Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,4,Mod(5,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.e (of order \(4\), degree \(2\), 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: | \(0.944030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(1.28199 - 1.53509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.5 |
Dual form | 16.4.e.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81708 | − | 0.253099i | −0.995988 | − | 0.0894841i | ||||
\(3\) | 5.49618 | − | 5.49618i | 1.05774 | − | 1.05774i | 0.0595129 | − | 0.998228i | \(-0.481045\pi\) |
0.998228 | − | 0.0595129i | \(-0.0189548\pi\) | |||||||
\(4\) | 7.87188 | + | 1.42600i | 0.983985 | + | 0.178250i | ||||
\(5\) | −4.66372 | − | 4.66372i | −0.417136 | − | 0.417136i | 0.467079 | − | 0.884215i | \(-0.345306\pi\) |
−0.884215 | + | 0.467079i | \(0.845306\pi\) | |||||||
\(6\) | −16.8743 | + | 14.0921i | −1.14815 | + | 0.958846i | ||||
\(7\) | 24.8965i | 1.34429i | 0.740422 | + | 0.672143i | \(0.234626\pi\) | ||||
−0.740422 | + | 0.672143i | \(0.765374\pi\) | |||||||
\(8\) | −21.8148 | − | 6.00953i | −0.964087 | − | 0.265586i | ||||
\(9\) | − | 33.4160i | − | 1.23763i | ||||||
\(10\) | 11.9577 | + | 14.3185i | 0.378136 | + | 0.452790i | ||||
\(11\) | 22.3431 | + | 22.3431i | 0.612427 | + | 0.612427i | 0.943578 | − | 0.331151i | \(-0.107437\pi\) |
−0.331151 | + | 0.943578i | \(0.607437\pi\) | |||||||
\(12\) | 51.1028 | − | 35.4277i | 1.22934 | − | 0.852259i | ||||
\(13\) | −11.2714 | + | 11.2714i | −0.240471 | + | 0.240471i | −0.817045 | − | 0.576574i | \(-0.804389\pi\) |
0.576574 | + | 0.817045i | \(0.304389\pi\) | |||||||
\(14\) | 6.30129 | − | 70.1355i | 0.120292 | − | 1.33889i | ||||
\(15\) | −51.2653 | −0.882443 | ||||||||
\(16\) | 59.9330 | + | 22.4506i | 0.936454 | + | 0.350791i | ||||
\(17\) | −88.4846 | −1.26239 | −0.631196 | − | 0.775623i | \(-0.717436\pi\) | ||||
−0.631196 | + | 0.775623i | \(0.717436\pi\) | |||||||
\(18\) | −8.45756 | + | 94.1356i | −0.110748 | + | 1.23266i | ||||
\(19\) | 37.8187 | − | 37.8187i | 0.456643 | − | 0.456643i | −0.440909 | − | 0.897552i | \(-0.645344\pi\) |
0.897552 | + | 0.440909i | \(0.145344\pi\) | |||||||
\(20\) | −30.0618 | − | 43.3627i | −0.336101 | − | 0.484810i | ||||
\(21\) | 136.836 | + | 136.836i | 1.42191 | + | 1.42191i | ||||
\(22\) | −57.2873 | − | 68.5974i | −0.555168 | − | 0.664773i | ||||
\(23\) | − | 48.1224i | − | 0.436270i | −0.975919 | − | 0.218135i | \(-0.930003\pi\) | ||
0.975919 | − | 0.218135i | \(-0.0699973\pi\) | |||||||
\(24\) | −152.928 | + | 86.8686i | −1.30068 | + | 0.738833i | ||||
\(25\) | − | 81.4994i | − | 0.651995i | ||||||
\(26\) | 34.6053 | − | 28.8997i | 0.261025 | − | 0.217988i | ||||
\(27\) | −35.2635 | − | 35.2635i | −0.251351 | − | 0.251351i | ||||
\(28\) | −35.5025 | + | 195.982i | −0.239619 | + | 1.32276i | ||||
\(29\) | 10.4432 | − | 10.4432i | 0.0668705 | − | 0.0668705i | −0.672881 | − | 0.739751i | \(-0.734943\pi\) |
0.739751 | + | 0.672881i | \(0.234943\pi\) | |||||||
\(30\) | 144.419 | + | 12.9752i | 0.878903 | + | 0.0789646i | ||||
\(31\) | −96.9578 | −0.561746 | −0.280873 | − | 0.959745i | \(-0.590624\pi\) | ||||
−0.280873 | + | 0.959745i | \(0.590624\pi\) | |||||||
\(32\) | −163.154 | − | 78.4142i | −0.901307 | − | 0.433181i | ||||
\(33\) | 245.604 | 1.29558 | ||||||||
\(34\) | 249.268 | + | 22.3954i | 1.25733 | + | 0.112964i | ||||
\(35\) | 116.110 | − | 116.110i | 0.560750 | − | 0.560750i | ||||
\(36\) | 47.6513 | − | 263.047i | 0.220608 | − | 1.21781i | ||||
\(37\) | −163.279 | − | 163.279i | −0.725484 | − | 0.725484i | 0.244233 | − | 0.969717i | \(-0.421464\pi\) |
−0.969717 | + | 0.244233i | \(0.921464\pi\) | |||||||
\(38\) | −116.110 | + | 96.9665i | −0.495673 | + | 0.413949i | ||||
\(39\) | 123.899i | 0.508713i | ||||||||
\(40\) | 73.7114 | + | 129.765i | 0.291370 | + | 0.512941i | ||||
\(41\) | 360.519i | 1.37326i | 0.727008 | + | 0.686629i | \(0.240910\pi\) | ||||
−0.727008 | + | 0.686629i | \(0.759090\pi\) | |||||||
\(42\) | −350.844 | − | 420.110i | −1.28896 | − | 1.54344i | ||||
\(43\) | −100.249 | − | 100.249i | −0.355531 | − | 0.355531i | 0.506632 | − | 0.862163i | \(-0.330890\pi\) |
−0.862163 | + | 0.506632i | \(0.830890\pi\) | |||||||
\(44\) | 144.021 | + | 207.744i | 0.493454 | + | 0.711785i | ||||
\(45\) | −155.843 | + | 155.843i | −0.516260 | + | 0.516260i | ||||
\(46\) | −12.1797 | + | 135.565i | −0.0390392 | + | 0.434520i | ||||
\(47\) | 220.669 | 0.684849 | 0.342425 | − | 0.939545i | \(-0.388752\pi\) | ||||
0.342425 | + | 0.939545i | \(0.388752\pi\) | |||||||
\(48\) | 452.796 | − | 206.010i | 1.36157 | − | 0.619479i | ||||
\(49\) | −276.837 | −0.807104 | ||||||||
\(50\) | −20.6274 | + | 229.590i | −0.0583432 | + | 0.649379i | ||||
\(51\) | −486.327 | + | 486.327i | −1.33528 | + | 1.33528i | ||||
\(52\) | −104.800 | + | 72.6542i | −0.279484 | + | 0.193756i | ||||
\(53\) | −175.752 | − | 175.752i | −0.455498 | − | 0.455498i | 0.441676 | − | 0.897174i | \(-0.354384\pi\) |
−0.897174 | + | 0.441676i | \(0.854384\pi\) | |||||||
\(54\) | 90.4150 | + | 108.265i | 0.227850 | + | 0.272834i | ||||
\(55\) | − | 208.404i | − | 0.510931i | ||||||
\(56\) | 149.616 | − | 543.113i | 0.357024 | − | 1.29601i | ||||
\(57\) | − | 415.717i | − | 0.966019i | ||||||
\(58\) | −32.0624 | + | 26.7761i | −0.0725861 | + | 0.0606184i | ||||
\(59\) | 405.008 | + | 405.008i | 0.893687 | + | 0.893687i | 0.994868 | − | 0.101181i | \(-0.0322622\pi\) |
−0.101181 | + | 0.994868i | \(0.532262\pi\) | |||||||
\(60\) | −403.555 | − | 73.1044i | −0.868311 | − | 0.157296i | ||||
\(61\) | 664.576 | − | 664.576i | 1.39492 | − | 1.39492i | 0.581061 | − | 0.813860i | \(-0.302638\pi\) |
0.813860 | − | 0.581061i | \(-0.197362\pi\) | |||||||
\(62\) | 273.138 | + | 24.5399i | 0.559493 | + | 0.0502674i | ||||
\(63\) | 831.942 | 1.66373 | ||||||||
\(64\) | 439.771 | + | 262.193i | 0.858928 | + | 0.512096i | ||||
\(65\) | 105.133 | 0.200619 | ||||||||
\(66\) | −691.885 | − | 62.1621i | −1.29038 | − | 0.115934i | ||||
\(67\) | −107.377 | + | 107.377i | −0.195794 | + | 0.195794i | −0.798194 | − | 0.602400i | \(-0.794211\pi\) |
0.602400 | + | 0.798194i | \(0.294211\pi\) | |||||||
\(68\) | −696.540 | − | 126.179i | −1.24218 | − | 0.225022i | ||||
\(69\) | −264.489 | − | 264.489i | −0.461461 | − | 0.461461i | ||||
\(70\) | −356.480 | + | 297.705i | −0.608679 | + | 0.508322i | ||||
\(71\) | − | 215.050i | − | 0.359461i | −0.983716 | − | 0.179731i | \(-0.942477\pi\) | ||
0.983716 | − | 0.179731i | \(-0.0575226\pi\) | |||||||
\(72\) | −200.814 | + | 728.964i | −0.328697 | + | 1.19318i | ||||
\(73\) | 668.587i | 1.07195i | 0.844235 | + | 0.535974i | \(0.180055\pi\) | ||||
−0.844235 | + | 0.535974i | \(0.819945\pi\) | |||||||
\(74\) | 418.644 | + | 501.296i | 0.657654 | + | 0.787492i | ||||
\(75\) | −447.935 | − | 447.935i | −0.689642 | − | 0.689642i | ||||
\(76\) | 351.634 | − | 243.775i | 0.530726 | − | 0.367933i | ||||
\(77\) | −556.266 | + | 556.266i | −0.823277 | + | 0.823277i | ||||
\(78\) | 31.3588 | − | 349.035i | 0.0455217 | − | 0.506672i | ||||
\(79\) | −822.956 | −1.17202 | −0.586012 | − | 0.810303i | \(-0.699303\pi\) | ||||
−0.586012 | + | 0.810303i | \(0.699303\pi\) | |||||||
\(80\) | −174.808 | − | 384.215i | −0.244301 | − | 0.536956i | ||||
\(81\) | 514.603 | 0.705902 | ||||||||
\(82\) | 91.2471 | − | 1015.61i | 0.122885 | − | 1.36775i | ||||
\(83\) | 326.873 | − | 326.873i | 0.432277 | − | 0.432277i | −0.457125 | − | 0.889402i | \(-0.651121\pi\) |
0.889402 | + | 0.457125i | \(0.151121\pi\) | |||||||
\(84\) | 882.027 | + | 1272.28i | 1.14568 | + | 1.65259i | ||||
\(85\) | 412.668 | + | 412.668i | 0.526589 | + | 0.526589i | ||||
\(86\) | 257.037 | + | 307.783i | 0.322290 | + | 0.385919i | ||||
\(87\) | − | 114.795i | − | 0.141463i | ||||||
\(88\) | −353.139 | − | 621.682i | −0.427781 | − | 0.753086i | ||||
\(89\) | 262.733i | 0.312918i | 0.987684 | + | 0.156459i | \(0.0500079\pi\) | ||||
−0.987684 | + | 0.156459i | \(0.949992\pi\) | |||||||
\(90\) | 478.466 | − | 399.578i | 0.560386 | − | 0.467992i | ||||
\(91\) | −280.619 | − | 280.619i | −0.323262 | − | 0.323262i | ||||
\(92\) | 68.6226 | − | 378.814i | 0.0777652 | − | 0.429283i | ||||
\(93\) | −532.898 | + | 532.898i | −0.594182 | + | 0.594182i | ||||
\(94\) | −621.643 | − | 55.8512i | −0.682102 | − | 0.0612831i | ||||
\(95\) | −352.752 | −0.380964 | ||||||||
\(96\) | −1327.70 | + | 465.745i | −1.41154 | + | 0.495155i | ||||
\(97\) | −150.801 | −0.157850 | −0.0789251 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789251 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(98\) | 779.871 | + | 70.0671i | 0.803866 | + | 0.0722229i | ||||
\(99\) | 746.618 | − | 746.618i | 0.757958 | − | 0.757958i | ||||
\(100\) | 116.218 | − | 641.553i | 0.116218 | − | 0.641553i | ||||
\(101\) | 487.985 | + | 487.985i | 0.480755 | + | 0.480755i | 0.905373 | − | 0.424617i | \(-0.139591\pi\) |
−0.424617 | + | 0.905373i | \(0.639591\pi\) | |||||||
\(102\) | 1493.11 | − | 1246.93i | 1.44941 | − | 1.21044i | ||||
\(103\) | 1840.58i | 1.76075i | 0.474275 | + | 0.880377i | \(0.342710\pi\) | ||||
−0.474275 | + | 0.880377i | \(0.657290\pi\) | |||||||
\(104\) | 313.620 | − | 178.148i | 0.295701 | − | 0.167970i | ||||
\(105\) | − | 1276.33i | − | 1.18626i | ||||||
\(106\) | 450.625 | + | 539.590i | 0.412911 | + | 0.494431i | ||||
\(107\) | −79.4098 | − | 79.4098i | −0.0717461 | − | 0.0717461i | 0.670323 | − | 0.742069i | \(-0.266155\pi\) |
−0.742069 | + | 0.670323i | \(0.766155\pi\) | |||||||
\(108\) | −227.304 | − | 327.876i | −0.202522 | − | 0.292129i | ||||
\(109\) | 952.979 | − | 952.979i | 0.837421 | − | 0.837421i | −0.151098 | − | 0.988519i | \(-0.548281\pi\) |
0.988519 | + | 0.151098i | \(0.0482809\pi\) | |||||||
\(110\) | −52.7469 | + | 587.091i | −0.0457202 | + | 0.508881i | ||||
\(111\) | −1794.82 | −1.53475 | ||||||||
\(112\) | −558.942 | + | 1492.12i | −0.471563 | + | 1.25886i | ||||
\(113\) | −720.469 | −0.599788 | −0.299894 | − | 0.953973i | \(-0.596951\pi\) | ||||
−0.299894 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(114\) | −105.218 | + | 1171.11i | −0.0864433 | + | 0.962144i | ||||
\(115\) | −224.430 | + | 224.430i | −0.181984 | + | 0.181984i | ||||
\(116\) | 97.0993 | − | 67.3153i | 0.0777193 | − | 0.0538799i | ||||
\(117\) | 376.646 | + | 376.646i | 0.297615 | + | 0.297615i | ||||
\(118\) | −1038.43 | − | 1243.45i | −0.810131 | − | 0.970072i | ||||
\(119\) | − | 2202.96i | − | 1.69702i | ||||||
\(120\) | 1118.34 | + | 308.080i | 0.850752 | + | 0.234365i | ||||
\(121\) | − | 332.571i | − | 0.249865i | ||||||
\(122\) | −2040.37 | + | 1703.96i | −1.51415 | + | 1.26450i | ||||
\(123\) | 1981.48 | + | 1981.48i | 1.45255 | + | 1.45255i | ||||
\(124\) | −763.240 | − | 138.262i | −0.552750 | − | 0.100131i | ||||
\(125\) | −963.056 | + | 963.056i | −0.689107 | + | 0.689107i | ||||
\(126\) | −2343.65 | − | 210.564i | −1.65705 | − | 0.148877i | ||||
\(127\) | 2622.35 | 1.83225 | 0.916124 | − | 0.400895i | \(-0.131301\pi\) | ||||
0.916124 | + | 0.400895i | \(0.131301\pi\) | |||||||
\(128\) | −1172.51 | − | 849.925i | −0.809658 | − | 0.586902i | ||||
\(129\) | −1101.97 | −0.752119 | ||||||||
\(130\) | −296.169 | − | 26.6092i | −0.199814 | − | 0.0179522i | ||||
\(131\) | 657.574 | − | 657.574i | 0.438569 | − | 0.438569i | −0.452961 | − | 0.891530i | \(-0.649632\pi\) |
0.891530 | + | 0.452961i | \(0.149632\pi\) | |||||||
\(132\) | 1933.36 | + | 350.231i | 1.27483 | + | 0.230937i | ||||
\(133\) | 941.555 | + | 941.555i | 0.613858 | + | 0.613858i | ||||
\(134\) | 329.666 | − | 275.312i | 0.212529 | − | 0.177488i | ||||
\(135\) | 328.919i | 0.209695i | ||||||||
\(136\) | 1930.27 | + | 531.751i | 1.21706 | + | 0.335274i | ||||
\(137\) | − | 2511.52i | − | 1.56623i | −0.621874 | − | 0.783117i | \(-0.713629\pi\) | ||
0.621874 | − | 0.783117i | \(-0.286371\pi\) | |||||||
\(138\) | 678.146 | + | 812.030i | 0.418316 | + | 0.500903i | ||||
\(139\) | −1086.02 | − | 1086.02i | −0.662697 | − | 0.662697i | 0.293318 | − | 0.956015i | \(-0.405241\pi\) |
−0.956015 | + | 0.293318i | \(0.905241\pi\) | |||||||
\(140\) | 1079.58 | − | 748.434i | 0.651723 | − | 0.451816i | ||||
\(141\) | 1212.84 | − | 1212.84i | 0.724393 | − | 0.724393i | ||||
\(142\) | −54.4290 | + | 605.813i | −0.0321661 | + | 0.358019i | ||||
\(143\) | −503.677 | −0.294543 | ||||||||
\(144\) | 750.210 | − | 2002.72i | 0.434149 | − | 1.15898i | ||||
\(145\) | −97.4080 | −0.0557882 | ||||||||
\(146\) | 169.219 | − | 1883.46i | 0.0959222 | − | 1.06765i | ||||
\(147\) | −1521.54 | + | 1521.54i | −0.853706 | + | 0.853706i | ||||
\(148\) | −1052.48 | − | 1518.15i | −0.584547 | − | 0.843183i | ||||
\(149\) | −2284.63 | − | 2284.63i | −1.25614 | − | 1.25614i | −0.952922 | − | 0.303214i | \(-0.901940\pi\) |
−0.303214 | − | 0.952922i | \(-0.598060\pi\) | |||||||
\(150\) | 1148.50 | + | 1375.24i | 0.625163 | + | 0.748587i | ||||
\(151\) | 2814.39i | 1.51677i | 0.651809 | + | 0.758383i | \(0.274010\pi\) | ||||
−0.651809 | + | 0.758383i | \(0.725990\pi\) | |||||||
\(152\) | −1052.28 | + | 597.735i | −0.561521 | + | 0.318965i | ||||
\(153\) | 2956.80i | 1.56237i | ||||||||
\(154\) | 1707.84 | − | 1426.25i | 0.893645 | − | 0.746304i | ||||
\(155\) | 452.184 | + | 452.184i | 0.234325 | + | 0.234325i | ||||
\(156\) | −176.681 | + | 975.322i | −0.0906781 | + | 0.500566i | ||||
\(157\) | −906.308 | + | 906.308i | −0.460709 | + | 0.460709i | −0.898888 | − | 0.438179i | \(-0.855624\pi\) |
0.438179 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(158\) | 2318.33 | + | 208.290i | 1.16732 | + | 0.104877i | ||||
\(159\) | −1931.93 | −0.963598 | ||||||||
\(160\) | 395.203 | + | 1126.61i | 0.195272 | + | 0.556663i | ||||
\(161\) | 1198.08 | 0.586472 | ||||||||
\(162\) | −1449.68 | − | 130.246i | −0.703070 | − | 0.0631670i | ||||
\(163\) | 1392.36 | − | 1392.36i | 0.669067 | − | 0.669067i | −0.288433 | − | 0.957500i | \(-0.593134\pi\) |
0.957500 | + | 0.288433i | \(0.0931342\pi\) | |||||||
\(164\) | −514.101 | + | 2837.96i | −0.244784 | + | 1.35127i | ||||
\(165\) | −1145.43 | − | 1145.43i | −0.540433 | − | 0.540433i | ||||
\(166\) | −1003.56 | + | 838.097i | −0.469225 | + | 0.391861i | ||||
\(167\) | 1221.66i | 0.566075i | 0.959109 | + | 0.283038i | \(0.0913421\pi\) | ||||
−0.959109 | + | 0.283038i | \(0.908658\pi\) | |||||||
\(168\) | −2162.73 | − | 3807.36i | −0.993202 | − | 1.74848i | ||||
\(169\) | 1942.91i | 0.884347i | ||||||||
\(170\) | −1058.07 | − | 1266.96i | −0.477356 | − | 0.571598i | ||||
\(171\) | −1263.75 | − | 1263.75i | −0.565155 | − | 0.565155i | ||||
\(172\) | −646.193 | − | 932.104i | −0.286464 | − | 0.413211i | ||||
\(173\) | −563.418 | + | 563.418i | −0.247606 | + | 0.247606i | −0.819988 | − | 0.572381i | \(-0.806020\pi\) |
0.572381 | + | 0.819988i | \(0.306020\pi\) | |||||||
\(174\) | −29.0545 | + | 323.387i | −0.0126587 | + | 0.140896i | ||||
\(175\) | 2029.05 | 0.876468 | ||||||||
\(176\) | 837.474 | + | 1840.71i | 0.358676 | + | 0.788344i | ||||
\(177\) | 4451.99 | 1.89058 | ||||||||
\(178\) | 66.4976 | − | 740.141i | 0.0280012 | − | 0.311662i | ||||
\(179\) | −2202.23 | + | 2202.23i | −0.919565 | + | 0.919565i | −0.996998 | − | 0.0774329i | \(-0.975328\pi\) |
0.0774329 | + | 0.996998i | \(0.475328\pi\) | |||||||
\(180\) | −1449.01 | + | 1004.55i | −0.600016 | + | 0.415969i | ||||
\(181\) | 121.294 | + | 121.294i | 0.0498104 | + | 0.0498104i | 0.731573 | − | 0.681763i | \(-0.238786\pi\) |
−0.681763 | + | 0.731573i | \(0.738786\pi\) | |||||||
\(182\) | 719.502 | + | 861.551i | 0.293039 | + | 0.350892i | ||||
\(183\) | − | 7305.26i | − | 2.95093i | ||||||
\(184\) | −289.193 | + | 1049.78i | −0.115867 | + | 0.420602i | ||||
\(185\) | 1522.98i | 0.605251i | ||||||||
\(186\) | 1636.09 | − | 1366.34i | 0.644968 | − | 0.538628i | ||||
\(187\) | −1977.02 | − | 1977.02i | −0.773124 | − | 0.773124i | ||||
\(188\) | 1737.08 | + | 314.675i | 0.673882 | + | 0.122074i | ||||
\(189\) | 877.939 | − | 877.939i | 0.337887 | − | 0.337887i | ||||
\(190\) | 993.731 | + | 89.2813i | 0.379436 | + | 0.0340902i | ||||
\(191\) | 3927.65 | 1.48793 | 0.743966 | − | 0.668218i | \(-0.232942\pi\) | ||||
0.743966 | + | 0.668218i | \(0.232942\pi\) | |||||||
\(192\) | 3858.12 | − | 976.000i | 1.45019 | − | 0.366858i | ||||
\(193\) | −3249.02 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(194\) | 424.817 | + | 38.1675i | 0.157217 | + | 0.0141251i | ||||
\(195\) | 577.833 | − | 577.833i | 0.212202 | − | 0.212202i | ||||
\(196\) | −2179.23 | − | 394.769i | −0.794178 | − | 0.143866i | ||||
\(197\) | 2420.90 | + | 2420.90i | 0.875545 | + | 0.875545i | 0.993070 | − | 0.117525i | \(-0.0374961\pi\) |
−0.117525 | + | 0.993070i | \(0.537496\pi\) | |||||||
\(198\) | −2292.25 | + | 1914.31i | −0.822743 | + | 0.687093i | ||||
\(199\) | − | 1371.30i | − | 0.488488i | −0.969714 | − | 0.244244i | \(-0.921460\pi\) | ||
0.969714 | − | 0.244244i | \(-0.0785397\pi\) | |||||||
\(200\) | −489.773 | + | 1777.89i | −0.173161 | + | 0.628580i | ||||
\(201\) | 1180.33i | 0.414198i | ||||||||
\(202\) | −1251.18 | − | 1498.20i | −0.435807 | − | 0.521847i | ||||
\(203\) | 259.998 | + | 259.998i | 0.0898931 | + | 0.0898931i | ||||
\(204\) | −4521.82 | + | 3134.81i | −1.55191 | + | 1.07588i | ||||
\(205\) | 1681.36 | − | 1681.36i | 0.572836 | − | 0.572836i | ||||
\(206\) | 465.849 | − | 5185.06i | 0.157559 | − | 1.75369i | ||||
\(207\) | −1608.06 | −0.539941 | ||||||||
\(208\) | −928.580 | + | 422.480i | −0.309546 | + | 0.140835i | ||||
\(209\) | 1689.98 | 0.559321 | ||||||||
\(210\) | −323.038 | + | 3595.52i | −0.106151 | + | 1.18150i | ||||
\(211\) | −1620.50 | + | 1620.50i | −0.528719 | + | 0.528719i | −0.920190 | − | 0.391471i | \(-0.871966\pi\) |
0.391471 | + | 0.920190i | \(0.371966\pi\) | |||||||
\(212\) | −1132.88 | − | 1634.12i | −0.367011 | − | 0.529396i | ||||
\(213\) | −1181.95 | − | 1181.95i | −0.380217 | − | 0.380217i | ||||
\(214\) | 203.605 | + | 243.802i | 0.0650382 | + | 0.0778784i | ||||
\(215\) | 935.068i | 0.296610i | ||||||||
\(216\) | 557.350 | + | 981.184i | 0.175569 | + | 0.309079i | ||||
\(217\) | − | 2413.91i | − | 0.755148i | ||||||
\(218\) | −2925.82 | + | 2443.42i | −0.908997 | + | 0.759125i | ||||
\(219\) | 3674.67 | + | 3674.67i | 1.13384 | + | 1.13384i | ||||
\(220\) | 297.185 | − | 1640.53i | 0.0910736 | − | 0.502749i | ||||
\(221\) | 997.347 | − | 997.347i | 0.303569 | − | 0.303569i | ||||
\(222\) | 5056.15 | + | 454.268i | 1.52859 | + | 0.137335i | ||||
\(223\) | −419.617 | −0.126007 | −0.0630036 | − | 0.998013i | \(-0.520068\pi\) | ||||
−0.0630036 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(224\) | 1952.24 | − | 4061.97i | 0.582320 | − | 1.21161i | ||||
\(225\) | −2723.38 | −0.806929 | ||||||||
\(226\) | 2029.62 | + | 182.350i | 0.597381 | + | 0.0536714i | ||||
\(227\) | −2133.64 | + | 2133.64i | −0.623853 | + | 0.623853i | −0.946515 | − | 0.322661i | \(-0.895423\pi\) |
0.322661 | + | 0.946515i | \(0.395423\pi\) | |||||||
\(228\) | 592.813 | − | 3272.48i | 0.172193 | − | 0.950548i | ||||
\(229\) | −1574.42 | − | 1574.42i | −0.454325 | − | 0.454325i | 0.442462 | − | 0.896787i | \(-0.354105\pi\) |
−0.896787 | + | 0.442462i | \(0.854105\pi\) | |||||||
\(230\) | 689.039 | − | 575.433i | 0.197539 | − | 0.164969i | ||||
\(231\) | 6114.67i | 1.74163i | ||||||||
\(232\) | −290.574 | + | 165.057i | −0.0822289 | + | 0.0467091i | ||||
\(233\) | − | 1194.86i | − | 0.335957i | −0.985791 | − | 0.167978i | \(-0.946276\pi\) | ||
0.985791 | − | 0.167978i | \(-0.0537239\pi\) | |||||||
\(234\) | −965.712 | − | 1156.37i | −0.269789 | − | 0.323052i | ||||
\(235\) | −1029.14 | − | 1029.14i | −0.285675 | − | 0.285675i | ||||
\(236\) | 2610.63 | + | 3765.71i | 0.720075 | + | 1.03867i | ||||
\(237\) | −4523.12 | + | 4523.12i | −1.23970 | + | 1.23970i | ||||
\(238\) | −557.567 | + | 6205.91i | −0.151856 | + | 1.69021i | ||||
\(239\) | −4241.03 | −1.14782 | −0.573911 | − | 0.818917i | \(-0.694575\pi\) | ||||
−0.573911 | + | 0.818917i | \(0.694575\pi\) | |||||||
\(240\) | −3072.49 | − | 1150.94i | −0.826367 | − | 0.309553i | ||||
\(241\) | −5571.19 | −1.48910 | −0.744548 | − | 0.667569i | \(-0.767335\pi\) | ||||
−0.744548 | + | 0.667569i | \(0.767335\pi\) | |||||||
\(242\) | −84.1734 | + | 936.878i | −0.0223590 | + | 0.248863i | ||||
\(243\) | 3780.46 | − | 3780.46i | 0.998012 | − | 0.998012i | ||||
\(244\) | 6179.15 | − | 4283.77i | 1.62123 | − | 1.12394i | ||||
\(245\) | 1291.09 | + | 1291.09i | 0.336672 | + | 0.336672i | ||||
\(246\) | −5080.47 | − | 6083.49i | −1.31674 | − | 1.57670i | ||||
\(247\) | 852.541i | 0.219619i | ||||||||
\(248\) | 2115.12 | + | 582.671i | 0.541572 | + | 0.149192i | ||||
\(249\) | − | 3593.11i | − | 0.914474i | ||||||
\(250\) | 2956.75 | − | 2469.26i | 0.748006 | − | 0.624678i | ||||
\(251\) | −482.728 | − | 482.728i | −0.121393 | − | 0.121393i | 0.643801 | − | 0.765193i | \(-0.277357\pi\) |
−0.765193 | + | 0.643801i | \(0.777357\pi\) | |||||||
\(252\) | 6548.95 | + | 1186.35i | 1.63708 | + | 0.296560i | ||||
\(253\) | 1075.20 | − | 1075.20i | 0.267184 | − | 0.267184i | ||||
\(254\) | −7387.36 | − | 663.713i | −1.82490 | − | 0.163957i | ||||
\(255\) | 4536.19 | 1.11399 | ||||||||
\(256\) | 3087.94 | + | 2691.07i | 0.753891 | + | 0.656999i | ||||
\(257\) | 8093.12 | 1.96434 | 0.982169 | − | 0.188002i | \(-0.0602013\pi\) | ||||
0.982169 | + | 0.188002i | \(0.0602013\pi\) | |||||||
\(258\) | 3104.35 | + | 278.909i | 0.749102 | + | 0.0673027i | ||||
\(259\) | 4065.08 | − | 4065.08i | 0.975257 | − | 0.975257i | ||||
\(260\) | 827.598 | + | 149.921i | 0.197406 | + | 0.0357603i | ||||
\(261\) | −348.969 | − | 348.969i | −0.0827610 | − | 0.0827610i | ||||
\(262\) | −2018.87 | + | 1686.01i | −0.476054 | + | 0.397564i | ||||
\(263\) | 410.300i | 0.0961984i | 0.998843 | + | 0.0480992i | \(0.0153164\pi\) | ||||
−0.998843 | + | 0.0480992i | \(0.984684\pi\) | |||||||
\(264\) | −5357.79 | − | 1475.96i | −1.24905 | − | 0.344088i | ||||
\(265\) | 1639.32i | 0.380009i | ||||||||
\(266\) | −2414.13 | − | 2890.74i | −0.556465 | − | 0.666326i | ||||
\(267\) | 1444.03 | + | 1444.03i | 0.330986 | + | 0.330986i | ||||
\(268\) | −998.378 | + | 692.139i | −0.227558 | + | 0.157758i | ||||
\(269\) | −4.77962 | + | 4.77962i | −0.00108334 | + | 0.00108334i | −0.707648 | − | 0.706565i | \(-0.750244\pi\) |
0.706565 | + | 0.707648i | \(0.250244\pi\) | |||||||
\(270\) | 83.2490 | − | 926.590i | 0.0187643 | − | 0.208854i | ||||
\(271\) | −2833.98 | −0.635247 | −0.317623 | − | 0.948217i | \(-0.602885\pi\) | ||||
−0.317623 | + | 0.948217i | \(0.602885\pi\) | |||||||
\(272\) | −5303.15 | − | 1986.54i | −1.18217 | − | 0.442836i | ||||
\(273\) | −3084.67 | −0.683855 | ||||||||
\(274\) | −635.665 | + | 7075.17i | −0.140153 | + | 1.55995i | ||||
\(275\) | 1820.95 | − | 1820.95i | 0.399300 | − | 0.399300i | ||||
\(276\) | −1704.87 | − | 2459.19i | −0.371815 | − | 0.536326i | ||||
\(277\) | 1525.80 | + | 1525.80i | 0.330962 | + | 0.330962i | 0.852952 | − | 0.521989i | \(-0.174810\pi\) |
−0.521989 | + | 0.852952i | \(0.674810\pi\) | |||||||
\(278\) | 2784.53 | + | 3334.27i | 0.600738 | + | 0.719339i | ||||
\(279\) | 3239.94i | 0.695234i | ||||||||
\(280\) | −3230.70 | + | 1835.16i | −0.689539 | + | 0.391684i | ||||
\(281\) | − | 4750.23i | − | 1.00845i | −0.863572 | − | 0.504226i | \(-0.831778\pi\) | ||
0.863572 | − | 0.504226i | \(-0.168222\pi\) | |||||||
\(282\) | −3723.63 | + | 3109.69i | −0.786308 | + | 0.656665i | ||||
\(283\) | 644.104 | + | 644.104i | 0.135293 | + | 0.135293i | 0.771510 | − | 0.636217i | \(-0.219502\pi\) |
−0.636217 | + | 0.771510i | \(0.719502\pi\) | |||||||
\(284\) | 306.662 | − | 1692.85i | 0.0640740 | − | 0.353705i | ||||
\(285\) | −1938.79 | + | 1938.79i | −0.402961 | + | 0.402961i | ||||
\(286\) | 1418.90 | + | 127.480i | 0.293361 | + | 0.0263569i | ||||
\(287\) | −8975.67 | −1.84605 | ||||||||
\(288\) | −2620.29 | + | 5451.95i | −0.536118 | + | 1.11548i | ||||
\(289\) | 2916.53 | 0.593635 | ||||||||
\(290\) | 274.406 | + | 24.6539i | 0.0555644 | + | 0.00499216i | ||||
\(291\) | −828.827 | + | 828.827i | −0.166965 | + | 0.166965i | ||||
\(292\) | −953.405 | + | 5263.03i | −0.191075 | + | 1.05478i | ||||
\(293\) | −1433.16 | − | 1433.16i | −0.285755 | − | 0.285755i | 0.549644 | − | 0.835399i | \(-0.314763\pi\) |
−0.835399 | + | 0.549644i | \(0.814763\pi\) | |||||||
\(294\) | 4671.41 | − | 3901.21i | 0.926675 | − | 0.773888i | ||||
\(295\) | − | 3777.69i | − | 0.745578i | ||||||
\(296\) | 2580.67 | + | 4543.13i | 0.506751 | + | 0.892108i | ||||
\(297\) | − | 1575.79i | − | 0.307868i | ||||||
\(298\) | 5857.75 | + | 7014.23i | 1.13869 | + | 1.36350i | ||||
\(299\) | 542.407 | + | 542.407i | 0.104910 | + | 0.104910i | ||||
\(300\) | −2887.34 | − | 4164.85i | −0.555668 | − | 0.801526i | ||||
\(301\) | 2495.85 | − | 2495.85i | 0.477935 | − | 0.477935i | ||||
\(302\) | 712.319 | − | 7928.36i | 0.135726 | − | 1.51068i | ||||
\(303\) | 5364.10 | 1.01703 | ||||||||
\(304\) | 3115.65 | − | 1417.54i | 0.587811 | − | 0.267439i | ||||
\(305\) | −6198.79 | −1.16374 | ||||||||
\(306\) | 748.364 | − | 8329.55i | 0.139808 | − | 1.55611i | ||||
\(307\) | −231.211 | + | 231.211i | −0.0429834 | + | 0.0429834i | −0.728272 | − | 0.685288i | \(-0.759676\pi\) |
0.685288 | + | 0.728272i | \(0.259676\pi\) | |||||||
\(308\) | −5172.09 | + | 3585.62i | −0.956842 | + | 0.663343i | ||||
\(309\) | 10116.2 | + | 10116.2i | 1.86242 | + | 1.86242i | ||||
\(310\) | −1159.39 | − | 1388.29i | −0.212416 | − | 0.254353i | ||||
\(311\) | − | 871.410i | − | 0.158885i | −0.996839 | − | 0.0794423i | \(-0.974686\pi\) | ||
0.996839 | − | 0.0794423i | \(-0.0253140\pi\) | |||||||
\(312\) | 744.577 | − | 2702.84i | 0.135107 | − | 0.490443i | ||||
\(313\) | 3515.02i | 0.634762i | 0.948298 | + | 0.317381i | \(0.102803\pi\) | ||||
−0.948298 | + | 0.317381i | \(0.897197\pi\) | |||||||
\(314\) | 2782.53 | − | 2323.76i | 0.500087 | − | 0.417634i | ||||
\(315\) | −3879.95 | − | 3879.95i | −0.694001 | − | 0.694001i | ||||
\(316\) | −6478.22 | − | 1173.54i | −1.15325 | − | 0.208913i | ||||
\(317\) | 4723.77 | − | 4723.77i | 0.836951 | − | 0.836951i | −0.151506 | − | 0.988456i | \(-0.548412\pi\) |
0.988456 | + | 0.151506i | \(0.0484121\pi\) | |||||||
\(318\) | 5442.40 | + | 488.970i | 0.959732 | + | 0.0862266i | ||||
\(319\) | 466.665 | 0.0819067 | ||||||||
\(320\) | −828.174 | − | 3273.77i | −0.144676 | − | 0.571904i | ||||
\(321\) | −872.901 | −0.151778 | ||||||||
\(322\) | −3375.09 | − | 303.233i | −0.584119 | − | 0.0524799i | ||||
\(323\) | −3346.38 | + | 3346.38i | −0.576462 | + | 0.576462i | ||||
\(324\) | 4050.89 | + | 733.824i | 0.694597 | + | 0.125827i | ||||
\(325\) | 918.613 | + | 918.613i | 0.156786 | + | 0.156786i | ||||
\(326\) | −4274.79 | + | 3569.98i | −0.726254 | + | 0.606512i | ||||
\(327\) | − | 10475.5i | − | 1.77155i | ||||||
\(328\) | 2166.55 | − | 7864.65i | 0.364718 | − | 1.32394i | ||||
\(329\) | 5493.90i | 0.920633i | ||||||||
\(330\) | 2936.85 | + | 3516.67i | 0.489904 | + | 0.586625i | ||||
\(331\) | −1820.26 | − | 1820.26i | −0.302268 | − | 0.302268i | 0.539633 | − | 0.841901i | \(-0.318563\pi\) |
−0.841901 | + | 0.539633i | \(0.818563\pi\) | |||||||
\(332\) | 3039.23 | − | 2106.99i | 0.502408 | − | 0.348301i | ||||
\(333\) | −5456.13 | + | 5456.13i | −0.897880 | + | 0.897880i | ||||
\(334\) | 309.200 | − | 3441.50i | 0.0506547 | − | 0.563804i | ||||
\(335\) | 1001.55 | 0.163345 | ||||||||
\(336\) | 5128.93 | + | 11273.0i | 0.832757 | + | 1.83034i | ||||
\(337\) | 74.0970 | 0.0119772 | 0.00598861 | − | 0.999982i | \(-0.498094\pi\) | ||||
0.00598861 | + | 0.999982i | \(0.498094\pi\) | |||||||
\(338\) | 491.749 | − | 5473.33i | 0.0791350 | − | 0.880799i | ||||
\(339\) | −3959.83 | + | 3959.83i | −0.634420 | + | 0.634420i | ||||
\(340\) | 2660.01 | + | 3836.94i | 0.424292 | + | 0.612021i | ||||
\(341\) | −2166.34 | − | 2166.34i | −0.344029 | − | 0.344029i | ||||
\(342\) | 3240.23 | + | 3879.94i | 0.512315 | + | 0.613460i | ||||
\(343\) | 1647.24i | 0.259307i | ||||||||
\(344\) | 1584.46 | + | 2789.36i | 0.248339 | + | 0.437187i | ||||
\(345\) | 2467.01i | 0.384984i | ||||||||
\(346\) | 1729.80 | − | 1444.59i | 0.268770 | − | 0.224456i | ||||
\(347\) | 2102.73 | + | 2102.73i | 0.325305 | + | 0.325305i | 0.850798 | − | 0.525493i | \(-0.176119\pi\) |
−0.525493 | + | 0.850798i | \(0.676119\pi\) | |||||||
\(348\) | 163.698 | − | 903.652i | 0.0252159 | − | 0.139198i | ||||
\(349\) | −6612.85 | + | 6612.85i | −1.01426 | + | 1.01426i | −0.0143661 | + | 0.999897i | \(0.504573\pi\) |
−0.999897 | + | 0.0143661i | \(0.995427\pi\) | |||||||
\(350\) | −5716.00 | − | 513.551i | −0.872951 | − | 0.0784299i | ||||
\(351\) | 794.940 | 0.120885 | ||||||||
\(352\) | −1893.35 | − | 5397.38i | −0.286693 | − | 0.817277i | ||||
\(353\) | 2216.90 | 0.334259 | 0.167130 | − | 0.985935i | \(-0.446550\pi\) | ||||
0.167130 | + | 0.985935i | \(0.446550\pi\) | |||||||
\(354\) | −12541.6 | − | 1126.80i | −1.88299 | − | 0.169177i | ||||
\(355\) | −1002.93 | + | 1002.93i | −0.149944 | + | 0.149944i | ||||
\(356\) | −374.658 | + | 2068.21i | −0.0557776 | + | 0.307906i | ||||
\(357\) | −12107.9 | − | 12107.9i | −1.79500 | − | 1.79500i | ||||
\(358\) | 6761.23 | − | 5646.46i | 0.998162 | − | 0.833589i | ||||
\(359\) | 2082.23i | 0.306117i | 0.988217 | + | 0.153059i | \(0.0489123\pi\) | ||||
−0.988217 | + | 0.153059i | \(0.951088\pi\) | |||||||
\(360\) | 4336.23 | − | 2463.14i | 0.634831 | − | 0.360608i | ||||
\(361\) | 3998.49i | 0.582955i | ||||||||
\(362\) | −310.995 | − | 372.393i | −0.0451533 | − | 0.0540678i | ||||
\(363\) | −1827.87 | − | 1827.87i | −0.264293 | − | 0.264293i | ||||
\(364\) | −1808.84 | − | 2609.16i | −0.260464 | − | 0.375707i | ||||
\(365\) | 3118.10 | − | 3118.10i | 0.447148 | − | 0.447148i | ||||
\(366\) | −1848.95 | + | 20579.5i | −0.264061 | + | 2.93909i | ||||
\(367\) | 4509.22 | 0.641360 | 0.320680 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320680 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(368\) | 1080.38 | − | 2884.12i | 0.153040 | − | 0.408547i | ||||
\(369\) | 12047.1 | 1.69959 | ||||||||
\(370\) | 385.464 | − | 4290.34i | 0.0541603 | − | 0.602823i | ||||
\(371\) | 4375.61 | − | 4375.61i | 0.612320 | − | 0.612320i | ||||
\(372\) | −4954.82 | + | 3434.99i | −0.690579 | + | 0.478753i | ||||
\(373\) | −8661.56 | − | 8661.56i | −1.20236 | − | 1.20236i | −0.973448 | − | 0.228908i | \(-0.926485\pi\) |
−0.228908 | − | 0.973448i | \(-0.573515\pi\) | |||||||
\(374\) | 5069.05 | + | 6069.81i | 0.700840 | + | 0.839205i | ||||
\(375\) | 10586.3i | 1.45779i | ||||||||
\(376\) | −4813.86 | − | 1326.12i | −0.660254 | − | 0.181886i | ||||
\(377\) | 235.418i | 0.0321609i | ||||||||
\(378\) | −2695.43 | + | 2251.02i | −0.366767 | + | 0.306296i | ||||
\(379\) | 3522.46 | + | 3522.46i | 0.477405 | + | 0.477405i | 0.904301 | − | 0.426896i | \(-0.140393\pi\) |
−0.426896 | + | 0.904301i | \(0.640393\pi\) | |||||||
\(380\) | −2776.82 | − | 503.025i | −0.374863 | − | 0.0679069i | ||||
\(381\) | 14412.9 | − | 14412.9i | 1.93804 | − | 1.93804i | ||||
\(382\) | −11064.5 | − | 994.086i | −1.48196 | − | 0.133146i | ||||
\(383\) | 3044.88 | 0.406229 | 0.203115 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203115 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(384\) | −11115.7 | + | 1772.98i | −1.47720 | + | 0.235618i | ||||
\(385\) | 5188.54 | 0.686837 | ||||||||
\(386\) | 9152.75 | + | 822.325i | 1.20690 | + | 0.108433i | ||||
\(387\) | −3349.92 | + | 3349.92i | −0.440016 | + | 0.440016i | ||||
\(388\) | −1187.08 | − | 215.042i | −0.155322 | − | 0.0281368i | ||||
\(389\) | 1932.73 | + | 1932.73i | 0.251911 | + | 0.251911i | 0.821754 | − | 0.569843i | \(-0.192996\pi\) |
−0.569843 | + | 0.821754i | \(0.692996\pi\) | |||||||
\(390\) | −1774.05 | + | 1481.55i | −0.230340 | + | 0.192362i | ||||
\(391\) | 4258.09i | 0.550744i | ||||||||
\(392\) | 6039.14 | + | 1663.66i | 0.778119 | + | 0.214356i | ||||
\(393\) | − | 7228.29i | − | 0.927784i | ||||||
\(394\) | −6207.15 | − | 7432.61i | −0.793685 | − | 0.950379i | ||||
\(395\) | 3838.04 | + | 3838.04i | 0.488893 | + | 0.488893i | ||||
\(396\) | 6941.96 | − | 4812.61i | 0.880926 | − | 0.610714i | ||||
\(397\) | −672.457 | + | 672.457i | −0.0850117 | + | 0.0850117i | −0.748334 | − | 0.663322i | \(-0.769146\pi\) |
0.663322 | + | 0.748334i | \(0.269146\pi\) | |||||||
\(398\) | −347.075 | + | 3863.07i | −0.0437119 | + | 0.486528i | ||||
\(399\) | 10349.9 | 1.29861 | ||||||||
\(400\) | 1829.71 | − | 4884.51i | 0.228714 | − | 0.610563i | ||||
\(401\) | −7606.74 | −0.947288 | −0.473644 | − | 0.880716i | \(-0.657062\pi\) | ||||
−0.473644 | + | 0.880716i | \(0.657062\pi\) | |||||||
\(402\) | 298.740 | − | 3325.07i | 0.0370641 | − | 0.412536i | ||||
\(403\) | 1092.85 | − | 1092.85i | 0.135084 | − | 0.135084i | ||||
\(404\) | 3145.49 | + | 4537.23i | 0.387361 | + | 0.558751i | ||||
\(405\) | −2399.96 | − | 2399.96i | −0.294457 | − | 0.294457i | ||||
\(406\) | −666.631 | − | 798.241i | −0.0814885 | − | 0.0975765i | ||||
\(407\) | − | 7296.32i | − | 0.888612i | ||||||
\(408\) | 13531.7 | − | 7686.54i | 1.64196 | − | 0.932697i | ||||
\(409\) | − | 4981.58i | − | 0.602257i | −0.953584 | − | 0.301129i | \(-0.902637\pi\) | ||
0.953584 | − | 0.301129i | \(-0.0973634\pi\) | |||||||
\(410\) | −5162.08 | + | 4310.98i | −0.621797 | + | 0.519278i | ||||
\(411\) | −13803.8 | − | 13803.8i | −1.65667 | − | 1.65667i | ||||
\(412\) | −2624.67 | + | 14488.8i | −0.313855 | + | 1.73256i | ||||
\(413\) | −10083.3 | + | 10083.3i | −1.20137 | + | 1.20137i | ||||
\(414\) | 4530.03 | + | 406.998i | 0.537775 | + | 0.0483161i | ||||
\(415\) | −3048.89 | −0.360637 | ||||||||
\(416\) | 2722.81 | − | 955.136i | 0.320906 | − | 0.112571i | ||||
\(417\) | −11937.9 | −1.40192 | ||||||||
\(418\) | −4760.80 | − | 427.732i | −0.557077 | − | 0.0500503i | ||||
\(419\) | −3433.38 | + | 3433.38i | −0.400314 | + | 0.400314i | −0.878344 | − | 0.478030i | \(-0.841351\pi\) |
0.478030 | + | 0.878344i | \(0.341351\pi\) | |||||||
\(420\) | 1820.05 | − | 10047.1i | 0.211450 | − | 1.16726i | ||||
\(421\) | 7973.72 | + | 7973.72i | 0.923077 | + | 0.923077i | 0.997246 | − | 0.0741686i | \(-0.0236303\pi\) |
−0.0741686 | + | 0.997246i | \(0.523630\pi\) | |||||||
\(422\) | 4975.22 | − | 4154.93i | 0.573910 | − | 0.479286i | ||||
\(423\) | − | 7373.88i | − | 0.847590i | ||||||
\(424\) | 2777.81 | + | 4890.18i | 0.318166 | + | 0.560114i | ||||
\(425\) | 7211.44i | 0.823074i | ||||||||
\(426\) | 3030.51 | + | 3628.81i | 0.344668 | + | 0.412715i | ||||
\(427\) | 16545.6 | + | 16545.6i | 1.87517 | + | 1.87517i | ||||
\(428\) | −511.866 | − | 738.343i | −0.0578084 | − | 0.0833859i | ||||
\(429\) | −2768.30 | + | 2768.30i | −0.311550 | + | 0.311550i | ||||
\(430\) | 236.665 | − | 2634.16i | 0.0265418 | − | 0.295420i | ||||
\(431\) | 4800.16 | 0.536463 | 0.268232 | − | 0.963354i | \(-0.413561\pi\) | ||||
0.268232 | + | 0.963354i | \(0.413561\pi\) | |||||||
\(432\) | −1321.76 | − | 2905.14i | −0.147207 | − | 0.323550i | ||||
\(433\) | 6242.32 | 0.692810 | 0.346405 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346405 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(434\) | −610.959 | + | 6800.18i | −0.0675737 | + | 0.752118i | ||||
\(435\) | −535.372 | + | 535.372i | −0.0590095 | + | 0.0590095i | ||||
\(436\) | 8860.69 | − | 6142.79i | 0.973280 | − | 0.674739i | ||||
\(437\) | −1819.93 | − | 1819.93i | −0.199220 | − | 0.199220i | ||||
\(438\) | −9421.79 | − | 11281.9i | −1.02783 | − | 1.23075i | ||||
\(439\) | − | 4929.27i | − | 0.535903i | −0.963432 | − | 0.267951i | \(-0.913653\pi\) | ||
0.963432 | − | 0.267951i | \(-0.0863466\pi\) | |||||||
\(440\) | −1252.41 | + | 4546.30i | −0.135696 | + | 0.492582i | ||||
\(441\) | 9250.77i | 0.998896i | ||||||||
\(442\) | −3062.03 | + | 2557.18i | −0.329516 | + | 0.275187i | ||||
\(443\) | −7670.67 | − | 7670.67i | −0.822674 | − | 0.822674i | 0.163817 | − | 0.986491i | \(-0.447619\pi\) |
−0.986491 | + | 0.163817i | \(0.947619\pi\) | |||||||
\(444\) | −14128.6 | − | 2559.42i | −1.51017 | − | 0.273569i | ||||
\(445\) | 1225.32 | − | 1225.32i | 0.130529 | − | 0.130529i | ||||
\(446\) | 1182.09 | + | 106.205i | 0.125502 | + | 0.0112756i | ||||
\(447\) | −25113.5 | −2.65733 | ||||||||
\(448\) | −6527.70 | + | 10948.8i | −0.688404 | + | 1.15464i | ||||
\(449\) | −11515.2 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(450\) | 7671.99 | + | 689.286i | 0.803691 | + | 0.0722073i | ||||
\(451\) | −8055.12 | + | 8055.12i | −0.841021 | + | 0.841021i | ||||
\(452\) | −5671.44 | − | 1027.39i | −0.590182 | − | 0.106912i | ||||
\(453\) | 15468.4 | + | 15468.4i | 1.60434 | + | 1.60434i | ||||
\(454\) | 6550.66 | − | 5470.61i | 0.677176 | − | 0.565526i | ||||
\(455\) | 2617.46i | 0.269689i | ||||||||
\(456\) | −2498.26 | + | 9068.79i | −0.256561 | + | 0.931326i | ||||
\(457\) | − | 4829.89i | − | 0.494383i | −0.968967 | − | 0.247191i | \(-0.920492\pi\) | ||
0.968967 | − | 0.247191i | \(-0.0795076\pi\) | |||||||
\(458\) | 4036.78 | + | 4833.74i | 0.411848 | + | 0.493157i | ||||
\(459\) | 3120.28 | + | 3120.28i | 0.317303 | + | 0.317303i | ||||
\(460\) | −2086.72 | + | 1446.65i | −0.211508 | + | 0.146631i | ||||
\(461\) | 8265.79 | − | 8265.79i | 0.835090 | − | 0.835090i | −0.153118 | − | 0.988208i | \(-0.548931\pi\) |
0.988208 | + | 0.153118i | \(0.0489315\pi\) | |||||||
\(462\) | 1547.62 | − | 17225.5i | 0.155848 | − | 1.73464i | ||||
\(463\) | −5043.86 | −0.506281 | −0.253141 | − | 0.967430i | \(-0.581464\pi\) | ||||
−0.253141 | + | 0.967430i | \(0.581464\pi\) | |||||||
\(464\) | 860.346 | − | 391.435i | 0.0860788 | − | 0.0391636i | ||||
\(465\) | 4970.57 | 0.495709 | ||||||||
\(466\) | −302.418 | + | 3366.02i | −0.0300628 | + | 0.334609i | ||||
\(467\) | 12438.8 | − | 12438.8i | 1.23255 | − | 1.23255i | 0.269564 | − | 0.962982i | \(-0.413120\pi\) |
0.962982 | − | 0.269564i | \(-0.0868796\pi\) | |||||||
\(468\) | 2427.81 | + | 3502.01i | 0.239798 | + | 0.345898i | ||||
\(469\) | −2673.31 | − | 2673.31i | −0.263203 | − | 0.263203i | ||||
\(470\) | 2638.70 | + | 3159.64i | 0.258966 | + | 0.310093i | ||||
\(471\) | 9962.47i | 0.974621i | ||||||||
\(472\) | −6401.26 | − | 11269.1i | −0.624241 | − | 1.09894i | ||||
\(473\) | − | 4479.75i | − | 0.435474i | ||||||
\(474\) | 13886.8 | − | 11597.2i | 1.34566 | − | 1.12379i | ||||
\(475\) | −3082.20 | − | 3082.20i | −0.297729 | − | 0.297729i | ||||
\(476\) | 3141.42 | − | 17341.4i | 0.302493 | − | 1.66984i | ||||
\(477\) | −5872.93 | + | 5872.93i | −0.563738 | + | 0.563738i | ||||
\(478\) | 11947.3 | + | 1073.40i | 1.14322 | + | 0.102712i | ||||
\(479\) | 13059.7 | 1.24575 | 0.622875 | − | 0.782321i | \(-0.285964\pi\) | ||||
0.622875 | + | 0.782321i | \(0.285964\pi\) | |||||||
\(480\) | 8364.14 | + | 4019.93i | 0.795352 | + | 0.382258i | ||||
\(481\) | 3680.77 | 0.348916 | ||||||||
\(482\) | 15694.5 | + | 1410.06i | 1.48312 | + | 0.133250i | ||||
\(483\) | 6584.87 | − | 6584.87i | 0.620335 | − | 0.620335i | ||||
\(484\) | 474.246 | − | 2617.96i | 0.0445385 | − | 0.245864i | ||||
\(485\) | 703.292 | + | 703.292i | 0.0658450 | + | 0.0658450i | ||||
\(486\) | −11606.7 | + | 9693.04i | −1.08331 | + | 0.904702i | ||||
\(487\) | − | 15549.3i | − | 1.44683i | −0.690414 | − | 0.723414i | \(-0.742572\pi\) | ||
0.690414 | − | 0.723414i | \(-0.257428\pi\) | |||||||
\(488\) | −18491.4 | + | 10503.8i | −1.71530 | + | 0.974354i | ||||
\(489\) | − | 15305.3i | − | 1.41540i | ||||||
\(490\) | −3310.33 | − | 3963.88i | −0.305195 | − | 0.365448i | ||||
\(491\) | −8628.34 | − | 8628.34i | −0.793058 | − | 0.793058i | 0.188932 | − | 0.981990i | \(-0.439497\pi\) |
−0.981990 | + | 0.188932i | \(0.939497\pi\) | |||||||
\(492\) | 12772.4 | + | 18423.5i | 1.17037 | + | 1.68821i | ||||
\(493\) | −924.059 | + | 924.059i | −0.0844169 | + | 0.0844169i | ||||
\(494\) | 215.777 | − | 2401.68i | 0.0196524 | − | 0.218738i | ||||
\(495\) | −6964.03 | −0.632344 | ||||||||
\(496\) | −5810.98 | − | 2176.76i | −0.526049 | − | 0.197056i | ||||
\(497\) | 5354.00 | 0.483219 | ||||||||
\(498\) | −909.413 | + | 10122.1i | −0.0818309 | + | 0.910806i | ||||
\(499\) | 1732.42 | − | 1732.42i | 0.155418 | − | 0.155418i | −0.625115 | − | 0.780533i | \(-0.714948\pi\) |
0.780533 | + | 0.625115i | \(0.214948\pi\) | |||||||
\(500\) | −8954.38 | + | 6207.74i | −0.800904 | + | 0.555237i | ||||
\(501\) | 6714.44 | + | 6714.44i | 0.598761 | + | 0.598761i | ||||
\(502\) | 1237.71 | + | 1482.06i | 0.110043 | + | 0.131768i | ||||
\(503\) | 16579.6i | 1.46968i | 0.678241 | + | 0.734839i | \(0.262742\pi\) | ||||
−0.678241 | + | 0.734839i | \(0.737258\pi\) | |||||||
\(504\) | −18148.7 | − | 4999.58i | −1.60398 | − | 0.441863i | ||||
\(505\) | − | 4551.65i | − | 0.401081i | ||||||
\(506\) | −3301.07 | + | 2756.80i | −0.290021 | + | 0.242203i | ||||
\(507\) | 10678.6 | + | 10678.6i | 0.935410 | + | 0.935410i | ||||
\(508\) | 20642.8 | + | 3739.47i | 1.80291 | + | 0.326599i | ||||
\(509\) | −7830.92 | + | 7830.92i | −0.681924 | + | 0.681924i | −0.960434 | − | 0.278509i | \(-0.910160\pi\) |
0.278509 | + | 0.960434i | \(0.410160\pi\) | |||||||
\(510\) | −12778.8 | − | 1148.11i | −1.10952 | − | 0.0996844i | ||||
\(511\) | −16645.5 | −1.44100 | ||||||||
\(512\) | −8017.86 | − | 8362.51i | −0.692076 | − | 0.721825i | ||||
\(513\) | −2667.24 | −0.229555 | ||||||||
\(514\) | −22799.0 | − | 2048.36i | −1.95646 | − | 0.175777i | ||||
\(515\) | 8583.95 | − | 8583.95i | 0.734474 | − | 0.734474i | ||||
\(516\) | −8674.61 | − | 1571.42i | −0.740074 | − | 0.134065i | ||||
\(517\) | 4930.44 | + | 4930.44i | 0.419420 | + | 0.419420i | ||||
\(518\) | −12480.5 | + | 10422.8i | −1.05861 | + | 0.884075i | ||||
\(519\) | 6193.30i | 0.523807i | ||||||||
\(520\) | −2293.47 | − | 631.803i | −0.193414 | − | 0.0532815i | ||||
\(521\) | 3400.02i | 0.285907i | 0.989729 | + | 0.142953i | \(0.0456599\pi\) | ||||
−0.989729 | + | 0.142953i | \(0.954340\pi\) | |||||||
\(522\) | 894.749 | + | 1071.40i | 0.0750232 | + | 0.0898348i | ||||
\(523\) | −2019.50 | − | 2019.50i | −0.168847 | − | 0.168847i | 0.617626 | − | 0.786472i | \(-0.288095\pi\) |
−0.786472 | + | 0.617626i | \(0.788095\pi\) | |||||||
\(524\) | 6114.05 | − | 4238.64i | 0.509720 | − | 0.353370i | ||||
\(525\) | 11152.0 | − | 11152.0i | 0.927075 | − | 0.927075i | ||||
\(526\) | 103.847 | − | 1155.85i | 0.00860822 | − | 0.0958124i | ||||
\(527\) | 8579.28 | 0.709144 | ||||||||
\(528\) | 14719.8 | + | 5513.95i | 1.21325 | + | 0.454477i | ||||
\(529\) | 9851.23 | 0.809668 | ||||||||
\(530\) | 414.910 | − | 4618.09i | 0.0340048 | − | 0.378485i | ||||
\(531\) | 13533.7 | − | 13533.7i | 1.10605 | − | 1.10605i | ||||
\(532\) | 6069.15 | + | 8754.47i | 0.494607 | + | 0.713448i | ||||
\(533\) | −4063.56 | − | 4063.56i | −0.330229 | − | 0.330229i | ||||
\(534\) | −3702.47 | − | 4433.43i | −0.300040 | − | 0.359276i | ||||
\(535\) | 740.691i | 0.0598558i | ||||||||
\(536\) | 2987.69 | − | 1697.12i | 0.240762 | − | 0.136762i | ||||
\(537\) | 24207.7i | 1.94532i | ||||||||
\(538\) | 14.6743 | − | 12.2548i | 0.00117594 | − | 0.000982052i | ||||
\(539\) | −6185.39 | − | 6185.39i | −0.494293 | − | 0.494293i | ||||
\(540\) | −469.038 | + | 2589.21i | −0.0373781 | + | 0.206337i | ||||
\(541\) | −13432.6 | + | 13432.6i | −1.06749 | + | 1.06749i | −0.0699388 | + | 0.997551i | \(0.522280\pi\) |
−0.997551 | + | 0.0699388i | \(0.977720\pi\) | |||||||
\(542\) | 7983.54 | + | 717.278i | 0.632699 | + | 0.0568445i | ||||
\(543\) | 1333.30 | 0.105373 | ||||||||
\(544\) | 14436.6 | + | 6938.45i | 1.13780 | + | 0.546845i | ||||
\(545\) | −8888.86 | −0.698637 | ||||||||
\(546\) | 8689.75 | + | 780.726i | 0.681112 | + | 0.0611941i | ||||
\(547\) | −5376.46 | + | 5376.46i | −0.420257 | + | 0.420257i | −0.885292 | − | 0.465035i | \(-0.846042\pi\) |
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(548\) | 3581.44 | − | 19770.4i | 0.279181 | − | 1.54115i | ||||
\(549\) | −22207.5 | − | 22207.5i | −1.72640 | − | 1.72640i | ||||
\(550\) | −5590.64 | + | 4668.88i | −0.433429 | + | 0.361967i | ||||
\(551\) | − | 789.894i | − | 0.0610719i | ||||||
\(552\) | 4180.33 | + | 7359.24i | 0.322331 | + | 0.567446i | ||||
\(553\) | − | 20488.7i | − | 1.57553i | ||||||
\(554\) | −3912.13 | − | 4684.49i | −0.300019 | − | 0.359251i | ||||
\(555\) | 8370.55 | + | 8370.55i | 0.640198 | + | 0.640198i | ||||
\(556\) | −7000.34 | − | 10097.7i | −0.533958 | − | 0.770210i | ||||
\(557\) | −2076.28 | + | 2076.28i | −0.157944 | + | 0.157944i | −0.781655 | − | 0.623711i | \(-0.785624\pi\) |
0.623711 | + | 0.781655i | \(0.285624\pi\) | |||||||
\(558\) | 820.027 | − | 9127.18i | 0.0622124 | − | 0.692445i | ||||
\(559\) | 2259.90 | 0.170990 | ||||||||
\(560\) | 9565.61 | − | 4352.10i | 0.721823 | − | 0.328410i | ||||
\(561\) | −21732.1 | −1.63553 | ||||||||
\(562\) | −1202.28 | + | 13381.8i | −0.0902405 | + | 1.00441i | ||||
\(563\) | −16643.1 | + | 16643.1i | −1.24587 | + | 1.24587i | −0.288339 | + | 0.957528i | \(0.593103\pi\) |
−0.957528 | + | 0.288339i | \(0.906897\pi\) | |||||||
\(564\) | 11276.8 | − | 7817.81i | 0.841915 | − | 0.583669i | ||||
\(565\) | 3360.07 | + | 3360.07i | 0.250193 | + | 0.250193i | ||||
\(566\) | −1651.47 | − | 1977.51i | −0.122644 | − | 0.146857i | ||||
\(567\) | 12811.8i | 0.948934i | ||||||||
\(568\) | −1292.35 | + | 4691.28i | −0.0954679 | + | 0.346552i | ||||
\(569\) | − | 5659.60i | − | 0.416982i | −0.978024 | − | 0.208491i | \(-0.933145\pi\) | ||
0.978024 | − | 0.208491i | \(-0.0668551\pi\) | |||||||
\(570\) | 5952.43 | − | 4971.02i | 0.437403 | − | 0.365286i | ||||
\(571\) | 4872.67 | + | 4872.67i | 0.357119 | + | 0.357119i | 0.862750 | − | 0.505631i | \(-0.168740\pi\) |
−0.505631 | + | 0.862750i | \(0.668740\pi\) | |||||||
\(572\) | −3964.89 | − | 718.244i | −0.289825 | − | 0.0525023i | ||||
\(573\) | 21587.1 | − | 21587.1i | 1.57385 | − | 1.57385i | ||||
\(574\) | 25285.2 | + | 2271.73i | 1.83865 | + | 0.165192i | ||||
\(575\) | −3921.95 | −0.284446 | ||||||||
\(576\) | 8761.45 | − | 14695.4i | 0.633786 | − | 1.06303i | ||||
\(577\) | 10652.2 | 0.768556 | 0.384278 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384278 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(578\) | −8216.10 | − | 738.171i | −0.591254 | − | 0.0531209i | ||||
\(579\) | −17857.2 | + | 17857.2i | −1.28173 | + | 1.28173i | ||||
\(580\) | −766.784 | − | 138.904i | −0.0548948 | − | 0.00994426i | ||||
\(581\) | 8138.01 | + | 8138.01i | 0.581104 | + | 0.581104i | ||||
\(582\) | 2544.65 | − | 2125.10i | 0.181235 | − | 0.151354i | ||||
\(583\) | − | 7853.69i | − | 0.557919i | ||||||
\(584\) | 4017.89 | − | 14585.1i | 0.284694 | − | 1.03345i | ||||
\(585\) | − | 3513.14i | − | 0.248291i | ||||||
\(586\) | 3674.61 | + | 4400.07i | 0.259039 | + | 0.310180i | ||||
\(587\) | 9903.95 | + | 9903.95i | 0.696388 | + | 0.696388i | 0.963630 | − | 0.267242i | \(-0.0861122\pi\) |
−0.267242 | + | 0.963630i | \(0.586112\pi\) | |||||||
\(588\) | −14147.1 | + | 9807.69i | −0.992208 | + | 0.687861i | ||||
\(589\) | −3666.82 | + | 3666.82i | −0.256517 | + | 0.256517i | ||||
\(590\) | −956.129 | + | 10642.0i | −0.0667173 | + | 0.742587i | ||||
\(591\) | 26611.5 | 1.85220 | ||||||||
\(592\) | −6120.09 | − | 13451.5i | −0.424889 | − | 0.933875i | ||||
\(593\) | −3528.04 | −0.244316 | −0.122158 | − | 0.992511i | \(-0.538981\pi\) | ||||
−0.122158 | + | 0.992511i | \(0.538981\pi\) | |||||||
\(594\) | −398.832 | + | 4439.14i | −0.0275493 | + | 0.306633i | ||||
\(595\) | −10274.0 | + | 10274.0i | −0.707887 | + | 0.707887i | ||||
\(596\) | −14726.5 | − | 21242.2i | −1.01211 | − | 1.45993i | ||||
\(597\) | −7536.93 | − | 7536.93i | −0.516693 | − | 0.516693i | ||||
\(598\) | −1390.72 | − | 1665.29i | −0.0951018 | − | 0.113877i | ||||
\(599\) | − | 19024.9i | − | 1.29772i | −0.760907 | − | 0.648861i | \(-0.775246\pi\) | ||
0.760907 | − | 0.648861i | \(-0.224754\pi\) | |||||||
\(600\) | 7079.74 | + | 12463.5i | 0.481715 | + | 0.848034i | ||||
\(601\) | − | 1065.92i | − | 0.0723460i | −0.999346 | − | 0.0361730i | \(-0.988483\pi\) | ||
0.999346 | − | 0.0361730i | \(-0.0115167\pi\) | |||||||
\(602\) | −7662.72 | + | 6399.32i | −0.518786 | + | 0.433250i | ||||
\(603\) | 3588.11 | + | 3588.11i | 0.242320 | + | 0.242320i | ||||
\(604\) | −4013.32 | + | 22154.5i | −0.270364 | + | 1.49248i | ||||
\(605\) | −1551.02 | + | 1551.02i | −0.104228 | + | 0.104228i | ||||
\(606\) | −15111.1 | − | 1357.65i | −1.01295 | − | 0.0910079i | ||||
\(607\) | 12909.7 | 0.863242 | 0.431621 | − | 0.902055i | \(-0.357942\pi\) | ||||
0.431621 | + | 0.902055i | \(0.357942\pi\) | |||||||
\(608\) | −9135.80 | + | 3204.75i | −0.609384 | + | 0.213766i | ||||
\(609\) | 2858.00 | 0.190167 | ||||||||
\(610\) | 17462.5 | + | 1568.91i | 1.15908 | + | 0.104137i | ||||
\(611\) | −2487.25 | + | 2487.25i | −0.164687 | + | 0.164687i | ||||
\(612\) | −4216.40 | + | 23275.6i | −0.278494 | + | 1.53735i | ||||
\(613\) | −8763.41 | − | 8763.41i | −0.577408 | − | 0.577408i | 0.356781 | − | 0.934188i | \(-0.383874\pi\) |
−0.934188 | + | 0.356781i | \(0.883874\pi\) | |||||||
\(614\) | 709.859 | − | 592.820i | 0.0466573 | − | 0.0389646i | ||||
\(615\) | − | 18482.1i | − | 1.21182i | ||||||
\(616\) | 15477.7 | − | 8791.93i | 1.01236 | − | 0.575060i | ||||
\(617\) | 18921.2i | 1.23459i | 0.786733 | + | 0.617293i | \(0.211771\pi\) | ||||
−0.786733 | + | 0.617293i | \(0.788229\pi\) | |||||||
\(618\) | −25937.6 | − | 31058.4i | −1.68829 | − | 2.02161i | ||||
\(619\) | −15116.6 | − | 15116.6i | −0.981565 | − | 0.981565i | 0.0182677 | − | 0.999833i | \(-0.494185\pi\) |
−0.999833 | + | 0.0182677i | \(0.994185\pi\) | |||||||
\(620\) | 2914.73 | + | 4204.36i | 0.188804 | + | 0.272340i | ||||
\(621\) | −1696.97 | + | 1696.97i | −0.109657 | + | 0.109657i | ||||
\(622\) | −220.553 | + | 2454.83i | −0.0142176 | + | 0.158247i | ||||
\(623\) | −6541.15 | −0.420651 | ||||||||
\(624\) | −2781.62 | + | 7425.67i | −0.178452 | + | 0.476386i | ||||
\(625\) | −1204.57 | −0.0770926 | ||||||||
\(626\) | 889.648 | − | 9902.09i | 0.0568011 | − | 0.632216i | ||||
\(627\) | 9288.42 | − | 9288.42i | 0.591617 | − | 0.591617i | ||||
\(628\) | −8426.75 | + | 5841.95i | −0.535452 | + | 0.371209i | ||||
\(629\) | 14447.7 | + | 14447.7i | 0.915845 | + | 0.915845i | ||||
\(630\) | 9948.11 | + | 11912.1i | 0.629115 | + | 0.753319i | ||||
\(631\) | 9602.80i | 0.605834i | 0.953017 | + | 0.302917i | \(0.0979605\pi\) | ||||
−0.953017 | + | 0.302917i | \(0.902039\pi\) | |||||||
\(632\) | 17952.6 | + | 4945.58i | 1.12993 | + | 0.311273i | ||||
\(633\) | 17813.1i | 1.11849i | ||||||||
\(634\) | −14502.8 | + | 12111.7i | −0.908487 | + | 0.758699i | ||||
\(635\) | −12229.9 | − | 12229.9i | −0.764297 | − | 0.764297i | ||||
\(636\) | −15207.9 | − | 2754.93i | −0.948166 | − | 0.171761i | ||||
\(637\) | 3120.34 | − | 3120.34i | 0.194085 | − | 0.194085i | ||||
\(638\) | −1314.63 | − | 118.113i | −0.0815781 | − | 0.00732935i | ||||
\(639\) | −7186.12 | −0.444880 | ||||||||
\(640\) | 1504.44 | + | 9432.08i | 0.0929194 | + | 0.582556i | ||||
\(641\) | 4450.84 | 0.274256 | 0.137128 | − | 0.990553i | \(-0.456213\pi\) | ||||
0.137128 | + | 0.990553i | \(0.456213\pi\) | |||||||
\(642\) | 2459.03 | + | 220.931i | 0.151169 | + | 0.0135817i | ||||
\(643\) | 6491.27 | − | 6491.27i | 0.398119 | − | 0.398119i | −0.479450 | − | 0.877569i | \(-0.659164\pi\) |
0.877569 | + | 0.479450i | \(0.159164\pi\) | |||||||
\(644\) | 9431.15 | + | 1708.46i | 0.577080 | + | 0.104539i | ||||
\(645\) | 5139.30 | + | 5139.30i | 0.313736 | + | 0.313736i | ||||
\(646\) | 10274.0 | − | 8580.05i | 0.625734 | − | 0.522566i | ||||
\(647\) | 5546.17i | 0.337005i | 0.985701 | + | 0.168503i | \(0.0538932\pi\) | ||||
−0.985701 | + | 0.168503i | \(0.946107\pi\) | |||||||
\(648\) | −11226.0 | − | 3092.52i | −0.680551 | − | 0.187478i | ||||
\(649\) | 18098.3i | 1.09464i | ||||||||
\(650\) | −2355.31 | − | 2820.31i | −0.142127 | − | 0.170187i | ||||
\(651\) | −13267.3 | − | 13267.3i | −0.798750 | − | 0.798750i | ||||
\(652\) | 12946.0 | − | 8974.98i | 0.777613 | − | 0.539091i | ||||
\(653\) | 6327.58 | − | 6327.58i | 0.379200 | − | 0.379200i | −0.491614 | − | 0.870813i | \(-0.663593\pi\) |
0.870813 | + | 0.491614i | \(0.163593\pi\) | |||||||
\(654\) | −2651.34 | + | 29510.3i | −0.158525 | + | 1.76444i | ||||
\(655\) | −6133.49 | −0.365886 | ||||||||
\(656\) | −8093.88 | + | 21607.0i | −0.481727 | + | 1.28599i | ||||
\(657\) | 22341.5 | 1.32667 | ||||||||
\(658\) | 1390.50 | − | 15476.7i | 0.0823820 | − | 0.916940i | ||||
\(659\) | 15135.2 | − | 15135.2i | 0.894663 | − | 0.894663i | −0.100294 | − | 0.994958i | \(-0.531978\pi\) |
0.994958 | + | 0.100294i | \(0.0319785\pi\) | |||||||
\(660\) | −7383.28 | − | 10650.0i | −0.435445 | − | 0.628110i | ||||
\(661\) | −23460.1 | − | 23460.1i | −1.38047 | − | 1.38047i | −0.843777 | − | 0.536694i | \(-0.819673\pi\) |
−0.536694 | − | 0.843777i | \(-0.680327\pi\) | |||||||
\(662\) | 4667.12 | + | 5588.53i | 0.274007 | + | 0.328103i | ||||
\(663\) | − | 10963.2i | − | 0.642195i | ||||||
\(664\) | −9095.03 | + | 5166.32i | −0.531560 | + | 0.301946i | ||||
\(665\) | − | 8782.30i | − | 0.512125i | ||||||
\(666\) | 16751.3 | − | 13989.4i | 0.974624 | − | 0.813932i | ||||
\(667\) | −502.550 | − | 502.550i | −0.0291736 | − | 0.0291736i | ||||
\(668\) | −1742.08 | + | 9616.73i | −0.100903 | + | 0.557009i | ||||
\(669\) | −2306.29 | + | 2306.29i | −0.133283 | + | 0.133283i | ||||
\(670\) | −2821.45 | − | 253.492i | −0.162690 | − | 0.0146168i | ||||
\(671\) | 29697.4 | 1.70858 | ||||||||
\(672\) | −11595.4 | − | 33055.2i | −0.665630 | − | 1.89752i | ||||
\(673\) | 30638.5 | 1.75487 | 0.877436 | − | 0.479694i | \(-0.159252\pi\) | ||||
0.877436 | + | 0.479694i | \(0.159252\pi\) | |||||||
\(674\) | −208.737 | − | 18.7539i | −0.0119292 | − | 0.00107177i | ||||
\(675\) | −2873.96 | + | 2873.96i | −0.163879 | + | 0.163879i | ||||
\(676\) | −2770.59 | + | 15294.4i | −0.157635 | + | 0.870184i | ||||
\(677\) | −12468.9 | − | 12468.9i | −0.707855 | − | 0.707855i | 0.258229 | − | 0.966084i | \(-0.416861\pi\) |
−0.966084 | + | 0.258229i | \(0.916861\pi\) | |||||||
\(678\) | 12157.4 | − | 10152.9i | 0.688645 | − | 0.575104i | ||||
\(679\) | − | 3754.41i | − | 0.212196i | ||||||
\(680\) | −6522.33 | − | 11482.2i | −0.367823 | − | 0.647533i | ||||
\(681\) | 23453.8i | 1.31975i | ||||||||
\(682\) | 5554.45 | + | 6651.05i | 0.311864 | + | 0.373434i | ||||
\(683\) | 13838.5 | + | 13838.5i | 0.775280 | + | 0.775280i | 0.979024 | − | 0.203744i | \(-0.0653111\pi\) |
−0.203744 | + | 0.979024i | \(0.565311\pi\) | |||||||
\(684\) | −8145.99 | − | 11750.2i | −0.455365 | − | 0.656843i | ||||
\(685\) | −11713.1 | + | 11713.1i | −0.653333 | + | 0.653333i | ||||
\(686\) | 416.914 | − | 4640.40i | 0.0232039 | − | 0.258267i | ||||
\(687\) | −17306.6 | −0.961116 | ||||||||
\(688\) | −3757.58 | − | 8258.89i | −0.208221 | − | 0.457656i | ||||
\(689\) | 3961.95 | 0.219068 | ||||||||
\(690\) | 624.398 | − | 6949.77i | 0.0344499 | − | 0.383439i | ||||
\(691\) | −106.012 | + | 106.012i | −0.00583628 | + | 0.00583628i | −0.710019 | − | 0.704183i | \(-0.751314\pi\) |
0.704183 | + | 0.710019i | \(0.251314\pi\) | |||||||
\(692\) | −5238.60 | + | 3631.73i | −0.287777 | + | 0.199505i | ||||
\(693\) | 18588.2 | + | 18588.2i | 1.01891 | + | 1.01891i | ||||
\(694\) | −5391.37 | − | 6455.77i | −0.294890 | − | 0.353109i | ||||
\(695\) | 10129.8i | 0.552870i | ||||||||
\(696\) | −689.863 | + | 2504.23i | −0.0375707 | + | 0.136383i | ||||
\(697\) | − | 31900.4i | − | 1.73359i | ||||||
\(698\) | 20302.6 | − | 16955.2i | 1.10095 | − | 0.919434i | ||||
\(699\) | −6567.17 | − | 6567.17i | −0.355355 | − | 0.355355i | ||||
\(700\) | 15972.4 | + | 2893.43i | 0.862431 | + | 0.156231i | ||||
\(701\) | 7839.35 | − | 7839.35i | 0.422380 | − | 0.422380i | −0.463643 | − | 0.886022i | \(-0.653458\pi\) |
0.886022 | + | 0.463643i | \(0.153458\pi\) | |||||||
\(702\) | −2239.41 | − | 201.199i | −0.120400 | − | 0.0108173i | ||||
\(703\) | −12350.0 | −0.662574 | ||||||||
\(704\) | 3967.64 | + | 15684.1i | 0.212409 | + | 0.839653i | ||||
\(705\) | −11312.7 | −0.604341 | ||||||||
\(706\) | −6245.17 | − | 561.095i | −0.332918 | − | 0.0299109i | ||||
\(707\) | −12149.1 | + | 12149.1i | −0.646273 | + | 0.646273i | ||||
\(708\) | 35045.5 | + | 6348.55i | 1.86030 | + | 0.336996i | ||||
\(709\) | 2728.30 | + | 2728.30i | 0.144518 | + | 0.144518i | 0.775664 | − | 0.631146i | \(-0.217415\pi\) |
−0.631146 | + | 0.775664i | \(0.717415\pi\) | |||||||
\(710\) | 3079.19 | − | 2571.50i | 0.162760 | − | 0.135925i | ||||
\(711\) | 27499.9i | 1.45053i | ||||||||
\(712\) | 1578.90 | − | 5731.48i | 0.0831066 | − | 0.301680i | ||||
\(713\) | 4665.84i | 0.245073i | ||||||||
\(714\) | 31044.3 | + | 37173.3i | 1.62718 | + | 1.94843i | ||||
\(715\) | 2349.01 | + | 2349.01i | 0.122864 | + | 0.122864i | ||||
\(716\) | −20476.0 | + | 14195.3i | −1.06875 | + | 0.740925i | ||||
\(717\) | −23309.5 | + | 23309.5i | −1.21410 | + | 1.21410i | ||||
\(718\) | 527.011 | − | 5865.82i | 0.0273926 | − | 0.304889i | ||||
\(719\) | −32717.8 | −1.69704 | −0.848519 | − | 0.529166i | \(-0.822505\pi\) | ||||
−0.848519 | + | 0.529166i | \(0.822505\pi\) | |||||||
\(720\) | −12838.9 | + | 5841.37i | −0.664553 | + | 0.302354i | ||||
\(721\) | −45824.0 | −2.36696 | ||||||||
\(722\) | 1012.01 | − | 11264.1i | 0.0521652 | − | 0.580616i | ||||
\(723\) | −30620.3 | + | 30620.3i | −1.57508 | + | 1.57508i | ||||
\(724\) | 781.844 | + | 1127.77i | 0.0401340 | + | 0.0578914i | ||||
\(725\) | −851.111 | − | 851.111i | −0.0435993 | − | 0.0435993i | ||||
\(726\) | 4686.62 | + | 5611.88i | 0.239582 | + | 0.286882i | ||||
\(727\) | − | 25847.2i | − | 1.31859i | −0.751883 | − | 0.659297i | \(-0.770854\pi\) | ||
0.751883 | − | 0.659297i | \(-0.229146\pi\) | |||||||
\(728\) | 4435.26 | + | 7808.03i | 0.225799 | + | 0.397507i | ||||
\(729\) | − | 27662.0i | − | 1.40537i | ||||||
\(730\) | −9573.13 | + | 7994.75i | −0.485366 | + | 0.405341i | ||||
\(731\) | 8870.50 | + | 8870.50i | 0.448820 | + | 0.448820i | ||||
\(732\) | 10417.3 | − | 57506.1i | 0.526004 | − | 2.90367i | ||||
\(733\) | 10131.9 | − | 10131.9i | 0.510547 | − | 0.510547i | −0.404147 | − | 0.914694i | \(-0.632432\pi\) |
0.914694 | + | 0.404147i | \(0.132432\pi\) | |||||||
\(734\) | −12702.8 | − | 1141.28i | −0.638787 | − | 0.0573915i | ||||
\(735\) | 14192.1 | 0.712223 | ||||||||
\(736\) | −3773.48 | + | 7851.36i | −0.188984 | + | 0.393213i | ||||
\(737\) | −4798.27 | −0.239819 | ||||||||
\(738\) | −33937.7 | − | 3049.11i | −1.69277 | − | 0.152086i | ||||
\(739\) | 19163.7 | − | 19163.7i | 0.953921 | − | 0.953921i | −0.0450633 | − | 0.998984i | \(-0.514349\pi\) |
0.998984 | + | 0.0450633i | \(0.0143490\pi\) | |||||||
\(740\) | −2171.76 | + | 11988.7i | −0.107886 | + | 0.595558i | ||||
\(741\) | 4685.72 | + | 4685.72i | 0.232300 | + | 0.232300i | ||||
\(742\) | −13433.9 | + | 11219.0i | −0.664656 | + | 0.555070i | ||||
\(743\) | 23322.1i | 1.15155i | 0.817607 | + | 0.575777i | \(0.195301\pi\) | ||||
−0.817607 | + | 0.575777i | \(0.804699\pi\) | |||||||
\(744\) | 14827.5 | − | 8422.59i | 0.730650 | − | 0.415037i | ||||
\(745\) | 21309.8i | 1.04796i | ||||||||
\(746\) | 22208.1 | + | 26592.5i | 1.08994 | + | 1.30512i | ||||
\(747\) | −10922.8 | − | 10922.8i | −0.534999 | − | 0.534999i | ||||
\(748\) | −12743.6 | − | 18382.1i | −0.622933 | − | 0.898552i | ||||
\(749\) | 1977.03 | − | 1977.03i | 0.0964473 | − | 0.0964473i | ||||
\(750\) | 2679.37 | − | 29822.3i | 0.130449 | − | 1.45194i | ||||
\(751\) | 25994.0 | 1.26303 | 0.631515 | − | 0.775364i | \(-0.282434\pi\) | ||||
0.631515 | + | 0.775364i | \(0.282434\pi\) | |||||||
\(752\) | 13225.4 | + | 4954.16i | 0.641330 | + | 0.240239i | ||||
\(753\) | −5306.32 | −0.256804 | ||||||||
\(754\) | 59.5842 | − | 663.192i | 0.00287789 | − | 0.0320319i | ||||
\(755\) | 13125.5 | − | 13125.5i | 0.632698 | − | 0.632698i | ||||
\(756\) | 8162.97 | − | 5659.09i | 0.392704 | − | 0.272247i | ||||
\(757\) | 22145.0 | + | 22145.0i | 1.06324 | + | 1.06324i | 0.997860 | + | 0.0653808i | \(0.0208262\pi\) |
0.0653808 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(758\) | −9031.52 | − | 10814.6i | −0.432770 | − | 0.518210i | ||||
\(759\) | − | 11819.0i | − | 0.565222i | ||||||
\(760\) | 7695.22 | + | 2119.87i | 0.367283 | + | 0.101179i | ||||
\(761\) | − | 16497.5i | − | 0.785853i | −0.919570 | − | 0.392926i | \(-0.871463\pi\) | ||
0.919570 | − | 0.392926i | \(-0.128537\pi\) | |||||||
\(762\) | −44250.1 | + | 36954.4i | −2.10369 | + | 1.75684i | ||||
\(763\) | 23725.9 | + | 23725.9i | 1.12573 | + | 1.12573i | ||||
\(764\) | 30918.0 | + | 5600.84i | 1.46410 | + | 0.265224i | ||||
\(765\) | 13789.7 | − | 13789.7i | 0.651723 | − | 0.651723i | ||||
\(766\) | −8577.66 | − | 770.656i | −0.404600 | − | 0.0363511i | ||||
\(767\) | −9130.02 | −0.429812 | ||||||||
\(768\) | 31762.5 | − | 2181.27i | 1.49236 | − | 0.102487i | ||||
\(769\) | −24867.3 | −1.16611 | −0.583055 | − | 0.812433i | \(-0.698143\pi\) | ||||
−0.583055 | + | 0.812433i | \(0.698143\pi\) | |||||||
\(770\) | −14616.5 | − | 1313.21i | −0.684082 | − | 0.0614610i | ||||
\(771\) | 44481.2 | − | 44481.2i | 2.07776 | − | 2.07776i | ||||
\(772\) | −25575.9 | − | 4633.11i | −1.19235 | − | 0.215996i | ||||
\(773\) | 1881.72 | + | 1881.72i | 0.0875559 | + | 0.0875559i | 0.749528 | − | 0.661972i | \(-0.230280\pi\) |
−0.661972 | + | 0.749528i | \(0.730280\pi\) | |||||||
\(774\) | 10284.9 | − | 8589.14i | 0.477625 | − | 0.398876i | ||||
\(775\) | 7902.00i | 0.366256i | ||||||||
\(776\) | 3289.68 | + | 906.240i | 0.152181 | + | 0.0419228i | ||||
\(777\) | − | 44684.8i | − | 2.06314i | ||||||
\(778\) | −4955.49 | − | 5933.84i | −0.228359 | − | 0.273443i | ||||
\(779\) | 13634.4 | + | 13634.4i | 0.627089 | + | 0.627089i | ||||
\(780\) | 5372.62 | − | 3724.64i | 0.246629 | − | 0.170979i | ||||
\(781\) | 4804.89 | − | 4804.89i | 0.220144 | − | 0.220144i | ||||
\(782\) | 1077.72 | − | 11995.4i | 0.0492828 | − | 0.548535i | ||||
\(783\) | −736.525 | −0.0336159 | ||||||||
\(784\) | −16591.7 | − | 6215.16i | −0.755815 | − | 0.283125i | ||||
\(785\) | 8453.54 | 0.384356 | ||||||||
\(786\) | −1829.47 | + | 20362.7i | −0.0830219 | + | 0.924062i | ||||
\(787\) | −7790.94 | + | 7790.94i | −0.352881 | + | 0.352881i | −0.861180 | − | 0.508300i | \(-0.830274\pi\) |
0.508300 | + | 0.861180i | \(0.330274\pi\) | |||||||
\(788\) | 15604.9 | + | 22509.3i | 0.705457 | + | 1.01759i | ||||
\(789\) | 2255.08 | + | 2255.08i | 0.101753 | + | 0.101753i | ||||
\(790\) | −9840.66 | − | 11783.5i | −0.443184 | − | 0.530680i | ||||
\(791\) | − | 17937.2i | − | 0.806286i | ||||||
\(792\) | −20774.1 | + | 11800.5i | −0.932041 | + | 0.529435i | ||||
\(793\) | 14981.4i | 0.670877i | ||||||||
\(794\) | 2064.56 | − | 1724.17i | 0.0922778 | − | 0.0770634i | ||||
\(795\) | 9009.98 | + | 9009.98i | 0.401951 | + | 0.401951i | ||||
\(796\) | 1955.48 | − | 10794.7i | 0.0870730 | − | 0.480665i | ||||
\(797\) | −4209.84 | + | 4209.84i | −0.187102 | + | 0.187102i | −0.794442 | − | 0.607340i | \(-0.792237\pi\) |
0.607340 | + | 0.794442i | \(0.292237\pi\) | |||||||
\(798\) | −29156.5 | − | 2619.55i | −1.29340 | − | 0.116205i | ||||
\(799\) | −19525.8 | −0.864549 | ||||||||
\(800\) | −6390.71 | + | 13296.9i | −0.282432 | + | 0.587648i | ||||
\(801\) | 8779.50 | 0.387276 | ||||||||
\(802\) | 21428.8 | + | 1925.26i | 0.943488 | + | 0.0847672i | ||||
\(803\) | −14938.3 | + | 14938.3i | −0.656490 | + | 0.656490i | ||||
\(804\) | −1683.15 | + | 9291.39i | −0.0738308 | + | 0.407565i | ||||
\(805\) | −5587.51 | − | 5587.51i | −0.244639 | − | 0.244639i | ||||
\(806\) | −3355.25 | + | 2802.05i | −0.146630 | + | 0.122454i | ||||
\(807\) | 52.5393i | 0.00229178i | ||||||||
\(808\) | −7712.73 | − | 13577.8i | −0.335808 | − | 0.591172i | ||||
\(809\) | − | 27554.3i | − | 1.19747i | −0.800946 | − | 0.598737i | \(-0.795670\pi\) | ||
0.800946 | − | 0.598737i | \(-0.204330\pi\) | |||||||
\(810\) | 6153.46 | + | 7368.32i | 0.266927 | + | 0.319625i | ||||
\(811\) | 3406.54 | + | 3406.54i | 0.147497 | + | 0.147497i | 0.776999 | − | 0.629502i | \(-0.216741\pi\) |
−0.629502 | + | 0.776999i | \(0.716741\pi\) | |||||||
\(812\) | 1675.92 | + | 2417.43i | 0.0724300 | + | 0.104477i | ||||
\(813\) | −15576.1 | + | 15576.1i | −0.671926 | + | 0.671926i | ||||
\(814\) | −1846.69 | + | 20554.3i | −0.0795166 | + | 0.885047i | ||||
\(815\) | −12987.1 | −0.558184 | ||||||||
\(816\) | −40065.4 | + | 18228.7i | −1.71884 | + | 0.782026i | ||||
\(817\) | −7582.59 | −0.324701 | ||||||||
\(818\) | −1260.83 | + | 14033.5i | −0.0538924 | + | 0.599841i | ||||
\(819\) | −9377.16 | + | 9377.16i | −0.400079 | + | 0.400079i | ||||
\(820\) | 15633.1 | − | 10837.8i | 0.665770 | − | 0.461554i | ||||
\(821\) | −9839.14 | − | 9839.14i | −0.418256 | − | 0.418256i | 0.466346 | − | 0.884602i | \(-0.345570\pi\) |
−0.884602 | + | 0.466346i | \(0.845570\pi\) | |||||||
\(822\) | 35392.7 | + | 42380.1i | 1.50178 | + | 1.79827i | ||||
\(823\) | 36653.5i | 1.55244i | 0.630461 | + | 0.776221i | \(0.282866\pi\) | ||||
−0.630461 | + | 0.776221i | \(0.717134\pi\) | |||||||
\(824\) | 11061.0 | − | 40151.9i | 0.467632 | − | 1.69752i | ||||
\(825\) | − | 20016.5i | − | 0.844711i | ||||||
\(826\) | 30957.5 | − | 25853.3i | 1.30405 | − | 1.08905i | ||||
\(827\) | −22223.2 | − | 22223.2i | −0.934431 | − | 0.934431i | 0.0635475 | − | 0.997979i | \(-0.479759\pi\) |
−0.997979 | + | 0.0635475i | \(0.979759\pi\) | |||||||
\(828\) | −12658.4 | − | 2293.09i | −0.531294 | − | 0.0962446i | ||||
\(829\) | 14715.5 | − | 14715.5i | 0.616516 | − | 0.616516i | −0.328120 | − | 0.944636i | \(-0.606415\pi\) |
0.944636 | + | 0.328120i | \(0.106415\pi\) | |||||||
\(830\) | 8588.98 | + | 771.672i | 0.359190 | + | 0.0322713i | ||||
\(831\) | 16772.2 | 0.700145 | ||||||||
\(832\) | −7912.13 | + | 2001.55i | −0.329692 | + | 0.0834031i | ||||
\(833\) | 24495.8 | 1.01888 | ||||||||
\(834\) | 33630.0 | + | 3021.47i | 1.39630 | + | 0.125450i | ||||
\(835\) | 5697.46 | − | 5697.46i | 0.236130 | − | 0.236130i | ||||
\(836\) | 13303.3 | + | 2409.91i | 0.550364 | + | 0.0996991i | ||||
\(837\) | 3419.07 | + | 3419.07i | 0.141195 | + | 0.141195i | ||||
\(838\) | 10541.1 | − | 8803.12i | 0.434530 | − | 0.362886i | ||||
\(839\) | 11010.0i | 0.453050i | 0.974005 | + | 0.226525i | \(0.0727365\pi\) | ||||
−0.974005 | + | 0.226525i | \(0.927263\pi\) | |||||||
\(840\) | −7670.13 | + | 27842.8i | −0.315053 | + | 1.14365i | ||||
\(841\) | 24170.9i | 0.991057i | ||||||||
\(842\) | −20444.5 | − | 24480.8i | −0.836773 | − | 1.00197i | ||||
\(843\) | −26108.1 | − | 26108.1i | −1.06668 | − | 1.06668i | ||||
\(844\) | −15067.2 | + | 10445.5i | −0.614496 | + | 0.426007i | ||||
\(845\) | 9061.20 | − | 9061.20i | 0.368893 | − | 0.368893i | ||||
\(846\) | −1866.32 | + | 20772.8i | −0.0758458 | + | 0.844190i | ||||
\(847\) | 8279.85 | 0.335890 | ||||||||
\(848\) | −6587.61 | − | 14479.1i | −0.266768 | − | 0.586338i | ||||
\(849\) | 7080.22 | 0.286210 | ||||||||
\(850\) | 1825.21 | − | 20315.2i | 0.0736520 | − | 0.819772i | ||||
\(851\) | −7857.37 | + | 7857.37i | −0.316507 | + | 0.316507i | ||||
\(852\) | −7618.74 | − | 10989.7i | −0.306354 | − | 0.441901i | ||||
\(853\) | 12809.9 | + | 12809.9i | 0.514190 | + | 0.514190i | 0.915808 | − | 0.401617i | \(-0.131552\pi\) |
−0.401617 | + | 0.915808i | \(0.631552\pi\) | |||||||
\(854\) | −42422.7 | − | 50798.0i | −1.69985 | − | 2.03545i | ||||
\(855\) | 11787.6i | 0.471493i | ||||||||
\(856\) | 1255.09 | + | 2209.52i | 0.0501147 | + | 0.0882243i | ||||
\(857\) | 38510.8i | 1.53501i | 0.641043 | + | 0.767505i | \(0.278502\pi\) | ||||
−0.641043 | + | 0.767505i | \(0.721498\pi\) | |||||||
\(858\) | 8499.18 | − | 7097.87i | 0.338178 | − | 0.282421i | ||||
\(859\) | 23234.6 | + | 23234.6i | 0.922882 | + | 0.922882i | 0.997232 | − | 0.0743503i | \(-0.0236883\pi\) |
−0.0743503 | + | 0.997232i | \(0.523688\pi\) | |||||||
\(860\) | −1333.41 | + | 7360.74i | −0.0528707 | + | 0.291860i | ||||
\(861\) | −49331.9 | + | 49331.9i | −1.95264 | + | 1.95264i | ||||
\(862\) | −13522.4 | − | 1214.92i | −0.534311 | − | 0.0480049i | ||||
\(863\) | −22079.5 | −0.870911 | −0.435456 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435456 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(864\) | 2988.22 | + | 8518.55i | 0.117664 | + | 0.335425i | ||||
\(865\) | 5255.26 | 0.206571 | ||||||||
\(866\) | −17585.1 | − | 1579.93i | −0.690031 | − | 0.0619955i | ||||
\(867\) | 16029.8 | − | 16029.8i | 0.627912 | − | 0.627912i | ||||
\(868\) | 3442.24 | − | 19002.0i | 0.134605 | − | 0.743054i | ||||
\(869\) | −18387.4 | − | 18387.4i | −0.717779 | − | 0.717779i | ||||
\(870\) | 1643.69 | − | 1372.68i | 0.0640531 | − | 0.0534923i | ||||
\(871\) | − | 2420.58i | − | 0.0941656i | ||||||
\(872\) | −26516.0 | + | 15062.1i | −1.02975 | + | 0.584939i | ||||
\(873\) | 5039.15i | 0.195360i | ||||||||
\(874\) | 4666.26 | + | 5587.51i | 0.180593 | + | 0.216247i | ||||
\(875\) | −23976.7 | − | 23976.7i | −0.926356 | − | 0.926356i | ||||
\(876\) | 23686.5 | + | 34166.7i | 0.913576 | + | 1.31779i | ||||
\(877\) | 4082.13 | − | 4082.13i | 0.157176 | − | 0.157176i | −0.624138 | − | 0.781314i | \(-0.714550\pi\) |
0.781314 | + | 0.624138i | \(0.214550\pi\) | |||||||
\(878\) | −1247.59 | + | 13886.2i | −0.0479547 | + | 0.533753i | ||||
\(879\) | −15753.9 | −0.604510 | ||||||||
\(880\) | 4678.80 | − | 12490.3i | 0.179230 | − | 0.478463i | ||||
\(881\) | 7132.59 | 0.272762 | 0.136381 | − | 0.990656i | \(-0.456453\pi\) | ||||
0.136381 | + | 0.990656i | \(0.456453\pi\) | |||||||
\(882\) | 2341.36 | − | 26060.2i | 0.0893853 | − | 0.994889i | ||||
\(883\) | 19170.0 | − | 19170.0i | 0.730601 | − | 0.730601i | −0.240138 | − | 0.970739i | \(-0.577193\pi\) |
0.970739 | + | 0.240138i | \(0.0771926\pi\) | |||||||
\(884\) | 9273.21 | − | 6428.78i | 0.352819 | − | 0.244596i | ||||
\(885\) | −20762.9 | − | 20762.9i | −0.788628 | − | 0.788628i | ||||
\(886\) | 19667.4 | + | 23550.3i | 0.745757 | + | 0.892989i | ||||
\(887\) | − | 45045.7i | − | 1.70517i | −0.522589 | − | 0.852585i | \(-0.675034\pi\) | ||
0.522589 | − | 0.852585i | \(-0.324966\pi\) | |||||||
\(888\) | 39153.7 | + | 10786.0i | 1.47963 | + | 0.407607i | ||||
\(889\) | 65287.3i | 2.46306i | ||||||||
\(890\) | −3761.94 | + | 3141.69i | −0.141686 | + | 0.118325i | ||||
\(891\) | 11497.8 | + | 11497.8i | 0.432314 | + | 0.432314i | ||||
\(892\) | −3303.17 | − | 598.374i | −0.123989 | − | 0.0224608i | ||||
\(893\) | 8345.43 | − | 8345.43i | 0.312731 | − | 0.312731i | ||||
\(894\) | 70746.8 | + | 6356.21i | 2.64667 | + | 0.237789i | ||||
\(895\) | 20541.1 | 0.767167 | ||||||||
\(896\) | 21160.2 | − | 29191.4i | 0.788964 | − | 1.08841i | ||||
\(897\) | 5962.34 | 0.221936 | ||||||||
\(898\) | 32439.2 | + | 2914.49i | 1.20547 | + | 0.108305i | ||||
\(899\) | −1012.55 | + | 1012.55i | −0.0375643 | + | 0.0375643i | ||||
\(900\) | −21438.2 | − | 3883.55i | −0.794006 | − | 0.143835i | ||||
\(901\) | 15551.4 | + | 15551.4i | 0.575017 | + | 0.575017i | ||||
\(902\) | 24730.6 | − | 20653.2i | 0.912905 | − | 0.762389i | ||||
\(903\) | − | 27435.3i | − | 1.01106i | ||||||
\(904\) | 15716.9 | + | 4329.68i | 0.578247 | + | 0.159295i | ||||
\(905\) | − | 1131.36i | − | 0.0415554i | ||||||
\(906\) | −39660.6 | − | 47490.7i | −1.45435 | − | 1.74147i | ||||
\(907\) | −33658.2 | − | 33658.2i | −1.23220 | − | 1.23220i | −0.963118 | − | 0.269079i | \(-0.913281\pi\) |
−0.269079 | − | 0.963118i | \(-0.586719\pi\) | |||||||
\(908\) | −19838.3 | + | 13753.2i | −0.725065 | + | 0.502661i | ||||
\(909\) | 16306.5 | − | 16306.5i | 0.594997 | − | 0.594997i | ||||
\(910\) | 662.476 | − | 7373.59i | 0.0241328 | − | 0.268607i | ||||
\(911\) | −42503.8 | −1.54579 | −0.772895 | − | 0.634534i | \(-0.781192\pi\) | ||||
−0.772895 | + | 0.634534i | \(0.781192\pi\) | |||||||
\(912\) | 9333.11 | − | 24915.2i | 0.338871 | − | 0.904632i | ||||
\(913\) | 14606.7 | 0.529477 | ||||||||
\(914\) | −1222.44 | + | 13606.2i | −0.0442394 | + | 0.492399i | ||||
\(915\) | −34069.7 | + | 34069.7i | −1.23094 | + | 1.23094i | ||||
\(916\) | −10148.5 | − | 14638.7i | −0.366066 | − | 0.528033i | ||||
\(917\) | 16371.3 | + | 16371.3i | 0.589562 | + | 0.589562i | ||||
\(918\) | −8000.34 | − | 9579.82i | −0.287637 | − | 0.344424i | ||||
\(919\) | − | 8819.41i | − | 0.316568i | −0.987394 | − | 0.158284i | \(-0.949404\pi\) | ||
0.987394 | − | 0.158284i | \(-0.0505961\pi\) | |||||||
\(920\) | 6244.60 | − | 3547.17i | 0.223781 | − | 0.127116i | ||||
\(921\) | 2541.55i | 0.0909305i | ||||||||
\(922\) | −25377.5 | + | 21193.3i | −0.906467 | + | 0.757012i | ||||
\(923\) | 2423.92 | + | 2423.92i | 0.0864402 | + | 0.0864402i | ||||
\(924\) | −8719.53 | + | 48134.0i | −0.310445 | + | 1.71374i | ||||
\(925\) | −13307.1 | + | 13307.1i | −0.473012 | + | 0.473012i | ||||
\(926\) | 14209.0 | + | 1276.60i | 0.504250 | + | 0.0453041i | ||||
\(927\) | 61504.8 | 2.17916 | ||||||||
\(928\) | −2522.73 | + | 884.950i | −0.0892380 | + | 0.0313038i | ||||
\(929\) | −14155.6 | −0.499925 | −0.249963 | − | 0.968256i | \(-0.580418\pi\) | ||||
−0.249963 | + | 0.968256i | \(0.580418\pi\) | |||||||
\(930\) | −14002.5 | − | 1258.05i | −0.493721 | − | 0.0443581i | ||||
\(931\) | −10469.6 | + | 10469.6i | −0.368558 | + | 0.368558i | ||||
\(932\) | 1703.87 | − | 9405.80i | 0.0598844 | − | 0.330577i | ||||
\(933\) | −4789.43 | − | 4789.43i | −0.168059 | − | 0.168059i | ||||
\(934\) | −38189.4 | + | 31892.9i | −1.33790 | + | 1.11731i | ||||
\(935\) | 18440.6i | 0.644996i | ||||||||
\(936\) | −5952.99 | − | 10479.9i | −0.207884 | − | 0.365969i | ||||
\(937\) | − | 38518.7i | − | 1.34296i | −0.741023 | − | 0.671479i | \(-0.765659\pi\) | ||
0.741023 | − | 0.671479i | \(-0.234341\pi\) | |||||||
\(938\) | 6854.32 | + | 8207.55i | 0.238594 | + | 0.285699i | ||||
\(939\) | 19319.2 | + | 19319.2i | 0.671414 | + | 0.671414i | ||||
\(940\) | −6633.71 | − | 9568.82i | −0.230179 | − | 0.332022i | ||||
\(941\) | 27998.2 | − | 27998.2i | 0.969942 | − | 0.969942i | −0.0296196 | − | 0.999561i | \(-0.509430\pi\) |
0.999561 | + | 0.0296196i | \(0.00942960\pi\) | |||||||
\(942\) | 2521.49 | − | 28065.1i | 0.0872130 | − | 0.970711i | ||||
\(943\) | 17349.0 | 0.599112 | ||||||||
\(944\) | 15180.7 | + | 33366.0i | 0.523399 | + | 1.15039i | ||||
\(945\) | −8188.93 | −0.281890 | ||||||||
\(946\) | −1133.82 | + | 12619.8i | −0.0389680 | + | 0.433727i | ||||
\(947\) | −32839.5 | + | 32839.5i | −1.12687 | + | 1.12687i | −0.136181 | + | 0.990684i | \(0.543483\pi\) |
−0.990684 | + | 0.136181i | \(0.956517\pi\) | |||||||
\(948\) | −42055.4 | + | 29155.5i | −1.44082 | + | 0.998867i | ||||
\(949\) | −7535.92 | − | 7535.92i | −0.257773 | − | 0.257773i | ||||
\(950\) | 7902.71 | + | 9462.92i | 0.269892 | + | 0.323176i | ||||
\(951\) | − | 51925.4i | − | 1.77055i | ||||||
\(952\) | −13238.7 | + | 48057.1i | −0.450704 | + | 1.63607i | ||||
\(953\) | − | 20600.1i | − | 0.700211i | −0.936710 | − | 0.350106i | \(-0.886146\pi\) | ||
0.936710 | − | 0.350106i | \(-0.113854\pi\) | |||||||
\(954\) | 18031.0 | − | 15058.1i | 0.611922 | − | 0.511031i | ||||
\(955\) | −18317.5 | − | 18317.5i | −0.620670 | − | 0.620670i | ||||
\(956\) | −33384.9 | − | 6047.72i | −1.12944 | − | 0.204600i | ||||
\(957\) | 2564.88 | − | 2564.88i | 0.0866360 | − | 0.0866360i | ||||
\(958\) | −36790.3 | − | 3305.41i | −1.24075 | − | 0.111475i | ||||
\(959\) | 62528.2 | 2.10547 | ||||||||
\(960\) | −22545.0 | − | 13441.4i | −0.757955 | − | 0.451896i | ||||
\(961\) | −20390.2 | −0.684441 | ||||||||
\(962\) | −10369.0 | − | 931.599i | −0.347516 | − | 0.0312224i | ||||
\(963\) | −2653.56 | + | 2653.56i | −0.0887951 | + | 0.0887951i | ||||
\(964\) | −43855.8 | − | 7944.53i | −1.46525 | − | 0.265432i | ||||
\(965\) | 15152.5 | + | 15152.5i | 0.505469 | + | 0.505469i | ||||
\(966\) | −20216.7 | + | 16883.5i | −0.673356 | + | 0.562336i | ||||
\(967\) | 38210.9i | 1.27071i | 0.772219 | + | 0.635356i | \(0.219147\pi\) | ||||
−0.772219 | + | 0.635356i | \(0.780853\pi\) | |||||||
\(968\) | −1998.59 | + | 7254.96i | −0.0663607 | + | 0.240892i | ||||
\(969\) | 36784.6i | 1.21950i | ||||||||
\(970\) | −1803.23 | − | 2159.23i | −0.0596888 | − | 0.0714730i | ||||
\(971\) | 37224.9 | + | 37224.9i | 1.23028 | + | 1.23028i | 0.963855 | + | 0.266427i | \(0.0858430\pi\) |
0.266427 | + | 0.963855i | \(0.414157\pi\) | |||||||
\(972\) | 35150.3 | − | 24368.4i | 1.15992 | − | 0.804133i | ||||
\(973\) | 27038.1 | − | 27038.1i | 0.890854 | − | 0.890854i | ||||
\(974\) | −3935.51 | + | 43803.6i | −0.129468 | + | 1.44102i | ||||
\(975\) | 10097.7 | 0.331678 | ||||||||
\(976\) | 54750.2 | − | 24909.9i | 1.79560 | − | 0.816953i | ||||
\(977\) | 7985.95 | 0.261508 | 0.130754 | − | 0.991415i | \(-0.458260\pi\) | ||||
0.130754 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(978\) | −3873.76 | + | 43116.3i | −0.126656 | + | 1.40972i | ||||
\(979\) | −5870.28 | + | 5870.28i | −0.191639 | + | 0.191639i | ||||
\(980\) | 8322.21 | + | 12004.4i | 0.271269 | + | 0.391292i | ||||
\(981\) | −31844.8 | − | 31844.8i | −1.03642 | − | 1.03642i | ||||
\(982\) | 22122.9 | + | 26490.5i | 0.718910 | + | 0.860842i | ||||
\(983\) | − | 10703.1i | − | 0.347279i | −0.984809 | − | 0.173639i | \(-0.944447\pi\) | ||
0.984809 | − | 0.173639i | \(-0.0555527\pi\) | |||||||
\(984\) | −31317.8 | − | 55133.3i | −1.01461 | − | 1.78616i | ||||
\(985\) | − | 22580.9i | − | 0.730442i | ||||||
\(986\) | 2837.03 | − | 2369.27i | 0.0916322 | − | 0.0765243i | ||||
\(987\) | 30195.4 | + | 30195.4i | 0.973791 | + | 0.973791i | ||||
\(988\) | −1215.72 | + | 6711.10i | −0.0391471 | + | 0.216102i | ||||
\(989\) | −4824.23 | + | 4824.23i | −0.155108 | + | 0.155108i | ||||
\(990\) | 19618.2 | + | 1762.59i | 0.629807 | + | 0.0565847i | ||||
\(991\) | −23945.4 | −0.767558 | −0.383779 | − | 0.923425i | \(-0.625377\pi\) | ||||
−0.383779 | + | 0.923425i | \(0.625377\pi\) | |||||||
\(992\) | 15819.0 | + | 7602.87i | 0.506306 | + | 0.243338i | ||||
\(993\) | −20009.0 | −0.639442 | ||||||||
\(994\) | −15082.6 | − | 1355.09i | −0.481280 | − | 0.0432404i | ||||
\(995\) | −6395.37 | + | 6395.37i | −0.203766 | + | 0.203766i | ||||
\(996\) | 5123.78 | − | 28284.5i | 0.163005 | − | 0.899829i | ||||
\(997\) | −14292.5 | − | 14292.5i | −0.454010 | − | 0.454010i | 0.442673 | − | 0.896683i | \(-0.354030\pi\) |
−0.896683 | + | 0.442673i | \(0.854030\pi\) | |||||||
\(998\) | −5318.83 | + | 4441.88i | −0.168702 | + | 0.140887i | ||||
\(999\) | 11515.6i | 0.364702i |
(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 | 16.4.e.a.5.1 | ✓ | 10 | |
3.2 | odd | 2 | 144.4.k.a.37.5 | 10 | |||
4.3 | odd | 2 | 64.4.e.a.49.1 | 10 | |||
8.3 | odd | 2 | 128.4.e.a.97.5 | 10 | |||
8.5 | even | 2 | 128.4.e.b.97.1 | 10 | |||
12.11 | even | 2 | 576.4.k.a.433.4 | 10 | |||
16.3 | odd | 4 | 64.4.e.a.17.1 | 10 | |||
16.5 | even | 4 | 128.4.e.b.33.1 | 10 | |||
16.11 | odd | 4 | 128.4.e.a.33.5 | 10 | |||
16.13 | even | 4 | inner | 16.4.e.a.13.1 | yes | 10 | |
32.3 | odd | 8 | 1024.4.a.m.1.2 | 10 | |||
32.5 | even | 8 | 1024.4.b.j.513.9 | 10 | |||
32.11 | odd | 8 | 1024.4.b.k.513.9 | 10 | |||
32.13 | even | 8 | 1024.4.a.n.1.2 | 10 | |||
32.19 | odd | 8 | 1024.4.a.m.1.9 | 10 | |||
32.21 | even | 8 | 1024.4.b.j.513.2 | 10 | |||
32.27 | odd | 8 | 1024.4.b.k.513.2 | 10 | |||
32.29 | even | 8 | 1024.4.a.n.1.9 | 10 | |||
48.29 | odd | 4 | 144.4.k.a.109.5 | 10 | |||
48.35 | even | 4 | 576.4.k.a.145.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
16.4.e.a.13.1 | yes | 10 | 16.13 | even | 4 | inner | |
64.4.e.a.17.1 | 10 | 16.3 | odd | 4 | |||
64.4.e.a.49.1 | 10 | 4.3 | odd | 2 | |||
128.4.e.a.33.5 | 10 | 16.11 | odd | 4 | |||
128.4.e.a.97.5 | 10 | 8.3 | odd | 2 | |||
128.4.e.b.33.1 | 10 | 16.5 | even | 4 | |||
128.4.e.b.97.1 | 10 | 8.5 | even | 2 | |||
144.4.k.a.37.5 | 10 | 3.2 | odd | 2 | |||
144.4.k.a.109.5 | 10 | 48.29 | odd | 4 | |||
576.4.k.a.145.4 | 10 | 48.35 | even | 4 | |||
576.4.k.a.433.4 | 10 | 12.11 | even | 2 | |||
1024.4.a.m.1.2 | 10 | 32.3 | odd | 8 | |||
1024.4.a.m.1.9 | 10 | 32.19 | odd | 8 | |||
1024.4.a.n.1.2 | 10 | 32.13 | even | 8 | |||
1024.4.a.n.1.9 | 10 | 32.29 | even | 8 | |||
1024.4.b.j.513.2 | 10 | 32.21 | even | 8 | |||
1024.4.b.j.513.9 | 10 | 32.5 | even | 8 | |||
1024.4.b.k.513.2 | 10 | 32.27 | odd | 8 | |||
1024.4.b.k.513.9 | 10 | 32.11 | odd | 8 |