Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(127,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.w (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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 703.6 | ||
Root | \(-1.35818 - 0.394157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.703 |
Dual form | 960.2.w.g.127.6 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.75233 | − | 1.38900i | 0.783667 | − | 0.621181i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47817 | − | 2.47817i | −0.936661 | − | 0.936661i | 0.0614493 | − | 0.998110i | \(-0.480428\pi\) |
−0.998110 | + | 0.0614493i | \(0.980428\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.02831i | − | 0.913069i | −0.889706 | − | 0.456534i | \(-0.849091\pi\) | ||
0.889706 | − | 0.456534i | \(-0.150909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.363328 | − | 0.363328i | −0.100769 | − | 0.100769i | 0.654925 | − | 0.755694i | \(-0.272700\pi\) |
−0.755694 | + | 0.654925i | \(0.772700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.256912 | − | 2.22126i | 0.0663344 | − | 0.573527i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.36333 | + | 2.36333i | −0.573191 | + | 0.573191i | −0.933019 | − | 0.359828i | \(-0.882836\pi\) |
0.359828 | + | 0.933019i | \(0.382836\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.95634 | −1.13706 | −0.568532 | − | 0.822661i | \(-0.692488\pi\) | ||||
−0.568532 | + | 0.822661i | \(0.692488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.50466 | −0.764780 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.900390 | − | 0.900390i | 0.187744 | − | 0.187744i | −0.606976 | − | 0.794720i | \(-0.707618\pi\) |
0.794720 | + | 0.606976i | \(0.207618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14134 | − | 4.86799i | 0.228267 | − | 0.973599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.50466i | 0.650800i | 0.945576 | + | 0.325400i | \(0.105499\pi\) | ||||
−0.945576 | + | 0.325400i | \(0.894501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.85607i | 0.692571i | 0.938129 | + | 0.346286i | \(0.112557\pi\) | ||||
−0.938129 | + | 0.346286i | \(0.887443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.14134 | − | 2.14134i | −0.372759 | − | 0.372759i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.78477 | − | 0.900390i | −1.31587 | − | 0.152194i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.363328 | − | 0.363328i | 0.0597308 | − | 0.0597308i | −0.676610 | − | 0.736341i | \(-0.736552\pi\) |
0.736341 | + | 0.676610i | \(0.236552\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.513824 | −0.0822776 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.72666 | 0.425832 | 0.212916 | − | 0.977070i | \(-0.431704\pi\) | ||||
0.212916 | + | 0.977070i | \(0.431704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.92870 | − | 3.92870i | 0.599121 | − | 0.599121i | −0.340958 | − | 0.940079i | \(-0.610751\pi\) |
0.940079 | + | 0.340958i | \(0.110751\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.38900 | − | 1.75233i | −0.207060 | − | 0.261222i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.85673 | − | 5.85673i | −0.854292 | − | 0.854292i | 0.136366 | − | 0.990659i | \(-0.456458\pi\) |
−0.990659 | + | 0.136366i | \(0.956458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.28267i | 0.754667i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.34225i | 0.468009i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.14134 | − | 3.14134i | −0.431496 | − | 0.431496i | 0.457641 | − | 0.889137i | \(-0.348694\pi\) |
−0.889137 | + | 0.457641i | \(0.848694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.20633 | − | 5.30660i | −0.567181 | − | 0.715542i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50466 | + | 3.50466i | −0.464204 | + | 0.464204i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.68516 | 1.13071 | 0.565356 | − | 0.824847i | \(-0.308739\pi\) | ||||
0.565356 | + | 0.824847i | \(0.308739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.2920 | 1.95794 | 0.978970 | − | 0.204004i | \(-0.0653956\pi\) | ||||
0.978970 | + | 0.204004i | \(0.0653956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.47817 | + | 2.47817i | −0.312220 | + | 0.312220i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.14134 | − | 0.132007i | −0.141565 | − | 0.0163735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.92870 | − | 3.92870i | −0.479967 | − | 0.479967i | 0.425154 | − | 0.905121i | \(-0.360220\pi\) |
−0.905121 | + | 0.425154i | \(0.860220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.27334i | − | 0.153293i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.25583i | − | 0.505075i | −0.967587 | − | 0.252537i | \(-0.918735\pi\) | ||
0.967587 | − | 0.252537i | \(-0.0812650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.28267 | + | 9.28267i | 1.08645 | + | 1.08645i | 0.995891 | + | 0.0905640i | \(0.0288670\pi\) |
0.0905640 | + | 0.995891i | \(0.471133\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.63514 | − | 4.24924i | −0.304280 | − | 0.490660i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50466 | + | 7.50466i | −0.855236 | + | 0.855236i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.399759 | −0.0449764 | −0.0224882 | − | 0.999747i | \(-0.507159\pi\) | ||||
−0.0224882 | + | 0.999747i | \(0.507159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.199879 | + | 0.199879i | −0.0219396 | + | 0.0219396i | −0.717991 | − | 0.696052i | \(-0.754938\pi\) |
0.696052 | + | 0.717991i | \(0.254938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.858664 | + | 7.42401i | −0.0931352 | + | 0.805247i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.47817 | + | 2.47817i | 0.265688 | + | 0.265688i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.28267i | − | 0.453962i | −0.973899 | − | 0.226981i | \(-0.927114\pi\) | ||
0.973899 | − | 0.226981i | \(-0.0728856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80078i | 0.188773i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.72666 | + | 2.72666i | 0.282741 | + | 0.282741i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.68516 | + | 6.88438i | −0.891079 | + | 0.706323i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.73599 | − | 6.73599i | 0.683936 | − | 0.683936i | −0.276949 | − | 0.960885i | \(-0.589323\pi\) |
0.960885 | + | 0.276949i | \(0.0893233\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.02831 | −0.304356 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.78734 | −0.575862 | −0.287931 | − | 0.957651i | \(-0.592967\pi\) | ||||
−0.287931 | + | 0.957651i | \(0.592967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0914 | − | 13.0914i | 1.28993 | − | 1.28993i | 0.355104 | − | 0.934827i | \(-0.384445\pi\) |
0.934827 | − | 0.355104i | \(-0.115555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.14134 | + | 4.86799i | −0.599333 | + | 0.475067i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.71281 | − | 9.71281i | −0.938973 | − | 0.938973i | 0.0592694 | − | 0.998242i | \(-0.481123\pi\) |
−0.998242 | + | 0.0592694i | \(0.981123\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.4626i | − | 1.00214i | −0.865407 | − | 0.501070i | \(-0.832940\pi\) | ||
0.865407 | − | 0.501070i | \(-0.167060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.513824i | − | 0.0487700i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6460 | − | 10.6460i | −1.00149 | − | 1.00149i | −0.999999 | − | 0.00149259i | \(-0.999525\pi\) |
−0.00149259 | − | 0.999999i | \(-0.500475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.327137 | − | 2.82843i | 0.0305057 | − | 0.263752i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.363328 | + | 0.363328i | −0.0335897 | + | 0.0335897i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7135 | 1.07377 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.82936 | 0.166305 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.92804 | − | 1.92804i | 0.173845 | − | 0.173845i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.76166 | − | 10.1157i | −0.425896 | − | 0.904772i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.77766 | + | 1.77766i | 0.157742 | + | 0.157742i | 0.781565 | − | 0.623823i | \(-0.214422\pi\) |
−0.623823 | + | 0.781565i | \(0.714422\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.55602i | − | 0.489180i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1981i | 1.58997i | 0.606626 | + | 0.794987i | \(0.292523\pi\) | ||||
−0.606626 | + | 0.794987i | \(0.707477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2827 | + | 12.2827i | 1.06504 | + | 1.06504i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.22126 | − | 0.256912i | −0.191176 | − | 0.0221115i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.91934 | + | 5.91934i | −0.505724 | + | 0.505724i | −0.913211 | − | 0.407487i | \(-0.866405\pi\) |
0.407487 | + | 0.913211i | \(0.366405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4140 | 1.05294 | 0.526470 | − | 0.850194i | \(-0.323515\pi\) | ||||
0.526470 | + | 0.850194i | \(0.323515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.28267 | −0.697527 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.10027 | + | 1.10027i | −0.0920091 | + | 0.0920091i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.86799 | + | 6.14134i | 0.404265 | + | 0.510010i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.73541 | + | 3.73541i | 0.308092 | + | 0.308092i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.78734i | − | 0.474117i | −0.971495 | − | 0.237059i | \(-0.923817\pi\) | ||
0.971495 | − | 0.237059i | \(-0.0761833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0708i | 1.47058i | 0.677751 | + | 0.735292i | \(0.262955\pi\) | ||||
−0.677751 | + | 0.735292i | \(0.737045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.36333 | + | 2.36333i | 0.191064 | + | 0.191064i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.35610 | + | 6.75712i | 0.430213 | + | 0.542745i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.91934 | − | 3.91934i | 0.312798 | − | 0.312798i | −0.533195 | − | 0.845992i | \(-0.679009\pi\) |
0.845992 | + | 0.533195i | \(0.179009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.44252 | −0.352315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.46264 | −0.351705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.22819 | + | 3.22819i | −0.252851 | + | 0.252851i | −0.822139 | − | 0.569287i | \(-0.807219\pi\) |
0.569287 | + | 0.822139i | \(0.307219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.72666 | − | 0.778008i | −0.523669 | − | 0.0605678i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.95700 | + | 6.95700i | 0.538349 | + | 0.538349i | 0.923044 | − | 0.384695i | \(-0.125693\pi\) |
−0.384695 | + | 0.923044i | \(0.625693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7360i | − | 0.979691i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.95634i | 0.379021i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.627343 | − | 0.627343i | −0.0476960 | − | 0.0476960i | 0.682857 | − | 0.730553i | \(-0.260737\pi\) |
−0.730553 | + | 0.682857i | \(0.760737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.8921 | + | 9.23530i | −1.12574 | + | 0.698123i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.14134 | − | 6.14134i | 0.461611 | − | 0.461611i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.93968 | 0.668183 | 0.334091 | − | 0.942541i | \(-0.391571\pi\) | ||||
0.334091 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00933 | 0.0750228 | 0.0375114 | − | 0.999296i | \(-0.488057\pi\) | ||||
0.0375114 | + | 0.999296i | \(0.488057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8131 | − | 10.8131i | 0.799326 | − | 0.799326i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.132007 | − | 1.14134i | 0.00970538 | − | 0.0839127i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.15688 | + | 7.15688i | 0.523363 | + | 0.523363i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.50466i | 0.254927i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6262i | 1.56481i | 0.622768 | + | 0.782407i | \(0.286008\pi\) | ||||
−0.622768 | + | 0.782407i | \(0.713992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5653 | + | 11.5653i | 0.832492 | + | 0.832492i | 0.987857 | − | 0.155365i | \(-0.0496555\pi\) |
−0.155365 | + | 0.987857i | \(0.549655\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.900390 | + | 0.713703i | −0.0644783 | + | 0.0511093i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.42401 | − | 9.42401i | 0.671433 | − | 0.671433i | −0.286614 | − | 0.958046i | \(-0.592530\pi\) |
0.958046 | + | 0.286614i | \(0.0925296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0130 | 0.780688 | 0.390344 | − | 0.920669i | \(-0.372356\pi\) | ||||
0.390344 | + | 0.920669i | \(0.372356\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.55602 | −0.391891 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.68516 | − | 8.68516i | 0.609579 | − | 0.609579i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.77801 | − | 3.78734i | 0.333711 | − | 0.264519i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.900390 | − | 0.900390i | −0.0625814 | − | 0.0625814i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0093i | 1.03822i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.9835i | 1.92646i | 0.268669 | + | 0.963232i | \(0.413416\pi\) | ||||
−0.268669 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00933 | − | 3.00933i | −0.206196 | − | 0.206196i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.42741 | − | 12.3414i | 0.0973483 | − | 0.841673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.55602 | − | 9.55602i | 0.648705 | − | 0.648705i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1277 | 0.887086 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.71733 | 0.115520 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.53479 | + | 8.53479i | −0.571531 | + | 0.571531i | −0.932556 | − | 0.361025i | \(-0.882427\pi\) |
0.361025 | + | 0.932556i | \(0.382427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.86799 | − | 1.14134i | −0.324533 | − | 0.0760891i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.02765 | + | 1.02765i | 0.0682074 | + | 0.0682074i | 0.740388 | − | 0.672180i | \(-0.234642\pi\) |
−0.672180 | + | 0.740388i | \(0.734642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.84802i | 0.584693i | 0.956312 | + | 0.292347i | \(0.0944361\pi\) | ||||
−0.956312 | + | 0.292347i | \(0.905564\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.6132i | 0.698297i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.91002 | − | 4.91002i | −0.321666 | − | 0.321666i | 0.527740 | − | 0.849406i | \(-0.323040\pi\) |
−0.849406 | + | 0.527740i | \(0.823040\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3980 | − | 2.12792i | −1.20015 | − | 0.138810i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.282672 | + | 0.282672i | −0.0183615 | + | 0.0183615i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0259 | 1.23068 | 0.615340 | − | 0.788262i | \(-0.289019\pi\) | ||||
0.615340 | + | 0.788262i | \(0.289019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.90663 | 0.187232 | 0.0936161 | − | 0.995608i | \(-0.470157\pi\) | ||||
0.0936161 | + | 0.995608i | \(0.470157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.33765 | + | 9.25700i | 0.468785 | + | 0.591408i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.80078 | + | 1.80078i | 0.114581 | + | 0.114581i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.282672i | 0.0179136i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.77379i | 0.175080i | 0.996161 | + | 0.0875401i | \(0.0279006\pi\) | ||||
−0.996161 | + | 0.0875401i | \(0.972099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.72666 | − | 2.72666i | −0.171423 | − | 0.171423i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.64240 | + | 5.85673i | 0.290718 | + | 0.366763i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.08066 | + | 2.08066i | −0.129788 | + | 0.129788i | −0.769017 | − | 0.639229i | \(-0.779254\pi\) |
0.639229 | + | 0.769017i | \(0.279254\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.80078 | −0.111895 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.50466 | 0.216933 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.75646 | − | 4.75646i | 0.293296 | − | 0.293296i | −0.545085 | − | 0.838381i | \(-0.683503\pi\) |
0.838381 | + | 0.545085i | \(0.183503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.86799 | − | 1.14134i | −0.606186 | − | 0.0701117i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.02831 | − | 3.02831i | −0.185329 | − | 0.185329i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.6846i | 1.32214i | 0.750326 | + | 0.661068i | \(0.229896\pi\) | ||||
−0.750326 | + | 0.661068i | \(0.770104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.15556i | − | 0.191687i | −0.995396 | − | 0.0958434i | \(-0.969445\pi\) | ||
0.995396 | − | 0.0958434i | \(-0.0305548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.27334 | + | 1.27334i | 0.0770663 | + | 0.0770663i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.7418 | − | 3.45632i | −0.888962 | − | 0.208424i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.53397 | − | 3.53397i | 0.212336 | − | 0.212336i | −0.592923 | − | 0.805259i | \(-0.702026\pi\) |
0.805259 | + | 0.592923i | \(0.202026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.85607 | 0.230857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.179969 | 0.0107361 | 0.00536804 | − | 0.999986i | \(-0.498291\pi\) | ||||
0.00536804 | + | 0.999986i | \(0.498291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.84007 | − | 9.84007i | 0.584931 | − | 0.584931i | −0.351323 | − | 0.936254i | \(-0.614268\pi\) |
0.936254 | + | 0.351323i | \(0.114268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.27334 | + | 11.0093i | −0.0754264 | + | 0.652136i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.75712 | − | 6.75712i | −0.398860 | − | 0.398860i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.82936i | 0.342903i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 9.52612i | − | 0.558431i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.8680 | − | 15.8680i | −0.927018 | − | 0.927018i | 0.0704942 | − | 0.997512i | \(-0.477542\pi\) |
−0.997512 | + | 0.0704942i | \(0.977542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2193 | − | 12.0637i | 0.886101 | − | 0.702377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.14134 | + | 2.14134i | −0.124253 | + | 0.124253i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.654274 | −0.0378376 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.4720 | −1.12235 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.09226 | + | 4.09226i | −0.235094 | + | 0.235094i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.7967 | − | 21.2406i | 1.53437 | − | 1.21624i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.78477 | + | 7.78477i | 0.444300 | + | 0.444300i | 0.893454 | − | 0.449154i | \(-0.148275\pi\) |
−0.449154 | + | 0.893454i | \(0.648275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18.5140i | − | 1.05322i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.05788i | 0.400215i | 0.979774 | + | 0.200108i | \(0.0641292\pi\) | ||||
−0.979774 | + | 0.200108i | \(0.935871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3013 | − | 11.3013i | −0.638789 | − | 0.638789i | 0.311468 | − | 0.950257i | \(-0.399179\pi\) |
−0.950257 | + | 0.311468i | \(0.899179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.900390 | + | 7.78477i | −0.0507312 | + | 0.438622i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4754 | + | 19.4754i | −1.09385 | + | 1.09385i | −0.0987310 | + | 0.995114i | \(0.531478\pi\) |
−0.995114 | + | 0.0987310i | \(0.968522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.6132 | 0.594225 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7360 | −0.766668 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.7135 | − | 11.7135i | 0.651755 | − | 0.651755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.18336 | + | 1.35400i | −0.121111 | + | 0.0751064i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.39820 | − | 7.39820i | −0.409122 | − | 0.409122i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.0280i | 1.60036i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.0143i | − | 0.825259i | −0.910899 | − | 0.412630i | \(-0.864610\pi\) | ||
0.910899 | − | 0.412630i | \(-0.135390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.363328 | − | 0.363328i | −0.0199103 | − | 0.0199103i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.3414 | − | 1.42741i | −0.674280 | − | 0.0779875i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.5840 | + | 21.5840i | −1.17576 | + | 1.17576i | −0.194940 | + | 0.980815i | \(0.562451\pi\) |
−0.980815 | + | 0.194940i | \(0.937549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.0557 | −0.817714 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6774 | 0.632365 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.25583 | + | 4.25583i | −0.229793 | + | 0.229793i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.76868 | − | 2.23132i | −0.0952225 | − | 0.120130i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.9969 | + | 16.9969i | 0.912444 | + | 0.912444i | 0.996464 | − | 0.0840201i | \(-0.0267760\pi\) |
−0.0840201 | + | 0.996464i | \(0.526776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.38538i | − | 0.234744i | −0.993088 | − | 0.117372i | \(-0.962553\pi\) | ||
0.993088 | − | 0.117372i | \(-0.0374469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.513824i | 0.0274259i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.62734 | − | 2.62734i | −0.139839 | − | 0.139839i | 0.633722 | − | 0.773561i | \(-0.281526\pi\) |
−0.773561 | + | 0.633722i | \(0.781526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.91137 | − | 7.45763i | −0.313743 | − | 0.395810i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.28267 | − | 8.28267i | 0.438366 | − | 0.438366i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.9952 | −1.84697 | −0.923487 | − | 0.383630i | \(-0.874674\pi\) | ||||
−0.923487 | + | 0.383630i | \(0.874674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.56534 | 0.292913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.29355 | − | 1.29355i | 0.0678939 | − | 0.0678939i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.1600 | + | 3.37266i | 1.52630 | + | 0.176533i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.93581 | − | 9.93581i | −0.518645 | − | 0.518645i | 0.398516 | − | 0.917161i | \(-0.369525\pi\) |
−0.917161 | + | 0.398516i | \(0.869525\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.72666i | − | 0.141944i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.5695i | 0.808330i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.08998 | + | 7.08998i | 0.367105 | + | 0.367105i | 0.866421 | − | 0.499315i | \(-0.166415\pi\) |
−0.499315 | + | 0.866421i | \(0.666415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5199 | − | 3.78585i | −0.543243 | − | 0.195500i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.27334 | − | 1.27334i | 0.0655805 | − | 0.0655805i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0388 | 1.54299 | 0.771495 | − | 0.636235i | \(-0.219509\pi\) | ||||
0.771495 | + | 0.636235i | \(0.219509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.51399 | 0.128796 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9133 | − | 11.9133i | 0.608744 | − | 0.608744i | −0.333874 | − | 0.942618i | \(-0.608356\pi\) |
0.942618 | + | 0.333874i | \(0.108356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.72666 | + | 23.5747i | −0.138963 | + | 1.20148i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.92870 | − | 3.92870i | −0.199707 | − | 0.199707i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3340i | 0.828168i | 0.910239 | + | 0.414084i | \(0.135898\pi\) | ||||
−0.910239 | + | 0.414084i | \(0.864102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.25583i | 0.215227i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.8680 | + | 12.8680i | 0.649104 | + | 0.649104i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.700510 | + | 0.555267i | −0.0352465 | + | 0.0279385i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1927 | − | 19.1927i | 0.963253 | − | 0.963253i | −0.0360950 | − | 0.999348i | \(-0.511492\pi\) |
0.999348 | + | 0.0360950i | \(0.0114919\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.3703 | 0.869604 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5653 | 1.32661 | 0.663305 | − | 0.748349i | \(-0.269153\pi\) | ||||
0.663305 | + | 0.748349i | \(0.269153\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.40102 | − | 1.40102i | 0.0697898 | − | 0.0697898i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.75233 | + | 1.38900i | −0.0870741 | + | 0.0690202i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.10027 | − | 1.10027i | −0.0545383 | − | 0.0545383i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.3947i | − | 1.25569i | −0.778339 | − | 0.627844i | \(-0.783938\pi\) | ||
0.778339 | − | 0.627844i | \(-0.216062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.37122i | 0.412922i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.5233 | − | 21.5233i | −1.05909 | − | 1.05909i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0726218 | + | 0.627889i | −0.00356487 | + | 0.0308218i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.77801 | − | 8.77801i | 0.429861 | − | 0.429861i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0788 | −1.95798 | −0.978988 | − | 0.203919i | \(-0.934632\pi\) | ||||
−0.978988 | + | 0.203919i | \(0.934632\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3947 | −0.945240 | −0.472620 | − | 0.881266i | \(-0.656692\pi\) | ||||
−0.472620 | + | 0.881266i | \(0.656692\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.85673 | + | 5.85673i | −0.284764 | + | 0.284764i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.80731 | + | 14.2020i | 0.427217 | + | 0.688899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.8962 | − | 37.8962i | −1.83393 | − | 1.83393i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.55602i | 0.0751251i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8241i | 0.762218i | 0.924530 | + | 0.381109i | \(0.124458\pi\) | ||||
−0.924530 | + | 0.381109i | \(0.875542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.1214 | − | 21.1214i | −1.01503 | − | 1.01503i | −0.999885 | − | 0.0151424i | \(-0.995180\pi\) |
−0.0151424 | − | 0.999885i | \(-0.504820\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.78477 | + | 0.900390i | 0.373251 | + | 0.0431704i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.46264 | + | 4.46264i | −0.213477 | + | 0.213477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.61188 | −0.315568 | −0.157784 | − | 0.987474i | \(-0.550435\pi\) | ||||
−0.157784 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.28267 | 0.251556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5419 | + | 14.5419i | −0.690906 | + | 0.690906i | −0.962431 | − | 0.271525i | \(-0.912472\pi\) |
0.271525 | + | 0.962431i | \(0.412472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.94865 | − | 7.50466i | −0.281993 | − | 0.355755i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.09226 | − | 4.09226i | −0.193557 | − | 0.193557i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.6120i | − | 1.58625i | −0.609060 | − | 0.793124i | \(-0.708453\pi\) | ||
0.609060 | − | 0.793124i | \(-0.291547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.25715i | − | 0.388814i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7780 | + | 12.7780i | 0.600363 | + | 0.600363i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.50129 | + | 3.15556i | 0.117262 | + | 0.147935i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5653 | − | 15.5653i | 0.728116 | − | 0.728116i | −0.242128 | − | 0.970244i | \(-0.577845\pi\) |
0.970244 | + | 0.242128i | \(0.0778454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.34225 | 0.156003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.1473 | 1.21780 | 0.608900 | − | 0.793247i | \(-0.291611\pi\) | ||||
0.608900 | + | 0.793247i | \(0.291611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.77898 | − | 5.77898i | 0.268572 | − | 0.268572i | −0.559953 | − | 0.828525i | \(-0.689181\pi\) |
0.828525 | + | 0.559953i | \(0.189181\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.56534 | + | 0.990671i | 0.397208 | + | 0.0459413i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.25517 | − | 2.25517i | −0.104357 | − | 0.104357i | 0.653000 | − | 0.757357i | \(-0.273510\pi\) |
−0.757357 | + | 0.653000i | \(0.773510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.4720i | 0.899132i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.54279i | − | 0.255398i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.8973 | − | 11.8973i | −0.547038 | − | 0.547038i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65685 | + | 24.1274i | −0.259554 | + | 1.10704i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.14134 | + | 3.14134i | −0.143832 | + | 0.143832i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.40102 | 0.0640143 | 0.0320071 | − | 0.999488i | \(-0.489810\pi\) | ||||
0.0320071 | + | 0.999488i | \(0.489810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.264015 | −0.0120380 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.15556 | + | 3.15556i | −0.143583 | + | 0.143583i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.44737 | − | 21.1600i | 0.111130 | − | 0.960826i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.978144 | + | 0.978144i | 0.0443239 | + | 0.0443239i | 0.728921 | − | 0.684597i | \(-0.240022\pi\) |
−0.684597 | + | 0.728921i | \(0.740022\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.56534i | 0.206452i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.1134i | − | 1.62978i | −0.579619 | − | 0.814888i | \(-0.696799\pi\) | ||
0.579619 | − | 0.814888i | \(-0.303201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.28267 | − | 8.28267i | −0.373033 | − | 0.373033i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.30660 | + | 4.20633i | −0.238514 | + | 0.189060i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.5467 | + | 10.5467i | −0.473084 | + | 0.473084i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.35736 | −0.284595 | −0.142297 | − | 0.989824i | \(-0.545449\pi\) | ||||
−0.142297 | + | 0.989824i | \(0.545449\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.83869 | 0.439560 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.1704 | − | 17.1704i | 0.765592 | − | 0.765592i | −0.211735 | − | 0.977327i | \(-0.567911\pi\) |
0.977327 | + | 0.211735i | \(0.0679114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1413 | + | 8.03863i | −0.451284 | + | 0.357714i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00570 | − | 9.00570i | −0.399957 | − | 0.399957i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 18.8739i | − | 0.836572i | −0.908315 | − | 0.418286i | \(-0.862631\pi\) | ||
0.908315 | − | 0.418286i | \(-0.137369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 46.0081i | − | 2.03528i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.50466 | + | 3.50466i | 0.154735 | + | 0.154735i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.75646 | − | 41.1244i | 0.209595 | − | 1.81216i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.7360 | + | 17.7360i | −0.780028 | + | 0.780028i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.887197 | −0.0389436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.9346 | −1.48670 | −0.743351 | − | 0.668901i | \(-0.766765\pi\) | ||||
−0.743351 | + | 0.668901i | \(0.766765\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.78345 | + | 3.78345i | −0.165439 | + | 0.165439i | −0.784971 | − | 0.619532i | \(-0.787322\pi\) |
0.619532 | + | 0.784971i | \(0.287322\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00000 | + | 17.0607i | −0.174574 | + | 0.744589i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.11317 | − | 9.11317i | −0.396976 | − | 0.396976i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3786i | 0.929504i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.68516i | − | 0.376904i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.990671 | − | 0.990671i | −0.0429107 | − | 0.0429107i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.5112 | − | 3.52894i | −1.31911 | − | 0.152569i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.32131 | − | 6.32131i | 0.272784 | − | 0.272784i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.9976 | 0.689063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4813 | −1.22451 | −0.612253 | − | 0.790662i | \(-0.709737\pi\) | ||||
−0.612253 | + | 0.790662i | \(0.709737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.713703 | − | 0.713703i | 0.0306279 | − | 0.0306279i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.5327 | − | 18.3340i | −0.622510 | − | 0.785343i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.726896 | − | 0.726896i | −0.0310798 | − | 0.0310798i | 0.691396 | − | 0.722476i | \(-0.256996\pi\) |
−0.722476 | + | 0.691396i | \(0.756996\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 15.2920i | − | 0.652647i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 17.3703i | − | 0.740001i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.990671 | + | 0.990671i | 0.0421276 | + | 0.0421276i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.713703 | − | 0.900390i | −0.0302950 | − | 0.0382194i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.4427 | − | 11.4427i | 0.484841 | − | 0.484841i | −0.421832 | − | 0.906674i | \(-0.638613\pi\) |
0.906674 | + | 0.421832i | \(0.138613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.85481 | −0.120746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1214 | 0.427324 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.08426 | − | 7.08426i | 0.298566 | − | 0.298566i | −0.541886 | − | 0.840452i | \(-0.682290\pi\) |
0.840452 | + | 0.541886i | \(0.182290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.4427 | − | 3.86799i | −1.40694 | − | 0.162728i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.47817 | + | 2.47817i | 0.104073 | + | 0.104073i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.2427i | 1.93860i | 0.245890 | + | 0.969298i | \(0.420920\pi\) | ||||
−0.245890 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.2381i | 1.30727i | 0.756808 | + | 0.653637i | \(0.226758\pi\) | ||||
−0.756808 | + | 0.653637i | \(0.773242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2920 | + | 15.2920i | 0.638833 | + | 0.638833i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.35544 | − | 5.41074i | −0.139932 | − | 0.225643i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.16131 | − | 1.16131i | 0.0483461 | − | 0.0483461i | −0.682520 | − | 0.730866i | \(-0.739116\pi\) |
0.730866 | + | 0.682520i | \(0.239116\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.3559 | 0.679727 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.990671 | 0.0411000 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.51293 | + | 9.51293i | −0.393985 | + | 0.393985i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.132007 | + | 1.14134i | −0.00545783 | + | 0.0471884i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.6268 | − | 23.6268i | −0.975183 | − | 0.975183i | 0.0245164 | − | 0.999699i | \(-0.492195\pi\) |
−0.999699 | + | 0.0245164i | \(0.992195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 19.1120i | − | 0.787498i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 13.3276i | − | 0.548223i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.260625 | − | 0.260625i | −0.0107026 | − | 0.0107026i | 0.701735 | − | 0.712438i | \(-0.252409\pi\) |
−0.712438 | + | 0.701735i | \(0.752409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.5259 | − | 16.2701i | 0.841479 | − | 0.667007i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.78734 | − | 7.78734i | 0.318714 | − | 0.318714i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.0851 | −1.35182 | −0.675910 | − | 0.736984i | \(-0.736249\pi\) | ||||
−0.675910 | + | 0.736984i | \(0.736249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3200 | −0.992033 | −0.496016 | − | 0.868313i | \(-0.665204\pi\) | ||||
−0.496016 | + | 0.868313i | \(0.665204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.92870 | + | 3.92870i | −0.159989 | + | 0.159989i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.20565 | − | 2.54099i | 0.130328 | − | 0.103306i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.53347 | − | 4.53347i | −0.184008 | − | 0.184008i | 0.609092 | − | 0.793100i | \(-0.291534\pi\) |
−0.793100 | + | 0.609092i | \(0.791534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 12.2827i | − | 0.497719i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.25583i | 0.172173i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2793 | + | 20.2793i | 0.819073 | + | 0.819073i | 0.985974 | − | 0.166901i | \(-0.0533761\pi\) |
−0.166901 | + | 0.985974i | \(0.553376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.700510 | − | 6.05661i | 0.0282473 | − | 0.244226i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.1086 | − | 17.1086i | 0.688768 | − | 0.688768i | −0.273192 | − | 0.961960i | \(-0.588079\pi\) |
0.961960 | + | 0.273192i | \(0.0880793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.4373 | −1.18319 | −0.591593 | − | 0.806237i | \(-0.701501\pi\) | ||||
−0.591593 | + | 0.806237i | \(0.701501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.27334 | −0.0510975 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.6132 | + | 10.6132i | −0.425209 | + | 0.425209i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3947 | − | 11.1120i | −0.895788 | − | 0.444481i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.6132 | + | 10.6132i | 0.423850 | + | 0.423850i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.71733i | 0.0684743i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.25710i | 0.209282i | 0.994510 | + | 0.104641i | \(0.0333693\pi\) | ||||
−0.994510 | + | 0.104641i | \(0.966631\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.7873 | + | 19.7873i | 0.786476 | + | 0.786476i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.58423 | + | 0.645875i | 0.221604 | + | 0.0256308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.91934 | − | 1.91934i | 0.0760472 | − | 0.0760472i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.25583 | −0.168358 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0773 | 0.793004 | 0.396502 | − | 0.918034i | \(-0.370224\pi\) | ||||
0.396502 | + | 0.918034i | \(0.370224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.28480 | − | 9.28480i | 0.366157 | − | 0.366157i | −0.499917 | − | 0.866073i | \(-0.666636\pi\) |
0.866073 | + | 0.499917i | \(0.166636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.71733 | − | 9.73599i | −0.303869 | − | 0.383354i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.7387 | + | 28.7387i | 1.12983 | + | 1.12983i | 0.990204 | + | 0.139630i | \(0.0445912\pi\) |
0.139630 | + | 0.990204i | \(0.455409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 26.3013i | − | 1.03242i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 13.5142i | − | 0.529665i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.9380 | + | 11.9380i | 0.467170 | + | 0.467170i | 0.900996 | − | 0.433826i | \(-0.142837\pi\) |
−0.433826 | + | 0.900996i | \(0.642837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.2772 | + | 31.8891i | 0.987663 | + | 1.24601i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.28267 | − | 9.28267i | 0.362152 | − | 0.362152i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.9963 | 0.701038 | 0.350519 | − | 0.936556i | \(-0.386005\pi\) | ||||
0.350519 | + | 0.936556i | \(0.386005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.06794 | 0.352702 | 0.176351 | − | 0.984327i | \(-0.443571\pi\) | ||||
0.176351 | + | 0.984327i | \(0.443571\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.21433 | − | 1.21433i | 0.0471608 | − | 0.0471608i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38.5840 | + | 4.46264i | 1.49622 | + | 0.173054i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.15556 | + | 3.15556i | 0.122184 | + | 0.122184i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0700i | 0.466654i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 46.3089i | − | 1.78773i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7640 | + | 35.7640i | 1.37860 | + | 1.37860i | 0.846988 | + | 0.531611i | \(0.178413\pi\) |
0.531611 | + | 0.846988i | \(0.321587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.24924 | + | 2.63514i | −0.163553 | + | 0.101427i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2020 | + | 16.2020i | −0.622694 | + | 0.622694i | −0.946219 | − | 0.323525i | \(-0.895132\pi\) |
0.323525 | + | 0.946219i | \(0.395132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.3859 | −1.28123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.45331 | 0.0556911 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.3943 | + | 33.3943i | −1.27780 | + | 1.27780i | −0.335897 | + | 0.941899i | \(0.609039\pi\) |
−0.941899 | + | 0.335897i | \(0.890961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.15066 | + | 18.5946i | −0.0821727 | + | 0.710465i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.25649 | + | 6.25649i | 0.238700 | + | 0.238700i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.28267i | 0.0869629i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.6365i | − | 0.937216i | −0.883406 | − | 0.468608i | \(-0.844756\pi\) | ||
0.883406 | − | 0.468608i | \(-0.155244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50466 | + | 7.50466i | 0.285079 | + | 0.285079i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.7534 | − | 17.2431i | 0.825154 | − | 0.654067i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.44398 | + | 6.44398i | −0.244083 | + | 0.244083i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.94381 | −0.262639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0420 | 0.870285 | 0.435143 | − | 0.900362i | \(-0.356698\pi\) | ||||
0.435143 | + | 0.900362i | \(0.356698\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.80078 | + | 1.80078i | −0.0679177 | + | 0.0679177i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5140 | + | 11.5047i | −0.546629 | + | 0.433291i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.3420 | + | 14.3420i | 0.539387 | + | 0.539387i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 37.7360i | − | 1.41720i | −0.705608 | − | 0.708602i | \(-0.749326\pi\) | ||
0.705608 | − | 0.708602i | \(-0.250674\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.399759i | 0.0149921i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.47197 | + | 3.47197i | 0.130026 | + | 0.130026i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.399759 | + | 3.45632i | −0.0149501 | + | 0.129259i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4533 | − | 13.4533i | 0.502423 | − | 0.502423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.3423 | 1.54181 | 0.770903 | − | 0.636953i | \(-0.219805\pi\) | ||||
0.770903 | + | 0.636953i | \(0.219805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.8853 | −2.41646 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.05529 | − | 2.05529i | 0.0764372 | − | 0.0764372i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.0607 | + | 4.00000i | 0.633618 | + | 0.148556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.48981 | + | 9.48981i | 0.351958 | + | 0.351958i | 0.860838 | − | 0.508880i | \(-0.169940\pi\) |
−0.508880 | + | 0.860838i | \(0.669940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.5696i | 0.686821i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.21134 | − | 3.21134i | −0.118614 | − | 0.118614i | 0.645308 | − | 0.763922i | \(-0.276729\pi\) |
−0.763922 | + | 0.645308i | \(0.776729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.7342 | + | 1.35718i | 0.432822 | + | 0.0500604i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.8973 | + | 11.8973i | −0.438243 | + | 0.438243i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3832 | −0.933737 | −0.466868 | − | 0.884327i | \(-0.654618\pi\) | ||||
−0.466868 | + | 0.884327i | \(0.654618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.54669 | 0.0935549 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.7400 | + | 32.7400i | −1.20111 | + | 1.20111i | −0.227285 | + | 0.973828i | \(0.572985\pi\) |
−0.973828 | + | 0.227285i | \(0.927015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.03863 | − | 10.1413i | −0.294513 | − | 0.371550i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.199879 | + | 0.199879i | 0.00731321 | + | 0.00731321i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.1400i | 1.75900i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4810i | 0.893323i | 0.894703 | + | 0.446662i | \(0.147387\pi\) | ||||
−0.894703 | + | 0.446662i | \(0.852613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.96137 | + | 1.96137i | 0.0714762 | + | 0.0714762i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.1005 | + | 31.6661i | 0.913499 | + | 1.15245i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9473 | + | 22.9473i | −0.834035 | + | 0.834035i | −0.988066 | − | 0.154031i | \(-0.950774\pi\) |
0.154031 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.85607 | −0.139967 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.0466 | 1.34294 | 0.671470 | − | 0.741032i | \(-0.265663\pi\) | ||||
0.671470 | + | 0.741032i | \(0.265663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.9282 | + | 25.9282i | −0.938665 | + | 0.938665i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.42401 | + | 0.858664i | 0.268416 | + | 0.0310451i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.15556 | − | 3.15556i | −0.113941 | − | 0.113941i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.62395i | − | 0.238866i | −0.992842 | − | 0.119433i | \(-0.961892\pi\) | ||
0.992842 | − | 0.119433i | \(-0.0381077\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.94249i | 0.105971i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2606 | − | 16.2606i | −0.584854 | − | 0.584854i | 0.351379 | − | 0.936233i | \(-0.385713\pi\) |
−0.936233 | + | 0.351379i | \(0.885713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.7713 | + | 4.40108i | 0.674287 | + | 0.158091i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.27334 | + | 1.27334i | −0.0456809 | + | 0.0456809i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.5142 | −0.484198 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8880 | −0.461168 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.47817 | − | 2.47817i | 0.0885626 | − | 0.0885626i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.42401 | − | 12.3120i | 0.0508250 | − | 0.439433i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.2117 | + | 31.2117i | 1.11258 | + | 1.11258i | 0.992801 | + | 0.119776i | \(0.0382177\pi\) |
0.119776 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 6.72666i | − | 0.239475i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52.7652i | 1.87612i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.55602 | − | 5.55602i | −0.197300 | − | 0.197300i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.78477 | + | 6.17068i | −0.276097 | + | 0.218851i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3540 | + | 17.3540i | −0.614710 | + | 0.614710i | −0.944170 | − | 0.329460i | \(-0.893133\pi\) |
0.329460 | + | 0.944170i | \(0.393133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.6828 | 0.979346 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.28267 | −0.151321 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.1108 | − | 28.1108i | 0.992008 | − | 0.992008i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.82003 | + | 6.19863i | −0.275620 | + | 0.218473i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3334 | + | 15.3334i | 0.539760 | + | 0.539760i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.4320i | − | 0.964458i | −0.876045 | − | 0.482229i | \(-0.839827\pi\) | ||
0.876045 | − | 0.482229i | \(-0.160173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.1840i | − | 0.954559i | −0.878751 | − | 0.477280i | \(-0.841623\pi\) | ||
0.878751 | − | 0.477280i | \(-0.158377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.23132 | − | 2.23132i | −0.0782558 | − | 0.0782558i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.17289 | + | 10.1408i | −0.0410846 | + | 0.355217i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.4720 | + | 19.4720i | −0.681238 | + | 0.681238i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.80078 | 0.0629243 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.6074 | −0.823903 | −0.411951 | − | 0.911206i | \(-0.635153\pi\) | ||||
−0.411951 | + | 0.911206i | \(0.635153\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6596 | − | 24.6596i | 0.859579 | − | 0.859579i | −0.131709 | − | 0.991288i | \(-0.542046\pi\) |
0.991288 | + | 0.131709i | \(0.0420465\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.8680 | + | 7.98002i | −0.448006 | + | 0.277829i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5406 | + | 13.5406i | 0.470854 | + | 0.470854i | 0.902191 | − | 0.431337i | \(-0.141958\pi\) |
−0.431337 | + | 0.902191i | \(0.641958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9.00933i | − | 0.312907i | −0.987685 | − | 0.156453i | \(-0.949994\pi\) | ||
0.987685 | − | 0.156453i | \(-0.0500061\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 4.99779i | − | 0.173371i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.4847 | − | 12.4847i | −0.432569 | − | 0.432569i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8543 | + | 2.52768i | 0.756299 | + | 0.0874738i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.72666 | − | 2.72666i | 0.0942470 | − | 0.0942470i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2597 | −0.354203 | −0.177102 | − | 0.984193i | \(-0.556672\pi\) | ||||
−0.177102 | + | 0.984193i | \(0.556672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.7173 | 0.576460 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.127258 | − | 0.127258i | 0.00438298 | − | 0.00438298i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.6903 | − | 22.3177i | −0.608566 | − | 0.767751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.53347 | − | 4.53347i | −0.155772 | − | 0.155772i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.9160i | − | 0.477594i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.654274i | − | 0.0224282i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1086 | − | 17.1086i | −0.585789 | − | 0.585789i | 0.350699 | − | 0.936488i | \(-0.385944\pi\) |
−0.936488 | + | 0.350699i | \(0.885944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.88438 | + | 8.68516i | 0.235441 | + | 0.297026i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.7674 | + | 26.7674i | −0.914356 | + | 0.914356i | −0.996611 | − | 0.0822556i | \(-0.973788\pi\) |
0.0822556 | + | 0.996611i | \(0.473788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.6378 | 0.977109 | 0.488554 | − | 0.872533i | \(-0.337524\pi\) | ||||
0.488554 | + | 0.872533i | \(0.337524\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.55602 | −0.325668 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8157 | + | 15.8157i | −0.538371 | + | 0.538371i | −0.923050 | − | 0.384679i | \(-0.874312\pi\) |
0.384679 | + | 0.923050i | \(0.374312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.97070 | − | 0.227931i | −0.0670057 | − | 0.00774990i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.12198 | + | 4.12198i | 0.139990 | + | 0.139990i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.21059i | 0.0410665i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.85481i | 0.0967316i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.73599 | − | 6.73599i | −0.227979 | − | 0.227979i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.2681 | + | 36.8686i | −0.448545 | + | 1.24638i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3727 | − | 17.3727i | 0.586633 | − | 0.586633i | −0.350085 | − | 0.936718i | \(-0.613847\pi\) |
0.936718 | + | 0.350085i | \(0.113847\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.4407 | −0.756907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.5254 | 1.90439 | 0.952194 | − | 0.305493i | \(-0.0988211\pi\) | ||||
0.952194 | + | 0.305493i | \(0.0988211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1962 | − | 15.1962i | 0.511392 | − | 0.511392i | −0.403561 | − | 0.914953i | \(-0.632228\pi\) |
0.914953 | + | 0.403561i | \(0.132228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.23132 | − | 19.2920i | 0.0750050 | − | 0.648494i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0676 | − | 11.0676i | −0.371613 | − | 0.371613i | 0.496451 | − | 0.868065i | \(-0.334636\pi\) |
−0.868065 | + | 0.496451i | \(0.834636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.81070i | − | 0.295501i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.02831i | 0.101452i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0280 | + | 29.0280i | 0.971385 | + | 0.971385i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6653 | − | 12.4172i | 0.523633 | − | 0.415063i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.462642 | + | 0.462642i | −0.0154472 | + | 0.0154472i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.5142 | −0.450725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8480 | 0.494659 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.7688 | + | 13.7688i | −0.458196 | + | 0.458196i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.76868 | − | 1.40196i | 0.0587929 | − | 0.0466028i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.1654 | + | 28.1654i | 0.935217 | + | 0.935217i | 0.998026 | − | 0.0628084i | \(-0.0200057\pi\) |
−0.0628084 | + | 0.998026i | \(0.520006\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.78734i | 0.191954i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 34.8499i | − | 1.15463i | −0.816522 | − | 0.577315i | \(-0.804101\pi\) | ||
0.816522 | − | 0.577315i | \(-0.195899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.605296 | + | 0.605296i | 0.0200324 | + | 0.0200324i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.92870 | − | 33.9675i | 0.129879 | − | 1.12293i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.0980 | − | 45.0980i | 1.48927 | − | 1.48927i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.1171 | −0.696590 | −0.348295 | − | 0.937385i | \(-0.613239\pi\) | ||||
−0.348295 | + | 0.937385i | \(0.613239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0093 | 0.362770 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.54626 | + | 1.54626i | −0.0508959 | + | 0.0508959i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.35400 | − | 2.18336i | −0.0445192 | − | 0.0717884i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.0914 | − | 13.0914i | −0.429977 | − | 0.429977i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.0653i | 1.28169i | 0.767670 | + | 0.640845i | \(0.221416\pi\) | ||||
−0.767670 | + | 0.640845i | \(0.778584\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 26.1827i | − | 0.858105i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.99067 | + | 4.99067i | 0.163387 | + | 0.163387i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.4822 | + | 2.60030i | 0.735246 | + | 0.0850388i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.82936 | − | 1.82936i | 0.0597626 | − | 0.0597626i | −0.676594 | − | 0.736356i | \(-0.736545\pi\) |
0.736356 | + | 0.676594i | \(0.236545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.9825 | −0.521569 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.58193 | −0.0515695 | −0.0257847 | − | 0.999668i | \(-0.508208\pi\) | ||||
−0.0257847 | + | 0.999668i | \(0.508208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.45505 | − | 2.45505i | 0.0799476 | − | 0.0799476i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.86799 | + | 6.14134i | 0.158356 | + | 0.199778i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9429 | + | 15.9429i | 0.518075 | + | 0.518075i | 0.916989 | − | 0.398913i | \(-0.130613\pi\) |
−0.398913 | + | 0.916989i | \(0.630613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.74531i | − | 0.218962i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.5423i | 0.893121i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.2113 | − | 27.2113i | −0.881462 | − | 0.881462i | 0.112221 | − | 0.993683i | \(-0.464203\pi\) |
−0.993683 | + | 0.112221i | \(0.964203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.0388 | + | 37.8962i | 0.972033 | + | 1.22629i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.50466 | − | 7.50466i | 0.242591 | − | 0.242591i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.3383 | 0.947383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1307 | 0.520345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.71281 | + | 9.71281i | −0.312991 | + | 0.312991i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.3306 | + | 4.20202i | 1.16952 | + | 0.135268i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.8921 | + | 14.8921i | 0.478899 | + | 0.478899i | 0.904780 | − | 0.425880i | \(-0.140036\pi\) |
−0.425880 | + | 0.904780i | \(0.640036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 16.5653i | − | 0.532156i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 41.6250i | − | 1.33581i | −0.744246 | − | 0.667905i | \(-0.767191\pi\) | ||
0.744246 | − | 0.667905i | \(-0.232809\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.7640 | − | 30.7640i | −0.986248 | − | 0.986248i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.586446 | + | 2.50129i | −0.0187813 | + | 0.0801054i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0807 | + | 12.0807i | −0.386494 | + | 0.386494i | −0.873435 | − | 0.486941i | \(-0.838113\pi\) |
0.486941 | + | 0.873435i | \(0.338113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9692 | −0.414499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.4626 | −0.334046 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.2258 | + | 22.2258i | −0.708893 | + | 0.708893i | −0.966302 | − | 0.257410i | \(-0.917131\pi\) |
0.257410 | + | 0.966302i | \(0.417131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.42401 | − | 29.6040i | 0.109098 | − | 0.943261i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.5259 | + | 20.5259i | 0.653346 | + | 0.653346i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 7.07472i | − | 0.224963i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.353523i | 0.0112300i | 0.999984 | + | 0.00561501i | \(0.00178732\pi\) | ||||
−0.999984 | + | 0.00561501i | \(0.998213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6167 | − | 10.6167i | −0.336911 | − | 0.336911i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2984 | − | 15.2970i | 0.611799 | − | 0.484949i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.9380 | + | 27.9380i | −0.884805 | + | 0.884805i | −0.994018 | − | 0.109213i | \(-0.965167\pi\) |
0.109213 | + | 0.994018i | \(0.465167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.513824 | −0.0162567 |
(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 | 960.2.w.g.703.6 | 12 | ||
4.3 | odd | 2 | inner | 960.2.w.g.703.3 | 12 | ||
5.2 | odd | 4 | inner | 960.2.w.g.127.3 | 12 | ||
8.3 | odd | 2 | 60.2.j.a.43.4 | yes | 12 | ||
8.5 | even | 2 | 60.2.j.a.43.6 | yes | 12 | ||
20.7 | even | 4 | inner | 960.2.w.g.127.6 | 12 | ||
24.5 | odd | 2 | 180.2.k.e.163.1 | 12 | |||
24.11 | even | 2 | 180.2.k.e.163.3 | 12 | |||
40.3 | even | 4 | 300.2.j.d.7.1 | 12 | |||
40.13 | odd | 4 | 300.2.j.d.7.3 | 12 | |||
40.19 | odd | 2 | 300.2.j.d.43.3 | 12 | |||
40.27 | even | 4 | 60.2.j.a.7.6 | yes | 12 | ||
40.29 | even | 2 | 300.2.j.d.43.1 | 12 | |||
40.37 | odd | 4 | 60.2.j.a.7.4 | ✓ | 12 | ||
120.29 | odd | 2 | 900.2.k.n.343.6 | 12 | |||
120.53 | even | 4 | 900.2.k.n.307.4 | 12 | |||
120.59 | even | 2 | 900.2.k.n.343.4 | 12 | |||
120.77 | even | 4 | 180.2.k.e.127.3 | 12 | |||
120.83 | odd | 4 | 900.2.k.n.307.6 | 12 | |||
120.107 | odd | 4 | 180.2.k.e.127.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.j.a.7.4 | ✓ | 12 | 40.37 | odd | 4 | ||
60.2.j.a.7.6 | yes | 12 | 40.27 | even | 4 | ||
60.2.j.a.43.4 | yes | 12 | 8.3 | odd | 2 | ||
60.2.j.a.43.6 | yes | 12 | 8.5 | even | 2 | ||
180.2.k.e.127.1 | 12 | 120.107 | odd | 4 | |||
180.2.k.e.127.3 | 12 | 120.77 | even | 4 | |||
180.2.k.e.163.1 | 12 | 24.5 | odd | 2 | |||
180.2.k.e.163.3 | 12 | 24.11 | even | 2 | |||
300.2.j.d.7.1 | 12 | 40.3 | even | 4 | |||
300.2.j.d.7.3 | 12 | 40.13 | odd | 4 | |||
300.2.j.d.43.1 | 12 | 40.29 | even | 2 | |||
300.2.j.d.43.3 | 12 | 40.19 | odd | 2 | |||
900.2.k.n.307.4 | 12 | 120.53 | even | 4 | |||
900.2.k.n.307.6 | 12 | 120.83 | odd | 4 | |||
900.2.k.n.343.4 | 12 | 120.59 | even | 2 | |||
900.2.k.n.343.6 | 12 | 120.29 | odd | 2 | |||
960.2.w.g.127.3 | 12 | 5.2 | odd | 4 | inner | ||
960.2.w.g.127.6 | 12 | 20.7 | even | 4 | inner | ||
960.2.w.g.703.3 | 12 | 4.3 | odd | 2 | inner | ||
960.2.w.g.703.6 | 12 | 1.1 | even | 1 | trivial |