Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), degree \(2\), not 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.a.147.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | + | 0.866025i | −0.530330 | + | 0.306186i | −0.741151 | − | 0.671339i | \(-0.765720\pi\) |
0.210821 | + | 0.977525i | \(0.432386\pi\) | |||||||
\(3\) | −1.00000 | − | 1.73205i | −0.192450 | − | 0.333333i | 0.753612 | − | 0.657320i | \(-0.228310\pi\) |
−0.946062 | + | 0.323987i | \(0.894977\pi\) | |||||||
\(4\) | −2.50000 | + | 4.33013i | −0.312500 | + | 0.541266i | ||||
\(5\) | − | 1.73205i | − | 0.154919i | −0.996995 | − | 0.0774597i | \(-0.975319\pi\) | ||
0.996995 | − | 0.0774597i | \(-0.0246809\pi\) | |||||||
\(6\) | 3.00000 | + | 1.73205i | 0.204124 | + | 0.117851i | ||||
\(7\) | 12.0000 | + | 6.92820i | 0.647939 | + | 0.374088i | 0.787666 | − | 0.616102i | \(-0.211289\pi\) |
−0.139727 | + | 0.990190i | \(0.544623\pi\) | |||||||
\(8\) | − | 22.5167i | − | 0.995105i | ||||||
\(9\) | 11.5000 | − | 19.9186i | 0.425926 | − | 0.737725i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.0474342 | + | 0.0821584i | ||||
\(11\) | −12.0000 | + | 6.92820i | −0.328921 | + | 0.189903i | −0.655362 | − | 0.755315i | \(-0.727484\pi\) |
0.326441 | + | 0.945218i | \(0.394151\pi\) | |||||||
\(12\) | 10.0000 | 0.240563 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −24.0000 | −0.458162 | ||||||||
\(15\) | −3.00000 | + | 1.73205i | −0.0516398 | + | 0.0298142i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.00781250 | − | 0.0135316i | ||||
\(17\) | −58.5000 | + | 101.325i | −0.834608 | + | 1.44558i | 0.0597414 | + | 0.998214i | \(0.480972\pi\) |
−0.894349 | + | 0.447369i | \(0.852361\pi\) | |||||||
\(18\) | 39.8372i | 0.521651i | ||||||||
\(19\) | 99.0000 | + | 57.1577i | 1.19538 | + | 0.690151i | 0.959521 | − | 0.281637i | \(-0.0908774\pi\) |
0.235856 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(20\) | 7.50000 | + | 4.33013i | 0.0838525 | + | 0.0484123i | ||||
\(21\) | − | 27.7128i | − | 0.287973i | ||||||
\(22\) | 12.0000 | − | 20.7846i | 0.116291 | − | 0.201422i | ||||
\(23\) | 39.0000 | + | 67.5500i | 0.353568 | + | 0.612398i | 0.986872 | − | 0.161506i | \(-0.0516350\pi\) |
−0.633304 | + | 0.773903i | \(0.718302\pi\) | |||||||
\(24\) | −39.0000 | + | 22.5167i | −0.331702 | + | 0.191508i | ||||
\(25\) | 122.000 | 0.976000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | −60.0000 | + | 34.6410i | −0.404962 | + | 0.233805i | ||||
\(29\) | 70.5000 | + | 122.110i | 0.451432 | + | 0.781903i | 0.998475 | − | 0.0552014i | \(-0.0175801\pi\) |
−0.547043 | + | 0.837104i | \(0.684247\pi\) | |||||||
\(30\) | 3.00000 | − | 5.19615i | 0.0182574 | − | 0.0316228i | ||||
\(31\) | 155.885i | 0.903151i | 0.892233 | + | 0.451576i | \(0.149138\pi\) | ||||
−0.892233 | + | 0.451576i | \(0.850862\pi\) | |||||||
\(32\) | 157.500 | + | 90.9327i | 0.870073 | + | 0.502337i | ||||
\(33\) | 24.0000 | + | 13.8564i | 0.126602 | + | 0.0730937i | ||||
\(34\) | − | 202.650i | − | 1.02218i | ||||||
\(35\) | 12.0000 | − | 20.7846i | 0.0579534 | − | 0.100378i | ||||
\(36\) | 57.5000 | + | 99.5929i | 0.266204 | + | 0.461078i | ||||
\(37\) | 124.500 | − | 71.8801i | 0.553180 | − | 0.319379i | −0.197223 | − | 0.980359i | \(-0.563192\pi\) |
0.750404 | + | 0.660980i | \(0.229859\pi\) | |||||||
\(38\) | −198.000 | −0.845259 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −39.0000 | −0.154161 | ||||||||
\(41\) | −235.500 | + | 135.966i | −0.897047 | + | 0.517910i | −0.876241 | − | 0.481873i | \(-0.839957\pi\) |
−0.0208059 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(42\) | 24.0000 | + | 41.5692i | 0.0881733 | + | 0.152721i | ||||
\(43\) | −52.0000 | + | 90.0666i | −0.184417 | + | 0.319419i | −0.943380 | − | 0.331714i | \(-0.892373\pi\) |
0.758963 | + | 0.651134i | \(0.225706\pi\) | |||||||
\(44\) | − | 69.2820i | − | 0.237379i | ||||||
\(45\) | −34.5000 | − | 19.9186i | −0.114288 | − | 0.0659842i | ||||
\(46\) | −117.000 | − | 67.5500i | −0.375015 | − | 0.216515i | ||||
\(47\) | 301.377i | 0.935326i | 0.883907 | + | 0.467663i | \(0.154904\pi\) | ||||
−0.883907 | + | 0.467663i | \(0.845096\pi\) | |||||||
\(48\) | −1.00000 | + | 1.73205i | −0.00300703 | + | 0.00520833i | ||||
\(49\) | −75.5000 | − | 130.770i | −0.220117 | − | 0.381253i | ||||
\(50\) | −183.000 | + | 105.655i | −0.517602 | + | 0.298838i | ||||
\(51\) | 234.000 | 0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.0000 | 0.241029 | 0.120514 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120514 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(54\) | 150.000 | − | 86.6025i | 0.378008 | − | 0.218243i | ||||
\(55\) | 12.0000 | + | 20.7846i | 0.0294196 | + | 0.0509563i | ||||
\(56\) | 156.000 | − | 270.200i | 0.372257 | − | 0.644768i | ||||
\(57\) | − | 228.631i | − | 0.531279i | ||||||
\(58\) | −211.500 | − | 122.110i | −0.478816 | − | 0.276444i | ||||
\(59\) | 246.000 | + | 142.028i | 0.542822 | + | 0.313398i | 0.746222 | − | 0.665698i | \(-0.231866\pi\) |
−0.203400 | + | 0.979096i | \(0.565199\pi\) | |||||||
\(60\) | − | 17.3205i | − | 0.0372678i | ||||||
\(61\) | −72.5000 | + | 125.574i | −0.152175 | + | 0.263575i | −0.932027 | − | 0.362389i | \(-0.881961\pi\) |
0.779852 | + | 0.625964i | \(0.215294\pi\) | |||||||
\(62\) | −135.000 | − | 233.827i | −0.276533 | − | 0.478968i | ||||
\(63\) | 276.000 | − | 159.349i | 0.551948 | − | 0.318667i | ||||
\(64\) | −307.000 | −0.599609 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −48.0000 | −0.0895211 | ||||||||
\(67\) | 681.000 | − | 393.176i | 1.24175 | − | 0.716926i | 0.272301 | − | 0.962212i | \(-0.412215\pi\) |
0.969451 | + | 0.245286i | \(0.0788819\pi\) | |||||||
\(68\) | −292.500 | − | 506.625i | −0.521630 | − | 0.903490i | ||||
\(69\) | 78.0000 | − | 135.100i | 0.136088 | − | 0.235712i | ||||
\(70\) | 41.5692i | 0.0709782i | ||||||||
\(71\) | −915.000 | − | 528.275i | −1.52944 | − | 0.883025i | −0.999385 | − | 0.0350641i | \(-0.988836\pi\) |
−0.530059 | − | 0.847961i | \(-0.677830\pi\) | |||||||
\(72\) | −448.500 | − | 258.942i | −0.734114 | − | 0.423841i | ||||
\(73\) | 458.993i | 0.735906i | 0.929844 | + | 0.367953i | \(0.119941\pi\) | ||||
−0.929844 | + | 0.367953i | \(0.880059\pi\) | |||||||
\(74\) | −124.500 | + | 215.640i | −0.195579 | + | 0.338752i | ||||
\(75\) | −122.000 | − | 211.310i | −0.187831 | − | 0.325333i | ||||
\(76\) | −495.000 | + | 285.788i | −0.747110 | + | 0.431344i | ||||
\(77\) | −192.000 | −0.284161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1276.00 | 1.81723 | 0.908615 | − | 0.417634i | \(-0.137141\pi\) | ||||
0.908615 | + | 0.417634i | \(0.137141\pi\) | |||||||
\(80\) | −1.50000 | + | 0.866025i | −0.00209631 | + | 0.00121031i | ||||
\(81\) | −210.500 | − | 364.597i | −0.288752 | − | 0.500133i | ||||
\(82\) | 235.500 | − | 407.898i | 0.317154 | − | 0.549327i | ||||
\(83\) | − | 789.815i | − | 1.04450i | −0.852793 | − | 0.522250i | \(-0.825093\pi\) | ||
0.852793 | − | 0.522250i | \(-0.174907\pi\) | |||||||
\(84\) | 120.000 | + | 69.2820i | 0.155870 | + | 0.0899915i | ||||
\(85\) | 175.500 | + | 101.325i | 0.223949 | + | 0.129297i | ||||
\(86\) | − | 180.133i | − | 0.225864i | ||||||
\(87\) | 141.000 | − | 244.219i | 0.173756 | − | 0.300955i | ||||
\(88\) | 156.000 | + | 270.200i | 0.188973 | + | 0.327311i | ||||
\(89\) | 846.000 | − | 488.438i | 1.00759 | − | 0.581734i | 0.0971073 | − | 0.995274i | \(-0.469041\pi\) |
0.910486 | + | 0.413540i | \(0.135708\pi\) | |||||||
\(90\) | 69.0000 | 0.0808138 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −390.000 | −0.441960 | ||||||||
\(93\) | 270.000 | − | 155.885i | 0.301050 | − | 0.173812i | ||||
\(94\) | −261.000 | − | 452.065i | −0.286384 | − | 0.496032i | ||||
\(95\) | 99.0000 | − | 171.473i | 0.106918 | − | 0.185187i | ||||
\(96\) | − | 363.731i | − | 0.386699i | ||||||
\(97\) | −174.000 | − | 100.459i | −0.182134 | − | 0.105155i | 0.406161 | − | 0.913802i | \(-0.366867\pi\) |
−0.588295 | + | 0.808646i | \(0.700201\pi\) | |||||||
\(98\) | 226.500 | + | 130.770i | 0.233469 | + | 0.134793i | ||||
\(99\) | 318.697i | 0.323538i | ||||||||
\(100\) | −305.000 | + | 528.275i | −0.305000 | + | 0.528275i | ||||
\(101\) | −214.500 | − | 371.525i | −0.211322 | − | 0.366021i | 0.740806 | − | 0.671719i | \(-0.234444\pi\) |
−0.952129 | + | 0.305698i | \(0.901110\pi\) | |||||||
\(102\) | −351.000 | + | 202.650i | −0.340727 | + | 0.196719i | ||||
\(103\) | 182.000 | 0.174107 | 0.0870534 | − | 0.996204i | \(-0.472255\pi\) | ||||
0.0870534 | + | 0.996204i | \(0.472255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −48.0000 | −0.0446126 | ||||||||
\(106\) | −139.500 | + | 80.5404i | −0.127825 | + | 0.0737997i | ||||
\(107\) | 753.000 | + | 1304.23i | 0.680330 | + | 1.17837i | 0.974880 | + | 0.222729i | \(0.0714967\pi\) |
−0.294551 | + | 0.955636i | \(0.595170\pi\) | |||||||
\(108\) | 250.000 | − | 433.013i | 0.222743 | − | 0.385802i | ||||
\(109\) | 1551.92i | 1.36373i | 0.731477 | + | 0.681866i | \(0.238831\pi\) | ||||
−0.731477 | + | 0.681866i | \(0.761169\pi\) | |||||||
\(110\) | −36.0000 | − | 20.7846i | −0.0312042 | − | 0.0180158i | ||||
\(111\) | −249.000 | − | 143.760i | −0.212919 | − | 0.122929i | ||||
\(112\) | − | 13.8564i | − | 0.0116902i | ||||||
\(113\) | 343.500 | − | 594.959i | 0.285962 | − | 0.495302i | −0.686880 | − | 0.726771i | \(-0.741020\pi\) |
0.972842 | + | 0.231470i | \(0.0743534\pi\) | |||||||
\(114\) | 198.000 | + | 342.946i | 0.162670 | + | 0.281753i | ||||
\(115\) | 117.000 | − | 67.5500i | 0.0948722 | − | 0.0547745i | ||||
\(116\) | −705.000 | −0.564290 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −492.000 | −0.383833 | ||||||||
\(119\) | −1404.00 | + | 810.600i | −1.08155 | + | 0.624433i | ||||
\(120\) | 39.0000 | + | 67.5500i | 0.0296683 | + | 0.0513870i | ||||
\(121\) | −569.500 | + | 986.403i | −0.427874 | + | 0.741099i | ||||
\(122\) | − | 251.147i | − | 0.186376i | ||||||
\(123\) | 471.000 | + | 271.932i | 0.345273 | + | 0.199344i | ||||
\(124\) | −675.000 | − | 389.711i | −0.488845 | − | 0.282235i | ||||
\(125\) | − | 427.817i | − | 0.306121i | ||||||
\(126\) | −276.000 | + | 478.046i | −0.195143 | + | 0.337998i | ||||
\(127\) | −143.000 | − | 247.683i | −0.0999149 | − | 0.173058i | 0.811734 | − | 0.584027i | \(-0.198524\pi\) |
−0.911649 | + | 0.410969i | \(0.865190\pi\) | |||||||
\(128\) | −799.500 | + | 461.592i | −0.552082 | + | 0.318745i | ||||
\(129\) | 208.000 | 0.141964 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1974.00 | −1.31656 | −0.658279 | − | 0.752774i | \(-0.728715\pi\) | ||||
−0.658279 | + | 0.752774i | \(0.728715\pi\) | |||||||
\(132\) | −120.000 | + | 69.2820i | −0.0791262 | + | 0.0456835i | ||||
\(133\) | 792.000 | + | 1371.78i | 0.516354 | + | 0.894352i | ||||
\(134\) | −681.000 | + | 1179.53i | −0.439026 | + | 0.760415i | ||||
\(135\) | 173.205i | 0.110423i | ||||||||
\(136\) | 2281.50 | + | 1317.22i | 1.43851 | + | 0.830523i | ||||
\(137\) | 733.500 | + | 423.486i | 0.457424 | + | 0.264094i | 0.710961 | − | 0.703232i | \(-0.248260\pi\) |
−0.253536 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(138\) | 270.200i | 0.166674i | ||||||||
\(139\) | −118.000 | + | 204.382i | −0.0720045 | + | 0.124716i | −0.899780 | − | 0.436344i | \(-0.856273\pi\) |
0.827775 | + | 0.561060i | \(0.189606\pi\) | |||||||
\(140\) | 60.0000 | + | 103.923i | 0.0362209 | + | 0.0627364i | ||||
\(141\) | 522.000 | − | 301.377i | 0.311775 | − | 0.180004i | ||||
\(142\) | 1830.00 | 1.08148 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −23.0000 | −0.0133102 | ||||||||
\(145\) | 211.500 | − | 122.110i | 0.121132 | − | 0.0699355i | ||||
\(146\) | −397.500 | − | 688.490i | −0.225324 | − | 0.390273i | ||||
\(147\) | −151.000 | + | 261.540i | −0.0847229 | + | 0.146744i | ||||
\(148\) | 718.801i | 0.399224i | ||||||||
\(149\) | 40.5000 | + | 23.3827i | 0.0222677 | + | 0.0128563i | 0.511093 | − | 0.859526i | \(-0.329241\pi\) |
−0.488825 | + | 0.872382i | \(0.662574\pi\) | |||||||
\(150\) | 366.000 | + | 211.310i | 0.199225 | + | 0.115023i | ||||
\(151\) | − | 1770.16i | − | 0.953995i | −0.878905 | − | 0.476998i | \(-0.841725\pi\) | ||
0.878905 | − | 0.476998i | \(-0.158275\pi\) | |||||||
\(152\) | 1287.00 | − | 2229.15i | 0.686773 | − | 1.18953i | ||||
\(153\) | 1345.50 | + | 2330.47i | 0.710962 | + | 1.23142i | ||||
\(154\) | 288.000 | − | 166.277i | 0.150699 | − | 0.0870063i | ||||
\(155\) | 270.000 | 0.139916 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1211.00 | 0.615594 | 0.307797 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307797 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(158\) | −1914.00 | + | 1105.05i | −0.963732 | + | 0.556411i | ||||
\(159\) | −93.0000 | − | 161.081i | −0.0463860 | − | 0.0803430i | ||||
\(160\) | 157.500 | − | 272.798i | 0.0778217 | − | 0.134791i | ||||
\(161\) | 1080.80i | 0.529062i | ||||||||
\(162\) | 631.500 | + | 364.597i | 0.306267 | + | 0.176824i | ||||
\(163\) | 870.000 | + | 502.295i | 0.418059 | + | 0.241367i | 0.694247 | − | 0.719737i | \(-0.255738\pi\) |
−0.276187 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(164\) | − | 1359.66i | − | 0.647388i | ||||||
\(165\) | 24.0000 | − | 41.5692i | 0.0113236 | − | 0.0196131i | ||||
\(166\) | 684.000 | + | 1184.72i | 0.319811 | + | 0.553930i | ||||
\(167\) | −792.000 | + | 457.261i | −0.366987 | + | 0.211880i | −0.672141 | − | 0.740423i | \(-0.734625\pi\) |
0.305154 | + | 0.952303i | \(0.401292\pi\) | |||||||
\(168\) | −624.000 | −0.286563 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −351.000 | −0.158356 | ||||||||
\(171\) | 2277.00 | − | 1314.63i | 1.01828 | − | 0.587906i | ||||
\(172\) | −260.000 | − | 450.333i | −0.115261 | − | 0.199637i | ||||
\(173\) | −1287.00 | + | 2229.15i | −0.565600 | + | 0.979648i | 0.431394 | + | 0.902164i | \(0.358022\pi\) |
−0.996994 | + | 0.0774841i | \(0.975311\pi\) | |||||||
\(174\) | 488.438i | 0.212807i | ||||||||
\(175\) | 1464.00 | + | 845.241i | 0.632389 | + | 0.365110i | ||||
\(176\) | 12.0000 | + | 6.92820i | 0.00513940 | + | 0.00296723i | ||||
\(177\) | − | 568.113i | − | 0.241254i | ||||||
\(178\) | −846.000 | + | 1465.31i | −0.356238 | + | 0.617022i | ||||
\(179\) | −1872.00 | − | 3242.40i | −0.781675 | − | 1.35390i | −0.930965 | − | 0.365108i | \(-0.881032\pi\) |
0.149290 | − | 0.988793i | \(-0.452301\pi\) | |||||||
\(180\) | 172.500 | − | 99.5929i | 0.0714299 | − | 0.0412401i | ||||
\(181\) | −637.000 | −0.261590 | −0.130795 | − | 0.991409i | \(-0.541753\pi\) | ||||
−0.130795 | + | 0.991409i | \(0.541753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 290.000 | 0.117144 | ||||||||
\(184\) | 1521.00 | − | 878.150i | 0.609400 | − | 0.351837i | ||||
\(185\) | −124.500 | − | 215.640i | −0.0494780 | − | 0.0856983i | ||||
\(186\) | −270.000 | + | 467.654i | −0.106437 | + | 0.184355i | ||||
\(187\) | − | 1621.20i | − | 0.633978i | ||||||
\(188\) | −1305.00 | − | 753.442i | −0.506260 | − | 0.292289i | ||||
\(189\) | −1200.00 | − | 692.820i | −0.461837 | − | 0.266642i | ||||
\(190\) | 342.946i | 0.130947i | ||||||||
\(191\) | 1299.00 | − | 2249.93i | 0.492106 | − | 0.852353i | −0.507852 | − | 0.861444i | \(-0.669560\pi\) |
0.999959 | + | 0.00909077i | \(0.00289372\pi\) | |||||||
\(192\) | 307.000 | + | 531.740i | 0.115395 | + | 0.199870i | ||||
\(193\) | −967.500 | + | 558.586i | −0.360840 | + | 0.208331i | −0.669449 | − | 0.742858i | \(-0.733470\pi\) |
0.308609 | + | 0.951189i | \(0.400137\pi\) | |||||||
\(194\) | 348.000 | 0.128788 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 755.000 | 0.275146 | ||||||||
\(197\) | −1776.00 | + | 1025.37i | −0.642308 | + | 0.370837i | −0.785503 | − | 0.618858i | \(-0.787596\pi\) |
0.143195 | + | 0.989695i | \(0.454262\pi\) | |||||||
\(198\) | −276.000 | − | 478.046i | −0.0990630 | − | 0.171582i | ||||
\(199\) | 1261.00 | − | 2184.12i | 0.449196 | − | 0.778030i | −0.549138 | − | 0.835732i | \(-0.685044\pi\) |
0.998334 | + | 0.0577019i | \(0.0183773\pi\) | |||||||
\(200\) | − | 2747.03i | − | 0.971223i | ||||||
\(201\) | −1362.00 | − | 786.351i | −0.477951 | − | 0.275945i | ||||
\(202\) | 643.500 | + | 371.525i | 0.224141 | + | 0.129408i | ||||
\(203\) | 1953.75i | 0.675500i | ||||||||
\(204\) | −585.000 | + | 1013.25i | −0.200775 | + | 0.347753i | ||||
\(205\) | 235.500 | + | 407.898i | 0.0802343 | + | 0.138970i | ||||
\(206\) | −273.000 | + | 157.617i | −0.0923340 | + | 0.0533091i | ||||
\(207\) | 1794.00 | 0.602375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1584.00 | −0.524247 | ||||||||
\(210\) | 72.0000 | − | 41.5692i | 0.0236594 | − | 0.0136598i | ||||
\(211\) | −521.000 | − | 902.398i | −0.169986 | − | 0.294425i | 0.768428 | − | 0.639936i | \(-0.221039\pi\) |
−0.938415 | + | 0.345511i | \(0.887706\pi\) | |||||||
\(212\) | −232.500 | + | 402.702i | −0.0753215 | + | 0.130461i | ||||
\(213\) | 2113.10i | 0.679753i | ||||||||
\(214\) | −2259.00 | − | 1304.23i | −0.721598 | − | 0.416615i | ||||
\(215\) | 156.000 | + | 90.0666i | 0.0494842 | + | 0.0285697i | ||||
\(216\) | 2251.67i | 0.709289i | ||||||||
\(217\) | −1080.00 | + | 1870.61i | −0.337858 | + | 0.585187i | ||||
\(218\) | −1344.00 | − | 2327.88i | −0.417556 | − | 0.723228i | ||||
\(219\) | 795.000 | − | 458.993i | 0.245302 | − | 0.141625i | ||||
\(220\) | −120.000 | −0.0367745 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 498.000 | 0.150557 | ||||||||
\(223\) | 2085.00 | − | 1203.78i | 0.626107 | − | 0.361483i | −0.153136 | − | 0.988205i | \(-0.548937\pi\) |
0.779243 | + | 0.626722i | \(0.215604\pi\) | |||||||
\(224\) | 1260.00 | + | 2182.38i | 0.375836 | + | 0.650967i | ||||
\(225\) | 1403.00 | − | 2430.07i | 0.415704 | − | 0.720020i | ||||
\(226\) | 1189.92i | 0.350231i | ||||||||
\(227\) | −2085.00 | − | 1203.78i | −0.609631 | − | 0.351971i | 0.163190 | − | 0.986595i | \(-0.447822\pi\) |
−0.772821 | + | 0.634624i | \(0.781155\pi\) | |||||||
\(228\) | 990.000 | + | 571.577i | 0.287563 | + | 0.166025i | ||||
\(229\) | 2508.01i | 0.723729i | 0.932231 | + | 0.361864i | \(0.117860\pi\) | ||||
−0.932231 | + | 0.361864i | \(0.882140\pi\) | |||||||
\(230\) | −117.000 | + | 202.650i | −0.0335424 | + | 0.0580971i | ||||
\(231\) | 192.000 | + | 332.554i | 0.0546869 | + | 0.0947205i | ||||
\(232\) | 2749.50 | − | 1587.42i | 0.778076 | − | 0.449222i | ||||
\(233\) | −5850.00 | −1.64483 | −0.822417 | − | 0.568885i | \(-0.807375\pi\) | ||||
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 522.000 | 0.144900 | ||||||||
\(236\) | −1230.00 | + | 710.141i | −0.339263 | + | 0.195874i | ||||
\(237\) | −1276.00 | − | 2210.10i | −0.349726 | − | 0.605744i | ||||
\(238\) | 1404.00 | − | 2431.80i | 0.382386 | − | 0.662312i | ||||
\(239\) | − | 5383.21i | − | 1.45695i | −0.685072 | − | 0.728475i | \(-0.740229\pi\) | ||
0.685072 | − | 0.728475i | \(-0.259771\pi\) | |||||||
\(240\) | 3.00000 | + | 1.73205i | 0.000806872 | + | 0.000465847i | ||||
\(241\) | −4258.50 | − | 2458.65i | −1.13823 | − | 0.657159i | −0.192240 | − | 0.981348i | \(-0.561575\pi\) |
−0.945992 | + | 0.324189i | \(0.894909\pi\) | |||||||
\(242\) | − | 1972.81i | − | 0.524036i | ||||||
\(243\) | −1771.00 | + | 3067.46i | −0.467530 | + | 0.809785i | ||||
\(244\) | −362.500 | − | 627.868i | −0.0951094 | − | 0.164734i | ||||
\(245\) | −226.500 | + | 130.770i | −0.0590635 | + | 0.0341003i | ||||
\(246\) | −942.000 | −0.244145 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3510.00 | 0.898731 | ||||||||
\(249\) | −1368.00 | + | 789.815i | −0.348167 | + | 0.201014i | ||||
\(250\) | 370.500 | + | 641.725i | 0.0937299 | + | 0.162345i | ||||
\(251\) | 1989.00 | − | 3445.05i | 0.500178 | − | 0.866333i | −0.499822 | − | 0.866128i | \(-0.666601\pi\) |
1.00000 | 0.000205037i | \(-6.52654e-5\pi\) | ||||||||
\(252\) | 1593.49i | 0.398334i | ||||||||
\(253\) | −936.000 | − | 540.400i | −0.232592 | − | 0.134287i | ||||
\(254\) | 429.000 | + | 247.683i | 0.105976 | + | 0.0611852i | ||||
\(255\) | − | 405.300i | − | 0.0995328i | ||||||
\(256\) | 2027.50 | − | 3511.73i | 0.494995 | − | 0.857357i | ||||
\(257\) | −1033.50 | − | 1790.07i | −0.250848 | − | 0.434482i | 0.712911 | − | 0.701254i | \(-0.247376\pi\) |
−0.963760 | + | 0.266772i | \(0.914043\pi\) | |||||||
\(258\) | −312.000 | + | 180.133i | −0.0752879 | + | 0.0434675i | ||||
\(259\) | 1992.00 | 0.477903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3243.00 | 0.769106 | ||||||||
\(262\) | 2961.00 | − | 1709.53i | 0.698211 | − | 0.403112i | ||||
\(263\) | 1026.00 | + | 1777.08i | 0.240555 | + | 0.416653i | 0.960872 | − | 0.276991i | \(-0.0893373\pi\) |
−0.720318 | + | 0.693644i | \(0.756004\pi\) | |||||||
\(264\) | 312.000 | − | 540.400i | 0.0727359 | − | 0.125982i | ||||
\(265\) | − | 161.081i | − | 0.0373400i | ||||||
\(266\) | −2376.00 | − | 1371.78i | −0.547676 | − | 0.316201i | ||||
\(267\) | −1692.00 | − | 976.877i | −0.387823 | − | 0.223910i | ||||
\(268\) | 3931.76i | 0.896157i | ||||||||
\(269\) | −1665.00 | + | 2883.86i | −0.377386 | + | 0.653652i | −0.990681 | − | 0.136202i | \(-0.956510\pi\) |
0.613295 | + | 0.789854i | \(0.289844\pi\) | |||||||
\(270\) | −150.000 | − | 259.808i | −0.0338100 | − | 0.0585607i | ||||
\(271\) | −2430.00 | + | 1402.96i | −0.544694 | + | 0.314479i | −0.746979 | − | 0.664848i | \(-0.768496\pi\) |
0.202285 | + | 0.979327i | \(0.435163\pi\) | |||||||
\(272\) | 117.000 | 0.0260815 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1467.00 | −0.323448 | ||||||||
\(275\) | −1464.00 | + | 845.241i | −0.321027 | + | 0.185345i | ||||
\(276\) | 390.000 | + | 675.500i | 0.0850552 | + | 0.147320i | ||||
\(277\) | −188.500 | + | 326.492i | −0.0408876 | + | 0.0708194i | −0.885745 | − | 0.464172i | \(-0.846352\pi\) |
0.844857 | + | 0.534992i | \(0.179685\pi\) | |||||||
\(278\) | − | 408.764i | − | 0.0881872i | ||||||
\(279\) | 3105.00 | + | 1792.67i | 0.666278 | + | 0.384676i | ||||
\(280\) | −468.000 | − | 270.200i | −0.0998870 | − | 0.0576698i | ||||
\(281\) | − | 36.3731i | − | 0.00772183i | −0.999993 | − | 0.00386092i | \(-0.998771\pi\) | ||
0.999993 | − | 0.00386092i | \(-0.00122897\pi\) | |||||||
\(282\) | −522.000 | + | 904.131i | −0.110229 | + | 0.190923i | ||||
\(283\) | 3562.00 | + | 6169.56i | 0.748194 | + | 1.29591i | 0.948688 | + | 0.316215i | \(0.102412\pi\) |
−0.200493 | + | 0.979695i | \(0.564255\pi\) | |||||||
\(284\) | 4575.00 | − | 2641.38i | 0.955902 | − | 0.551891i | ||||
\(285\) | −396.000 | −0.0823053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3768.00 | −0.774976 | ||||||||
\(288\) | 3622.50 | − | 2091.45i | 0.741173 | − | 0.427917i | ||||
\(289\) | −4388.00 | − | 7600.24i | −0.893141 | − | 1.54696i | ||||
\(290\) | −211.500 | + | 366.329i | −0.0428266 | + | 0.0741778i | ||||
\(291\) | 401.836i | 0.0809486i | ||||||||
\(292\) | −1987.50 | − | 1147.48i | −0.398321 | − | 0.229971i | ||||
\(293\) | 7207.50 | + | 4161.25i | 1.43709 | + | 0.829703i | 0.997646 | − | 0.0685685i | \(-0.0218432\pi\) |
0.439441 | + | 0.898271i | \(0.355177\pi\) | |||||||
\(294\) | − | 523.079i | − | 0.103764i | ||||||
\(295\) | 246.000 | − | 426.084i | 0.0485514 | − | 0.0840936i | ||||
\(296\) | −1618.50 | − | 2803.32i | −0.317816 | − | 0.550473i | ||||
\(297\) | 1200.00 | − | 692.820i | 0.234448 | − | 0.135359i | ||||
\(298\) | −81.0000 | −0.0157457 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1220.00 | 0.234789 | ||||||||
\(301\) | −1248.00 | + | 720.533i | −0.238982 | + | 0.137976i | ||||
\(302\) | 1533.00 | + | 2655.23i | 0.292100 | + | 0.505932i | ||||
\(303\) | −429.000 | + | 743.050i | −0.0813380 | + | 0.140882i | ||||
\(304\) | − | 114.315i | − | 0.0215672i | ||||||
\(305\) | 217.500 | + | 125.574i | 0.0408328 | + | 0.0235748i | ||||
\(306\) | −4036.50 | − | 2330.47i | −0.754089 | − | 0.435374i | ||||
\(307\) | − | 2220.49i | − | 0.412801i | −0.978468 | − | 0.206401i | \(-0.933825\pi\) | ||
0.978468 | − | 0.206401i | \(-0.0661750\pi\) | |||||||
\(308\) | 480.000 | − | 831.384i | 0.0888004 | − | 0.153807i | ||||
\(309\) | −182.000 | − | 315.233i | −0.0335069 | − | 0.0580356i | ||||
\(310\) | −405.000 | + | 233.827i | −0.0742015 | + | 0.0428402i | ||||
\(311\) | 4914.00 | 0.895972 | 0.447986 | − | 0.894041i | \(-0.352141\pi\) | ||||
0.447986 | + | 0.894041i | \(0.352141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −518.000 | −0.0935434 | −0.0467717 | − | 0.998906i | \(-0.514893\pi\) | ||||
−0.0467717 | + | 0.998906i | \(0.514893\pi\) | |||||||
\(314\) | −1816.50 | + | 1048.76i | −0.326468 | + | 0.188487i | ||||
\(315\) | −276.000 | − | 478.046i | −0.0493677 | − | 0.0855074i | ||||
\(316\) | −3190.00 | + | 5525.24i | −0.567885 | + | 0.983605i | ||||
\(317\) | 3916.17i | 0.693861i | 0.937891 | + | 0.346930i | \(0.112776\pi\) | ||||
−0.937891 | + | 0.346930i | \(0.887224\pi\) | |||||||
\(318\) | 279.000 | + | 161.081i | 0.0491998 | + | 0.0284055i | ||||
\(319\) | −1692.00 | − | 976.877i | −0.296971 | − | 0.171456i | ||||
\(320\) | 531.740i | 0.0928911i | ||||||||
\(321\) | 1506.00 | − | 2608.47i | 0.261859 | − | 0.453553i | ||||
\(322\) | −936.000 | − | 1621.20i | −0.161991 | − | 0.280577i | ||||
\(323\) | −11583.0 | + | 6687.45i | −1.99534 | + | 1.15201i | ||||
\(324\) | 2105.00 | 0.360940 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1740.00 | −0.295613 | ||||||||
\(327\) | 2688.00 | − | 1551.92i | 0.454577 | − | 0.262450i | ||||
\(328\) | 3061.50 | + | 5302.67i | 0.515375 | + | 0.892656i | ||||
\(329\) | −2088.00 | + | 3616.52i | −0.349894 | + | 0.606034i | ||||
\(330\) | 83.1384i | 0.0138685i | ||||||||
\(331\) | 6456.00 | + | 3727.37i | 1.07207 | + | 0.618958i | 0.928745 | − | 0.370719i | \(-0.120889\pi\) |
0.143321 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(332\) | 3420.00 | + | 1974.54i | 0.565352 | + | 0.326406i | ||||
\(333\) | − | 3306.48i | − | 0.544127i | ||||||
\(334\) | 792.000 | − | 1371.78i | 0.129749 | − | 0.224733i | ||||
\(335\) | −681.000 | − | 1179.53i | −0.111066 | − | 0.192371i | ||||
\(336\) | −24.0000 | + | 13.8564i | −0.00389675 | + | 0.00224979i | ||||
\(337\) | −3575.00 | −0.577871 | −0.288936 | − | 0.957349i | \(-0.593301\pi\) | ||||
−0.288936 | + | 0.957349i | \(0.593301\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1374.00 | −0.220134 | ||||||||
\(340\) | −877.500 | + | 506.625i | −0.139968 | + | 0.0808106i | ||||
\(341\) | −1080.00 | − | 1870.61i | −0.171511 | − | 0.297066i | ||||
\(342\) | −2277.00 | + | 3943.88i | −0.360018 | + | 0.623569i | ||||
\(343\) | − | 6845.06i | − | 1.07755i | ||||||
\(344\) | 2028.00 | + | 1170.87i | 0.317856 | + | 0.183514i | ||||
\(345\) | −234.000 | − | 135.100i | −0.0365163 | − | 0.0210827i | ||||
\(346\) | − | 4458.30i | − | 0.692716i | ||||||
\(347\) | 3483.00 | − | 6032.73i | 0.538839 | − | 0.933297i | −0.460128 | − | 0.887853i | \(-0.652196\pi\) |
0.998967 | − | 0.0454442i | \(-0.0144703\pi\) | |||||||
\(348\) | 705.000 | + | 1221.10i | 0.108598 | + | 0.188097i | ||||
\(349\) | 5760.00 | − | 3325.54i | 0.883455 | − | 0.510063i | 0.0116588 | − | 0.999932i | \(-0.496289\pi\) |
0.871796 | + | 0.489869i | \(0.162955\pi\) | |||||||
\(350\) | −2928.00 | −0.447166 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2520.00 | −0.381581 | ||||||||
\(353\) | −4876.50 | + | 2815.45i | −0.735269 | + | 0.424508i | −0.820347 | − | 0.571867i | \(-0.806219\pi\) |
0.0850777 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(354\) | 492.000 | + | 852.169i | 0.0738687 | + | 0.127944i | ||||
\(355\) | −915.000 | + | 1584.83i | −0.136798 | + | 0.236940i | ||||
\(356\) | 4884.38i | 0.727168i | ||||||||
\(357\) | 2808.00 | + | 1621.20i | 0.416289 | + | 0.240344i | ||||
\(358\) | 5616.00 | + | 3242.40i | 0.829092 | + | 0.478676i | ||||
\(359\) | − | 7129.12i | − | 1.04808i | −0.851694 | − | 0.524040i | \(-0.824424\pi\) | ||
0.851694 | − | 0.524040i | \(-0.175576\pi\) | |||||||
\(360\) | −448.500 | + | 776.825i | −0.0656612 | + | 0.113729i | ||||
\(361\) | 3104.50 | + | 5377.15i | 0.452617 | + | 0.783956i | ||||
\(362\) | 955.500 | − | 551.658i | 0.138729 | − | 0.0800953i | ||||
\(363\) | 2278.00 | 0.329377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 795.000 | 0.114006 | ||||||||
\(366\) | −435.000 | + | 251.147i | −0.0621252 | + | 0.0358680i | ||||
\(367\) | −1.00000 | − | 1.73205i | −0.000142233 | − | 0.000246355i | 0.865954 | − | 0.500123i | \(-0.166712\pi\) |
−0.866097 | + | 0.499877i | \(0.833379\pi\) | |||||||
\(368\) | 39.0000 | − | 67.5500i | 0.00552450 | − | 0.00956871i | ||||
\(369\) | 6254.44i | 0.882366i | ||||||||
\(370\) | 373.500 | + | 215.640i | 0.0524793 | + | 0.0302989i | ||||
\(371\) | 1116.00 | + | 644.323i | 0.156172 | + | 0.0901660i | ||||
\(372\) | 1558.85i | 0.217264i | ||||||||
\(373\) | −1749.50 | + | 3030.22i | −0.242857 | + | 0.420641i | −0.961527 | − | 0.274711i | \(-0.911418\pi\) |
0.718670 | + | 0.695351i | \(0.244751\pi\) | |||||||
\(374\) | 1404.00 | + | 2431.80i | 0.194115 | + | 0.336218i | ||||
\(375\) | −741.000 | + | 427.817i | −0.102040 | + | 0.0589129i | ||||
\(376\) | 6786.00 | 0.930748 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2400.00 | 0.326568 | ||||||||
\(379\) | −4779.00 | + | 2759.16i | −0.647706 | + | 0.373953i | −0.787577 | − | 0.616216i | \(-0.788665\pi\) |
0.139871 | + | 0.990170i | \(0.455331\pi\) | |||||||
\(380\) | 495.000 | + | 857.365i | 0.0668236 | + | 0.115742i | ||||
\(381\) | −286.000 | + | 495.367i | −0.0384573 | + | 0.0666100i | ||||
\(382\) | 4499.87i | 0.602705i | ||||||||
\(383\) | 6378.00 | + | 3682.34i | 0.850915 | + | 0.491276i | 0.860960 | − | 0.508673i | \(-0.169864\pi\) |
−0.0100443 | + | 0.999950i | \(0.503197\pi\) | |||||||
\(384\) | 1599.00 | + | 923.183i | 0.212496 | + | 0.122685i | ||||
\(385\) | 332.554i | 0.0440221i | ||||||||
\(386\) | 967.500 | − | 1675.76i | 0.127576 | − | 0.220969i | ||||
\(387\) | 1196.00 | + | 2071.53i | 0.157096 | + | 0.272098i | ||||
\(388\) | 870.000 | − | 502.295i | 0.113834 | − | 0.0657220i | ||||
\(389\) | −1209.00 | −0.157580 | −0.0787901 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787901 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9126.00 | −1.18036 | ||||||||
\(392\) | −2944.50 | + | 1700.01i | −0.379387 | + | 0.219039i | ||||
\(393\) | 1974.00 | + | 3419.07i | 0.253372 | + | 0.438853i | ||||
\(394\) | 1776.00 | − | 3076.12i | 0.227090 | − | 0.393332i | ||||
\(395\) | − | 2210.10i | − | 0.281524i | ||||||
\(396\) | −1380.00 | − | 796.743i | −0.175120 | − | 0.101106i | ||||
\(397\) | −10128.0 | − | 5847.40i | −1.28038 | − | 0.739226i | −0.303460 | − | 0.952844i | \(-0.598142\pi\) |
−0.976917 | + | 0.213618i | \(0.931475\pi\) | |||||||
\(398\) | 4368.23i | 0.550150i | ||||||||
\(399\) | 1584.00 | − | 2743.57i | 0.198745 | − | 0.344236i | ||||
\(400\) | −61.0000 | − | 105.655i | −0.00762500 | − | 0.0132069i | ||||
\(401\) | 2581.50 | − | 1490.43i | 0.321481 | − | 0.185607i | −0.330571 | − | 0.943781i | \(-0.607241\pi\) |
0.652053 | + | 0.758174i | \(0.273908\pi\) | |||||||
\(402\) | 2724.00 | 0.337962 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2145.00 | 0.264153 | ||||||||
\(405\) | −631.500 | + | 364.597i | −0.0774802 | + | 0.0447332i | ||||
\(406\) | −1692.00 | − | 2930.63i | −0.206829 | − | 0.358238i | ||||
\(407\) | −996.000 | + | 1725.12i | −0.121302 | + | 0.210101i | ||||
\(408\) | − | 5268.90i | − | 0.639337i | ||||||
\(409\) | −37.5000 | − | 21.6506i | −0.00453363 | − | 0.00261749i | 0.497731 | − | 0.867331i | \(-0.334167\pi\) |
−0.502265 | + | 0.864714i | \(0.667500\pi\) | |||||||
\(410\) | −706.500 | − | 407.898i | −0.0851013 | − | 0.0491333i | ||||
\(411\) | − | 1693.95i | − | 0.203300i | ||||||
\(412\) | −455.000 | + | 788.083i | −0.0544084 | + | 0.0942380i | ||||
\(413\) | 1968.00 | + | 3408.68i | 0.234477 | + | 0.406126i | ||||
\(414\) | −2691.00 | + | 1553.65i | −0.319458 | + | 0.184439i | ||||
\(415\) | −1368.00 | −0.161813 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 472.000 | 0.0554291 | ||||||||
\(418\) | 2376.00 | − | 1371.78i | 0.278024 | − | 0.160517i | ||||
\(419\) | 4731.00 | + | 8194.33i | 0.551610 | + | 0.955416i | 0.998159 | + | 0.0606569i | \(0.0193195\pi\) |
−0.446549 | + | 0.894759i | \(0.647347\pi\) | |||||||
\(420\) | 120.000 | − | 207.846i | 0.0139414 | − | 0.0241473i | ||||
\(421\) | 7068.50i | 0.818284i | 0.912471 | + | 0.409142i | \(0.134172\pi\) | ||||
−0.912471 | + | 0.409142i | \(0.865828\pi\) | |||||||
\(422\) | 1563.00 | + | 902.398i | 0.180298 | + | 0.104095i | ||||
\(423\) | 6003.00 | + | 3465.83i | 0.690014 | + | 0.398380i | ||||
\(424\) | − | 2094.05i | − | 0.239849i | ||||||
\(425\) | −7137.00 | + | 12361.6i | −0.814577 | + | 1.41089i | ||||
\(426\) | −1830.00 | − | 3169.65i | −0.208131 | − | 0.360493i | ||||
\(427\) | −1740.00 | + | 1004.59i | −0.197200 | + | 0.113854i | ||||
\(428\) | −7530.00 | −0.850412 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −312.000 | −0.0349906 | ||||||||
\(431\) | 8598.00 | − | 4964.06i | 0.960907 | − | 0.554780i | 0.0644552 | − | 0.997921i | \(-0.479469\pi\) |
0.896452 | + | 0.443140i | \(0.146136\pi\) | |||||||
\(432\) | 50.0000 | + | 86.6025i | 0.00556858 | + | 0.00964506i | ||||
\(433\) | 3308.50 | − | 5730.49i | 0.367197 | − | 0.636004i | −0.621929 | − | 0.783074i | \(-0.713651\pi\) |
0.989126 | + | 0.147070i | \(0.0469841\pi\) | |||||||
\(434\) | − | 3741.23i | − | 0.413790i | ||||||
\(435\) | −423.000 | − | 244.219i | −0.0466237 | − | 0.0269182i | ||||
\(436\) | −6720.00 | − | 3879.79i | −0.738141 | − | 0.426166i | ||||
\(437\) | 8916.60i | 0.976061i | ||||||||
\(438\) | −795.000 | + | 1376.98i | −0.0867273 | + | 0.150216i | ||||
\(439\) | −6994.00 | − | 12114.0i | −0.760377 | − | 1.31701i | −0.942656 | − | 0.333765i | \(-0.891681\pi\) |
0.182280 | − | 0.983247i | \(-0.441652\pi\) | |||||||
\(440\) | 468.000 | − | 270.200i | 0.0507069 | − | 0.0292756i | ||||
\(441\) | −3473.00 | −0.375013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2004.00 | 0.214928 | 0.107464 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107464 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(444\) | 1245.00 | − | 718.801i | 0.133075 | − | 0.0768306i | ||||
\(445\) | −846.000 | − | 1465.31i | −0.0901219 | − | 0.156096i | ||||
\(446\) | −2085.00 | + | 3611.33i | −0.221362 | + | 0.383411i | ||||
\(447\) | − | 93.5307i | − | 0.00989676i | ||||||
\(448\) | −3684.00 | − | 2126.96i | −0.388510 | − | 0.224307i | ||||
\(449\) | −7866.00 | − | 4541.44i | −0.826769 | − | 0.477336i | 0.0259758 | − | 0.999663i | \(-0.491731\pi\) |
−0.852745 | + | 0.522327i | \(0.825064\pi\) | |||||||
\(450\) | 4860.13i | 0.509131i | ||||||||
\(451\) | 1884.00 | − | 3263.18i | 0.196705 | − | 0.340704i | ||||
\(452\) | 1717.50 | + | 2974.80i | 0.178727 | + | 0.309563i | ||||
\(453\) | −3066.00 | + | 1770.16i | −0.317998 | + | 0.183596i | ||||
\(454\) | 4170.00 | 0.431074 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5148.00 | −0.528678 | ||||||||
\(457\) | −2185.50 | + | 1261.80i | −0.223705 | + | 0.129156i | −0.607665 | − | 0.794194i | \(-0.707894\pi\) |
0.383959 | + | 0.923350i | \(0.374560\pi\) | |||||||
\(458\) | −2172.00 | − | 3762.01i | −0.221596 | − | 0.383815i | ||||
\(459\) | 5850.00 | − | 10132.5i | 0.594890 | − | 1.03038i | ||||
\(460\) | 675.500i | 0.0684681i | ||||||||
\(461\) | −16963.5 | − | 9793.88i | −1.71382 | − | 0.989472i | −0.929270 | − | 0.369400i | \(-0.879563\pi\) |
−0.784545 | − | 0.620072i | \(-0.787103\pi\) | |||||||
\(462\) | −576.000 | − | 332.554i | −0.0580042 | − | 0.0334887i | ||||
\(463\) | 8632.54i | 0.866497i | 0.901274 | + | 0.433249i | \(0.142633\pi\) | ||||
−0.901274 | + | 0.433249i | \(0.857367\pi\) | |||||||
\(464\) | 70.5000 | − | 122.110i | 0.00705362 | − | 0.0122172i | ||||
\(465\) | −270.000 | − | 467.654i | −0.0269268 | − | 0.0466385i | ||||
\(466\) | 8775.00 | − | 5066.25i | 0.872305 | − | 0.503625i | ||||
\(467\) | 5460.00 | 0.541025 | 0.270512 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270512 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10896.0 | 1.07277 | ||||||||
\(470\) | −783.000 | + | 452.065i | −0.0768449 | + | 0.0443664i | ||||
\(471\) | −1211.00 | − | 2097.51i | −0.118471 | − | 0.205198i | ||||
\(472\) | 3198.00 | − | 5539.10i | 0.311864 | − | 0.540165i | ||||
\(473\) | − | 1441.07i | − | 0.140085i | ||||||
\(474\) | 3828.00 | + | 2210.10i | 0.370941 | + | 0.214163i | ||||
\(475\) | 12078.0 | + | 6973.24i | 1.16669 | + | 0.673587i | ||||
\(476\) | − | 8106.00i | − | 0.780542i | ||||||
\(477\) | 1069.50 | − | 1852.43i | 0.102660 | − | 0.177813i | ||||
\(478\) | 4662.00 | + | 8074.82i | 0.446098 | + | 0.772665i | ||||
\(479\) | 2211.00 | − | 1276.52i | 0.210904 | − | 0.121766i | −0.390827 | − | 0.920464i | \(-0.627811\pi\) |
0.601732 | + | 0.798698i | \(0.294478\pi\) | |||||||
\(480\) | −630.000 | −0.0599072 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8517.00 | 0.804852 | ||||||||
\(483\) | 1872.00 | − | 1080.80i | 0.176354 | − | 0.101818i | ||||
\(484\) | −2847.50 | − | 4932.01i | −0.267421 | − | 0.463187i | ||||
\(485\) | −174.000 | + | 301.377i | −0.0162906 | + | 0.0282161i | ||||
\(486\) | − | 6134.92i | − | 0.572605i | ||||||
\(487\) | −9378.00 | − | 5414.39i | −0.872603 | − | 0.503798i | −0.00439074 | − | 0.999990i | \(-0.501398\pi\) |
−0.868212 | + | 0.496193i | \(0.834731\pi\) | |||||||
\(488\) | 2827.50 | + | 1632.46i | 0.262285 | + | 0.151430i | ||||
\(489\) | − | 2009.18i | − | 0.185804i | ||||||
\(490\) | 226.500 | − | 392.310i | 0.0208821 | − | 0.0361689i | ||||
\(491\) | −5694.00 | − | 9862.30i | −0.523354 | − | 0.906475i | −0.999631 | − | 0.0271797i | \(-0.991347\pi\) |
0.476277 | − | 0.879295i | \(-0.341986\pi\) | |||||||
\(492\) | −2355.00 | + | 1359.66i | −0.215796 | + | 0.124590i | ||||
\(493\) | −16497.0 | −1.50707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 552.000 | 0.0501223 | ||||||||
\(496\) | 135.000 | − | 77.9423i | 0.0122211 | − | 0.00705587i | ||||
\(497\) | −7320.00 | − | 12678.6i | −0.660658 | − | 1.14429i | ||||
\(498\) | 1368.00 | − | 2369.45i | 0.123095 | − | 0.213208i | ||||
\(499\) | − | 17677.3i | − | 1.58586i | −0.609311 | − | 0.792931i | \(-0.708554\pi\) | ||
0.609311 | − | 0.792931i | \(-0.291446\pi\) | |||||||
\(500\) | 1852.50 | + | 1069.54i | 0.165693 | + | 0.0956627i | ||||
\(501\) | 1584.00 | + | 914.523i | 0.141253 | + | 0.0815526i | ||||
\(502\) | 6890.10i | 0.612590i | ||||||||
\(503\) | −1938.00 | + | 3356.71i | −0.171792 | + | 0.297552i | −0.939046 | − | 0.343791i | \(-0.888289\pi\) |
0.767255 | + | 0.641343i | \(0.221622\pi\) | |||||||
\(504\) | −3588.00 | − | 6214.60i | −0.317108 | − | 0.549246i | ||||
\(505\) | −643.500 | + | 371.525i | −0.0567037 | + | 0.0327379i | ||||
\(506\) | 1872.00 | 0.164467 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1430.00 | 0.124894 | ||||||||
\(509\) | 14779.5 | − | 8532.95i | 1.28701 | − | 0.743058i | 0.308893 | − | 0.951097i | \(-0.400042\pi\) |
0.978120 | + | 0.208039i | \(0.0667082\pi\) | |||||||
\(510\) | 351.000 | + | 607.950i | 0.0304756 | + | 0.0527852i | ||||
\(511\) | −3180.00 | + | 5507.92i | −0.275293 | + | 0.476822i | ||||
\(512\) | − | 361.999i | − | 0.0312465i | ||||||
\(513\) | −9900.00 | − | 5715.77i | −0.852038 | − | 0.491925i | ||||
\(514\) | 3100.50 | + | 1790.07i | 0.266065 | + | 0.153612i | ||||
\(515\) | − | 315.233i | − | 0.0269725i | ||||||
\(516\) | −520.000 | + | 900.666i | −0.0443638 | + | 0.0768404i | ||||
\(517\) | −2088.00 | − | 3616.52i | −0.177621 | − | 0.307649i | ||||
\(518\) | −2988.00 | + | 1725.12i | −0.253446 | + | 0.146327i | ||||
\(519\) | 5148.00 | 0.435399 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2121.00 | 0.178355 | 0.0891773 | − | 0.996016i | \(-0.471576\pi\) | ||||
0.0891773 | + | 0.996016i | \(0.471576\pi\) | |||||||
\(522\) | −4864.50 | + | 2808.52i | −0.407880 | + | 0.235490i | ||||
\(523\) | 5732.00 | + | 9928.12i | 0.479241 | + | 0.830069i | 0.999717 | − | 0.0238072i | \(-0.00757878\pi\) |
−0.520476 | + | 0.853876i | \(0.674245\pi\) | |||||||
\(524\) | 4935.00 | − | 8547.67i | 0.411425 | − | 0.712608i | ||||
\(525\) | − | 3380.96i | − | 0.281062i | ||||||
\(526\) | −3078.00 | − | 1777.08i | −0.255147 | − | 0.147309i | ||||
\(527\) | −15795.0 | − | 9119.25i | −1.30558 | − | 0.753777i | ||||
\(528\) | − | 27.7128i | − | 0.00228418i | ||||||
\(529\) | 3041.50 | − | 5268.03i | 0.249979 | − | 0.432977i | ||||
\(530\) | 139.500 | + | 241.621i | 0.0114330 | + | 0.0198025i | ||||
\(531\) | 5658.00 | − | 3266.65i | 0.462404 | − | 0.266969i | ||||
\(532\) | −7920.00 | −0.645443 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3384.00 | 0.274232 | ||||||||
\(535\) | 2259.00 | − | 1304.23i | 0.182552 | − | 0.105396i | ||||
\(536\) | −8853.00 | − | 15333.8i | −0.713417 | − | 1.23567i | ||||
\(537\) | −3744.00 | + | 6484.80i | −0.300867 | + | 0.521117i | ||||
\(538\) | − | 5767.73i | − | 0.462202i | ||||||
\(539\) | 1812.00 | + | 1046.16i | 0.144802 | + | 0.0836016i | ||||
\(540\) | −750.000 | − | 433.013i | −0.0597683 | − | 0.0345072i | ||||
\(541\) | − | 4764.87i | − | 0.378665i | −0.981913 | − | 0.189333i | \(-0.939368\pi\) | ||
0.981913 | − | 0.189333i | \(-0.0606324\pi\) | |||||||
\(542\) | 2430.00 | − | 4208.88i | 0.192578 | − | 0.333555i | ||||
\(543\) | 637.000 | + | 1103.32i | 0.0503431 | + | 0.0871968i | ||||
\(544\) | −18427.5 | + | 10639.1i | −1.45234 | + | 0.838508i | ||||
\(545\) | 2688.00 | 0.211268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6554.00 | 0.512301 | 0.256151 | − | 0.966637i | \(-0.417546\pi\) | ||||
0.256151 | + | 0.966637i | \(0.417546\pi\) | |||||||
\(548\) | −3667.50 | + | 2117.43i | −0.285890 | + | 0.165059i | ||||
\(549\) | 1667.50 | + | 2888.19i | 0.129631 | + | 0.224527i | ||||
\(550\) | 1464.00 | − | 2535.72i | 0.113500 | − | 0.196588i | ||||
\(551\) | 16118.5i | 1.24622i | ||||||||
\(552\) | −3042.00 | − | 1756.30i | −0.234558 | − | 0.135422i | ||||
\(553\) | 15312.0 | + | 8840.39i | 1.17745 | + | 0.679804i | ||||
\(554\) | − | 652.983i | − | 0.0500769i | ||||||
\(555\) | −249.000 | + | 431.281i | −0.0190441 | + | 0.0329853i | ||||
\(556\) | −590.000 | − | 1021.91i | −0.0450028 | − | 0.0779472i | ||||
\(557\) | 15685.5 | − | 9056.03i | 1.19321 | − | 0.688898i | 0.234174 | − | 0.972195i | \(-0.424761\pi\) |
0.959032 | + | 0.283297i | \(0.0914281\pi\) | |||||||
\(558\) | −6210.00 | −0.471130 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −0.00181104 | ||||||||
\(561\) | −2808.00 | + | 1621.20i | −0.211326 | + | 0.122009i | ||||
\(562\) | 31.5000 | + | 54.5596i | 0.00236432 | + | 0.00409512i | ||||
\(563\) | 6084.00 | − | 10537.8i | 0.455435 | − | 0.788837i | −0.543278 | − | 0.839553i | \(-0.682817\pi\) |
0.998713 | + | 0.0507160i | \(0.0161503\pi\) | |||||||
\(564\) | 3013.77i | 0.225005i | ||||||||
\(565\) | −1030.50 | − | 594.959i | −0.0767318 | − | 0.0443011i | ||||
\(566\) | −10686.0 | − | 6169.56i | −0.793580 | − | 0.458173i | ||||
\(567\) | − | 5833.55i | − | 0.432074i | ||||||
\(568\) | −11895.0 | + | 20602.7i | −0.878703 | + | 1.52196i | ||||
\(569\) | 3861.00 | + | 6687.45i | 0.284467 | + | 0.492711i | 0.972480 | − | 0.232988i | \(-0.0748502\pi\) |
−0.688013 | + | 0.725698i | \(0.741517\pi\) | |||||||
\(570\) | 594.000 | − | 342.946i | 0.0436490 | − | 0.0252008i | ||||
\(571\) | 11440.0 | 0.838440 | 0.419220 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419220 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5196.00 | −0.378824 | ||||||||
\(574\) | 5652.00 | − | 3263.18i | 0.410993 | − | 0.237287i | ||||
\(575\) | 4758.00 | + | 8241.10i | 0.345082 | + | 0.597700i | ||||
\(576\) | −3530.50 | + | 6115.01i | −0.255389 | + | 0.442347i | ||||
\(577\) | 15444.7i | 1.11433i | 0.830400 | + | 0.557167i | \(0.188112\pi\) | ||||
−0.830400 | + | 0.557167i | \(0.811888\pi\) | |||||||
\(578\) | 13164.0 | + | 7600.24i | 0.947319 | + | 0.546935i | ||||
\(579\) | 1935.00 | + | 1117.17i | 0.138887 | + | 0.0801867i | ||||
\(580\) | 1221.10i | 0.0874194i | ||||||||
\(581\) | 5472.00 | − | 9477.78i | 0.390735 | − | 0.676772i | ||||
\(582\) | −348.000 | − | 602.754i | −0.0247853 | − | 0.0429295i | ||||
\(583\) | −1116.00 | + | 644.323i | −0.0792796 | + | 0.0457721i | ||||
\(584\) | 10335.0 | 0.732304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14415.0 | −1.01617 | ||||||||
\(587\) | 12186.0 | − | 7035.59i | 0.856848 | − | 0.494702i | −0.00610719 | − | 0.999981i | \(-0.501944\pi\) |
0.862956 | + | 0.505280i | \(0.168611\pi\) | |||||||
\(588\) | −755.000 | − | 1307.70i | −0.0529518 | − | 0.0917153i | ||||
\(589\) | −8910.00 | + | 15432.6i | −0.623311 | + | 1.07961i | ||||
\(590\) | 852.169i | 0.0594631i | ||||||||
\(591\) | 3552.00 | + | 2050.75i | 0.247225 | + | 0.142735i | ||||
\(592\) | −124.500 | − | 71.8801i | −0.00864344 | − | 0.00499029i | ||||
\(593\) | 26938.6i | 1.86549i | 0.360538 | + | 0.932745i | \(0.382593\pi\) | ||||
−0.360538 | + | 0.932745i | \(0.617407\pi\) | |||||||
\(594\) | −1200.00 | + | 2078.46i | −0.0828899 | + | 0.143570i | ||||
\(595\) | 1404.00 | + | 2431.80i | 0.0967368 | + | 0.167553i | ||||
\(596\) | −202.500 | + | 116.913i | −0.0139173 | + | 0.00803517i | ||||
\(597\) | −5044.00 | −0.345791 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10554.0 | −0.719908 | −0.359954 | − | 0.932970i | \(-0.617208\pi\) | ||||
−0.359954 | + | 0.932970i | \(0.617208\pi\) | |||||||
\(600\) | −4758.00 | + | 2747.03i | −0.323741 | + | 0.186912i | ||||
\(601\) | 7415.50 | + | 12844.0i | 0.503302 | + | 0.871745i | 0.999993 | + | 0.00381713i | \(0.00121503\pi\) |
−0.496691 | + | 0.867928i | \(0.665452\pi\) | |||||||
\(602\) | 1248.00 | − | 2161.60i | 0.0844928 | − | 0.146346i | ||||
\(603\) | − | 18086.1i | − | 1.22143i | ||||||
\(604\) | 7665.00 | + | 4425.39i | 0.516365 | + | 0.298123i | ||||
\(605\) | 1708.50 | + | 986.403i | 0.114811 | + | 0.0662859i | ||||
\(606\) | − | 1486.10i | − | 0.0996183i | ||||||
\(607\) | 3977.00 | − | 6888.37i | 0.265933 | − | 0.460610i | −0.701874 | − | 0.712301i | \(-0.747653\pi\) |
0.967808 | + | 0.251691i | \(0.0809866\pi\) | |||||||
\(608\) | 10395.0 | + | 18004.7i | 0.693377 | + | 1.20096i | ||||
\(609\) | 3384.00 | − | 1953.75i | 0.225167 | − | 0.130000i | ||||
\(610\) | −435.000 | −0.0288732 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −13455.0 | −0.888703 | ||||||||
\(613\) | −21841.5 | + | 12610.2i | −1.43910 | + | 0.830866i | −0.997787 | − | 0.0664859i | \(-0.978821\pi\) |
−0.441315 | + | 0.897352i | \(0.645488\pi\) | |||||||
\(614\) | 1923.00 | + | 3330.73i | 0.126394 | + | 0.218921i | ||||
\(615\) | 471.000 | − | 815.796i | 0.0308822 | − | 0.0534895i | ||||
\(616\) | 4323.20i | 0.282771i | ||||||||
\(617\) | 15055.5 | + | 8692.30i | 0.982353 | + | 0.567162i | 0.902980 | − | 0.429683i | \(-0.141375\pi\) |
0.0793731 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(618\) | 546.000 | + | 315.233i | 0.0355394 | + | 0.0205187i | ||||
\(619\) | − | 8209.92i | − | 0.533093i | −0.963822 | − | 0.266547i | \(-0.914117\pi\) | ||
0.963822 | − | 0.266547i | \(-0.0858826\pi\) | |||||||
\(620\) | −675.000 | + | 1169.13i | −0.0437236 | + | 0.0757316i | ||||
\(621\) | −3900.00 | − | 6755.00i | −0.252015 | − | 0.436504i | ||||
\(622\) | −7371.00 | + | 4255.65i | −0.475161 | + | 0.274334i | ||||
\(623\) | 13536.0 | 0.870479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14509.0 | 0.928576 | ||||||||
\(626\) | 777.000 | − | 448.601i | 0.0496089 | − | 0.0286417i | ||||
\(627\) | 1584.00 | + | 2743.57i | 0.100891 | + | 0.174749i | ||||
\(628\) | −3027.50 | + | 5243.78i | −0.192373 | + | 0.333200i | ||||
\(629\) | 16819.9i | 1.06622i | ||||||||
\(630\) | 828.000 | + | 478.046i | 0.0523624 | + | 0.0302314i | ||||
\(631\) | −11142.0 | − | 6432.84i | −0.702941 | − | 0.405843i | 0.105501 | − | 0.994419i | \(-0.466355\pi\) |
−0.808442 | + | 0.588576i | \(0.799689\pi\) | |||||||
\(632\) | − | 28731.3i | − | 1.80834i | ||||||
\(633\) | −1042.00 | + | 1804.80i | −0.0654278 | + | 0.113324i | ||||
\(634\) | −3391.50 | − | 5874.25i | −0.212451 | − | 0.367975i | ||||
\(635\) | −429.000 | + | 247.683i | −0.0268100 | + | 0.0154788i | ||||
\(636\) | 930.000 | 0.0579825 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3384.00 | 0.209990 | ||||||||
\(639\) | −21045.0 | + | 12150.3i | −1.30286 | + | 0.752206i | ||||
\(640\) | 799.500 | + | 1384.77i | 0.0493797 | + | 0.0855282i | ||||
\(641\) | −3100.50 | + | 5370.22i | −0.191049 | + | 0.330907i | −0.945598 | − | 0.325337i | \(-0.894522\pi\) |
0.754549 | + | 0.656244i | \(0.227856\pi\) | |||||||
\(642\) | 5216.94i | 0.320710i | ||||||||
\(643\) | 14568.0 | + | 8410.84i | 0.893477 | + | 0.515849i | 0.875078 | − | 0.483981i | \(-0.160810\pi\) |
0.0183989 | + | 0.999831i | \(0.494143\pi\) | |||||||
\(644\) | −4680.00 | − | 2702.00i | −0.286363 | − | 0.165332i | ||||
\(645\) | − | 360.267i | − | 0.0219930i | ||||||
\(646\) | 11583.0 | − | 20062.3i | 0.705460 | − | 1.22189i | ||||
\(647\) | 6747.00 | + | 11686.1i | 0.409972 | + | 0.710092i | 0.994886 | − | 0.101003i | \(-0.0322051\pi\) |
−0.584914 | + | 0.811095i | \(0.698872\pi\) | |||||||
\(648\) | −8209.50 | + | 4739.76i | −0.497685 | + | 0.287338i | ||||
\(649\) | −3936.00 | −0.238061 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4320.00 | 0.260083 | ||||||||
\(652\) | −4350.00 | + | 2511.47i | −0.261287 | + | 0.150854i | ||||
\(653\) | 5667.00 | + | 9815.53i | 0.339612 | + | 0.588226i | 0.984360 | − | 0.176170i | \(-0.0563708\pi\) |
−0.644747 | + | 0.764396i | \(0.723037\pi\) | |||||||
\(654\) | −2688.00 | + | 4655.75i | −0.160717 | + | 0.278371i | ||||
\(655\) | 3419.07i | 0.203960i | ||||||||
\(656\) | 235.500 | + | 135.966i | 0.0140164 | + | 0.00809235i | ||||
\(657\) | 9142.50 | + | 5278.42i | 0.542896 | + | 0.313441i | ||||
\(658\) | − | 7233.04i | − | 0.428531i | ||||||
\(659\) | −6618.00 | + | 11462.7i | −0.391200 | + | 0.677578i | −0.992608 | − | 0.121364i | \(-0.961273\pi\) |
0.601408 | + | 0.798942i | \(0.294607\pi\) | |||||||
\(660\) | 120.000 | + | 207.846i | 0.00707726 | + | 0.0122582i | ||||
\(661\) | 10264.5 | − | 5926.21i | 0.603998 | − | 0.348718i | −0.166615 | − | 0.986022i | \(-0.553284\pi\) |
0.770613 | + | 0.637304i | \(0.219950\pi\) | |||||||
\(662\) | −12912.0 | −0.758065 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17784.0 | −1.03939 | ||||||||
\(665\) | 2376.00 | − | 1371.78i | 0.138552 | − | 0.0799932i | ||||
\(666\) | 2863.50 | + | 4959.73i | 0.166604 | + | 0.288567i | ||||
\(667\) | −5499.00 | + | 9524.55i | −0.319224 | + | 0.552911i | ||||
\(668\) | − | 4572.61i | − | 0.264850i | ||||||
\(669\) | −4170.00 | − | 2407.55i | −0.240989 | − | 0.139135i | ||||
\(670\) | 2043.00 | + | 1179.53i | 0.117803 | + | 0.0680136i | ||||
\(671\) | − | 2009.18i | − | 0.115594i | ||||||
\(672\) | 2520.00 | − | 4364.77i | 0.144659 | − | 0.250557i | ||||
\(673\) | −4010.50 | − | 6946.39i | −0.229708 | − | 0.397866i | 0.728014 | − | 0.685563i | \(-0.240444\pi\) |
−0.957722 | + | 0.287697i | \(0.907110\pi\) | |||||||
\(674\) | 5362.50 | − | 3096.04i | 0.306463 | − | 0.176936i | ||||
\(675\) | −12200.0 | −0.695671 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21630.0 | −1.22793 | −0.613965 | − | 0.789333i | \(-0.710426\pi\) | ||||
−0.613965 | + | 0.789333i | \(0.710426\pi\) | |||||||
\(678\) | 2061.00 | − | 1189.92i | 0.116744 | − | 0.0674020i | ||||
\(679\) | −1392.00 | − | 2411.01i | −0.0786746 | − | 0.136268i | ||||
\(680\) | 2281.50 | − | 3951.67i | 0.128664 | − | 0.222853i | ||||
\(681\) | 4815.10i | 0.270947i | ||||||||
\(682\) | 3240.00 | + | 1870.61i | 0.181915 | + | 0.105029i | ||||
\(683\) | 22983.0 | + | 13269.2i | 1.28758 | + | 0.743387i | 0.978223 | − | 0.207557i | \(-0.0665514\pi\) |
0.309361 | + | 0.950945i | \(0.399885\pi\) | |||||||
\(684\) | 13146.3i | 0.734883i | ||||||||
\(685\) | 733.500 | − | 1270.46i | 0.0409133 | − | 0.0708639i | ||||
\(686\) | 5928.00 | + | 10267.6i | 0.329930 | + | 0.571456i | ||||
\(687\) | 4344.00 | − | 2508.01i | 0.241243 | − | 0.139282i | ||||
\(688\) | 104.000 | 0.00576303 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 468.000 | 0.0258210 | ||||||||
\(691\) | 720.000 | − | 415.692i | 0.0396383 | − | 0.0228852i | −0.480050 | − | 0.877241i | \(-0.659381\pi\) |
0.519688 | + | 0.854356i | \(0.326048\pi\) | |||||||
\(692\) | −6435.00 | − | 11145.7i | −0.353500 | − | 0.612280i | ||||
\(693\) | −2208.00 | + | 3824.37i | −0.121032 | + | 0.209633i | ||||
\(694\) | 12065.5i | 0.659941i | ||||||||
\(695\) | 354.000 | + | 204.382i | 0.0193208 | + | 0.0111549i | ||||
\(696\) | −5499.00 | − | 3174.85i | −0.299481 | − | 0.172906i | ||||
\(697\) | − | 31816.0i | − | 1.72901i | ||||||
\(698\) | −5760.00 | + | 9976.61i | −0.312348 | + | 0.541003i | ||||
\(699\) | 5850.00 | + | 10132.5i | 0.316548 | + | 0.548278i | ||||
\(700\) | −7320.00 | + | 4226.20i | −0.395243 | + | 0.228194i | ||||
\(701\) | 30186.0 | 1.62640 | 0.813202 | − | 0.581981i | \(-0.197722\pi\) | ||||
0.813202 | + | 0.581981i | \(0.197722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16434.0 | 0.881679 | ||||||||
\(704\) | 3684.00 | − | 2126.96i | 0.197224 | − | 0.113868i | ||||
\(705\) | −522.000 | − | 904.131i | −0.0278860 | − | 0.0483000i | ||||
\(706\) | 4876.50 | − | 8446.35i | 0.259957 | − | 0.450258i | ||||
\(707\) | − | 5944.40i | − | 0.316212i | ||||||
\(708\) | 2460.00 | + | 1420.28i | 0.130583 | + | 0.0753919i | ||||
\(709\) | 10288.5 | + | 5940.07i | 0.544983 | + | 0.314646i | 0.747096 | − | 0.664716i | \(-0.231448\pi\) |
−0.202113 | + | 0.979362i | \(0.564781\pi\) | |||||||
\(710\) | − | 3169.65i | − | 0.167542i | ||||||
\(711\) | 14674.0 | − | 25416.1i | 0.774006 | − | 1.34062i | ||||
\(712\) | −10998.0 | − | 19049.1i | −0.578887 | − | 1.00266i | ||||
\(713\) | −10530.0 | + | 6079.50i | −0.553088 | + | 0.319325i | ||||
\(714\) | −5616.00 | −0.294361 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18720.0 | 0.977094 | ||||||||
\(717\) | −9324.00 | + | 5383.21i | −0.485650 | + | 0.280390i | ||||
\(718\) | 6174.00 | + | 10693.7i | 0.320908 | + | 0.555828i | ||||
\(719\) | −9204.00 | + | 15941.8i | −0.477401 | + | 0.826883i | −0.999665 | − | 0.0259014i | \(-0.991754\pi\) |
0.522264 | + | 0.852784i | \(0.325088\pi\) | |||||||
\(720\) | 39.8372i | 0.00206201i | ||||||||
\(721\) | 2184.00 | + | 1260.93i | 0.112811 | + | 0.0651312i | ||||
\(722\) | −9313.50 | − | 5377.15i | −0.480073 | − | 0.277170i | ||||
\(723\) | 9834.58i | 0.505881i | ||||||||
\(724\) | 1592.50 | − | 2758.29i | 0.0817470 | − | 0.141590i | ||||
\(725\) | 8601.00 | + | 14897.4i | 0.440597 | + | 0.763137i | ||||
\(726\) | −3417.00 | + | 1972.81i | −0.174679 | + | 0.100851i | ||||
\(727\) | 21112.0 | 1.07703 | 0.538515 | − | 0.842616i | \(-0.318986\pi\) | ||||
0.538515 | + | 0.842616i | \(0.318986\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | −1192.50 | + | 688.490i | −0.0604608 | + | 0.0349071i | ||||
\(731\) | −6084.00 | − | 10537.8i | −0.307832 | − | 0.533180i | ||||
\(732\) | −725.000 | + | 1255.74i | −0.0366076 | + | 0.0634062i | ||||
\(733\) | − | 23959.5i | − | 1.20732i | −0.797243 | − | 0.603658i | \(-0.793709\pi\) | ||
0.797243 | − | 0.603658i | \(-0.206291\pi\) | |||||||
\(734\) | 3.00000 | + | 1.73205i | 0.000150861 | + | 8.70997e-5i | ||||
\(735\) | 453.000 | + | 261.540i | 0.0227335 | + | 0.0131252i | ||||
\(736\) | 14185.5i | 0.710441i | ||||||||
\(737\) | −5448.00 | + | 9436.21i | −0.272293 | + | 0.471625i | ||||
\(738\) | −5416.50 | − | 9381.65i | −0.270168 | − | 0.467945i | ||||
\(739\) | −2742.00 | + | 1583.09i | −0.136490 | + | 0.0788025i | −0.566690 | − | 0.823931i | \(-0.691776\pi\) |
0.430200 | + | 0.902734i | \(0.358443\pi\) | |||||||
\(740\) | 1245.00 | 0.0618474 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2232.00 | −0.110430 | ||||||||
\(743\) | 26070.0 | − | 15051.5i | 1.28723 | − | 0.743185i | 0.309075 | − | 0.951038i | \(-0.399981\pi\) |
0.978160 | + | 0.207852i | \(0.0666474\pi\) | |||||||
\(744\) | −3510.00 | − | 6079.50i | −0.172961 | − | 0.299577i | ||||
\(745\) | 40.5000 | − | 70.1481i | 0.00199168 | − | 0.00344970i | ||||
\(746\) | − | 6060.45i | − | 0.297438i | ||||||
\(747\) | −15732.0 | − | 9082.87i | −0.770554 | − | 0.444880i | ||||
\(748\) | 7020.00 | + | 4053.00i | 0.343151 | + | 0.198118i | ||||
\(749\) | 20867.7i | 1.01801i | ||||||||
\(750\) | 741.000 | − | 1283.45i | 0.0360767 | − | 0.0624866i | ||||
\(751\) | −14248.0 | − | 24678.3i | −0.692299 | − | 1.19910i | −0.971083 | − | 0.238744i | \(-0.923264\pi\) |
0.278783 | − | 0.960354i | \(-0.410069\pi\) | |||||||
\(752\) | 261.000 | − | 150.688i | 0.0126565 | − | 0.00730724i | ||||
\(753\) | −7956.00 | −0.385037 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3066.00 | −0.147792 | ||||||||
\(756\) | 6000.00 | − | 3464.10i | 0.288648 | − | 0.166651i | ||||
\(757\) | −8711.00 | − | 15087.9i | −0.418239 | − | 0.724411i | 0.577524 | − | 0.816374i | \(-0.304019\pi\) |
−0.995762 | + | 0.0919633i | \(0.970686\pi\) | |||||||
\(758\) | 4779.00 | − | 8277.47i | 0.228999 | − | 0.396638i | ||||
\(759\) | 2161.60i | 0.103374i | ||||||||
\(760\) | −3861.00 | − | 2229.15i | −0.184281 | − | 0.106394i | ||||
\(761\) | −35790.0 | − | 20663.4i | −1.70484 | − | 0.984292i | −0.940695 | − | 0.339252i | \(-0.889826\pi\) |
−0.764149 | − | 0.645040i | \(-0.776841\pi\) | |||||||
\(762\) | − | 990.733i | − | 0.0471004i | ||||||
\(763\) | −10752.0 | + | 18623.0i | −0.510155 | + | 0.883615i | ||||
\(764\) | 6495.00 | + | 11249.7i | 0.307567 | + | 0.532721i | ||||
\(765\) | 4036.50 | − | 2330.47i | 0.190771 | − | 0.110142i | ||||
\(766\) | −12756.0 | −0.601688 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8110.00 | −0.381047 | ||||||||
\(769\) | 12186.0 | − | 7035.59i | 0.571441 | − | 0.329922i | −0.186283 | − | 0.982496i | \(-0.559644\pi\) |
0.757725 | + | 0.652574i | \(0.226311\pi\) | |||||||
\(770\) | −288.000 | − | 498.831i | −0.0134790 | − | 0.0233462i | ||||
\(771\) | −2067.00 | + | 3580.15i | −0.0965515 | + | 0.167232i | ||||
\(772\) | − | 5585.86i | − | 0.260414i | ||||||
\(773\) | −174.000 | − | 100.459i | −0.00809618 | − | 0.00467433i | 0.495946 | − | 0.868353i | \(-0.334821\pi\) |
−0.504043 | + | 0.863679i | \(0.668155\pi\) | |||||||
\(774\) | −3588.00 | − | 2071.53i | −0.166625 | − | 0.0962012i | ||||
\(775\) | 19017.9i | 0.881476i | ||||||||
\(776\) | −2262.00 | + | 3917.90i | −0.104641 | + | 0.181243i | ||||
\(777\) | −1992.00 | − | 3450.25i | −0.0919725 | − | 0.159301i | ||||
\(778\) | 1813.50 | − | 1047.02i | 0.0835696 | − | 0.0482489i | ||||
\(779\) | −31086.0 | −1.42975 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14640.0 | 0.670756 | ||||||||
\(782\) | 13689.0 | − | 7903.35i | 0.625982 | − | 0.361411i | ||||
\(783\) | −7050.00 | − | 12211.0i | −0.321771 | − | 0.557323i | ||||
\(784\) | −75.5000 | + | 130.770i | −0.00343932 | + | 0.00595708i | ||||
\(785\) | − | 2097.51i | − | 0.0953675i | ||||||
\(786\) | −5922.00 | − | 3419.07i | −0.268741 | − | 0.155158i | ||||
\(787\) | 5979.00 | + | 3451.98i | 0.270811 | + | 0.156353i | 0.629256 | − | 0.777198i | \(-0.283360\pi\) |
−0.358445 | + | 0.933551i | \(0.616693\pi\) | |||||||
\(788\) | − | 10253.7i | − | 0.463546i | ||||||
\(789\) | 2052.00 | − | 3554.17i | 0.0925895 | − | 0.160370i | ||||
\(790\) | 1914.00 | + | 3315.15i | 0.0861988 | + | 0.149301i | ||||
\(791\) | 8244.00 | − | 4759.68i | 0.370573 | − | 0.213950i | ||||
\(792\) | 7176.00 | 0.321955 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20256.0 | 0.905363 | ||||||||
\(795\) | −279.000 | + | 161.081i | −0.0124467 | + | 0.00718609i | ||||
\(796\) | 6305.00 | + | 10920.6i | 0.280747 | + | 0.486268i | ||||
\(797\) | 15639.0 | − | 27087.5i | 0.695059 | − | 1.20388i | −0.275102 | − | 0.961415i | \(-0.588712\pi\) |
0.970161 | − | 0.242462i | \(-0.0779550\pi\) | |||||||
\(798\) | 5487.14i | 0.243412i | ||||||||
\(799\) | −30537.0 | − | 17630.5i | −1.35209 | − | 0.780631i | ||||
\(800\) | 19215.0 | + | 11093.8i | 0.849191 | + | 0.490281i | ||||
\(801\) | − | 22468.2i | − | 0.991103i | ||||||
\(802\) | −2581.50 | + | 4471.29i | −0.113661 | + | 0.196866i | ||||
\(803\) | −3180.00 | − | 5507.92i | −0.139751 | − | 0.242055i | ||||
\(804\) | 6810.00 | − | 3931.76i | 0.298719 | − | 0.172466i | ||||
\(805\) | 1872.00 | 0.0819619 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6660.00 | 0.290512 | ||||||||
\(808\) | −8365.50 | + | 4829.82i | −0.364229 | + | 0.210288i | ||||
\(809\) | −4024.50 | − | 6970.64i | −0.174900 | − | 0.302935i | 0.765227 | − | 0.643761i | \(-0.222627\pi\) |
−0.940127 | + | 0.340826i | \(0.889293\pi\) | |||||||
\(810\) | 631.500 | − | 1093.79i | 0.0273934 | − | 0.0474467i | ||||
\(811\) | 14026.1i | 0.607305i | 0.952783 | + | 0.303653i | \(0.0982062\pi\) | ||||
−0.952783 | + | 0.303653i | \(0.901794\pi\) | |||||||
\(812\) | −8460.00 | − | 4884.38i | −0.365625 | − | 0.211094i | ||||
\(813\) | 4860.00 | + | 2805.92i | 0.209653 | + | 0.121043i | ||||
\(814\) | − | 3450.25i | − | 0.148564i | ||||||
\(815\) | 870.000 | − | 1506.88i | 0.0373924 | − | 0.0647655i | ||||
\(816\) | −117.000 | − | 202.650i | −0.00501939 | − | 0.00869383i | ||||
\(817\) | −10296.0 | + | 5944.40i | −0.440895 | + | 0.254551i | ||||
\(818\) | 75.0000 | 0.00320576 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2355.00 | −0.100293 | ||||||||
\(821\) | 6960.00 | − | 4018.36i | 0.295866 | − | 0.170818i | −0.344718 | − | 0.938706i | \(-0.612026\pi\) |
0.640584 | + | 0.767888i | \(0.278692\pi\) | |||||||
\(822\) | 1467.00 | + | 2540.92i | 0.0622476 | + | 0.107816i | ||||
\(823\) | 20150.0 | − | 34900.8i | 0.853445 | − | 1.47821i | −0.0246361 | − | 0.999696i | \(-0.507843\pi\) |
0.878081 | − | 0.478513i | \(-0.158824\pi\) | |||||||
\(824\) | − | 4098.03i | − | 0.173255i | ||||||
\(825\) | 2928.00 | + | 1690.48i | 0.123563 | + | 0.0713394i | ||||
\(826\) | −5904.00 | − | 3408.68i | −0.248700 | − | 0.143587i | ||||
\(827\) | 39525.4i | 1.66195i | 0.556310 | + | 0.830975i | \(0.312217\pi\) | ||||
−0.556310 | + | 0.830975i | \(0.687783\pi\) | |||||||
\(828\) | −4485.00 | + | 7768.25i | −0.188242 | + | 0.326045i | ||||
\(829\) | 6155.50 | + | 10661.6i | 0.257888 | + | 0.446676i | 0.965676 | − | 0.259750i | \(-0.0836400\pi\) |
−0.707788 | + | 0.706425i | \(0.750307\pi\) | |||||||
\(830\) | 2052.00 | − | 1184.72i | 0.0858144 | − | 0.0495450i | ||||
\(831\) | 754.000 | 0.0314753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17667.0 | 0.734844 | ||||||||
\(834\) | −708.000 | + | 408.764i | −0.0293957 | + | 0.0169716i | ||||
\(835\) | 792.000 | + | 1371.78i | 0.0328243 | + | 0.0568534i | ||||
\(836\) | 3960.00 | − | 6858.92i | 0.163827 | − | 0.283757i | ||||
\(837\) | − | 15588.5i | − | 0.643747i | ||||||
\(838\) | −14193.0 | − | 8194.33i | −0.585070 | − | 0.337791i | ||||
\(839\) | −18591.0 | − | 10733.5i | −0.764997 | − | 0.441671i | 0.0660899 | − | 0.997814i | \(-0.478948\pi\) |
−0.831087 | + | 0.556142i | \(0.812281\pi\) | |||||||
\(840\) | 1080.80i | 0.0443942i | ||||||||
\(841\) | 2254.00 | − | 3904.04i | 0.0924187 | − | 0.160074i | ||||
\(842\) | −6121.50 | − | 10602.7i | −0.250547 | − | 0.433961i | ||||
\(843\) | −63.0000 | + | 36.3731i | −0.00257394 | + | 0.00148607i | ||||
\(844\) | 5210.00 | 0.212483 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12006.0 | −0.487913 | ||||||||
\(847\) | −13668.0 | + | 7891.22i | −0.554472 | + | 0.320125i | ||||
\(848\) | −46.5000 | − | 80.5404i | −0.00188304 | − | 0.00326152i | ||||
\(849\) | 7124.00 | − | 12339.1i | 0.287980 | − | 0.498796i | ||||
\(850\) | − | 24723.3i | − | 0.997649i | ||||||
\(851\) | 9711.00 | + | 5606.65i | 0.391174 | + | 0.225844i | ||||
\(852\) | −9150.00 | − | 5282.75i | −0.367927 | − | 0.212423i | ||||
\(853\) | 774.227i | 0.0310774i | 0.999879 | + | 0.0155387i | \(0.00494632\pi\) | ||||
−0.999879 | + | 0.0155387i | \(0.995054\pi\) | |||||||
\(854\) | 1740.00 | − | 3013.77i | 0.0697208 | − | 0.120760i | ||||
\(855\) | −2277.00 | − | 3943.88i | −0.0910781 | − | 0.157752i | ||||
\(856\) | 29367.0 | − | 16955.0i | 1.17260 | − | 0.676999i | ||||
\(857\) | 13923.0 | 0.554960 | 0.277480 | − | 0.960731i | \(-0.410501\pi\) | ||||
0.277480 | + | 0.960731i | \(0.410501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22358.0 | −0.888062 | −0.444031 | − | 0.896011i | \(-0.646452\pi\) | ||||
−0.444031 | + | 0.896011i | \(0.646452\pi\) | |||||||
\(860\) | −780.000 | + | 450.333i | −0.0309277 | + | 0.0178561i | ||||
\(861\) | 3768.00 | + | 6526.37i | 0.149144 | + | 0.258325i | ||||
\(862\) | −8598.00 | + | 14892.2i | −0.339732 | + | 0.588433i | ||||
\(863\) | − | 2230.88i | − | 0.0879955i | −0.999032 | − | 0.0439977i | \(-0.985991\pi\) | ||
0.999032 | − | 0.0439977i | \(-0.0140094\pi\) | |||||||
\(864\) | −15750.0 | − | 9093.27i | −0.620169 | − | 0.358055i | ||||
\(865\) | 3861.00 | + | 2229.15i | 0.151766 | + | 0.0876224i | ||||
\(866\) | 11461.0i | 0.449723i | ||||||||
\(867\) | −8776.00 | + | 15200.5i | −0.343770 | + | 0.595427i | ||||
\(868\) | −5400.00 | − | 9353.07i | −0.211161 | − | 0.365742i | ||||
\(869\) | −15312.0 | + | 8840.39i | −0.597726 | + | 0.345097i | ||||
\(870\) | 846.000 | 0.0329679 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 34944.0 | 1.35706 | ||||||||
\(873\) | −4002.00 | + | 2310.56i | −0.155151 | + | 0.0895767i | ||||
\(874\) | −7722.00 | − | 13374.9i | −0.298856 | − | 0.517635i | ||||
\(875\) | 2964.00 | − | 5133.80i | 0.114516 | − | 0.198348i | ||||
\(876\) | 4589.93i | 0.177031i | ||||||||
\(877\) | 14509.5 | + | 8377.06i | 0.558667 | + | 0.322547i | 0.752610 | − | 0.658466i | \(-0.228794\pi\) |
−0.193943 | + | 0.981013i | \(0.562128\pi\) | |||||||
\(878\) | 20982.0 | + | 12114.0i | 0.806501 | + | 0.465634i | ||||
\(879\) | − | 16645.0i | − | 0.638706i | ||||||
\(880\) | 12.0000 | − | 20.7846i | 0.000459682 | − | 0.000796192i | ||||
\(881\) | −8677.50 | − | 15029.9i | −0.331842 | − | 0.574766i | 0.651031 | − | 0.759051i | \(-0.274337\pi\) |
−0.982873 | + | 0.184284i | \(0.941003\pi\) | |||||||
\(882\) | 5209.50 | − | 3007.71i | 0.198881 | − | 0.114824i | ||||
\(883\) | −46982.0 | −1.79057 | −0.895283 | − | 0.445497i | \(-0.853027\pi\) | ||||
−0.895283 | + | 0.445497i | \(0.853027\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −984.000 | −0.0373749 | ||||||||
\(886\) | −3006.00 | + | 1735.51i | −0.113983 | + | 0.0658079i | ||||
\(887\) | 4458.00 | + | 7721.48i | 0.168754 | + | 0.292291i | 0.937982 | − | 0.346684i | \(-0.112692\pi\) |
−0.769228 | + | 0.638975i | \(0.779359\pi\) | |||||||
\(888\) | −3237.00 | + | 5606.65i | −0.122327 | + | 0.211877i | ||||
\(889\) | − | 3962.93i | − | 0.149508i | ||||||
\(890\) | 2538.00 | + | 1465.31i | 0.0955887 | + | 0.0551882i | ||||
\(891\) | 5052.00 | + | 2916.77i | 0.189953 | + | 0.109670i | ||||
\(892\) | 12037.8i | 0.451854i | ||||||||
\(893\) | −17226.0 | + | 29836.3i | −0.645516 | + | 1.11807i | ||||
\(894\) | 81.0000 | + | 140.296i | 0.00303025 | + | 0.00524855i | ||||
\(895\) | −5616.00 | + | 3242.40i | −0.209745 | + | 0.121097i | ||||
\(896\) | −12792.0 | −0.476954 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15732.0 | 0.584614 | ||||||||
\(899\) | −19035.0 | + | 10989.9i | −0.706177 | + | 0.407711i | ||||
\(900\) | 7015.00 | + | 12150.3i | 0.259815 | + | 0.450012i | ||||
\(901\) | −5440.50 | + | 9423.22i | −0.201165 | + | 0.348427i | ||||
\(902\) | 6526.37i | 0.240914i | ||||||||
\(903\) | 2496.00 | + | 1441.07i | 0.0919841 | + | 0.0531071i | ||||
\(904\) | −13396.5 | − | 7734.47i | −0.492877 | − | 0.284563i | ||||
\(905\) | 1103.32i | 0.0405254i | ||||||||
\(906\) | 3066.00 | − | 5310.47i | 0.112429 | − | 0.194733i | ||||
\(907\) | 15418.0 | + | 26704.8i | 0.564439 | + | 0.977637i | 0.997102 | + | 0.0760813i | \(0.0242408\pi\) |
−0.432662 | + | 0.901556i | \(0.642426\pi\) | |||||||
\(908\) | 10425.0 | − | 6018.88i | 0.381020 | − | 0.219982i | ||||
\(909\) | −9867.00 | −0.360031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27480.0 | −0.999400 | −0.499700 | − | 0.866199i | \(-0.666556\pi\) | ||||
−0.499700 | + | 0.866199i | \(0.666556\pi\) | |||||||
\(912\) | −198.000 | + | 114.315i | −0.00718907 | + | 0.00415061i | ||||
\(913\) | 5472.00 | + | 9477.78i | 0.198354 | + | 0.343558i | ||||
\(914\) | 2185.50 | − | 3785.40i | 0.0790918 | − | 0.136991i | ||||
\(915\) | − | 502.295i | − | 0.0181479i | ||||||
\(916\) | −10860.0 | − | 6270.02i | −0.391730 | − | 0.226165i | ||||
\(917\) | −23688.0 | − | 13676.3i | −0.853050 | − | 0.492509i | ||||
\(918\) | 20265.0i | 0.728589i | ||||||||
\(919\) | 14221.0 | − | 24631.5i | 0.510454 | − | 0.884133i | −0.489472 | − | 0.872019i | \(-0.662811\pi\) |
0.999927 | − | 0.0121140i | \(-0.00385609\pi\) | |||||||
\(920\) | −1521.00 | − | 2634.45i | −0.0545064 | − | 0.0944078i | ||||
\(921\) | −3846.00 | + | 2220.49i | −0.137600 | + | 0.0794437i | ||||
\(922\) | 33927.0 | 1.21185 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1920.00 | −0.0683586 | ||||||||
\(925\) | 15189.0 | − | 8769.37i | 0.539904 | − | 0.311714i | ||||
\(926\) | −7476.00 | − | 12948.8i | −0.265310 | − | 0.459530i | ||||
\(927\) | 2093.00 | − | 3625.18i | 0.0741566 | − | 0.128443i | ||||
\(928\) | 25643.0i | 0.907083i | ||||||||
\(929\) | −6043.50 | − | 3489.22i | −0.213435 | − | 0.123227i | 0.389472 | − | 0.921038i | \(-0.372658\pi\) |
−0.602907 | + | 0.797812i | \(0.705991\pi\) | |||||||
\(930\) | 810.000 | + | 467.654i | 0.0285602 | + | 0.0164892i | ||||
\(931\) | − | 17261.6i | − | 0.607655i | ||||||
\(932\) | 14625.0 | − | 25331.2i | 0.514011 | − | 0.890292i | ||||
\(933\) | −4914.00 | − | 8511.30i | −0.172430 | − | 0.298657i | ||||
\(934\) | −8190.00 | + | 4728.50i | −0.286922 | + | 0.165654i | ||||
\(935\) | −2808.00 | −0.0982154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38465.0 | −1.34109 | −0.670543 | − | 0.741871i | \(-0.733939\pi\) | ||||
−0.670543 | + | 0.741871i | \(0.733939\pi\) | |||||||
\(938\) | −16344.0 | + | 9436.21i | −0.568924 | + | 0.328468i | ||||
\(939\) | 518.000 | + | 897.202i | 0.0180024 | + | 0.0311811i | ||||
\(940\) | −1305.00 | + | 2260.33i | −0.0452813 | + | 0.0784295i | ||||
\(941\) | 4884.38i | 0.169210i | 0.996415 | + | 0.0846049i | \(0.0269628\pi\) | ||||
−0.996415 | + | 0.0846049i | \(0.973037\pi\) | |||||||
\(942\) | 3633.00 | + | 2097.51i | 0.125658 | + | 0.0725485i | ||||
\(943\) | −18369.0 | − | 10605.3i | −0.634334 | − | 0.366233i | ||||
\(944\) | − | 284.056i | − | 0.00979369i | ||||||
\(945\) | −1200.00 | + | 2078.46i | −0.0413079 | + | 0.0715475i | ||||
\(946\) | 1248.00 | + | 2161.60i | 0.0428922 | + | 0.0742914i | ||||
\(947\) | −18849.0 | + | 10882.5i | −0.646790 | + | 0.373424i | −0.787225 | − | 0.616665i | \(-0.788483\pi\) |
0.140435 | + | 0.990090i | \(0.455150\pi\) | |||||||
\(948\) | 12760.0 | 0.437158 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −24156.0 | −0.824973 | ||||||||
\(951\) | 6783.00 | − | 3916.17i | 0.231287 | − | 0.133534i | ||||
\(952\) | 18252.0 | + | 31613.4i | 0.621377 | + | 1.07626i | ||||
\(953\) | −3237.00 | + | 5606.65i | −0.110028 | + | 0.190574i | −0.915781 | − | 0.401677i | \(-0.868427\pi\) |
0.805753 | + | 0.592251i | \(0.201761\pi\) | |||||||
\(954\) | 3704.86i | 0.125733i | ||||||||
\(955\) | −3897.00 | − | 2249.93i | −0.132046 | − | 0.0762368i | ||||
\(956\) | 23310.0 | + | 13458.0i | 0.788598 | + | 0.455297i | ||||
\(957\) | 3907.51i | 0.131987i | ||||||||
\(958\) | −2211.00 | + | 3829.56i | −0.0745659 | + | 0.129152i | ||||
\(959\) | 5868.00 | + | 10163.7i | 0.197589 | + | 0.342234i | ||||
\(960\) | 921.000 | − | 531.740i | 0.0309637 | − | 0.0178769i | ||||
\(961\) | 5491.00 | 0.184317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34638.0 | 1.15908 | ||||||||
\(964\) | 21292.5 | − | 12293.2i | 0.711395 | − | 0.410724i | ||||
\(965\) | 967.500 | + | 1675.76i | 0.0322745 | + | 0.0559011i | ||||
\(966\) | −1872.00 | + | 3242.40i | −0.0623505 | + | 0.107994i | ||||
\(967\) | 7541.35i | 0.250789i | 0.992107 | + | 0.125395i | \(0.0400197\pi\) | ||||
−0.992107 | + | 0.125395i | \(0.959980\pi\) | |||||||
\(968\) | 22210.5 | + | 12823.2i | 0.737472 | + | 0.425779i | ||||
\(969\) | 23166.0 | + | 13374.9i | 0.768007 | + | 0.443409i | ||||
\(970\) | − | 602.754i | − | 0.0199518i | ||||||
\(971\) | −17499.0 | + | 30309.2i | −0.578342 | + | 1.00172i | 0.417328 | + | 0.908756i | \(0.362967\pi\) |
−0.995670 | + | 0.0929611i | \(0.970367\pi\) | |||||||
\(972\) | −8855.00 | − | 15337.3i | −0.292206 | − | 0.506116i | ||||
\(973\) | −2832.00 | + | 1635.06i | −0.0933091 | + | 0.0538720i | ||||
\(974\) | 18756.0 | 0.617024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 145.000 | 0.00475547 | ||||||||
\(977\) | 21838.5 | − | 12608.5i | 0.715123 | − | 0.412877i | −0.0978318 | − | 0.995203i | \(-0.531191\pi\) |
0.812955 | + | 0.582326i | \(0.197857\pi\) | |||||||
\(978\) | 1740.00 | + | 3013.77i | 0.0568907 | + | 0.0985375i | ||||
\(979\) | −6768.00 | + | 11722.5i | −0.220946 | + | 0.382690i | ||||
\(980\) | − | 1307.70i | − | 0.0426254i | ||||||
\(981\) | 30912.0 | + | 17847.1i | 1.00606 | + | 0.580849i | ||||
\(982\) | 17082.0 | + | 9862.30i | 0.555100 | + | 0.320487i | ||||
\(983\) | − | 56440.6i | − | 1.83131i | −0.401967 | − | 0.915654i | \(-0.631673\pi\) | ||
0.401967 | − | 0.915654i | \(-0.368327\pi\) | |||||||
\(984\) | 6123.00 | − | 10605.3i | 0.198368 | − | 0.343583i | ||||
\(985\) | 1776.00 | + | 3076.12i | 0.0574498 | + | 0.0995060i | ||||
\(986\) | 24745.5 | − | 14286.8i | 0.799247 | − | 0.461445i | ||||
\(987\) | 8352.00 | 0.269349 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8112.00 | −0.260816 | ||||||||
\(990\) | −828.000 | + | 478.046i | −0.0265814 | + | 0.0153468i | ||||
\(991\) | −29641.0 | − | 51339.7i | −0.950129 | − | 1.64567i | −0.745142 | − | 0.666906i | \(-0.767618\pi\) |
−0.204987 | − | 0.978765i | \(-0.565715\pi\) | |||||||
\(992\) | −14175.0 | + | 24551.8i | −0.453686 | + | 0.785808i | ||||
\(993\) | − | 14909.5i | − | 0.476474i | ||||||
\(994\) | 21960.0 | + | 12678.6i | 0.700733 | + | 0.404569i | ||||
\(995\) | −3783.00 | − | 2184.12i | −0.120532 | − | 0.0695891i | ||||
\(996\) | − | 7898.15i | − | 0.251268i | ||||||
\(997\) | 18855.5 | − | 32658.7i | 0.598957 | − | 1.03742i | −0.394019 | − | 0.919102i | \(-0.628916\pi\) |
0.992975 | − | 0.118321i | \(-0.0377511\pi\) | |||||||
\(998\) | 15309.0 | + | 26516.0i | 0.485569 | + | 0.841030i | ||||
\(999\) | −12450.0 | + | 7188.01i | −0.394295 | + | 0.227646i |
(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 | 169.4.e.a.23.1 | 2 | ||
13.2 | odd | 12 | 169.4.a.i.1.1 | 2 | |||
13.3 | even | 3 | 169.4.b.d.168.1 | 2 | |||
13.4 | even | 6 | inner | 169.4.e.a.147.1 | 2 | ||
13.5 | odd | 4 | 169.4.c.h.146.2 | 4 | |||
13.6 | odd | 12 | 169.4.c.h.22.2 | 4 | |||
13.7 | odd | 12 | 169.4.c.h.22.1 | 4 | |||
13.8 | odd | 4 | 169.4.c.h.146.1 | 4 | |||
13.9 | even | 3 | 13.4.e.b.4.1 | ✓ | 2 | ||
13.10 | even | 6 | 169.4.b.d.168.2 | 2 | |||
13.11 | odd | 12 | 169.4.a.i.1.2 | 2 | |||
13.12 | even | 2 | 13.4.e.b.10.1 | yes | 2 | ||
39.2 | even | 12 | 1521.4.a.o.1.2 | 2 | |||
39.11 | even | 12 | 1521.4.a.o.1.1 | 2 | |||
39.35 | odd | 6 | 117.4.q.a.82.1 | 2 | |||
39.38 | odd | 2 | 117.4.q.a.10.1 | 2 | |||
52.35 | odd | 6 | 208.4.w.b.17.1 | 2 | |||
52.51 | odd | 2 | 208.4.w.b.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.e.b.4.1 | ✓ | 2 | 13.9 | even | 3 | ||
13.4.e.b.10.1 | yes | 2 | 13.12 | even | 2 | ||
117.4.q.a.10.1 | 2 | 39.38 | odd | 2 | |||
117.4.q.a.82.1 | 2 | 39.35 | odd | 6 | |||
169.4.a.i.1.1 | 2 | 13.2 | odd | 12 | |||
169.4.a.i.1.2 | 2 | 13.11 | odd | 12 | |||
169.4.b.d.168.1 | 2 | 13.3 | even | 3 | |||
169.4.b.d.168.2 | 2 | 13.10 | even | 6 | |||
169.4.c.h.22.1 | 4 | 13.7 | odd | 12 | |||
169.4.c.h.22.2 | 4 | 13.6 | odd | 12 | |||
169.4.c.h.146.1 | 4 | 13.8 | odd | 4 | |||
169.4.c.h.146.2 | 4 | 13.5 | odd | 4 | |||
169.4.e.a.23.1 | 2 | 1.1 | even | 1 | trivial | ||
169.4.e.a.147.1 | 2 | 13.4 | even | 6 | inner | ||
208.4.w.b.17.1 | 2 | 52.35 | odd | 6 | |||
208.4.w.b.49.1 | 2 | 52.51 | odd | 2 | |||
1521.4.a.o.1.1 | 2 | 39.11 | even | 12 | |||
1521.4.a.o.1.2 | 2 | 39.2 | even | 12 |