Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(161,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.l (of order \(4\), 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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(1.32070 + 0.505727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.481 |
Dual form | 640.2.l.a.161.2 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.66366 | + | 1.66366i | −0.960517 | + | 0.960517i | −0.999250 | − | 0.0387330i | \(-0.987668\pi\) |
0.0387330 | + | 0.999250i | \(0.487668\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.89402i | − | 1.09384i | −0.837186 | − | 0.546919i | \(-0.815801\pi\) | ||
0.837186 | − | 0.546919i | \(-0.184199\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.53555i | − | 0.845184i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.84462 | + | 1.84462i | 0.556175 | + | 0.556175i | 0.928216 | − | 0.372041i | \(-0.121342\pi\) |
−0.372041 | + | 0.928216i | \(0.621342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.08011 | − | 3.08011i | 0.854268 | − | 0.854268i | −0.136388 | − | 0.990656i | \(-0.543549\pi\) |
0.990656 | + | 0.136388i | \(0.0435493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.35278 | −0.607484 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.29875 | 1.77021 | 0.885104 | − | 0.465393i | \(-0.154087\pi\) | ||||
0.885104 | + | 0.465393i | \(0.154087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23593 | + | 1.23593i | −0.283542 | + | 0.283542i | −0.834520 | − | 0.550978i | \(-0.814255\pi\) |
0.550978 | + | 0.834520i | \(0.314255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.81468 | + | 4.81468i | 1.05065 | + | 1.05065i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.60490i | 0.960189i | 0.877217 | + | 0.480094i | \(0.159398\pi\) | ||||
−0.877217 | + | 0.480094i | \(0.840602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.772683 | − | 0.772683i | −0.148703 | − | 0.148703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24680 | + | 4.24680i | −0.788611 | + | 0.788611i | −0.981266 | − | 0.192656i | \(-0.938290\pi\) |
0.192656 | + | 0.981266i | \(0.438290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06299 | −0.370524 | −0.185262 | − | 0.982689i | \(-0.559313\pi\) | ||||
−0.185262 | + | 0.982689i | \(0.559313\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.13767 | −1.06843 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.04638 | − | 2.04638i | 0.345902 | − | 0.345902i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.17899 | + | 1.17899i | 0.193825 | + | 0.193825i | 0.797346 | − | 0.603522i | \(-0.206236\pi\) |
−0.603522 | + | 0.797346i | \(0.706236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.2485i | 1.64108i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.61484i | 0.720717i | 0.932814 | + | 0.360359i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360359i | \(0.882654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03019 | + | 3.03019i | 0.462099 | + | 0.462099i | 0.899343 | − | 0.437244i | \(-0.144045\pi\) |
−0.437244 | + | 0.899343i | \(0.644045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.79291 | − | 1.79291i | 0.267271 | − | 0.267271i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7111 | 1.70823 | 0.854117 | − | 0.520081i | \(-0.174098\pi\) | ||||
0.854117 | + | 0.520081i | \(0.174098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37537 | −0.196481 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.1427 | + | 12.1427i | −1.70031 | + | 1.70031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.73048 | − | 2.73048i | −0.375061 | − | 0.375061i | 0.494256 | − | 0.869316i | \(-0.335441\pi\) |
−0.869316 | + | 0.494256i | \(0.835441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.60869i | 0.351756i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.11235i | − | 0.544694i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.11306 | + | 3.11306i | 0.405285 | + | 0.405285i | 0.880091 | − | 0.474805i | \(-0.157482\pi\) |
−0.474805 | + | 0.880091i | \(0.657482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.34962 | + | 2.34962i | −0.300838 | + | 0.300838i | −0.841342 | − | 0.540503i | \(-0.818234\pi\) |
0.540503 | + | 0.841342i | \(0.318234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.33795 | −0.924495 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.35593 | 0.540286 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.24311 | − | 8.24311i | 1.00706 | − | 1.00706i | 0.00708173 | − | 0.999975i | \(-0.497746\pi\) |
0.999975 | − | 0.00708173i | \(-0.00225420\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.66101 | − | 7.66101i | −0.922277 | − | 0.922277i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.25937i | 0.386816i | 0.981118 | + | 0.193408i | \(0.0619541\pi\) | ||||
−0.981118 | + | 0.193408i | \(0.938046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6877i | 1.48499i | 0.669853 | + | 0.742494i | \(0.266357\pi\) | ||||
−0.669853 | + | 0.742494i | \(0.733643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.66366 | − | 1.66366i | −0.192103 | − | 0.192103i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.33839 | − | 5.33839i | 0.608365 | − | 0.608365i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.113885 | 0.0128130 | 0.00640652 | − | 0.999979i | \(-0.497961\pi\) | ||||
0.00640652 | + | 0.999979i | \(0.497961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1776 | 1.13085 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.76813 | − | 9.76813i | 1.07219 | − | 1.07219i | 0.0750089 | − | 0.997183i | \(-0.476101\pi\) |
0.997183 | − | 0.0750089i | \(-0.0238985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.16100 | + | 5.16100i | 0.559789 | + | 0.559789i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 14.1305i | − | 1.51495i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.74593i | − | 0.397068i | −0.980094 | − | 0.198534i | \(-0.936382\pi\) | ||
0.980094 | − | 0.198534i | \(-0.0636180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.91390 | − | 8.91390i | −0.934430 | − | 0.934430i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.43212 | − | 3.43212i | 0.355894 | − | 0.355894i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.74787 | −0.179328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9853 | −1.41999 | −0.709995 | − | 0.704206i | \(-0.751303\pi\) | ||||
−0.709995 | + | 0.704206i | \(0.751303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.67714 | − | 4.67714i | 0.470071 | − | 0.470071i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52228 | − | 3.52228i | −0.350480 | − | 0.350480i | 0.509808 | − | 0.860288i | \(-0.329716\pi\) |
−0.860288 | + | 0.509808i | \(0.829716\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.150216i | − | 0.0148013i | −0.999973 | − | 0.00740063i | \(-0.997644\pi\) | ||
0.999973 | − | 0.00740063i | \(-0.00235572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.80899i | 0.664489i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.75062 | − | 2.75062i | −0.265912 | − | 0.265912i | 0.561539 | − | 0.827451i | \(-0.310210\pi\) |
−0.827451 | + | 0.561539i | \(0.810210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.90778 | − | 6.90778i | 0.661646 | − | 0.661646i | −0.294122 | − | 0.955768i | \(-0.595027\pi\) |
0.955768 | + | 0.294122i | \(0.0950273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.92288 | −0.372344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.49507 | −0.328788 | −0.164394 | − | 0.986395i | \(-0.552567\pi\) | ||||
−0.164394 | + | 0.986395i | \(0.552567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.25616 | + | 3.25616i | −0.303638 | + | 0.303638i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.80977 | − | 7.80977i | −0.722014 | − | 0.722014i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 21.1228i | − | 1.93632i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.19472i | − | 0.381338i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.67755 | − | 7.67755i | −0.692261 | − | 0.692261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.25357 | −0.554915 | −0.277458 | − | 0.960738i | \(-0.589492\pi\) | ||||
−0.277458 | + | 0.960738i | \(0.589492\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.0824 | −0.887708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.16490 | + | 5.16490i | −0.451259 | + | 0.451259i | −0.895772 | − | 0.444513i | \(-0.853377\pi\) |
0.444513 | + | 0.895772i | \(0.353377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.57681 | + | 3.57681i | 0.310149 | + | 0.310149i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.09274i | − | 0.0940480i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.9408i | − | 1.61823i | −0.587654 | − | 0.809113i | \(-0.699948\pi\) | ||
0.587654 | − | 0.809113i | \(-0.300052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.79057 | + | 2.79057i | 0.236693 | + | 0.236693i | 0.815479 | − | 0.578786i | \(-0.196473\pi\) |
−0.578786 | + | 0.815479i | \(0.696473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.4833 | + | 19.4833i | −1.64079 | + | 1.64079i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3633 | 0.950245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00588 | −0.498761 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.28815 | − | 2.28815i | 0.188723 | − | 0.188723i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.60372 | + | 1.60372i | 0.131382 | + | 0.131382i | 0.769740 | − | 0.638358i | \(-0.220386\pi\) |
−0.638358 | + | 0.769740i | \(0.720386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.53754i | − | 0.206502i | −0.994655 | − | 0.103251i | \(-0.967076\pi\) | ||
0.994655 | − | 0.103251i | \(-0.0329245\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 18.5064i | − | 1.49615i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.45875 | − | 1.45875i | −0.117170 | − | 0.117170i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2405 | + | 10.2405i | −0.817278 | + | 0.817278i | −0.985713 | − | 0.168435i | \(-0.946129\pi\) |
0.168435 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.08521 | 0.720504 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3267 | 1.05029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.02607 | − | 8.02607i | 0.628650 | − | 0.628650i | −0.319078 | − | 0.947728i | \(-0.603373\pi\) |
0.947728 | + | 0.319078i | \(0.103373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.33999 | − | 4.33999i | −0.337868 | − | 0.337868i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.82611i | 0.528221i | 0.964492 | + | 0.264110i | \(0.0850783\pi\) | ||||
−0.964492 | + | 0.264110i | \(0.914922\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.97411i | − | 0.459547i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.13377 | + | 3.13377i | 0.239645 | + | 0.239645i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.08901 | + | 5.08901i | −0.386910 | + | 0.386910i | −0.873584 | − | 0.486674i | \(-0.838210\pi\) |
0.486674 | + | 0.873584i | \(0.338210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.89402 | 0.218768 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3582 | −0.778567 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.63797 | − | 1.63797i | 0.122428 | − | 0.122428i | −0.643238 | − | 0.765666i | \(-0.722410\pi\) |
0.765666 | + | 0.643238i | \(0.222410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7757 | + | 16.7757i | 1.24693 | + | 1.24693i | 0.957071 | + | 0.289855i | \(0.0936070\pi\) |
0.289855 | + | 0.957071i | \(0.406393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.81797i | − | 0.577921i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66734i | 0.122585i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4635 | + | 13.4635i | 0.984546 | + | 0.984546i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.23616 | + | 2.23616i | −0.162657 | + | 0.162657i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.85815 | −0.423881 | −0.211940 | − | 0.977283i | \(-0.567978\pi\) | ||||
−0.211940 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0241155 | −0.00173587 | −0.000867935 | − | 1.00000i | \(-0.500276\pi\) | ||||
−0.000867935 | 1.00000i | \(0.500276\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.24680 | + | 7.24680i | −0.518954 | + | 0.518954i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9086 | − | 14.9086i | −1.06219 | − | 1.06219i | −0.997933 | − | 0.0642576i | \(-0.979532\pi\) |
−0.0642576 | − | 0.997933i | \(-0.520468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.6525i | − | 0.967801i | −0.875123 | − | 0.483900i | \(-0.839220\pi\) | ||
0.875123 | − | 0.483900i | \(-0.160780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.4275i | 1.93459i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2903 | + | 12.2903i | 0.862612 | + | 0.862612i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.26319 | + | 3.26319i | −0.227911 | + | 0.227911i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.6760 | 0.811537 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.55966 | −0.315398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.45103 | + | 2.45103i | −0.168736 | + | 0.168736i | −0.786424 | − | 0.617688i | \(-0.788070\pi\) |
0.617688 | + | 0.786424i | \(0.288070\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.42249 | − | 5.42249i | −0.371543 | − | 0.371543i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.28533i | 0.292257i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.97033i | 0.405293i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.1081 | − | 21.1081i | −1.42636 | − | 1.42636i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4809 | − | 22.4809i | 1.51223 | − | 1.51223i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9483 | −0.934045 | −0.467023 | − | 0.884245i | \(-0.654673\pi\) | ||||
−0.467023 | + | 0.884245i | \(0.654673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.53555 | 0.169037 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.43883 | − | 4.43883i | 0.294616 | − | 0.294616i | −0.544285 | − | 0.838901i | \(-0.683199\pi\) |
0.838901 | + | 0.544285i | \(0.183199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.35068 | + | 5.35068i | 0.353583 | + | 0.353583i | 0.861441 | − | 0.507858i | \(-0.169562\pi\) |
−0.507858 | + | 0.861441i | \(0.669562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.7626i | 1.16869i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.9370i | − | 0.782019i | −0.920387 | − | 0.391010i | \(-0.872126\pi\) | ||
0.920387 | − | 0.391010i | \(-0.127874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.28097 | + | 8.28097i | 0.540191 | + | 0.540191i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.189466 | + | 0.189466i | −0.0123071 | + | 0.0123071i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.7720 | 1.08489 | 0.542445 | − | 0.840091i | \(-0.317499\pi\) | ||||
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0294 | −1.41904 | −0.709519 | − | 0.704686i | \(-0.751088\pi\) | ||||
−0.709519 | + | 0.704686i | \(0.751088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6141 | + | 14.6141i | −0.937495 | + | 0.937495i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.972532 | − | 0.972532i | −0.0621328 | − | 0.0621328i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.61360i | 0.484442i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.5018i | 2.05972i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.63925 | + | 6.63925i | 0.419066 | + | 0.419066i | 0.884882 | − | 0.465816i | \(-0.154239\pi\) |
−0.465816 | + | 0.884882i | \(0.654239\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.49432 | + | 8.49432i | −0.534033 | + | 0.534033i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.1723 | −1.07537 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.25821 | −0.452755 | −0.226377 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226377 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.41202 | − | 3.41202i | 0.212013 | − | 0.212013i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.7680 | + | 10.7680i | 0.666521 | + | 0.666521i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.27431i | 0.571878i | 0.958248 | + | 0.285939i | \(0.0923055\pi\) | ||||
−0.958248 | + | 0.285939i | \(0.907694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.86149i | − | 0.237209i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.23197 | + | 6.23197i | 0.381390 | + | 0.381390i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4195 | − | 13.4195i | 0.818199 | − | 0.818199i | −0.167648 | − | 0.985847i | \(-0.553617\pi\) |
0.985847 | + | 0.167648i | \(0.0536173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.5999 | −1.37285 | −0.686423 | − | 0.727202i | \(-0.740820\pi\) | ||||
−0.686423 | + | 0.727202i | \(0.740820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.6595 | 1.79507 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.84462 | + | 1.84462i | −0.111235 | + | 0.111235i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2015 | − | 16.2015i | −0.973451 | − | 0.973451i | 0.0262056 | − | 0.999657i | \(-0.491658\pi\) |
−0.999657 | + | 0.0262056i | \(0.991658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.23082i | 0.313161i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.84793i | − | 0.527824i | −0.964547 | − | 0.263912i | \(-0.914987\pi\) | ||
0.964547 | − | 0.263912i | \(-0.0850128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.3062 | − | 20.3062i | −1.20708 | − | 1.20708i | −0.971969 | − | 0.235109i | \(-0.924455\pi\) |
−0.235109 | − | 0.971969i | \(-0.575545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.90787 | − | 2.90787i | 0.172247 | − | 0.172247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3555 | 0.788348 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.2718 | 2.13364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.2668 | − | 23.2668i | 1.36392 | − | 1.36392i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.16936 | + | 7.16936i | 0.418839 | + | 0.418839i | 0.884803 | − | 0.465965i | \(-0.154293\pi\) |
−0.465965 | + | 0.884803i | \(0.654293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.40253i | 0.256325i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.85062i | − | 0.165410i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.1836 | + | 14.1836i | 0.820258 | + | 0.820258i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.76943 | − | 8.76943i | 0.505461 | − | 0.505461i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.7198 | 0.673284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.32287 | −0.190267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4308 | + | 18.4308i | −1.05190 | + | 1.05190i | −0.0533241 | + | 0.998577i | \(0.516982\pi\) |
−0.998577 | + | 0.0533241i | \(0.983018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.249910 | + | 0.249910i | 0.0142169 | + | 0.0142169i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.08961i | − | 0.402015i | −0.979590 | − | 0.201007i | \(-0.935578\pi\) | ||
0.979590 | − | 0.201007i | \(-0.0644215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0477i | 1.24621i | 0.782139 | + | 0.623104i | \(0.214129\pi\) | ||||
−0.782139 | + | 0.623104i | \(0.785871\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.18871 | − | 5.18871i | −0.292351 | − | 0.292351i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.19670 | − | 6.19670i | 0.348042 | − | 0.348042i | −0.511338 | − | 0.859380i | \(-0.670850\pi\) |
0.859380 | + | 0.511338i | \(0.170850\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.6675 | −0.877211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.15220 | 0.510826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.02076 | + | 9.02076i | −0.501929 | + | 0.501929i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.08011 | + | 3.08011i | 0.170854 | + | 0.170854i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.9845i | 1.27104i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 33.8921i | − | 1.86853i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6174 | − | 18.6174i | −1.02330 | − | 1.02330i | −0.999722 | − | 0.0235823i | \(-0.992493\pi\) |
−0.0235823 | − | 0.999722i | \(-0.507507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.98939 | − | 2.98939i | 0.163818 | − | 0.163818i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6575 | 0.636919 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2577 | 0.776666 | 0.388333 | − | 0.921519i | \(-0.373051\pi\) | ||||
0.388333 | + | 0.921519i | \(0.373051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.81462 | − | 5.81462i | 0.315807 | − | 0.315807i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.80544 | − | 3.80544i | −0.206076 | − | 0.206076i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.2778i | − | 0.878919i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 10.8343i | − | 0.583299i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.5395 | − | 23.5395i | −1.26367 | − | 1.26367i | −0.949303 | − | 0.314363i | \(-0.898209\pi\) |
−0.314363 | − | 0.949303i | \(-0.601791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.56682 | − | 1.56682i | 0.0838701 | − | 0.0838701i | −0.663927 | − | 0.747797i | \(-0.731112\pi\) |
0.747797 | + | 0.663927i | \(0.231112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.75989 | −0.254064 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.44678 | 0.502801 | 0.251401 | − | 0.967883i | \(-0.419109\pi\) | ||||
0.251401 | + | 0.967883i | \(0.419109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.30472 | + | 2.30472i | −0.122322 | + | 0.122322i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.1412 | + | 35.1412i | 1.85987 | + | 1.85987i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.0452i | 0.952392i | 0.879339 | + | 0.476196i | \(0.157985\pi\) | ||||
−0.879339 | + | 0.476196i | \(0.842015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9449i | 0.839208i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.97860 | + | 6.97860i | 0.366282 | + | 0.366282i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.97159 | + | 8.97159i | −0.469594 | + | 0.469594i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.1329 | −1.52073 | −0.760363 | − | 0.649498i | \(-0.774979\pi\) | ||||
−0.760363 | + | 0.649498i | \(0.774979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.7012 | 0.609139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90208 | + | 7.90208i | −0.410255 | + | 0.410255i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.35598 | − | 3.35598i | −0.173766 | − | 0.173766i | 0.614866 | − | 0.788632i | \(-0.289210\pi\) |
−0.788632 | + | 0.614866i | \(0.789210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.35278i | − | 0.121497i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.1612i | 1.34737i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6507 | + | 11.6507i | 0.598457 | + | 0.598457i | 0.939902 | − | 0.341445i | \(-0.110916\pi\) |
−0.341445 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4038 | − | 10.4038i | 0.533005 | − | 0.533005i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8044 | 1.11415 | 0.557077 | − | 0.830461i | \(-0.311923\pi\) | ||||
0.557077 | + | 0.830461i | \(0.311923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.54962 | 0.384764 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.68320 | − | 7.68320i | 0.390559 | − | 0.390559i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8899 | + | 11.8899i | 0.602842 | + | 0.602842i | 0.941066 | − | 0.338224i | \(-0.109826\pi\) |
−0.338224 | + | 0.941066i | \(0.609826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.6101i | 1.69973i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.1853i | − | 0.866884i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0805287 | + | 0.0805287i | 0.00405184 | + | 0.00405184i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.23905 | − | 9.23905i | 0.463694 | − | 0.463694i | −0.436170 | − | 0.899864i | \(-0.643665\pi\) |
0.899864 | + | 0.436170i | \(0.143665\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.9012 | −0.595807 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4744 | −0.722818 | −0.361409 | − | 0.932407i | \(-0.617704\pi\) | ||||
−0.361409 | + | 0.932407i | \(0.617704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.35422 | + | 6.35422i | −0.316526 | + | 0.316526i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.19667 | + | 7.19667i | 0.357605 | + | 0.357605i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.34958i | 0.215601i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.54117i | − | 0.471781i | −0.971780 | − | 0.235890i | \(-0.924199\pi\) | ||
0.971780 | − | 0.235890i | \(-0.0758006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.5112 | + | 31.5112i | 1.55433 | + | 1.55433i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.00925 | − | 9.00925i | 0.443316 | − | 0.443316i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8142 | 0.678114 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.28514 | −0.454695 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.837667 | − | 0.837667i | 0.0409227 | − | 0.0409227i | −0.686349 | − | 0.727272i | \(-0.740788\pi\) |
0.727272 | + | 0.686349i | \(0.240788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9679 | − | 17.9679i | −0.875702 | − | 0.875702i | 0.117385 | − | 0.993087i | \(-0.462549\pi\) |
−0.993087 | + | 0.117385i | \(0.962549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 29.6940i | − | 1.44377i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.29875i | 0.354042i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.79986 | + | 6.79986i | 0.329068 | + | 0.329068i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.9047 | + | 18.9047i | −0.912726 | + | 0.912726i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.85473 | 0.185676 | 0.0928380 | − | 0.995681i | \(-0.470406\pi\) | ||||
0.0928380 | + | 0.995681i | \(0.470406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5651 | −1.22858 | −0.614289 | − | 0.789081i | \(-0.710557\pi\) | ||||
−0.614289 | + | 0.789081i | \(0.710557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.99176 | − | 9.99176i | 0.479068 | − | 0.479068i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.69135 | − | 5.69135i | −0.272254 | − | 0.272254i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.1311i | 1.43808i | 0.694970 | + | 0.719039i | \(0.255418\pi\) | ||||
−0.694970 | + | 0.719039i | \(0.744582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.48732i | 0.166063i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.1625 | + | 20.1625i | 0.957948 | + | 0.957948i | 0.999151 | − | 0.0412027i | \(-0.0131189\pi\) |
−0.0412027 | + | 0.999151i | \(0.513119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.64877 | − | 2.64877i | 0.125564 | − | 0.125564i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.33610 | −0.252389 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.5827 | −1.72644 | −0.863221 | − | 0.504826i | \(-0.831557\pi\) | ||||
−0.863221 | + | 0.504826i | \(0.831557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.51265 | + | 8.51265i | −0.400845 | + | 0.400845i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.22161 | + | 4.22161i | 0.198349 | + | 0.198349i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 12.6062i | − | 0.590986i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.7340i | − | 0.782785i | −0.920224 | − | 0.391392i | \(-0.871994\pi\) | ||
0.920224 | − | 0.391392i | \(-0.128006\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.63962 | − | 5.63962i | −0.263235 | − | 0.263235i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8377 | + | 11.8377i | −0.551335 | + | 0.551335i | −0.926826 | − | 0.375491i | \(-0.877474\pi\) |
0.375491 | + | 0.926826i | \(0.377474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2711 | 1.49976 | 0.749882 | − | 0.661572i | \(-0.230110\pi\) | ||||
0.749882 | + | 0.661572i | \(0.230110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.85375 | 0.225087 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.22565 | − | 1.22565i | 0.0567163 | − | 0.0567163i | −0.678180 | − | 0.734896i | \(-0.737231\pi\) |
0.734896 | + | 0.678180i | \(0.237231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.8558 | − | 23.8558i | −1.10156 | − | 1.10156i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 34.0734i | − | 1.57002i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1791i | 0.514016i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.23593 | − | 1.23593i | −0.0567084 | − | 0.0567084i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.92328 | + | 6.92328i | −0.316995 | + | 0.316995i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.8399 | −1.31773 | −0.658865 | − | 0.752261i | \(-0.728963\pi\) | ||||
−0.658865 | + | 0.752261i | \(0.728963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.26282 | 0.331156 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.1711 | + | 22.1711i | −1.00882 | + | 1.00882i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.88909 | − | 9.88909i | −0.449041 | − | 0.449041i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.1668i | − | 1.45762i | −0.684718 | − | 0.728808i | \(-0.740075\pi\) | ||
0.684718 | − | 0.728808i | \(-0.259925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.7054i | 1.20766i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.43607 | − | 5.43607i | −0.245326 | − | 0.245326i | 0.573723 | − | 0.819049i | \(-0.305499\pi\) |
−0.819049 | + | 0.573723i | \(0.805499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.9963 | + | 30.9963i | −1.39600 | + | 1.39600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.61448 | 0.297299 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.43268 | 0.423114 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1282 | + | 17.1282i | −0.766762 | + | 0.766762i | −0.977535 | − | 0.210773i | \(-0.932402\pi\) |
0.210773 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.3564 | − | 11.3564i | −0.507365 | − | 0.507365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.5180i | 1.04862i | 0.851529 | + | 0.524308i | \(0.175676\pi\) | ||||
−0.851529 | + | 0.524308i | \(0.824324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.98126i | − | 0.221663i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.93890 | + | 9.93890i | 0.441402 | + | 0.441402i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3147 | + | 20.3147i | −0.900434 | + | 0.900434i | −0.995474 | − | 0.0950391i | \(-0.969702\pi\) |
0.0950391 | + | 0.995474i | \(0.469702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.7186 | 1.62434 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.90997 | 0.0843271 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.106219 | − | 0.106219i | 0.00468057 | − | 0.00468057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6025 | + | 21.6025i | 0.950077 | + | 0.950077i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.9328i | − | 0.743268i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.5082i | − | 1.55564i | −0.628487 | − | 0.777820i | \(-0.716325\pi\) | ||
0.628487 | − | 0.777820i | \(-0.283675\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.677766 | + | 0.677766i | 0.0296366 | + | 0.0296366i | 0.721770 | − | 0.692133i | \(-0.243329\pi\) |
−0.692133 | + | 0.721770i | \(0.743329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.81468 | + | 4.81468i | −0.210130 | + | 0.210130i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0572 | −0.655904 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.79485 | 0.0780371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.89332 | − | 7.89332i | 0.342541 | − | 0.342541i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.2142 | + | 14.2142i | 0.615686 | + | 0.615686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.88996i | − | 0.168178i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.45007i | 0.235188i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.53704 | − | 2.53704i | −0.109278 | − | 0.109278i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.37099 | + | 5.37099i | −0.230917 | + | 0.230917i | −0.813075 | − | 0.582158i | \(-0.802208\pi\) |
0.582158 | + | 0.813075i | \(0.302208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −55.8181 | −2.39539 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.76908 | 0.418461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.86782 | − | 8.86782i | 0.379161 | − | 0.379161i | −0.491639 | − | 0.870799i | \(-0.663602\pi\) |
0.870799 | + | 0.491639i | \(0.163602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.95760 | + | 5.95760i | 0.254264 | + | 0.254264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.4975i | − | 0.447209i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.329585i | − | 0.0140154i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.77390 | − | 2.77390i | −0.117745 | − | 0.117745i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8089 | − | 22.8089i | 0.966446 | − | 0.966446i | −0.0330091 | − | 0.999455i | \(-0.510509\pi\) |
0.999455 | + | 0.0330091i | \(0.0105090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.6666 | 0.789513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.7973 | −1.89135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.9711 | − | 20.9711i | 0.883826 | − | 0.883826i | −0.110095 | − | 0.993921i | \(-0.535116\pi\) |
0.993921 | + | 0.110095i | \(0.0351156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.47139 | − | 2.47139i | −0.103972 | − | 0.103972i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 29.4543i | − | 1.23696i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.05295i | − | 0.337597i | −0.985651 | − | 0.168799i | \(-0.946011\pi\) | ||
0.985651 | − | 0.168799i | \(-0.0539888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5040 | − | 22.5040i | −0.941762 | − | 0.941762i | 0.0566333 | − | 0.998395i | \(-0.481963\pi\) |
−0.998395 | + | 0.0566333i | \(0.981963\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.74599 | − | 9.74599i | 0.407144 | − | 0.407144i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.60490 | −0.192038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.9819 | 0.665334 | 0.332667 | − | 0.943044i | \(-0.392051\pi\) | ||||
0.332667 | + | 0.943044i | \(0.392051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0401200 | − | 0.0401200i | 0.00166733 | − | 0.00166733i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.2692 | − | 28.2692i | −1.17280 | − | 1.17280i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.0734i | − | 0.417199i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 11.0447i | − | 0.456642i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.25752 | − | 5.25752i | −0.217001 | − | 0.217001i | 0.590232 | − | 0.807233i | \(-0.299036\pi\) |
−0.807233 | + | 0.590232i | \(0.799036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.54971 | − | 2.54971i | 0.105059 | − | 0.105059i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.6057 | 2.04050 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.96571 | 0.162852 | 0.0814260 | − | 0.996679i | \(-0.474053\pi\) | ||||
0.0814260 | + | 0.996679i | \(0.474053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9360 | − | 14.9360i | 0.612318 | − | 0.612318i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.7132 | + | 22.7132i | 0.929589 | + | 0.929589i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.31600i | − | 0.339783i | −0.985463 | − | 0.169891i | \(-0.945658\pi\) | ||
0.985463 | − | 0.169891i | \(-0.0543417\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.0550i | − | 1.87862i | −0.343068 | − | 0.939310i | \(-0.611466\pi\) | ||
0.343068 | − | 0.939310i | \(-0.388534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.9009 | − | 20.9009i | −0.851149 | − | 0.851149i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.96612 | − | 2.96612i | 0.120590 | − | 0.120590i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.05760 | 0.205282 | 0.102641 | − | 0.994718i | \(-0.467271\pi\) | ||||
0.102641 | + | 0.994718i | \(0.467271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.8940 | −1.65711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.0713 | − | 36.0713i | 1.45929 | − | 1.45929i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2000 | − | 31.2000i | −1.26016 | − | 1.26016i | −0.951016 | − | 0.309141i | \(-0.899958\pi\) |
−0.309141 | − | 0.951016i | \(-0.600042\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 10.8577i | − | 0.437824i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.7412i | 1.23759i | 0.785551 | + | 0.618796i | \(0.212379\pi\) | ||||
−0.785551 | + | 0.618796i | \(0.787621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8766 | − | 16.8766i | −0.678329 | − | 0.678329i | 0.281293 | − | 0.959622i | \(-0.409237\pi\) |
−0.959622 | + | 0.281293i | \(0.909237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.55813 | − | 3.55813i | 0.142783 | − | 0.142783i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8408 | −0.434328 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.58574 | − | 7.58574i | 0.302945 | − | 0.302945i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.60515 | + | 8.60515i | 0.343110 | + | 0.343110i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.7318i | − | 1.22342i | −0.791084 | − | 0.611708i | \(-0.790483\pi\) | ||
0.791084 | − | 0.611708i | \(-0.209517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 8.15539i | − | 0.324147i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.42195 | − | 4.42195i | −0.175480 | − | 0.175480i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.23628 | + | 4.23628i | −0.167848 | + | 0.167848i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.26430 | 0.326931 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1658 | 0.875496 | 0.437748 | − | 0.899098i | \(-0.355776\pi\) | ||||
0.437748 | + | 0.899098i | \(0.355776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.975773 | − | 0.975773i | 0.0384807 | − | 0.0384807i | −0.687605 | − | 0.726085i | \(-0.741338\pi\) |
0.726085 | + | 0.687605i | \(0.241338\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.12935 | − | 7.12935i | −0.280718 | − | 0.280718i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.2610i | 0.914484i | 0.889342 | + | 0.457242i | \(0.151163\pi\) | ||||
−0.889342 | + | 0.457242i | \(0.848837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4848i | 0.450819i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.93263 | − | 9.93263i | −0.389290 | − | 0.389290i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.9372 | − | 23.9372i | 0.936735 | − | 0.936735i | −0.0613792 | − | 0.998115i | \(-0.519550\pi\) |
0.998115 | + | 0.0613792i | \(0.0195499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.30427 | −0.285401 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.1704 | 1.25509 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1064 | + | 14.1064i | −0.549508 | + | 0.549508i | −0.926299 | − | 0.376790i | \(-0.877028\pi\) |
0.376790 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.04121 | + | 3.04121i | 0.118289 | + | 0.118289i | 0.763774 | − | 0.645484i | \(-0.223344\pi\) |
−0.645484 | + | 0.763774i | \(0.723344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 74.8014i | 2.90505i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.05838i | 0.196156i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5561 | − | 19.5561i | −0.757215 | − | 0.757215i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.2052 | − | 23.2052i | 0.897166 | − | 0.897166i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.66835 | −0.334638 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.3628 | −0.977662 | −0.488831 | − | 0.872378i | \(-0.662577\pi\) | ||||
−0.488831 | + | 0.872378i | \(0.662577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.772683 | − | 0.772683i | 0.0297406 | − | 0.0297406i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.36526 | − | 9.36526i | −0.359936 | − | 0.359936i | 0.503853 | − | 0.863789i | \(-0.331915\pi\) |
−0.863789 | + | 0.503853i | \(0.831915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.4737i | 1.55324i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7695i | 0.565967i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.20530 | + | 4.20530i | 0.160911 | + | 0.160911i | 0.782970 | − | 0.622059i | \(-0.213704\pi\) |
−0.622059 | + | 0.782970i | \(0.713704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3932 | − | 13.3932i | 0.511728 | − | 0.511728i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.8035 | −0.679245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.8204 | −0.640804 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.79295 | − | 5.79295i | 0.220374 | − | 0.220374i | −0.588282 | − | 0.808656i | \(-0.700195\pi\) |
0.808656 | + | 0.588282i | \(0.200195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.5358 | − | 13.5358i | −0.514181 | − | 0.514181i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.94646i | 0.149698i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.6826i | 1.27582i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8592 | + | 19.8592i | 0.751142 | + | 0.751142i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.258991 | − | 0.258991i | 0.00978196 | − | 0.00978196i | −0.702199 | − | 0.711981i | \(-0.747798\pi\) |
0.711981 | + | 0.702199i | \(0.247798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.91430 | −0.109915 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.5535 | −1.03772 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.1936 | + | 10.1936i | −0.383368 | + | 0.383368i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.751674 | + | 0.751674i | 0.0282297 | + | 0.0282297i | 0.721081 | − | 0.692851i | \(-0.243646\pi\) |
−0.692851 | + | 0.721081i | \(0.743646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.288761i | − | 0.0108294i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.49986i | − | 0.355773i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.03505 | + | 8.03505i | 0.300494 | + | 0.300494i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.9029 | + | 27.9029i | −1.04205 | + | 1.04205i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.6557 | −1.47891 | −0.739455 | − | 0.673206i | \(-0.764917\pi\) | ||||
−0.739455 | + | 0.673206i | \(0.764917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.434730 | −0.0161902 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6495 | − | 36.6495i | 1.36301 | − | 1.36301i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.24680 | − | 4.24680i | −0.157722 | − | 0.157722i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.2952i | − | 0.826881i | −0.910531 | − | 0.413441i | \(-0.864327\pi\) | ||
0.910531 | − | 0.413441i | \(-0.135673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 18.0930i | − | 0.670112i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.1166 | + | 22.1166i | 0.818011 | + | 0.818011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.2309 | + | 28.2309i | −1.04273 | + | 1.04273i | −0.0436851 | + | 0.999045i | \(0.513910\pi\) |
−0.999045 | + | 0.0436851i | \(0.986090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.23593 | 0.119359 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.4109 | 1.12020 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.45140 | + | 5.45140i | −0.200533 | + | 0.200533i | −0.800228 | − | 0.599695i | \(-0.795288\pi\) |
0.599695 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.6665 | − | 12.6665i | −0.465314 | − | 0.465314i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 52.5667i | − | 1.92849i | −0.265020 | − | 0.964243i | \(-0.585379\pi\) | ||
0.265020 | − | 0.964243i | \(-0.414621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.26800i | 0.0830931i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.7676 | − | 24.7676i | −0.906200 | − | 0.906200i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.96035 | + | 7.96035i | −0.290865 | + | 0.290865i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0189 | −1.13190 | −0.565948 | − | 0.824441i | \(-0.691490\pi\) | ||||
−0.565948 | + | 0.824441i | \(0.691490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0910 | −0.805040 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.79431 | − | 1.79431i | 0.0653016 | − | 0.0653016i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.47389 | + | 2.47389i | 0.0899152 | + | 0.0899152i | 0.750634 | − | 0.660719i | \(-0.229748\pi\) |
−0.660719 | + | 0.750634i | \(0.729748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 28.2634i | − | 1.02590i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.48375i | − | 0.0900358i | −0.998986 | − | 0.0450179i | \(-0.985666\pi\) | ||
0.998986 | − | 0.0450179i | \(-0.0143345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.9913 | − | 19.9913i | −0.723733 | − | 0.723733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.0860 | − | 13.0860i | 0.473125 | − | 0.473125i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1771 | 0.692444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.4690 | 1.56753 | 0.783767 | − | 0.621055i | \(-0.213296\pi\) | ||||
0.783767 | + | 0.621055i | \(0.213296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0752 | − | 12.0752i | 0.434879 | − | 0.434879i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.297026 | − | 0.297026i | −0.0106833 | − | 0.0106833i | 0.701745 | − | 0.712428i | \(-0.252405\pi\) |
−0.712428 | + | 0.701745i | \(0.752405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.06299i | − | 0.0741047i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.3529i | 0.407283i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.70363 | − | 5.70363i | −0.204354 | − | 0.204354i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.01231 | + | 6.01231i | −0.215137 | + | 0.215137i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.56286 | 0.234537 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.4822 | −0.516892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.6931 | + | 23.6931i | −0.844567 | + | 0.844567i | −0.989449 | − | 0.144882i | \(-0.953720\pi\) |
0.144882 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4293 | − | 15.4293i | −0.549299 | − | 0.549299i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1148i | 0.359641i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.4742i | 0.513993i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.42421 | + | 6.42421i | 0.227843 | + | 0.227843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.2292 | + | 38.2292i | −1.35415 | + | 1.35415i | −0.473186 | + | 0.880963i | \(0.656896\pi\) |
−0.880963 | + | 0.473186i | \(0.843104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 85.4762 | 3.02393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.49801 | −0.335596 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4041 | + | 23.4041i | −0.825913 | + | 0.825913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.42340 | + | 9.42340i | 0.332131 | + | 0.332131i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.6509i | 1.57179i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.8310i | 1.89260i | 0.323296 | + | 0.946298i | \(0.395209\pi\) | ||||
−0.323296 | + | 0.946298i | \(0.604791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0549 | + | 27.0549i | 0.950025 | + | 0.950025i | 0.998809 | − | 0.0487847i | \(-0.0155348\pi\) |
−0.0487847 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.5986 | − | 37.5986i | 1.31864 | − | 1.31864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.3506 | 0.397593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.49020 | −0.262049 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.6017 | + | 22.6017i | −0.789766 | + | 0.789766i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2170 | + | 24.2170i | 0.845180 | + | 0.845180i | 0.989527 | − | 0.144347i | \(-0.0461082\pi\) |
−0.144347 | + | 0.989527i | \(0.546108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.3013i | 1.43967i | 0.694144 | + | 0.719836i | \(0.255783\pi\) | ||||
−0.694144 | + | 0.719836i | \(0.744217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.13767i | − | 0.213686i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7264 | + | 15.7264i | 0.546862 | + | 0.546862i | 0.925532 | − | 0.378670i | \(-0.123618\pi\) |
−0.378670 | + | 0.925532i | \(0.623618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7323 | − | 20.7323i | 0.720061 | − | 0.720061i | −0.248556 | − | 0.968618i | \(-0.579956\pi\) |
0.968618 | + | 0.248556i | \(0.0799560\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.9075 | 1.87003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.0385 | −0.347813 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.82679 | + | 4.82679i | −0.167038 | + | 0.167038i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.59404 | + | 1.59404i | 0.0550980 | + | 0.0550980i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 43.6919i | − | 1.50841i | −0.656638 | − | 0.754206i | \(-0.728022\pi\) | ||
0.656638 | − | 0.754206i | \(-0.271978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.07060i | − | 0.243814i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.7200 | + | 14.7200i | 0.506983 | + | 0.506983i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.22433 | − | 4.22433i | 0.145321 | − | 0.145321i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.1396 | −0.417122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 67.5654 | 2.31884 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.42913 | + | 5.42913i | −0.186108 | + | 0.186108i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0610 | + | 35.0610i | 1.20046 | + | 1.20046i | 0.974025 | + | 0.226439i | \(0.0727084\pi\) |
0.226439 | + | 0.974025i | \(0.427292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.43182i | 0.151565i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 45.3397i | − | 1.54878i | −0.632711 | − | 0.774388i | \(-0.718058\pi\) | ||
0.632711 | − | 0.774388i | \(-0.281942\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.1229 | + | 32.1229i | 1.09602 | + | 1.09602i | 0.994871 | + | 0.101147i | \(0.0322514\pi\) |
0.101147 | + | 0.994871i | \(0.467749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.2190 | + | 22.2190i | −0.757221 | + | 0.757221i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.9142 | −1.25657 | −0.628287 | − | 0.777981i | \(-0.716244\pi\) | ||||
−0.628287 | + | 0.777981i | \(0.716244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.19695 | −0.244704 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −60.3441 | + | 60.3441i | −2.04939 | + | 2.04939i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.210075 | + | 0.210075i | 0.00712630 | + | 0.00712630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 50.7793i | − | 1.72059i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.4604i | 1.20015i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.04638 | + | 2.04638i | 0.0691804 | + | 0.0691804i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7178 | − | 15.7178i | 0.530753 | − | 0.530753i | −0.390044 | − | 0.920796i | \(-0.627540\pi\) |
0.920796 | + | 0.390044i | \(0.127540\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.8548 | −0.804603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16748 | 0.0393335 | 0.0196667 | − | 0.999807i | \(-0.493739\pi\) | ||||
0.0196667 | + | 0.999807i | \(0.493739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2410 | − | 32.2410i | 1.08500 | − | 1.08500i | 0.0889621 | − | 0.996035i | \(-0.471645\pi\) |
0.996035 | − | 0.0889621i | \(-0.0283550\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.32432 | − | 7.32432i | −0.246204 | − | 0.246204i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.7282i | 1.43467i | 0.696728 | + | 0.717336i | \(0.254639\pi\) | ||||
−0.696728 | + | 0.717336i | \(0.745361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0980i | 0.606987i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.7739 | + | 18.7739i | 0.628949 | + | 0.628949i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.4741 | + | 14.4741i | −0.484356 | + | 0.484356i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.31644 | 0.0774302 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.1935 | −1.57574 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.76109 | − | 8.76109i | 0.292199 | − | 0.292199i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.9291 | − | 19.9291i | −0.663935 | − | 0.663935i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.1788i | 0.971008i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.7244i | 0.788625i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.23335 | + | 1.23335i | 0.0409528 | + | 0.0409528i | 0.727287 | − | 0.686334i | \(-0.240781\pi\) |
−0.686334 | + | 0.727287i | \(0.740781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.93093 | + | 8.93093i | −0.296220 | + | 0.296220i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.9284 | −0.792785 | −0.396392 | − | 0.918081i | \(-0.629738\pi\) | ||||
−0.396392 | + | 0.918081i | \(0.629738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0371 | 1.19265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.52814 | − | 5.52814i | 0.182755 | − | 0.182755i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9473 | + | 14.9473i | 0.493605 | + | 0.493605i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.3844i | 1.49709i | 0.663082 | + | 0.748546i | \(0.269248\pi\) | ||||
−0.663082 | + | 0.748546i | \(0.730752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 61.3253i | − | 2.02074i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0392 | + | 10.0392i | 0.330444 | + | 0.330444i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.17899 | + | 1.17899i | −0.0387649 | + | 0.0387649i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.380882 | −0.0125098 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.51036 | −0.213598 | −0.106799 | − | 0.994281i | \(-0.534060\pi\) | ||||
−0.106799 | + | 0.994281i | \(0.534060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.69986 | − | 1.69986i | 0.0557107 | − | 0.0557107i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7947 | + | 11.7947i | 0.386142 | + | 0.386142i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.0402i | 0.622681i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.2986i | − | 1.31650i | −0.752801 | − | 0.658248i | \(-0.771298\pi\) | ||
0.752801 | − | 0.658248i | \(-0.228702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.6799 | − | 36.6799i | −1.19700 | − | 1.19700i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10649 | + | 1.10649i | −0.0360705 | + | 0.0360705i | −0.724912 | − | 0.688841i | \(-0.758120\pi\) |
0.688841 | + | 0.724912i | \(0.258120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.2509 | −0.692025 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.16241 | −0.102873 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.83833 | + | 8.83833i | −0.287207 | + | 0.287207i | −0.835975 | − | 0.548768i | \(-0.815097\pi\) |
0.548768 | + | 0.835975i | \(0.315097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.0796 | + | 39.0796i | 1.26858 | + | 1.26858i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.6185i | 0.668600i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.9610i | 0.484636i | 0.970197 | + | 0.242318i | \(0.0779077\pi\) | ||||
−0.970197 | + | 0.242318i | \(0.922092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.14234 | − | 4.14234i | −0.134043 | − | 0.134043i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.0654 | − | 26.0654i | 0.842576 | − | 0.842576i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −54.8152 | −1.77008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7441 | −0.862712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.97433 | + | 6.97433i | −0.224745 | + | 0.224745i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0170522 | − | 0.0170522i | −0.000548930 | − | 0.000548930i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.95287i | 0.127116i | 0.997978 | + | 0.0635578i | \(0.0202447\pi\) | ||||
−0.997978 | + | 0.0635578i | \(0.979755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 30.0150i | − | 0.964221i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.0538 | − | 29.0538i | −0.932380 | − | 0.932380i | 0.0654740 | − | 0.997854i | \(-0.479144\pi\) |
−0.997854 | + | 0.0654740i | \(0.979144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.07597 | − | 8.07597i | 0.258904 | − | 0.258904i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.2485 | −0.328215 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8962 | 0.828494 | 0.414247 | − | 0.910164i | \(-0.364045\pi\) | ||||
0.414247 | + | 0.910164i | \(0.364045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.90984 | − | 6.90984i | 0.220839 | − | 0.220839i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.5151 | − | 17.5151i | −0.559213 | − | 0.559213i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 22.0151i | − | 0.702173i | −0.936343 | − | 0.351087i | \(-0.885812\pi\) | ||
0.936343 | − | 0.351087i | \(-0.114188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 21.0839i | − | 0.671789i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.3850 | + | 56.3850i | 1.79476 | + | 1.79476i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.9537 | + | 13.9537i | −0.443702 | + | 0.443702i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.3207 | 1.72556 | 0.862778 | − | 0.505583i | \(-0.168723\pi\) | ||||
0.862778 | + | 0.505583i | \(0.168723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.9461 | 1.96580 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.65378 | − | 9.65378i | 0.306045 | − | 0.306045i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.14405 | − | 8.14405i | −0.257925 | − | 0.257925i | 0.566285 | − | 0.824210i | \(-0.308380\pi\) |
−0.824210 | + | 0.566285i | \(0.808380\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.82197i | − | 0.0576446i |
(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 | 640.2.l.a.481.2 | 16 | ||
4.3 | odd | 2 | 640.2.l.b.481.7 | 16 | |||
8.3 | odd | 2 | 80.2.l.a.21.4 | ✓ | 16 | ||
8.5 | even | 2 | 320.2.l.a.241.7 | 16 | |||
16.3 | odd | 4 | 640.2.l.b.161.7 | 16 | |||
16.5 | even | 4 | 320.2.l.a.81.7 | 16 | |||
16.11 | odd | 4 | 80.2.l.a.61.4 | yes | 16 | ||
16.13 | even | 4 | inner | 640.2.l.a.161.2 | 16 | ||
24.5 | odd | 2 | 2880.2.t.c.2161.6 | 16 | |||
24.11 | even | 2 | 720.2.t.c.181.5 | 16 | |||
32.3 | odd | 8 | 5120.2.a.s.1.8 | 8 | |||
32.13 | even | 8 | 5120.2.a.t.1.8 | 8 | |||
32.19 | odd | 8 | 5120.2.a.v.1.1 | 8 | |||
32.29 | even | 8 | 5120.2.a.u.1.1 | 8 | |||
40.3 | even | 4 | 400.2.q.h.149.7 | 16 | |||
40.13 | odd | 4 | 1600.2.q.g.49.7 | 16 | |||
40.19 | odd | 2 | 400.2.l.h.101.5 | 16 | |||
40.27 | even | 4 | 400.2.q.g.149.2 | 16 | |||
40.29 | even | 2 | 1600.2.l.i.1201.2 | 16 | |||
40.37 | odd | 4 | 1600.2.q.h.49.2 | 16 | |||
48.5 | odd | 4 | 2880.2.t.c.721.7 | 16 | |||
48.11 | even | 4 | 720.2.t.c.541.5 | 16 | |||
80.27 | even | 4 | 400.2.q.h.349.7 | 16 | |||
80.37 | odd | 4 | 1600.2.q.g.849.7 | 16 | |||
80.43 | even | 4 | 400.2.q.g.349.2 | 16 | |||
80.53 | odd | 4 | 1600.2.q.h.849.2 | 16 | |||
80.59 | odd | 4 | 400.2.l.h.301.5 | 16 | |||
80.69 | even | 4 | 1600.2.l.i.401.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.4 | ✓ | 16 | 8.3 | odd | 2 | ||
80.2.l.a.61.4 | yes | 16 | 16.11 | odd | 4 | ||
320.2.l.a.81.7 | 16 | 16.5 | even | 4 | |||
320.2.l.a.241.7 | 16 | 8.5 | even | 2 | |||
400.2.l.h.101.5 | 16 | 40.19 | odd | 2 | |||
400.2.l.h.301.5 | 16 | 80.59 | odd | 4 | |||
400.2.q.g.149.2 | 16 | 40.27 | even | 4 | |||
400.2.q.g.349.2 | 16 | 80.43 | even | 4 | |||
400.2.q.h.149.7 | 16 | 40.3 | even | 4 | |||
400.2.q.h.349.7 | 16 | 80.27 | even | 4 | |||
640.2.l.a.161.2 | 16 | 16.13 | even | 4 | inner | ||
640.2.l.a.481.2 | 16 | 1.1 | even | 1 | trivial | ||
640.2.l.b.161.7 | 16 | 16.3 | odd | 4 | |||
640.2.l.b.481.7 | 16 | 4.3 | odd | 2 | |||
720.2.t.c.181.5 | 16 | 24.11 | even | 2 | |||
720.2.t.c.541.5 | 16 | 48.11 | even | 4 | |||
1600.2.l.i.401.2 | 16 | 80.69 | even | 4 | |||
1600.2.l.i.1201.2 | 16 | 40.29 | even | 2 | |||
1600.2.q.g.49.7 | 16 | 40.13 | odd | 4 | |||
1600.2.q.g.849.7 | 16 | 80.37 | odd | 4 | |||
1600.2.q.h.49.2 | 16 | 40.37 | odd | 4 | |||
1600.2.q.h.849.2 | 16 | 80.53 | odd | 4 | |||
2880.2.t.c.721.7 | 16 | 48.5 | odd | 4 | |||
2880.2.t.c.2161.6 | 16 | 24.5 | odd | 2 | |||
5120.2.a.s.1.8 | 8 | 32.3 | odd | 8 | |||
5120.2.a.t.1.8 | 8 | 32.13 | even | 8 | |||
5120.2.a.u.1.1 | 8 | 32.29 | even | 8 | |||
5120.2.a.v.1.1 | 8 | 32.19 | odd | 8 |