −2.21670 | + | 1.12946i | ||||
\(739\) | −884.508 | + | 287.394i | −1.19690 | + | 0.388896i | −0.838619 | − | 0.544718i | \(-0.816637\pi\) |
−0.358280 | + | 0.933614i | \(0.616637\pi\) | |||||||
\(740\) | 237.697 | + | 282.934i | 0.321213 | + | 0.382343i | ||||
\(741\) | 35.7893 | − | 110.148i | 0.0482986 | − | 0.148648i | ||||
\(742\) | −1417.13 | + | 224.451i | −1.90987 | + | 0.302494i | ||||
\(743\) | −527.824 | − | 527.824i | −0.710395 | − | 0.710395i | 0.256223 | − | 0.966618i | \(-0.417522\pi\) |
−0.966618 | + | 0.256223i | \(0.917522\pi\) | |||||||
\(744\) | −295.976 | + | 407.376i | −0.397817 | + | 0.547549i | ||||
\(745\) | −1070.29 | − | 453.557i | −1.43663 | − | 0.608802i | ||||
\(746\) | 868.041 | − | 630.669i | 1.16359 | − | 0.845401i | ||||
\(747\) | −189.811 | + | 1198.42i | −0.254097 | + | 1.60431i | ||||
\(748\) | 136.208 | − | 267.322i | 0.182096 | − | 0.357383i | ||||
\(749\) | 1358.97i | 1.81438i | ||||||||
\(750\) | 1640.85 | + | 436.521i | 2.18780 | + | 0.582028i | ||||
\(751\) | 166.431 | 0.221612 | 0.110806 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110806 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(752\) | 39.4875 | + | 20.1199i | 0.0525100 | + | 0.0267552i | ||||
\(753\) | 817.099 | + | 129.416i | 1.08512 | + | 0.171867i | ||||
\(754\) | −19.4329 | − | 26.7471i | −0.0257731 | − | 0.0354737i | ||||
\(755\) | 336.926 | − | 795.066i | 0.446260 | − | 1.05307i | ||||
\(756\) | 265.252 | + | 192.717i | 0.350862 | + | 0.254916i | ||||
\(757\) | 317.868 | − | 317.868i | 0.419905 | − | 0.419905i | −0.465266 | − | 0.885171i | \(-0.654041\pi\) |
0.885171 | + | 0.465266i | \(0.154041\pi\) | |||||||
\(758\) | 170.079 | + | 1073.84i | 0.224379 | + | 1.41667i | ||||
\(759\) | 471.865 | + | 153.318i | 0.621693 | + | 0.202000i | ||||
\(760\) | 300.561 | − | 252.506i | 0.395474 | − | 0.332244i | ||||
\(761\) | −371.860 | − | 1144.47i | −0.488646 | − | 1.50390i | −0.826629 | − | 0.562747i | \(-0.809745\pi\) |
0.337983 | − | 0.941152i | \(-0.390255\pi\) | |||||||
\(762\) | 304.350 | + | 597.321i | 0.399410 | + | 0.783885i | ||||
\(763\) | 817.032 | − | 416.298i | 1.07081 | − | 0.545607i | ||||
\(764\) | 451.731 | − | 146.776i | 0.591271 | − | 0.192115i | ||||
\(765\) | −136.552 | + | 218.818i | −0.178499 | + | 0.286037i | ||||
\(766\) | 50.7565 | − | 156.213i | 0.0662618 | − | 0.203933i | ||||
\(767\) | 83.3466 | − | 13.2008i | 0.108666 | − | 0.0172110i | ||||
\(768\) | 144.761 | + | 144.761i | 0.188490 | + | 0.188490i | ||||
\(769\) | 827.508 | − | 1138.97i | 1.07608 | − | 1.48110i | 0.212321 | − | 0.977200i | \(-0.431898\pi\) |
0.863761 | − | 0.503901i | \(-0.168102\pi\) | |||||||
\(770\) | −1240.26 | + | 287.115i | −1.61072 | + | 0.372876i | ||||
\(771\) | −565.376 | + | 410.770i | −0.733302 | + | 0.532775i | ||||
\(772\) | −148.355 | + | 936.674i | −0.192169 | + | 1.21331i | ||||
\(773\) | −460.242 | + | 903.275i | −0.595397 | + | 1.16853i | 0.375002 | + | 0.927024i | \(0.377642\pi\) |
−0.970399 | + | 0.241508i | \(0.922358\pi\) | |||||||
\(774\) | − | 1719.20i | − | 2.22119i | ||||||
\(775\) | 109.823 | + | 774.731i | 0.141707 | + | 0.999653i | ||||
\(776\) | 206.316 | 0.265871 | ||||||||
\(777\) | 384.475 | + | 195.900i | 0.494819 | + | 0.252123i | ||||
\(778\) | −1071.63 | − | 169.729i | −1.37741 | − | 0.218161i | ||||
\(779\) | 702.381 | + | 966.744i | 0.901644 | + | 1.24101i | ||||
\(780\) | 117.611 | − | 70.7634i | 0.150784 | − | 0.0907223i | ||||
\(781\) | −434.516 | − | 315.694i | −0.556358 | − | 0.404218i | ||||
\(782\) | 88.7036 | − | 88.7036i | 0.113432 | − | 0.113432i | ||||
\(783\) | −13.5274 | − | 85.4089i | −0.0172764 | − | 0.109079i | ||||
\(784\) | 31.7984 | + | 10.3319i | 0.0405592 | + | 0.0131785i | ||||
\(785\) | 409.763 | + | 1012.46i | 0.521991 | + | 1.28976i | ||||
\(786\) | −569.539 | − | 1752.86i | −0.724604 | − | 2.23010i | ||||
\(787\) | −574.499 | − | 1127.52i | −0.729986 | − | 1.43268i | −0.894852 | − | 0.446363i | \(-0.852719\pi\) |
0.164866 | − | 0.986316i | \(-0.447281\pi\) | |||||||
\(788\) | 568.135 | − | 289.479i | 0.720983 | − | 0.367359i | ||||
\(789\) | 1412.91 | − | 459.083i | 1.79076 | − | 0.581854i | ||||
\(790\) | −687.581 | − | 170.998i | −0.870356 | − | 0.216453i | ||||
\(791\) | 194.314 | − | 598.038i | 0.245657 | − | 0.756053i | ||||
\(792\) | −489.074 | + | 77.4618i | −0.617518 | + | 0.0978053i | ||||
\(793\) | −40.7817 | − | 40.7817i | −0.0514272 | − | 0.0514272i | ||||
\(794\) | −102.013 | + | 140.409i | −0.128480 | + | 0.176838i | ||||
\(795\) | −1030.00 | + | 1186.30i | −1.29559 | + | 1.49220i | ||||
\(796\) | −1636.57 | + | 1189.04i | −2.05599 | + | 1.49376i | ||||
\(797\) | 153.706 | − | 970.462i | 0.192856 | − | 1.21764i | −0.681302 | − | 0.732002i | \(-0.738586\pi\) |
0.874158 | − | 0.485641i | \(-0.161414\pi\) | |||||||
\(798\) | 910.919 | − | 1787.78i | 1.14150 | − | 2.24032i | ||||
\(799\) | − | 20.9097i | − | 0.0261699i | ||||||
\(800\) | −1105.80 | − | 17.9833i | −1.38225 | − | 0.0224792i | ||||
\(801\) | 734.952 | 0.917543 | ||||||||
\(802\) | 1107.82 | + | 564.464i | 1.38133 | + | 0.703821i | ||||
\(803\) | 739.636 | + | 117.147i | 0.921090 | + | 0.145886i | ||||
\(804\) | −1099.46 | − | 1513.28i | −1.36749 | − | 1.88219i | ||||
\(805\) | −299.339 | − | 26.0090i | −0.371850 | − | 0.0323093i | ||||
\(806\) | 90.6572 | + | 65.8663i | 0.112478 | + | 0.0817200i | ||||
\(807\) | −1653.22 | + | 1653.22i | −2.04860 | + | 2.04860i | ||||
\(808\) | −2.30411 | − | 14.5476i | −0.00285163 | − | 0.0180045i | ||||
\(809\) | −748.876 | − | 243.325i | −0.925681 | − | 0.300772i | −0.192886 | − | 0.981221i | \(-0.561785\pi\) |
−0.732795 | + | 0.680449i | \(0.761785\pi\) | |||||||
\(810\) | −874.143 | + | 61.6496i | −1.07919 | + | 0.0761106i | ||||
\(811\) | −0.441685 | − | 1.35937i | −0.000544618 | − | 0.00167616i | 0.950784 | − | 0.309855i | \(-0.100280\pi\) |
−0.951328 | + | 0.308179i | \(0.900280\pi\) | |||||||
\(812\) | −146.783 | − | 288.078i | −0.180768 | − | 0.354776i | ||||
\(813\) | −163.989 | + | 83.5565i | −0.201708 | + | 0.102776i | ||||
\(814\) | −511.139 | + | 166.079i | −0.627935 | + | 0.204028i | ||||
\(815\) | −12.7096 | − | 180.213i | −0.0155946 | − | 0.221120i | ||||
\(816\) | 63.5260 | − | 195.513i | 0.0778505 | − | 0.239599i | ||||
\(817\) | −1105.14 | + | 175.037i | −1.35268 | + | 0.214244i | ||||
\(818\) | 520.483 | + | 520.483i | 0.636287 | + | 0.636287i | ||||
\(819\) | 52.0037 | − | 71.5770i | 0.0634966 | − | 0.0873956i | ||||
\(820\) | −122.588 | + | 1410.88i | −0.149498 | + | 1.72058i | ||||
\(821\) | −266.252 | + | 193.444i | −0.324303 | + | 0.235620i | −0.738009 | − | 0.674791i | \(-0.764234\pi\) |
0.413707 | + | 0.910410i | \(0.364234\pi\) | |||||||
\(822\) | 394.215 | − | 2488.97i | 0.479580 | − | 3.02795i | ||||
\(823\) | 384.423 | − | 754.474i | 0.467100 | − | 0.916736i | −0.530512 | − | 0.847677i | \(-0.678000\pi\) |
0.997613 | − | 0.0690586i | \(-0.0219995\pi\) | |||||||
\(824\) | − | 339.015i | − | 0.411425i | ||||||
\(825\) | −837.577 | + | 1114.26i | −1.01524 | + | 1.35062i | ||||
\(826\) | 1461.94 | 1.76991 | ||||||||
\(827\) | −308.853 | − | 157.369i | −0.373462 | − | 0.190289i | 0.257177 | − | 0.966364i | \(-0.417208\pi\) |
−0.630640 | + | 0.776076i | \(0.717208\pi\) | |||||||
\(828\) | −505.270 | − | 80.0269i | −0.610230 | − | 0.0966509i | ||||
\(829\) | 172.734 | + | 237.748i | 0.208364 | + | 0.286789i | 0.900390 | − | 0.435084i | \(-0.143281\pi\) |
−0.692026 | + | 0.721873i | \(0.743281\pi\) | |||||||
\(830\) | 1251.95 | + | 1086.99i | 1.50837 | + | 1.30963i | ||||
\(831\) | 1920.29 | + | 1395.17i | 2.31082 | + | 1.67891i | ||||
\(832\) | −79.0484 | + | 79.0484i | −0.0950102 | + | 0.0950102i | ||||
\(833\) | −2.46775 | − | 15.5808i | −0.00296249 | − | 0.0187044i | ||||
\(834\) | −1669.02 | − | 542.297i | −2.00122 | − | 0.650236i | ||||
\(835\) | −13.9178 | + | 55.9632i | −0.0166680 | + | 0.0670218i | ||||
\(836\) | 435.922 | + | 1341.63i | 0.521438 | + | 1.60482i | ||||
\(837\) | 133.062 | + | 261.149i | 0.158975 | + | 0.312007i | ||||
\(838\) | 126.329 | − | 64.3676i | 0.150750 | − | 0.0768110i | ||||
\(839\) | −613.225 | + | 199.249i | −0.730900 | + | 0.237484i | −0.650743 | − | 0.759298i | \(-0.725542\pi\) |
−0.0801576 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(840\) | 503.573 | − | 203.806i | 0.599492 | − | 0.242626i | ||||
\(841\) | 233.532 | − | 718.739i | 0.277684 | − | 0.854624i | ||||
\(842\) | 1909.17 | − | 302.382i | 2.26742 | − | 0.359124i | ||||
\(843\) | −512.856 | − | 512.856i | −0.608370 | − | 0.608370i | ||||
\(844\) | 340.301 | − | 468.385i | 0.403201 | − | 0.554958i | ||||
\(845\) | 432.041 | + | 718.067i | 0.511291 | + | 0.849784i | ||||
\(846\) | −122.210 | + | 88.7907i | −0.144456 | + | 0.104954i | ||||
\(847\) | 35.6649 | − | 225.179i | 0.0421073 | − | 0.265855i | ||||
\(848\) | 313.793 | − | 615.854i | 0.370039 | − | 0.726243i | ||||
\(849\) | 1433.12i | 1.68801i | ||||||||
\(850\) | 154.880 | + | 316.593i | 0.182212 | + | 0.372462i | ||||
\(851\) | −126.847 | −0.149057 | ||||||||
\(852\) | 893.886 | + | 455.458i | 1.04916 | + | 0.534575i | ||||
\(853\) | −959.328 | − | 151.943i | −1.12465 | − | 0.178127i | −0.433720 | − | 0.901048i | \(-0.642799\pi\) |
−0.690931 | + | 0.722920i | \(0.742799\pi\) | |||||||
\(854\) | −587.302 | − | 808.352i | −0.687708 | − | 0.946548i | ||||
\(855\) | −273.515 | − | 1181.51i | −0.319901 | − | 1.38188i | ||||
\(856\) | 584.344 | + | 424.551i | 0.682645 | + | 0.495970i | ||||
\(857\) | −41.2739 | + | 41.2739i | −0.0481609 | + | 0.0481609i | −0.730777 | − | 0.682616i | \(-0.760842\pi\) |
0.682616 | + | 0.730777i | \(0.260842\pi\) | |||||||
\(858\) | 31.2288 | + | 197.171i | 0.0363972 | + | 0.229803i | ||||
\(859\) | 1517.56 | + | 493.085i | 1.76666 | + | 0.574023i | 0.997855 | − | 0.0654608i | \(-0.0208517\pi\) |
0.768805 | + | 0.639483i | \(0.220852\pi\) | |||||||
\(860\) | −1124.99 | − | 702.039i | −1.30813 | − | 0.816324i | ||||
\(861\) | 511.025 | + | 1572.77i | 0.593525 | + | 1.82668i | ||||
\(862\) | −215.731 | − | 423.396i | −0.250268 | − | 0.491179i | ||||
\(863\) | −179.583 | + | 91.5021i | −0.208092 | + | 0.106028i | −0.554930 | − | 0.831897i | \(-0.687255\pi\) |
0.346839 | + | 0.937925i | \(0.387255\pi\) | |||||||
\(864\) | −393.984 | + | 128.013i | −0.456000 | + | 0.148163i | ||||
\(865\) | 311.816 | + | 371.158i | 0.360481 | + | 0.429085i | ||||
\(866\) | −123.245 | + | 379.309i | −0.142315 | + | 0.438001i | ||||
\(867\) | 1183.58 | − | 187.461i | 1.36515 | − | 0.216218i | ||||
\(868\) | 774.889 | + | 774.889i | 0.892730 | + | 0.892730i | ||||
\(869\) | 341.905 | − | 470.592i | 0.393447 | − | 0.541533i | ||||
\(870\) | −577.457 | − | 244.710i | −0.663744 | − | 0.281276i | ||||
\(871\) | −76.9356 | + | 55.8970i | −0.0883302 | + | 0.0641756i | ||||
\(872\) | 76.2413 | − | 481.369i | 0.0874327 | − | 0.552028i | ||||
\(873\) | 289.373 | − | 567.927i | 0.331470 | − | 0.650546i | ||||
\(874\) | 589.832i | 0.674864i | ||||||||
\(875\) | 341.979 | − | 771.809i | 0.390833 | − | 0.882067i | ||||
\(876\) | −1398.79 | −1.59679 | ||||||||
\(877\) | 1256.66 | + | 640.303i | 1.43291 | + | 0.730106i | 0.986352 | − | 0.164647i | \(-0.0526487\pi\) |
0.446561 | + | 0.894753i | \(0.352649\pi\) | |||||||
\(878\) | 2041.23 | + | 323.299i | 2.32486 | + | 0.368222i | ||||
\(879\) | −941.479 | − | 1295.83i | −1.07108 | − | 1.47421i | ||||
\(880\) | 239.289 | − | 564.666i | 0.271920 | − | 0.641666i | ||||
\(881\) | 640.260 | + | 465.176i | 0.726742 | + | 0.528009i | 0.888531 | − | 0.458816i | \(-0.151726\pi\) |
−0.161789 | + | 0.986825i | \(0.551726\pi\) | |||||||
\(882\) | −80.5850 | + | 80.5850i | −0.0913663 | + | 0.0913663i | ||||
\(883\) | 196.982 | + | 1243.69i | 0.223082 | + | 1.40849i | 0.804051 | + | 0.594560i | \(0.202674\pi\) |
−0.580969 | + | 0.813925i | \(0.697326\pi\) | |||||||
\(884\) | 27.0970 | + | 8.80436i | 0.0306527 | + | 0.00995968i | ||||
\(885\) | 1225.66 | − | 1029.69i | 1.38492 | − | 1.16350i | ||||
\(886\) | 4.04306 | + | 12.4433i | 0.00456327 | + | 0.0140443i | ||||
\(887\) | 417.143 | + | 818.690i | 0.470286 | + | 0.922988i | 0.997321 | + | 0.0731444i | \(0.0233034\pi\) |
−0.527036 | + | 0.849843i | \(0.676697\pi\) | |||||||
\(888\) | 204.347 | − | 104.120i | 0.230120 | − | 0.117252i | ||||
\(889\) | 316.993 | − | 102.997i | 0.356573 | − | 0.115858i | ||||
\(890\) | 531.675 | − | 851.988i | 0.597388 | − | 0.957290i | ||||
\(891\) | 222.318 | − | 684.224i | 0.249515 | − | 0.767928i | ||||
\(892\) | −231.453 | + | 36.6586i | −0.259477 | + | 0.0410971i | ||||
\(893\) | 69.5194 | + | 69.5194i | 0.0778492 | + | 0.0778492i | ||||
\(894\) | −1856.18 | + | 2554.82i | −2.07627 | + | 2.85774i | ||||
\(895\) | 987.948 | − | 228.706i | 1.10385 | − | 0.255538i | ||||
\(896\) | −600.052 | + | 435.963i | −0.669701 | + | 0.486566i | ||||
\(897\) | −7.37063 | + | 46.5363i | −0.00821698 | + | 0.0518800i | ||||
\(898\) | 94.7391 | − | 185.936i | 0.105500 | − | 0.207056i | ||||
\(899\) | − | 289.026i | − | 0.321498i | ||||||
\(900\) | 673.249 | − | 1269.85i | 0.748055 | − | 1.41094i | ||||
\(901\) | −326.112 | −0.361945 | ||||||||
\(902\) | −1835.21 | − | 935.089i | −2.03461 | − | 1.03668i | ||||
\(903\) | −1529.41 | − | 242.235i | −1.69370 | − | 0.268256i | ||||
\(904\) | −196.445 | − | 270.383i | −0.217307 | − | 0.299097i | ||||
\(905\) | −1300.77 | + | 782.639i | −1.43732 | + | 0.864795i | ||||
\(906\) | −1897.85 | − | 1378.87i | −2.09476 | − | 1.52193i | ||||
\(907\) | −718.126 | + | 718.126i | −0.791759 | + | 0.791759i | −0.981780 | − | 0.190021i | \(-0.939145\pi\) |
0.190021 | + | 0.981780i | \(0.439145\pi\) | |||||||
\(908\) | −97.4096 | − | 615.020i | −0.107279 | − | 0.677335i | ||||
\(909\) | −43.2769 | − | 14.0615i | −0.0476094 | − | 0.0154692i | ||||
\(910\) | −45.3549 | − | 112.065i | −0.0498405 | − | 0.123148i | ||||
\(911\) | −253.082 | − | 778.907i | −0.277807 | − | 0.855002i | −0.988463 | − | 0.151462i | \(-0.951602\pi\) |
0.710656 | − | 0.703540i | \(-0.248398\pi\) | |||||||
\(912\) | 438.822 | + | 861.236i | 0.481164 | + | 0.944337i | ||||
\(913\) | −1212.81 | + | 617.959i | −1.32838 | + | 0.676844i | ||||
\(914\) | −543.885 | + | 176.719i | −0.595060 | + | 0.193347i | ||||
\(915\) | −1061.73 | − | 264.047i | −1.16036 | − | 0.288576i | ||||
\(916\) | 194.002 | − | 597.076i | 0.211792 | − | 0.651829i | ||||
\(917\) | −905.062 | + | 143.348i | −0.986981 | + | 0.156322i | ||||
\(918\) | 93.3504 | + | 93.3504i | 0.101689 | + | 0.101689i | ||||
\(919\) | 879.635 | − | 1210.71i | 0.957165 | − | 1.31742i | 0.00889471 | − | 0.999960i | \(-0.497169\pi\) |
0.948270 | − | 0.317464i | \(-0.102831\pi\) | |||||||
\(920\) | −104.699 | + | 120.587i | −0.113803 | + | 0.131073i | ||||
\(921\) | −1337.32 | + | 971.617i | −1.45203 | + | 1.05496i | ||||
\(922\) | −216.987 | + | 1370.00i | −0.235344 | + | 1.48590i | ||||
\(923\) | 23.1556 | − | 45.4453i | 0.0250873 | − | 0.0492366i | ||||
\(924\) | 1952.24i | 2.11281i | ||||||||
\(925\) | 115.626 | − | 337.107i | 0.125001 | − | 0.364440i | ||||
\(926\) | −715.981 | −0.773197 | ||||||||
\(927\) | −933.206 | − | 475.492i | −1.00669 | − | 0.512937i | ||||
\(928\) | 403.479 | + | 63.9048i | 0.434783 | + | 0.0688629i | ||||
\(929\) | −648.674 | − | 892.823i | −0.698250 | − | 0.961058i | −0.999971 | − | 0.00766213i | \(-0.997561\pi\) |
0.301721 | − | 0.953396i | \(-0.402439\pi\) | |||||||
\(930\) | 2117.75 | + | 184.008i | 2.27715 | + | 0.197858i | ||||
\(931\) | 60.0066 | + | 43.5974i | 0.0644539 | + | 0.0468285i | ||||
\(932\) | 723.893 | − | 723.893i | 0.776709 | − | 0.776709i | ||||
\(933\) | −266.773 | − | 1684.34i | −0.285931 | − | 1.80530i | ||||
\(934\) | 1094.85 | + | 355.737i | 1.17221 | + | 0.380875i | ||||
\(935\) | −288.635 | + | 20.3562i | −0.308700 | + | 0.0217713i | ||||
\(936\) | −14.5311 | − | 44.7221i | −0.0155247 | − | 0.0477800i | ||||
\(937\) | −26.6874 | − | 52.3769i | −0.0284817 | − | 0.0558985i | 0.876327 | − | 0.481716i | \(-0.159986\pi\) |
−0.904809 | + | 0.425818i | \(0.859986\pi\) | |||||||
\(938\) | −1467.95 | + | 747.960i | −1.56498 | + | 0.797399i | ||||
\(939\) | 1750.43 | − | 568.751i | 1.86415 | − | 0.605698i | ||||
\(940\) | 8.19708 | + | 116.228i | 0.00872030 | + | 0.123647i | ||||
\(941\) | −455.101 | + | 1400.66i | −0.483635 | + | 1.48848i | 0.350312 | + | 0.936633i | \(0.386075\pi\) |
−0.833948 | + | 0.551844i | \(0.813925\pi\) | |||||||
\(942\) | 2930.72 | − | 464.181i | 3.11117 | − | 0.492761i | ||||
\(943\) | −343.748 | − | 343.748i | −0.364526 | − | 0.364526i | ||||
\(944\) | −413.959 | + | 569.765i | −0.438516 | + | 0.603565i | ||||
\(945\) | 27.3715 | − | 315.020i | 0.0289646 | − | 0.333355i | ||||
\(946\) | 1560.30 | − | 1133.62i | 1.64936 | − | 1.19833i | ||||
\(947\) | 214.634 | − | 1355.15i | 0.226646 | − | 1.43099i | −0.567555 | − | 0.823335i | \(-0.692111\pi\) |
0.794202 | − | 0.607654i | \(-0.207889\pi\) | |||||||
\(948\) | −493.273 | + | 968.103i | −0.520330 | + | 1.02121i | ||||
\(949\) | 71.1146i | 0.0749363i | ||||||||
\(950\) | −1567.52 | − | 537.652i | −1.65002 | − | 0.565950i | ||||
\(951\) | 779.503 | 0.819667 | ||||||||
\(952\) | 100.475 | + | 51.1947i | 0.105541 | + | 0.0537759i | ||||
\(953\) | −1007.09 | − | 159.507i | −1.05676 | − | 0.167374i | −0.396211 | − | 0.918159i | \(-0.629675\pi\) |
−0.660546 | + | 0.750786i | \(0.729675\pi\) | |||||||
\(954\) | 1384.80 | + | 1906.01i | 1.45157 | + | 1.99791i | ||||
\(955\) | −345.899 | − | 300.324i | −0.362198 | − | 0.314475i | ||||
\(956\) | −463.109 | − | 336.469i | −0.484424 | − | 0.351955i | ||||
\(957\) | 364.083 | − | 364.083i | 0.380442 | − | 0.380442i | ||||
\(958\) | −109.884 | − | 693.783i | −0.114702 | − | 0.724200i | ||||
\(959\) | −1191.58 | − | 387.169i | −1.24253 | − | 0.403721i | ||||
\(960\) | −511.809 | + | 2057.98i | −0.533135 | + | 2.14373i | ||||
\(961\) | 5.75717 | + | 17.7188i | 0.00599082 | + | 0.0184378i | ||||
\(962\) | −23.1708 | − | 45.4752i | −0.0240860 | − | 0.0472715i | ||||
\(963\) | 1988.25 | − | 1013.06i | 2.06464 | − | 1.05199i | ||||
\(964\) | 335.093 | − | 108.878i | 0.347607 | − | 0.112944i | ||||
\(965\) | 847.815 | − | 343.127i | 0.878565 | − | 0.355572i | ||||
\(966\) | −252.242 | + | 776.320i | −0.261120 | + | 0.803644i | ||||
\(967\) | 461.511 | − | 73.0962i | 0.477261 | − | 0.0755907i | 0.0868303 | − | 0.996223i | \(-0.472326\pi\) |
0.390430 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(968\) | −85.6828 | − | 85.6828i | −0.0885153 | − | 0.0885153i | ||||
\(969\) | 268.059 | − | 368.951i | 0.276634 | − | 0.380755i | ||||
\(970\) | −449.028 | − | 746.300i | −0.462916 | − | 0.769382i | ||||
\(971\) | 805.523 | − | 585.247i | 0.829581 | − | 0.602726i | −0.0898601 | − | 0.995954i | \(-0.528642\pi\) |
0.919441 | + | 0.393229i | \(0.128642\pi\) | |||||||
\(972\) | −278.574 | + | 1758.84i | −0.286598 | + | 1.80951i | ||||
\(973\) | −396.113 | + | 777.415i | −0.407105 | + | 0.798988i | ||||
\(974\) | 435.351i | 0.446973i | ||||||||
\(975\) | −116.955 | − | 62.0075i | −0.119954 | − | 0.0635975i | ||||
\(976\) | 481.339 | 0.493175 | ||||||||
\(977\) | −1580.72 | − | 805.418i | −1.61793 | − | 0.824378i | −0.999249 | − | 0.0387385i | \(-0.987666\pi\) |
−0.618684 | − | 0.785640i | \(-0.712334\pi\) | |||||||
\(978\) | −484.752 | − | 76.7772i | −0.495657 | − | 0.0785043i | ||||
\(979\) | 484.621 | + | 667.023i | 0.495016 | + | 0.681331i | ||||
\(980\) | 19.8252 | + | 85.6394i | 0.0202298 | + | 0.0873872i | ||||
\(981\) | −1218.13 | − | 885.024i | −1.24172 | − | 0.902165i | ||||
\(982\) | −256.716 | + | 256.716i | −0.261421 | + | 0.261421i | ||||
\(983\) | −113.706 | − | 717.913i | −0.115673 | − | 0.730329i | −0.975542 | − | 0.219814i | \(-0.929455\pi\) |
0.859869 | − | 0.510515i | \(-0.170545\pi\) | |||||||
\(984\) | 835.923 | + | 271.608i | 0.849515 | + | 0.276024i | ||||
\(985\) | −521.704 | − | 325.564i | −0.529648 | − | 0.330522i | ||||
\(986\) | −40.2293 | − | 123.813i | −0.0408005 | − | 0.125571i | ||||
\(987\) | 61.7695 | + | 121.229i | 0.0625831 | + | 0.122826i | ||||
\(988\) | −119.363 | + | 60.8183i | −0.120812 | + | 0.0615569i | ||||
\(989\) | 432.918 | − | 140.664i | 0.437733 | − | 0.142228i | ||||
\(990\) | 1344.63 | + | 1600.52i | 1.35821 | + | 1.61669i | ||||
\(991\) | −468.726 | + | 1442.59i | −0.472983 | + | 1.45569i | 0.375675 | + | 0.926751i | \(0.377411\pi\) |
−0.848658 | + | 0.528941i | \(0.822589\pi\) | |||||||
\(992\) | −1367.56 | + | 216.600i | −1.37859 | + | 0.218347i | ||||
\(993\) | −125.229 | − | 125.229i | −0.126112 | − | 0.126112i | ||||
\(994\) | 519.385 | − | 714.872i | 0.522520 | − | 0.719187i | ||||
\(995\) | 1796.32 | + | 761.229i | 1.80535 | + | 0.765055i | ||||
\(996\) | 2056.95 | − | 1494.46i | 2.06521 | − | 1.50046i | ||||
\(997\) | −125.911 | + | 794.973i | −0.126290 | + | 0.797365i | 0.840503 | + | 0.541806i | \(0.182259\pi\) |
−0.966794 | + | 0.255559i | \(0.917741\pi\) | |||||||
\(998\) | −377.336 | + | 740.565i | −0.378093 | + | 0.742049i | ||||
\(999\) | − | 133.493i | − | 0.133626i |
(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 | 25.3.f.a.8.4 | ✓ | 32 | |
3.2 | odd | 2 | 225.3.r.a.208.1 | 32 | |||
4.3 | odd | 2 | 400.3.bg.c.33.4 | 32 | |||
5.2 | odd | 4 | 125.3.f.a.107.1 | 32 | |||
5.3 | odd | 4 | 125.3.f.b.107.4 | 32 | |||
5.4 | even | 2 | 125.3.f.c.18.1 | 32 | |||
25.3 | odd | 20 | 125.3.f.c.7.1 | 32 | |||
25.4 | even | 10 | 125.3.f.b.118.4 | 32 | |||
25.21 | even | 5 | 125.3.f.a.118.1 | 32 | |||
25.22 | odd | 20 | inner | 25.3.f.a.22.4 | yes | 32 | |
75.47 | even | 20 | 225.3.r.a.172.1 | 32 | |||
100.47 | even | 20 | 400.3.bg.c.97.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.3.f.a.8.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
25.3.f.a.22.4 | yes | 32 | 25.22 | odd | 20 | inner | |
125.3.f.a.107.1 | 32 | 5.2 | odd | 4 | |||
125.3.f.a.118.1 | 32 | 25.21 | even | 5 | |||
125.3.f.b.107.4 | 32 | 5.3 | odd | 4 | |||
125.3.f.b.118.4 | 32 | 25.4 | even | 10 | |||
125.3.f.c.7.1 | 32 | 25.3 | odd | 20 | |||
125.3.f.c.18.1 | 32 | 5.4 | even | 2 | |||
225.3.r.a.172.1 | 32 | 75.47 | even | 20 | |||
225.3.r.a.208.1 | 32 | 3.2 | odd | 2 | |||
400.3.bg.c.33.4 | 32 | 4.3 | odd | 2 | |||
400.3.bg.c.97.4 | 32 | 100.47 | even | 20 |