Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.41342275584.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(-1.10890 - 1.92067i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.577 |
Dual form | 1216.2.i.q.961.2 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.207107 | − | 0.358719i | −0.119573 | − | 0.207107i | 0.800025 | − | 0.599966i | \(-0.204819\pi\) |
−0.919599 | + | 0.392859i | \(0.871486\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.401794 | + | 0.695928i | 0.179688 | + | 0.311228i | 0.941774 | − | 0.336248i | \(-0.109158\pi\) |
−0.762086 | + | 0.647476i | \(0.775825\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55066 | −0.964058 | −0.482029 | − | 0.876155i | \(-0.660100\pi\) | ||||
−0.482029 | + | 0.876155i | \(0.660100\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | − | 2.44949i | 0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80359 | −0.543802 | −0.271901 | − | 0.962325i | \(-0.587652\pi\) | ||||
−0.271901 | + | 0.962325i | \(0.587652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.540678 | + | 0.936482i | −0.149957 | + | 0.259733i | −0.931211 | − | 0.364480i | \(-0.881247\pi\) |
0.781254 | + | 0.624213i | \(0.214580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.166429 | − | 0.288263i | 0.0429717 | − | 0.0744291i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.26291 | − | 2.18742i | −0.306301 | − | 0.530528i | 0.671249 | − | 0.741232i | \(-0.265758\pi\) |
−0.977550 | + | 0.210703i | \(0.932425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.70538 | + | 4.01144i | −0.391241 | + | 0.920288i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.528259 | + | 0.914971i | 0.115275 | + | 0.199663i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.555803 | + | 0.962679i | −0.115893 | + | 0.200732i | −0.918136 | − | 0.396265i | \(-0.870306\pi\) |
0.802243 | + | 0.596997i | \(0.203640\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.17712 | − | 3.77089i | 0.435425 | − | 0.754178i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.36667 | + | 7.56329i | −0.810870 | + | 1.40447i | 0.101387 | + | 0.994847i | \(0.467672\pi\) |
−0.912256 | + | 0.409620i | \(0.865661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.10620 | −0.917100 | −0.458550 | − | 0.888669i | \(-0.651631\pi\) | ||||
−0.458550 | + | 0.888669i | \(0.651631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.373535 | + | 0.646982i | 0.0650241 | + | 0.112625i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.02484 | − | 1.77507i | −0.173229 | − | 0.300042i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.37909 | −0.884316 | −0.442158 | − | 0.896937i | \(-0.645787\pi\) | ||||
−0.442158 | + | 0.896937i | \(0.645787\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.447913 | 0.0717234 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.71780 | − | 2.97532i | −0.268276 | − | 0.464667i | 0.700141 | − | 0.714005i | \(-0.253120\pi\) |
−0.968417 | + | 0.249338i | \(0.919787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.30531 | − | 3.99292i | −0.351557 | − | 0.608914i | 0.634966 | − | 0.772540i | \(-0.281014\pi\) |
−0.986522 | + | 0.163626i | \(0.947681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.27289 | 0.338822 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.38423 | + | 4.12961i | −0.347776 | + | 0.602365i | −0.985854 | − | 0.167606i | \(-0.946396\pi\) |
0.638078 | + | 0.769971i | \(0.279730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.494141 | −0.0705916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.523114 | + | 0.906061i | −0.0732507 | + | 0.126874i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.848696 | − | 1.46998i | 0.116577 | − | 0.201918i | −0.801832 | − | 0.597550i | \(-0.796141\pi\) |
0.918409 | + | 0.395632i | \(0.129474\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.724671 | − | 1.25517i | −0.0977146 | − | 0.169247i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.79218 | − | 0.219043i | 0.237380 | − | 0.0290130i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.01069 | − | 5.21468i | −0.391959 | − | 0.678893i | 0.600749 | − | 0.799438i | \(-0.294869\pi\) |
−0.992708 | + | 0.120545i | \(0.961536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23022 | − | 2.13081i | 0.157514 | − | 0.272822i | −0.776458 | − | 0.630169i | \(-0.782985\pi\) |
0.933971 | + | 0.357348i | \(0.116319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.60718 | + | 6.24781i | −0.454461 | + | 0.787150i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.868965 | −0.107782 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.22850 | + | 7.32397i | −0.516593 | + | 0.894765i | 0.483221 | + | 0.875498i | \(0.339467\pi\) |
−0.999814 | + | 0.0192672i | \(0.993867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.460442 | 0.0554307 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.87736 | − | 11.9119i | −0.816193 | − | 1.41369i | −0.908468 | − | 0.417954i | \(-0.862747\pi\) |
0.0922759 | − | 0.995733i | \(-0.470586\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.85425 | + | 8.40780i | 0.568147 | + | 0.984059i | 0.996749 | + | 0.0805657i | \(0.0256727\pi\) |
−0.428603 | + | 0.903493i | \(0.640994\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.80359 | −0.208260 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.60034 | 0.524257 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.63817 | − | 4.56944i | −0.296817 | − | 0.514103i | 0.678589 | − | 0.734518i | \(-0.262592\pi\) |
−0.975406 | + | 0.220416i | \(0.929259\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | − | 6.48244i | −0.415849 | − | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.90490 | −0.977440 | −0.488720 | − | 0.872441i | \(-0.662536\pi\) | ||||
−0.488720 | + | 0.872441i | \(0.662536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.01486 | − | 1.75779i | 0.110077 | − | 0.190659i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.61746 | 0.387833 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.09134 | + | 7.08640i | −0.433681 | + | 0.751157i | −0.997187 | − | 0.0749547i | \(-0.976119\pi\) |
0.563506 | + | 0.826112i | \(0.309452\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37909 | − | 2.38865i | 0.144567 | − | 0.250398i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.05753 | + | 1.83169i | 0.109661 | + | 0.189938i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.47689 | + | 0.424951i | −0.356721 | + | 0.0435991i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.34982 | + | 9.26615i | 0.543192 | + | 0.940835i | 0.998718 | + | 0.0506133i | \(0.0161176\pi\) |
−0.455527 | + | 0.890222i | \(0.650549\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.55066 | + | 4.41787i | −0.256351 | + | 0.444013i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.79117 | − | 3.10239i | 0.178228 | − | 0.308700i | −0.763046 | − | 0.646345i | \(-0.776297\pi\) |
0.941274 | + | 0.337645i | \(0.109630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.04968 | 0.201961 | 0.100980 | − | 0.994888i | \(-0.467802\pi\) | ||||
0.100980 | + | 0.994888i | \(0.467802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.424502 | + | 0.735260i | −0.0414272 | + | 0.0717540i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.88697 | 0.955809 | 0.477905 | − | 0.878412i | \(-0.341396\pi\) | ||||
0.477905 | + | 0.878412i | \(0.341396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.72335 | − | 9.91314i | −0.548198 | − | 0.949506i | −0.998398 | − | 0.0565787i | \(-0.981981\pi\) |
0.450200 | − | 0.892928i | \(-0.351353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.11405 | + | 1.92958i | 0.105740 | + | 0.183148i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.970282 | 0.0912765 | 0.0456382 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456382 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.893273 | −0.0832981 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.52927 | + | 2.64877i | 0.141381 | + | 0.244879i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.22125 | + | 5.57937i | 0.295292 | + | 0.511460i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.74707 | −0.704279 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.711537 | + | 1.23242i | −0.0641571 | + | 0.111123i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.51696 | 0.672337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.65956 | + | 14.9988i | −0.768412 | + | 1.33093i | 0.170012 | + | 0.985442i | \(0.445619\pi\) |
−0.938424 | + | 0.345486i | \(0.887714\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.954892 | + | 1.65392i | −0.0840735 | + | 0.145620i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.34355 | + | 10.9874i | 0.554239 | + | 0.959970i | 0.997962 | + | 0.0638059i | \(0.0203239\pi\) |
−0.443724 | + | 0.896164i | \(0.646343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.34985 | − | 10.2318i | 0.377180 | − | 0.887211i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.970016 | − | 1.68012i | −0.0834857 | − | 0.144602i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.29330 | + | 9.16826i | −0.452237 | + | 0.783298i | −0.998525 | − | 0.0543001i | \(-0.982707\pi\) |
0.546288 | + | 0.837598i | \(0.316041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.81428 | − | 11.8027i | 0.577980 | − | 1.00109i | −0.417731 | − | 0.908571i | \(-0.637175\pi\) |
0.995711 | − | 0.0925198i | \(-0.0294921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.97516 | 0.166339 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.975161 | − | 1.68903i | 0.0815470 | − | 0.141244i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.01800 | −0.582813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.102340 | + | 0.177258i | 0.00844086 | + | 0.0146200i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.09378 | + | 1.89448i | 0.0896056 | + | 0.155202i | 0.907344 | − | 0.420388i | \(-0.138106\pi\) |
−0.817739 | + | 0.575589i | \(0.804773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2592 | 0.916257 | 0.458128 | − | 0.888886i | \(-0.348520\pi\) | ||||
0.458128 | + | 0.888886i | \(0.348520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.14410 | −0.577566 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.05164 | − | 3.55354i | −0.164792 | − | 0.285427i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2843 | − | 17.8129i | −0.820776 | − | 1.42163i | −0.905105 | − | 0.425188i | \(-0.860208\pi\) |
0.0843284 | − | 0.996438i | \(-0.473126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.703083 | −0.0557581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.41766 | − | 2.45546i | 0.111728 | − | 0.193518i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9546 | −1.32799 | −0.663993 | − | 0.747739i | \(-0.731139\pi\) | ||||
−0.663993 | + | 0.747739i | \(0.731139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.300168 | + | 0.519907i | −0.0233681 | + | 0.0404747i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9836 | − | 19.0241i | 0.849933 | − | 1.47213i | −0.0313341 | − | 0.999509i | \(-0.509976\pi\) |
0.881267 | − | 0.472618i | \(-0.156691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.91533 | + | 10.2457i | 0.455026 | + | 0.788128i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.41421 | + | 9.85035i | 0.566979 | + | 0.753275i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.84870 | + | 4.93409i | 0.216582 | + | 0.375132i | 0.953761 | − | 0.300566i | \(-0.0971757\pi\) |
−0.737179 | + | 0.675698i | \(0.763842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.55310 | + | 9.61825i | −0.419775 | + | 0.727071i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.24707 | + | 2.15999i | −0.0937356 | + | 0.162355i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.72447 | 0.652098 | 0.326049 | − | 0.945353i | \(-0.394283\pi\) | ||||
0.326049 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0426688 | − | 0.0739045i | 0.00317155 | − | 0.00549328i | −0.864435 | − | 0.502744i | \(-0.832324\pi\) |
0.867607 | + | 0.497251i | \(0.165657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.01915 | −0.0753376 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.16128 | − | 3.74345i | −0.158901 | − | 0.275224i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.27777 | + | 3.94521i | 0.166567 | + | 0.288502i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.15783 | 0.447917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.12646 | + | 10.6113i | 0.440993 | + | 0.763822i | 0.997763 | − | 0.0668446i | \(-0.0212932\pi\) |
−0.556771 | + | 0.830666i | \(0.687960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.179969 | + | 0.311715i | 0.0128878 | + | 0.0223224i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.72223 | −0.550186 | −0.275093 | − | 0.961418i | \(-0.588709\pi\) | ||||
−0.275093 | + | 0.961418i | \(0.588709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.35154 | − | 11.0012i | 0.450249 | − | 0.779854i | −0.548152 | − | 0.836378i | \(-0.684669\pi\) |
0.998401 | + | 0.0565246i | \(0.0180019\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50300 | 0.247083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.1379 | − | 19.2914i | 0.781725 | − | 1.35399i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.38040 | − | 2.39093i | 0.0964116 | − | 0.166990i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.57205 | + | 2.72287i | 0.109265 | + | 0.189252i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.07581 | − | 7.23499i | 0.212758 | − | 0.500455i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.19912 | − | 3.80898i | −0.151393 | − | 0.262221i | 0.780347 | − | 0.625347i | \(-0.215043\pi\) |
−0.931740 | + | 0.363126i | \(0.881709\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.84870 | + | 4.93409i | −0.195189 | + | 0.338078i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.85252 | − | 3.20866i | 0.126341 | − | 0.218829i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.0242 | 0.884138 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.01069 | − | 3.48263i | 0.135870 | − | 0.235334i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.73131 | 0.183728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.580642 | + | 1.00570i | 0.0388827 | + | 0.0673468i | 0.884812 | − | 0.465949i | \(-0.154287\pi\) |
−0.845929 | + | 0.533295i | \(0.820953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.15783 | − | 10.6657i | −0.410522 | − | 0.711045i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4507 | 0.760009 | 0.380004 | − | 0.924985i | \(-0.375922\pi\) | ||||
0.380004 | + | 0.924985i | \(0.375922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.14410 | −0.472095 | −0.236048 | − | 0.971742i | \(-0.575852\pi\) | ||||
−0.236048 | + | 0.971742i | \(0.575852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.952761 | − | 1.65023i | −0.0626871 | − | 0.108577i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0720 | − | 17.4453i | −0.659842 | − | 1.14288i | −0.980656 | − | 0.195737i | \(-0.937290\pi\) |
0.320815 | − | 0.947142i | \(-0.396043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.83188 | −0.249964 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.09277 | + | 1.89273i | −0.0709828 | + | 0.122946i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.7085 | 1.72763 | 0.863814 | − | 0.503810i | \(-0.168069\pi\) | ||||
0.863814 | + | 0.503810i | \(0.168069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.66128 | − | 6.34153i | 0.235844 | − | 0.408494i | −0.723674 | − | 0.690142i | \(-0.757548\pi\) |
0.959518 | + | 0.281649i | \(0.0908812\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.17157 | + | 8.95743i | −0.331757 | + | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.198543 | − | 0.343886i | −0.0126844 | − | 0.0219701i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.83458 | − | 3.76596i | −0.180360 | − | 0.239622i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.84427 | + | 3.19436i | 0.116876 | + | 0.202435i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.8502 | − | 23.9893i | 0.874218 | − | 1.51419i | 0.0166252 | − | 0.999862i | \(-0.494708\pi\) |
0.857593 | − | 0.514329i | \(-0.171959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00244 | − | 1.73628i | 0.0630228 | − | 0.109159i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.840737 | −0.0526490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.02582 | + | 8.70497i | −0.313502 | + | 0.543001i | −0.979118 | − | 0.203293i | \(-0.934836\pi\) |
0.665616 | + | 0.746294i | \(0.268169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.7202 | 0.852532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.3508 | + | 21.3922i | 0.764495 | + | 1.32414i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.48698 | − | 11.2358i | −0.400004 | − | 0.692827i | 0.593722 | − | 0.804670i | \(-0.297658\pi\) |
−0.993726 | + | 0.111843i | \(0.964325\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36400 | 0.0837901 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.38937 | 0.207426 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.26779 | + | 2.19587i | 0.0772984 | + | 0.133885i | 0.902083 | − | 0.431562i | \(-0.142037\pi\) |
−0.824785 | + | 0.565446i | \(0.808704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2692 | + | 17.7867i | 0.623808 | + | 1.08047i | 0.988770 | + | 0.149445i | \(0.0477486\pi\) |
−0.364962 | + | 0.931022i | \(0.618918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.14247 | −0.0691455 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.92663 | + | 6.80113i | −0.236785 | + | 0.410123i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00202 | 0.120290 | 0.0601449 | − | 0.998190i | \(-0.480844\pi\) | ||||
0.0601449 | + | 0.998190i | \(0.480844\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.22125 | + | 12.5076i | −0.432325 | + | 0.748809i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6738 | − | 25.4158i | 0.875366 | − | 1.51618i | 0.0189944 | − | 0.999820i | \(-0.493954\pi\) |
0.856372 | − | 0.516359i | \(-0.172713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1155 | + | 20.9846i | 0.720189 | + | 1.24740i | 0.960924 | + | 0.276814i | \(0.0892785\pi\) |
−0.240734 | + | 0.970591i | \(0.577388\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.872525 | + | 1.15922i | 0.0516839 | + | 0.0686660i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.38152 | + | 7.58902i | 0.258633 | + | 0.447966i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.31012 | − | 9.19739i | 0.312360 | − | 0.541023i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.21597 | − | 3.83817i | 0.129902 | − | 0.224997i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3274 | −0.603336 | −0.301668 | − | 0.953413i | \(-0.597543\pi\) | ||||
−0.301668 | + | 0.953413i | \(0.597543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.41936 | − | 4.19045i | 0.140860 | − | 0.243977i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.35425 | 0.252659 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.601021 | − | 1.04100i | −0.0347579 | − | 0.0602025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.88007 | + | 10.1846i | 0.338921 | + | 0.587029i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.48385 | −0.0852451 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.97718 | 0.113213 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.2236 | + | 26.3681i | 0.868858 | + | 1.50491i | 0.863165 | + | 0.504922i | \(0.168479\pi\) |
0.00569274 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.424502 | − | 0.735260i | −0.0241491 | − | 0.0418275i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.6343 | 1.56699 | 0.783497 | − | 0.621395i | \(-0.213434\pi\) | ||||
0.783497 | + | 0.621395i | \(0.213434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.939053 | + | 1.62649i | −0.0530784 | + | 0.0919345i | −0.891344 | − | 0.453328i | \(-0.850237\pi\) |
0.838265 | + | 0.545262i | \(0.183570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.79737 | −0.326645 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.24917 | + | 16.0200i | −0.519485 | + | 0.899775i | 0.480258 | + | 0.877127i | \(0.340543\pi\) |
−0.999744 | + | 0.0226477i | \(0.992790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.87567 | − | 13.6411i | 0.440953 | − | 0.763752i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.04766 | − | 3.54665i | −0.114289 | − | 0.197955i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.9285 | − | 1.33570i | 0.608076 | − | 0.0743202i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.35425 | + | 4.07767i | 0.130590 | + | 0.226189i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.37069 | + | 4.10616i | −0.131099 | + | 0.227071i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.08136 | − | 10.5332i | 0.335276 | − | 0.580715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.03566 | −0.166855 | −0.0834275 | − | 0.996514i | \(-0.526587\pi\) | ||||
−0.0834275 | + | 0.996514i | \(0.526587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.60718 | + | 13.1760i | −0.416871 | + | 0.722041i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.79594 | −0.371302 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4897 | + | 18.1687i | 0.571411 | + | 0.989713i | 0.996421 | + | 0.0845244i | \(0.0269371\pi\) |
−0.425010 | + | 0.905188i | \(0.639730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.200952 | − | 0.348059i | −0.0109142 | − | 0.0189040i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.20947 | 0.498721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1150 | 1.03211 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.185003 | + | 0.320434i | 0.00996022 | + | 0.0172516i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.7329 | − | 18.5900i | −0.576174 | − | 0.997962i | −0.995913 | − | 0.0903174i | \(-0.971212\pi\) |
0.419739 | − | 0.907645i | \(-0.362121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.1324 | −1.82706 | −0.913532 | − | 0.406767i | \(-0.866656\pi\) | ||||
−0.913532 | + | 0.406767i | \(0.866656\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.30531 | − | 2.26087i | 0.0696724 | − | 0.120676i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1827 | 0.808092 | 0.404046 | − | 0.914739i | \(-0.367604\pi\) | ||||
0.404046 | + | 0.914739i | \(0.367604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.52656 | − | 9.57229i | 0.293320 | − | 0.508044i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33429 | − | 2.31105i | 0.0706179 | − | 0.122314i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0128 | − | 27.7350i | −0.845123 | − | 1.46380i | −0.885514 | − | 0.464612i | \(-0.846194\pi\) |
0.0403913 | − | 0.999184i | \(-0.487140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1833 | − | 13.6821i | −0.693860 | − | 0.720110i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.60447 | + | 2.77903i | 0.0842129 | + | 0.145861i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.90081 | + | 6.75641i | −0.204178 | + | 0.353647i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2375 | + | 24.6601i | −0.743191 | + | 1.28725i | 0.207844 | + | 0.978162i | \(0.433355\pi\) |
−0.951035 | + | 0.309083i | \(0.899978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.71735 | −0.505865 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16473 | + | 3.74943i | −0.112387 | + | 0.194661i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8196 | −1.02622 | −0.513109 | − | 0.858323i | \(-0.671506\pi\) | ||||
−0.513109 | + | 0.858323i | \(0.671506\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.55681 | − | 2.69648i | −0.0803935 | − | 0.139246i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.72192 | − | 8.17861i | −0.243191 | − | 0.421220i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.38307 | −0.225143 | −0.112572 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112572 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.17381 | 0.367526 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.95628 | − | 17.2448i | −0.508742 | − | 0.881167i | −0.999949 | − | 0.0101240i | \(-0.996777\pi\) |
0.491207 | − | 0.871043i | \(-0.336556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.84839 | + | 3.20150i | 0.0942026 | + | 0.163164i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.0408 | −0.662902 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.42419 | − | 14.5911i | 0.427124 | − | 0.739800i | −0.569493 | − | 0.821997i | \(-0.692860\pi\) |
0.996616 | + | 0.0821968i | \(0.0261936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.80772 | 0.141992 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.62759 | − | 4.55111i | 0.132544 | − | 0.229573i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.12000 | − | 3.67195i | 0.106669 | − | 0.184756i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.44457 | − | 12.8944i | −0.373632 | − | 0.647150i | 0.616489 | − | 0.787364i | \(-0.288555\pi\) |
−0.990121 | + | 0.140213i | \(0.955221\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.57124 | + | 0.558705i | −0.228848 | + | 0.0279702i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.01351 | − | 12.1478i | −0.350238 | − | 0.606630i | 0.636053 | − | 0.771645i | \(-0.280566\pi\) |
−0.986291 | + | 0.165015i | \(0.947233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.76081 | − | 4.78186i | 0.137526 | − | 0.238201i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.00754 | − | 5.20921i | 0.149446 | − | 0.258848i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.70165 | 0.480893 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.9804 | + | 31.1430i | −0.889074 | + | 1.53992i | −0.0481015 | + | 0.998842i | \(0.515317\pi\) |
−0.840972 | + | 0.541078i | \(0.818016\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.38511 | 0.216302 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.67925 | + | 13.3009i | 0.377871 | + | 0.654492i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.57794 | − | 6.19717i | −0.175634 | − | 0.304207i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.64514 | −0.276444 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0916 | −0.639565 | −0.319782 | − | 0.947491i | \(-0.603610\pi\) | ||||
−0.319782 | + | 0.947491i | \(0.603610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1489 | + | 22.7745i | 0.640836 | + | 1.10996i | 0.985246 | + | 0.171142i | \(0.0547457\pi\) |
−0.344410 | + | 0.938819i | \(0.611921\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.74362 | + | 11.6803i | 0.327886 | + | 0.567915i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.9980 | −0.533483 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.13787 | + | 5.43496i | −0.151852 | + | 0.263016i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.807850 | −0.0390033 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.8311 | + | 23.9562i | −0.666222 | + | 1.15393i | 0.312730 | + | 0.949842i | \(0.398756\pi\) |
−0.978952 | + | 0.204089i | \(0.934577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.24152 | − | 3.88243i | 0.107721 | − | 0.186578i | −0.807126 | − | 0.590379i | \(-0.798978\pi\) |
0.914846 | + | 0.403802i | \(0.132311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.45348 | + | 2.51749i | 0.0696888 | + | 0.120705i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.91387 | − | 3.87131i | −0.139390 | − | 0.185190i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1630 | + | 21.0669i | 0.580507 | + | 1.00547i | 0.995419 | + | 0.0956066i | \(0.0304791\pi\) |
−0.414912 | + | 0.909862i | \(0.636188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.698821 | + | 1.21039i | −0.0332772 | + | 0.0576378i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3133 | − | 17.8632i | 0.490000 | − | 0.848705i | −0.509934 | − | 0.860214i | \(-0.670330\pi\) |
0.999934 | + | 0.0115090i | \(0.00366351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.57550 | −0.311708 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.453057 | − | 0.784718i | 0.0214289 | − | 0.0371159i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.3729 | −0.819876 | −0.409938 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409938 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.09821 | + | 5.36625i | 0.145889 | + | 0.252687i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.33185 | − | 4.03888i | −0.109560 | − | 0.189763i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.21643 | 0.103908 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.5791 | 1.33687 | 0.668437 | − | 0.743769i | \(-0.266964\pi\) | ||||
0.668437 | + | 0.743769i | \(0.266964\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.04893 | + | 5.28091i | 0.142312 | + | 0.246492i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.33053 | + | 4.03659i | 0.108543 | + | 0.188003i | 0.915180 | − | 0.403044i | \(-0.132048\pi\) |
−0.806637 | + | 0.591047i | \(0.798715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.42674 | −0.159254 | −0.0796271 | − | 0.996825i | \(-0.525373\pi\) | ||||
−0.0796271 | + | 0.996825i | \(0.525373\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.849817 | + | 1.47193i | −0.0394093 | + | 0.0682589i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.0559 | −1.39082 | −0.695411 | − | 0.718613i | \(-0.744777\pi\) | ||||
−0.695411 | + | 0.718613i | \(0.744777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7854 | − | 18.6809i | 0.498026 | − | 0.862606i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.25990 | + | 7.37836i | −0.196286 | + | 0.339977i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.15783 | + | 7.20158i | 0.191177 | + | 0.331129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.4139 | + | 15.1642i | 0.523704 | + | 0.695782i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.40048 | − | 4.15774i | −0.109910 | − | 0.190370i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4280 | − | 18.0619i | 0.476468 | − | 0.825267i | −0.523168 | − | 0.852230i | \(-0.675250\pi\) |
0.999636 | + | 0.0269621i | \(0.00858334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.90835 | − | 5.03742i | 0.132610 | − | 0.229686i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.17443 | −0.0534385 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.29905 | + | 7.44617i | −0.195210 | + | 0.338113i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.5551 | −1.65647 | −0.828236 | − | 0.560380i | \(-0.810655\pi\) | ||||
−0.828236 | + | 0.560380i | \(0.810655\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.51141 | + | 6.08194i | 0.158791 | + | 0.275035i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.94221 | − | 6.82810i | −0.177909 | − | 0.308148i | 0.763255 | − | 0.646097i | \(-0.223600\pi\) |
−0.941164 | + | 0.337949i | \(0.890267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0588 | 0.993479 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.09936 | −0.184252 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.5418 | + | 30.3833i | 0.786857 | + | 1.36288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5414 | − | 18.2582i | −0.471898 | − | 0.817351i | 0.527585 | − | 0.849502i | \(-0.323097\pi\) |
−0.999483 | + | 0.0321514i | \(0.989764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.09908 | −0.406517 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.20921 | − | 9.02261i | 0.232267 | − | 0.402298i | −0.726208 | − | 0.687475i | \(-0.758719\pi\) |
0.958475 | + | 0.285177i | \(0.0920523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.87872 | 0.128101 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.45021 | − | 4.24389i | 0.108818 | − | 0.188478i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.0260 | − | 31.2219i | 0.798987 | − | 1.38389i | −0.121290 | − | 0.992617i | \(-0.538703\pi\) |
0.920277 | − | 0.391268i | \(-0.127964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.3815 | − | 21.4454i | −0.547726 | − | 0.948690i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.11716 | − | 9.68448i | 0.181777 | − | 0.427580i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.823548 | + | 1.42643i | 0.0362899 | + | 0.0628559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.30017 | − | 7.44811i | 0.189121 | − | 0.327568i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.17997 | − | 2.04377i | 0.0517949 | − | 0.0897113i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.5888 | −1.42774 | −0.713871 | − | 0.700277i | \(-0.753060\pi\) | ||||
−0.713871 | + | 0.700277i | \(0.753060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.275595 | − | 0.477344i | 0.0120509 | − | 0.0208728i | −0.859937 | − | 0.510400i | \(-0.829497\pi\) |
0.871988 | + | 0.489527i | \(0.162831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.60034 | 0.200775 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.44866 | + | 11.1694i | 0.280908 | + | 0.486547i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8822 | + | 18.8485i | 0.473138 | + | 0.819498i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.0311 | −0.739085 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.71511 | 0.160919 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.97252 | + | 6.88061i | 0.171747 | + | 0.297475i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.80690 | − | 3.12964i | −0.0779734 | − | 0.135054i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.891227 | 0.0383879 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.33743 | + | 12.7088i | −0.315461 | + | 0.546394i | −0.979535 | − | 0.201272i | \(-0.935492\pi\) |
0.664075 | + | 0.747666i | \(0.268826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.0353480 | −0.00151693 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.59922 | − | 7.96608i | 0.197009 | − | 0.341229i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5045 | + | 37.2469i | −0.919466 | + | 1.59256i | −0.119238 | + | 0.992866i | \(0.538045\pi\) |
−0.800228 | + | 0.599696i | \(0.795288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.47959 | − | 6.02683i | −0.148505 | − | 0.257219i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.8929 | − | 30.4149i | −0.975269 | − | 1.29572i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.72907 | + | 11.6551i | 0.286149 | + | 0.495625i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.895233 | + | 1.55059i | −0.0380005 | + | 0.0658189i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.6882 | − | 37.5651i | 0.918960 | − | 1.59168i | 0.117961 | − | 0.993018i | \(-0.462364\pi\) |
0.800998 | − | 0.598666i | \(-0.204302\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.98573 | 0.210874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.943483 | − | 1.63416i | 0.0398339 | − | 0.0689943i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9925 | 1.60119 | 0.800597 | − | 0.599203i | \(-0.204516\pi\) | ||||
0.800597 | + | 0.599203i | \(0.204516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.389853 | + | 0.675246i | 0.0164013 | + | 0.0284078i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.54620 | + | 16.5345i | 0.400903 | + | 0.694384i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3448 | 1.18827 | 0.594137 | − | 0.804364i | \(-0.297494\pi\) | ||||
0.594137 | + | 0.804364i | \(0.297494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.9591 | −1.79778 | −0.898890 | − | 0.438173i | \(-0.855626\pi\) | ||||
−0.898890 | + | 0.438173i | \(0.855626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.65685 | − | 2.86976i | −0.0692161 | − | 0.119886i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.42010 | + | 4.19174i | 0.100925 | + | 0.174808i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.8775 | −1.41034 | −0.705169 | − | 0.709039i | \(-0.749129\pi\) | ||||
−0.705169 | + | 0.709039i | \(0.749129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.53766 | − | 4.39536i | 0.105462 | − | 0.182665i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.7134 | 0.942309 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.53070 | + | 2.65125i | −0.0633950 | + | 0.109803i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.22890 | + | 2.12852i | −0.0508089 | + | 0.0880035i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.325273 | − | 0.563390i | −0.0134255 | − | 0.0232536i | 0.859235 | − | 0.511582i | \(-0.170940\pi\) |
−0.872660 | + | 0.488328i | \(0.837607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.70801 | − | 20.4832i | 0.358807 | − | 0.843996i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.59933 | + | 2.77011i | 0.0657875 | + | 0.113947i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4152 | + | 21.5037i | −0.509831 | + | 0.883053i | 0.490104 | + | 0.871664i | \(0.336959\pi\) |
−0.999935 | + | 0.0113892i | \(0.996375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.58856 | + | 4.48352i | −0.106121 | + | 0.183806i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.26179 | −0.215351 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.54206 | + | 2.67093i | −0.0630070 | + | 0.109131i | −0.895808 | − | 0.444441i | \(-0.853402\pi\) |
0.832801 | + | 0.553572i | \(0.186736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9545 | −0.650799 | −0.325399 | − | 0.945577i | \(-0.605499\pi\) | ||||
−0.325399 | + | 0.945577i | \(0.605499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9600 | + | 20.7153i | 0.487049 | + | 0.843593i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.11273 | − | 5.39140i | −0.126550 | − | 0.219192i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.7258 | −1.24712 | −0.623561 | − | 0.781775i | \(-0.714315\pi\) | ||||
−0.623561 | + | 0.781775i | \(0.714315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.22692 | −0.373894 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.57820 | − | 4.46558i | −0.104303 | − | 0.180658i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0776 | − | 17.4549i | −0.407030 | − | 0.704997i | 0.587525 | − | 0.809206i | \(-0.300102\pi\) |
−0.994555 | + | 0.104209i | \(0.966769\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.14356 | −0.0461130 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.9253 | + | 24.1194i | −0.560612 | + | 0.971009i | 0.436831 | + | 0.899544i | \(0.356101\pi\) |
−0.997443 | + | 0.0714650i | \(0.977233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.5555 | −0.826197 | −0.413098 | − | 0.910686i | \(-0.635553\pi\) | ||||
−0.413098 | + | 0.910686i | \(0.635553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.34183 | − | 2.32411i | 0.0538457 | − | 0.0932634i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.4356 | − | 18.0750i | 0.418094 | − | 0.724159i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.86535 | − | 13.6232i | −0.314614 | − | 0.544927i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.23235 | + | 0.395064i | −0.129088 | + | 0.0157773i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.79330 | + | 11.7663i | 0.270867 | + | 0.469155i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.2127 | + | 29.8132i | −0.685225 | + | 1.18684i | 0.288141 | + | 0.957588i | \(0.406963\pi\) |
−0.973366 | + | 0.229257i | \(0.926371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.910904 | + | 1.57773i | −0.0362052 | + | 0.0627092i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.9174 | −0.552297 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.267171 | − | 0.462754i | 0.0105857 | − | 0.0183350i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.9042 | −1.53903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.22711 | + | 3.85747i | 0.0879656 | + | 0.152361i | 0.906651 | − | 0.421881i | \(-0.138630\pi\) |
−0.818685 | + | 0.574242i | \(0.805297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9267 | − | 20.6577i | −0.470343 | − | 0.814658i | 0.529082 | − | 0.848571i | \(-0.322537\pi\) |
−0.999425 | + | 0.0339127i | \(0.989203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.53468 | −0.0604279 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.8836 | −1.13553 | −0.567767 | − | 0.823189i | \(-0.692192\pi\) | ||||
−0.567767 | + | 0.823189i | \(0.692192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.43005 | + | 9.40513i | 0.213148 | + | 0.369184i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.69739 | − | 4.67202i | −0.105719 | − | 0.183111i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.7094 | −0.771288 | −0.385644 | − | 0.922648i | \(-0.626021\pi\) | ||||
−0.385644 | + | 0.922648i | \(0.626021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.09760 | + | 8.82930i | −0.199180 | + | 0.344989i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.4598 | 1.07131 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.1400 | − | 38.3475i | 0.862450 | − | 1.49381i | −0.00710614 | − | 0.999975i | \(-0.502262\pi\) |
0.869557 | − | 0.493833i | \(-0.164405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.2921 | − | 17.8265i | 0.400318 | − | 0.693371i | −0.593446 | − | 0.804874i | \(-0.702233\pi\) |
0.993764 | + | 0.111502i | \(0.0355663\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.565673 | − | 0.979775i | −0.0219689 | − | 0.0380513i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.86835 | − | 1.08391i | 0.343900 | − | 0.0420320i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.85401 | − | 8.40739i | −0.187948 | − | 0.325536i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.240510 | − | 0.416575i | 0.00929865 | − | 0.0161057i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.21881 | + | 3.84309i | −0.0856563 | + | 0.148361i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4695 | −0.750495 | −0.375247 | − | 0.926925i | \(-0.622442\pi\) | ||||
−0.375247 | + | 0.926925i | \(0.622442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.25604 | + | 9.10373i | −0.202305 | + | 0.350403i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.7238 | −1.71888 | −0.859438 | − | 0.511241i | \(-0.829186\pi\) | ||||
−0.859438 | + | 0.511241i | \(0.829186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.6456 | − | 23.6348i | −0.523668 | − | 0.907020i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.37151 | − | 4.10758i | −0.0908766 | − | 0.157403i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.5797 | −1.20836 | −0.604182 | − | 0.796847i | \(-0.706500\pi\) | ||||
−0.604182 | + | 0.796847i | \(0.706500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.50726 | −0.325046 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.47959 | + | 2.56273i | 0.0564499 | + | 0.0977741i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.917743 | + | 1.58958i | 0.0349632 | + | 0.0605581i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.65685 | −0.0630297 | −0.0315149 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315149 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.50586 | − | 11.2685i | 0.247137 | − | 0.428054i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.9518 | 0.415424 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.33886 | + | 7.51512i | −0.164346 | + | 0.284655i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.17198 | + | 7.22608i | −0.157799 | + | 0.273315i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5990 | + | 21.8221i | 0.475858 | + | 0.824211i | 0.999618 | − | 0.0276556i | \(-0.00880416\pi\) |
−0.523759 | + | 0.851866i | \(0.675471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.17340 | − | 21.5779i | 0.345981 | − | 0.813826i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.793608 | + | 1.37457i | 0.0298890 | + | 0.0517693i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.56866 | + | 7.91315i | −0.171822 | + | 0.297605i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.6472 | + | 34.0300i | −0.737866 | + | 1.27802i | 0.215588 | + | 0.976484i | \(0.430833\pi\) |
−0.953454 | + | 0.301538i | \(0.902500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.9237 | −0.559684 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.83804 | − | 4.91563i | 0.106285 | − | 0.184092i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.56725 | 0.0586120 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.53151 | − | 9.58086i | −0.206578 | − | 0.357804i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.36385 | + | 4.09431i | 0.0881568 | + | 0.152692i | 0.906732 | − | 0.421707i | \(-0.138569\pi\) |
−0.818575 | + | 0.574399i | \(0.805236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.22803 | −0.194702 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.03311 | −0.112802 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.0135 | + | 32.9324i | 0.706145 | + | 1.22308i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2530 | + | 42.0074i | 0.899494 | + | 1.55797i | 0.828142 | + | 0.560518i | \(0.189398\pi\) |
0.0713515 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.82280 | + | 10.0854i | −0.215364 | + | 0.373022i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.3496 | 1.12099 | 0.560495 | − | 0.828158i | \(-0.310611\pi\) | ||||
0.560495 | + | 0.828158i | \(0.310611\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0822392 | + | 0.142442i | −0.00303344 | + | 0.00525407i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.62646 | − | 13.2094i | 0.280924 | − | 0.486575i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.82538 | − | 4.89371i | −0.103933 | − | 0.180018i | 0.809369 | − | 0.587301i | \(-0.199810\pi\) |
−0.913302 | + | 0.407283i | \(0.866476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.763862 | + | 1.79678i | −0.0280612 | + | 0.0660062i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.29544 | − | 10.9040i | −0.230957 | − | 0.400030i | 0.727133 | − | 0.686497i | \(-0.240852\pi\) |
−0.958090 | + | 0.286467i | \(0.907519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.878945 | + | 1.52238i | −0.0322021 | + | 0.0557756i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5934 | + | 21.8125i | −0.460770 | + | 0.798077i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.2183 | −0.921456 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.09861 | − | 10.5631i | 0.222542 | − | 0.385453i | −0.733038 | − | 0.680188i | \(-0.761898\pi\) |
0.955579 | + | 0.294735i | \(0.0952314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4739 | −0.418132 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.52386 | + | 7.83555i | 0.164640 | + | 0.285165i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.30230 | − | 14.3800i | −0.301752 | − | 0.522650i | 0.674781 | − | 0.738018i | \(-0.264238\pi\) |
−0.976533 | + | 0.215368i | \(0.930905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.830448 | −0.0301434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.9722 | −0.651493 | −0.325747 | − | 0.945457i | \(-0.605616\pi\) | ||||
−0.325747 | + | 0.945457i | \(0.605616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.5983 | + | 25.2850i | 0.528495 | + | 0.915379i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.87045 | − | 4.97177i | −0.103782 | − | 0.179755i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.51127 | 0.235108 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.4284 | − | 47.5074i | 0.989093 | − | 1.71316i | 0.366989 | − | 0.930225i | \(-0.380389\pi\) |
0.622104 | − | 0.782934i | \(-0.286278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.16353 | 0.149946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9250 | − | 32.7790i | 0.680684 | − | 1.17898i | −0.294088 | − | 0.955778i | \(-0.595016\pi\) |
0.974772 | − | 0.223201i | \(-0.0716507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.1168 | + | 19.2549i | −0.399328 | + | 0.691656i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.84155 | − | 4.92171i | −0.101940 | − | 0.176565i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8648 | − | 1.81681i | 0.532588 | − | 0.0650938i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4039 | + | 21.4842i | 0.443847 | + | 0.768766i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5421 | − | 18.2594i | 0.376743 | − | 0.652537i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.26434 | − | 14.3143i | 0.294967 | − | 0.510898i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.5892 | −0.377466 | −0.188733 | − | 0.982028i | \(-0.560438\pi\) | ||||
−0.188733 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.68699 | + | 4.65401i | −0.0956595 | + | 0.165687i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.47486 | −0.0879958 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.33031 | + | 2.30416i | 0.0472406 | + | 0.0818231i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.282494 | − | 0.489295i | −0.0100190 | − | 0.0173535i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.2209 | −0.680838 | −0.340419 | − | 0.940274i | \(-0.610569\pi\) | ||||
−0.340419 | + | 0.940274i | \(0.610569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0443 | 0.426096 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.5720 | + | 20.0434i | 0.408878 | + | 0.708198i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.75506 | − | 15.1642i | −0.308959 | − | 0.535133i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.27843 | 0.0803043 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.525135 | − | 0.909561i | 0.0184856 | − | 0.0320181i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.4108 | 0.506658 | 0.253329 | − | 0.967380i | \(-0.418475\pi\) | ||||
0.253329 | + | 0.967380i | \(0.418475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.60447 | + | 2.77903i | −0.0563406 | + | 0.0975848i | −0.892820 | − | 0.450413i | \(-0.851277\pi\) |
0.836480 | + | 0.547998i | \(0.184610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.25363 | − | 7.36751i | 0.149181 | − | 0.258390i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.81225 | − | 11.7992i | −0.238623 | − | 0.413307i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.9488 | − | 2.43818i | 0.697920 | − | 0.0853011i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.90064 | − | 6.75611i | −0.136300 | − | 0.236078i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0191 | + | 36.4061i | −0.733570 | + | 1.27058i | 0.221778 | + | 0.975097i | \(0.428814\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.8422 | + | 32.6357i | −0.656799 | + | 1.13761i | 0.324641 | + | 0.945837i | \(0.394757\pi\) |
−0.981440 | + | 0.191772i | \(0.938577\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.25293 | 0.113252 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.33867 | + | 16.1751i | −0.324737 | + | 0.562462i | −0.981459 | − | 0.191671i | \(-0.938609\pi\) |
0.656722 | + | 0.754133i | \(0.271943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.28371 | 0.218242 | 0.109121 | − | 0.994028i | \(-0.465196\pi\) | ||||
0.109121 | + | 0.994028i | \(0.465196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.414632 | − | 0.718164i | −0.0143834 | − | 0.0249128i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.624056 | + | 1.08090i | 0.0216222 | + | 0.0374508i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.6525 | 0.610890 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.3274 | 0.426099 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.27458 | − | 14.3320i | −0.285670 | − | 0.494796i | 0.687101 | − | 0.726562i | \(-0.258883\pi\) |
−0.972772 | + | 0.231766i | \(0.925550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6355 | − | 40.9380i | −0.815019 | − | 1.41165i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1562 | −0.418681 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.75349 | + | 8.23329i | −0.163525 | + | 0.283234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.7601 | 0.678966 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.01839 | − | 8.69210i | 0.172231 | − | 0.298312i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.98971 | − | 5.17833i | 0.102486 | − | 0.177511i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2071 | + | 36.7319i | 0.726119 | + | 1.25767i | 0.958512 | + | 0.285053i | \(0.0920111\pi\) |
−0.232393 | + | 0.972622i | \(0.574656\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.87615 | + | 9.11757i | −0.132561 | + | 0.311814i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.3484 | + | 38.7085i | 0.763406 | + | 1.32226i | 0.941085 | + | 0.338170i | \(0.109808\pi\) |
−0.177679 | + | 0.984089i | \(0.556859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.45320 | − | 11.1773i | 0.220180 | − | 0.381363i | −0.734682 | − | 0.678411i | \(-0.762669\pi\) |
0.954863 | + | 0.297048i | \(0.0960021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81489 | − | 3.14348i | 0.0618512 | − | 0.107129i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.3069 | 0.487012 | 0.243506 | − | 0.969899i | \(-0.421703\pi\) | ||||
0.243506 | + | 0.969899i | \(0.421703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.28918 | + | 3.96497i | −0.0778344 | + | 0.134813i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.39905 | −0.149399 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.75817 | + | 8.24139i | 0.161410 | + | 0.279570i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.57251 | − | 7.91982i | −0.154934 | − | 0.268353i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.2631 | 1.02425 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.1732 | −0.648172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5307 | + | 44.2205i | 0.862111 | + | 1.49322i | 0.869887 | + | 0.493251i | \(0.164191\pi\) |
−0.00777597 | + | 0.999970i | \(0.502475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.13888 | + | 3.70466i | 0.0721428 | + | 0.124955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1375 | −1.04905 | −0.524524 | − | 0.851396i | \(-0.675757\pi\) | ||||
−0.524524 | + | 0.851396i | \(0.675757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7460 | − | 34.2011i | 0.664505 | − | 1.15096i | −0.314914 | − | 0.949120i | \(-0.601976\pi\) |
0.979419 | − | 0.201837i | \(-0.0646911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.00426 | −0.0673725 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.5853 | + | 28.7266i | −0.556881 | + | 0.964546i | 0.440874 | + | 0.897569i | \(0.354669\pi\) |
−0.997755 | + | 0.0669765i | \(0.978665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.0876 | − | 38.2568i | 0.740794 | − | 1.28309i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.75018 | + | 11.6917i | 0.226140 | + | 0.391685i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4997 | − | 16.6068i | −0.418285 | − | 0.555724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.50544 | + | 6.07160i | 0.117174 | + | 0.202951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.248951 | + | 0.431196i | −0.00831223 | + | 0.0143972i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.2971 | − | 38.6196i | 0.743648 | − | 1.28804i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.28731 | −0.142831 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.43560 | − | 4.21859i | 0.0810518 | − | 0.140386i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0685763 | 0.00227955 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3726 | + | 21.4300i | 0.410825 | + | 0.711570i | 0.994980 | − | 0.100072i | \(-0.0319073\pi\) |
−0.584155 | + | 0.811642i | \(0.698574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.06619 | − | 8.77490i | −0.168035 | − | 0.291045i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.4852 | 0.778100 | 0.389050 | − | 0.921217i | \(-0.372803\pi\) | ||||
0.389050 | + | 0.921217i | \(0.372803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0608 | 0.531534 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.409488 | − | 0.709254i | −0.0135372 | − | 0.0234472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.1802 | − | 28.0250i | −0.534318 | − | 0.925467i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6516 | 0.384350 | 0.192175 | − | 0.981361i | \(-0.438446\pi\) | ||||
0.192175 | + | 0.981361i | \(0.438446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.30583 | − | 10.9220i | 0.207784 | − | 0.359893i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8738 | 0.489576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7109 | + | 20.2839i | −0.385053 | + | 0.666931i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.89868 | − | 5.02067i | 0.0952052 | − | 0.164900i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.97418 | + | 5.15143i | 0.0975797 | + | 0.169013i | 0.910682 | − | 0.413107i | \(-0.135557\pi\) |
−0.813103 | + | 0.582120i | \(0.802223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.842699 | − | 1.98222i | 0.0276184 | − | 0.0649646i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.72324 | − | 9.91295i | −0.187371 | − | 0.324535i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.83039 | + | 3.17032i | −0.0598601 | + | 0.103681i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5608 | − | 28.6841i | 0.541017 | − | 0.937069i | −0.457829 | − | 0.889040i | \(-0.651373\pi\) |
0.998846 | − | 0.0480287i | \(-0.0152939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.777937 | 0.0253870 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2526 | + | 42.0068i | −0.790613 | + | 1.36938i | 0.134975 | + | 0.990849i | \(0.456905\pi\) |
−0.925588 | + | 0.378533i | \(0.876429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.81904 | 0.124365 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.47418 | + | 4.28541i | 0.0804851 | + | 0.139404i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.7734 | + | 25.5883i | 0.480071 | + | 0.831508i | 0.999739 | − | 0.0228609i | \(-0.00727749\pi\) |
−0.519667 | + | 0.854369i | \(0.673944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4983 | −0.340791 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.66226 | 0.248466 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.88592 | + | 15.3909i | 0.287843 | + | 0.498559i | 0.973295 | − | 0.229559i | \(-0.0737284\pi\) |
−0.685451 | + | 0.728118i | \(0.740395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.21435 | + | 5.56742i | 0.104014 | + | 0.180157i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.52442 | −0.210904 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.5014 | − | 23.3851i | 0.435983 | − | 0.755145i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.92677 | −0.158928 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.9823 | − | 24.2180i | 0.450573 | − | 0.780415i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.92315 | + | 8.52715i | −0.158482 | + | 0.274499i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.83458 | − | 15.3019i | −0.284101 | − | 0.492077i | 0.688290 | − | 0.725436i | \(-0.258362\pi\) |
−0.972391 | + | 0.233358i | \(0.925028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.74250 | − | 3.64362i | −0.0881018 | − | 0.117050i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.67986 | + | 15.0340i | 0.278550 | + | 0.482463i | 0.971025 | − | 0.238980i | \(-0.0768129\pi\) |
−0.692475 | + | 0.721442i | \(0.743480\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.3809 | + | 30.1046i | −0.557206 | + | 0.965110i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.975161 | − | 1.68903i | 0.0312301 | − | 0.0540922i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.07940 | −0.290476 | −0.145238 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145238 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.37909 | − | 12.7810i | 0.235837 | − | 0.408481i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.3762 | −1.03369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.1697 | + | 17.6144i | 0.324362 | + | 0.561812i | 0.981383 | − | 0.192060i | \(-0.0615169\pi\) |
−0.657021 | + | 0.753873i | \(0.728184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.10275 | − | 5.37411i | −0.0988617 | − | 0.171233i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.03796 | −0.160360 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.12520 | 0.162972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.7306 | − | 32.4424i | −0.594998 | − | 1.03057i | −0.993547 | − | 0.113420i | \(-0.963820\pi\) |
0.398549 | − | 0.917147i | \(-0.369514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.628706 | + | 1.08895i | 0.0199514 | + | 0.0345568i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2080 | 0.323617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.1668 | − | 28.0017i | 0.512008 | − | 0.886824i | −0.487895 | − | 0.872902i | \(-0.662235\pi\) |
0.999903 | − | 0.0139214i | \(-0.00443146\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.9863 | 0.410867 |
(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 | 1216.2.i.q.577.2 | 8 | ||
4.3 | odd | 2 | 1216.2.i.o.577.4 | 8 | |||
8.3 | odd | 2 | 608.2.i.e.577.1 | yes | 8 | ||
8.5 | even | 2 | 608.2.i.c.577.3 | yes | 8 | ||
19.11 | even | 3 | inner | 1216.2.i.q.961.2 | 8 | ||
76.11 | odd | 6 | 1216.2.i.o.961.4 | 8 | |||
152.11 | odd | 6 | 608.2.i.e.353.1 | yes | 8 | ||
152.125 | even | 6 | 608.2.i.c.353.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.c.353.3 | ✓ | 8 | 152.125 | even | 6 | ||
608.2.i.c.577.3 | yes | 8 | 8.5 | even | 2 | ||
608.2.i.e.353.1 | yes | 8 | 152.11 | odd | 6 | ||
608.2.i.e.577.1 | yes | 8 | 8.3 | odd | 2 | ||
1216.2.i.o.577.4 | 8 | 4.3 | odd | 2 | |||
1216.2.i.o.961.4 | 8 | 76.11 | odd | 6 | |||
1216.2.i.q.577.2 | 8 | 1.1 | even | 1 | trivial | ||
1216.2.i.q.961.2 | 8 | 19.11 | even | 3 | inner |