Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(16,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("65.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.e (of order \(3\), degree \(2\), 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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.809017 - 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.61 |
Dual form | 65.2.e.a.16.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 1.40126i | −0.572061 | + | 0.990839i | 0.424293 | + | 0.905525i | \(0.360523\pi\) |
−0.996354 | + | 0.0853143i | \(0.972811\pi\) | |||||||
\(3\) | 1.11803 | − | 1.93649i | 0.645497 | − | 1.11803i | −0.338689 | − | 0.940898i | \(-0.609984\pi\) |
0.984186 | − | 0.177136i | \(-0.0566831\pi\) | |||||||
\(4\) | −0.309017 | − | 0.535233i | −0.154508 | − | 0.267617i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.80902 | + | 3.13331i | 0.738528 | + | 1.27917i | ||||
\(7\) | 0.118034 | + | 0.204441i | 0.0446127 | + | 0.0772714i | 0.887469 | − | 0.460866i | \(-0.152461\pi\) |
−0.842857 | + | 0.538138i | \(0.819128\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −1.00000 | − | 1.73205i | −0.333333 | − | 0.577350i | ||||
\(10\) | −0.809017 | + | 1.40126i | −0.255834 | + | 0.443117i | ||||
\(11\) | −2.11803 | + | 3.66854i | −0.638611 | + | 1.10611i | 0.347126 | + | 0.937818i | \(0.387157\pi\) |
−0.985738 | + | 0.168289i | \(0.946176\pi\) | |||||||
\(12\) | −1.38197 | −0.398939 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | 1.11803 | − | 1.93649i | 0.288675 | − | 0.500000i | ||||
\(16\) | 2.42705 | − | 4.20378i | 0.606763 | − | 1.05094i | ||||
\(17\) | −2.73607 | − | 4.73901i | −0.663594 | − | 1.14938i | −0.979664 | − | 0.200643i | \(-0.935697\pi\) |
0.316071 | − | 0.948736i | \(-0.397636\pi\) | |||||||
\(18\) | 3.23607 | 0.762749 | ||||||||
\(19\) | 0.118034 | + | 0.204441i | 0.0270789 | + | 0.0469020i | 0.879247 | − | 0.476366i | \(-0.158046\pi\) |
−0.852168 | + | 0.523268i | \(0.824713\pi\) | |||||||
\(20\) | −0.309017 | − | 0.535233i | −0.0690983 | − | 0.119682i | ||||
\(21\) | 0.527864 | 0.115189 | ||||||||
\(22\) | −3.42705 | − | 5.93583i | −0.730650 | − | 1.26552i | ||||
\(23\) | −4.11803 | + | 7.13264i | −0.858669 | + | 1.48726i | 0.0145291 | + | 0.999894i | \(0.495375\pi\) |
−0.873199 | + | 0.487365i | \(0.837958\pi\) | |||||||
\(24\) | −2.50000 | + | 4.33013i | −0.510310 | + | 0.883883i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.66312 | + | 1.40126i | 1.11063 | + | 0.274809i | ||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0.0729490 | − | 0.126351i | 0.0137861 | − | 0.0238782i | ||||
\(29\) | −0.736068 | + | 1.27491i | −0.136684 | + | 0.236744i | −0.926240 | − | 0.376935i | \(-0.876978\pi\) |
0.789555 | + | 0.613679i | \(0.210311\pi\) | |||||||
\(30\) | 1.80902 | + | 3.13331i | 0.330280 | + | 0.572061i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.69098 | + | 2.92887i | 0.298926 | + | 0.517756i | ||||
\(33\) | 4.73607 | + | 8.20311i | 0.824444 | + | 1.42798i | ||||
\(34\) | 8.85410 | 1.51847 | ||||||||
\(35\) | 0.118034 | + | 0.204441i | 0.0199514 | + | 0.0345568i | ||||
\(36\) | −0.618034 | + | 1.07047i | −0.103006 | + | 0.178411i | ||||
\(37\) | −1.50000 | + | 2.59808i | −0.246598 | + | 0.427121i | −0.962580 | − | 0.270998i | \(-0.912646\pi\) |
0.715981 | + | 0.698119i | \(0.245980\pi\) | |||||||
\(38\) | −0.381966 | −0.0619631 | ||||||||
\(39\) | −7.82624 | − | 1.93649i | −1.25320 | − | 0.310087i | ||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | 2.97214 | − | 5.14789i | 0.464170 | − | 0.803965i | −0.534994 | − | 0.844856i | \(-0.679686\pi\) |
0.999164 | + | 0.0408904i | \(0.0130195\pi\) | |||||||
\(42\) | −0.427051 | + | 0.739674i | −0.0658954 | + | 0.114134i | ||||
\(43\) | 0.881966 | + | 1.52761i | 0.134499 | + | 0.232958i | 0.925406 | − | 0.378978i | \(-0.123724\pi\) |
−0.790907 | + | 0.611936i | \(0.790391\pi\) | |||||||
\(44\) | 2.61803 | 0.394683 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | −6.66312 | − | 11.5409i | −0.982423 | − | 1.70161i | ||||
\(47\) | 12.9443 | 1.88812 | 0.944058 | − | 0.329779i | \(-0.106974\pi\) | ||||
0.944058 | + | 0.329779i | \(0.106974\pi\) | |||||||
\(48\) | −5.42705 | − | 9.39993i | −0.783327 | − | 1.35676i | ||||
\(49\) | 3.47214 | − | 6.01392i | 0.496019 | − | 0.859131i | ||||
\(50\) | −0.809017 | + | 1.40126i | −0.114412 | + | 0.198168i | ||||
\(51\) | −12.2361 | −1.71339 | ||||||||
\(52\) | −1.54508 | + | 1.60570i | −0.214265 | + | 0.222670i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −1.80902 | + | 3.13331i | −0.246176 | + | 0.426389i | ||||
\(55\) | −2.11803 | + | 3.66854i | −0.285596 | + | 0.494666i | ||||
\(56\) | −0.263932 | − | 0.457144i | −0.0352694 | − | 0.0610884i | ||||
\(57\) | 0.527864 | 0.0699173 | ||||||||
\(58\) | −1.19098 | − | 2.06284i | −0.156384 | − | 0.270865i | ||||
\(59\) | −6.35410 | − | 11.0056i | −0.827234 | − | 1.43281i | −0.900200 | − | 0.435476i | \(-0.856580\pi\) |
0.0729666 | − | 0.997334i | \(-0.476753\pi\) | |||||||
\(60\) | −1.38197 | −0.178411 | ||||||||
\(61\) | 6.20820 | + | 10.7529i | 0.794879 | + | 1.37677i | 0.922916 | + | 0.385002i | \(0.125799\pi\) |
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.236068 | − | 0.408882i | 0.0297418 | − | 0.0515143i | ||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −1.00000 | − | 3.46410i | −0.124035 | − | 0.429669i | ||||
\(66\) | −15.3262 | −1.88653 | ||||||||
\(67\) | −5.35410 | + | 9.27358i | −0.654108 | + | 1.13295i | 0.328009 | + | 0.944675i | \(0.393622\pi\) |
−0.982117 | + | 0.188273i | \(0.939711\pi\) | |||||||
\(68\) | −1.69098 | + | 2.92887i | −0.205062 | + | 0.355177i | ||||
\(69\) | 9.20820 | + | 15.9491i | 1.10854 | + | 1.92004i | ||||
\(70\) | −0.381966 | −0.0456537 | ||||||||
\(71\) | 0.881966 | + | 1.52761i | 0.104670 | + | 0.181294i | 0.913603 | − | 0.406607i | \(-0.133288\pi\) |
−0.808933 | + | 0.587900i | \(0.799955\pi\) | |||||||
\(72\) | 2.23607 | + | 3.87298i | 0.263523 | + | 0.456435i | ||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −2.42705 | − | 4.20378i | −0.282139 | − | 0.488679i | ||||
\(75\) | 1.11803 | − | 1.93649i | 0.129099 | − | 0.223607i | ||||
\(76\) | 0.0729490 | − | 0.126351i | 0.00836783 | − | 0.0144935i | ||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 9.04508 | − | 9.39993i | 1.02415 | − | 1.06433i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 2.42705 | − | 4.20378i | 0.271353 | − | 0.469996i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 4.80902 | + | 8.32946i | 0.531067 | + | 0.919835i | ||||
\(83\) | −8.94427 | −0.981761 | −0.490881 | − | 0.871227i | \(-0.663325\pi\) | ||||
−0.490881 | + | 0.871227i | \(0.663325\pi\) | |||||||
\(84\) | −0.163119 | − | 0.282530i | −0.0177977 | − | 0.0308266i | ||||
\(85\) | −2.73607 | − | 4.73901i | −0.296768 | − | 0.514018i | ||||
\(86\) | −2.85410 | −0.307766 | ||||||||
\(87\) | 1.64590 | + | 2.85078i | 0.176459 | + | 0.305636i | ||||
\(88\) | 4.73607 | − | 8.20311i | 0.504867 | − | 0.874455i | ||||
\(89\) | 4.50000 | − | 7.79423i | 0.476999 | − | 0.826187i | −0.522654 | − | 0.852545i | \(-0.675058\pi\) |
0.999653 | + | 0.0263586i | \(0.00839118\pi\) | |||||||
\(90\) | 3.23607 | 0.341112 | ||||||||
\(91\) | 0.590170 | − | 0.613323i | 0.0618666 | − | 0.0642937i | ||||
\(92\) | 5.09017 | 0.530687 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.4721 | + | 18.1383i | −1.08012 | + | 1.87082i | ||||
\(95\) | 0.118034 | + | 0.204441i | 0.0121100 | + | 0.0209752i | ||||
\(96\) | 7.56231 | 0.771825 | ||||||||
\(97\) | −2.73607 | − | 4.73901i | −0.277806 | − | 0.481173i | 0.693034 | − | 0.720905i | \(-0.256274\pi\) |
−0.970839 | + | 0.239732i | \(0.922940\pi\) | |||||||
\(98\) | 5.61803 | + | 9.73072i | 0.567507 | + | 0.982951i | ||||
\(99\) | 8.47214 | 0.851482 | ||||||||
\(100\) | −0.309017 | − | 0.535233i | −0.0309017 | − | 0.0535233i | ||||
\(101\) | −4.73607 | + | 8.20311i | −0.471256 | + | 0.816240i | −0.999459 | − | 0.0328781i | \(-0.989533\pi\) |
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(102\) | 9.89919 | − | 17.1459i | 0.980166 | − | 1.69770i | ||||
\(103\) | −4.94427 | −0.487174 | −0.243587 | − | 0.969879i | \(-0.578324\pi\) | ||||
−0.243587 | + | 0.969879i | \(0.578324\pi\) | |||||||
\(104\) | 2.23607 | + | 7.74597i | 0.219265 | + | 0.759555i | ||||
\(105\) | 0.527864 | 0.0515143 | ||||||||
\(106\) | −4.85410 | + | 8.40755i | −0.471472 | + | 0.816614i | ||||
\(107\) | 5.11803 | − | 8.86469i | 0.494779 | − | 0.856982i | −0.505203 | − | 0.863001i | \(-0.668582\pi\) |
0.999982 | + | 0.00601821i | \(0.00191567\pi\) | |||||||
\(108\) | −0.690983 | − | 1.19682i | −0.0664899 | − | 0.115164i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −3.42705 | − | 5.93583i | −0.326756 | − | 0.565959i | ||||
\(111\) | 3.35410 | + | 5.80948i | 0.318357 | + | 0.551411i | ||||
\(112\) | 1.14590 | 0.108277 | ||||||||
\(113\) | 3.73607 | + | 6.47106i | 0.351460 | + | 0.608746i | 0.986505 | − | 0.163728i | \(-0.0523521\pi\) |
−0.635046 | + | 0.772475i | \(0.719019\pi\) | |||||||
\(114\) | −0.427051 | + | 0.739674i | −0.0399970 | + | 0.0692768i | ||||
\(115\) | −4.11803 | + | 7.13264i | −0.384009 | + | 0.665122i | ||||
\(116\) | 0.909830 | 0.0844756 | ||||||||
\(117\) | −5.00000 | + | 5.19615i | −0.462250 | + | 0.480384i | ||||
\(118\) | 20.5623 | 1.89291 | ||||||||
\(119\) | 0.645898 | − | 1.11873i | 0.0592094 | − | 0.102554i | ||||
\(120\) | −2.50000 | + | 4.33013i | −0.228218 | + | 0.395285i | ||||
\(121\) | −3.47214 | − | 6.01392i | −0.315649 | − | 0.546720i | ||||
\(122\) | −20.0902 | −1.81888 | ||||||||
\(123\) | −6.64590 | − | 11.5110i | −0.599240 | − | 1.03791i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.381966 | + | 0.661585i | 0.0340282 | + | 0.0589386i | ||||
\(127\) | −0.118034 | + | 0.204441i | −0.0104738 | + | 0.0181412i | −0.871215 | − | 0.490902i | \(-0.836667\pi\) |
0.860741 | + | 0.509043i | \(0.170001\pi\) | |||||||
\(128\) | −6.80902 | + | 11.7936i | −0.601838 | + | 1.04241i | ||||
\(129\) | 3.94427 | 0.347274 | ||||||||
\(130\) | 5.66312 | + | 1.40126i | 0.496688 | + | 0.122899i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 2.92705 | − | 5.06980i | 0.254767 | − | 0.441270i | ||||
\(133\) | −0.0278640 | + | 0.0482619i | −0.00241612 | + | 0.00418484i | ||||
\(134\) | −8.66312 | − | 15.0050i | −0.748379 | − | 1.29623i | ||||
\(135\) | 2.23607 | 0.192450 | ||||||||
\(136\) | 6.11803 | + | 10.5967i | 0.524617 | + | 0.908663i | ||||
\(137\) | 3.73607 | + | 6.47106i | 0.319194 | + | 0.552860i | 0.980320 | − | 0.197415i | \(-0.0632546\pi\) |
−0.661126 | + | 0.750275i | \(0.729921\pi\) | |||||||
\(138\) | −29.7984 | −2.53661 | ||||||||
\(139\) | 1.64590 | + | 2.85078i | 0.139603 | + | 0.241800i | 0.927346 | − | 0.374204i | \(-0.122084\pi\) |
−0.787743 | + | 0.616004i | \(0.788751\pi\) | |||||||
\(140\) | 0.0729490 | − | 0.126351i | 0.00616532 | − | 0.0106786i | ||||
\(141\) | 14.4721 | − | 25.0665i | 1.21877 | − | 2.11098i | ||||
\(142\) | −2.85410 | −0.239511 | ||||||||
\(143\) | 14.8262 | + | 3.66854i | 1.23983 | + | 0.306779i | ||||
\(144\) | −9.70820 | −0.809017 | ||||||||
\(145\) | −0.736068 | + | 1.27491i | −0.0611271 | + | 0.105875i | ||||
\(146\) | 4.85410 | − | 8.40755i | 0.401728 | − | 0.695814i | ||||
\(147\) | −7.76393 | − | 13.4475i | −0.640358 | − | 1.10913i | ||||
\(148\) | 1.85410 | 0.152406 | ||||||||
\(149\) | −6.73607 | − | 11.6672i | −0.551840 | − | 0.955815i | −0.998142 | − | 0.0609327i | \(-0.980593\pi\) |
0.446302 | − | 0.894883i | \(-0.352741\pi\) | |||||||
\(150\) | 1.80902 | + | 3.13331i | 0.147706 | + | 0.255834i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −0.263932 | − | 0.457144i | −0.0214077 | − | 0.0370792i | ||||
\(153\) | −5.47214 | + | 9.47802i | −0.442396 | + | 0.766252i | ||||
\(154\) | 0.809017 | − | 1.40126i | 0.0651924 | − | 0.112917i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.38197 | + | 4.78727i | 0.110646 | + | 0.383288i | ||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.70820 | − | 11.6190i | 0.531995 | − | 0.921443i | ||||
\(160\) | 1.69098 | + | 2.92887i | 0.133684 | + | 0.231547i | ||||
\(161\) | −1.94427 | −0.153230 | ||||||||
\(162\) | 8.89919 | + | 15.4138i | 0.699186 | + | 1.21103i | ||||
\(163\) | −0.645898 | − | 1.11873i | −0.0505906 | − | 0.0876256i | 0.839621 | − | 0.543173i | \(-0.182777\pi\) |
−0.890212 | + | 0.455547i | \(0.849444\pi\) | |||||||
\(164\) | −3.67376 | −0.286873 | ||||||||
\(165\) | 4.73607 | + | 8.20311i | 0.368702 | + | 0.638611i | ||||
\(166\) | 7.23607 | − | 12.5332i | 0.561628 | − | 0.972768i | ||||
\(167\) | −2.59017 | + | 4.48631i | −0.200433 | + | 0.347161i | −0.948668 | − | 0.316273i | \(-0.897568\pi\) |
0.748235 | + | 0.663434i | \(0.230902\pi\) | |||||||
\(168\) | −1.18034 | −0.0910652 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 8.85410 | 0.679079 | ||||||||
\(171\) | 0.236068 | − | 0.408882i | 0.0180526 | − | 0.0312680i | ||||
\(172\) | 0.545085 | − | 0.944115i | 0.0415623 | − | 0.0719881i | ||||
\(173\) | −8.44427 | − | 14.6259i | −0.642006 | − | 1.11199i | −0.984984 | − | 0.172644i | \(-0.944769\pi\) |
0.342978 | − | 0.939343i | \(-0.388564\pi\) | |||||||
\(174\) | −5.32624 | −0.403781 | ||||||||
\(175\) | 0.118034 | + | 0.204441i | 0.00892253 | + | 0.0154543i | ||||
\(176\) | 10.2812 | + | 17.8075i | 0.774971 | + | 1.34229i | ||||
\(177\) | −28.4164 | −2.13591 | ||||||||
\(178\) | 7.28115 | + | 12.6113i | 0.545745 | + | 0.945259i | ||||
\(179\) | 1.88197 | − | 3.25966i | 0.140665 | − | 0.243638i | −0.787082 | − | 0.616848i | \(-0.788409\pi\) |
0.927747 | + | 0.373209i | \(0.121743\pi\) | |||||||
\(180\) | −0.618034 | + | 1.07047i | −0.0460655 | + | 0.0797878i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0.381966 | + | 1.32317i | 0.0283132 | + | 0.0980798i | ||||
\(183\) | 27.7639 | 2.05237 | ||||||||
\(184\) | 9.20820 | − | 15.9491i | 0.678838 | − | 1.17578i | ||||
\(185\) | −1.50000 | + | 2.59808i | −0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1803 | 1.69511 | ||||||||
\(188\) | −4.00000 | − | 6.92820i | −0.291730 | − | 0.505291i | ||||
\(189\) | 0.263932 | + | 0.457144i | 0.0191982 | + | 0.0332523i | ||||
\(190\) | −0.381966 | −0.0277107 | ||||||||
\(191\) | 2.40983 | + | 4.17395i | 0.174369 | + | 0.302016i | 0.939943 | − | 0.341332i | \(-0.110878\pi\) |
−0.765574 | + | 0.643348i | \(0.777545\pi\) | |||||||
\(192\) | 4.73607 | − | 8.20311i | 0.341796 | − | 0.592008i | ||||
\(193\) | −2.73607 | + | 4.73901i | −0.196946 | + | 0.341121i | −0.947537 | − | 0.319646i | \(-0.896436\pi\) |
0.750590 | + | 0.660768i | \(0.229769\pi\) | |||||||
\(194\) | 8.85410 | 0.635687 | ||||||||
\(195\) | −7.82624 | − | 1.93649i | −0.560449 | − | 0.138675i | ||||
\(196\) | −4.29180 | −0.306557 | ||||||||
\(197\) | −1.50000 | + | 2.59808i | −0.106871 | + | 0.185105i | −0.914501 | − | 0.404584i | \(-0.867416\pi\) |
0.807630 | + | 0.589689i | \(0.200750\pi\) | |||||||
\(198\) | −6.85410 | + | 11.8717i | −0.487100 | + | 0.843682i | ||||
\(199\) | 7.35410 | + | 12.7377i | 0.521318 | + | 0.902950i | 0.999693 | + | 0.0247939i | \(0.00789296\pi\) |
−0.478374 | + | 0.878156i | \(0.658774\pi\) | |||||||
\(200\) | −2.23607 | −0.158114 | ||||||||
\(201\) | 11.9721 | + | 20.7363i | 0.844449 | + | 1.46263i | ||||
\(202\) | −7.66312 | − | 13.2729i | −0.539175 | − | 0.933879i | ||||
\(203\) | −0.347524 | −0.0243914 | ||||||||
\(204\) | 3.78115 | + | 6.54915i | 0.264734 | + | 0.458532i | ||||
\(205\) | 2.97214 | − | 5.14789i | 0.207583 | − | 0.359544i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | 16.4721 | 1.14489 | ||||||||
\(208\) | −16.9894 | − | 4.20378i | −1.17800 | − | 0.291479i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −0.427051 | + | 0.739674i | −0.0294693 | + | 0.0510424i | ||||
\(211\) | −4.59017 | + | 7.95041i | −0.316000 | + | 0.547329i | −0.979650 | − | 0.200715i | \(-0.935673\pi\) |
0.663649 | + | 0.748044i | \(0.269007\pi\) | |||||||
\(212\) | −1.85410 | − | 3.21140i | −0.127340 | − | 0.220560i | ||||
\(213\) | 3.94427 | 0.270257 | ||||||||
\(214\) | 8.28115 | + | 14.3434i | 0.566088 | + | 0.980493i | ||||
\(215\) | 0.881966 | + | 1.52761i | 0.0601496 | + | 0.104182i | ||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.61803 | − | 2.80252i | 0.109587 | − | 0.189810i | ||||
\(219\) | −6.70820 | + | 11.6190i | −0.453298 | + | 0.785136i | ||||
\(220\) | 2.61803 | 0.176508 | ||||||||
\(221\) | −13.6803 | + | 14.2170i | −0.920239 | + | 0.956341i | ||||
\(222\) | −10.8541 | −0.728480 | ||||||||
\(223\) | 6.35410 | − | 11.0056i | 0.425502 | − | 0.736991i | −0.570965 | − | 0.820974i | \(-0.693431\pi\) |
0.996467 | + | 0.0839830i | \(0.0267642\pi\) | |||||||
\(224\) | −0.399187 | + | 0.691412i | −0.0266718 | + | 0.0461969i | ||||
\(225\) | −1.00000 | − | 1.73205i | −0.0666667 | − | 0.115470i | ||||
\(226\) | −12.0902 | −0.804226 | ||||||||
\(227\) | 0.881966 | + | 1.52761i | 0.0585381 | + | 0.101391i | 0.893809 | − | 0.448447i | \(-0.148023\pi\) |
−0.835271 | + | 0.549838i | \(0.814689\pi\) | |||||||
\(228\) | −0.163119 | − | 0.282530i | −0.0108028 | − | 0.0187110i | ||||
\(229\) | −19.8885 | −1.31427 | −0.657136 | − | 0.753772i | \(-0.728232\pi\) | ||||
−0.657136 | + | 0.753772i | \(0.728232\pi\) | |||||||
\(230\) | −6.66312 | − | 11.5409i | −0.439353 | − | 0.760982i | ||||
\(231\) | −1.11803 | + | 1.93649i | −0.0735612 | + | 0.127412i | ||||
\(232\) | 1.64590 | − | 2.85078i | 0.108058 | − | 0.187163i | ||||
\(233\) | 19.8885 | 1.30294 | 0.651471 | − | 0.758674i | \(-0.274152\pi\) | ||||
0.651471 | + | 0.758674i | \(0.274152\pi\) | |||||||
\(234\) | −3.23607 | − | 11.2101i | −0.211548 | − | 0.732825i | ||||
\(235\) | 12.9443 | 0.844391 | ||||||||
\(236\) | −3.92705 | + | 6.80185i | −0.255629 | + | 0.442763i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.04508 | + | 1.81014i | 0.0677428 | + | 0.117334i | ||||
\(239\) | 9.88854 | 0.639637 | 0.319818 | − | 0.947479i | \(-0.396378\pi\) | ||||
0.319818 | + | 0.947479i | \(0.396378\pi\) | |||||||
\(240\) | −5.42705 | − | 9.39993i | −0.350315 | − | 0.606763i | ||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 11.2361 | 0.722282 | ||||||||
\(243\) | −8.94427 | − | 15.4919i | −0.573775 | − | 0.993808i | ||||
\(244\) | 3.83688 | − | 6.64567i | 0.245631 | − | 0.425446i | ||||
\(245\) | 3.47214 | − | 6.01392i | 0.221827 | − | 0.384215i | ||||
\(246\) | 21.5066 | 1.37121 | ||||||||
\(247\) | 0.590170 | − | 0.613323i | 0.0375516 | − | 0.0390248i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | + | 17.3205i | −0.633724 | + | 1.09764i | ||||
\(250\) | −0.809017 | + | 1.40126i | −0.0511667 | + | 0.0886234i | ||||
\(251\) | −7.88197 | − | 13.6520i | −0.497505 | − | 0.861704i | 0.502491 | − | 0.864583i | \(-0.332417\pi\) |
−0.999996 | + | 0.00287826i | \(0.999084\pi\) | |||||||
\(252\) | −0.291796 | −0.0183814 | ||||||||
\(253\) | −17.4443 | − | 30.2144i | −1.09671 | − | 1.89956i | ||||
\(254\) | −0.190983 | − | 0.330792i | −0.0119833 | − | 0.0207558i | ||||
\(255\) | −12.2361 | −0.766252 | ||||||||
\(256\) | −6.78115 | − | 11.7453i | −0.423822 | − | 0.734081i | ||||
\(257\) | −4.26393 | + | 7.38535i | −0.265977 | + | 0.460685i | −0.967819 | − | 0.251647i | \(-0.919028\pi\) |
0.701842 | + | 0.712332i | \(0.252361\pi\) | |||||||
\(258\) | −3.19098 | + | 5.52694i | −0.198662 | + | 0.344093i | ||||
\(259\) | −0.708204 | −0.0440057 | ||||||||
\(260\) | −1.54508 | + | 1.60570i | −0.0958221 | + | 0.0995812i | ||||
\(261\) | 2.94427 | 0.182246 | ||||||||
\(262\) | 9.70820 | − | 16.8151i | 0.599775 | − | 1.03884i | ||||
\(263\) | −4.11803 | + | 7.13264i | −0.253929 | + | 0.439818i | −0.964604 | − | 0.263703i | \(-0.915056\pi\) |
0.710675 | + | 0.703520i | \(0.248390\pi\) | |||||||
\(264\) | −10.5902 | − | 18.3427i | −0.651780 | − | 1.12892i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −0.0450850 | − | 0.0780895i | −0.00276434 | − | 0.00478797i | ||||
\(267\) | −10.0623 | − | 17.4284i | −0.615803 | − | 1.06660i | ||||
\(268\) | 6.61803 | 0.404261 | ||||||||
\(269\) | 7.73607 | + | 13.3993i | 0.471676 | + | 0.816967i | 0.999475 | − | 0.0324021i | \(-0.0103157\pi\) |
−0.527799 | + | 0.849370i | \(0.676982\pi\) | |||||||
\(270\) | −1.80902 | + | 3.13331i | −0.110093 | + | 0.190687i | ||||
\(271\) | −7.35410 | + | 12.7377i | −0.446730 | + | 0.773759i | −0.998171 | − | 0.0604550i | \(-0.980745\pi\) |
0.551441 | + | 0.834214i | \(0.314078\pi\) | |||||||
\(272\) | −26.5623 | −1.61058 | ||||||||
\(273\) | −0.527864 | − | 1.82857i | −0.0319478 | − | 0.110670i | ||||
\(274\) | −12.0902 | −0.730394 | ||||||||
\(275\) | −2.11803 | + | 3.66854i | −0.127722 | + | 0.221221i | ||||
\(276\) | 5.69098 | − | 9.85707i | 0.342557 | − | 0.593326i | ||||
\(277\) | 9.44427 | + | 16.3580i | 0.567451 | + | 0.982854i | 0.996817 | + | 0.0797238i | \(0.0254038\pi\) |
−0.429366 | + | 0.903131i | \(0.641263\pi\) | |||||||
\(278\) | −5.32624 | −0.319447 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.263932 | − | 0.457144i | −0.0157730 | − | 0.0273196i | ||||
\(281\) | 19.8885 | 1.18645 | 0.593226 | − | 0.805036i | \(-0.297854\pi\) | ||||
0.593226 | + | 0.805036i | \(0.297854\pi\) | |||||||
\(282\) | 23.4164 | + | 40.5584i | 1.39443 | + | 2.41522i | ||||
\(283\) | −1.35410 | + | 2.34537i | −0.0804930 | + | 0.139418i | −0.903462 | − | 0.428669i | \(-0.858983\pi\) |
0.822969 | + | 0.568087i | \(0.192316\pi\) | |||||||
\(284\) | 0.545085 | − | 0.944115i | 0.0323448 | − | 0.0560229i | ||||
\(285\) | 0.527864 | 0.0312680 | ||||||||
\(286\) | −17.1353 | + | 17.8075i | −1.01323 | + | 1.05298i | ||||
\(287\) | 1.40325 | 0.0828314 | ||||||||
\(288\) | 3.38197 | − | 5.85774i | 0.199284 | − | 0.345170i | ||||
\(289\) | −6.47214 | + | 11.2101i | −0.380714 | + | 0.659416i | ||||
\(290\) | −1.19098 | − | 2.06284i | −0.0699369 | − | 0.121134i | ||||
\(291\) | −12.2361 | −0.717291 | ||||||||
\(292\) | 1.85410 | + | 3.21140i | 0.108503 | + | 0.187933i | ||||
\(293\) | 6.02786 | + | 10.4406i | 0.352152 | + | 0.609944i | 0.986626 | − | 0.162999i | \(-0.0521168\pi\) |
−0.634475 | + | 0.772944i | \(0.718783\pi\) | |||||||
\(294\) | 25.1246 | 1.46530 | ||||||||
\(295\) | −6.35410 | − | 11.0056i | −0.369950 | − | 0.640772i | ||||
\(296\) | 3.35410 | − | 5.80948i | 0.194953 | − | 0.337669i | ||||
\(297\) | −4.73607 | + | 8.20311i | −0.274815 | + | 0.475993i | ||||
\(298\) | 21.7984 | 1.26275 | ||||||||
\(299\) | 28.8262 | + | 7.13264i | 1.66706 | + | 0.412491i | ||||
\(300\) | −1.38197 | −0.0797878 | ||||||||
\(301\) | −0.208204 | + | 0.360620i | −0.0120007 | + | 0.0207858i | ||||
\(302\) | −6.47214 | + | 11.2101i | −0.372430 | + | 0.645067i | ||||
\(303\) | 10.5902 | + | 18.3427i | 0.608389 | + | 1.05376i | ||||
\(304\) | 1.14590 | 0.0657218 | ||||||||
\(305\) | 6.20820 | + | 10.7529i | 0.355481 | + | 0.615711i | ||||
\(306\) | −8.85410 | − | 15.3358i | −0.506155 | − | 0.876687i | ||||
\(307\) | 7.05573 | 0.402692 | 0.201346 | − | 0.979520i | \(-0.435468\pi\) | ||||
0.201346 | + | 0.979520i | \(0.435468\pi\) | |||||||
\(308\) | 0.309017 | + | 0.535233i | 0.0176079 | + | 0.0304977i | ||||
\(309\) | −5.52786 | + | 9.57454i | −0.314469 | + | 0.544677i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 17.5000 | + | 4.33013i | 0.990742 | + | 0.245145i | ||||
\(313\) | −31.8885 | −1.80245 | −0.901224 | − | 0.433355i | \(-0.857330\pi\) | ||||
−0.901224 | + | 0.433355i | \(0.857330\pi\) | |||||||
\(314\) | 14.5623 | − | 25.2227i | 0.821798 | − | 1.42340i | ||||
\(315\) | 0.236068 | − | 0.408882i | 0.0133009 | − | 0.0230379i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8885 | 1.34171 | 0.670857 | − | 0.741587i | \(-0.265926\pi\) | ||||
0.670857 | + | 0.741587i | \(0.265926\pi\) | |||||||
\(318\) | 10.8541 | + | 18.7999i | 0.608668 | + | 1.05424i | ||||
\(319\) | −3.11803 | − | 5.40059i | −0.174576 | − | 0.302375i | ||||
\(320\) | 4.23607 | 0.236803 | ||||||||
\(321\) | −11.4443 | − | 19.8221i | −0.638757 | − | 1.10636i | ||||
\(322\) | 1.57295 | − | 2.72443i | 0.0876570 | − | 0.151826i | ||||
\(323\) | 0.645898 | − | 1.11873i | 0.0359387 | − | 0.0622477i | ||||
\(324\) | −6.79837 | −0.377687 | ||||||||
\(325\) | −1.00000 | − | 3.46410i | −0.0554700 | − | 0.192154i | ||||
\(326\) | 2.09017 | 0.115764 | ||||||||
\(327\) | −2.23607 | + | 3.87298i | −0.123655 | + | 0.214176i | ||||
\(328\) | −6.64590 | + | 11.5110i | −0.366958 | + | 0.635590i | ||||
\(329\) | 1.52786 | + | 2.64634i | 0.0842339 | + | 0.145897i | ||||
\(330\) | −15.3262 | −0.843682 | ||||||||
\(331\) | −12.8262 | − | 22.2157i | −0.704994 | − | 1.22109i | −0.966694 | − | 0.255936i | \(-0.917616\pi\) |
0.261700 | − | 0.965149i | \(-0.415717\pi\) | |||||||
\(332\) | 2.76393 | + | 4.78727i | 0.151690 | + | 0.262736i | ||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | −4.19098 | − | 7.25900i | −0.229320 | − | 0.397195i | ||||
\(335\) | −5.35410 | + | 9.27358i | −0.292526 | + | 0.506670i | ||||
\(336\) | 1.28115 | − | 2.21902i | 0.0698926 | − | 0.121058i | ||||
\(337\) | 27.8885 | 1.51919 | 0.759593 | − | 0.650399i | \(-0.225398\pi\) | ||||
0.759593 | + | 0.650399i | \(0.225398\pi\) | |||||||
\(338\) | −0.809017 | − | 21.0189i | −0.0440047 | − | 1.14328i | ||||
\(339\) | 16.7082 | 0.907465 | ||||||||
\(340\) | −1.69098 | + | 2.92887i | −0.0917064 | + | 0.158840i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.381966 | + | 0.661585i | 0.0206544 | + | 0.0357744i | ||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −1.97214 | − | 3.41584i | −0.106330 | − | 0.184170i | ||||
\(345\) | 9.20820 | + | 15.9491i | 0.495753 | + | 0.858669i | ||||
\(346\) | 27.3262 | 1.46907 | ||||||||
\(347\) | −8.64590 | − | 14.9751i | −0.464136 | − | 0.803907i | 0.535026 | − | 0.844836i | \(-0.320302\pi\) |
−0.999162 | + | 0.0409283i | \(0.986968\pi\) | |||||||
\(348\) | 1.01722 | − | 1.76188i | 0.0545288 | − | 0.0944466i | ||||
\(349\) | 12.2082 | − | 21.1452i | 0.653490 | − | 1.13188i | −0.328780 | − | 0.944407i | \(-0.606637\pi\) |
0.982270 | − | 0.187472i | \(-0.0600293\pi\) | |||||||
\(350\) | −0.381966 | −0.0204169 | ||||||||
\(351\) | −2.23607 | − | 7.74597i | −0.119352 | − | 0.413449i | ||||
\(352\) | −14.3262 | −0.763591 | ||||||||
\(353\) | 5.26393 | − | 9.11740i | 0.280171 | − | 0.485270i | −0.691256 | − | 0.722610i | \(-0.742942\pi\) |
0.971427 | + | 0.237340i | \(0.0762756\pi\) | |||||||
\(354\) | 22.9894 | − | 39.8187i | 1.22187 | − | 2.11634i | ||||
\(355\) | 0.881966 | + | 1.52761i | 0.0468099 | + | 0.0810771i | ||||
\(356\) | −5.56231 | −0.294802 | ||||||||
\(357\) | −1.44427 | − | 2.50155i | −0.0764390 | − | 0.132396i | ||||
\(358\) | 3.04508 | + | 5.27424i | 0.160938 | + | 0.278752i | ||||
\(359\) | −17.8885 | −0.944121 | −0.472061 | − | 0.881566i | \(-0.656490\pi\) | ||||
−0.472061 | + | 0.881566i | \(0.656490\pi\) | |||||||
\(360\) | 2.23607 | + | 3.87298i | 0.117851 | + | 0.204124i | ||||
\(361\) | 9.47214 | − | 16.4062i | 0.498533 | − | 0.863485i | ||||
\(362\) | −4.85410 | + | 8.40755i | −0.255126 | + | 0.441891i | ||||
\(363\) | −15.5279 | −0.815001 | ||||||||
\(364\) | −0.510643 | − | 0.126351i | −0.0267650 | − | 0.00662261i | ||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −22.4615 | + | 38.9044i | −1.17408 | + | 2.03357i | ||||
\(367\) | 12.8262 | − | 22.2157i | 0.669524 | − | 1.15965i | −0.308513 | − | 0.951220i | \(-0.599831\pi\) |
0.978037 | − | 0.208430i | \(-0.0668353\pi\) | |||||||
\(368\) | 19.9894 | + | 34.6226i | 1.04202 | + | 1.80483i | ||||
\(369\) | −11.8885 | −0.618893 | ||||||||
\(370\) | −2.42705 | − | 4.20378i | −0.126176 | − | 0.218544i | ||||
\(371\) | 0.708204 | + | 1.22665i | 0.0367681 | + | 0.0636842i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.02786 | − | 8.70852i | −0.260333 | − | 0.450910i | 0.705997 | − | 0.708214i | \(-0.250499\pi\) |
−0.966330 | + | 0.257305i | \(0.917166\pi\) | |||||||
\(374\) | −18.7533 | + | 32.4816i | −0.969709 | + | 1.67959i | ||||
\(375\) | 1.11803 | − | 1.93649i | 0.0577350 | − | 0.100000i | ||||
\(376\) | −28.9443 | −1.49269 | ||||||||
\(377\) | 5.15248 | + | 1.27491i | 0.265366 | + | 0.0656611i | ||||
\(378\) | −0.854102 | −0.0439303 | ||||||||
\(379\) | −16.5902 | + | 28.7350i | −0.852180 | + | 1.47602i | 0.0270571 | + | 0.999634i | \(0.491386\pi\) |
−0.879237 | + | 0.476385i | \(0.841947\pi\) | |||||||
\(380\) | 0.0729490 | − | 0.126351i | 0.00374221 | − | 0.00648169i | ||||
\(381\) | 0.263932 | + | 0.457144i | 0.0135216 | + | 0.0234202i | ||||
\(382\) | −7.79837 | −0.399000 | ||||||||
\(383\) | 0.118034 | + | 0.204441i | 0.00603126 | + | 0.0104464i | 0.869025 | − | 0.494768i | \(-0.164747\pi\) |
−0.862994 | + | 0.505214i | \(0.831414\pi\) | |||||||
\(384\) | 15.2254 | + | 26.3712i | 0.776969 | + | 1.34575i | ||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −4.42705 | − | 7.66788i | −0.225331 | − | 0.390285i | ||||
\(387\) | 1.76393 | − | 3.05522i | 0.0896657 | − | 0.155306i | ||||
\(388\) | −1.69098 | + | 2.92887i | −0.0858467 | + | 0.148691i | ||||
\(389\) | −35.8885 | −1.81962 | −0.909811 | − | 0.415023i | \(-0.863773\pi\) | ||||
−0.909811 | + | 0.415023i | \(0.863773\pi\) | |||||||
\(390\) | 9.04508 | − | 9.39993i | 0.458016 | − | 0.475984i | ||||
\(391\) | 45.0689 | 2.27923 | ||||||||
\(392\) | −7.76393 | + | 13.4475i | −0.392138 | + | 0.679203i | ||||
\(393\) | −13.4164 | + | 23.2379i | −0.676768 | + | 1.17220i | ||||
\(394\) | −2.42705 | − | 4.20378i | −0.122273 | − | 0.211783i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.61803 | − | 4.53457i | −0.131561 | − | 0.227871i | ||||
\(397\) | −5.02786 | − | 8.70852i | −0.252341 | − | 0.437068i | 0.711829 | − | 0.702353i | \(-0.247867\pi\) |
−0.964170 | + | 0.265285i | \(0.914534\pi\) | |||||||
\(398\) | −23.7984 | −1.19290 | ||||||||
\(399\) | 0.0623059 | + | 0.107917i | 0.00311920 | + | 0.00540261i | ||||
\(400\) | 2.42705 | − | 4.20378i | 0.121353 | − | 0.210189i | ||||
\(401\) | 13.4443 | − | 23.2862i | 0.671375 | − | 1.16286i | −0.306139 | − | 0.951987i | \(-0.599037\pi\) |
0.977514 | − | 0.210869i | \(-0.0676293\pi\) | |||||||
\(402\) | −38.7426 | −1.93231 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.85410 | 0.291252 | ||||||||
\(405\) | 5.50000 | − | 9.52628i | 0.273297 | − | 0.473365i | ||||
\(406\) | 0.281153 | − | 0.486971i | 0.0139534 | − | 0.0241680i | ||||
\(407\) | −6.35410 | − | 11.0056i | −0.314961 | − | 0.545529i | ||||
\(408\) | 27.3607 | 1.35456 | ||||||||
\(409\) | 5.44427 | + | 9.42976i | 0.269202 | + | 0.466271i | 0.968656 | − | 0.248406i | \(-0.0799068\pi\) |
−0.699454 | + | 0.714678i | \(0.746573\pi\) | |||||||
\(410\) | 4.80902 | + | 8.32946i | 0.237500 | + | 0.411363i | ||||
\(411\) | 16.7082 | 0.824155 | ||||||||
\(412\) | 1.52786 | + | 2.64634i | 0.0752725 | + | 0.130376i | ||||
\(413\) | 1.50000 | − | 2.59808i | 0.0738102 | − | 0.127843i | ||||
\(414\) | −13.3262 | + | 23.0817i | −0.654949 | + | 1.13440i | ||||
\(415\) | −8.94427 | −0.439057 | ||||||||
\(416\) | 8.45492 | − | 8.78661i | 0.414536 | − | 0.430799i | ||||
\(417\) | 7.36068 | 0.360454 | ||||||||
\(418\) | 0.809017 | − | 1.40126i | 0.0395703 | − | 0.0685378i | ||||
\(419\) | 6.82624 | − | 11.8234i | 0.333484 | − | 0.577610i | −0.649709 | − | 0.760183i | \(-0.725109\pi\) |
0.983192 | + | 0.182573i | \(0.0584425\pi\) | |||||||
\(420\) | −0.163119 | − | 0.282530i | −0.00795939 | − | 0.0137861i | ||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | −7.42705 | − | 12.8640i | −0.361543 | − | 0.626211i | ||||
\(423\) | −12.9443 | − | 22.4201i | −0.629372 | − | 1.09010i | ||||
\(424\) | −13.4164 | −0.651558 | ||||||||
\(425\) | −2.73607 | − | 4.73901i | −0.132719 | − | 0.229876i | ||||
\(426\) | −3.19098 | + | 5.52694i | −0.154604 | + | 0.267781i | ||||
\(427\) | −1.46556 | + | 2.53842i | −0.0709233 | + | 0.122843i | ||||
\(428\) | −6.32624 | −0.305790 | ||||||||
\(429\) | 23.6803 | − | 24.6093i | 1.14330 | − | 1.18815i | ||||
\(430\) | −2.85410 | −0.137637 | ||||||||
\(431\) | −2.40983 | + | 4.17395i | −0.116077 | + | 0.201052i | −0.918210 | − | 0.396094i | \(-0.870365\pi\) |
0.802133 | + | 0.597146i | \(0.203699\pi\) | |||||||
\(432\) | 5.42705 | − | 9.39993i | 0.261109 | − | 0.452254i | ||||
\(433\) | 11.7361 | + | 20.3275i | 0.563999 | + | 0.976876i | 0.997142 | + | 0.0755503i | \(0.0240713\pi\) |
−0.433143 | + | 0.901325i | \(0.642595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.64590 | + | 2.85078i | 0.0789148 | + | 0.136684i | ||||
\(436\) | 0.618034 | + | 1.07047i | 0.0295985 | + | 0.0512660i | ||||
\(437\) | −1.94427 | −0.0930071 | ||||||||
\(438\) | −10.8541 | − | 18.7999i | −0.518629 | − | 0.898292i | ||||
\(439\) | 4.64590 | − | 8.04693i | 0.221737 | − | 0.384059i | −0.733599 | − | 0.679583i | \(-0.762161\pi\) |
0.955335 | + | 0.295524i | \(0.0954941\pi\) | |||||||
\(440\) | 4.73607 | − | 8.20311i | 0.225783 | − | 0.391068i | ||||
\(441\) | −13.8885 | −0.661359 | ||||||||
\(442\) | −8.85410 | − | 30.6715i | −0.421147 | − | 1.45889i | ||||
\(443\) | −16.9443 | −0.805047 | −0.402523 | − | 0.915410i | \(-0.631867\pi\) | ||||
−0.402523 | + | 0.915410i | \(0.631867\pi\) | |||||||
\(444\) | 2.07295 | − | 3.59045i | 0.0983778 | − | 0.170395i | ||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | 10.2812 | + | 17.8075i | 0.486827 | + | 0.843209i | ||||
\(447\) | −30.1246 | −1.42485 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | 6.97214 | + | 12.0761i | 0.329035 | + | 0.569906i | 0.982321 | − | 0.187206i | \(-0.0599431\pi\) |
−0.653285 | + | 0.757112i | \(0.726610\pi\) | |||||||
\(450\) | 3.23607 | 0.152550 | ||||||||
\(451\) | 12.5902 | + | 21.8068i | 0.592848 | + | 1.02684i | ||||
\(452\) | 2.30902 | − | 3.99933i | 0.108607 | − | 0.188113i | ||||
\(453\) | 8.94427 | − | 15.4919i | 0.420239 | − | 0.727875i | ||||
\(454\) | −2.85410 | −0.133950 | ||||||||
\(455\) | 0.590170 | − | 0.613323i | 0.0276676 | − | 0.0287530i | ||||
\(456\) | −1.18034 | −0.0552745 | ||||||||
\(457\) | 14.2082 | − | 24.6093i | 0.664632 | − | 1.15118i | −0.314753 | − | 0.949174i | \(-0.601922\pi\) |
0.979385 | − | 0.202002i | \(-0.0647449\pi\) | |||||||
\(458\) | 16.0902 | − | 27.8690i | 0.751844 | − | 1.30223i | ||||
\(459\) | −6.11803 | − | 10.5967i | −0.285565 | − | 0.494614i | ||||
\(460\) | 5.09017 | 0.237330 | ||||||||
\(461\) | 14.2082 | + | 24.6093i | 0.661742 | + | 1.14617i | 0.980158 | + | 0.198220i | \(0.0635159\pi\) |
−0.318416 | + | 0.947951i | \(0.603151\pi\) | |||||||
\(462\) | −1.80902 | − | 3.13331i | −0.0841631 | − | 0.145775i | ||||
\(463\) | 28.9443 | 1.34515 | 0.672577 | − | 0.740027i | \(-0.265187\pi\) | ||||
0.672577 | + | 0.740027i | \(0.265187\pi\) | |||||||
\(464\) | 3.57295 | + | 6.18853i | 0.165870 | + | 0.287295i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0902 | + | 27.8690i | −0.745363 | + | 1.29101i | ||||
\(467\) | −8.94427 | −0.413892 | −0.206946 | − | 0.978352i | \(-0.566352\pi\) | ||||
−0.206946 | + | 0.978352i | \(0.566352\pi\) | |||||||
\(468\) | 4.32624 | + | 1.07047i | 0.199980 | + | 0.0494823i | ||||
\(469\) | −2.52786 | −0.116726 | ||||||||
\(470\) | −10.4721 | + | 18.1383i | −0.483044 | + | 0.836656i | ||||
\(471\) | −20.1246 | + | 34.8569i | −0.927293 | + | 1.60612i | ||||
\(472\) | 14.2082 | + | 24.6093i | 0.653986 | + | 1.13274i | ||||
\(473\) | −7.47214 | −0.343569 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.118034 | + | 0.204441i | 0.00541577 | + | 0.00938039i | ||||
\(476\) | −0.798374 | −0.0365934 | ||||||||
\(477\) | −6.00000 | − | 10.3923i | −0.274721 | − | 0.475831i | ||||
\(478\) | −8.00000 | + | 13.8564i | −0.365911 | + | 0.633777i | ||||
\(479\) | 4.06231 | − | 7.03612i | 0.185611 | − | 0.321489i | −0.758171 | − | 0.652056i | \(-0.773907\pi\) |
0.943782 | + | 0.330567i | \(0.107240\pi\) | |||||||
\(480\) | 7.56231 | 0.345170 | ||||||||
\(481\) | 10.5000 | + | 2.59808i | 0.478759 | + | 0.118462i | ||||
\(482\) | 24.2705 | 1.10549 | ||||||||
\(483\) | −2.17376 | + | 3.76507i | −0.0989096 | + | 0.171316i | ||||
\(484\) | −2.14590 | + | 3.71680i | −0.0975408 | + | 0.168946i | ||||
\(485\) | −2.73607 | − | 4.73901i | −0.124238 | − | 0.215187i | ||||
\(486\) | 28.9443 | 1.31294 | ||||||||
\(487\) | 13.0623 | + | 22.6246i | 0.591910 | + | 1.02522i | 0.993975 | + | 0.109607i | \(0.0349591\pi\) |
−0.402065 | + | 0.915611i | \(0.631708\pi\) | |||||||
\(488\) | −13.8820 | − | 24.0443i | −0.628407 | − | 1.08843i | ||||
\(489\) | −2.88854 | −0.130624 | ||||||||
\(490\) | 5.61803 | + | 9.73072i | 0.253797 | + | 0.439589i | ||||
\(491\) | −2.11803 | + | 3.66854i | −0.0955855 | + | 0.165559i | −0.909853 | − | 0.414931i | \(-0.863806\pi\) |
0.814267 | + | 0.580490i | \(0.197139\pi\) | |||||||
\(492\) | −4.10739 | + | 7.11421i | −0.185175 | + | 0.320733i | ||||
\(493\) | 8.05573 | 0.362812 | ||||||||
\(494\) | 0.381966 | + | 1.32317i | 0.0171855 | + | 0.0595322i | ||||
\(495\) | 8.47214 | 0.380794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.208204 | + | 0.360620i | −0.00933922 | + | 0.0161760i | ||||
\(498\) | −16.1803 | − | 28.0252i | −0.725058 | − | 1.25584i | ||||
\(499\) | 13.8885 | 0.621737 | 0.310868 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310868 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(500\) | −0.309017 | − | 0.535233i | −0.0138197 | − | 0.0239364i | ||||
\(501\) | 5.79180 | + | 10.0317i | 0.258758 | + | 0.448183i | ||||
\(502\) | 25.5066 | 1.13841 | ||||||||
\(503\) | 6.59017 | + | 11.4145i | 0.293841 | + | 0.508948i | 0.974715 | − | 0.223453i | \(-0.0717330\pi\) |
−0.680873 | + | 0.732401i | \(0.738400\pi\) | |||||||
\(504\) | −0.527864 | + | 0.914287i | −0.0235129 | + | 0.0407256i | ||||
\(505\) | −4.73607 | + | 8.20311i | −0.210752 | + | 0.365034i | ||||
\(506\) | 56.4508 | 2.50955 | ||||||||
\(507\) | 1.11803 | + | 29.0474i | 0.0496536 | + | 1.29004i | ||||
\(508\) | 0.145898 | 0.00647318 | ||||||||
\(509\) | −5.68034 | + | 9.83864i | −0.251777 | + | 0.436090i | −0.964015 | − | 0.265848i | \(-0.914348\pi\) |
0.712238 | + | 0.701938i | \(0.247681\pi\) | |||||||
\(510\) | 9.89919 | − | 17.1459i | 0.438343 | − | 0.759233i | ||||
\(511\) | −0.708204 | − | 1.22665i | −0.0313291 | − | 0.0542636i | ||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0.263932 | + | 0.457144i | 0.0116529 | + | 0.0201834i | ||||
\(514\) | −6.89919 | − | 11.9497i | −0.304310 | − | 0.527081i | ||||
\(515\) | −4.94427 | −0.217871 | ||||||||
\(516\) | −1.21885 | − | 2.11111i | −0.0536567 | − | 0.0929362i | ||||
\(517\) | −27.4164 | + | 47.4866i | −1.20577 | + | 2.08846i | ||||
\(518\) | 0.572949 | − | 0.992377i | 0.0251739 | − | 0.0436025i | ||||
\(519\) | −37.7639 | −1.65765 | ||||||||
\(520\) | 2.23607 | + | 7.74597i | 0.0980581 | + | 0.339683i | ||||
\(521\) | −41.7771 | −1.83029 | −0.915144 | − | 0.403128i | \(-0.867923\pi\) | ||||
−0.915144 | + | 0.403128i | \(0.867923\pi\) | |||||||
\(522\) | −2.38197 | + | 4.12569i | −0.104256 | + | 0.180576i | ||||
\(523\) | −9.35410 | + | 16.2018i | −0.409026 | + | 0.708454i | −0.994781 | − | 0.102034i | \(-0.967465\pi\) |
0.585755 | + | 0.810488i | \(0.300798\pi\) | |||||||
\(524\) | 3.70820 | + | 6.42280i | 0.161994 | + | 0.280581i | ||||
\(525\) | 0.527864 | 0.0230379 | ||||||||
\(526\) | −6.66312 | − | 11.5409i | −0.290526 | − | 0.503205i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 45.9787 | 2.00097 | ||||||||
\(529\) | −22.4164 | − | 38.8264i | −0.974626 | − | 1.68810i | ||||
\(530\) | −4.85410 | + | 8.40755i | −0.210849 | + | 0.365201i | ||||
\(531\) | −12.7082 | + | 22.0113i | −0.551489 | + | 0.955207i | ||||
\(532\) | 0.0344419 | 0.00149324 | ||||||||
\(533\) | −20.8050 | − | 5.14789i | −0.901162 | − | 0.222980i | ||||
\(534\) | 32.5623 | 1.40911 | ||||||||
\(535\) | 5.11803 | − | 8.86469i | 0.221272 | − | 0.383254i | ||||
\(536\) | 11.9721 | − | 20.7363i | 0.517118 | − | 0.895674i | ||||
\(537\) | −4.20820 | − | 7.28882i | −0.181597 | − | 0.314536i | ||||
\(538\) | −25.0344 | −1.07931 | ||||||||
\(539\) | 14.7082 | + | 25.4754i | 0.633527 | + | 1.09730i | ||||
\(540\) | −0.690983 | − | 1.19682i | −0.0297352 | − | 0.0515028i | ||||
\(541\) | 7.88854 | 0.339155 | 0.169577 | − | 0.985517i | \(-0.445760\pi\) | ||||
0.169577 | + | 0.985517i | \(0.445760\pi\) | |||||||
\(542\) | −11.8992 | − | 20.6100i | −0.511114 | − | 0.885275i | ||||
\(543\) | 6.70820 | − | 11.6190i | 0.287877 | − | 0.498617i | ||||
\(544\) | 9.25329 | − | 16.0272i | 0.396731 | − | 0.687159i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 2.98936 | + | 0.739674i | 0.127933 | + | 0.0316551i | ||||
\(547\) | −34.8328 | −1.48934 | −0.744672 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744672 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(548\) | 2.30902 | − | 3.99933i | 0.0986363 | − | 0.170843i | ||||
\(549\) | 12.4164 | − | 21.5058i | 0.529919 | − | 0.917847i | ||||
\(550\) | −3.42705 | − | 5.93583i | −0.146130 | − | 0.253104i | ||||
\(551\) | −0.347524 | −0.0148050 | ||||||||
\(552\) | −20.5902 | − | 35.6632i | −0.876376 | − | 1.51793i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −30.5623 | −1.29847 | ||||||||
\(555\) | 3.35410 | + | 5.80948i | 0.142374 | + | 0.246598i | ||||
\(556\) | 1.01722 | − | 1.76188i | 0.0431398 | − | 0.0747203i | ||||
\(557\) | −3.97214 | + | 6.87994i | −0.168305 | + | 0.291512i | −0.937824 | − | 0.347111i | \(-0.887163\pi\) |
0.769519 | + | 0.638624i | \(0.220496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.40983 | − | 4.58283i | 0.186516 | − | 0.193833i | ||||
\(560\) | 1.14590 | 0.0484230 | ||||||||
\(561\) | 25.9164 | − | 44.8885i | 1.09419 | − | 1.89520i | ||||
\(562\) | −16.0902 | + | 27.8690i | −0.678723 | + | 1.17558i | ||||
\(563\) | −8.64590 | − | 14.9751i | −0.364381 | − | 0.631127i | 0.624295 | − | 0.781188i | \(-0.285386\pi\) |
−0.988677 | + | 0.150062i | \(0.952053\pi\) | |||||||
\(564\) | −17.8885 | −0.753244 | ||||||||
\(565\) | 3.73607 | + | 6.47106i | 0.157178 | + | 0.272240i | ||||
\(566\) | −2.19098 | − | 3.79489i | −0.0920939 | − | 0.159511i | ||||
\(567\) | 2.59675 | 0.109053 | ||||||||
\(568\) | −1.97214 | − | 3.41584i | −0.0827490 | − | 0.143325i | ||||
\(569\) | 9.44427 | − | 16.3580i | 0.395924 | − | 0.685761i | −0.597294 | − | 0.802022i | \(-0.703758\pi\) |
0.993219 | + | 0.116261i | \(0.0370909\pi\) | |||||||
\(570\) | −0.427051 | + | 0.739674i | −0.0178872 | + | 0.0309815i | ||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | −2.61803 | − | 9.06914i | −0.109466 | − | 0.379200i | ||||
\(573\) | 10.7771 | 0.450219 | ||||||||
\(574\) | −1.13525 | + | 1.96632i | −0.0473846 | + | 0.0820726i | ||||
\(575\) | −4.11803 | + | 7.13264i | −0.171734 | + | 0.297452i | ||||
\(576\) | −4.23607 | − | 7.33708i | −0.176503 | − | 0.305712i | ||||
\(577\) | −7.88854 | −0.328404 | −0.164202 | − | 0.986427i | \(-0.552505\pi\) | ||||
−0.164202 | + | 0.986427i | \(0.552505\pi\) | |||||||
\(578\) | −10.4721 | − | 18.1383i | −0.435583 | − | 0.754453i | ||||
\(579\) | 6.11803 | + | 10.5967i | 0.254257 | + | 0.440386i | ||||
\(580\) | 0.909830 | 0.0377786 | ||||||||
\(581\) | −1.05573 | − | 1.82857i | −0.0437990 | − | 0.0758621i | ||||
\(582\) | 9.89919 | − | 17.1459i | 0.410335 | − | 0.710720i | ||||
\(583\) | −12.7082 | + | 22.0113i | −0.526320 | + | 0.911613i | ||||
\(584\) | 13.4164 | 0.555175 | ||||||||
\(585\) | −5.00000 | + | 5.19615i | −0.206725 | + | 0.214834i | ||||
\(586\) | −19.5066 | −0.805809 | ||||||||
\(587\) | −2.88197 | + | 4.99171i | −0.118951 | + | 0.206030i | −0.919352 | − | 0.393435i | \(-0.871287\pi\) |
0.800401 | + | 0.599465i | \(0.204620\pi\) | |||||||
\(588\) | −4.79837 | + | 8.31103i | −0.197882 | + | 0.342741i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 20.5623 | 0.846537 | ||||||||
\(591\) | 3.35410 | + | 5.80948i | 0.137969 | + | 0.238970i | ||||
\(592\) | 7.28115 | + | 12.6113i | 0.299254 | + | 0.518322i | ||||
\(593\) | 27.8885 | 1.14525 | 0.572623 | − | 0.819819i | \(-0.305926\pi\) | ||||
0.572623 | + | 0.819819i | \(0.305926\pi\) | |||||||
\(594\) | −7.66312 | − | 13.2729i | −0.314422 | − | 0.544594i | ||||
\(595\) | 0.645898 | − | 1.11873i | 0.0264792 | − | 0.0458634i | ||||
\(596\) | −4.16312 | + | 7.21073i | −0.170528 | + | 0.295363i | ||||
\(597\) | 32.8885 | 1.34604 | ||||||||
\(598\) | −33.3156 | + | 34.6226i | −1.36238 | + | 1.41582i | ||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −2.50000 | + | 4.33013i | −0.102062 | + | 0.176777i | ||||
\(601\) | −13.0279 | + | 22.5649i | −0.531418 | + | 0.920442i | 0.467910 | + | 0.883776i | \(0.345007\pi\) |
−0.999328 | + | 0.0366662i | \(0.988326\pi\) | |||||||
\(602\) | −0.336881 | − | 0.583495i | −0.0137302 | − | 0.0237815i | ||||
\(603\) | 21.4164 | 0.872144 | ||||||||
\(604\) | −2.47214 | − | 4.28187i | −0.100590 | − | 0.174227i | ||||
\(605\) | −3.47214 | − | 6.01392i | −0.141162 | − | 0.244500i | ||||
\(606\) | −34.2705 | −1.39214 | ||||||||
\(607\) | −6.35410 | − | 11.0056i | −0.257905 | − | 0.446705i | 0.707775 | − | 0.706437i | \(-0.249699\pi\) |
−0.965681 | + | 0.259733i | \(0.916366\pi\) | |||||||
\(608\) | −0.399187 | + | 0.691412i | −0.0161892 | + | 0.0280405i | ||||
\(609\) | −0.388544 | + | 0.672978i | −0.0157446 | + | 0.0272704i | ||||
\(610\) | −20.0902 | −0.813427 | ||||||||
\(611\) | −12.9443 | − | 44.8403i | −0.523669 | − | 1.81404i | ||||
\(612\) | 6.76393 | 0.273416 | ||||||||
\(613\) | −11.0279 | + | 19.1008i | −0.445411 | + | 0.771475i | −0.998081 | − | 0.0619256i | \(-0.980276\pi\) |
0.552670 | + | 0.833400i | \(0.313609\pi\) | |||||||
\(614\) | −5.70820 | + | 9.88690i | −0.230364 | + | 0.399003i | ||||
\(615\) | −6.64590 | − | 11.5110i | −0.267988 | − | 0.464170i | ||||
\(616\) | 2.23607 | 0.0900937 | ||||||||
\(617\) | 6.79180 | + | 11.7637i | 0.273427 | + | 0.473590i | 0.969737 | − | 0.244151i | \(-0.0785093\pi\) |
−0.696310 | + | 0.717741i | \(0.745176\pi\) | |||||||
\(618\) | −8.94427 | − | 15.4919i | −0.359791 | − | 0.623177i | ||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.20820 | + | 15.9491i | −0.369512 | + | 0.640014i | ||||
\(622\) | 19.4164 | − | 33.6302i | 0.778527 | − | 1.34845i | ||||
\(623\) | 2.12461 | 0.0851208 | ||||||||
\(624\) | −27.1353 | + | 28.1998i | −1.08628 | + | 1.12889i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.7984 | − | 44.6841i | 1.03111 | − | 1.78594i | ||||
\(627\) | −1.11803 | + | 1.93649i | −0.0446500 | + | 0.0773360i | ||||
\(628\) | 5.56231 | + | 9.63420i | 0.221960 | + | 0.384446i | ||||
\(629\) | 16.4164 | 0.654565 | ||||||||
\(630\) | 0.381966 | + | 0.661585i | 0.0152179 | + | 0.0263582i | ||||
\(631\) | −12.0623 | − | 20.8925i | −0.480193 | − | 0.831718i | 0.519549 | − | 0.854441i | \(-0.326100\pi\) |
−0.999742 | + | 0.0227223i | \(0.992767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.2639 | + | 17.7777i | 0.407955 | + | 0.706598i | ||||
\(634\) | −19.3262 | + | 33.4740i | −0.767543 | + | 1.32942i | ||||
\(635\) | −0.118034 | + | 0.204441i | −0.00468404 | + | 0.00811299i | ||||
\(636\) | −8.29180 | −0.328791 | ||||||||
\(637\) | −24.3050 | − | 6.01392i | −0.962997 | − | 0.238280i | ||||
\(638\) | 10.0902 | 0.399474 | ||||||||
\(639\) | 1.76393 | − | 3.05522i | 0.0697801 | − | 0.120863i | ||||
\(640\) | −6.80902 | + | 11.7936i | −0.269150 | + | 0.466182i | ||||
\(641\) | 13.4443 | + | 23.2862i | 0.531017 | + | 0.919748i | 0.999345 | + | 0.0361934i | \(0.0115232\pi\) |
−0.468328 | + | 0.883555i | \(0.655143\pi\) | |||||||
\(642\) | 37.0344 | 1.46163 | ||||||||
\(643\) | 15.3541 | + | 26.5941i | 0.605507 | + | 1.04877i | 0.991971 | + | 0.126464i | \(0.0403628\pi\) |
−0.386465 | + | 0.922304i | \(0.626304\pi\) | |||||||
\(644\) | 0.600813 | + | 1.04064i | 0.0236754 | + | 0.0410069i | ||||
\(645\) | 3.94427 | 0.155306 | ||||||||
\(646\) | 1.04508 | + | 1.81014i | 0.0411183 | + | 0.0712190i | ||||
\(647\) | 23.2984 | − | 40.3540i | 0.915954 | − | 1.58648i | 0.110454 | − | 0.993881i | \(-0.464769\pi\) |
0.805499 | − | 0.592597i | \(-0.201897\pi\) | |||||||
\(648\) | −12.2984 | + | 21.3014i | −0.483126 | + | 0.836798i | ||||
\(649\) | 53.8328 | 2.11312 | ||||||||
\(650\) | 5.66312 | + | 1.40126i | 0.222126 | + | 0.0549619i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.399187 | + | 0.691412i | −0.0156334 | + | 0.0270778i | ||||
\(653\) | 10.5000 | − | 18.1865i | 0.410897 | − | 0.711694i | −0.584091 | − | 0.811688i | \(-0.698549\pi\) |
0.994988 | + | 0.0999939i | \(0.0318823\pi\) | |||||||
\(654\) | −3.61803 | − | 6.26662i | −0.141476 | − | 0.245044i | ||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | −14.4271 | − | 24.9884i | −0.563282 | − | 0.975633i | ||||
\(657\) | 6.00000 | + | 10.3923i | 0.234082 | + | 0.405442i | ||||
\(658\) | −4.94427 | −0.192748 | ||||||||
\(659\) | 24.1180 | + | 41.7737i | 0.939505 | + | 1.62727i | 0.766396 | + | 0.642368i | \(0.222048\pi\) |
0.173109 | + | 0.984903i | \(0.444619\pi\) | |||||||
\(660\) | 2.92705 | − | 5.06980i | 0.113935 | − | 0.197342i | ||||
\(661\) | −1.68034 | + | 2.91043i | −0.0653576 | + | 0.113203i | −0.896853 | − | 0.442330i | \(-0.854152\pi\) |
0.831495 | + | 0.555532i | \(0.187485\pi\) | |||||||
\(662\) | 41.5066 | 1.61320 | ||||||||
\(663\) | 12.2361 | + | 42.3870i | 0.475210 | + | 1.64617i | ||||
\(664\) | 20.0000 | 0.776151 | ||||||||
\(665\) | −0.0278640 | + | 0.0482619i | −0.00108052 | + | 0.00187152i | ||||
\(666\) | −4.85410 | + | 8.40755i | −0.188093 | + | 0.325786i | ||||
\(667\) | −6.06231 | − | 10.5002i | −0.234733 | − | 0.406570i | ||||
\(668\) | 3.20163 | 0.123875 | ||||||||
\(669\) | −14.2082 | − | 24.6093i | −0.549321 | − | 0.951452i | ||||
\(670\) | −8.66312 | − | 15.0050i | −0.334685 | − | 0.579692i | ||||
\(671\) | −52.5967 | −2.03047 | ||||||||
\(672\) | 0.892609 | + | 1.54604i | 0.0344331 | + | 0.0596400i | ||||
\(673\) | 18.2082 | − | 31.5375i | 0.701875 | − | 1.21568i | −0.265933 | − | 0.963992i | \(-0.585680\pi\) |
0.967808 | − | 0.251691i | \(-0.0809867\pi\) | |||||||
\(674\) | −22.5623 | + | 39.0791i | −0.869068 | + | 1.50527i | ||||
\(675\) | 2.23607 | 0.0860663 | ||||||||
\(676\) | 7.10739 | + | 3.74663i | 0.273361 | + | 0.144101i | ||||
\(677\) | 47.8885 | 1.84051 | 0.920253 | − | 0.391324i | \(-0.127983\pi\) | ||||
0.920253 | + | 0.391324i | \(0.127983\pi\) | |||||||
\(678\) | −13.5172 | + | 23.4125i | −0.519126 | + | 0.899152i | ||||
\(679\) | 0.645898 | − | 1.11873i | 0.0247873 | − | 0.0429328i | ||||
\(680\) | 6.11803 | + | 10.5967i | 0.234616 | + | 0.406367i | ||||
\(681\) | 3.94427 | 0.151145 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.1180 | − | 26.1852i | −0.578475 | − | 1.00195i | −0.995654 | − | 0.0931246i | \(-0.970315\pi\) |
0.417179 | − | 0.908824i | \(-0.363019\pi\) | |||||||
\(684\) | −0.291796 | −0.0111571 | ||||||||
\(685\) | 3.73607 | + | 6.47106i | 0.142748 | + | 0.247246i | ||||
\(686\) | −2.66312 | + | 4.61266i | −0.101678 | + | 0.176112i | ||||
\(687\) | −22.2361 | + | 38.5140i | −0.848359 | + | 1.46940i | ||||
\(688\) | 8.56231 | 0.326435 | ||||||||
\(689\) | −6.00000 | − | 20.7846i | −0.228582 | − | 0.791831i | ||||
\(690\) | −29.7984 | −1.13440 | ||||||||
\(691\) | 5.29837 | − | 9.17705i | 0.201560 | − | 0.349112i | −0.747471 | − | 0.664294i | \(-0.768732\pi\) |
0.949031 | + | 0.315182i | \(0.102066\pi\) | |||||||
\(692\) | −5.21885 | + | 9.03931i | −0.198391 | + | 0.343623i | ||||
\(693\) | 1.00000 | + | 1.73205i | 0.0379869 | + | 0.0657952i | ||||
\(694\) | 27.9787 | 1.06206 | ||||||||
\(695\) | 1.64590 | + | 2.85078i | 0.0624325 | + | 0.108136i | ||||
\(696\) | −3.68034 | − | 6.37454i | −0.139503 | − | 0.241626i | ||||
\(697\) | −32.5279 | −1.23208 | ||||||||
\(698\) | 19.7533 | + | 34.2137i | 0.747673 | + | 1.29501i | ||||
\(699\) | 22.2361 | − | 38.5140i | 0.841045 | − | 1.45673i | ||||
\(700\) | 0.0729490 | − | 0.126351i | 0.00275721 | − | 0.00477563i | ||||
\(701\) | −27.8885 | −1.05334 | −0.526668 | − | 0.850071i | \(-0.676559\pi\) | ||||
−0.526668 | + | 0.850071i | \(0.676559\pi\) | |||||||
\(702\) | 12.6631 | + | 3.13331i | 0.477939 | + | 0.118259i | ||||
\(703\) | −0.708204 | −0.0267104 | ||||||||
\(704\) | −8.97214 | + | 15.5402i | −0.338150 | + | 0.585693i | ||||
\(705\) | 14.4721 | − | 25.0665i | 0.545052 | − | 0.944058i | ||||
\(706\) | 8.51722 | + | 14.7523i | 0.320550 | + | 0.555209i | ||||
\(707\) | −2.23607 | −0.0840960 | ||||||||
\(708\) | 8.78115 | + | 15.2094i | 0.330016 | + | 0.571604i | ||||
\(709\) | 19.1525 | + | 33.1731i | 0.719286 | + | 1.24584i | 0.961283 | + | 0.275563i | \(0.0888644\pi\) |
−0.241997 | + | 0.970277i | \(0.577802\pi\) | |||||||
\(710\) | −2.85410 | −0.107113 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.0623 | + | 17.4284i | −0.377101 | + | 0.653158i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 4.67376 | 0.174911 | ||||||||
\(715\) | 14.8262 | + | 3.66854i | 0.554470 | + | 0.137196i | ||||
\(716\) | −2.32624 | −0.0869356 | ||||||||
\(717\) | 11.0557 | − | 19.1491i | 0.412884 | − | 0.715136i | ||||
\(718\) | 14.4721 | − | 25.0665i | 0.540095 | − | 0.935473i | ||||
\(719\) | −4.06231 | − | 7.03612i | −0.151498 | − | 0.262403i | 0.780280 | − | 0.625430i | \(-0.215077\pi\) |
−0.931779 | + | 0.363027i | \(0.881743\pi\) | |||||||
\(720\) | −9.70820 | −0.361803 | ||||||||
\(721\) | −0.583592 | − | 1.01081i | −0.0217341 | − | 0.0376446i | ||||
\(722\) | 15.3262 | + | 26.5458i | 0.570384 | + | 0.987933i | ||||
\(723\) | −33.5410 | −1.24740 | ||||||||
\(724\) | −1.85410 | − | 3.21140i | −0.0689072 | − | 0.119351i | ||||
\(725\) | −0.736068 | + | 1.27491i | −0.0273369 | + | 0.0473489i | ||||
\(726\) | 12.5623 | − | 21.7586i | 0.466231 | − | 0.807536i | ||||
\(727\) | 11.0557 | 0.410034 | 0.205017 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205017 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(728\) | −1.31966 | + | 1.37143i | −0.0489099 | + | 0.0508286i | ||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 4.85410 | − | 8.40755i | 0.179658 | − | 0.311177i | ||||
\(731\) | 4.82624 | − | 8.35929i | 0.178505 | − | 0.309179i | ||||
\(732\) | −8.57953 | − | 14.8602i | −0.317108 | − | 0.549248i | ||||
\(733\) | −8.11146 | −0.299603 | −0.149802 | − | 0.988716i | \(-0.547864\pi\) | ||||
−0.149802 | + | 0.988716i | \(0.547864\pi\) | |||||||
\(734\) | 20.7533 | + | 35.9458i | 0.766018 | + | 1.32678i | ||||
\(735\) | −7.76393 | − | 13.4475i | −0.286377 | − | 0.496019i | ||||
\(736\) | −27.8541 | −1.02672 | ||||||||
\(737\) | −22.6803 | − | 39.2835i | −0.835441 | − | 1.44703i | ||||
\(738\) | 9.61803 | − | 16.6589i | 0.354045 | − | 0.613223i | ||||
\(739\) | 19.7705 | − | 34.2435i | 0.727270 | − | 1.25967i | −0.230763 | − | 0.973010i | \(-0.574122\pi\) |
0.958033 | − | 0.286659i | \(-0.0925445\pi\) | |||||||
\(740\) | 1.85410 | 0.0681581 | ||||||||
\(741\) | −0.527864 | − | 1.82857i | −0.0193916 | − | 0.0671744i | ||||
\(742\) | −2.29180 | −0.0841345 | ||||||||
\(743\) | −1.06231 | + | 1.83997i | −0.0389722 | + | 0.0675019i | −0.884854 | − | 0.465869i | \(-0.845742\pi\) |
0.845881 | + | 0.533371i | \(0.179075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.73607 | − | 11.6672i | −0.246790 | − | 0.427454i | ||||
\(746\) | 16.2705 | 0.595706 | ||||||||
\(747\) | 8.94427 | + | 15.4919i | 0.327254 | + | 0.566820i | ||||
\(748\) | −7.16312 | − | 12.4069i | −0.261910 | − | 0.453641i | ||||
\(749\) | 2.41641 | 0.0882936 | ||||||||
\(750\) | 1.80902 | + | 3.13331i | 0.0660560 | + | 0.114412i | ||||
\(751\) | 8.64590 | − | 14.9751i | 0.315493 | − | 0.546450i | −0.664049 | − | 0.747689i | \(-0.731163\pi\) |
0.979542 | + | 0.201239i | \(0.0644967\pi\) | |||||||
\(752\) | 31.4164 | − | 54.4148i | 1.14564 | − | 1.98430i | ||||
\(753\) | −35.2492 | −1.28455 | ||||||||
\(754\) | −5.95492 | + | 6.18853i | −0.216865 | + | 0.225373i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0.163119 | − | 0.282530i | 0.00593258 | − | 0.0102755i | ||||
\(757\) | −14.4443 | + | 25.0182i | −0.524986 | + | 0.909302i | 0.474591 | + | 0.880207i | \(0.342596\pi\) |
−0.999577 | + | 0.0290958i | \(0.990737\pi\) | |||||||
\(758\) | −26.8435 | − | 46.4942i | −0.974998 | − | 1.68875i | ||||
\(759\) | −78.0132 | −2.83170 | ||||||||
\(760\) | −0.263932 | − | 0.457144i | −0.00957382 | − | 0.0165823i | ||||
\(761\) | 10.0279 | + | 17.3688i | 0.363510 | + | 0.629617i | 0.988536 | − | 0.150986i | \(-0.0482450\pi\) |
−0.625026 | + | 0.780604i | \(0.714912\pi\) | |||||||
\(762\) | −0.854102 | −0.0309408 | ||||||||
\(763\) | −0.236068 | − | 0.408882i | −0.00854623 | − | 0.0148025i | ||||
\(764\) | 1.48936 | − | 2.57964i | 0.0538830 | − | 0.0933282i | ||||
\(765\) | −5.47214 | + | 9.47802i | −0.197845 | + | 0.342678i | ||||
\(766\) | −0.381966 | −0.0138010 | ||||||||
\(767\) | −31.7705 | + | 33.0169i | −1.14717 | + | 1.19217i | ||||
\(768\) | −30.3262 | −1.09430 | ||||||||
\(769\) | 11.9164 | − | 20.6398i | 0.429717 | − | 0.744291i | −0.567131 | − | 0.823627i | \(-0.691947\pi\) |
0.996848 | + | 0.0793363i | \(0.0252801\pi\) | |||||||
\(770\) | 0.809017 | − | 1.40126i | 0.0291549 | − | 0.0504979i | ||||
\(771\) | 9.53444 | + | 16.5141i | 0.343375 | + | 0.594742i | ||||
\(772\) | 3.38197 | 0.121720 | ||||||||
\(773\) | 18.9721 | + | 32.8607i | 0.682380 | + | 1.18192i | 0.974252 | + | 0.225460i | \(0.0723885\pi\) |
−0.291872 | + | 0.956457i | \(0.594278\pi\) | |||||||
\(774\) | 2.85410 | + | 4.94345i | 0.102589 | + | 0.177689i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.11803 | + | 10.5967i | 0.219625 | + | 0.380401i | ||||
\(777\) | −0.791796 | + | 1.37143i | −0.0284055 | + | 0.0491998i | ||||
\(778\) | 29.0344 | − | 50.2891i | 1.04094 | − | 1.80295i | ||||
\(779\) | 1.40325 | 0.0502767 | ||||||||
\(780\) | 1.38197 | + | 4.78727i | 0.0494823 | + | 0.171412i | ||||
\(781\) | −7.47214 | −0.267374 | ||||||||
\(782\) | −36.4615 | + | 63.1532i | −1.30386 | + | 2.25835i | ||||
\(783\) | −1.64590 | + | 2.85078i | −0.0588196 | + | 0.101879i | ||||
\(784\) | −16.8541 | − | 29.1922i | −0.601932 | − | 1.04258i | ||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −21.7082 | − | 37.5997i | −0.774306 | − | 1.34114i | ||||
\(787\) | 18.7705 | + | 32.5115i | 0.669096 | + | 1.15891i | 0.978157 | + | 0.207867i | \(0.0666520\pi\) |
−0.309061 | + | 0.951042i | \(0.600015\pi\) | |||||||
\(788\) | 1.85410 | 0.0660496 | ||||||||
\(789\) | 9.20820 | + | 15.9491i | 0.327821 | + | 0.567802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.881966 | + | 1.52761i | −0.0313591 | + | 0.0543156i | ||||
\(792\) | −18.9443 | −0.673155 | ||||||||
\(793\) | 31.0410 | − | 32.2588i | 1.10230 | − | 1.14554i | ||||
\(794\) | 16.2705 | 0.577419 | ||||||||
\(795\) | 6.70820 | − | 11.6190i | 0.237915 | − | 0.412082i | ||||
\(796\) | 4.54508 | − | 7.87232i | 0.161096 | − | 0.279027i | ||||
\(797\) | −0.0835921 | − | 0.144786i | −0.00296099 | − | 0.00512858i | 0.864541 | − | 0.502562i | \(-0.167609\pi\) |
−0.867502 | + | 0.497434i | \(0.834276\pi\) | |||||||
\(798\) | −0.201626 | −0.00713749 | ||||||||
\(799\) | −35.4164 | − | 61.3430i | −1.25294 | − | 2.17016i | ||||
\(800\) | 1.69098 | + | 2.92887i | 0.0597853 | + | 0.103551i | ||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 21.7533 | + | 37.6778i | 0.768135 | + | 1.33045i | ||||
\(803\) | 12.7082 | − | 22.0113i | 0.448463 | − | 0.776760i | ||||
\(804\) | 7.39919 | − | 12.8158i | 0.260949 | − | 0.451977i | ||||
\(805\) | −1.94427 | −0.0685266 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.5967 | 1.21786 | ||||||||
\(808\) | 10.5902 | − | 18.3427i | 0.372561 | − | 0.645294i | ||||
\(809\) | −16.4443 | + | 28.4823i | −0.578150 | + | 1.00138i | 0.417542 | + | 0.908658i | \(0.362892\pi\) |
−0.995692 | + | 0.0927271i | \(0.970442\pi\) | |||||||
\(810\) | 8.89919 | + | 15.4138i | 0.312686 | + | 0.541587i | ||||
\(811\) | −39.7771 | −1.39676 | −0.698381 | − | 0.715726i | \(-0.746096\pi\) | ||||
−0.698381 | + | 0.715726i | \(0.746096\pi\) | |||||||
\(812\) | 0.107391 | + | 0.186006i | 0.00376868 | + | 0.00652755i | ||||
\(813\) | 16.4443 | + | 28.4823i | 0.576726 | + | 0.998918i | ||||
\(814\) | 20.5623 | 0.720708 | ||||||||
\(815\) | −0.645898 | − | 1.11873i | −0.0226248 | − | 0.0391873i | ||||
\(816\) | −29.6976 | + | 51.4377i | −1.03962 | + | 1.80068i | ||||
\(817\) | −0.208204 | + | 0.360620i | −0.00728413 | + | 0.0126165i | ||||
\(818\) | −17.6180 | −0.616000 | ||||||||
\(819\) | −1.65248 | − | 0.408882i | −0.0577422 | − | 0.0142875i | ||||
\(820\) | −3.67376 | −0.128293 | ||||||||
\(821\) | −9.68034 | + | 16.7668i | −0.337846 | + | 0.585167i | −0.984027 | − | 0.178017i | \(-0.943032\pi\) |
0.646181 | + | 0.763184i | \(0.276365\pi\) | |||||||
\(822\) | −13.5172 | + | 23.4125i | −0.471467 | + | 0.816605i | ||||
\(823\) | −11.2984 | − | 19.5694i | −0.393837 | − | 0.682145i | 0.599115 | − | 0.800663i | \(-0.295519\pi\) |
−0.992952 | + | 0.118518i | \(0.962186\pi\) | |||||||
\(824\) | 11.0557 | 0.385145 | ||||||||
\(825\) | 4.73607 | + | 8.20311i | 0.164889 | + | 0.285596i | ||||
\(826\) | 2.42705 | + | 4.20378i | 0.0844479 | + | 0.146268i | ||||
\(827\) | 8.94427 | 0.311023 | 0.155511 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155511 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(828\) | −5.09017 | − | 8.81643i | −0.176896 | − | 0.306392i | ||||
\(829\) | −18.6246 | + | 32.2588i | −0.646860 | + | 1.12039i | 0.337009 | + | 0.941501i | \(0.390585\pi\) |
−0.983869 | + | 0.178892i | \(0.942749\pi\) | |||||||
\(830\) | 7.23607 | − | 12.5332i | 0.251168 | − | 0.435035i | ||||
\(831\) | 42.2361 | 1.46515 | ||||||||
\(832\) | −4.23607 | − | 14.6742i | −0.146859 | − | 0.508735i | ||||
\(833\) | −38.0000 | −1.31662 | ||||||||
\(834\) | −5.95492 | + | 10.3142i | −0.206202 | + | 0.357152i | ||||
\(835\) | −2.59017 | + | 4.48631i | −0.0896365 | + | 0.155255i | ||||
\(836\) | 0.309017 | + | 0.535233i | 0.0106876 | + | 0.0185114i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.0451 | + | 19.1306i | 0.381546 | + | 0.660857i | ||||
\(839\) | −8.64590 | − | 14.9751i | −0.298490 | − | 0.516999i | 0.677301 | − | 0.735706i | \(-0.263149\pi\) |
−0.975791 | + | 0.218707i | \(0.929816\pi\) | |||||||
\(840\) | −1.18034 | −0.0407256 | ||||||||
\(841\) | 13.4164 | + | 23.2379i | 0.462635 | + | 0.801307i | ||||
\(842\) | −4.85410 | + | 8.40755i | −0.167283 | + | 0.289743i | ||||
\(843\) | 22.2361 | − | 38.5140i | 0.765851 | − | 1.32649i | ||||
\(844\) | 5.67376 | 0.195299 | ||||||||
\(845\) | −11.0000 | + | 6.92820i | −0.378412 | + | 0.238337i | ||||
\(846\) | 41.8885 | 1.44016 | ||||||||
\(847\) | 0.819660 | − | 1.41969i | 0.0281639 | − | 0.0487812i | ||||
\(848\) | 14.5623 | − | 25.2227i | 0.500072 | − | 0.866149i | ||||
\(849\) | 3.02786 | + | 5.24441i | 0.103916 | + | 0.179988i | ||||
\(850\) | 8.85410 | 0.303693 | ||||||||
\(851\) | −12.3541 | − | 21.3979i | −0.423493 | − | 0.733512i | ||||
\(852\) | −1.21885 | − | 2.11111i | −0.0417570 | − | 0.0723253i | ||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | −2.37132 | − | 4.10725i | −0.0811450 | − | 0.140547i | ||||
\(855\) | 0.236068 | − | 0.408882i | 0.00807335 | − | 0.0139835i | ||||
\(856\) | −11.4443 | + | 19.8221i | −0.391157 | + | 0.677504i | ||||
\(857\) | 0.111456 | 0.00380727 | 0.00190364 | − | 0.999998i | \(-0.499394\pi\) | ||||
0.00190364 | + | 0.999998i | \(0.499394\pi\) | |||||||
\(858\) | 15.3262 | + | 53.0916i | 0.523229 | + | 1.81252i | ||||
\(859\) | −13.8885 | −0.473871 | −0.236935 | − | 0.971525i | \(-0.576143\pi\) | ||||
−0.236935 | + | 0.971525i | \(0.576143\pi\) | |||||||
\(860\) | 0.545085 | − | 0.944115i | 0.0185872 | − | 0.0321940i | ||||
\(861\) | 1.56888 | − | 2.71739i | 0.0534674 | − | 0.0926083i | ||||
\(862\) | −3.89919 | − | 6.75359i | −0.132807 | − | 0.230028i | ||||
\(863\) | −38.8328 | −1.32188 | −0.660942 | − | 0.750437i | \(-0.729843\pi\) | ||||
−0.660942 | + | 0.750437i | \(0.729843\pi\) | |||||||
\(864\) | 3.78115 | + | 6.54915i | 0.128637 | + | 0.222807i | ||||
\(865\) | −8.44427 | − | 14.6259i | −0.287114 | − | 0.497296i | ||||
\(866\) | −37.9787 | −1.29057 | ||||||||
\(867\) | 14.4721 | + | 25.0665i | 0.491500 | + | 0.851302i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −5.32624 | −0.180576 | ||||||||
\(871\) | 37.4787 | + | 9.27358i | 1.26992 | + | 0.314223i | ||||
\(872\) | 4.47214 | 0.151446 | ||||||||
\(873\) | −5.47214 | + | 9.47802i | −0.185204 | + | 0.320782i | ||||
\(874\) | 1.57295 | − | 2.72443i | 0.0532058 | − | 0.0921551i | ||||
\(875\) | 0.118034 | + | 0.204441i | 0.00399028 | + | 0.00691136i | ||||
\(876\) | 8.29180 | 0.280154 | ||||||||
\(877\) | −27.8607 | − | 48.2561i | −0.940788 | − | 1.62949i | −0.763972 | − | 0.645249i | \(-0.776754\pi\) |
−0.176816 | − | 0.984244i | \(-0.556580\pi\) | |||||||
\(878\) | 7.51722 | + | 13.0202i | 0.253694 | + | 0.439411i | ||||
\(879\) | 26.9574 | 0.909251 | ||||||||
\(880\) | 10.2812 | + | 17.8075i | 0.346578 | + | 0.600290i | ||||
\(881\) | −7.50000 | + | 12.9904i | −0.252681 | + | 0.437657i | −0.964263 | − | 0.264946i | \(-0.914646\pi\) |
0.711582 | + | 0.702603i | \(0.247979\pi\) | |||||||
\(882\) | 11.2361 | − | 19.4614i | 0.378338 | − | 0.655301i | ||||
\(883\) | 10.8328 | 0.364553 | 0.182277 | − | 0.983247i | \(-0.441653\pi\) | ||||
0.182277 | + | 0.983247i | \(0.441653\pi\) | |||||||
\(884\) | 11.8369 | + | 2.92887i | 0.398117 | + | 0.0985085i | ||||
\(885\) | −28.4164 | −0.955207 | ||||||||
\(886\) | 13.7082 | − | 23.7433i | 0.460536 | − | 0.797672i | ||||
\(887\) | 20.2426 | − | 35.0613i | 0.679682 | − | 1.17724i | −0.295395 | − | 0.955375i | \(-0.595451\pi\) |
0.975077 | − | 0.221868i | \(-0.0712153\pi\) | |||||||
\(888\) | −7.50000 | − | 12.9904i | −0.251684 | − | 0.435929i | ||||
\(889\) | −0.0557281 | −0.00186906 | ||||||||
\(890\) | 7.28115 | + | 12.6113i | 0.244065 | + | 0.422733i | ||||
\(891\) | 23.2984 | + | 40.3540i | 0.780525 | + | 1.35191i | ||||
\(892\) | −7.85410 | −0.262975 | ||||||||
\(893\) | 1.52786 | + | 2.64634i | 0.0511280 | + | 0.0885563i | ||||
\(894\) | 24.3713 | − | 42.2124i | 0.815099 | − | 1.41179i | ||||
\(895\) | 1.88197 | − | 3.25966i | 0.0629072 | − | 0.108958i | ||||
\(896\) | −3.21478 | −0.107398 | ||||||||
\(897\) | 46.0410 | − | 47.8472i | 1.53726 | − | 1.59757i | ||||
\(898\) | −22.5623 | −0.752914 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.618034 | + | 1.07047i | −0.0206011 | + | 0.0356822i | ||||
\(901\) | −16.4164 | − | 28.4341i | −0.546910 | − | 0.947276i | ||||
\(902\) | −40.7426 | −1.35658 | ||||||||
\(903\) | 0.465558 | + | 0.806370i | 0.0154928 | + | 0.0268343i | ||||
\(904\) | −8.35410 | − | 14.4697i | −0.277853 | − | 0.481256i | ||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 14.4721 | + | 25.0665i | 0.480805 | + | 0.832778i | ||||
\(907\) | 10.0623 | − | 17.4284i | 0.334113 | − | 0.578701i | −0.649201 | − | 0.760617i | \(-0.724896\pi\) |
0.983314 | + | 0.181916i | \(0.0582298\pi\) | |||||||
\(908\) | 0.545085 | − | 0.944115i | 0.0180893 | − | 0.0313316i | ||||
\(909\) | 18.9443 | 0.628342 | ||||||||
\(910\) | 0.381966 | + | 1.32317i | 0.0126620 | + | 0.0438626i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 1.28115 | − | 2.21902i | 0.0424232 | − | 0.0734792i | ||||
\(913\) | 18.9443 | − | 32.8124i | 0.626964 | − | 1.08593i | ||||
\(914\) | 22.9894 | + | 39.8187i | 0.760420 | + | 1.31709i | ||||
\(915\) | 27.7639 | 0.917847 | ||||||||
\(916\) | 6.14590 | + | 10.6450i | 0.203066 | + | 0.351721i | ||||
\(917\) | −1.41641 | − | 2.45329i | −0.0467739 | − | 0.0810148i | ||||
\(918\) | 19.7984 | 0.653444 | ||||||||
\(919\) | −16.6459 | − | 28.8315i | −0.549098 | − | 0.951065i | −0.998337 | − | 0.0576532i | \(-0.981638\pi\) |
0.449239 | − | 0.893412i | \(-0.351695\pi\) | |||||||
\(920\) | 9.20820 | − | 15.9491i | 0.303585 | − | 0.525825i | ||||
\(921\) | 7.88854 | − | 13.6634i | 0.259936 | − | 0.450223i | ||||
\(922\) | −45.9787 | −1.51423 | ||||||||
\(923\) | 4.40983 | − | 4.58283i | 0.145151 | − | 0.150846i | ||||
\(924\) | 1.38197 | 0.0454633 | ||||||||
\(925\) | −1.50000 | + | 2.59808i | −0.0493197 | + | 0.0854242i | ||||
\(926\) | −23.4164 | + | 40.5584i | −0.769511 | + | 1.33283i | ||||
\(927\) | 4.94427 | + | 8.56373i | 0.162391 | + | 0.281270i | ||||
\(928\) | −4.97871 | −0.163434 | ||||||||
\(929\) | −1.02786 | − | 1.78031i | −0.0337231 | − | 0.0584102i | 0.848671 | − | 0.528921i | \(-0.177403\pi\) |
−0.882394 | + | 0.470511i | \(0.844070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.63932 | 0.0537266 | ||||||||
\(932\) | −6.14590 | − | 10.6450i | −0.201316 | − | 0.348689i | ||||
\(933\) | −26.8328 | + | 46.4758i | −0.878467 | + | 1.52155i | ||||
\(934\) | 7.23607 | − | 12.5332i | 0.236771 | − | 0.410100i | ||||
\(935\) | 23.1803 | 0.758078 | ||||||||
\(936\) | 11.1803 | − | 11.6190i | 0.365441 | − | 0.379777i | ||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 2.04508 | − | 3.54219i | 0.0667744 | − | 0.115657i | ||||
\(939\) | −35.6525 | + | 61.7519i | −1.16347 | + | 2.01520i | ||||
\(940\) | −4.00000 | − | 6.92820i | −0.130466 | − | 0.225973i | ||||
\(941\) | 23.8885 | 0.778744 | 0.389372 | − | 0.921081i | \(-0.372692\pi\) | ||||
0.389372 | + | 0.921081i | \(0.372692\pi\) | |||||||
\(942\) | −32.5623 | − | 56.3996i | −1.06094 | − | 1.83760i | ||||
\(943\) | 24.4787 | + | 42.3984i | 0.797137 | + | 1.38068i | ||||
\(944\) | −61.6869 | −2.00774 | ||||||||
\(945\) | 0.263932 | + | 0.457144i | 0.00858571 | + | 0.0148709i | ||||
\(946\) | 6.04508 | − | 10.4704i | 0.196543 | − | 0.340422i | ||||
\(947\) | −8.40983 | + | 14.5663i | −0.273283 | + | 0.473340i | −0.969700 | − | 0.244297i | \(-0.921443\pi\) |
0.696418 | + | 0.717637i | \(0.254776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | + | 20.7846i | 0.194768 | + | 0.674697i | ||||
\(950\) | −0.381966 | −0.0123926 | ||||||||
\(951\) | 26.7082 | − | 46.2600i | 0.866073 | − | 1.50008i | ||||
\(952\) | −1.44427 | + | 2.50155i | −0.0468091 | + | 0.0810758i | ||||
\(953\) | 28.0967 | + | 48.6650i | 0.910143 | + | 1.57641i | 0.813861 | + | 0.581060i | \(0.197362\pi\) |
0.0962820 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(954\) | 19.4164 | 0.628629 | ||||||||
\(955\) | 2.40983 | + | 4.17395i | 0.0779803 | + | 0.135066i | ||||
\(956\) | −3.05573 | − | 5.29268i | −0.0988293 | − | 0.171177i | ||||
\(957\) | −13.9443 | −0.450754 | ||||||||
\(958\) | 6.57295 | + | 11.3847i | 0.212362 | + | 0.367822i | ||||
\(959\) | −0.881966 | + | 1.52761i | −0.0284802 | + | 0.0493291i | ||||
\(960\) | 4.73607 | − | 8.20311i | 0.152856 | − | 0.264754i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −12.1353 | + | 12.6113i | −0.391256 | + | 0.406605i | ||||
\(963\) | −20.4721 | −0.659705 | ||||||||
\(964\) | −4.63525 | + | 8.02850i | −0.149292 | + | 0.258580i | ||||
\(965\) | −2.73607 | + | 4.73901i | −0.0880771 | + | 0.152554i | ||||
\(966\) | −3.51722 | − | 6.09201i | −0.113165 | − | 0.196007i | ||||
\(967\) | −1.16718 | −0.0375341 | −0.0187671 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187671 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(968\) | 7.76393 | + | 13.4475i | 0.249542 | + | 0.432220i | ||||
\(969\) | −1.44427 | − | 2.50155i | −0.0463967 | − | 0.0803614i | ||||
\(970\) | 8.85410 | 0.284288 | ||||||||
\(971\) | 8.11803 | + | 14.0608i | 0.260520 | + | 0.451234i | 0.966380 | − | 0.257117i | \(-0.0827726\pi\) |
−0.705860 | + | 0.708351i | \(0.749439\pi\) | |||||||
\(972\) | −5.52786 | + | 9.57454i | −0.177306 | + | 0.307104i | ||||
\(973\) | −0.388544 | + | 0.672978i | −0.0124561 | + | 0.0215747i | ||||
\(974\) | −42.2705 | −1.35443 | ||||||||
\(975\) | −7.82624 | − | 1.93649i | −0.250640 | − | 0.0620174i | ||||
\(976\) | 60.2705 | 1.92921 | ||||||||
\(977\) | −17.2082 | + | 29.8055i | −0.550539 | + | 0.953562i | 0.447696 | + | 0.894186i | \(0.352245\pi\) |
−0.998236 | + | 0.0593763i | \(0.981089\pi\) | |||||||
\(978\) | 2.33688 | − | 4.04760i | 0.0747252 | − | 0.129428i | ||||
\(979\) | 19.0623 | + | 33.0169i | 0.609234 | + | 1.05522i | ||||
\(980\) | −4.29180 | −0.137096 | ||||||||
\(981\) | 2.00000 | + | 3.46410i | 0.0638551 | + | 0.110600i | ||||
\(982\) | −3.42705 | − | 5.93583i | −0.109362 | − | 0.189420i | ||||
\(983\) | −14.8328 | −0.473093 | −0.236547 | − | 0.971620i | \(-0.576016\pi\) | ||||
−0.236547 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(984\) | 14.8607 | + | 25.7395i | 0.473741 | + | 0.820544i | ||||
\(985\) | −1.50000 | + | 2.59808i | −0.0477940 | + | 0.0827816i | ||||
\(986\) | −6.51722 | + | 11.2882i | −0.207551 | + | 0.359488i | ||||
\(987\) | 6.83282 | 0.217491 | ||||||||
\(988\) | −0.510643 | − | 0.126351i | −0.0162457 | − | 0.00401977i | ||||
\(989\) | −14.5279 | −0.461959 | ||||||||
\(990\) | −6.85410 | + | 11.8717i | −0.217838 | + | 0.377306i | ||||
\(991\) | 16.6459 | − | 28.8315i | 0.528774 | − | 0.915864i | −0.470663 | − | 0.882313i | \(-0.655985\pi\) |
0.999437 | − | 0.0335508i | \(-0.0106816\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −57.3607 | −1.82029 | ||||||||
\(994\) | −0.336881 | − | 0.583495i | −0.0106852 | − | 0.0185073i | ||||
\(995\) | 7.35410 | + | 12.7377i | 0.233141 | + | 0.403812i | ||||
\(996\) | 12.3607 | 0.391663 | ||||||||
\(997\) | −8.44427 | − | 14.6259i | −0.267433 | − | 0.463207i | 0.700765 | − | 0.713392i | \(-0.252842\pi\) |
−0.968198 | + | 0.250185i | \(0.919509\pi\) | |||||||
\(998\) | −11.2361 | + | 19.4614i | −0.355672 | + | 0.616041i | ||||
\(999\) | −3.35410 | + | 5.80948i | −0.106119 | + | 0.183804i |
(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 | 65.2.e.a.61.1 | yes | 4 | |
3.2 | odd | 2 | 585.2.j.e.451.2 | 4 | |||
4.3 | odd | 2 | 1040.2.q.n.321.1 | 4 | |||
5.2 | odd | 4 | 325.2.o.a.74.1 | 8 | |||
5.3 | odd | 4 | 325.2.o.a.74.4 | 8 | |||
5.4 | even | 2 | 325.2.e.b.126.2 | 4 | |||
13.2 | odd | 12 | 845.2.m.e.361.1 | 8 | |||
13.3 | even | 3 | inner | 65.2.e.a.16.1 | ✓ | 4 | |
13.4 | even | 6 | 845.2.a.b.1.1 | 2 | |||
13.5 | odd | 4 | 845.2.m.e.316.4 | 8 | |||
13.6 | odd | 12 | 845.2.c.c.506.1 | 4 | |||
13.7 | odd | 12 | 845.2.c.c.506.4 | 4 | |||
13.8 | odd | 4 | 845.2.m.e.316.1 | 8 | |||
13.9 | even | 3 | 845.2.a.e.1.2 | 2 | |||
13.10 | even | 6 | 845.2.e.g.146.2 | 4 | |||
13.11 | odd | 12 | 845.2.m.e.361.4 | 8 | |||
13.12 | even | 2 | 845.2.e.g.191.2 | 4 | |||
39.17 | odd | 6 | 7605.2.a.bf.1.2 | 2 | |||
39.29 | odd | 6 | 585.2.j.e.406.2 | 4 | |||
39.35 | odd | 6 | 7605.2.a.ba.1.1 | 2 | |||
52.3 | odd | 6 | 1040.2.q.n.81.1 | 4 | |||
65.3 | odd | 12 | 325.2.o.a.224.1 | 8 | |||
65.4 | even | 6 | 4225.2.a.y.1.2 | 2 | |||
65.9 | even | 6 | 4225.2.a.u.1.1 | 2 | |||
65.29 | even | 6 | 325.2.e.b.276.2 | 4 | |||
65.42 | odd | 12 | 325.2.o.a.224.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.a.16.1 | ✓ | 4 | 13.3 | even | 3 | inner | |
65.2.e.a.61.1 | yes | 4 | 1.1 | even | 1 | trivial | |
325.2.e.b.126.2 | 4 | 5.4 | even | 2 | |||
325.2.e.b.276.2 | 4 | 65.29 | even | 6 | |||
325.2.o.a.74.1 | 8 | 5.2 | odd | 4 | |||
325.2.o.a.74.4 | 8 | 5.3 | odd | 4 | |||
325.2.o.a.224.1 | 8 | 65.3 | odd | 12 | |||
325.2.o.a.224.4 | 8 | 65.42 | odd | 12 | |||
585.2.j.e.406.2 | 4 | 39.29 | odd | 6 | |||
585.2.j.e.451.2 | 4 | 3.2 | odd | 2 | |||
845.2.a.b.1.1 | 2 | 13.4 | even | 6 | |||
845.2.a.e.1.2 | 2 | 13.9 | even | 3 | |||
845.2.c.c.506.1 | 4 | 13.6 | odd | 12 | |||
845.2.c.c.506.4 | 4 | 13.7 | odd | 12 | |||
845.2.e.g.146.2 | 4 | 13.10 | even | 6 | |||
845.2.e.g.191.2 | 4 | 13.12 | even | 2 | |||
845.2.m.e.316.1 | 8 | 13.8 | odd | 4 | |||
845.2.m.e.316.4 | 8 | 13.5 | odd | 4 | |||
845.2.m.e.361.1 | 8 | 13.2 | odd | 12 | |||
845.2.m.e.361.4 | 8 | 13.11 | odd | 12 | |||
1040.2.q.n.81.1 | 4 | 52.3 | odd | 6 | |||
1040.2.q.n.321.1 | 4 | 4.3 | odd | 2 | |||
4225.2.a.u.1.1 | 2 | 65.9 | even | 6 | |||
4225.2.a.y.1.2 | 2 | 65.4 | even | 6 | |||
7605.2.a.ba.1.1 | 2 | 39.35 | odd | 6 | |||
7605.2.a.bf.1.2 | 2 | 39.17 | odd | 6 |