Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.d (of order \(2\), degree \(1\), 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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 120x^{10} + 5196x^{8} + 96803x^{6} + 702900x^{4} + 976752x^{2} + 254016 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.10 | ||
Root | \(3.92558i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.4.d.b.287.9 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.31028 | + | 2.90198i | 0.829513 | + | 0.558487i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 9.74037i | − | 0.871205i | −0.900139 | − | 0.435603i | \(-0.856535\pi\) | ||
0.900139 | − | 0.435603i | \(-0.143465\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.39870i | 0.399492i | 0.979848 | + | 0.199746i | \(0.0640117\pi\) | ||||
−0.979848 | + | 0.199746i | \(0.935988\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.1570 | + | 25.0167i | 0.376184 | + | 0.926545i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.2115 | −1.10220 | −0.551101 | − | 0.834438i | \(-0.685792\pi\) | ||||
−0.551101 | + | 0.834438i | \(0.685792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28.2664 | − | 41.9837i | 0.486557 | − | 0.722676i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 69.5142i | 0.991745i | 0.868395 | + | 0.495872i | \(0.165152\pi\) | ||||
−0.868395 | + | 0.495872i | \(0.834848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 17.1044i | − | 0.206527i | −0.994654 | − | 0.103264i | \(-0.967071\pi\) | ||
0.994654 | − | 0.103264i | \(-0.0329285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.4709 | + | 31.8904i | −0.223111 | + | 0.331384i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −166.760 | −1.51182 | −0.755912 | − | 0.654674i | \(-0.772806\pi\) | ||||
−0.755912 | + | 0.654674i | \(0.772806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.1252 | 0.241002 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −28.8188 | + | 137.304i | −0.205414 | + | 0.978675i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 250.179i | 1.60197i | 0.598684 | + | 0.800985i | \(0.295691\pi\) | ||||
−0.598684 | + | 0.800985i | \(0.704309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 234.386i | − | 1.35796i | −0.734155 | − | 0.678982i | \(-0.762421\pi\) | ||
0.734155 | − | 0.678982i | \(-0.237579\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −173.323 | − | 116.693i | −0.914292 | − | 0.615566i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 72.0660 | 0.348039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −373.210 | −1.65825 | −0.829126 | − | 0.559062i | \(-0.811162\pi\) | ||||
−0.829126 | + | 0.559062i | \(0.811162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −56.0336 | − | 37.7258i | −0.230066 | − | 0.154896i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 112.865i | 0.429916i | 0.976623 | + | 0.214958i | \(0.0689615\pi\) | ||||
−0.976623 | + | 0.214958i | \(0.931039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 393.675i | 1.39616i | 0.716021 | + | 0.698079i | \(0.245962\pi\) | ||||
−0.716021 | + | 0.698079i | \(0.754038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 243.672 | − | 98.9326i | 0.807211 | − | 0.327733i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −227.157 | −0.704985 | −0.352493 | − | 0.935815i | \(-0.614666\pi\) | ||||
−0.352493 | + | 0.935815i | \(0.614666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 288.259 | 0.840406 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −201.729 | + | 299.625i | −0.553877 | + | 0.822665i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 83.6563i | 0.216813i | 0.994107 | + | 0.108406i | \(0.0345748\pi\) | ||||
−0.994107 | + | 0.108406i | \(0.965425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 391.675i | 0.960245i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 49.6367 | − | 73.7247i | 0.115343 | − | 0.171317i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −120.477 | −0.265844 | −0.132922 | − | 0.991126i | \(-0.542436\pi\) | ||||
−0.132922 | + | 0.991126i | \(0.542436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 706.102 | 1.48208 | 0.741042 | − | 0.671458i | \(-0.234332\pi\) | ||||
0.741042 | + | 0.671458i | \(0.234332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −185.091 | + | 75.1483i | −0.370147 | + | 0.150283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 126.625i | 0.241629i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 647.317i | 1.18033i | 0.807281 | + | 0.590167i | \(0.200938\pi\) | ||||
−0.807281 | + | 0.590167i | \(0.799062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −718.783 | − | 483.936i | −1.25408 | − | 0.844334i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −20.1069 | −0.0336092 | −0.0168046 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168046 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −388.286 | −0.622540 | −0.311270 | − | 0.950322i | \(-0.600754\pi\) | ||||
−0.311270 | + | 0.950322i | \(0.600754\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 129.848 | + | 87.4230i | 0.199914 | + | 0.134596i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 297.513i | − | 0.440321i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 301.434i | 0.429291i | 0.976692 | + | 0.214646i | \(0.0688597\pi\) | ||||
−0.976692 | + | 0.214646i | \(0.931140\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −522.672 | + | 508.188i | −0.716971 | + | 0.697103i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1385.97 | −1.83289 | −0.916443 | − | 0.400166i | \(-0.868952\pi\) | ||||
−0.916443 | + | 0.400166i | \(0.868952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 677.094 | 0.864013 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −726.017 | + | 1078.34i | −0.894680 | + | 1.32886i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 225.557i | 0.268640i | 0.990938 | + | 0.134320i | \(0.0428850\pi\) | ||||
−0.990938 | + | 0.134320i | \(0.957115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 96.1830i | − | 0.110799i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 680.184 | − | 1010.27i | 0.758406 | − | 1.12645i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −166.603 | −0.179928 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −512.787 | −0.536759 | −0.268379 | − | 0.963313i | \(-0.586488\pi\) | ||||
−0.268379 | + | 0.963313i | \(0.586488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −408.427 | − | 1005.96i | −0.414631 | − | 1.02124i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 397.173i | − | 0.391289i | −0.980675 | − | 0.195644i | \(-0.937320\pi\) | ||
0.980675 | − | 0.195644i | \(-0.0626798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1878.32i | − | 1.79686i | −0.439118 | − | 0.898429i | \(-0.644709\pi\) | ||
0.439118 | − | 0.898429i | \(-0.355291\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 310.624 | + | 209.135i | 0.288703 | + | 0.194376i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −310.026 | −0.280106 | −0.140053 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140053 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1416.14 | 1.24442 | 0.622211 | − | 0.782849i | \(-0.286234\pi\) | ||||
0.622211 | + | 0.782849i | \(0.286234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1608.64 | − | 1083.05i | −1.37554 | − | 0.926113i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2017.51i | − | 1.67957i | −0.542918 | − | 0.839786i | \(-0.682680\pi\) | ||
0.542918 | − | 0.839786i | \(-0.317320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1624.31i | 1.31711i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −132.041 | − | 325.217i | −0.104335 | − | 0.256977i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −514.314 | −0.396194 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 285.966 | 0.214851 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −327.533 | + | 486.480i | −0.240103 | + | 0.356621i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1510.98i | − | 1.08117i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1694.52i | 1.18397i | 0.805948 | + | 0.591986i | \(0.201656\pi\) | ||||
−0.805948 | + | 0.591986i | \(0.798344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1142.44 | + | 1696.85i | −0.779737 | + | 1.15813i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1461.10 | −0.974477 | −0.487239 | − | 0.873269i | \(-0.661996\pi\) | ||||
−0.487239 | + | 0.873269i | \(0.661996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 126.550 | 0.0825060 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1337.39 | + | 280.706i | 0.852627 | + | 0.178958i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2397.25i | 1.49497i | 0.664278 | + | 0.747486i | \(0.268739\pi\) | ||||
−0.664278 | + | 0.747486i | \(0.731261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1526.15i | 0.931270i | 0.884977 | + | 0.465635i | \(0.154174\pi\) | ||||
−0.884977 | + | 0.465635i | \(0.845826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −979.111 | − | 659.207i | −0.584795 | − | 0.393725i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 522.750 | 0.305696 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2436.84 | 1.39565 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1242.48 | + | 836.524i | 0.697128 | + | 0.469356i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 439.031i | 0.241388i | 0.992690 | + | 0.120694i | \(0.0385120\pi\) | ||||
−0.992690 | + | 0.120694i | \(0.961488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 520.091i | 0.280294i | 0.990131 | + | 0.140147i | \(0.0447575\pi\) | ||||
−0.990131 | + | 0.140147i | \(0.955243\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1739.02 | + | 706.053i | −0.918896 | + | 0.373079i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2283.00 | −1.18307 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1732.36 | −0.880620 | −0.440310 | − | 0.897846i | \(-0.645132\pi\) | ||||
−0.440310 | + | 0.897846i | \(0.645132\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −242.769 | + | 360.582i | −0.121087 | + | 0.179849i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1233.81i | − | 0.603961i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1359.90i | − | 0.653471i | −0.945116 | − | 0.326735i | \(-0.894051\pi\) | ||
0.945116 | − | 0.326735i | \(-0.105949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1136.63 | + | 1688.23i | −0.536284 | + | 0.796535i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.56410 | −0.00211485 | −0.00105743 | − | 0.999999i | \(-0.500337\pi\) | ||||
−0.00105743 | + | 0.999999i | \(0.500337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 427.896 | − | 173.729i | 0.191357 | − | 0.0776923i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1543.85i | 0.678478i | 0.940700 | + | 0.339239i | \(0.110169\pi\) | ||||
−0.940700 | + | 0.339239i | \(0.889831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 222.887i | 0.0962783i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −519.291 | − | 349.624i | −0.220521 | − | 0.148471i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −130.180 | −0.0543581 | −0.0271790 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271790 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −702.455 | −0.288470 | −0.144235 | − | 0.989543i | \(-0.546072\pi\) | ||||
−0.144235 | + | 0.989543i | \(0.546072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3043.50 | + | 2049.10i | 1.22941 | + | 0.827725i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3635.20i | 1.44468i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2795.27i | − | 1.09310i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1015.87 | − | 213.221i | −0.390973 | − | 0.0820613i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4299.41 | 1.62877 | 0.814384 | − | 0.580327i | \(-0.197075\pi\) | ||||
0.814384 | + | 0.580327i | \(0.197075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3779.52 | 1.40962 | 0.704809 | − | 0.709398i | \(-0.251033\pi\) | ||||
0.704809 | + | 0.709398i | \(0.251033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −367.463 | + | 545.788i | −0.134947 | + | 0.200434i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 384.794i | − | 0.139165i | −0.997576 | − | 0.0695823i | \(-0.977833\pi\) | ||
0.997576 | − | 0.0695823i | \(-0.0221666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1016.18i | 0.361984i | 0.983485 | + | 0.180992i | \(0.0579308\pi\) | ||||
−0.983485 | + | 0.180992i | \(0.942069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1878.50 | + | 2790.12i | −0.659201 | + | 0.979102i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1851.00 | −0.639975 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1099.35 | 0.374545 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1693.78 | − | 4171.80i | −0.568724 | − | 1.40077i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 687.794i | 0.227635i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1416.76i | 0.462246i | 0.972925 | + | 0.231123i | \(0.0742399\pi\) | ||||
−0.972925 | + | 0.231123i | \(0.925760\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −86.6665 | − | 58.3500i | −0.0278793 | − | 0.0187703i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3834.53 | 1.21634 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1734.15 | 0.542496 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1673.62 | − | 1126.80i | −0.516405 | − | 0.347681i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 903.684i | − | 0.275061i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5904.24i | − | 1.77299i | −0.462736 | − | 0.886496i | \(-0.653132\pi\) | ||
0.462736 | − | 0.886496i | \(-0.346868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 305.981 | + | 753.634i | 0.0906610 | + | 0.223299i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3060.83 | 0.894954 | 0.447477 | − | 0.894296i | \(-0.352323\pi\) | ||||
0.447477 | + | 0.894296i | \(0.352323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3758.45 | 1.08457 | 0.542283 | − | 0.840196i | \(-0.317560\pi\) | ||||
0.542283 | + | 0.840196i | \(0.317560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 863.378 | − | 1282.36i | 0.245914 | − | 0.365252i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3967.07i | − | 1.11541i | −0.830038 | − | 0.557706i | \(-0.811682\pi\) | ||
0.830038 | − | 0.557706i | \(-0.188318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2212.60i | 0.614187i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −874.758 | + | 1299.27i | −0.239754 | + | 0.356103i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 853.047 | 0.230874 | 0.115437 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115437 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2985.05 | −0.797858 | −0.398929 | − | 0.916982i | \(-0.630618\pi\) | ||||
−0.398929 | + | 0.916982i | \(0.630618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3727.61 | + | 673.644i | −0.984060 | + | 0.177837i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2807.75i | − | 0.732166i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 222.357i | 0.0572804i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5973.89 | − | 4022.05i | −1.52040 | − | 1.02364i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4134.93 | 1.03982 | 0.519909 | − | 0.854222i | \(-0.325966\pi\) | ||||
0.519909 | + | 0.854222i | \(0.325966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6705.69 | 1.66634 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2918.46 | + | 1964.92i | 0.716710 | + | 0.482540i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6118.58i | − | 1.48508i | −0.669800 | − | 0.742542i | \(-0.733620\pi\) | ||
0.669800 | − | 0.742542i | \(-0.266380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2761.27i | − | 0.662459i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6258.67 | + | 2541.06i | −1.48430 | + | 0.602636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3717.92 | 0.871699 | 0.435850 | − | 0.900020i | \(-0.356448\pi\) | ||||
0.435850 | + | 0.900020i | \(0.356448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 814.843 | 0.188888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −654.562 | + | 972.212i | −0.150032 | + | 0.222841i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1363.32i | 0.309007i | 0.987992 | + | 0.154503i | \(0.0493778\pi\) | ||||
−0.987992 | + | 0.154503i | \(0.950622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7954.61i | − | 1.78306i | −0.452966 | − | 0.891528i | \(-0.649634\pi\) | ||
0.452966 | − | 0.891528i | \(-0.350366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 279.122 | − | 414.576i | 0.0618799 | − | 0.0919094i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1211.38 | −0.265633 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 998.868 | 0.216665 | 0.108332 | − | 0.994115i | \(-0.465449\pi\) | ||||
0.108332 | + | 0.994115i | \(0.465449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5863.56 | − | 2380.65i | 1.25822 | − | 0.510845i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6916.88i | 1.46842i | 0.678921 | + | 0.734211i | \(0.262448\pi\) | ||||
−0.678921 | + | 0.734211i | \(0.737552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2364.19i | − | 0.496596i | −0.968684 | − | 0.248298i | \(-0.920129\pi\) | ||
0.968684 | − | 0.248298i | \(-0.0798713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −718.106 | − | 483.480i | −0.149252 | − | 0.100487i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −835.054 | −0.171748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 80.7808 | 0.0164423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2210.25 | − | 1488.10i | −0.445248 | − | 0.299773i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7233.06i | 1.44218i | 0.692839 | + | 0.721092i | \(0.256360\pi\) | ||||
−0.692839 | + | 0.721092i | \(0.743640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1173.49i | 0.231605i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1158.85 | − | 5521.22i | 0.226408 | − | 1.07870i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2167.88 | 0.419304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2912.68 | −0.557754 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1152.59 | − | 1711.92i | 0.218530 | − | 0.324579i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6877.70i | − | 1.29120i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 253.054i | − | 0.0470441i | −0.999723 | − | 0.0235220i | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235220i | \(-0.00748799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5450.86 | − | 8096.08i | 1.00352 | − | 1.49052i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 374.616 | 0.0683039 | 0.0341519 | − | 0.999417i | \(-0.489127\pi\) | ||||
0.0341519 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7578.97 | 1.36865 | 0.684327 | − | 0.729175i | \(-0.260096\pi\) | ||||
0.684327 | + | 0.729175i | \(0.260096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 731.972 | + | 1802.86i | 0.130927 | + | 0.322474i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2992.77i | − | 0.530255i | −0.964213 | − | 0.265127i | \(-0.914586\pi\) | ||
0.964213 | − | 0.265127i | \(-0.0854140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10060.1i | − | 1.76570i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1336.30 | − | 899.689i | −0.232351 | − | 0.156435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1189.00 | 0.204822 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −391.628 | −0.0668419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6103.98 | + | 4109.63i | 1.03226 | + | 0.694994i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1680.67i | − | 0.281636i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8242.60i | 1.36874i | 0.729133 | + | 0.684372i | \(0.239924\pi\) | ||||
−0.729133 | + | 0.684372i | \(0.760076\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3790.68 | − | 9336.49i | −0.623808 | − | 1.53645i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6305.11 | 1.02831 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9334.33 | 1.50882 | 0.754412 | − | 0.656402i | \(-0.227922\pi\) | ||||
0.754412 | + | 0.656402i | \(0.227922\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5854.79 | − | 8696.04i | 0.938020 | − | 1.39323i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9425.00i | 1.49675i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4670.50i | 0.735228i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4713.71 | + | 7001.21i | −0.735588 | + | 1.09256i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3119.98 | −0.482677 | −0.241339 | − | 0.970441i | \(-0.577586\pi\) | ||||
−0.241339 | + | 0.970441i | \(0.577586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7604.58 | 1.16637 | 0.583186 | − | 0.812339i | \(-0.301806\pi\) | ||||
0.583186 | + | 0.812339i | \(0.301806\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 374.644 | − | 1784.96i | 0.0569716 | − | 0.271436i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1079.00i | 0.162689i | 0.996686 | + | 0.0813445i | \(0.0259214\pi\) | ||||
−0.996686 | + | 0.0813445i | \(0.974079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 195.849i | 0.0292805i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2216.84 | − | 1492.53i | −0.328648 | − | 0.221269i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2495.63 | −0.366892 | −0.183446 | − | 0.983030i | \(-0.558725\pi\) | ||||
−0.183446 | + | 0.983030i | \(0.558725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6566.44 | 0.957346 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1232.59 | + | 829.870i | 0.178222 | + | 0.119991i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3782.05i | 0.542360i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4253.25i | 0.604954i | 0.953157 | + | 0.302477i | \(0.0978135\pi\) | ||||
−0.953157 | + | 0.302477i | \(0.902187\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2823.51 | + | 1146.37i | −0.398337 | + | 0.161728i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −618.947 | −0.0866149 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8121.75 | −1.12742 | −0.563711 | − | 0.825972i | \(-0.690627\pi\) | ||||
−0.563711 | + | 0.825972i | \(0.690627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4384.83 | − | 6512.73i | 0.603818 | − | 0.896842i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3252.33i | − | 0.444307i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1385.36i | 0.187761i | 0.995583 | + | 0.0938804i | \(0.0299271\pi\) | ||||
−0.995583 | + | 0.0938804i | \(0.970073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4917.47 | + | 7303.86i | −0.661233 | + | 0.982120i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3745.59 | −0.499714 | −0.249857 | − | 0.968283i | \(-0.580384\pi\) | ||||
−0.249857 | + | 0.968283i | \(0.580384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2897.88 | −0.383610 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9848.44 | + | 3998.54i | −1.29360 | + | 0.525212i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4921.61i | 0.641479i | 0.947167 | + | 0.320740i | \(0.103931\pi\) | ||||
−0.947167 | + | 0.320740i | \(0.896069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11592.2i | − | 1.49934i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6297.73 | − | 4240.08i | −0.808342 | − | 0.544233i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2936.08 | 0.374001 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1356.50 | −0.171489 | −0.0857444 | − | 0.996317i | \(-0.527327\pi\) | ||||
−0.0857444 | + | 0.996317i | \(0.527327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 545.467 | + | 367.247i | 0.0684398 | + | 0.0460786i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10471.3i | − | 1.30402i | −0.758209 | − | 0.652011i | \(-0.773925\pi\) | ||
0.758209 | − | 0.652011i | \(-0.226075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3047.01i | 0.376632i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4949.94 | + | 5091.02i | 0.607319 | + | 0.624629i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15007.3 | 1.82773 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3404.75 | −0.411624 | −0.205812 | − | 0.978592i | \(-0.565984\pi\) | ||||
−0.205812 | + | 0.978592i | \(0.565984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6956.79 | + | 10332.8i | −0.834922 | + | 1.24010i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 891.376i | − | 0.106203i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13499.8i | 1.59682i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4428.87 | + | 6578.14i | −0.520103 | + | 0.772501i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11029.0 | −1.28592 | −0.642960 | − | 0.765899i | \(-0.722294\pi\) | ||||
−0.642960 | + | 0.765899i | \(0.722294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 307.919 | 0.0356462 | 0.0178231 | − | 0.999841i | \(-0.494326\pi\) | ||||
0.0178231 | + | 0.999841i | \(0.494326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2307.23 | − | 5682.73i | −0.265204 | − | 0.653201i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2094.13i | 0.239012i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5224.24i | 0.592081i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2253.20 | + | 1517.01i | 0.253579 | + | 0.170727i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7719.32 | 0.862706 | 0.431353 | − | 0.902183i | \(-0.358036\pi\) | ||||
0.431353 | + | 0.902183i | \(0.358036\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −998.047 | −0.110769 | −0.0553846 | − | 0.998465i | \(-0.517638\pi\) | ||||
−0.0553846 | + | 0.998465i | \(0.517638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10503.5 | + | 7071.67i | 1.15771 | + | 0.779450i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2852.34i | 0.312233i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2305.00i | − | 0.250596i | −0.992119 | − | 0.125298i | \(-0.960011\pi\) | ||
0.992119 | − | 0.125298i | \(-0.0399886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2927.84 | + | 7211.30i | 0.316147 | + | 0.778674i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10854.6 | −1.16414 | −0.582072 | − | 0.813137i | \(-0.697758\pi\) | ||||
−0.582072 | + | 0.813137i | \(0.697758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2197.01 | 0.234041 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1274.06 | + | 1892.34i | −0.134812 | + | 0.200235i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15526.2i | 1.63191i | 0.578118 | + | 0.815953i | \(0.303787\pi\) | ||||
−0.578118 | + | 0.815953i | \(0.696213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4538.48i | − | 0.473855i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1509.29 | + | 2241.73i | −0.156541 | + | 0.232507i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −936.858 | −0.0965288 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10148.3 | 1.03877 | 0.519386 | − | 0.854540i | \(-0.326161\pi\) | ||||
0.519386 | + | 0.854540i | \(0.326161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9544.60 | − | 2003.31i | −0.970596 | − | 0.203718i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7974.58i | 0.805668i | 0.915273 | + | 0.402834i | \(0.131975\pi\) | ||||
−0.915273 | + | 0.402834i | \(0.868025\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9857.82i | 0.989486i | 0.869039 | + | 0.494743i | \(0.164738\pi\) | ||||
−0.869039 | + | 0.494743i | \(0.835262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9840.37 | − | 6625.24i | −0.981368 | − | 0.660727i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5020.39 | −0.497464 | −0.248732 | − | 0.968572i | \(-0.580014\pi\) | ||||
−0.248732 | + | 0.968572i | \(0.580014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4789.30 | −0.471534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7466.95 | − | 5027.28i | −0.730486 | − | 0.491815i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 15830.3i | − | 1.53885i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 515.274i | − | 0.0497735i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2092.80 | + | 849.694i | −0.200887 | + | 0.0815615i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13924.4 | −1.32823 | −0.664115 | − | 0.747631i | \(-0.731191\pi\) | ||||
−0.664115 | + | 0.747631i | \(0.731191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4851.73 | 0.459916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3580.50 | − | 5318.06i | 0.337305 | − | 0.500994i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4994.73i | 0.467627i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17105.5i | − | 1.59163i | −0.605537 | − | 0.795817i | \(-0.707042\pi\) | ||
0.605537 | − | 0.795817i | \(-0.292958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3946.41 | − | 5861.55i | 0.364955 | − | 0.542062i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3292.61 | 0.302634 | 0.151317 | − | 0.988485i | \(-0.451649\pi\) | ||||
0.151317 | + | 0.988485i | \(0.451649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17391.0 | −1.58875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9798.42 | + | 3978.23i | −0.889710 | + | 0.361229i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 148.765i | − | 0.0134266i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7587.44i | − | 0.680682i | −0.940302 | − | 0.340341i | \(-0.889457\pi\) | ||
0.940302 | − | 0.340341i | \(-0.110543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6725 | − | 13.2449i | −0.00175430 | − | 0.00118112i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15294.5 | −1.35576 | −0.677882 | − | 0.735170i | \(-0.737102\pi\) | ||||
−0.677882 | + | 0.735170i | \(0.737102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3868.61 | −0.340893 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 728.437 | + | 490.435i | 0.0638087 | + | 0.0429606i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 15799.9i | − | 1.37587i | −0.725771 | − | 0.687936i | \(-0.758517\pi\) | ||
0.725771 | − | 0.687936i | \(-0.241483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2872.81i | − | 0.248700i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2348.51 | + | 492.928i | 0.202123 | + | 0.0424236i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18295.5 | −1.56543 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9134.34 | 0.777037 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4480.22 | + | 6654.41i | −0.378921 | + | 0.562806i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13510.6i | 1.13610i | 0.822993 | + | 0.568052i | \(0.192303\pi\) | ||||
−0.822993 | + | 0.568052i | \(0.807697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15580.7i | 1.30267i | 0.758790 | + | 0.651336i | \(0.225791\pi\) | ||||
−0.758790 | + | 0.651336i | \(0.774209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −646.816 | + | 960.706i | −0.0537702 | + | 0.0798641i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16293.1 | 1.34675 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15642.0 | 1.28561 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1223.68 | − | 3013.95i | −0.100006 | − | 0.246317i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1467.25i | − | 0.119237i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3019.76i | 0.244029i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −561.111 | − | 377.780i | −0.0450907 | − | 0.0303583i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11591.3 | −0.926298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3006.57 | 0.238932 | 0.119466 | − | 0.992838i | \(-0.461882\pi\) | ||||
0.119466 | + | 0.992838i | \(0.461882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3027.78 | − | 2038.51i | −0.239290 | − | 0.161107i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13793.8i | − | 1.08415i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10848.7i | 0.848002i | 0.905662 | + | 0.424001i | \(0.139375\pi\) | ||||
−0.905662 | + | 0.424001i | \(0.860625\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7171.86 | + | 17664.4i | 0.557536 | + | 1.37322i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4279.17 | 0.330851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2230.22 | −0.171499 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10549.3 | + | 15668.7i | −0.806834 | + | 1.19838i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23506.2i | − | 1.78814i | −0.447932 | − | 0.894068i | \(-0.647839\pi\) | ||
0.447932 | − | 0.894068i | \(-0.352161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5117.77i | − | 0.387225i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8111.83 | − | 12048.4i | 0.610485 | − | 0.906744i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5146.05 | 0.385222 | 0.192611 | − | 0.981275i | \(-0.438304\pi\) | ||||
0.192611 | + | 0.981275i | \(0.438304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19651.3 | −1.46325 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3759.93 | − | 3867.09i | −0.278487 | − | 0.286424i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18204.3i | 1.34124i | 0.741802 | + | 0.670619i | \(0.233972\pi\) | ||||
−0.741802 | + | 0.670619i | \(0.766028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14558.7i | 1.06701i | 0.845797 | + | 0.533505i | \(0.179125\pi\) | ||||
−0.845797 | + | 0.533505i | \(0.820875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18531.7 | + | 12476.8i | 1.35108 | + | 0.909646i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5023.69 | −0.364352 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12638.2 | 0.911847 | 0.455924 | − | 0.890019i | \(-0.349309\pi\) | ||||
0.455924 | + | 0.890019i | \(0.349309\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16290.8 | + | 10968.1i | 1.16930 | + | 0.787253i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 10254.3i | − | 0.732223i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3363.95i | − | 0.238972i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3167.74 | + | 1286.12i | −0.223880 | + | 0.0908969i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14489.0 | −1.01878 | −0.509390 | − | 0.860536i | \(-0.670129\pi\) | ||||
−0.509390 | + | 0.860536i | \(0.670129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4009.03 | −0.280457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1116.67 | − | 1658.57i | 0.0777216 | − | 0.115439i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2580.48i | 0.178697i | 0.996000 | + | 0.0893487i | \(0.0284785\pi\) | ||||
−0.996000 | + | 0.0893487i | \(0.971521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5009.61i | 0.345166i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2948.93 | + | 4380.00i | −0.202163 | + | 0.300270i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13625.6 | 0.929431 | 0.464715 | − | 0.885460i | \(-0.346157\pi\) | ||||
0.464715 | + | 0.885460i | \(0.346157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16856.6 | −1.14409 | −0.572043 | − | 0.820223i | \(-0.693849\pi\) | ||||
−0.572043 | + | 0.820223i | \(0.693849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16193.7 | + | 6574.78i | −1.09363 | + | 0.444023i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2785.42i | − | 0.187179i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7976.37i | 0.533362i | 0.963785 | + | 0.266681i | \(0.0859270\pi\) | ||||
−0.963785 | + | 0.266681i | \(0.914073\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7978.33 | − | 5371.58i | −0.530867 | − | 0.357418i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2953.05 | 0.195528 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 881.451 | 0.0580774 | 0.0290387 | − | 0.999578i | \(-0.490755\pi\) | ||||
0.0290387 | + | 0.999578i | \(0.490755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4738.49 | + | 3190.29i | 0.310690 | + | 0.209179i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1846.48i | 0.120481i | 0.998184 | + | 0.0602404i | \(0.0191867\pi\) | ||||
−0.998184 | + | 0.0602404i | \(0.980813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25535.3i | 1.65808i | 0.559189 | + | 0.829040i | \(0.311113\pi\) | ||||
−0.559189 | + | 0.829040i | \(0.688887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4805.83 | − | 22896.9i | 0.310550 | − | 1.47958i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1668.83 | −0.107320 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10951.8 | −0.700916 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1995.97 | + | 2964.58i | −0.127131 | + | 0.188826i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 25943.4i | − | 1.64456i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17340.8i | 1.09402i | 0.837126 | + | 0.547009i | \(0.184234\pi\) | ||||
−0.837126 | + | 0.547009i | \(0.815766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4111.42 | + | 6106.63i | −0.258158 | + | 0.383439i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16505.3 | 1.03148 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3747.37 | −0.233087 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −204.226 | − | 503.010i | −0.0126433 | − | 0.0311405i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1271.80i | 0.0783668i | 0.999232 | + | 0.0391834i | \(0.0124757\pi\) | ||||
−0.999232 | + | 0.0391834i | \(0.987524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5662.47i | − | 0.347288i | −0.984808 | − | 0.173644i | \(-0.944446\pi\) | ||
0.984808 | − | 0.173644i | \(-0.0555542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16527.9 | + | 11127.8i | 1.00897 | + | 0.679310i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22748.8 | −1.38230 | −0.691149 | − | 0.722712i | \(-0.742895\pi\) | ||||
−0.691149 | + | 0.722712i | \(0.742895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4844.58 | 0.293014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7474.66 | + | 5032.47i | 0.450008 | + | 0.302977i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 727.610i | − | 0.0436043i | −0.999762 | − | 0.0218021i | \(-0.993060\pi\) | ||
0.999762 | − | 0.0218021i | \(-0.00694038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14231.6i | 0.848969i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3943.81 | − | 9713.64i | −0.234190 | − | 0.576811i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25989.0 | −1.53625 | −0.768126 | − | 0.640299i | \(-0.778810\pi\) | ||||
−0.768126 | + | 0.640299i | \(0.778810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −683.734 | −0.0402333 | −0.0201166 | − | 0.999798i | \(-0.506404\pi\) | ||||
−0.0201166 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2622.48 | − | 3895.13i | 0.153618 | − | 0.228166i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1232.65i | − | 0.0718797i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 41720.0i | − | 2.42190i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17134.0 | − | 25448.9i | 0.990194 | − | 1.47072i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28393.5 | −1.63356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11692.5 | −0.669705 | −0.334853 | − | 0.942271i | \(-0.608686\pi\) | ||||
−0.334853 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −868.173 | + | 4136.32i | −0.0495051 | + | 0.235863i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 23194.7i | − | 1.31676i | −0.752686 | − | 0.658380i | \(-0.771242\pi\) | ||
0.752686 | − | 0.658380i | \(-0.228758\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3793.95i | − | 0.214431i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13193.0 | + | 8882.49i | 0.742376 | + | 0.499820i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13096.4 | 0.733706 | 0.366853 | − | 0.930279i | \(-0.380435\pi\) | ||||
0.366853 | + | 0.930279i | \(0.380435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23350.1 | 1.30243 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16200.0 | + | 10907.0i | 0.899661 | + | 0.605716i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1087.53i | − | 0.0601330i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 33382.5i | − | 1.83782i | −0.394472 | − | 0.918908i | \(-0.629073\pi\) | ||
0.394472 | − | 0.918908i | \(-0.370927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7442.79 | − | 3021.83i | 0.407977 | − | 0.165642i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14865.3 | 0.811327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7845.72 | −0.426367 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11512.4 | − | 17099.1i | 0.622944 | − | 0.925249i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17639.5i | 0.950409i | 0.879875 | + | 0.475204i | \(0.157626\pi\) | ||||
−0.879875 | + | 0.475204i | \(0.842374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6383.53i | 0.342474i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6420.92 | + | 9536.90i | −0.343015 | + | 0.509476i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2938.56 | 0.156317 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5863.12 | −0.310570 | −0.155285 | − | 0.987870i | \(-0.549630\pi\) | ||||
−0.155285 | + | 0.987870i | \(0.549630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7540.90 | + | 3061.66i | −0.397758 | + | 0.161493i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39086.2i | 2.05300i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5091.78i | − | 0.266324i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3676.87 | + | 2475.53i | 0.191513 | + | 0.128940i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3072.01 | −0.159342 | −0.0796708 | − | 0.996821i | \(-0.525387\pi\) | ||||
−0.0796708 | + | 0.996821i | \(0.525387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13897.1 | 0.717831 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12866.4 | − | 8662.57i | −0.661834 | − | 0.445594i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7536.71i | 0.386078i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28176.7i | − | 1.43743i | −0.695303 | − | 0.718717i | \(-0.744730\pi\) | ||
0.695303 | − | 0.718717i | \(-0.255270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18022.0 | − | 7913.89i | −0.915610 | − | 0.402067i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27366.0 | −1.38463 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28596.5 | −1.44098 | −0.720490 | − | 0.693466i | \(-0.756083\pi\) | ||||
−0.720490 | + | 0.693466i | \(0.756083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8148.05 | − | 12102.2i | 0.408905 | − | 0.607341i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 26029.6i | − | 1.30097i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35285.7i | 1.75644i | 0.478261 | + | 0.878218i | \(0.341267\pi\) | ||||
−0.478261 | + | 0.878218i | \(0.658733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −645.277 | + | 958.421i | −0.0319904 | + | 0.0475148i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34165.6 | 1.68696 | 0.843482 | − | 0.537158i | \(-0.180502\pi\) | ||||
0.843482 | + | 0.537158i | \(0.180502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4276.32 | 0.210298 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14077.2 | − | 34672.3i | −0.689502 | − | 1.69825i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2293.78i | − | 0.111900i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32825.1i | 1.59495i | 0.603353 | + | 0.797474i | \(0.293831\pi\) | ||||
−0.603353 | + | 0.797474i | \(0.706169\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17822.7 | + | 11999.5i | 0.862543 | + | 0.580725i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5065.87 | 0.244193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32213.7 | −1.54667 | −0.773334 | − | 0.633999i | \(-0.781413\pi\) | ||||
−0.773334 | + | 0.633999i | \(0.781413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28903.4 | + | 19459.8i | 1.38225 | + | 0.930627i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39231.3i | 1.86877i | 0.356264 | + | 0.934385i | \(0.384051\pi\) | ||||
−0.356264 | + | 0.934385i | \(0.615949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10477.6i | 0.497137i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6877.22 | + | 16938.7i | 0.325028 | + | 0.800547i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1566.21 | 0.0737320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20637.3 | −0.967752 | −0.483876 | − | 0.875137i | \(-0.660771\pi\) | ||||
−0.483876 | + | 0.875137i | \(0.660771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17756.0 | − | 26372.8i | 0.829400 | − | 1.23190i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14291.6i | 0.664986i | 0.943106 | + | 0.332493i | \(0.107890\pi\) | ||||
−0.943106 | + | 0.332493i | \(0.892110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7060.92i | − | 0.327272i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8013.15 | − | 11901.8i | 0.369975 | − | 0.549518i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1930.49 | 0.0887894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 808.531 | 0.0370442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −34350.7 | − | 7209.87i | −1.56781 | − | 0.329067i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16873.8i | 0.767201i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31135.5i | − | 1.41024i | −0.709088 | − | 0.705120i | \(-0.750893\pi\) | ||
0.709088 | − | 0.705120i | \(-0.249107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16025.3 | + | 10789.4i | 0.723086 | + | 0.486833i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14927.0 | 0.670976 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9179.33 | −0.411056 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3512.20 | + | 2364.66i | 0.156685 | + | 0.105492i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17943.6i | 0.797485i | 0.917063 | + | 0.398742i | \(0.130553\pi\) | ||||
−0.917063 | + | 0.398742i | \(0.869447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15790.7i | − | 0.699166i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5642.69 | + | 2290.97i | −0.248907 | + | 0.101058i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15613.6 | 0.686165 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12017.8 | −0.526174 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3956.32 | + | 5876.27i | −0.172576 | + | 0.256325i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10039.8i | − | 0.436317i | −0.975913 | − | 0.218159i | \(-0.929995\pi\) | ||
0.975913 | − | 0.218159i | \(-0.0700050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31349.9i | − | 1.35739i | −0.734420 | − | 0.678695i | \(-0.762546\pi\) | ||
0.734420 | − | 0.678695i | \(-0.237454\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23084.2 | − | 34286.6i | 0.995814 | − | 1.47907i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13245.9 | −0.569307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6733.57 | 0.288345 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2406.18 | − | 976.928i | 0.102660 | − | 0.0416809i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36012.2i | 1.53086i | 0.643521 | + | 0.765429i | \(0.277473\pi\) | ||||
−0.643521 | + | 0.765429i | \(0.722527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5750.21i | − | 0.243548i | −0.992558 | − | 0.121774i | \(-0.961142\pi\) | ||
0.992558 | − | 0.121774i | \(-0.0388583\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5221.39 | − | 3515.41i | −0.220346 | − | 0.148353i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2668.08 | 0.112186 | 0.0560932 | − | 0.998426i | \(-0.482136\pi\) | ||||
0.0560932 | + | 0.998426i | \(0.482136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20803.0 | −0.871553 | −0.435777 | − | 0.900055i | \(-0.643526\pi\) | ||||
−0.435777 | + | 0.900055i | \(0.643526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4305.40 | + | 2898.70i | 0.179726 | + | 0.121005i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20038.1i | 0.833468i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.4560i | 0.00184247i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32182.2 | + | 6754.71i | 1.32901 | + | 0.278945i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44034.2 | 1.81196 | 0.905978 | − | 0.423325i | \(-0.139137\pi\) | ||||
0.905978 | + | 0.423325i | \(0.139137\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38200.7 | −1.56631 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20072.7 | + | 29813.7i | −0.820095 | + | 1.21808i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1646.12i | − | 0.0670158i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2115.78i | 0.0858312i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6860.85 | − | 10190.3i | 0.277343 | − | 0.411933i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62236.6 | 2.50698 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22838.0 | −0.916715 | −0.458357 | − | 0.888768i | \(-0.651562\pi\) | ||||
−0.458357 | + | 0.888768i | \(0.651562\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1692.18 | − | 4167.86i | −0.0676859 | − | 0.166711i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33000.9i | − | 1.31539i | −0.753284 | − | 0.657695i | \(-0.771532\pi\) | ||
0.753284 | − | 0.657695i | \(-0.228468\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9649.22i | − | 0.383268i | −0.981466 | − | 0.191634i | \(-0.938621\pi\) | ||
0.981466 | − | 0.191634i | \(-0.0613787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3599.32 | − | 2423.32i | −0.142467 | − | 0.0959191i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2249.42 | −0.0887266 | −0.0443633 | − | 0.999015i | \(-0.514126\pi\) | ||||
−0.0443633 | + | 0.999015i | \(0.514126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15037.7 | 0.591093 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 348.188 | + | 234.425i | 0.0136391 | + | 0.00918279i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 12121.1i | − | 0.473166i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8415.12i | − | 0.327366i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5208.36 | − | 12828.2i | −0.201920 | − | 0.497331i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11179.3 | 0.431918 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −562.158 | −0.0216451 | −0.0108225 | − | 0.999941i | \(-0.503445\pi\) | ||||
−0.0108225 | + | 0.999941i | \(0.503445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20990.2 | + | 31176.5i | −0.805442 | + | 1.19631i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14155.3i | 0.541320i | 0.962675 | + | 0.270660i | \(0.0872419\pi\) | ||||
−0.962675 | + | 0.270660i | \(0.912758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51391.0i | 1.95860i | 0.202413 | + | 0.979300i | \(0.435122\pi\) | ||||
−0.202413 | + | 0.979300i | \(0.564878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3405.46 | + | 5058.08i | −0.129348 | + | 0.192119i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24844.4 | −0.940467 | −0.470233 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470233 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12537.2 | −0.472987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21017.4 | − | 20435.0i | 0.790248 | − | 0.768349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3885.39i | 0.145599i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1268.00i | 0.0473570i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9344.18 | + | 6291.17i | 0.347818 | + | 0.234176i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58638.5 | 2.17542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5815.30 | −0.215023 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12554.4 | − | 8452.55i | −0.462664 | − | 0.311499i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6842.17i | 0.251317i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7191.92i | − | 0.263290i | −0.991297 | − | 0.131645i | \(-0.957974\pi\) | ||
0.991297 | − | 0.131645i | \(-0.0420258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9935.96 | − | 4034.07i | 0.362547 | − | 0.147197i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17622.8 | 0.640910 | 0.320455 | − | 0.947264i | \(-0.396164\pi\) | ||||
0.320455 | + | 0.947264i | \(0.396164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55731.8 | 2.02021 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19959.0 | − | 29644.8i | 0.721118 | − | 1.07107i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10810.2i | − | 0.389296i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21839.1i | 0.783902i | 0.919986 | + | 0.391951i | \(0.128200\pi\) | ||||
−0.919986 | + | 0.391951i | \(0.871800\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 734.358 | − | 1090.73i | 0.0262735 | − | 0.0390237i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 261.390 | 0.00932152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11243.0 | −0.399642 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 46989.4 | − | 19078.0i | 1.66487 | − | 0.675949i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8108.45i | 0.286361i | 0.989697 | + | 0.143181i | \(0.0457330\pi\) | ||||
−0.989697 | + | 0.143181i | \(0.954267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4930.50i | − | 0.173567i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1614.70 | + | 1087.13i | 0.0566589 | + | 0.0381468i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27227.0 | −0.952318 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25761.6 | 0.898180 | 0.449090 | − | 0.893487i | \(-0.351748\pi\) | ||||
0.449090 | + | 0.893487i | \(0.351748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32667.4 | + | 21994.0i | 1.13532 | + | 0.764376i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8189.74i | 0.283717i | 0.989887 | + | 0.141859i | \(0.0453078\pi\) | ||||
−0.989887 | + | 0.141859i | \(0.954692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 18821.4i | − | 0.649957i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2076.86 | + | 9894.98i | −0.0714922 | + | 0.340618i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55018.7 | 1.88793 | 0.943964 | − | 0.330050i | \(-0.107065\pi\) | ||||
0.943964 | + | 0.330050i | \(0.107065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5047.72 | 0.172662 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8684.98 | − | 12899.7i | 0.296141 | − | 0.439853i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36617.4i | − | 1.24465i | −0.782758 | − | 0.622327i | \(-0.786188\pi\) | ||
0.782758 | − | 0.622327i | \(-0.213812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 41877.9i | − | 1.41899i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29194.2 | − | 43361.8i | 0.986119 | − | 1.46467i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17736.5 | −0.597229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25145.6 | −0.844068 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3148.92 | − | 7755.82i | −0.105371 | − | 0.259530i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 36814.0i | − | 1.22807i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7464.23i | − | 0.248225i | −0.992268 | − | 0.124112i | \(-0.960392\pi\) | ||
0.992268 | − | 0.124112i | \(-0.0396083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5124.91 | + | 3450.45i | 0.169903 | + | 0.114391i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36787.0 | −1.21581 | −0.607906 | − | 0.794009i | \(-0.707990\pi\) | ||||
−0.607906 | + | 0.794009i | \(0.707990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11291.5 | −0.372035 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1688.02 | − | 1136.50i | −0.0554462 | − | 0.0373303i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27402.6i | − | 0.897326i | −0.893701 | − | 0.448663i | \(-0.851900\pi\) | ||
0.893701 | − | 0.448663i | \(-0.148100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9069.98i | − | 0.296096i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14383.7 | + | 35427.3i | 0.468132 | + | 1.15301i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53135.8 | −1.72408 | −0.862040 | − | 0.506841i | \(-0.830813\pi\) | ||||
−0.862040 | + | 0.506841i | \(0.830813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3748.03 | −0.121241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4877.27 | − | 7244.15i | 0.157290 | − | 0.233621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 65649.3i | − | 2.11074i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 10055.2i | − | 0.322315i | −0.986929 | − | 0.161158i | \(-0.948477\pi\) | ||
0.986929 | − | 0.161158i | \(-0.0515228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23919.9 | + | 35527.9i | −0.764426 | + | 1.13539i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9897.92 | 0.315362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39092.2 | −1.24179 | −0.620894 | − | 0.783895i | \(-0.713230\pi\) | ||||
−0.620894 | + | 0.783895i | \(0.713230\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10755.5 | − | 51243.3i | 0.340628 | − | 1.62289i |
(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 | 624.4.d.b.287.10 | yes | 12 | |
3.2 | odd | 2 | inner | 624.4.d.b.287.4 | yes | 12 | |
4.3 | odd | 2 | inner | 624.4.d.b.287.3 | ✓ | 12 | |
12.11 | even | 2 | inner | 624.4.d.b.287.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.4.d.b.287.3 | ✓ | 12 | 4.3 | odd | 2 | inner | |
624.4.d.b.287.4 | yes | 12 | 3.2 | odd | 2 | inner | |
624.4.d.b.287.9 | yes | 12 | 12.11 | even | 2 | inner | |
624.4.d.b.287.10 | yes | 12 | 1.1 | even | 1 | trivial |