Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(43,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.g (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 327.4 | ||
Root | \(-1.66045 - 0.156295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.327 |
Dual form | 370.2.g.d.43.4 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.05122 | + | 1.05122i | 0.606924 | + | 0.606924i | 0.942141 | − | 0.335217i | \(-0.108810\pi\) |
−0.335217 | + | 0.942141i | \(0.608810\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.609231 | + | 2.15147i | 0.272456 | + | 0.962168i | ||||
\(6\) | −1.05122 | + | 1.05122i | −0.429160 | + | 0.429160i | ||||
\(7\) | −1.21846 | − | 1.21846i | −0.460535 | − | 0.460535i | 0.438296 | − | 0.898831i | \(-0.355582\pi\) |
−0.898831 | + | 0.438296i | \(0.855582\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 0.789858i | − | 0.263286i | ||||||
\(10\) | −2.15147 | + | 0.609231i | −0.680356 | + | 0.192656i | ||||
\(11\) | 4.85196i | 1.46292i | 0.681884 | + | 0.731461i | \(0.261161\pi\) | ||||
−0.681884 | + | 0.731461i | \(0.738839\pi\) | |||||||
\(12\) | −1.05122 | − | 1.05122i | −0.303462 | − | 0.303462i | ||||
\(13\) | 5.57745i | 1.54691i | 0.633853 | + | 0.773454i | \(0.281472\pi\) | ||||
−0.633853 | + | 0.773454i | \(0.718528\pi\) | |||||||
\(14\) | 1.21846 | − | 1.21846i | 0.325648 | − | 0.325648i | ||||
\(15\) | −1.62124 | + | 2.90212i | −0.418603 | + | 0.749324i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00832 | 0.244553 | 0.122277 | − | 0.992496i | \(-0.460980\pi\) | ||||
0.122277 | + | 0.992496i | \(0.460980\pi\) | |||||||
\(18\) | 0.789858 | 0.186171 | ||||||||
\(19\) | −1.94395 | − | 1.94395i | −0.445974 | − | 0.445974i | 0.448040 | − | 0.894014i | \(-0.352122\pi\) |
−0.894014 | + | 0.448040i | \(0.852122\pi\) | |||||||
\(20\) | −0.609231 | − | 2.15147i | −0.136228 | − | 0.481084i | ||||
\(21\) | − | 2.56175i | − | 0.559020i | ||||||
\(22\) | −4.85196 | −1.03444 | ||||||||
\(23\) | − | 3.14053i | − | 0.654846i | −0.944878 | − | 0.327423i | \(-0.893820\pi\) | ||
0.944878 | − | 0.327423i | \(-0.106180\pi\) | |||||||
\(24\) | 1.05122 | − | 1.05122i | 0.214580 | − | 0.214580i | ||||
\(25\) | −4.25768 | + | 2.62149i | −0.851535 | + | 0.524298i | ||||
\(26\) | −5.57745 | −1.09383 | ||||||||
\(27\) | 3.98399 | − | 3.98399i | 0.766719 | − | 0.766719i | ||||
\(28\) | 1.21846 | + | 1.21846i | 0.230268 | + | 0.230268i | ||||
\(29\) | 4.77672 | − | 4.77672i | 0.887014 | − | 0.887014i | −0.107221 | − | 0.994235i | \(-0.534195\pi\) |
0.994235 | + | 0.107221i | \(0.0341953\pi\) | |||||||
\(30\) | −2.90212 | − | 1.62124i | −0.529852 | − | 0.295997i | ||||
\(31\) | −1.71430 | − | 1.71430i | −0.307898 | − | 0.307898i | 0.536196 | − | 0.844094i | \(-0.319861\pi\) |
−0.844094 | + | 0.536196i | \(0.819861\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −5.10050 | + | 5.10050i | −0.887882 | + | 0.887882i | ||||
\(34\) | 1.00832i | 0.172925i | ||||||||
\(35\) | 1.87916 | − | 3.36381i | 0.317637 | − | 0.568588i | ||||
\(36\) | 0.789858i | 0.131643i | ||||||||
\(37\) | 3.78986 | + | 4.75783i | 0.623049 | + | 0.782183i | ||||
\(38\) | 1.94395 | − | 1.94395i | 0.315351 | − | 0.315351i | ||||
\(39\) | −5.86315 | + | 5.86315i | −0.938856 | + | 0.938856i | ||||
\(40\) | 2.15147 | − | 0.609231i | 0.340178 | − | 0.0963279i | ||||
\(41\) | 0.412903i | 0.0644846i | 0.999480 | + | 0.0322423i | \(0.0102648\pi\) | ||||
−0.999480 | + | 0.0322423i | \(0.989735\pi\) | |||||||
\(42\) | 2.56175 | 0.395287 | ||||||||
\(43\) | 1.47727i | 0.225281i | 0.993636 | + | 0.112641i | \(0.0359309\pi\) | ||||
−0.993636 | + | 0.112641i | \(0.964069\pi\) | |||||||
\(44\) | − | 4.85196i | − | 0.731461i | ||||||
\(45\) | 1.69936 | − | 0.481206i | 0.253325 | − | 0.0717339i | ||||
\(46\) | 3.14053 | 0.463046 | ||||||||
\(47\) | 8.35899 | + | 8.35899i | 1.21928 | + | 1.21928i | 0.967883 | + | 0.251401i | \(0.0808914\pi\) |
0.251401 | + | 0.967883i | \(0.419109\pi\) | |||||||
\(48\) | 1.05122 | + | 1.05122i | 0.151731 | + | 0.151731i | ||||
\(49\) | − | 4.03070i | − | 0.575814i | ||||||
\(50\) | −2.62149 | − | 4.25768i | −0.370734 | − | 0.602126i | ||||
\(51\) | 1.05997 | + | 1.05997i | 0.148425 | + | 0.148425i | ||||
\(52\) | − | 5.57745i | − | 0.773454i | ||||||
\(53\) | 3.85196 | − | 3.85196i | 0.529108 | − | 0.529108i | −0.391199 | − | 0.920306i | \(-0.627939\pi\) |
0.920306 | + | 0.391199i | \(0.127939\pi\) | |||||||
\(54\) | 3.98399 | + | 3.98399i | 0.542152 | + | 0.542152i | ||||
\(55\) | −10.4389 | + | 2.95597i | −1.40758 | + | 0.398582i | ||||
\(56\) | −1.21846 | + | 1.21846i | −0.162824 | + | 0.162824i | ||||
\(57\) | − | 4.08706i | − | 0.541345i | ||||||
\(58\) | 4.77672 | + | 4.77672i | 0.627214 | + | 0.627214i | ||||
\(59\) | −7.33529 | − | 7.33529i | −0.954973 | − | 0.954973i | 0.0440560 | − | 0.999029i | \(-0.485972\pi\) |
−0.999029 | + | 0.0440560i | \(0.985972\pi\) | |||||||
\(60\) | 1.62124 | − | 2.90212i | 0.209301 | − | 0.374662i | ||||
\(61\) | −0.457758 | − | 0.457758i | −0.0586099 | − | 0.0586099i | 0.677194 | − | 0.735804i | \(-0.263196\pi\) |
−0.735804 | + | 0.677194i | \(0.763196\pi\) | |||||||
\(62\) | 1.71430 | − | 1.71430i | 0.217717 | − | 0.217717i | ||||
\(63\) | −0.962411 | + | 0.962411i | −0.121252 | + | 0.121252i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −11.9997 | + | 3.39796i | −1.48839 | + | 0.421465i | ||||
\(66\) | −5.10050 | − | 5.10050i | −0.627828 | − | 0.627828i | ||||
\(67\) | 5.29402 | − | 5.29402i | 0.646767 | − | 0.646767i | −0.305443 | − | 0.952210i | \(-0.598805\pi\) |
0.952210 | + | 0.305443i | \(0.0988046\pi\) | |||||||
\(68\) | −1.00832 | −0.122277 | ||||||||
\(69\) | 3.30140 | − | 3.30140i | 0.397442 | − | 0.397442i | ||||
\(70\) | 3.36381 | + | 1.87916i | 0.402053 | + | 0.224603i | ||||
\(71\) | 7.15491 | 0.849131 | 0.424566 | − | 0.905397i | \(-0.360427\pi\) | ||||
0.424566 | + | 0.905397i | \(0.360427\pi\) | |||||||
\(72\) | −0.789858 | −0.0930856 | ||||||||
\(73\) | 9.08993 | + | 9.08993i | 1.06390 | + | 1.06390i | 0.997814 | + | 0.0660820i | \(0.0210499\pi\) |
0.0660820 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(74\) | −4.75783 | + | 3.78986i | −0.553087 | + | 0.440562i | ||||
\(75\) | −7.23154 | − | 1.72000i | −0.835026 | − | 0.198608i | ||||
\(76\) | 1.94395 | + | 1.94395i | 0.222987 | + | 0.222987i | ||||
\(77\) | 5.91193 | − | 5.91193i | 0.673727 | − | 0.673727i | ||||
\(78\) | −5.86315 | − | 5.86315i | −0.663871 | − | 0.663871i | ||||
\(79\) | −1.46413 | − | 1.46413i | −0.164727 | − | 0.164727i | 0.619930 | − | 0.784657i | \(-0.287161\pi\) |
−0.784657 | + | 0.619930i | \(0.787161\pi\) | |||||||
\(80\) | 0.609231 | + | 2.15147i | 0.0681141 | + | 0.240542i | ||||
\(81\) | 6.00655 | 0.667395 | ||||||||
\(82\) | −0.412903 | −0.0455975 | ||||||||
\(83\) | 9.88040 | − | 9.88040i | 1.08451 | − | 1.08451i | 0.0884327 | − | 0.996082i | \(-0.471814\pi\) |
0.996082 | − | 0.0884327i | \(-0.0281858\pi\) | |||||||
\(84\) | 2.56175i | 0.279510i | ||||||||
\(85\) | 0.614300 | + | 2.16937i | 0.0666301 | + | 0.235302i | ||||
\(86\) | −1.47727 | −0.159298 | ||||||||
\(87\) | 10.0428 | 1.07670 | ||||||||
\(88\) | 4.85196 | 0.517221 | ||||||||
\(89\) | −7.09280 | + | 7.09280i | −0.751836 | + | 0.751836i | −0.974822 | − | 0.222986i | \(-0.928420\pi\) |
0.222986 | + | 0.974822i | \(0.428420\pi\) | |||||||
\(90\) | 0.481206 | + | 1.69936i | 0.0507235 | + | 0.179128i | ||||
\(91\) | 6.79592 | − | 6.79592i | 0.712406 | − | 0.712406i | ||||
\(92\) | 3.14053i | 0.327423i | ||||||||
\(93\) | − | 3.60423i | − | 0.373741i | ||||||
\(94\) | −8.35899 | + | 8.35899i | −0.862164 | + | 0.862164i | ||||
\(95\) | 2.99805 | − | 5.36668i | 0.307593 | − | 0.550610i | ||||
\(96\) | −1.05122 | + | 1.05122i | −0.107290 | + | 0.107290i | ||||
\(97\) | 2.10245 | 0.213471 | 0.106736 | − | 0.994287i | \(-0.465960\pi\) | ||||
0.106736 | + | 0.994287i | \(0.465960\pi\) | |||||||
\(98\) | 4.03070 | 0.407162 | ||||||||
\(99\) | 3.83236 | 0.385166 | ||||||||
\(100\) | 4.25768 | − | 2.62149i | 0.425768 | − | 0.262149i | ||||
\(101\) | 6.66420i | 0.663113i | 0.943435 | + | 0.331556i | \(0.107574\pi\) | ||||
−0.943435 | + | 0.331556i | \(0.892426\pi\) | |||||||
\(102\) | −1.05997 | + | 1.05997i | −0.104953 | + | 0.104953i | ||||
\(103\) | −3.38743 | −0.333774 | −0.166887 | − | 0.985976i | \(-0.553371\pi\) | ||||
−0.166887 | + | 0.985976i | \(0.553371\pi\) | |||||||
\(104\) | 5.57745 | 0.546914 | ||||||||
\(105\) | 5.51154 | − | 1.56070i | 0.537871 | − | 0.152309i | ||||
\(106\) | 3.85196 | + | 3.85196i | 0.374136 | + | 0.374136i | ||||
\(107\) | −6.68246 | − | 6.68246i | −0.646018 | − | 0.646018i | 0.306010 | − | 0.952028i | \(-0.401006\pi\) |
−0.952028 | + | 0.306010i | \(0.901006\pi\) | |||||||
\(108\) | −3.98399 | + | 3.98399i | −0.383359 | + | 0.383359i | ||||
\(109\) | 11.6763 | + | 11.6763i | 1.11839 | + | 1.11839i | 0.991978 | + | 0.126410i | \(0.0403456\pi\) |
0.126410 | + | 0.991978i | \(0.459654\pi\) | |||||||
\(110\) | −2.95597 | − | 10.4389i | −0.281840 | − | 0.995307i | ||||
\(111\) | −1.01756 | + | 8.98554i | −0.0965825 | + | 0.852869i | ||||
\(112\) | −1.21846 | − | 1.21846i | −0.115134 | − | 0.115134i | ||||
\(113\) | 4.19525 | 0.394656 | 0.197328 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197328 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(114\) | 4.08706 | 0.382788 | ||||||||
\(115\) | 6.75677 | − | 1.91331i | 0.630072 | − | 0.178417i | ||||
\(116\) | −4.77672 | + | 4.77672i | −0.443507 | + | 0.443507i | ||||
\(117\) | 4.40539 | 0.407279 | ||||||||
\(118\) | 7.33529 | − | 7.33529i | 0.675268 | − | 0.675268i | ||||
\(119\) | −1.22860 | − | 1.22860i | −0.112625 | − | 0.112625i | ||||
\(120\) | 2.90212 | + | 1.62124i | 0.264926 | + | 0.147998i | ||||
\(121\) | −12.5415 | −1.14014 | ||||||||
\(122\) | 0.457758 | − | 0.457758i | 0.0414434 | − | 0.0414434i | ||||
\(123\) | −0.434053 | + | 0.434053i | −0.0391373 | + | 0.0391373i | ||||
\(124\) | 1.71430 | + | 1.71430i | 0.153949 | + | 0.153949i | ||||
\(125\) | −8.23397 | − | 7.56318i | −0.736469 | − | 0.676472i | ||||
\(126\) | −0.962411 | − | 0.962411i | −0.0857384 | − | 0.0857384i | ||||
\(127\) | −8.69347 | − | 8.69347i | −0.771421 | − | 0.771421i | 0.206934 | − | 0.978355i | \(-0.433651\pi\) |
−0.978355 | + | 0.206934i | \(0.933651\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −1.55294 | + | 1.55294i | −0.136729 | + | 0.136729i | ||||
\(130\) | −3.39796 | − | 11.9997i | −0.298021 | − | 1.05245i | ||||
\(131\) | −7.96621 | − | 7.96621i | −0.696011 | − | 0.696011i | 0.267537 | − | 0.963548i | \(-0.413790\pi\) |
−0.963548 | + | 0.267537i | \(0.913790\pi\) | |||||||
\(132\) | 5.10050 | − | 5.10050i | 0.443941 | − | 0.443941i | ||||
\(133\) | 4.73727i | 0.410773i | ||||||||
\(134\) | 5.29402 | + | 5.29402i | 0.457333 | + | 0.457333i | ||||
\(135\) | 10.9986 | + | 6.14427i | 0.946610 | + | 0.528815i | ||||
\(136\) | − | 1.00832i | − | 0.0864627i | ||||||
\(137\) | −13.2365 | − | 13.2365i | −1.13087 | − | 1.13087i | −0.990032 | − | 0.140840i | \(-0.955020\pi\) |
−0.140840 | − | 0.990032i | \(-0.544980\pi\) | |||||||
\(138\) | 3.30140 | + | 3.30140i | 0.281034 | + | 0.281034i | ||||
\(139\) | −15.1028 | −1.28100 | −0.640500 | − | 0.767958i | \(-0.721273\pi\) | ||||
−0.640500 | + | 0.767958i | \(0.721273\pi\) | |||||||
\(140\) | −1.87916 | + | 3.36381i | −0.158818 | + | 0.284294i | ||||
\(141\) | 17.5743i | 1.48003i | ||||||||
\(142\) | 7.15491i | 0.600427i | ||||||||
\(143\) | −27.0616 | −2.26300 | ||||||||
\(144\) | − | 0.789858i | − | 0.0658215i | ||||||
\(145\) | 13.1871 | + | 7.36685i | 1.09513 | + | 0.611784i | ||||
\(146\) | −9.08993 | + | 9.08993i | −0.752288 | + | 0.752288i | ||||
\(147\) | 4.23717 | − | 4.23717i | 0.349476 | − | 0.349476i | ||||
\(148\) | −3.78986 | − | 4.75783i | −0.311524 | − | 0.391092i | ||||
\(149\) | − | 21.2958i | − | 1.74462i | −0.488957 | − | 0.872308i | \(-0.662622\pi\) | ||
0.488957 | − | 0.872308i | \(-0.337378\pi\) | |||||||
\(150\) | 1.72000 | − | 7.23154i | 0.140437 | − | 0.590453i | ||||
\(151\) | − | 5.71666i | − | 0.465215i | −0.972571 | − | 0.232608i | \(-0.925274\pi\) | ||
0.972571 | − | 0.232608i | \(-0.0747258\pi\) | |||||||
\(152\) | −1.94395 | + | 1.94395i | −0.157676 | + | 0.157676i | ||||
\(153\) | − | 0.796429i | − | 0.0643875i | ||||||
\(154\) | 5.91193 | + | 5.91193i | 0.476397 | + | 0.476397i | ||||
\(155\) | 2.64387 | − | 4.73268i | 0.212361 | − | 0.380138i | ||||
\(156\) | 5.86315 | − | 5.86315i | 0.469428 | − | 0.469428i | ||||
\(157\) | 4.70753 | + | 4.70753i | 0.375702 | + | 0.375702i | 0.869549 | − | 0.493847i | \(-0.164410\pi\) |
−0.493847 | + | 0.869549i | \(0.664410\pi\) | |||||||
\(158\) | 1.46413 | − | 1.46413i | 0.116480 | − | 0.116480i | ||||
\(159\) | 8.09855 | 0.642256 | ||||||||
\(160\) | −2.15147 | + | 0.609231i | −0.170089 | + | 0.0481639i | ||||
\(161\) | −3.82662 | + | 3.82662i | −0.301580 | + | 0.301580i | ||||
\(162\) | 6.00655i | 0.471919i | ||||||||
\(163\) | 7.46188 | 0.584460 | 0.292230 | − | 0.956348i | \(-0.405603\pi\) | ||||
0.292230 | + | 0.956348i | \(0.405603\pi\) | |||||||
\(164\) | − | 0.412903i | − | 0.0322423i | ||||||
\(165\) | −14.0810 | − | 7.86620i | −1.09620 | − | 0.612383i | ||||
\(166\) | 9.88040 | + | 9.88040i | 0.766868 | + | 0.766868i | ||||
\(167\) | −19.1080 | −1.47862 | −0.739310 | − | 0.673365i | \(-0.764848\pi\) | ||||
−0.739310 | + | 0.673365i | \(0.764848\pi\) | |||||||
\(168\) | −2.56175 | −0.197643 | ||||||||
\(169\) | −18.1080 | −1.39292 | ||||||||
\(170\) | −2.16937 | + | 0.614300i | −0.166383 | + | 0.0471146i | ||||
\(171\) | −1.53545 | + | 1.53545i | −0.117419 | + | 0.117419i | ||||
\(172\) | − | 1.47727i | − | 0.112641i | ||||||
\(173\) | 15.1632 | + | 15.1632i | 1.15284 | + | 1.15284i | 0.985981 | + | 0.166858i | \(0.0533621\pi\) |
0.166858 | + | 0.985981i | \(0.446638\pi\) | |||||||
\(174\) | 10.0428i | 0.761342i | ||||||||
\(175\) | 8.38200 | + | 1.99363i | 0.633620 | + | 0.150704i | ||||
\(176\) | 4.85196i | 0.365730i | ||||||||
\(177\) | − | 15.4221i | − | 1.15919i | ||||||
\(178\) | −7.09280 | − | 7.09280i | −0.531628 | − | 0.531628i | ||||
\(179\) | −9.36945 | + | 9.36945i | −0.700305 | + | 0.700305i | −0.964476 | − | 0.264171i | \(-0.914902\pi\) |
0.264171 | + | 0.964476i | \(0.414902\pi\) | |||||||
\(180\) | −1.69936 | + | 0.481206i | −0.126663 | + | 0.0358670i | ||||
\(181\) | −11.6623 | −0.866849 | −0.433424 | − | 0.901190i | \(-0.642695\pi\) | ||||
−0.433424 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(182\) | 6.79592 | + | 6.79592i | 0.503747 | + | 0.503747i | ||||
\(183\) | − | 0.962411i | − | 0.0711435i | ||||||
\(184\) | −3.14053 | −0.231523 | ||||||||
\(185\) | −7.92745 | + | 11.0524i | −0.582838 | + | 0.812588i | ||||
\(186\) | 3.60423 | 0.264275 | ||||||||
\(187\) | 4.89233i | 0.357762i | ||||||||
\(188\) | −8.35899 | − | 8.35899i | −0.609642 | − | 0.609642i | ||||
\(189\) | −9.70868 | −0.706202 | ||||||||
\(190\) | 5.36668 | + | 2.99805i | 0.389340 | + | 0.217501i | ||||
\(191\) | 17.6354 | − | 17.6354i | 1.27605 | − | 1.27605i | 0.333191 | − | 0.942859i | \(-0.391875\pi\) |
0.942859 | − | 0.333191i | \(-0.108125\pi\) | |||||||
\(192\) | −1.05122 | − | 1.05122i | −0.0758655 | − | 0.0758655i | ||||
\(193\) | 13.5647i | 0.976408i | 0.872729 | + | 0.488204i | \(0.162348\pi\) | ||||
−0.872729 | + | 0.488204i | \(0.837652\pi\) | |||||||
\(194\) | 2.10245i | 0.150947i | ||||||||
\(195\) | −16.1864 | − | 9.04240i | −1.15913 | − | 0.647540i | ||||
\(196\) | 4.03070i | 0.287907i | ||||||||
\(197\) | 16.8769 | + | 16.8769i | 1.20243 | + | 1.20243i | 0.973425 | + | 0.229006i | \(0.0735474\pi\) |
0.229006 | + | 0.973425i | \(0.426453\pi\) | |||||||
\(198\) | 3.83236i | 0.272354i | ||||||||
\(199\) | −9.13039 | + | 9.13039i | −0.647236 | + | 0.647236i | −0.952324 | − | 0.305088i | \(-0.901314\pi\) |
0.305088 | + | 0.952324i | \(0.401314\pi\) | |||||||
\(200\) | 2.62149 | + | 4.25768i | 0.185367 | + | 0.301063i | ||||
\(201\) | 11.1304 | 0.785077 | ||||||||
\(202\) | −6.66420 | −0.468891 | ||||||||
\(203\) | −11.6405 | −0.817003 | ||||||||
\(204\) | −1.05997 | − | 1.05997i | −0.0742127 | − | 0.0742127i | ||||
\(205\) | −0.888349 | + | 0.251553i | −0.0620450 | + | 0.0175692i | ||||
\(206\) | − | 3.38743i | − | 0.236014i | ||||||
\(207\) | −2.48057 | −0.172412 | ||||||||
\(208\) | 5.57745i | 0.386727i | ||||||||
\(209\) | 9.43199 | − | 9.43199i | 0.652425 | − | 0.652425i | ||||
\(210\) | 1.56070 | + | 5.51154i | 0.107698 | + | 0.380333i | ||||
\(211\) | −10.0888 | −0.694540 | −0.347270 | − | 0.937765i | \(-0.612891\pi\) | ||||
−0.347270 | + | 0.937765i | \(0.612891\pi\) | |||||||
\(212\) | −3.85196 | + | 3.85196i | −0.264554 | + | 0.264554i | ||||
\(213\) | 7.52141 | + | 7.52141i | 0.515358 | + | 0.515358i | ||||
\(214\) | 6.68246 | − | 6.68246i | 0.456804 | − | 0.456804i | ||||
\(215\) | −3.17830 | + | 0.899997i | −0.216758 | + | 0.0613793i | ||||
\(216\) | −3.98399 | − | 3.98399i | −0.271076 | − | 0.271076i | ||||
\(217\) | 4.17762i | 0.283596i | ||||||||
\(218\) | −11.6763 | + | 11.6763i | −0.790820 | + | 0.790820i | ||||
\(219\) | 19.1111i | 1.29141i | ||||||||
\(220\) | 10.4389 | − | 2.95597i | 0.703788 | − | 0.199291i | ||||
\(221\) | 5.62386i | 0.378302i | ||||||||
\(222\) | −8.98554 | − | 1.01756i | −0.603070 | − | 0.0682941i | ||||
\(223\) | 2.45704 | − | 2.45704i | 0.164536 | − | 0.164536i | −0.620037 | − | 0.784573i | \(-0.712882\pi\) |
0.784573 | + | 0.620037i | \(0.212882\pi\) | |||||||
\(224\) | 1.21846 | − | 1.21846i | 0.0814119 | − | 0.0814119i | ||||
\(225\) | 2.07060 | + | 3.36296i | 0.138040 | + | 0.224197i | ||||
\(226\) | 4.19525i | 0.279064i | ||||||||
\(227\) | −19.5967 | −1.30068 | −0.650340 | − | 0.759643i | \(-0.725374\pi\) | ||||
−0.650340 | + | 0.759643i | \(0.725374\pi\) | |||||||
\(228\) | 4.08706i | 0.270672i | ||||||||
\(229\) | − | 8.54964i | − | 0.564976i | −0.959271 | − | 0.282488i | \(-0.908840\pi\) | ||
0.959271 | − | 0.282488i | \(-0.0911597\pi\) | |||||||
\(230\) | 1.91331 | + | 6.75677i | 0.126160 | + | 0.445528i | ||||
\(231\) | 12.4295 | 0.817803 | ||||||||
\(232\) | −4.77672 | − | 4.77672i | −0.313607 | − | 0.313607i | ||||
\(233\) | −18.6855 | − | 18.6855i | −1.22413 | − | 1.22413i | −0.966150 | − | 0.257980i | \(-0.916943\pi\) |
−0.257980 | − | 0.966150i | \(-0.583057\pi\) | |||||||
\(234\) | 4.40539i | 0.287990i | ||||||||
\(235\) | −12.8916 | + | 23.0767i | −0.840955 | + | 1.50536i | ||||
\(236\) | 7.33529 | + | 7.33529i | 0.477487 | + | 0.477487i | ||||
\(237\) | − | 3.07825i | − | 0.199954i | ||||||
\(238\) | 1.22860 | − | 1.22860i | 0.0796383 | − | 0.0796383i | ||||
\(239\) | −14.5251 | − | 14.5251i | −0.939550 | − | 0.939550i | 0.0587243 | − | 0.998274i | \(-0.481297\pi\) |
−0.998274 | + | 0.0587243i | \(0.981297\pi\) | |||||||
\(240\) | −1.62124 | + | 2.90212i | −0.104651 | + | 0.187331i | ||||
\(241\) | −8.39707 | + | 8.39707i | −0.540903 | + | 0.540903i | −0.923794 | − | 0.382891i | \(-0.874929\pi\) |
0.382891 | + | 0.923794i | \(0.374929\pi\) | |||||||
\(242\) | − | 12.5415i | − | 0.806200i | ||||||
\(243\) | −5.63773 | − | 5.63773i | −0.361661 | − | 0.361661i | ||||
\(244\) | 0.457758 | + | 0.457758i | 0.0293049 | + | 0.0293049i | ||||
\(245\) | 8.67194 | − | 2.45563i | 0.554030 | − | 0.156884i | ||||
\(246\) | −0.434053 | − | 0.434053i | −0.0276742 | − | 0.0276742i | ||||
\(247\) | 10.8423 | − | 10.8423i | 0.689880 | − | 0.689880i | ||||
\(248\) | −1.71430 | + | 1.71430i | −0.108858 | + | 0.108858i | ||||
\(249\) | 20.7730 | 1.31644 | ||||||||
\(250\) | 7.56318 | − | 8.23397i | 0.478338 | − | 0.520762i | ||||
\(251\) | 6.65372 | + | 6.65372i | 0.419979 | + | 0.419979i | 0.885197 | − | 0.465217i | \(-0.154024\pi\) |
−0.465217 | + | 0.885197i | \(0.654024\pi\) | |||||||
\(252\) | 0.962411 | − | 0.962411i | 0.0606262 | − | 0.0606262i | ||||
\(253\) | 15.2377 | 0.957988 | ||||||||
\(254\) | 8.69347 | − | 8.69347i | 0.545477 | − | 0.545477i | ||||
\(255\) | −1.63473 | + | 2.92626i | −0.102371 | + | 0.183250i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.1881 | 0.885028 | 0.442514 | − | 0.896762i | \(-0.354087\pi\) | ||||
0.442514 | + | 0.896762i | \(0.354087\pi\) | |||||||
\(258\) | −1.55294 | − | 1.55294i | −0.0966817 | − | 0.0966817i | ||||
\(259\) | 1.17944 | − | 10.4150i | 0.0732870 | − | 0.647159i | ||||
\(260\) | 11.9997 | − | 3.39796i | 0.744193 | − | 0.210732i | ||||
\(261\) | −3.77293 | − | 3.77293i | −0.233538 | − | 0.233538i | ||||
\(262\) | 7.96621 | − | 7.96621i | 0.492154 | − | 0.492154i | ||||
\(263\) | 8.87946 | + | 8.87946i | 0.547531 | + | 0.547531i | 0.925726 | − | 0.378195i | \(-0.123455\pi\) |
−0.378195 | + | 0.925726i | \(0.623455\pi\) | |||||||
\(264\) | 5.10050 | + | 5.10050i | 0.313914 | + | 0.313914i | ||||
\(265\) | 10.6341 | + | 5.94066i | 0.653249 | + | 0.364932i | ||||
\(266\) | −4.73727 | −0.290461 | ||||||||
\(267\) | −14.9122 | −0.912615 | ||||||||
\(268\) | −5.29402 | + | 5.29402i | −0.323384 | + | 0.323384i | ||||
\(269\) | − | 13.1011i | − | 0.798790i | −0.916779 | − | 0.399395i | \(-0.869220\pi\) | ||
0.916779 | − | 0.399395i | \(-0.130780\pi\) | |||||||
\(270\) | −6.14427 | + | 10.9986i | −0.373929 | + | 0.669354i | ||||
\(271\) | −6.98656 | −0.424403 | −0.212202 | − | 0.977226i | \(-0.568063\pi\) | ||||
−0.212202 | + | 0.977226i | \(0.568063\pi\) | |||||||
\(272\) | 1.00832 | 0.0611384 | ||||||||
\(273\) | 14.2881 | 0.864752 | ||||||||
\(274\) | 13.2365 | − | 13.2365i | 0.799648 | − | 0.799648i | ||||
\(275\) | −12.7194 | − | 20.6581i | −0.767006 | − | 1.24573i | ||||
\(276\) | −3.30140 | + | 3.30140i | −0.198721 | + | 0.198721i | ||||
\(277\) | 14.9569i | 0.898672i | 0.893363 | + | 0.449336i | \(0.148339\pi\) | ||||
−0.893363 | + | 0.449336i | \(0.851661\pi\) | |||||||
\(278\) | − | 15.1028i | − | 0.905804i | ||||||
\(279\) | −1.35405 | + | 1.35405i | −0.0810651 | + | 0.0810651i | ||||
\(280\) | −3.36381 | − | 1.87916i | −0.201026 | − | 0.112302i | ||||
\(281\) | 13.8446 | − | 13.8446i | 0.825898 | − | 0.825898i | −0.161048 | − | 0.986947i | \(-0.551487\pi\) |
0.986947 | + | 0.161048i | \(0.0514875\pi\) | |||||||
\(282\) | −17.5743 | −1.04654 | ||||||||
\(283\) | −9.08448 | −0.540017 | −0.270008 | − | 0.962858i | \(-0.587026\pi\) | ||||
−0.270008 | + | 0.962858i | \(0.587026\pi\) | |||||||
\(284\) | −7.15491 | −0.424566 | ||||||||
\(285\) | 8.79321 | − | 2.48997i | 0.520865 | − | 0.147493i | ||||
\(286\) | − | 27.0616i | − | 1.60019i | ||||||
\(287\) | 0.503106 | − | 0.503106i | 0.0296974 | − | 0.0296974i | ||||
\(288\) | 0.789858 | 0.0465428 | ||||||||
\(289\) | −15.9833 | −0.940194 | ||||||||
\(290\) | −7.36685 | + | 13.1871i | −0.432597 | + | 0.774373i | ||||
\(291\) | 2.21014 | + | 2.21014i | 0.129561 | + | 0.129561i | ||||
\(292\) | −9.08993 | − | 9.08993i | −0.531948 | − | 0.531948i | ||||
\(293\) | −7.79244 | + | 7.79244i | −0.455239 | + | 0.455239i | −0.897089 | − | 0.441850i | \(-0.854322\pi\) |
0.441850 | + | 0.897089i | \(0.354322\pi\) | |||||||
\(294\) | 4.23717 | + | 4.23717i | 0.247117 | + | 0.247117i | ||||
\(295\) | 11.3128 | − | 20.2506i | 0.658656 | − | 1.17903i | ||||
\(296\) | 4.75783 | − | 3.78986i | 0.276543 | − | 0.220281i | ||||
\(297\) | 19.3302 | + | 19.3302i | 1.12165 | + | 1.12165i | ||||
\(298\) | 21.2958 | 1.23363 | ||||||||
\(299\) | 17.5162 | 1.01299 | ||||||||
\(300\) | 7.23154 | + | 1.72000i | 0.417513 | + | 0.0993041i | ||||
\(301\) | 1.79999 | − | 1.79999i | 0.103750 | − | 0.103750i | ||||
\(302\) | 5.71666 | 0.328957 | ||||||||
\(303\) | −7.00556 | + | 7.00556i | −0.402459 | + | 0.402459i | ||||
\(304\) | −1.94395 | − | 1.94395i | −0.111493 | − | 0.111493i | ||||
\(305\) | 0.705973 | − | 1.26373i | 0.0404239 | − | 0.0723612i | ||||
\(306\) | 0.796429 | 0.0455288 | ||||||||
\(307\) | 2.77527 | − | 2.77527i | 0.158393 | − | 0.158393i | −0.623461 | − | 0.781854i | \(-0.714274\pi\) |
0.781854 | + | 0.623461i | \(0.214274\pi\) | |||||||
\(308\) | −5.91193 | + | 5.91193i | −0.336864 | + | 0.336864i | ||||
\(309\) | −3.56095 | − | 3.56095i | −0.202575 | − | 0.202575i | ||||
\(310\) | 4.73268 | + | 2.64387i | 0.268798 | + | 0.150162i | ||||
\(311\) | −2.34988 | − | 2.34988i | −0.133249 | − | 0.133249i | 0.637336 | − | 0.770586i | \(-0.280036\pi\) |
−0.770586 | + | 0.637336i | \(0.780036\pi\) | |||||||
\(312\) | 5.86315 | + | 5.86315i | 0.331936 | + | 0.331936i | ||||
\(313\) | − | 10.8979i | − | 0.615983i | −0.951389 | − | 0.307991i | \(-0.900343\pi\) | ||
0.951389 | − | 0.307991i | \(-0.0996568\pi\) | |||||||
\(314\) | −4.70753 | + | 4.70753i | −0.265661 | + | 0.265661i | ||||
\(315\) | −2.65693 | − | 1.48427i | −0.149701 | − | 0.0836292i | ||||
\(316\) | 1.46413 | + | 1.46413i | 0.0823636 | + | 0.0823636i | ||||
\(317\) | 1.04250 | − | 1.04250i | 0.0585527 | − | 0.0585527i | −0.677224 | − | 0.735777i | \(-0.736817\pi\) |
0.735777 | + | 0.677224i | \(0.236817\pi\) | |||||||
\(318\) | 8.09855i | 0.454144i | ||||||||
\(319\) | 23.1764 | + | 23.1764i | 1.29763 | + | 1.29763i | ||||
\(320\) | −0.609231 | − | 2.15147i | −0.0340570 | − | 0.120271i | ||||
\(321\) | − | 14.0495i | − | 0.784168i | ||||||
\(322\) | −3.82662 | − | 3.82662i | −0.213249 | − | 0.213249i | ||||
\(323\) | −1.96013 | − | 1.96013i | −0.109064 | − | 0.109064i | ||||
\(324\) | −6.00655 | −0.333697 | ||||||||
\(325\) | −14.6212 | − | 23.7470i | −0.811040 | − | 1.31725i | ||||
\(326\) | 7.46188i | 0.413275i | ||||||||
\(327\) | 24.5488i | 1.35755i | ||||||||
\(328\) | 0.412903 | 0.0227987 | ||||||||
\(329\) | − | 20.3702i | − | 1.12305i | ||||||
\(330\) | 7.86620 | − | 14.0810i | 0.433020 | − | 0.775132i | ||||
\(331\) | 15.4412 | − | 15.4412i | 0.848726 | − | 0.848726i | −0.141248 | − | 0.989974i | \(-0.545112\pi\) |
0.989974 | + | 0.141248i | \(0.0451116\pi\) | |||||||
\(332\) | −9.88040 | + | 9.88040i | −0.542257 | + | 0.542257i | ||||
\(333\) | 3.75801 | − | 2.99345i | 0.205938 | − | 0.164040i | ||||
\(334\) | − | 19.1080i | − | 1.04554i | ||||||
\(335\) | 14.6152 | + | 8.16466i | 0.798515 | + | 0.446083i | ||||
\(336\) | − | 2.56175i | − | 0.139755i | ||||||
\(337\) | −12.1788 | + | 12.1788i | −0.663422 | + | 0.663422i | −0.956185 | − | 0.292763i | \(-0.905425\pi\) |
0.292763 | + | 0.956185i | \(0.405425\pi\) | |||||||
\(338\) | − | 18.1080i | − | 0.984945i | ||||||
\(339\) | 4.41015 | + | 4.41015i | 0.239526 | + | 0.239526i | ||||
\(340\) | −0.614300 | − | 2.16937i | −0.0333151 | − | 0.117651i | ||||
\(341\) | 8.31773 | − | 8.31773i | 0.450430 | − | 0.450430i | ||||
\(342\) | −1.53545 | − | 1.53545i | −0.0830275 | − | 0.0830275i | ||||
\(343\) | −13.4405 | + | 13.4405i | −0.725718 | + | 0.725718i | ||||
\(344\) | 1.47727 | 0.0796489 | ||||||||
\(345\) | 9.11419 | + | 5.09156i | 0.490691 | + | 0.274120i | ||||
\(346\) | −15.1632 | + | 15.1632i | −0.815180 | + | 0.815180i | ||||
\(347\) | 13.0029i | 0.698035i | 0.937116 | + | 0.349017i | \(0.113485\pi\) | ||||
−0.937116 | + | 0.349017i | \(0.886515\pi\) | |||||||
\(348\) | −10.0428 | −0.538350 | ||||||||
\(349\) | 21.6550i | 1.15917i | 0.814913 | + | 0.579584i | \(0.196785\pi\) | ||||
−0.814913 | + | 0.579584i | \(0.803215\pi\) | |||||||
\(350\) | −1.99363 | + | 8.38200i | −0.106564 | + | 0.448037i | ||||
\(351\) | 22.2205 | + | 22.2205i | 1.18604 | + | 1.18604i | ||||
\(352\) | −4.85196 | −0.258610 | ||||||||
\(353\) | −2.78988 | −0.148490 | −0.0742452 | − | 0.997240i | \(-0.523655\pi\) | ||||
−0.0742452 | + | 0.997240i | \(0.523655\pi\) | |||||||
\(354\) | 15.4221 | 0.819673 | ||||||||
\(355\) | 4.35899 | + | 15.3936i | 0.231351 | + | 0.817007i | ||||
\(356\) | 7.09280 | − | 7.09280i | 0.375918 | − | 0.375918i | ||||
\(357\) | − | 2.58307i | − | 0.136710i | ||||||
\(358\) | −9.36945 | − | 9.36945i | −0.495191 | − | 0.495191i | ||||
\(359\) | − | 1.30687i | − | 0.0689740i | −0.999405 | − | 0.0344870i | \(-0.989020\pi\) | ||
0.999405 | − | 0.0344870i | \(-0.0109797\pi\) | |||||||
\(360\) | −0.481206 | − | 1.69936i | −0.0253618 | − | 0.0895640i | ||||
\(361\) | − | 11.4421i | − | 0.602215i | ||||||
\(362\) | − | 11.6623i | − | 0.612955i | ||||||
\(363\) | −13.1840 | − | 13.1840i | −0.691978 | − | 0.691978i | ||||
\(364\) | −6.79592 | + | 6.79592i | −0.356203 | + | 0.356203i | ||||
\(365\) | −14.0189 | + | 25.0946i | −0.733782 | + | 1.31351i | ||||
\(366\) | 0.962411 | 0.0503061 | ||||||||
\(367\) | 19.2822 | + | 19.2822i | 1.00652 | + | 1.00652i | 0.999979 | + | 0.00654459i | \(0.00208322\pi\) |
0.00654459 | + | 0.999979i | \(0.497917\pi\) | |||||||
\(368\) | − | 3.14053i | − | 0.163711i | ||||||
\(369\) | 0.326134 | 0.0169779 | ||||||||
\(370\) | −11.0524 | − | 7.92745i | −0.574587 | − | 0.412129i | ||||
\(371\) | −9.38694 | −0.487346 | ||||||||
\(372\) | 3.60423i | 0.186871i | ||||||||
\(373\) | −7.69384 | − | 7.69384i | −0.398372 | − | 0.398372i | 0.479287 | − | 0.877658i | \(-0.340895\pi\) |
−0.877658 | + | 0.479287i | \(0.840895\pi\) | |||||||
\(374\) | −4.89233 | −0.252976 | ||||||||
\(375\) | −0.705149 | − | 16.6063i | −0.0364137 | − | 0.857548i | ||||
\(376\) | 8.35899 | − | 8.35899i | 0.431082 | − | 0.431082i | ||||
\(377\) | 26.6419 | + | 26.6419i | 1.37213 | + | 1.37213i | ||||
\(378\) | − | 9.70868i | − | 0.499360i | ||||||
\(379\) | − | 16.7516i | − | 0.860474i | −0.902716 | − | 0.430237i | \(-0.858430\pi\) | ||
0.902716 | − | 0.430237i | \(-0.141570\pi\) | |||||||
\(380\) | −2.99805 | + | 5.36668i | −0.153797 | + | 0.275305i | ||||
\(381\) | − | 18.2776i | − | 0.936388i | ||||||
\(382\) | 17.6354 | + | 17.6354i | 0.902304 | + | 0.902304i | ||||
\(383\) | − | 11.5317i | − | 0.589241i | −0.955614 | − | 0.294620i | \(-0.904807\pi\) | ||
0.955614 | − | 0.294620i | \(-0.0951932\pi\) | |||||||
\(384\) | 1.05122 | − | 1.05122i | 0.0536450 | − | 0.0536450i | ||||
\(385\) | 16.3211 | + | 9.11763i | 0.831800 | + | 0.464677i | ||||
\(386\) | −13.5647 | −0.690425 | ||||||||
\(387\) | 1.16683 | 0.0593134 | ||||||||
\(388\) | −2.10245 | −0.106736 | ||||||||
\(389\) | 19.8314 | + | 19.8314i | 1.00549 | + | 1.00549i | 0.999985 | + | 0.00550900i | \(0.00175358\pi\) |
0.00550900 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(390\) | 9.04240 | − | 16.1864i | 0.457880 | − | 0.819632i | ||||
\(391\) | − | 3.16666i | − | 0.160145i | ||||||
\(392\) | −4.03070 | −0.203581 | ||||||||
\(393\) | − | 16.7485i | − | 0.844852i | ||||||
\(394\) | −16.8769 | + | 16.8769i | −0.850247 | + | 0.850247i | ||||
\(395\) | 2.25804 | − | 4.04202i | 0.113614 | − | 0.203376i | ||||
\(396\) | −3.83236 | −0.192583 | ||||||||
\(397\) | 15.8870 | − | 15.8870i | 0.797343 | − | 0.797343i | −0.185333 | − | 0.982676i | \(-0.559336\pi\) |
0.982676 | + | 0.185333i | \(0.0593362\pi\) | |||||||
\(398\) | −9.13039 | − | 9.13039i | −0.457665 | − | 0.457665i | ||||
\(399\) | −4.97993 | + | 4.97993i | −0.249308 | + | 0.249308i | ||||
\(400\) | −4.25768 | + | 2.62149i | −0.212884 | + | 0.131074i | ||||
\(401\) | −13.4312 | − | 13.4312i | −0.670721 | − | 0.670721i | 0.287161 | − | 0.957882i | \(-0.407289\pi\) |
−0.957882 | + | 0.287161i | \(0.907289\pi\) | |||||||
\(402\) | 11.1304i | 0.555134i | ||||||||
\(403\) | 9.56144 | − | 9.56144i | 0.476289 | − | 0.476289i | ||||
\(404\) | − | 6.66420i | − | 0.331556i | ||||||
\(405\) | 3.65938 | + | 12.9229i | 0.181836 | + | 0.642146i | ||||
\(406\) | − | 11.6405i | − | 0.577708i | ||||||
\(407\) | −23.0848 | + | 18.3882i | −1.14427 | + | 0.911471i | ||||
\(408\) | 1.05997 | − | 1.05997i | 0.0524763 | − | 0.0524763i | ||||
\(409\) | −16.9289 | + | 16.9289i | −0.837082 | + | 0.837082i | −0.988474 | − | 0.151392i | \(-0.951624\pi\) |
0.151392 | + | 0.988474i | \(0.451624\pi\) | |||||||
\(410\) | −0.251553 | − | 0.888349i | −0.0124233 | − | 0.0438725i | ||||
\(411\) | − | 27.8291i | − | 1.37271i | ||||||
\(412\) | 3.38743 | 0.166887 | ||||||||
\(413\) | 17.8755i | 0.879598i | ||||||||
\(414\) | − | 2.48057i | − | 0.121913i | ||||||
\(415\) | 27.2769 | + | 15.2380i | 1.33897 | + | 0.748003i | ||||
\(416\) | −5.57745 | −0.273457 | ||||||||
\(417\) | −15.8764 | − | 15.8764i | −0.777470 | − | 0.777470i | ||||
\(418\) | 9.43199 | + | 9.43199i | 0.461334 | + | 0.461334i | ||||
\(419\) | − | 32.5124i | − | 1.58834i | −0.607698 | − | 0.794169i | \(-0.707907\pi\) | ||
0.607698 | − | 0.794169i | \(-0.292093\pi\) | |||||||
\(420\) | −5.51154 | + | 1.56070i | −0.268936 | + | 0.0761543i | ||||
\(421\) | −18.5316 | − | 18.5316i | −0.903173 | − | 0.903173i | 0.0925362 | − | 0.995709i | \(-0.470503\pi\) |
−0.995709 | + | 0.0925362i | \(0.970503\pi\) | |||||||
\(422\) | − | 10.0888i | − | 0.491114i | ||||||
\(423\) | 6.60241 | − | 6.60241i | 0.321020 | − | 0.321020i | ||||
\(424\) | −3.85196 | − | 3.85196i | −0.187068 | − | 0.187068i | ||||
\(425\) | −4.29310 | + | 2.64330i | −0.208246 | + | 0.128219i | ||||
\(426\) | −7.52141 | + | 7.52141i | −0.364413 | + | 0.364413i | ||||
\(427\) | 1.11552i | 0.0539838i | ||||||||
\(428\) | 6.68246 | + | 6.68246i | 0.323009 | + | 0.323009i | ||||
\(429\) | −28.4478 | − | 28.4478i | −1.37347 | − | 1.37347i | ||||
\(430\) | −0.899997 | − | 3.17830i | −0.0434017 | − | 0.153271i | ||||
\(431\) | 25.9149 | + | 25.9149i | 1.24828 | + | 1.24828i | 0.956481 | + | 0.291796i | \(0.0942529\pi\) |
0.291796 | + | 0.956481i | \(0.405747\pi\) | |||||||
\(432\) | 3.98399 | − | 3.98399i | 0.191680 | − | 0.191680i | ||||
\(433\) | 21.8138 | − | 21.8138i | 1.04830 | − | 1.04830i | 0.0495314 | − | 0.998773i | \(-0.484227\pi\) |
0.998773 | − | 0.0495314i | \(-0.0157728\pi\) | |||||||
\(434\) | −4.17762 | −0.200532 | ||||||||
\(435\) | 6.11838 | + | 21.6068i | 0.293354 | + | 1.03597i | ||||
\(436\) | −11.6763 | − | 11.6763i | −0.559194 | − | 0.559194i | ||||
\(437\) | −6.10505 | + | 6.10505i | −0.292044 | + | 0.292044i | ||||
\(438\) | −19.1111 | −0.913164 | ||||||||
\(439\) | 12.9479 | − | 12.9479i | 0.617971 | − | 0.617971i | −0.327040 | − | 0.945011i | \(-0.606051\pi\) |
0.945011 | + | 0.327040i | \(0.106051\pi\) | |||||||
\(440\) | 2.95597 | + | 10.4389i | 0.140920 | + | 0.497653i | ||||
\(441\) | −3.18368 | −0.151604 | ||||||||
\(442\) | −5.62386 | −0.267500 | ||||||||
\(443\) | −2.00074 | − | 2.00074i | −0.0950579 | − | 0.0950579i | 0.657979 | − | 0.753037i | \(-0.271412\pi\) |
−0.753037 | + | 0.657979i | \(0.771412\pi\) | |||||||
\(444\) | 1.01756 | − | 8.98554i | 0.0482912 | − | 0.426435i | ||||
\(445\) | −19.5811 | − | 10.9388i | −0.928235 | − | 0.518550i | ||||
\(446\) | 2.45704 | + | 2.45704i | 0.116344 | + | 0.116344i | ||||
\(447\) | 22.3866 | − | 22.3866i | 1.05885 | − | 1.05885i | ||||
\(448\) | 1.21846 | + | 1.21846i | 0.0575669 | + | 0.0575669i | ||||
\(449\) | 17.2995 | + | 17.2995i | 0.816412 | + | 0.816412i | 0.985586 | − | 0.169174i | \(-0.0541100\pi\) |
−0.169174 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(450\) | −3.36296 | + | 2.07060i | −0.158531 | + | 0.0976091i | ||||
\(451\) | −2.00339 | −0.0943359 | ||||||||
\(452\) | −4.19525 | −0.197328 | ||||||||
\(453\) | 6.00949 | − | 6.00949i | 0.282350 | − | 0.282350i | ||||
\(454\) | − | 19.5967i | − | 0.919720i | ||||||
\(455\) | 18.7615 | + | 10.4809i | 0.879553 | + | 0.491354i | ||||
\(456\) | −4.08706 | −0.191394 | ||||||||
\(457\) | −24.4123 | −1.14196 | −0.570979 | − | 0.820965i | \(-0.693436\pi\) | ||||
−0.570979 | + | 0.820965i | \(0.693436\pi\) | |||||||
\(458\) | 8.54964 | 0.399498 | ||||||||
\(459\) | 4.01713 | − | 4.01713i | 0.187504 | − | 0.187504i | ||||
\(460\) | −6.75677 | + | 1.91331i | −0.315036 | + | 0.0892085i | ||||
\(461\) | −14.1676 | + | 14.1676i | −0.659853 | + | 0.659853i | −0.955345 | − | 0.295492i | \(-0.904516\pi\) |
0.295492 | + | 0.955345i | \(0.404516\pi\) | |||||||
\(462\) | 12.4295i | 0.578274i | ||||||||
\(463\) | 9.45035i | 0.439195i | 0.975591 | + | 0.219597i | \(0.0704744\pi\) | ||||
−0.975591 | + | 0.219597i | \(0.929526\pi\) | |||||||
\(464\) | 4.77672 | − | 4.77672i | 0.221753 | − | 0.221753i | ||||
\(465\) | 7.75441 | − | 2.19581i | 0.359602 | − | 0.101828i | ||||
\(466\) | 18.6855 | − | 18.6855i | 0.865591 | − | 0.865591i | ||||
\(467\) | 5.91129 | 0.273542 | 0.136771 | − | 0.990603i | \(-0.456328\pi\) | ||||
0.136771 | + | 0.990603i | \(0.456328\pi\) | |||||||
\(468\) | −4.40539 | −0.203639 | ||||||||
\(469\) | −12.9011 | −0.595718 | ||||||||
\(470\) | −23.0767 | − | 12.8916i | −1.06445 | − | 0.594645i | ||||
\(471\) | 9.89733i | 0.456045i | ||||||||
\(472\) | −7.33529 | + | 7.33529i | −0.337634 | + | 0.337634i | ||||
\(473\) | −7.16765 | −0.329569 | ||||||||
\(474\) | 3.07825 | 0.141389 | ||||||||
\(475\) | 13.3728 | + | 3.18067i | 0.613585 | + | 0.145939i | ||||
\(476\) | 1.22860 | + | 1.22860i | 0.0563127 | + | 0.0563127i | ||||
\(477\) | −3.04250 | − | 3.04250i | −0.139307 | − | 0.139307i | ||||
\(478\) | 14.5251 | − | 14.5251i | 0.664362 | − | 0.664362i | ||||
\(479\) | 15.1619 | + | 15.1619i | 0.692764 | + | 0.692764i | 0.962839 | − | 0.270075i | \(-0.0870485\pi\) |
−0.270075 | + | 0.962839i | \(0.587049\pi\) | |||||||
\(480\) | −2.90212 | − | 1.62124i | −0.132463 | − | 0.0739992i | ||||
\(481\) | −26.5366 | + | 21.1378i | −1.20996 | + | 0.963799i | ||||
\(482\) | −8.39707 | − | 8.39707i | −0.382476 | − | 0.382476i | ||||
\(483\) | −8.04526 | −0.366072 | ||||||||
\(484\) | 12.5415 | 0.570069 | ||||||||
\(485\) | 1.28088 | + | 4.52336i | 0.0581616 | + | 0.205395i | ||||
\(486\) | 5.63773 | − | 5.63773i | 0.255733 | − | 0.255733i | ||||
\(487\) | −21.5964 | −0.978624 | −0.489312 | − | 0.872109i | \(-0.662752\pi\) | ||||
−0.489312 | + | 0.872109i | \(0.662752\pi\) | |||||||
\(488\) | −0.457758 | + | 0.457758i | −0.0207217 | + | 0.0207217i | ||||
\(489\) | 7.84411 | + | 7.84411i | 0.354723 | + | 0.354723i | ||||
\(490\) | 2.45563 | + | 8.67194i | 0.110934 | + | 0.391759i | ||||
\(491\) | 36.1012 | 1.62922 | 0.814612 | − | 0.580006i | \(-0.196950\pi\) | ||||
0.814612 | + | 0.580006i | \(0.196950\pi\) | |||||||
\(492\) | 0.434053 | − | 0.434053i | 0.0195686 | − | 0.0195686i | ||||
\(493\) | 4.81646 | − | 4.81646i | 0.216922 | − | 0.216922i | ||||
\(494\) | 10.8423 | + | 10.8423i | 0.487819 | + | 0.487819i | ||||
\(495\) | 2.33479 | + | 8.24522i | 0.104941 | + | 0.370595i | ||||
\(496\) | −1.71430 | − | 1.71430i | −0.0769744 | − | 0.0769744i | ||||
\(497\) | −8.71798 | − | 8.71798i | −0.391055 | − | 0.391055i | ||||
\(498\) | 20.7730i | 0.930861i | ||||||||
\(499\) | −8.86811 | + | 8.86811i | −0.396991 | + | 0.396991i | −0.877170 | − | 0.480179i | \(-0.840572\pi\) |
0.480179 | + | 0.877170i | \(0.340572\pi\) | |||||||
\(500\) | 8.23397 | + | 7.56318i | 0.368234 | + | 0.338236i | ||||
\(501\) | −20.0868 | − | 20.0868i | −0.897411 | − | 0.897411i | ||||
\(502\) | −6.65372 | + | 6.65372i | −0.296970 | + | 0.296970i | ||||
\(503\) | − | 27.8555i | − | 1.24202i | −0.783804 | − | 0.621008i | \(-0.786723\pi\) | ||
0.783804 | − | 0.621008i | \(-0.213277\pi\) | |||||||
\(504\) | 0.962411 | + | 0.962411i | 0.0428692 | + | 0.0428692i | ||||
\(505\) | −14.3378 | + | 4.06004i | −0.638026 | + | 0.180669i | ||||
\(506\) | 15.2377i | 0.677400i | ||||||||
\(507\) | −19.0356 | − | 19.0356i | −0.845399 | − | 0.845399i | ||||
\(508\) | 8.69347 | + | 8.69347i | 0.385710 | + | 0.385710i | ||||
\(509\) | 37.8029 | 1.67558 | 0.837791 | − | 0.545990i | \(-0.183847\pi\) | ||||
0.837791 | + | 0.545990i | \(0.183847\pi\) | |||||||
\(510\) | −2.92626 | − | 1.63473i | −0.129577 | − | 0.0723870i | ||||
\(511\) | − | 22.1515i | − | 0.979924i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −15.4894 | −0.683873 | ||||||||
\(514\) | 14.1881i | 0.625809i | ||||||||
\(515\) | −2.06373 | − | 7.28797i | −0.0909387 | − | 0.321146i | ||||
\(516\) | 1.55294 | − | 1.55294i | 0.0683643 | − | 0.0683643i | ||||
\(517\) | −40.5575 | + | 40.5575i | −1.78372 | + | 1.78372i | ||||
\(518\) | 10.4150 | + | 1.17944i | 0.457610 | + | 0.0518217i | ||||
\(519\) | 31.8799i | 1.39937i | ||||||||
\(520\) | 3.39796 | + | 11.9997i | 0.149010 | + | 0.526224i | ||||
\(521\) | − | 24.2905i | − | 1.06419i | −0.846685 | − | 0.532094i | \(-0.821405\pi\) | ||
0.846685 | − | 0.532094i | \(-0.178595\pi\) | |||||||
\(522\) | 3.77293 | − | 3.77293i | 0.165136 | − | 0.165136i | ||||
\(523\) | 34.6818i | 1.51653i | 0.651946 | + | 0.758265i | \(0.273953\pi\) | ||||
−0.651946 | + | 0.758265i | \(0.726047\pi\) | |||||||
\(524\) | 7.96621 | + | 7.96621i | 0.348005 | + | 0.348005i | ||||
\(525\) | 6.71560 | + | 10.9071i | 0.293093 | + | 0.476025i | ||||
\(526\) | −8.87946 | + | 8.87946i | −0.387163 | + | 0.387163i | ||||
\(527\) | −1.72856 | − | 1.72856i | −0.0752975 | − | 0.0752975i | ||||
\(528\) | −5.10050 | + | 5.10050i | −0.221971 | + | 0.221971i | ||||
\(529\) | 13.1371 | 0.571177 | ||||||||
\(530\) | −5.94066 | + | 10.6341i | −0.258046 | + | 0.461917i | ||||
\(531\) | −5.79383 | + | 5.79383i | −0.251431 | + | 0.251431i | ||||
\(532\) | − | 4.73727i | − | 0.205387i | ||||||
\(533\) | −2.30295 | −0.0997517 | ||||||||
\(534\) | − | 14.9122i | − | 0.645316i | ||||||
\(535\) | 10.3060 | − | 18.4483i | 0.445566 | − | 0.797590i | ||||
\(536\) | −5.29402 | − | 5.29402i | −0.228667 | − | 0.228667i | ||||
\(537\) | −19.6988 | −0.850065 | ||||||||
\(538\) | 13.1011 | 0.564830 | ||||||||
\(539\) | 19.5568 | 0.842371 | ||||||||
\(540\) | −10.9986 | − | 6.14427i | −0.473305 | − | 0.264407i | ||||
\(541\) | 6.04272 | − | 6.04272i | 0.259797 | − | 0.259797i | −0.565175 | − | 0.824971i | \(-0.691191\pi\) |
0.824971 | + | 0.565175i | \(0.191191\pi\) | |||||||
\(542\) | − | 6.98656i | − | 0.300098i | ||||||
\(543\) | −12.2596 | − | 12.2596i | −0.526111 | − | 0.526111i | ||||
\(544\) | 1.00832i | 0.0432313i | ||||||||
\(545\) | −18.0077 | + | 32.2349i | −0.771366 | + | 1.38079i | ||||
\(546\) | 14.2881i | 0.611472i | ||||||||
\(547\) | − | 34.2347i | − | 1.46377i | −0.681428 | − | 0.731885i | \(-0.738641\pi\) | ||
0.681428 | − | 0.731885i | \(-0.261359\pi\) | |||||||
\(548\) | 13.2365 | + | 13.2365i | 0.565436 | + | 0.565436i | ||||
\(549\) | −0.361563 | + | 0.361563i | −0.0154311 | + | 0.0154311i | ||||
\(550\) | 20.6581 | − | 12.7194i | 0.880863 | − | 0.542355i | ||||
\(551\) | −18.5714 | −0.791170 | ||||||||
\(552\) | −3.30140 | − | 3.30140i | −0.140517 | − | 0.140517i | ||||
\(553\) | 3.56797i | 0.151725i | ||||||||
\(554\) | −14.9569 | −0.635457 | ||||||||
\(555\) | −19.9521 | + | 3.28502i | −0.846918 | + | 0.139441i | ||||
\(556\) | 15.1028 | 0.640500 | ||||||||
\(557\) | 21.2394i | 0.899943i | 0.893043 | + | 0.449971i | \(0.148566\pi\) | ||||
−0.893043 | + | 0.449971i | \(0.851434\pi\) | |||||||
\(558\) | −1.35405 | − | 1.35405i | −0.0573217 | − | 0.0573217i | ||||
\(559\) | −8.23939 | −0.348489 | ||||||||
\(560\) | 1.87916 | − | 3.36381i | 0.0794092 | − | 0.142147i | ||||
\(561\) | −5.14293 | + | 5.14293i | −0.217135 | + | 0.217135i | ||||
\(562\) | 13.8446 | + | 13.8446i | 0.583998 | + | 0.583998i | ||||
\(563\) | 20.2289i | 0.852546i | 0.904594 | + | 0.426273i | \(0.140174\pi\) | ||||
−0.904594 | + | 0.426273i | \(0.859826\pi\) | |||||||
\(564\) | − | 17.5743i | − | 0.740013i | ||||||
\(565\) | 2.55588 | + | 9.02597i | 0.107527 | + | 0.379725i | ||||
\(566\) | − | 9.08448i | − | 0.381849i | ||||||
\(567\) | −7.31876 | − | 7.31876i | −0.307359 | − | 0.307359i | ||||
\(568\) | − | 7.15491i | − | 0.300213i | ||||||
\(569\) | −2.40147 | + | 2.40147i | −0.100675 | + | 0.100675i | −0.755650 | − | 0.654975i | \(-0.772679\pi\) |
0.654975 | + | 0.755650i | \(0.272679\pi\) | |||||||
\(570\) | 2.48997 | + | 8.79321i | 0.104293 | + | 0.368307i | ||||
\(571\) | −7.39594 | −0.309510 | −0.154755 | − | 0.987953i | \(-0.549459\pi\) | ||||
−0.154755 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(572\) | 27.0616 | 1.13150 | ||||||||
\(573\) | 37.0774 | 1.54893 | ||||||||
\(574\) | 0.503106 | + | 0.503106i | 0.0209993 | + | 0.0209993i | ||||
\(575\) | 8.23286 | + | 13.3714i | 0.343334 | + | 0.557624i | ||||
\(576\) | 0.789858i | 0.0329107i | ||||||||
\(577\) | −38.1791 | −1.58942 | −0.794708 | − | 0.606993i | \(-0.792376\pi\) | ||||
−0.794708 | + | 0.606993i | \(0.792376\pi\) | |||||||
\(578\) | − | 15.9833i | − | 0.664817i | ||||||
\(579\) | −14.2595 | + | 14.2595i | −0.592606 | + | 0.592606i | ||||
\(580\) | −13.1871 | − | 7.36685i | −0.547565 | − | 0.305892i | ||||
\(581\) | −24.0778 | −0.998915 | ||||||||
\(582\) | −2.21014 | + | 2.21014i | −0.0916134 | + | 0.0916134i | ||||
\(583\) | 18.6896 | + | 18.6896i | 0.774043 | + | 0.774043i | ||||
\(584\) | 9.08993 | − | 9.08993i | 0.376144 | − | 0.376144i | ||||
\(585\) | 2.68390 | + | 9.47809i | 0.110966 | + | 0.391871i | ||||
\(586\) | −7.79244 | − | 7.79244i | −0.321903 | − | 0.321903i | ||||
\(587\) | 21.8152i | 0.900410i | 0.892925 | + | 0.450205i | \(0.148649\pi\) | ||||
−0.892925 | + | 0.450205i | \(0.851351\pi\) | |||||||
\(588\) | −4.23717 | + | 4.23717i | −0.174738 | + | 0.174738i | ||||
\(589\) | 6.66505i | 0.274629i | ||||||||
\(590\) | 20.2506 | + | 11.3128i | 0.833702 | + | 0.465740i | ||||
\(591\) | 35.4828i | 1.45957i | ||||||||
\(592\) | 3.78986 | + | 4.75783i | 0.155762 | + | 0.195546i | ||||
\(593\) | −4.84337 | + | 4.84337i | −0.198893 | + | 0.198893i | −0.799526 | − | 0.600632i | \(-0.794916\pi\) |
0.600632 | + | 0.799526i | \(0.294916\pi\) | |||||||
\(594\) | −19.3302 | + | 19.3302i | −0.793126 | + | 0.793126i | ||||
\(595\) | 1.89480 | − | 3.39180i | 0.0776791 | − | 0.139050i | ||||
\(596\) | 21.2958i | 0.872308i | ||||||||
\(597\) | −19.1962 | −0.785647 | ||||||||
\(598\) | 17.5162i | 0.716289i | ||||||||
\(599\) | 29.5415i | 1.20703i | 0.797350 | + | 0.603517i | \(0.206234\pi\) | ||||
−0.797350 | + | 0.603517i | \(0.793766\pi\) | |||||||
\(600\) | −1.72000 | + | 7.23154i | −0.0702186 | + | 0.295226i | ||||
\(601\) | 6.21588 | 0.253551 | 0.126776 | − | 0.991931i | \(-0.459537\pi\) | ||||
0.126776 | + | 0.991931i | \(0.459537\pi\) | |||||||
\(602\) | 1.79999 | + | 1.79999i | 0.0733623 | + | 0.0733623i | ||||
\(603\) | −4.18152 | − | 4.18152i | −0.170285 | − | 0.170285i | ||||
\(604\) | 5.71666i | 0.232608i | ||||||||
\(605\) | −7.64069 | − | 26.9828i | −0.310638 | − | 1.09701i | ||||
\(606\) | −7.00556 | − | 7.00556i | −0.284582 | − | 0.284582i | ||||
\(607\) | 35.5553i | 1.44314i | 0.692340 | + | 0.721572i | \(0.256580\pi\) | ||||
−0.692340 | + | 0.721572i | \(0.743420\pi\) | |||||||
\(608\) | 1.94395 | − | 1.94395i | 0.0788378 | − | 0.0788378i | ||||
\(609\) | −12.2368 | − | 12.2368i | −0.495859 | − | 0.495859i | ||||
\(610\) | 1.26373 | + | 0.705973i | 0.0511671 | + | 0.0285840i | ||||
\(611\) | −46.6219 | + | 46.6219i | −1.88612 | + | 1.88612i | ||||
\(612\) | 0.796429i | 0.0321937i | ||||||||
\(613\) | −23.4695 | − | 23.4695i | −0.947925 | − | 0.947925i | 0.0507843 | − | 0.998710i | \(-0.483828\pi\) |
−0.998710 | + | 0.0507843i | \(0.983828\pi\) | |||||||
\(614\) | 2.77527 | + | 2.77527i | 0.112001 | + | 0.112001i | ||||
\(615\) | −1.19829 | − | 0.669415i | −0.0483198 | − | 0.0269934i | ||||
\(616\) | −5.91193 | − | 5.91193i | −0.238198 | − | 0.238198i | ||||
\(617\) | 4.77446 | − | 4.77446i | 0.192212 | − | 0.192212i | −0.604439 | − | 0.796651i | \(-0.706603\pi\) |
0.796651 | + | 0.604439i | \(0.206603\pi\) | |||||||
\(618\) | 3.56095 | − | 3.56095i | 0.143242 | − | 0.143242i | ||||
\(619\) | 16.3058 | 0.655385 | 0.327692 | − | 0.944784i | \(-0.393729\pi\) | ||||
0.327692 | + | 0.944784i | \(0.393729\pi\) | |||||||
\(620\) | −2.64387 | + | 4.73268i | −0.106180 | + | 0.190069i | ||||
\(621\) | −12.5118 | − | 12.5118i | −0.502083 | − | 0.502083i | ||||
\(622\) | 2.34988 | − | 2.34988i | 0.0942216 | − | 0.0942216i | ||||
\(623\) | 17.2846 | 0.692494 | ||||||||
\(624\) | −5.86315 | + | 5.86315i | −0.234714 | + | 0.234714i | ||||
\(625\) | 11.2556 | − | 22.3229i | 0.450224 | − | 0.892916i | ||||
\(626\) | 10.8979 | 0.435566 | ||||||||
\(627\) | 19.8303 | 0.791945 | ||||||||
\(628\) | −4.70753 | − | 4.70753i | −0.187851 | − | 0.187851i | ||||
\(629\) | 3.82139 | + | 4.79742i | 0.152369 | + | 0.191286i | ||||
\(630\) | 1.48427 | − | 2.65693i | 0.0591348 | − | 0.105855i | ||||
\(631\) | 12.0883 | + | 12.0883i | 0.481228 | + | 0.481228i | 0.905524 | − | 0.424296i | \(-0.139478\pi\) |
−0.424296 | + | 0.905524i | \(0.639478\pi\) | |||||||
\(632\) | −1.46413 | + | 1.46413i | −0.0582398 | + | 0.0582398i | ||||
\(633\) | −10.6056 | − | 10.6056i | −0.421533 | − | 0.421533i | ||||
\(634\) | 1.04250 | + | 1.04250i | 0.0414030 | + | 0.0414030i | ||||
\(635\) | 13.4074 | − | 24.0001i | 0.532058 | − | 0.952415i | ||||
\(636\) | −8.09855 | −0.321128 | ||||||||
\(637\) | 22.4810 | 0.890731 | ||||||||
\(638\) | −23.1764 | + | 23.1764i | −0.917564 | + | 0.917564i | ||||
\(639\) | − | 5.65136i | − | 0.223564i | ||||||
\(640\) | 2.15147 | − | 0.609231i | 0.0850445 | − | 0.0240820i | ||||
\(641\) | 3.28760 | 0.129853 | 0.0649263 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649263 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(642\) | 14.0495 | 0.554490 | ||||||||
\(643\) | 31.8234 | 1.25499 | 0.627496 | − | 0.778620i | \(-0.284080\pi\) | ||||
0.627496 | + | 0.778620i | \(0.284080\pi\) | |||||||
\(644\) | 3.82662 | − | 3.82662i | 0.150790 | − | 0.150790i | ||||
\(645\) | −4.28720 | − | 2.39501i | −0.168809 | − | 0.0943033i | ||||
\(646\) | 1.96013 | − | 1.96013i | 0.0771202 | − | 0.0771202i | ||||
\(647\) | − | 26.7710i | − | 1.05248i | −0.850337 | − | 0.526239i | \(-0.823602\pi\) | ||
0.850337 | − | 0.526239i | \(-0.176398\pi\) | |||||||
\(648\) | − | 6.00655i | − | 0.235960i | ||||||
\(649\) | 35.5905 | − | 35.5905i | 1.39705 | − | 1.39705i | ||||
\(650\) | 23.7470 | − | 14.6212i | 0.931433 | − | 0.573492i | ||||
\(651\) | −4.39162 | + | 4.39162i | −0.172121 | + | 0.172121i | ||||
\(652\) | −7.46188 | −0.292230 | ||||||||
\(653\) | −12.7656 | −0.499558 | −0.249779 | − | 0.968303i | \(-0.580358\pi\) | ||||
−0.249779 | + | 0.968303i | \(0.580358\pi\) | |||||||
\(654\) | −24.5488 | −0.959936 | ||||||||
\(655\) | 12.2858 | − | 21.9923i | 0.480047 | − | 0.859312i | ||||
\(656\) | 0.412903i | 0.0161211i | ||||||||
\(657\) | 7.17975 | − | 7.17975i | 0.280109 | − | 0.280109i | ||||
\(658\) | 20.3702 | 0.794114 | ||||||||
\(659\) | −26.8508 | −1.04596 | −0.522980 | − | 0.852345i | \(-0.675180\pi\) | ||||
−0.522980 | + | 0.852345i | \(0.675180\pi\) | |||||||
\(660\) | 14.0810 | + | 7.86620i | 0.548101 | + | 0.306191i | ||||
\(661\) | −0.244360 | − | 0.244360i | −0.00950449 | − | 0.00950449i | 0.702339 | − | 0.711843i | \(-0.252139\pi\) |
−0.711843 | + | 0.702339i | \(0.752139\pi\) | |||||||
\(662\) | 15.4412 | + | 15.4412i | 0.600140 | + | 0.600140i | ||||
\(663\) | −5.91193 | + | 5.91193i | −0.229600 | + | 0.229600i | ||||
\(664\) | −9.88040 | − | 9.88040i | −0.383434 | − | 0.383434i | ||||
\(665\) | −10.1921 | + | 2.88609i | −0.395233 | + | 0.111918i | ||||
\(666\) | 2.99345 | + | 3.75801i | 0.115994 | + | 0.145620i | ||||
\(667\) | −15.0014 | − | 15.0014i | −0.580857 | − | 0.580857i | ||||
\(668\) | 19.1080 | 0.739310 | ||||||||
\(669\) | 5.16581 | 0.199722 | ||||||||
\(670\) | −8.16466 | + | 14.6152i | −0.315428 | + | 0.564635i | ||||
\(671\) | 2.22102 | − | 2.22102i | 0.0857416 | − | 0.0857416i | ||||
\(672\) | 2.56175 | 0.0988217 | ||||||||
\(673\) | −21.2991 | + | 21.2991i | −0.821019 | + | 0.821019i | −0.986254 | − | 0.165236i | \(-0.947162\pi\) |
0.165236 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(674\) | −12.1788 | − | 12.1788i | −0.469110 | − | 0.469110i | ||||
\(675\) | −6.51855 | + | 27.4065i | −0.250899 | + | 1.05488i | ||||
\(676\) | 18.1080 | 0.696461 | ||||||||
\(677\) | 19.3523 | − | 19.3523i | 0.743770 | − | 0.743770i | −0.229531 | − | 0.973301i | \(-0.573719\pi\) |
0.973301 | + | 0.229531i | \(0.0737193\pi\) | |||||||
\(678\) | −4.41015 | + | 4.41015i | −0.169371 | + | 0.169371i | ||||
\(679\) | −2.56175 | − | 2.56175i | −0.0983110 | − | 0.0983110i | ||||
\(680\) | 2.16937 | − | 0.614300i | 0.0831916 | − | 0.0235573i | ||||
\(681\) | −20.6005 | − | 20.6005i | −0.789414 | − | 0.789414i | ||||
\(682\) | 8.31773 | + | 8.31773i | 0.318502 | + | 0.318502i | ||||
\(683\) | 23.3423i | 0.893169i | 0.894742 | + | 0.446584i | \(0.147360\pi\) | ||||
−0.894742 | + | 0.446584i | \(0.852640\pi\) | |||||||
\(684\) | 1.53545 | − | 1.53545i | 0.0587093 | − | 0.0587093i | ||||
\(685\) | 20.4139 | − | 36.5421i | 0.779976 | − | 1.39620i | ||||
\(686\) | −13.4405 | − | 13.4405i | −0.513160 | − | 0.513160i | ||||
\(687\) | 8.98758 | − | 8.98758i | 0.342898 | − | 0.342898i | ||||
\(688\) | 1.47727i | 0.0563203i | ||||||||
\(689\) | 21.4841 | + | 21.4841i | 0.818480 | + | 0.818480i | ||||
\(690\) | −5.09156 | + | 9.11419i | −0.193832 | + | 0.346971i | ||||
\(691\) | 19.1059i | 0.726822i | 0.931629 | + | 0.363411i | \(0.118388\pi\) | ||||
−0.931629 | + | 0.363411i | \(0.881612\pi\) | |||||||
\(692\) | −15.1632 | − | 15.1632i | −0.576419 | − | 0.576419i | ||||
\(693\) | −4.66958 | − | 4.66958i | −0.177383 | − | 0.177383i | ||||
\(694\) | −13.0029 | −0.493585 | ||||||||
\(695\) | −9.20107 | − | 32.4932i | −0.349017 | − | 1.23254i | ||||
\(696\) | − | 10.0428i | − | 0.380671i | ||||||
\(697\) | 0.416338i | 0.0157699i | ||||||||
\(698\) | −21.6550 | −0.819655 | ||||||||
\(699\) | − | 39.2854i | − | 1.48591i | ||||||
\(700\) | −8.38200 | − | 1.99363i | −0.316810 | − | 0.0753522i | ||||
\(701\) | 35.3393 | − | 35.3393i | 1.33475 | − | 1.33475i | 0.433679 | − | 0.901067i | \(-0.357215\pi\) |
0.901067 | − | 0.433679i | \(-0.142785\pi\) | |||||||
\(702\) | −22.2205 | + | 22.2205i | −0.838659 | + | 0.838659i | ||||
\(703\) | 1.88170 | − | 16.6163i | 0.0709697 | − | 0.626697i | ||||
\(704\) | − | 4.85196i | − | 0.182865i | ||||||
\(705\) | −37.8107 | + | 10.7068i | −1.42403 | + | 0.403243i | ||||
\(706\) | − | 2.78988i | − | 0.104999i | ||||||
\(707\) | 8.12007 | − | 8.12007i | 0.305387 | − | 0.305387i | ||||
\(708\) | 15.4221i | 0.579596i | ||||||||
\(709\) | −29.5655 | − | 29.5655i | −1.11036 | − | 1.11036i | −0.993102 | − | 0.117254i | \(-0.962591\pi\) |
−0.117254 | − | 0.993102i | \(-0.537409\pi\) | |||||||
\(710\) | −15.3936 | + | 4.35899i | −0.577711 | + | 0.163590i | ||||
\(711\) | −1.15645 | + | 1.15645i | −0.0433703 | + | 0.0433703i | ||||
\(712\) | 7.09280 | + | 7.09280i | 0.265814 | + | 0.265814i | ||||
\(713\) | −5.38382 | + | 5.38382i | −0.201626 | + | 0.201626i | ||||
\(714\) | 2.58307 | 0.0966688 | ||||||||
\(715\) | −16.4868 | − | 58.2223i | −0.616570 | − | 2.17739i | ||||
\(716\) | 9.36945 | − | 9.36945i | 0.350153 | − | 0.350153i | ||||
\(717\) | − | 30.5382i | − | 1.14047i | ||||||
\(718\) | 1.30687 | 0.0487720 | ||||||||
\(719\) | 0.762333i | 0.0284302i | 0.999899 | + | 0.0142151i | \(0.00452496\pi\) | ||||
−0.999899 | + | 0.0142151i | \(0.995475\pi\) | |||||||
\(720\) | 1.69936 | − | 0.481206i | 0.0633313 | − | 0.0179335i | ||||
\(721\) | 4.12746 | + | 4.12746i | 0.153715 | + | 0.153715i | ||||
\(722\) | 11.4421 | 0.425830 | ||||||||
\(723\) | −17.6544 | −0.656574 | ||||||||
\(724\) | 11.6623 | 0.433424 | ||||||||
\(725\) | −7.81560 | + | 32.8598i | −0.290264 | + | 1.22038i | ||||
\(726\) | 13.1840 | − | 13.1840i | 0.489302 | − | 0.489302i | ||||
\(727\) | − | 3.28968i | − | 0.122007i | −0.998138 | − | 0.0610037i | \(-0.980570\pi\) | ||
0.998138 | − | 0.0610037i | \(-0.0194302\pi\) | |||||||
\(728\) | −6.79592 | − | 6.79592i | −0.251873 | − | 0.251873i | ||||
\(729\) | − | 29.8727i | − | 1.10640i | ||||||
\(730\) | −25.0946 | − | 14.0189i | −0.928794 | − | 0.518862i | ||||
\(731\) | 1.48956i | 0.0550933i | ||||||||
\(732\) | 0.962411i | 0.0355718i | ||||||||
\(733\) | −1.10605 | − | 1.10605i | −0.0408531 | − | 0.0408531i | 0.686385 | − | 0.727238i | \(-0.259196\pi\) |
−0.727238 | + | 0.686385i | \(0.759196\pi\) | |||||||
\(734\) | −19.2822 | + | 19.2822i | −0.711719 | + | 0.711719i | ||||
\(735\) | 11.6976 | + | 6.53474i | 0.431471 | + | 0.241037i | ||||
\(736\) | 3.14053 | 0.115761 | ||||||||
\(737\) | 25.6864 | + | 25.6864i | 0.946169 | + | 0.946169i | ||||
\(738\) | 0.326134i | 0.0120052i | ||||||||
\(739\) | −15.8878 | −0.584443 | −0.292221 | − | 0.956351i | \(-0.594394\pi\) | ||||
−0.292221 | + | 0.956351i | \(0.594394\pi\) | |||||||
\(740\) | 7.92745 | − | 11.0524i | 0.291419 | − | 0.406294i | ||||
\(741\) | 22.7954 | 0.837410 | ||||||||
\(742\) | − | 9.38694i | − | 0.344605i | ||||||
\(743\) | −7.35293 | − | 7.35293i | −0.269753 | − | 0.269753i | 0.559248 | − | 0.829001i | \(-0.311090\pi\) |
−0.829001 | + | 0.559248i | \(0.811090\pi\) | |||||||
\(744\) | −3.60423 | −0.132137 | ||||||||
\(745\) | 45.8172 | − | 12.9740i | 1.67861 | − | 0.475332i | ||||
\(746\) | 7.69384 | − | 7.69384i | 0.281691 | − | 0.281691i | ||||
\(747\) | −7.80411 | − | 7.80411i | −0.285537 | − | 0.285537i | ||||
\(748\) | − | 4.89233i | − | 0.178881i | ||||||
\(749\) | 16.2847i | 0.595028i | ||||||||
\(750\) | 16.6063 | − | 0.705149i | 0.606378 | − | 0.0257484i | ||||
\(751\) | 33.7019i | 1.22980i | 0.788605 | + | 0.614900i | \(0.210804\pi\) | ||||
−0.788605 | + | 0.614900i | \(0.789196\pi\) | |||||||
\(752\) | 8.35899 | + | 8.35899i | 0.304821 | + | 0.304821i | ||||
\(753\) | 13.9891i | 0.509791i | ||||||||
\(754\) | −26.6419 | + | 26.6419i | −0.970241 | + | 0.970241i | ||||
\(755\) | 12.2992 | − | 3.48277i | 0.447615 | − | 0.126751i | ||||
\(756\) | 9.70868 | 0.353101 | ||||||||
\(757\) | −33.6937 | −1.22462 | −0.612309 | − | 0.790618i | \(-0.709759\pi\) | ||||
−0.612309 | + | 0.790618i | \(0.709759\pi\) | |||||||
\(758\) | 16.7516 | 0.608447 | ||||||||
\(759\) | 16.0183 | + | 16.0183i | 0.581426 | + | 0.581426i | ||||
\(760\) | −5.36668 | − | 2.99805i | −0.194670 | − | 0.108751i | ||||
\(761\) | − | 8.01511i | − | 0.290548i | −0.989391 | − | 0.145274i | \(-0.953594\pi\) | ||
0.989391 | − | 0.145274i | \(-0.0464063\pi\) | |||||||
\(762\) | 18.2776 | 0.662126 | ||||||||
\(763\) | − | 28.4543i | − | 1.03011i | ||||||
\(764\) | −17.6354 | + | 17.6354i | −0.638025 | + | 0.638025i | ||||
\(765\) | 1.71350 | − | 0.485209i | 0.0619516 | − | 0.0175428i | ||||
\(766\) | 11.5317 | 0.416656 | ||||||||
\(767\) | 40.9122 | − | 40.9122i | 1.47725 | − | 1.47725i | ||||
\(768\) | 1.05122 | + | 1.05122i | 0.0379328 | + | 0.0379328i | ||||
\(769\) | 3.76573 | − | 3.76573i | 0.135796 | − | 0.135796i | −0.635941 | − | 0.771737i | \(-0.719388\pi\) |
0.771737 | + | 0.635941i | \(0.219388\pi\) | |||||||
\(770\) | −9.11763 | + | 16.3211i | −0.328577 | + | 0.588171i | ||||
\(771\) | 14.9148 | + | 14.9148i | 0.537145 | + | 0.537145i | ||||
\(772\) | − | 13.5647i | − | 0.488204i | ||||||
\(773\) | 27.2082 | − | 27.2082i | 0.978611 | − | 0.978611i | −0.0211650 | − | 0.999776i | \(-0.506738\pi\) |
0.999776 | + | 0.0211650i | \(0.00673753\pi\) | |||||||
\(774\) | 1.16683i | 0.0419409i | ||||||||
\(775\) | 11.7930 | + | 2.80492i | 0.423616 | + | 0.100756i | ||||
\(776\) | − | 2.10245i | − | 0.0754735i | ||||||
\(777\) | 12.1884 | − | 9.70868i | 0.437256 | − | 0.348297i | ||||
\(778\) | −19.8314 | + | 19.8314i | −0.710992 | + | 0.710992i | ||||
\(779\) | 0.802664 | − | 0.802664i | 0.0287584 | − | 0.0287584i | ||||
\(780\) | 16.1864 | + | 9.04240i | 0.579567 | + | 0.323770i | ||||
\(781\) | 34.7153i | 1.24221i | ||||||||
\(782\) | 3.16666 | 0.113239 | ||||||||
\(783\) | − | 38.0608i | − | 1.36018i | ||||||
\(784\) | − | 4.03070i | − | 0.143954i | ||||||
\(785\) | −7.26015 | + | 12.9961i | −0.259126 | + | 0.463851i | ||||
\(786\) | 16.7485 | 0.597400 | ||||||||
\(787\) | −8.43368 | − | 8.43368i | −0.300628 | − | 0.300628i | 0.540631 | − | 0.841260i | \(-0.318185\pi\) |
−0.841260 | + | 0.540631i | \(0.818185\pi\) | |||||||
\(788\) | −16.8769 | − | 16.8769i | −0.601215 | − | 0.601215i | ||||
\(789\) | 18.6686i | 0.664620i | ||||||||
\(790\) | 4.04202 | + | 2.25804i | 0.143809 | + | 0.0803374i | ||||
\(791\) | −5.11175 | − | 5.11175i | −0.181753 | − | 0.181753i | ||||
\(792\) | − | 3.83236i | − | 0.136177i | ||||||
\(793\) | 2.55312 | − | 2.55312i | 0.0906640 | − | 0.0906640i | ||||
\(794\) | 15.8870 | + | 15.8870i | 0.563807 | + | 0.563807i | ||||
\(795\) | 4.93389 | + | 17.4238i | 0.174987 | + | 0.617959i | ||||
\(796\) | 9.13039 | − | 9.13039i | 0.323618 | − | 0.323618i | ||||
\(797\) | − | 10.2289i | − | 0.362327i | −0.983453 | − | 0.181163i | \(-0.942014\pi\) | ||
0.983453 | − | 0.181163i | \(-0.0579863\pi\) | |||||||
\(798\) | −4.97993 | − | 4.97993i | −0.176288 | − | 0.176288i | ||||
\(799\) | 8.42854 | + | 8.42854i | 0.298180 | + | 0.298180i | ||||
\(800\) | −2.62149 | − | 4.25768i | −0.0926836 | − | 0.150532i | ||||
\(801\) | 5.60230 | + | 5.60230i | 0.197948 | + | 0.197948i | ||||
\(802\) | 13.4312 | − | 13.4312i | 0.474272 | − | 0.474272i | ||||
\(803\) | −44.1040 | + | 44.1040i | −1.55640 | + | 1.55640i | ||||
\(804\) | −11.1304 | −0.392539 | ||||||||
\(805\) | −10.5642 | − | 5.90157i | −0.372338 | − | 0.208003i | ||||
\(806\) | 9.56144 | + | 9.56144i | 0.336787 | + | 0.336787i | ||||
\(807\) | 13.7722 | − | 13.7722i | 0.484805 | − | 0.484805i | ||||
\(808\) | 6.66420 | 0.234446 | ||||||||
\(809\) | 14.1279 | − | 14.1279i | 0.496711 | − | 0.496711i | −0.413701 | − | 0.910413i | \(-0.635764\pi\) |
0.910413 | + | 0.413701i | \(0.135764\pi\) | |||||||
\(810\) | −12.9229 | + | 3.65938i | −0.454066 | + | 0.128577i | ||||
\(811\) | 36.1729 | 1.27020 | 0.635102 | − | 0.772428i | \(-0.280958\pi\) | ||||
0.635102 | + | 0.772428i | \(0.280958\pi\) | |||||||
\(812\) | 11.6405 | 0.408501 | ||||||||
\(813\) | −7.34444 | − | 7.34444i | −0.257581 | − | 0.257581i | ||||
\(814\) | −18.3882 | − | 23.0848i | −0.644508 | − | 0.809123i | ||||
\(815\) | 4.54601 | + | 16.0540i | 0.159240 | + | 0.562349i | ||||
\(816\) | 1.05997 | + | 1.05997i | 0.0371064 | + | 0.0371064i | ||||
\(817\) | 2.87174 | − | 2.87174i | 0.100470 | − | 0.100470i | ||||
\(818\) | −16.9289 | − | 16.9289i | −0.591906 | − | 0.591906i | ||||
\(819\) | −5.36781 | − | 5.36781i | −0.187566 | − | 0.187566i | ||||
\(820\) | 0.888349 | − | 0.251553i | 0.0310225 | − | 0.00878462i | ||||
\(821\) | −9.97250 | −0.348043 | −0.174021 | − | 0.984742i | \(-0.555676\pi\) | ||||
−0.174021 | + | 0.984742i | \(0.555676\pi\) | |||||||
\(822\) | 27.8291 | 0.970651 | ||||||||
\(823\) | −37.3136 | + | 37.3136i | −1.30067 | + | 1.30067i | −0.372732 | + | 0.927939i | \(0.621579\pi\) |
−0.927939 | + | 0.372732i | \(0.878421\pi\) | |||||||
\(824\) | 3.38743i | 0.118007i | ||||||||
\(825\) | 8.34536 | − | 35.0872i | 0.290548 | − | 1.22158i | ||||
\(826\) | −17.8755 | −0.621970 | ||||||||
\(827\) | −20.4583 | −0.711404 | −0.355702 | − | 0.934599i | \(-0.615758\pi\) | ||||
−0.355702 | + | 0.934599i | \(0.615758\pi\) | |||||||
\(828\) | 2.48057 | 0.0862058 | ||||||||
\(829\) | −29.2865 | + | 29.2865i | −1.01716 | + | 1.01716i | −0.0173134 | + | 0.999850i | \(0.505511\pi\) |
−0.999850 | + | 0.0173134i | \(0.994489\pi\) | |||||||
\(830\) | −15.2380 | + | 27.2769i | −0.528918 | + | 0.946794i | ||||
\(831\) | −15.7230 | + | 15.7230i | −0.545426 | + | 0.545426i | ||||
\(832\) | − | 5.57745i | − | 0.193363i | ||||||
\(833\) | − | 4.06423i | − | 0.140817i | ||||||
\(834\) | 15.8764 | − | 15.8764i | 0.549754 | − | 0.549754i | ||||
\(835\) | −11.6412 | − | 41.1103i | −0.402860 | − | 1.42268i | ||||
\(836\) | −9.43199 | + | 9.43199i | −0.326212 | + | 0.326212i | ||||
\(837\) | −13.6595 | −0.472142 | ||||||||
\(838\) | 32.5124 | 1.12312 | ||||||||
\(839\) | 43.3795 | 1.49763 | 0.748814 | − | 0.662780i | \(-0.230624\pi\) | ||||
0.748814 | + | 0.662780i | \(0.230624\pi\) | |||||||
\(840\) | −1.56070 | − | 5.51154i | −0.0538492 | − | 0.190166i | ||||
\(841\) | − | 16.6340i | − | 0.573588i | ||||||
\(842\) | 18.5316 | − | 18.5316i | 0.638640 | − | 0.638640i | ||||
\(843\) | 29.1075 | 1.00252 | ||||||||
\(844\) | 10.0888 | 0.347270 | ||||||||
\(845\) | −11.0320 | − | 38.9589i | −0.379511 | − | 1.34023i | ||||
\(846\) | 6.60241 | + | 6.60241i | 0.226996 | + | 0.226996i | ||||
\(847\) | 15.2814 | + | 15.2814i | 0.525074 | + | 0.525074i | ||||
\(848\) | 3.85196 | − | 3.85196i | 0.132277 | − | 0.132277i | ||||
\(849\) | −9.54983 | − | 9.54983i | −0.327749 | − | 0.327749i | ||||
\(850\) | −2.64330 | − | 4.29310i | −0.0906644 | − | 0.147252i | ||||
\(851\) | 14.9421 | − | 11.9022i | 0.512209 | − | 0.408001i | ||||
\(852\) | −7.52141 | − | 7.52141i | −0.257679 | − | 0.257679i | ||||
\(853\) | −6.00476 | −0.205599 | −0.102800 | − | 0.994702i | \(-0.532780\pi\) | ||||
−0.102800 | + | 0.994702i | \(0.532780\pi\) | |||||||
\(854\) | −1.11552 | −0.0381723 | ||||||||
\(855\) | −4.23892 | − | 2.36803i | −0.144968 | − | 0.0809850i | ||||
\(856\) | −6.68246 | + | 6.68246i | −0.228402 | + | 0.228402i | ||||
\(857\) | 0.245134 | 0.00837363 | 0.00418681 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418681 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(858\) | 28.4478 | − | 28.4478i | 0.971191 | − | 0.971191i | ||||
\(859\) | −19.6130 | − | 19.6130i | −0.669187 | − | 0.669187i | 0.288341 | − | 0.957528i | \(-0.406896\pi\) |
−0.957528 | + | 0.288341i | \(0.906896\pi\) | |||||||
\(860\) | 3.17830 | − | 0.899997i | 0.108379 | − | 0.0306897i | ||||
\(861\) | 1.05775 | 0.0360482 | ||||||||
\(862\) | −25.9149 | + | 25.9149i | −0.882665 | + | 0.882665i | ||||
\(863\) | 34.4543 | − | 34.4543i | 1.17284 | − | 1.17284i | 0.191306 | − | 0.981530i | \(-0.438728\pi\) |
0.981530 | − | 0.191306i | \(-0.0612722\pi\) | |||||||
\(864\) | 3.98399 | + | 3.98399i | 0.135538 | + | 0.135538i | ||||
\(865\) | −23.3854 | + | 41.8612i | −0.795126 | + | 1.42332i | ||||
\(866\) | 21.8138 | + | 21.8138i | 0.741263 | + | 0.741263i | ||||
\(867\) | −16.8020 | − | 16.8020i | −0.570626 | − | 0.570626i | ||||
\(868\) | − | 4.17762i | − | 0.141798i | ||||||
\(869\) | 7.10389 | − | 7.10389i | 0.240983 | − | 0.240983i | ||||
\(870\) | −21.6068 | + | 6.11838i | −0.732539 | + | 0.207433i | ||||
\(871\) | 29.5271 | + | 29.5271i | 1.00049 | + | 1.00049i | ||||
\(872\) | 11.6763 | − | 11.6763i | 0.395410 | − | 0.395410i | ||||
\(873\) | − | 1.66063i | − | 0.0562039i | ||||||
\(874\) | −6.10505 | − | 6.10505i | −0.206506 | − | 0.206506i | ||||
\(875\) | 0.817330 | + | 19.2482i | 0.0276308 | + | 0.650709i | ||||
\(876\) | − | 19.1111i | − | 0.645704i | ||||||
\(877\) | −4.63548 | − | 4.63548i | −0.156529 | − | 0.156529i | 0.624498 | − | 0.781027i | \(-0.285304\pi\) |
−0.781027 | + | 0.624498i | \(0.785304\pi\) | |||||||
\(878\) | 12.9479 | + | 12.9479i | 0.436971 | + | 0.436971i | ||||
\(879\) | −16.3832 | −0.552591 | ||||||||
\(880\) | −10.4389 | + | 2.95597i | −0.351894 | + | 0.0996456i | ||||
\(881\) | 20.6076i | 0.694288i | 0.937812 | + | 0.347144i | \(0.112848\pi\) | ||||
−0.937812 | + | 0.347144i | \(0.887152\pi\) | |||||||
\(882\) | − | 3.18368i | − | 0.107200i | ||||||
\(883\) | −27.2177 | −0.915950 | −0.457975 | − | 0.888965i | \(-0.651425\pi\) | ||||
−0.457975 | + | 0.888965i | \(0.651425\pi\) | |||||||
\(884\) | − | 5.62386i | − | 0.189151i | ||||||
\(885\) | 33.1801 | − | 9.39559i | 1.11534 | − | 0.315829i | ||||
\(886\) | 2.00074 | − | 2.00074i | 0.0672161 | − | 0.0672161i | ||||
\(887\) | −10.8845 | + | 10.8845i | −0.365465 | + | 0.365465i | −0.865820 | − | 0.500355i | \(-0.833203\pi\) |
0.500355 | + | 0.865820i | \(0.333203\pi\) | |||||||
\(888\) | 8.98554 | + | 1.01756i | 0.301535 | + | 0.0341471i | ||||
\(889\) | 21.1853i | 0.710533i | ||||||||
\(890\) | 10.9388 | − | 19.5811i | 0.366670 | − | 0.656361i | ||||
\(891\) | 29.1436i | 0.976346i | ||||||||
\(892\) | −2.45704 | + | 2.45704i | −0.0822679 | + | 0.0822679i | ||||
\(893\) | − | 32.4990i | − | 1.08754i | ||||||
\(894\) | 22.3866 | + | 22.3866i | 0.748720 | + | 0.748720i | ||||
\(895\) | −25.8663 | − | 14.4500i | −0.864614 | − | 0.483009i | ||||
\(896\) | −1.21846 | + | 1.21846i | −0.0407060 | + | 0.0407060i | ||||
\(897\) | 18.4134 | + | 18.4134i | 0.614806 | + | 0.614806i | ||||
\(898\) | −17.2995 | + | 17.2995i | −0.577291 | + | 0.577291i | ||||
\(899\) | −16.3775 | −0.546219 | ||||||||
\(900\) | −2.07060 | − | 3.36296i | −0.0690201 | − | 0.112099i | ||||
\(901\) | 3.88401 | − | 3.88401i | 0.129395 | − | 0.129395i | ||||
\(902\) | − | 2.00339i | − | 0.0667055i | ||||||
\(903\) | 3.78439 | 0.125937 | ||||||||
\(904\) | − | 4.19525i | − | 0.139532i | ||||||
\(905\) | −7.10501 | − | 25.0910i | −0.236178 | − | 0.834054i | ||||
\(906\) | 6.00949 | + | 6.00949i | 0.199652 | + | 0.199652i | ||||
\(907\) | 35.7043 | 1.18554 | 0.592771 | − | 0.805371i | \(-0.298034\pi\) | ||||
0.592771 | + | 0.805371i | \(0.298034\pi\) | |||||||
\(908\) | 19.5967 | 0.650340 | ||||||||
\(909\) | 5.26377 | 0.174588 | ||||||||
\(910\) | −10.4809 | + | 18.7615i | −0.347440 | + | 0.621938i | ||||
\(911\) | −29.2800 | + | 29.2800i | −0.970091 | + | 0.970091i | −0.999566 | − | 0.0294748i | \(-0.990617\pi\) |
0.0294748 | + | 0.999566i | \(0.490617\pi\) | |||||||
\(912\) | − | 4.08706i | − | 0.135336i | ||||||
\(913\) | 47.9393 | + | 47.9393i | 1.58656 | + | 1.58656i | ||||
\(914\) | − | 24.4123i | − | 0.807486i | ||||||
\(915\) | 2.07060 | − | 0.586331i | 0.0684520 | − | 0.0193835i | ||||
\(916\) | 8.54964i | 0.282488i | ||||||||
\(917\) | 19.4130i | 0.641075i | ||||||||
\(918\) | 4.01713 | + | 4.01713i | 0.132585 | + | 0.132585i | ||||
\(919\) | −22.4493 | + | 22.4493i | −0.740535 | + | 0.740535i | −0.972681 | − | 0.232146i | \(-0.925425\pi\) |
0.232146 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(920\) | −1.91331 | − | 6.75677i | −0.0630799 | − | 0.222764i | ||||
\(921\) | 5.83485 | 0.192265 | ||||||||
\(922\) | −14.1676 | − | 14.1676i | −0.466587 | − | 0.466587i | ||||
\(923\) | 39.9062i | 1.31353i | ||||||||
\(924\) | −12.4295 | −0.408901 | ||||||||
\(925\) | −28.6086 | − | 10.3222i | −0.940645 | − | 0.339393i | ||||
\(926\) | −9.45035 | −0.310558 | ||||||||
\(927\) | 2.67559i | 0.0878778i | ||||||||
\(928\) | 4.77672 | + | 4.77672i | 0.156803 | + | 0.156803i | ||||
\(929\) | 49.8210 | 1.63457 | 0.817286 | − | 0.576232i | \(-0.195477\pi\) | ||||
0.817286 | + | 0.576232i | \(0.195477\pi\) | |||||||
\(930\) | 2.19581 | + | 7.75441i | 0.0720034 | + | 0.254277i | ||||
\(931\) | −7.83550 | + | 7.83550i | −0.256798 | + | 0.256798i | ||||
\(932\) | 18.6855 | + | 18.6855i | 0.612065 | + | 0.612065i | ||||
\(933\) | − | 4.94050i | − | 0.161745i | ||||||
\(934\) | 5.91129i | 0.193423i | ||||||||
\(935\) | −10.5257 | + | 2.98056i | −0.344228 | + | 0.0974747i | ||||
\(936\) | − | 4.40539i | − | 0.143995i | ||||||
\(937\) | −2.85125 | − | 2.85125i | −0.0931464 | − | 0.0931464i | 0.658998 | − | 0.752145i | \(-0.270980\pi\) |
−0.752145 | + | 0.658998i | \(0.770980\pi\) | |||||||
\(938\) | − | 12.9011i | − | 0.421236i | ||||||
\(939\) | 11.4561 | − | 11.4561i | 0.373855 | − | 0.373855i | ||||
\(940\) | 12.8916 | − | 23.0767i | 0.420477 | − | 0.752679i | ||||
\(941\) | 45.3259 | 1.47758 | 0.738792 | − | 0.673934i | \(-0.235397\pi\) | ||||
0.738792 | + | 0.673934i | \(0.235397\pi\) | |||||||
\(942\) | −9.89733 | −0.322473 | ||||||||
\(943\) | 1.29673 | 0.0422275 | ||||||||
\(944\) | −7.33529 | − | 7.33529i | −0.238743 | − | 0.238743i | ||||
\(945\) | −5.91483 | − | 20.8880i | −0.192409 | − | 0.679485i | ||||
\(946\) | − | 7.16765i | − | 0.233040i | ||||||
\(947\) | 35.8239 | 1.16412 | 0.582060 | − | 0.813146i | \(-0.302247\pi\) | ||||
0.582060 | + | 0.813146i | \(0.302247\pi\) | |||||||
\(948\) | 3.07825i | 0.0999769i | ||||||||
\(949\) | −50.6987 | + | 50.6987i | −1.64575 | + | 1.64575i | ||||
\(950\) | −3.18067 | + | 13.3728i | −0.103195 | + | 0.433870i | ||||
\(951\) | 2.19180 | 0.0710741 | ||||||||
\(952\) | −1.22860 | + | 1.22860i | −0.0398191 | + | 0.0398191i | ||||
\(953\) | −38.2197 | − | 38.2197i | −1.23806 | − | 1.23806i | −0.960794 | − | 0.277263i | \(-0.910573\pi\) |
−0.277263 | − | 0.960794i | \(-0.589427\pi\) | |||||||
\(954\) | 3.04250 | − | 3.04250i | 0.0985046 | − | 0.0985046i | ||||
\(955\) | 48.6860 | + | 27.1980i | 1.57544 | + | 0.880107i | ||||
\(956\) | 14.5251 | + | 14.5251i | 0.469775 | + | 0.469775i | ||||
\(957\) | 48.7273i | 1.57513i | ||||||||
\(958\) | −15.1619 | + | 15.1619i | −0.489858 | + | 0.489858i | ||||
\(959\) | 32.2564i | 1.04161i | ||||||||
\(960\) | 1.62124 | − | 2.90212i | 0.0523253 | − | 0.0936654i | ||||
\(961\) | − | 25.1223i | − | 0.810398i | ||||||
\(962\) | −21.1378 | − | 26.5366i | −0.681509 | − | 0.855574i | ||||
\(963\) | −5.27819 | + | 5.27819i | −0.170087 | + | 0.170087i | ||||
\(964\) | 8.39707 | − | 8.39707i | 0.270452 | − | 0.270452i | ||||
\(965\) | −29.1841 | + | 8.26403i | −0.939469 | + | 0.266029i | ||||
\(966\) | − | 8.04526i | − | 0.258852i | ||||||
\(967\) | −12.1533 | −0.390823 | −0.195411 | − | 0.980721i | \(-0.562604\pi\) | ||||
−0.195411 | + | 0.980721i | \(0.562604\pi\) | |||||||
\(968\) | 12.5415i | 0.403100i | ||||||||
\(969\) | − | 4.12107i | − | 0.132388i | ||||||
\(970\) | −4.52336 | + | 1.28088i | −0.145236 | + | 0.0411265i | ||||
\(971\) | 17.0273 | 0.546432 | 0.273216 | − | 0.961953i | \(-0.411913\pi\) | ||||
0.273216 | + | 0.961953i | \(0.411913\pi\) | |||||||
\(972\) | 5.63773 | + | 5.63773i | 0.180830 | + | 0.180830i | ||||
\(973\) | 18.4021 | + | 18.4021i | 0.589946 | + | 0.589946i | ||||
\(974\) | − | 21.5964i | − | 0.691992i | ||||||
\(975\) | 9.59321 | − | 40.3336i | 0.307229 | − | 1.29171i | ||||
\(976\) | −0.457758 | − | 0.457758i | −0.0146525 | − | 0.0146525i | ||||
\(977\) | − | 51.9854i | − | 1.66316i | −0.555405 | − | 0.831580i | \(-0.687437\pi\) | ||
0.555405 | − | 0.831580i | \(-0.312563\pi\) | |||||||
\(978\) | −7.84411 | + | 7.84411i | −0.250827 | + | 0.250827i | ||||
\(979\) | −34.4140 | − | 34.4140i | −1.09988 | − | 1.09988i | ||||
\(980\) | −8.67194 | + | 2.45563i | −0.277015 | + | 0.0784422i | ||||
\(981\) | 9.22263 | − | 9.22263i | 0.294456 | − | 0.294456i | ||||
\(982\) | 36.1012i | 1.15204i | ||||||||
\(983\) | 29.0021 | + | 29.0021i | 0.925025 | + | 0.925025i | 0.997379 | − | 0.0723544i | \(-0.0230513\pi\) |
−0.0723544 | + | 0.997379i | \(0.523051\pi\) | |||||||
\(984\) | 0.434053 | + | 0.434053i | 0.0138371 | + | 0.0138371i | ||||
\(985\) | −26.0283 | + | 46.5922i | −0.829331 | + | 1.48455i | ||||
\(986\) | 4.81646 | + | 4.81646i | 0.153387 | + | 0.153387i | ||||
\(987\) | 21.4137 | − | 21.4137i | 0.681605 | − | 0.681605i | ||||
\(988\) | −10.8423 | + | 10.8423i | −0.344940 | + | 0.344940i | ||||
\(989\) | 4.63940 | 0.147524 | ||||||||
\(990\) | −8.24522 | + | 2.33479i | −0.262050 | + | 0.0742045i | ||||
\(991\) | −33.1692 | − | 33.1692i | −1.05366 | − | 1.05366i | −0.998476 | − | 0.0551795i | \(-0.982427\pi\) |
−0.0551795 | − | 0.998476i | \(-0.517573\pi\) | |||||||
\(992\) | 1.71430 | − | 1.71430i | 0.0544292 | − | 0.0544292i | ||||
\(993\) | 32.4643 | 1.03022 | ||||||||
\(994\) | 8.71798 | − | 8.71798i | 0.276518 | − | 0.276518i | ||||
\(995\) | −25.2063 | − | 14.0813i | −0.799094 | − | 0.446407i | ||||
\(996\) | −20.7730 | −0.658218 | ||||||||
\(997\) | 15.7013 | 0.497264 | 0.248632 | − | 0.968598i | \(-0.420019\pi\) | ||||
0.248632 | + | 0.968598i | \(0.420019\pi\) | |||||||
\(998\) | −8.86811 | − | 8.86811i | −0.280715 | − | 0.280715i | ||||
\(999\) | 34.0539 | + | 3.85640i | 1.07742 | + | 0.122011i |
(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 | 370.2.g.d.327.4 | yes | 10 | |
5.3 | odd | 4 | 370.2.h.d.253.2 | yes | 10 | ||
37.6 | odd | 4 | 370.2.h.d.117.2 | yes | 10 | ||
185.43 | even | 4 | inner | 370.2.g.d.43.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.d.43.4 | ✓ | 10 | 185.43 | even | 4 | inner | |
370.2.g.d.327.4 | yes | 10 | 1.1 | even | 1 | trivial | |
370.2.h.d.117.2 | yes | 10 | 37.6 | odd | 4 | ||
370.2.h.d.253.2 | yes | 10 | 5.3 | odd | 4 |