Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(146,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(1.20036 - 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.191 |
Dual form | 845.2.e.m.146.1 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24775 | + | 2.16117i | −0.882295 | + | 1.52818i | −0.0335125 | + | 0.999438i | \(0.510669\pi\) |
−0.848783 | + | 0.528742i | \(0.822664\pi\) | |||||||
\(3\) | 1.41342 | − | 2.44811i | 0.816038 | − | 1.41342i | −0.0925423 | − | 0.995709i | \(-0.529499\pi\) |
0.908580 | − | 0.417710i | \(-0.137167\pi\) | |||||||
\(4\) | −2.11378 | − | 3.66117i | −1.05689 | − | 1.83059i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.52720 | + | 6.10929i | 1.43997 | + | 2.49411i | ||||
\(7\) | −0.952606 | − | 1.64996i | −0.360051 | − | 0.623627i | 0.627918 | − | 0.778280i | \(-0.283907\pi\) |
−0.987969 | + | 0.154653i | \(0.950574\pi\) | |||||||
\(8\) | 5.55889 | 1.96536 | ||||||||
\(9\) | −2.49551 | − | 4.32235i | −0.831836 | − | 1.44078i | ||||
\(10\) | 1.24775 | − | 2.16117i | 0.394574 | − | 0.683423i | ||||
\(11\) | −0.534695 | + | 0.926118i | −0.161217 | + | 0.279235i | −0.935305 | − | 0.353842i | \(-0.884875\pi\) |
0.774089 | + | 0.633077i | \(0.218208\pi\) | |||||||
\(12\) | −11.9506 | −3.44985 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.75447 | 1.27069 | ||||||||
\(15\) | −1.41342 | + | 2.44811i | −0.364943 | + | 0.632100i | ||||
\(16\) | −2.70857 | + | 4.69138i | −0.677142 | + | 1.17284i | ||||
\(17\) | −0.318632 | − | 0.551886i | −0.0772795 | − | 0.133852i | 0.824796 | − | 0.565431i | \(-0.191290\pi\) |
−0.902075 | + | 0.431579i | \(0.857957\pi\) | |||||||
\(18\) | 12.4551 | 2.93570 | ||||||||
\(19\) | −2.86603 | − | 4.96410i | −0.657511 | − | 1.13884i | −0.981258 | − | 0.192699i | \(-0.938276\pi\) |
0.323747 | − | 0.946144i | \(-0.395057\pi\) | |||||||
\(20\) | 2.11378 | + | 3.66117i | 0.472655 | + | 0.818663i | ||||
\(21\) | −5.38573 | −1.17526 | ||||||||
\(22\) | −1.33433 | − | 2.31114i | −0.284481 | − | 0.492736i | ||||
\(23\) | −1.90893 | + | 3.30636i | −0.398039 | + | 0.689423i | −0.993484 | − | 0.113973i | \(-0.963642\pi\) |
0.595445 | + | 0.803396i | \(0.296976\pi\) | |||||||
\(24\) | 7.85704 | − | 13.6088i | 1.60381 | − | 2.77788i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62828 | −1.08316 | ||||||||
\(28\) | −4.02720 | + | 6.97531i | −0.761069 | + | 1.31821i | ||||
\(29\) | −4.72756 | + | 8.18837i | −0.877886 | + | 1.52054i | −0.0242288 | + | 0.999706i | \(0.507713\pi\) |
−0.853657 | + | 0.520836i | \(0.825620\pi\) | |||||||
\(30\) | −3.52720 | − | 6.10929i | −0.643975 | − | 1.11540i | ||||
\(31\) | −1.46410 | −0.262960 | −0.131480 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131480 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(32\) | −1.20036 | − | 2.07908i | −0.212196 | − | 0.367534i | ||||
\(33\) | 1.51150 | + | 2.61799i | 0.263118 | + | 0.455733i | ||||
\(34\) | 1.59030 | 0.272733 | ||||||||
\(35\) | 0.952606 | + | 1.64996i | 0.161020 | + | 0.278895i | ||||
\(36\) | −10.5499 | + | 18.2730i | −1.75832 | + | 3.04550i | ||||
\(37\) | −0.378725 | + | 0.655970i | −0.0622619 | + | 0.107841i | −0.895476 | − | 0.445110i | \(-0.853165\pi\) |
0.833214 | + | 0.552950i | \(0.186498\pi\) | |||||||
\(38\) | 14.3044 | 2.32048 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.55889 | −0.878938 | ||||||||
\(41\) | −0.133975 | + | 0.232051i | −0.0209233 | + | 0.0362402i | −0.876297 | − | 0.481770i | \(-0.839994\pi\) |
0.855374 | + | 0.518011i | \(0.173327\pi\) | |||||||
\(42\) | 6.72006 | − | 11.6395i | 1.03693 | − | 1.79601i | ||||
\(43\) | −0.318632 | − | 0.551886i | −0.0485909 | − | 0.0841618i | 0.840707 | − | 0.541490i | \(-0.182140\pi\) |
−0.889298 | + | 0.457328i | \(0.848806\pi\) | |||||||
\(44\) | 4.52091 | 0.681552 | ||||||||
\(45\) | 2.49551 | + | 4.32235i | 0.372008 | + | 0.644337i | ||||
\(46\) | −4.76374 | − | 8.25104i | −0.702375 | − | 1.21655i | ||||
\(47\) | −9.44613 | −1.37786 | −0.688930 | − | 0.724828i | \(-0.741919\pi\) | ||||
−0.688930 | + | 0.724828i | \(0.741919\pi\) | |||||||
\(48\) | 7.65668 | + | 13.2618i | 1.10515 | + | 1.91417i | ||||
\(49\) | 1.68508 | − | 2.91865i | 0.240726 | − | 0.416950i | ||||
\(50\) | −1.24775 | + | 2.16117i | −0.176459 | + | 0.305636i | ||||
\(51\) | −1.80144 | −0.252252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.99102 | −0.960290 | −0.480145 | − | 0.877189i | \(-0.659416\pi\) | ||||
−0.480145 | + | 0.877189i | \(0.659416\pi\) | |||||||
\(54\) | 7.02271 | − | 12.1637i | 0.955669 | − | 1.65527i | ||||
\(55\) | 0.534695 | − | 0.926118i | 0.0720982 | − | 0.124878i | ||||
\(56\) | −5.29543 | − | 9.17196i | −0.707632 | − | 1.22565i | ||||
\(57\) | −16.2036 | −2.14622 | ||||||||
\(58\) | −11.7977 | − | 20.4341i | −1.54911 | − | 2.68313i | ||||
\(59\) | −0.370518 | − | 0.641756i | −0.0482373 | − | 0.0835495i | 0.840899 | − | 0.541193i | \(-0.182027\pi\) |
−0.889136 | + | 0.457643i | \(0.848694\pi\) | |||||||
\(60\) | 11.9506 | 1.54282 | ||||||||
\(61\) | −2.09928 | − | 3.63606i | −0.268785 | − | 0.465550i | 0.699763 | − | 0.714375i | \(-0.253289\pi\) |
−0.968548 | + | 0.248825i | \(0.919956\pi\) | |||||||
\(62\) | 1.82684 | − | 3.16418i | 0.232009 | − | 0.401851i | ||||
\(63\) | −4.75447 | + | 8.23499i | −0.599007 | + | 1.03751i | ||||
\(64\) | −4.84325 | −0.605406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.54390 | −0.928589 | ||||||||
\(67\) | −4.04739 | + | 7.01029i | −0.494468 | + | 0.856443i | −0.999980 | − | 0.00637624i | \(-0.997970\pi\) |
0.505512 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(68\) | −1.34703 | + | 2.33313i | −0.163352 | + | 0.282934i | ||||
\(69\) | 5.39623 | + | 9.34654i | 0.649629 | + | 1.12519i | ||||
\(70\) | −4.75447 | −0.568268 | ||||||||
\(71\) | −4.88244 | − | 8.45663i | −0.579439 | − | 1.00362i | −0.995544 | − | 0.0943010i | \(-0.969938\pi\) |
0.416105 | − | 0.909317i | \(-0.363395\pi\) | |||||||
\(72\) | −13.8723 | − | 24.0274i | −1.63486 | − | 2.83166i | ||||
\(73\) | −3.71649 | −0.434982 | −0.217491 | − | 0.976062i | \(-0.569787\pi\) | ||||
−0.217491 | + | 0.976062i | \(0.569787\pi\) | |||||||
\(74\) | −0.945110 | − | 1.63698i | −0.109867 | − | 0.190295i | ||||
\(75\) | 1.41342 | − | 2.44811i | 0.163208 | − | 0.282684i | ||||
\(76\) | −12.1163 | + | 20.9860i | −1.38983 | + | 2.40726i | ||||
\(77\) | 2.03741 | 0.232185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.31937 | −1.04851 | −0.524255 | − | 0.851561i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851561i | \(0.675656\pi\) | |||||||
\(80\) | 2.70857 | − | 4.69138i | 0.302827 | − | 0.524512i | ||||
\(81\) | −0.468594 | + | 0.811629i | −0.0520660 | + | 0.0901809i | ||||
\(82\) | −0.334335 | − | 0.579085i | −0.0369211 | − | 0.0639492i | ||||
\(83\) | 5.11778 | 0.561749 | 0.280875 | − | 0.959744i | \(-0.409376\pi\) | ||||
0.280875 | + | 0.959744i | \(0.409376\pi\) | |||||||
\(84\) | 11.3842 | + | 19.7181i | 1.24212 | + | 2.15142i | ||||
\(85\) | 0.318632 | + | 0.551886i | 0.0345605 | + | 0.0598605i | ||||
\(86\) | 1.59030 | 0.171486 | ||||||||
\(87\) | 13.3640 | + | 23.1472i | 1.43278 | + | 2.48164i | ||||
\(88\) | −2.97231 | + | 5.14819i | −0.316849 | + | 0.548799i | ||||
\(89\) | 6.28917 | − | 10.8932i | 0.666650 | − | 1.15467i | −0.312185 | − | 0.950021i | \(-0.601061\pi\) |
0.978835 | − | 0.204651i | \(-0.0656059\pi\) | |||||||
\(90\) | −12.4551 | −1.31288 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.1402 | 1.68273 | ||||||||
\(93\) | −2.06939 | + | 3.58429i | −0.214586 | + | 0.371673i | ||||
\(94\) | 11.7864 | − | 20.4147i | 1.21568 | − | 2.10562i | ||||
\(95\) | 2.86603 | + | 4.96410i | 0.294048 | + | 0.509306i | ||||
\(96\) | −6.78645 | −0.692639 | ||||||||
\(97\) | 2.11078 | + | 3.65597i | 0.214317 | + | 0.371208i | 0.953061 | − | 0.302778i | \(-0.0979142\pi\) |
−0.738744 | + | 0.673986i | \(0.764581\pi\) | |||||||
\(98\) | 4.20514 | + | 7.28351i | 0.424783 | + | 0.735746i | ||||
\(99\) | 5.33734 | 0.536423 | ||||||||
\(100\) | −2.11378 | − | 3.66117i | −0.211378 | − | 0.366117i | ||||
\(101\) | 7.62379 | − | 13.2048i | 0.758595 | − | 1.31393i | −0.184972 | − | 0.982744i | \(-0.559219\pi\) |
0.943567 | − | 0.331181i | \(-0.107447\pi\) | |||||||
\(102\) | 2.24775 | − | 3.89322i | 0.222561 | − | 0.385487i | ||||
\(103\) | −13.5269 | −1.33285 | −0.666423 | − | 0.745574i | \(-0.732176\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732176\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.38573 | 0.525593 | ||||||||
\(106\) | 8.72307 | − | 15.1088i | 0.847259 | − | 1.46750i | ||||
\(107\) | 3.68137 | − | 6.37632i | 0.355891 | − | 0.616422i | −0.631379 | − | 0.775475i | \(-0.717511\pi\) |
0.987270 | + | 0.159053i | \(0.0508440\pi\) | |||||||
\(108\) | 11.8969 | + | 20.6061i | 1.14478 | + | 1.98282i | ||||
\(109\) | 10.0760 | 0.965103 | 0.482551 | − | 0.875868i | \(-0.339710\pi\) | ||||
0.482551 | + | 0.875868i | \(0.339710\pi\) | |||||||
\(110\) | 1.33433 | + | 2.31114i | 0.127224 | + | 0.220358i | ||||
\(111\) | 1.07059 | + | 1.85432i | 0.101616 | + | 0.176004i | ||||
\(112\) | 10.3208 | 0.975223 | ||||||||
\(113\) | 3.34403 | + | 5.79203i | 0.314580 | + | 0.544868i | 0.979348 | − | 0.202181i | \(-0.0648030\pi\) |
−0.664768 | + | 0.747050i | \(0.731470\pi\) | |||||||
\(114\) | 20.2181 | − | 35.0187i | 1.89360 | − | 3.27981i | ||||
\(115\) | 1.90893 | − | 3.30636i | 0.178008 | − | 0.308320i | ||||
\(116\) | 39.9721 | 3.71131 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.84926 | 0.170238 | ||||||||
\(119\) | −0.607061 | + | 1.05146i | −0.0556492 | + | 0.0963872i | ||||
\(120\) | −7.85704 | + | 13.6088i | −0.717246 | + | 1.24231i | ||||
\(121\) | 4.92820 | + | 8.53590i | 0.448018 | + | 0.775991i | ||||
\(122\) | 10.4775 | 0.948592 | ||||||||
\(123\) | 0.378725 | + | 0.655970i | 0.0341484 | + | 0.0591468i | ||||
\(124\) | 3.09479 | + | 5.36033i | 0.277920 | + | 0.481372i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −11.8648 | − | 20.5505i | −1.05700 | − | 1.83078i | ||||
\(127\) | −0.744750 | + | 1.28994i | −0.0660859 | + | 0.114464i | −0.897175 | − | 0.441675i | \(-0.854384\pi\) |
0.831089 | + | 0.556139i | \(0.187718\pi\) | |||||||
\(128\) | 8.44391 | − | 14.6253i | 0.746343 | − | 1.29270i | ||||
\(129\) | −1.80144 | −0.158608 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.12676 | 0.360557 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(132\) | 6.38994 | − | 11.0677i | 0.556172 | − | 0.963319i | ||||
\(133\) | −5.46039 | + | 9.45767i | −0.473476 | + | 0.820084i | ||||
\(134\) | −10.1003 | − | 17.4942i | −0.872533 | − | 1.51127i | ||||
\(135\) | 5.62828 | 0.484405 | ||||||||
\(136\) | −1.77124 | − | 3.06787i | −0.151882 | − | 0.263068i | ||||
\(137\) | 10.0548 | + | 17.4155i | 0.859041 | + | 1.48790i | 0.872844 | + | 0.487999i | \(0.162273\pi\) |
−0.0138029 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(138\) | −26.9327 | −2.29266 | ||||||||
\(139\) | −10.4126 | − | 18.0352i | −0.883189 | − | 1.52973i | −0.847776 | − | 0.530355i | \(-0.822059\pi\) |
−0.0354130 | − | 0.999373i | \(-0.511275\pi\) | |||||||
\(140\) | 4.02720 | − | 6.97531i | 0.340360 | − | 0.589521i | ||||
\(141\) | −13.3513 | + | 23.1252i | −1.12439 | + | 1.94749i | ||||
\(142\) | 24.3683 | 2.04494 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 27.0370 | 2.25308 | ||||||||
\(145\) | 4.72756 | − | 8.18837i | 0.392602 | − | 0.680007i | ||||
\(146\) | 4.63726 | − | 8.03198i | 0.383783 | − | 0.664731i | ||||
\(147\) | −4.76346 | − | 8.25055i | −0.392883 | − | 0.680494i | ||||
\(148\) | 3.20216 | 0.263216 | ||||||||
\(149\) | −6.68388 | − | 11.5768i | −0.547565 | − | 0.948410i | −0.998441 | − | 0.0558233i | \(-0.982222\pi\) |
0.450876 | − | 0.892587i | \(-0.351112\pi\) | |||||||
\(150\) | 3.52720 | + | 6.10929i | 0.287995 | + | 0.498821i | ||||
\(151\) | 18.2984 | 1.48910 | 0.744550 | − | 0.667567i | \(-0.232664\pi\) | ||||
0.744550 | + | 0.667567i | \(0.232664\pi\) | |||||||
\(152\) | −15.9319 | − | 27.5949i | −1.29225 | − | 2.23824i | ||||
\(153\) | −1.59030 | + | 2.75447i | −0.128568 | + | 0.222686i | ||||
\(154\) | −2.54219 | + | 4.40320i | −0.204856 | + | 0.354820i | ||||
\(155\) | 1.46410 | 0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.42229 | 0.193320 | 0.0966599 | − | 0.995317i | \(-0.469184\pi\) | ||||
0.0966599 | + | 0.995317i | \(0.469184\pi\) | |||||||
\(158\) | 11.6283 | − | 20.1408i | 0.925096 | − | 1.60231i | ||||
\(159\) | −9.88124 | + | 17.1148i | −0.783633 | + | 1.35729i | ||||
\(160\) | 1.20036 | + | 2.07908i | 0.0948968 | + | 0.164366i | ||||
\(161\) | 7.27382 | 0.573258 | ||||||||
\(162\) | −1.16938 | − | 2.02543i | −0.0918752 | − | 0.159132i | ||||
\(163\) | −7.99144 | − | 13.8416i | −0.625938 | − | 1.08416i | −0.988359 | − | 0.152142i | \(-0.951383\pi\) |
0.362421 | − | 0.932015i | \(-0.381950\pi\) | |||||||
\(164\) | 1.13277 | 0.0884545 | ||||||||
\(165\) | −1.51150 | − | 2.61799i | −0.117670 | − | 0.203810i | ||||
\(166\) | −6.38573 | + | 11.0604i | −0.495629 | + | 0.858454i | ||||
\(167\) | 7.19658 | − | 12.4648i | 0.556888 | − | 0.964558i | −0.440866 | − | 0.897573i | \(-0.645329\pi\) |
0.997754 | − | 0.0669853i | \(-0.0213381\pi\) | |||||||
\(168\) | −29.9387 | −2.30982 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.59030 | −0.121970 | ||||||||
\(171\) | −14.3044 | + | 24.7759i | −1.09388 | + | 1.89466i | ||||
\(172\) | −1.34703 | + | 2.33313i | −0.102710 | + | 0.177900i | ||||
\(173\) | 12.1745 | + | 21.0868i | 0.925608 | + | 1.60320i | 0.790581 | + | 0.612358i | \(0.209779\pi\) |
0.135027 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(174\) | −66.7001 | −5.05653 | ||||||||
\(175\) | −0.952606 | − | 1.64996i | −0.0720103 | − | 0.124725i | ||||
\(176\) | −2.89651 | − | 5.01691i | −0.218333 | − | 0.378164i | ||||
\(177\) | −2.09479 | −0.157454 | ||||||||
\(178\) | 15.6947 | + | 27.1840i | 1.17636 | + | 2.03752i | ||||
\(179\) | −1.89414 | + | 3.28075i | −0.141575 | + | 0.245215i | −0.928090 | − | 0.372356i | \(-0.878550\pi\) |
0.786515 | + | 0.617571i | \(0.211883\pi\) | |||||||
\(180\) | 10.5499 | − | 18.2730i | 0.786343 | − | 1.36199i | ||||
\(181\) | −8.48794 | −0.630904 | −0.315452 | − | 0.948942i | \(-0.602156\pi\) | ||||
−0.315452 | + | 0.948942i | \(0.602156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.8687 | −0.877356 | ||||||||
\(184\) | −10.6115 | + | 18.3797i | −0.782291 | + | 1.35497i | ||||
\(185\) | 0.378725 | − | 0.655970i | 0.0278444 | − | 0.0482279i | ||||
\(186\) | −5.16418 | − | 8.94462i | −0.378656 | − | 0.655851i | ||||
\(187\) | 0.681482 | 0.0498349 | ||||||||
\(188\) | 19.9670 | + | 34.5839i | 1.45625 | + | 2.52229i | ||||
\(189\) | 5.36153 | + | 9.28645i | 0.389994 | + | 0.675490i | ||||
\(190\) | −14.3044 | −1.03775 | ||||||||
\(191\) | 2.72155 | + | 4.71386i | 0.196924 | + | 0.341083i | 0.947530 | − | 0.319668i | \(-0.103571\pi\) |
−0.750605 | + | 0.660751i | \(0.770238\pi\) | |||||||
\(192\) | −6.84555 | + | 11.8568i | −0.494035 | + | 0.855693i | ||||
\(193\) | −6.07880 | + | 10.5288i | −0.437562 | + | 0.757879i | −0.997501 | − | 0.0706548i | \(-0.977491\pi\) |
0.559939 | + | 0.828534i | \(0.310824\pi\) | |||||||
\(194\) | −10.5349 | −0.756363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.2476 | −1.01768 | ||||||||
\(197\) | 2.18915 | − | 3.79172i | 0.155970 | − | 0.270149i | −0.777442 | − | 0.628955i | \(-0.783483\pi\) |
0.933412 | + | 0.358807i | \(0.116816\pi\) | |||||||
\(198\) | −6.65968 | + | 11.5349i | −0.473283 | + | 0.819751i | ||||
\(199\) | −10.4186 | − | 18.0456i | −0.738558 | − | 1.27922i | −0.953144 | − | 0.302516i | \(-0.902174\pi\) |
0.214586 | − | 0.976705i | \(-0.431160\pi\) | |||||||
\(200\) | 5.55889 | 0.393073 | ||||||||
\(201\) | 11.4413 | + | 19.8170i | 0.807009 | + | 1.39778i | ||||
\(202\) | 19.0252 | + | 32.9526i | 1.33861 | + | 2.31854i | ||||
\(203\) | 18.0140 | 1.26434 | ||||||||
\(204\) | 3.80785 | + | 6.59538i | 0.266603 | + | 0.461769i | ||||
\(205\) | 0.133975 | − | 0.232051i | 0.00935719 | − | 0.0162071i | ||||
\(206\) | 16.8783 | − | 29.2340i | 1.17596 | − | 2.03683i | ||||
\(207\) | 19.0550 | 1.32441 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.12979 | 0.424007 | ||||||||
\(210\) | −6.72006 | + | 11.6395i | −0.463728 | + | 0.803201i | ||||
\(211\) | 5.32684 | − | 9.22635i | 0.366715 | − | 0.635168i | −0.622335 | − | 0.782751i | \(-0.713816\pi\) |
0.989050 | + | 0.147583i | \(0.0471492\pi\) | |||||||
\(212\) | 14.7775 | + | 25.5953i | 1.01492 | + | 1.75789i | ||||
\(213\) | −27.6037 | −1.89138 | ||||||||
\(214\) | 9.18688 | + | 15.9121i | 0.628002 | + | 1.08773i | ||||
\(215\) | 0.318632 | + | 0.551886i | 0.0217305 | + | 0.0376383i | ||||
\(216\) | −31.2870 | −2.12881 | ||||||||
\(217\) | 1.39471 | + | 2.41571i | 0.0946792 | + | 0.163989i | ||||
\(218\) | −12.5723 | + | 21.7759i | −0.851505 | + | 1.47485i | ||||
\(219\) | −5.25296 | + | 9.09839i | −0.354962 | + | 0.614812i | ||||
\(220\) | −4.52091 | −0.304799 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.34335 | −0.358622 | ||||||||
\(223\) | −10.6697 | + | 18.4804i | −0.714494 | + | 1.23754i | 0.248661 | + | 0.968591i | \(0.420010\pi\) |
−0.963155 | + | 0.268949i | \(0.913324\pi\) | |||||||
\(224\) | −2.28694 | + | 3.96110i | −0.152803 | + | 0.264662i | ||||
\(225\) | −2.49551 | − | 4.32235i | −0.166367 | − | 0.288156i | ||||
\(226\) | −16.6901 | −1.11021 | ||||||||
\(227\) | −7.84283 | − | 13.5842i | −0.520547 | − | 0.901613i | −0.999715 | − | 0.0238900i | \(-0.992395\pi\) |
0.479168 | − | 0.877723i | \(-0.340938\pi\) | |||||||
\(228\) | 34.2508 | + | 59.3241i | 2.26831 | + | 3.92884i | ||||
\(229\) | −7.62085 | −0.503600 | −0.251800 | − | 0.967779i | \(-0.581023\pi\) | ||||
−0.251800 | + | 0.967779i | \(0.581023\pi\) | |||||||
\(230\) | 4.76374 | + | 8.25104i | 0.314112 | + | 0.544058i | ||||
\(231\) | 2.87972 | − | 4.98782i | 0.189472 | − | 0.328175i | ||||
\(232\) | −26.2800 | + | 45.5182i | −1.72536 | + | 2.98842i | ||||
\(233\) | −19.0550 | −1.24833 | −0.624166 | − | 0.781292i | \(-0.714561\pi\) | ||||
−0.624166 | + | 0.781292i | \(0.714561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.44613 | 0.616198 | ||||||||
\(236\) | −1.56639 | + | 2.71306i | −0.101963 | + | 0.176605i | ||||
\(237\) | −13.1722 | + | 22.8149i | −0.855625 | + | 1.48199i | ||||
\(238\) | −1.51493 | − | 2.62393i | −0.0981980 | − | 0.170084i | ||||
\(239\) | 12.7535 | 0.824954 | 0.412477 | − | 0.910968i | \(-0.364664\pi\) | ||||
0.412477 | + | 0.910968i | \(0.364664\pi\) | |||||||
\(240\) | −7.65668 | − | 13.2618i | −0.494237 | − | 0.856043i | ||||
\(241\) | −12.9644 | − | 22.4550i | −0.835111 | − | 1.44646i | −0.893940 | − | 0.448187i | \(-0.852070\pi\) |
0.0588285 | − | 0.998268i | \(-0.481263\pi\) | |||||||
\(242\) | −24.5967 | −1.58114 | ||||||||
\(243\) | −7.11778 | − | 12.3284i | −0.456606 | − | 0.790864i | ||||
\(244\) | −8.87483 | + | 15.3717i | −0.568153 | + | 0.984069i | ||||
\(245\) | −1.68508 | + | 2.91865i | −0.107656 | + | 0.186466i | ||||
\(246\) | −1.89022 | −0.120516 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.13878 | −0.516813 | ||||||||
\(249\) | 7.23357 | − | 12.5289i | 0.458409 | − | 0.793987i | ||||
\(250\) | 1.24775 | − | 2.16117i | 0.0789149 | − | 0.136685i | ||||
\(251\) | −3.80593 | − | 6.59207i | −0.240228 | − | 0.416088i | 0.720551 | − | 0.693402i | \(-0.243889\pi\) |
−0.960779 | + | 0.277314i | \(0.910556\pi\) | |||||||
\(252\) | 40.1996 | 2.53234 | ||||||||
\(253\) | −2.04139 | − | 3.53578i | −0.128341 | − | 0.222293i | ||||
\(254\) | −1.85853 | − | 3.21907i | −0.116614 | − | 0.201982i | ||||
\(255\) | 1.80144 | 0.112811 | ||||||||
\(256\) | 16.2286 | + | 28.1087i | 1.01429 | + | 1.75680i | ||||
\(257\) | −0.167891 | + | 0.290796i | −0.0104728 | + | 0.0181394i | −0.871214 | − | 0.490903i | \(-0.836667\pi\) |
0.860742 | + | 0.509042i | \(0.170000\pi\) | |||||||
\(258\) | 2.24775 | − | 3.89322i | 0.139939 | − | 0.242382i | ||||
\(259\) | 1.44310 | 0.0896700 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 47.1906 | 2.92103 | ||||||||
\(262\) | −5.14918 | + | 8.91865i | −0.318118 | + | 0.550996i | ||||
\(263\) | 2.68795 | − | 4.65566i | 0.165746 | − | 0.287080i | −0.771174 | − | 0.636624i | \(-0.780330\pi\) |
0.936920 | + | 0.349544i | \(0.113664\pi\) | |||||||
\(264\) | 8.40224 | + | 14.5531i | 0.517122 | + | 0.895681i | ||||
\(265\) | 6.99102 | 0.429455 | ||||||||
\(266\) | −13.6264 | − | 23.6017i | −0.835491 | − | 1.44711i | ||||
\(267\) | −17.7785 | − | 30.7932i | −1.08802 | − | 1.88451i | ||||
\(268\) | 34.2212 | 2.09039 | ||||||||
\(269\) | 0.655192 | + | 1.13483i | 0.0399478 | + | 0.0691916i | 0.885308 | − | 0.465005i | \(-0.153948\pi\) |
−0.845360 | + | 0.534197i | \(0.820614\pi\) | |||||||
\(270\) | −7.02271 | + | 12.1637i | −0.427388 | + | 0.740258i | ||||
\(271\) | 5.82266 | − | 10.0851i | 0.353701 | − | 0.612629i | −0.633194 | − | 0.773994i | \(-0.718256\pi\) |
0.986895 | + | 0.161365i | \(0.0515896\pi\) | |||||||
\(272\) | 3.45214 | 0.209317 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −50.1838 | −3.03171 | ||||||||
\(275\) | −0.534695 | + | 0.926118i | −0.0322433 | + | 0.0558470i | ||||
\(276\) | 22.8129 | − | 39.5130i | 1.37317 | − | 2.37841i | ||||
\(277\) | 10.1581 | + | 17.5943i | 0.610338 | + | 1.05714i | 0.991183 | + | 0.132498i | \(0.0422999\pi\) |
−0.380845 | + | 0.924639i | \(0.624367\pi\) | |||||||
\(278\) | 51.9697 | 3.11693 | ||||||||
\(279\) | 3.65368 | + | 6.32835i | 0.218740 | + | 0.378869i | ||||
\(280\) | 5.29543 | + | 9.17196i | 0.316463 | + | 0.548129i | ||||
\(281\) | −11.8744 | −0.708366 | −0.354183 | − | 0.935176i | \(-0.615241\pi\) | ||||
−0.354183 | + | 0.935176i | \(0.615241\pi\) | |||||||
\(282\) | −33.3184 | − | 57.7091i | −1.98408 | − | 3.43653i | ||||
\(283\) | 11.3261 | − | 19.6173i | 0.673264 | − | 1.16613i | −0.303709 | − | 0.952765i | \(-0.598225\pi\) |
0.976973 | − | 0.213363i | \(-0.0684418\pi\) | |||||||
\(284\) | −20.6408 | + | 35.7509i | −1.22481 | + | 2.12143i | ||||
\(285\) | 16.2036 | 0.959817 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.510500 | 0.0301339 | ||||||||
\(288\) | −5.99102 | + | 10.3767i | −0.353024 | + | 0.611455i | ||||
\(289\) | 8.29695 | − | 14.3707i | 0.488056 | − | 0.845337i | ||||
\(290\) | 11.7977 | + | 20.4341i | 0.692782 | + | 1.19993i | ||||
\(291\) | 11.9336 | 0.699562 | ||||||||
\(292\) | 7.85584 | + | 13.6067i | 0.459728 | + | 0.796272i | ||||
\(293\) | −9.30636 | − | 16.1191i | −0.543683 | − | 0.941687i | −0.998689 | − | 0.0511983i | \(-0.983696\pi\) |
0.455005 | − | 0.890489i | \(-0.349637\pi\) | |||||||
\(294\) | 23.7745 | 1.38656 | ||||||||
\(295\) | 0.370518 | + | 0.641756i | 0.0215724 | + | 0.0373645i | ||||
\(296\) | −2.10529 | + | 3.64647i | −0.122367 | + | 0.211946i | ||||
\(297\) | 3.00941 | − | 5.21245i | 0.174624 | − | 0.302457i | ||||
\(298\) | 33.3593 | 1.93245 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −11.9506 | −0.689970 | ||||||||
\(301\) | −0.607061 | + | 1.05146i | −0.0349904 | + | 0.0606052i | ||||
\(302\) | −22.8319 | + | 39.5459i | −1.31383 | + | 2.27561i | ||||
\(303\) | −21.5512 | − | 37.3278i | −1.23808 | − | 2.14443i | ||||
\(304\) | 31.0513 | 1.78091 | ||||||||
\(305\) | 2.09928 | + | 3.63606i | 0.120204 | + | 0.208200i | ||||
\(306\) | −3.96859 | − | 6.87381i | −0.226869 | − | 0.392949i | ||||
\(307\) | 3.14776 | 0.179652 | 0.0898262 | − | 0.995957i | \(-0.471369\pi\) | ||||
0.0898262 | + | 0.995957i | \(0.471369\pi\) | |||||||
\(308\) | −4.30664 | − | 7.45932i | −0.245394 | − | 0.425034i | ||||
\(309\) | −19.1192 | + | 33.1154i | −1.08765 | + | 1.88387i | ||||
\(310\) | −1.82684 | + | 3.16418i | −0.103757 | + | 0.179713i | ||||
\(311\) | −3.18059 | −0.180355 | −0.0901774 | − | 0.995926i | \(-0.528743\pi\) | ||||
−0.0901774 | + | 0.995926i | \(0.528743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 35.3533 | 1.99829 | 0.999144 | − | 0.0413596i | \(-0.0131689\pi\) | ||||
0.999144 | + | 0.0413596i | \(0.0131689\pi\) | |||||||
\(314\) | −3.02242 | + | 5.23499i | −0.170565 | + | 0.295427i | ||||
\(315\) | 4.75447 | − | 8.23499i | 0.267884 | − | 0.463989i | ||||
\(316\) | 19.6991 | + | 34.1198i | 1.10816 | + | 1.91939i | ||||
\(317\) | −13.6357 | −0.765858 | −0.382929 | − | 0.923778i | \(-0.625085\pi\) | ||||
−0.382929 | + | 0.923778i | \(0.625085\pi\) | |||||||
\(318\) | −24.6587 | − | 42.7101i | −1.38279 | − | 2.39506i | ||||
\(319\) | −5.05560 | − | 8.75656i | −0.283059 | − | 0.490273i | ||||
\(320\) | 4.84325 | 0.270746 | ||||||||
\(321\) | −10.4066 | − | 18.0248i | −0.580842 | − | 1.00605i | ||||
\(322\) | −9.07594 | + | 15.7200i | −0.505782 | + | 0.876041i | ||||
\(323\) | −1.82641 | + | 3.16344i | −0.101624 | + | 0.176018i | ||||
\(324\) | 3.96202 | 0.220112 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.8854 | 2.20905 | ||||||||
\(327\) | 14.2416 | − | 24.6671i | 0.787560 | − | 1.36409i | ||||
\(328\) | −0.744750 | + | 1.28994i | −0.0411219 | + | 0.0712253i | ||||
\(329\) | 8.99844 | + | 15.5858i | 0.496100 | + | 0.859271i | ||||
\(330\) | 7.54390 | 0.415278 | ||||||||
\(331\) | 14.3980 | + | 24.9380i | 0.791383 | + | 1.37072i | 0.925110 | + | 0.379698i | \(0.123972\pi\) |
−0.133727 | + | 0.991018i | \(0.542695\pi\) | |||||||
\(332\) | −10.8179 | − | 18.7371i | −0.593707 | − | 1.02833i | ||||
\(333\) | 3.78044 | 0.207167 | ||||||||
\(334\) | 17.9591 | + | 31.1061i | 0.982679 | + | 1.70205i | ||||
\(335\) | 4.04739 | − | 7.01029i | 0.221133 | − | 0.383013i | ||||
\(336\) | 14.5876 | − | 25.2665i | 0.795819 | − | 1.37840i | ||||
\(337\) | 11.7493 | 0.640026 | 0.320013 | − | 0.947413i | \(-0.396313\pi\) | ||||
0.320013 | + | 0.947413i | \(0.396313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9061 | 1.02684 | ||||||||
\(340\) | 1.34703 | − | 2.33313i | 0.0730532 | − | 0.126532i | ||||
\(341\) | 0.782847 | − | 1.35593i | 0.0423936 | − | 0.0734278i | ||||
\(342\) | −35.6967 | − | 61.8285i | −1.93026 | − | 3.34330i | ||||
\(343\) | −19.7574 | −1.06680 | ||||||||
\(344\) | −1.77124 | − | 3.06787i | −0.0954987 | − | 0.165409i | ||||
\(345\) | −5.39623 | − | 9.34654i | −0.290523 | − | 0.503201i | ||||
\(346\) | −60.7630 | −3.26664 | ||||||||
\(347\) | −0.949887 | − | 1.64525i | −0.0509926 | − | 0.0883218i | 0.839402 | − | 0.543510i | \(-0.182905\pi\) |
−0.890395 | + | 0.455189i | \(0.849572\pi\) | |||||||
\(348\) | 56.4973 | − | 97.8562i | 3.02857 | − | 5.24564i | ||||
\(349\) | 5.13454 | − | 8.89329i | 0.274846 | − | 0.476047i | −0.695250 | − | 0.718768i | \(-0.744707\pi\) |
0.970096 | + | 0.242721i | \(0.0780398\pi\) | |||||||
\(350\) | 4.75447 | 0.254137 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.56730 | 0.136838 | ||||||||
\(353\) | −0.400294 | + | 0.693330i | −0.0213055 | + | 0.0369022i | −0.876482 | − | 0.481435i | \(-0.840116\pi\) |
0.855176 | + | 0.518338i | \(0.173449\pi\) | |||||||
\(354\) | 2.61378 | − | 4.52720i | 0.138921 | − | 0.240618i | ||||
\(355\) | 4.88244 | + | 8.45663i | 0.259133 | + | 0.448831i | ||||
\(356\) | −53.1756 | −2.81830 | ||||||||
\(357\) | 1.71606 | + | 2.97231i | 0.0908237 | + | 0.157311i | ||||
\(358\) | −4.72685 | − | 8.18714i | −0.249822 | − | 0.432704i | ||||
\(359\) | 8.13272 | 0.429228 | 0.214614 | − | 0.976699i | \(-0.431151\pi\) | ||||
0.214614 | + | 0.976699i | \(0.431151\pi\) | |||||||
\(360\) | 13.8723 | + | 24.0274i | 0.731132 | + | 1.26636i | ||||
\(361\) | −6.92820 | + | 12.0000i | −0.364642 | + | 0.631579i | ||||
\(362\) | 10.5909 | − | 18.3439i | 0.556643 | − | 0.964135i | ||||
\(363\) | 27.8625 | 1.46240 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.71649 | 0.194530 | ||||||||
\(366\) | 14.8092 | − | 25.6502i | 0.774087 | − | 1.34076i | ||||
\(367\) | 10.2632 | − | 17.7765i | 0.535737 | − | 0.927924i | −0.463390 | − | 0.886154i | \(-0.653367\pi\) |
0.999127 | − | 0.0417696i | \(-0.0132996\pi\) | |||||||
\(368\) | −10.3409 | − | 17.9110i | −0.539057 | − | 0.933675i | ||||
\(369\) | 1.33734 | 0.0696191 | ||||||||
\(370\) | 0.945110 | + | 1.63698i | 0.0491339 | + | 0.0851025i | ||||
\(371\) | 6.65968 | + | 11.5349i | 0.345754 | + | 0.598863i | ||||
\(372\) | 17.4969 | 0.907173 | ||||||||
\(373\) | 8.90292 | + | 15.4203i | 0.460976 | + | 0.798433i | 0.999010 | − | 0.0444897i | \(-0.0141662\pi\) |
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(374\) | −0.850322 | + | 1.47280i | −0.0439691 | + | 0.0761568i | ||||
\(375\) | −1.41342 | + | 2.44811i | −0.0729887 | + | 0.126420i | ||||
\(376\) | −52.5100 | −2.70800 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −26.7595 | −1.37636 | ||||||||
\(379\) | −1.02277 | + | 1.77150i | −0.0525363 | + | 0.0909956i | −0.891098 | − | 0.453812i | \(-0.850064\pi\) |
0.838561 | + | 0.544807i | \(0.183397\pi\) | |||||||
\(380\) | 12.1163 | − | 20.9860i | 0.621553 | − | 1.07656i | ||||
\(381\) | 2.10529 | + | 3.64647i | 0.107857 | + | 0.186814i | ||||
\(382\) | −13.5833 | −0.694982 | ||||||||
\(383\) | 3.95261 | + | 6.84611i | 0.201969 | + | 0.349820i | 0.949163 | − | 0.314786i | \(-0.101933\pi\) |
−0.747194 | + | 0.664606i | \(0.768599\pi\) | |||||||
\(384\) | −23.8696 | − | 41.3433i | −1.21809 | − | 2.10979i | ||||
\(385\) | −2.03741 | −0.103836 | ||||||||
\(386\) | −15.1697 | − | 26.2747i | −0.772117 | − | 1.33735i | ||||
\(387\) | −1.59030 | + | 2.75447i | −0.0808393 | + | 0.140018i | ||||
\(388\) | 8.92343 | − | 15.4558i | 0.453018 | − | 0.784651i | ||||
\(389\) | −9.21171 | −0.467052 | −0.233526 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233526 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43298 | 0.123041 | ||||||||
\(392\) | 9.36719 | − | 16.2244i | 0.473114 | − | 0.819458i | ||||
\(393\) | 5.83285 | − | 10.1028i | 0.294228 | − | 0.509618i | ||||
\(394\) | 5.46304 | + | 9.46226i | 0.275224 | + | 0.476702i | ||||
\(395\) | 9.31937 | 0.468908 | ||||||||
\(396\) | −11.2820 | − | 19.5409i | −0.566940 | − | 0.981968i | ||||
\(397\) | 3.17719 | + | 5.50305i | 0.159458 | + | 0.276190i | 0.934674 | − | 0.355507i | \(-0.115692\pi\) |
−0.775215 | + | 0.631697i | \(0.782359\pi\) | |||||||
\(398\) | 51.9996 | 2.60651 | ||||||||
\(399\) | 15.4356 | + | 26.7353i | 0.772748 | + | 1.33844i | ||||
\(400\) | −2.70857 | + | 4.69138i | −0.135428 | + | 0.234569i | ||||
\(401\) | −2.08460 | + | 3.61063i | −0.104100 | + | 0.180306i | −0.913370 | − | 0.407130i | \(-0.866530\pi\) |
0.809270 | + | 0.587437i | \(0.199863\pi\) | |||||||
\(402\) | −57.1038 | −2.84808 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −64.4600 | −3.20701 | ||||||||
\(405\) | 0.468594 | − | 0.811629i | 0.0232846 | − | 0.0403301i | ||||
\(406\) | −22.4770 | + | 38.9314i | −1.11552 | + | 1.93213i | ||||
\(407\) | −0.405004 | − | 0.701487i | −0.0200753 | − | 0.0347714i | ||||
\(408\) | −10.0140 | −0.495767 | ||||||||
\(409\) | −5.08403 | − | 8.80580i | −0.251389 | − | 0.435419i | 0.712519 | − | 0.701652i | \(-0.247554\pi\) |
−0.963909 | + | 0.266234i | \(0.914221\pi\) | |||||||
\(410\) | 0.334335 | + | 0.579085i | 0.0165116 | + | 0.0285989i | ||||
\(411\) | 56.8467 | 2.80404 | ||||||||
\(412\) | 28.5929 | + | 49.5244i | 1.40867 | + | 2.43989i | ||||
\(413\) | −0.705915 | + | 1.22268i | −0.0347358 | + | 0.0601642i | ||||
\(414\) | −23.7759 | + | 41.1811i | −1.16852 | + | 2.02394i | ||||
\(415\) | −5.11778 | −0.251222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −58.8697 | −2.88286 | ||||||||
\(418\) | −7.64847 | + | 13.2475i | −0.374099 | + | 0.647959i | ||||
\(419\) | −14.2954 | + | 24.7604i | −0.698378 | + | 1.20963i | 0.270651 | + | 0.962677i | \(0.412761\pi\) |
−0.969029 | + | 0.246948i | \(0.920572\pi\) | |||||||
\(420\) | −11.3842 | − | 19.7181i | −0.555494 | − | 0.962144i | ||||
\(421\) | 2.01797 | 0.0983498 | 0.0491749 | − | 0.998790i | \(-0.484341\pi\) | ||||
0.0491749 | + | 0.998790i | \(0.484341\pi\) | |||||||
\(422\) | 13.2932 | + | 23.0244i | 0.647101 | + | 1.12081i | ||||
\(423\) | 23.5729 | + | 40.8295i | 1.14615 | + | 1.98520i | ||||
\(424\) | −38.8623 | −1.88732 | ||||||||
\(425\) | −0.318632 | − | 0.551886i | −0.0154559 | − | 0.0267704i | ||||
\(426\) | 34.4427 | − | 59.6564i | 1.66875 | − | 2.89036i | ||||
\(427\) | −3.99957 | + | 6.92747i | −0.193553 | + | 0.335244i | ||||
\(428\) | −31.1264 | −1.50455 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.59030 | −0.0766908 | ||||||||
\(431\) | 10.3061 | − | 17.8508i | 0.496430 | − | 0.859842i | −0.503562 | − | 0.863959i | \(-0.667977\pi\) |
0.999992 | + | 0.00411765i | \(0.00131069\pi\) | |||||||
\(432\) | 15.2446 | − | 26.4044i | 0.733455 | − | 1.27038i | ||||
\(433\) | −14.7178 | − | 25.4920i | −0.707292 | − | 1.22507i | −0.965858 | − | 0.259072i | \(-0.916583\pi\) |
0.258566 | − | 0.965994i | \(-0.416750\pi\) | |||||||
\(434\) | −6.96103 | −0.334140 | ||||||||
\(435\) | −13.3640 | − | 23.1472i | −0.640757 | − | 1.10982i | ||||
\(436\) | −21.2984 | − | 36.8899i | −1.02001 | − | 1.76670i | ||||
\(437\) | 21.8841 | 1.04686 | ||||||||
\(438\) | −13.1088 | − | 22.7051i | −0.626362 | − | 1.08489i | ||||
\(439\) | −8.47602 | + | 14.6809i | −0.404538 | + | 0.700681i | −0.994268 | − | 0.106920i | \(-0.965901\pi\) |
0.589729 | + | 0.807601i | \(0.299235\pi\) | |||||||
\(440\) | 2.97231 | − | 5.14819i | 0.141699 | − | 0.245430i | ||||
\(441\) | −16.8205 | −0.800978 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.1399 | −1.14692 | −0.573461 | − | 0.819233i | \(-0.694400\pi\) | ||||
−0.573461 | + | 0.819233i | \(0.694400\pi\) | |||||||
\(444\) | 4.52599 | − | 7.83925i | 0.214794 | − | 0.372034i | ||||
\(445\) | −6.28917 | + | 10.8932i | −0.298135 | + | 0.516385i | ||||
\(446\) | −26.6262 | − | 46.1180i | −1.26079 | − | 2.18375i | ||||
\(447\) | −37.7885 | −1.78733 | ||||||||
\(448\) | 4.61371 | + | 7.99118i | 0.217977 | + | 0.377548i | ||||
\(449\) | 10.4315 | + | 18.0679i | 0.492293 | + | 0.852676i | 0.999961 | − | 0.00887706i | \(-0.00282569\pi\) |
−0.507668 | + | 0.861553i | \(0.669492\pi\) | |||||||
\(450\) | 12.4551 | 0.587140 | ||||||||
\(451\) | −0.143271 | − | 0.248153i | −0.00674637 | − | 0.0116851i | ||||
\(452\) | 14.1371 | − | 24.4861i | 0.664952 | − | 1.15173i | ||||
\(453\) | 25.8633 | − | 44.7965i | 1.21516 | − | 2.10472i | ||||
\(454\) | 39.1437 | 1.83710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −90.0739 | −4.21810 | ||||||||
\(457\) | 15.2830 | − | 26.4708i | 0.714906 | − | 1.23825i | −0.248089 | − | 0.968737i | \(-0.579803\pi\) |
0.962996 | − | 0.269517i | \(-0.0868640\pi\) | |||||||
\(458\) | 9.50894 | − | 16.4700i | 0.444324 | − | 0.769591i | ||||
\(459\) | 1.79335 | + | 3.10617i | 0.0837063 | + | 0.144984i | ||||
\(460\) | −16.1402 | −0.752541 | ||||||||
\(461\) | −2.33911 | − | 4.05146i | −0.108943 | − | 0.188695i | 0.806399 | − | 0.591372i | \(-0.201413\pi\) |
−0.915342 | + | 0.402676i | \(0.868080\pi\) | |||||||
\(462\) | 7.18636 | + | 12.4471i | 0.334340 | + | 0.579094i | ||||
\(463\) | −14.0011 | −0.650688 | −0.325344 | − | 0.945596i | \(-0.605480\pi\) | ||||
−0.325344 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(464\) | −25.6098 | − | 44.3575i | −1.18891 | − | 2.05925i | ||||
\(465\) | 2.06939 | − | 3.58429i | 0.0959656 | − | 0.166217i | ||||
\(466\) | 23.7759 | − | 41.1811i | 1.10140 | − | 1.90768i | ||||
\(467\) | −6.98506 | −0.323230 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4223 | 0.712135 | ||||||||
\(470\) | −11.7864 | + | 20.4147i | −0.543668 | + | 0.941661i | ||||
\(471\) | 3.42371 | − | 5.93004i | 0.157756 | − | 0.273242i | ||||
\(472\) | −2.05967 | − | 3.56745i | −0.0948039 | − | 0.164205i | ||||
\(473\) | 0.681482 | 0.0313346 | ||||||||
\(474\) | −32.8713 | − | 56.9347i | −1.50983 | − | 2.61510i | ||||
\(475\) | −2.86603 | − | 4.96410i | −0.131502 | − | 0.227769i | ||||
\(476\) | 5.13277 | 0.235260 | ||||||||
\(477\) | 17.4461 | + | 30.2176i | 0.798804 | + | 1.38357i | ||||
\(478\) | −15.9132 | + | 27.5625i | −0.727853 | + | 1.26068i | ||||
\(479\) | 8.14438 | − | 14.1065i | 0.372126 | − | 0.644542i | −0.617766 | − | 0.786362i | \(-0.711962\pi\) |
0.989892 | + | 0.141820i | \(0.0452955\pi\) | |||||||
\(480\) | 6.78645 | 0.309758 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 64.7056 | 2.94726 | ||||||||
\(483\) | 10.2810 | − | 17.8071i | 0.467800 | − | 0.810253i | ||||
\(484\) | 20.8343 | − | 36.0860i | 0.947012 | − | 1.64027i | ||||
\(485\) | −2.11078 | − | 3.65597i | −0.0958454 | − | 0.166009i | ||||
\(486\) | 35.5249 | 1.61144 | ||||||||
\(487\) | −10.0204 | − | 17.3559i | −0.454069 | − | 0.786471i | 0.544565 | − | 0.838719i | \(-0.316695\pi\) |
−0.998634 | + | 0.0522474i | \(0.983362\pi\) | |||||||
\(488\) | −11.6697 | − | 20.2125i | −0.528261 | − | 0.914975i | ||||
\(489\) | −45.1810 | −2.04316 | ||||||||
\(490\) | −4.20514 | − | 7.28351i | −0.189969 | − | 0.329035i | ||||
\(491\) | 7.89916 | − | 13.6818i | 0.356484 | − | 0.617449i | −0.630887 | − | 0.775875i | \(-0.717309\pi\) |
0.987371 | + | 0.158426i | \(0.0506420\pi\) | |||||||
\(492\) | 1.60108 | − | 2.77315i | 0.0721823 | − | 0.125023i | ||||
\(493\) | 6.02540 | 0.271370 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.33734 | −0.239896 | ||||||||
\(496\) | 3.96562 | − | 6.86865i | 0.178061 | − | 0.308411i | ||||
\(497\) | −9.30208 | + | 16.1117i | −0.417255 | + | 0.722708i | ||||
\(498\) | 18.0514 | + | 31.2660i | 0.808903 | + | 1.40106i | ||||
\(499\) | 1.24651 | 0.0558016 | 0.0279008 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0279008 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(500\) | 2.11378 | + | 3.66117i | 0.0945311 | + | 0.163733i | ||||
\(501\) | −20.3436 | − | 35.2361i | −0.908883 | − | 1.57423i | ||||
\(502\) | 18.9955 | 0.847809 | ||||||||
\(503\) | 3.82672 | + | 6.62808i | 0.170625 | + | 0.295532i | 0.938639 | − | 0.344902i | \(-0.112088\pi\) |
−0.768013 | + | 0.640434i | \(0.778755\pi\) | |||||||
\(504\) | −26.4296 | + | 45.7774i | −1.17727 | + | 2.03909i | ||||
\(505\) | −7.62379 | + | 13.2048i | −0.339254 | + | 0.587605i | ||||
\(506\) | 10.1886 | 0.452938 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.29695 | 0.279382 | ||||||||
\(509\) | −12.8621 | + | 22.2777i | −0.570101 | + | 0.987444i | 0.426454 | + | 0.904509i | \(0.359763\pi\) |
−0.996555 | + | 0.0829345i | \(0.973571\pi\) | |||||||
\(510\) | −2.24775 | + | 3.89322i | −0.0995322 | + | 0.172395i | ||||
\(511\) | 3.54035 | + | 6.13207i | 0.156616 | + | 0.271267i | ||||
\(512\) | −47.2215 | −2.08691 | ||||||||
\(513\) | 16.1308 | + | 27.9393i | 0.712192 | + | 1.23355i | ||||
\(514\) | −0.418974 | − | 0.725685i | −0.0184802 | − | 0.0320086i | ||||
\(515\) | 13.5269 | 0.596067 | ||||||||
\(516\) | 3.80785 | + | 6.59538i | 0.167631 | + | 0.290346i | ||||
\(517\) | 5.05080 | − | 8.74824i | 0.222134 | − | 0.384747i | ||||
\(518\) | −1.80064 | + | 3.11879i | −0.0791154 | + | 0.137032i | ||||
\(519\) | 68.8305 | 3.02132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1519 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(522\) | −58.8823 | + | 101.987i | −2.57721 | + | 4.46386i | ||||
\(523\) | −1.96876 | + | 3.41000i | −0.0860880 | + | 0.149109i | −0.905854 | − | 0.423589i | \(-0.860770\pi\) |
0.819766 | + | 0.572698i | \(0.194103\pi\) | |||||||
\(524\) | −8.72307 | − | 15.1088i | −0.381069 | − | 0.660031i | ||||
\(525\) | −5.38573 | −0.235052 | ||||||||
\(526\) | 6.70779 | + | 11.6182i | 0.292473 | + | 0.506579i | ||||
\(527\) | 0.466509 | + | 0.808017i | 0.0203215 | + | 0.0351978i | ||||
\(528\) | −16.3759 | −0.712672 | ||||||||
\(529\) | 4.21200 | + | 7.29539i | 0.183130 | + | 0.317191i | ||||
\(530\) | −8.72307 | + | 15.1088i | −0.378906 | + | 0.656284i | ||||
\(531\) | −1.84926 | + | 3.20301i | −0.0802510 | + | 0.138999i | ||||
\(532\) | 46.1682 | 2.00165 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 88.7326 | 3.83983 | ||||||||
\(535\) | −3.68137 | + | 6.37632i | −0.159159 | + | 0.275672i | ||||
\(536\) | −22.4990 | + | 38.9694i | −0.971809 | + | 1.68322i | ||||
\(537\) | 5.35444 | + | 9.27415i | 0.231061 | + | 0.400209i | ||||
\(538\) | −3.27007 | −0.140983 | ||||||||
\(539\) | 1.80201 | + | 3.12117i | 0.0776180 | + | 0.134438i | ||||
\(540\) | −11.8969 | − | 20.6061i | −0.511963 | − | 0.886745i | ||||
\(541\) | −15.8881 | −0.683083 | −0.341541 | − | 0.939867i | \(-0.610949\pi\) | ||||
−0.341541 | + | 0.939867i | \(0.610949\pi\) | |||||||
\(542\) | 14.5305 | + | 25.1675i | 0.624138 | + | 1.08104i | ||||
\(543\) | −11.9970 | + | 20.7795i | −0.514842 | + | 0.891732i | ||||
\(544\) | −0.764945 | + | 1.32492i | −0.0327968 | + | 0.0568057i | ||||
\(545\) | −10.0760 | −0.431607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.56107 | −0.280531 | −0.140266 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140266 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(548\) | 42.5074 | − | 73.6249i | 1.81582 | − | 3.14510i | ||||
\(549\) | −10.4775 | + | 18.1476i | −0.447170 | + | 0.774522i | ||||
\(550\) | −1.33433 | − | 2.31114i | −0.0568962 | − | 0.0985471i | ||||
\(551\) | 54.1972 | 2.30888 | ||||||||
\(552\) | 29.9970 | + | 51.9564i | 1.27676 | + | 2.21141i | ||||
\(553\) | 8.87769 | + | 15.3766i | 0.377518 | + | 0.653880i | ||||
\(554\) | −50.6990 | −2.15399 | ||||||||
\(555\) | −1.07059 | − | 1.85432i | −0.0454441 | − | 0.0787116i | ||||
\(556\) | −44.0200 | + | 76.2450i | −1.86687 | + | 3.23351i | ||||
\(557\) | −3.92503 | + | 6.79835i | −0.166309 | + | 0.288055i | −0.937119 | − | 0.349009i | \(-0.886518\pi\) |
0.770810 | + | 0.637065i | \(0.219852\pi\) | |||||||
\(558\) | −18.2356 | −0.771973 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.3208 | −0.436133 | ||||||||
\(561\) | 0.963220 | − | 1.66835i | 0.0406672 | − | 0.0704377i | ||||
\(562\) | 14.8163 | − | 25.6626i | 0.624988 | − | 1.08251i | ||||
\(563\) | 7.77976 | + | 13.4749i | 0.327878 | + | 0.567901i | 0.982091 | − | 0.188410i | \(-0.0603333\pi\) |
−0.654213 | + | 0.756310i | \(0.727000\pi\) | |||||||
\(564\) | 112.887 | 4.75341 | ||||||||
\(565\) | −3.34403 | − | 5.79203i | −0.140684 | − | 0.243673i | ||||
\(566\) | 28.2643 | + | 48.9552i | 1.18804 | + | 2.05774i | ||||
\(567\) | 1.78554 | 0.0749857 | ||||||||
\(568\) | −27.1409 | − | 47.0095i | −1.13881 | − | 1.97247i | ||||
\(569\) | −1.73957 | + | 3.01303i | −0.0729267 | + | 0.126313i | −0.900183 | − | 0.435512i | \(-0.856567\pi\) |
0.827256 | + | 0.561825i | \(0.189901\pi\) | |||||||
\(570\) | −20.2181 | + | 35.0187i | −0.846842 | + | 1.46677i | ||||
\(571\) | −21.5118 | −0.900240 | −0.450120 | − | 0.892968i | \(-0.648619\pi\) | ||||
−0.450120 | + | 0.892968i | \(0.648619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3868 | 0.642791 | ||||||||
\(574\) | −0.636978 | + | 1.10328i | −0.0265870 | + | 0.0460500i | ||||
\(575\) | −1.90893 | + | 3.30636i | −0.0796078 | + | 0.137885i | ||||
\(576\) | 12.0864 | + | 20.9342i | 0.503599 | + | 0.872259i | ||||
\(577\) | 9.97608 | 0.415310 | 0.207655 | − | 0.978202i | \(-0.433417\pi\) | ||||
0.207655 | + | 0.978202i | \(0.433417\pi\) | |||||||
\(578\) | 20.7051 | + | 35.8623i | 0.861218 | + | 1.49167i | ||||
\(579\) | 17.1838 | + | 29.7632i | 0.714134 | + | 1.23692i | ||||
\(580\) | −39.9721 | −1.65975 | ||||||||
\(581\) | −4.87523 | − | 8.44414i | −0.202259 | − | 0.350322i | ||||
\(582\) | −14.8902 | + | 25.7907i | −0.617221 | + | 1.06906i | ||||
\(583\) | 3.73806 | − | 6.47451i | 0.154815 | − | 0.268147i | ||||
\(584\) | −20.6595 | −0.854898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.4482 | 1.91876 | ||||||||
\(587\) | 12.0286 | − | 20.8341i | 0.496472 | − | 0.859915i | −0.503519 | − | 0.863984i | \(-0.667962\pi\) |
0.999992 | + | 0.00406862i | \(0.00129509\pi\) | |||||||
\(588\) | −20.1378 | + | 34.8797i | −0.830469 | + | 1.43841i | ||||
\(589\) | 4.19615 | + | 7.26795i | 0.172899 | + | 0.299471i | ||||
\(590\) | −1.84926 | −0.0761328 | ||||||||
\(591\) | −6.18837 | − | 10.7186i | −0.254556 | − | 0.440903i | ||||
\(592\) | −2.05160 | − | 3.55348i | −0.0843203 | − | 0.146047i | ||||
\(593\) | 0.940219 | 0.0386102 | 0.0193051 | − | 0.999814i | \(-0.493855\pi\) | ||||
0.0193051 | + | 0.999814i | \(0.493855\pi\) | |||||||
\(594\) | 7.51001 | + | 13.0077i | 0.308139 | + | 0.533713i | ||||
\(595\) | 0.607061 | − | 1.05146i | 0.0248871 | − | 0.0431057i | ||||
\(596\) | −28.2565 | + | 48.9417i | −1.15743 | + | 2.00473i | ||||
\(597\) | −58.9037 | −2.41077 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.4270 | −0.466896 | −0.233448 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233448 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(600\) | 7.85704 | − | 13.6088i | 0.320762 | − | 0.555577i | ||||
\(601\) | 18.0215 | − | 31.2142i | 0.735114 | − | 1.27325i | −0.219560 | − | 0.975599i | \(-0.570462\pi\) |
0.954674 | − | 0.297655i | \(-0.0962045\pi\) | |||||||
\(602\) | −1.51493 | − | 2.62393i | −0.0617437 | − | 0.106943i | ||||
\(603\) | 40.4012 | 1.64526 | ||||||||
\(604\) | −38.6787 | − | 66.9935i | −1.57381 | − | 2.72593i | ||||
\(605\) | −4.92820 | − | 8.53590i | −0.200360 | − | 0.347034i | ||||
\(606\) | 107.562 | 4.36942 | ||||||||
\(607\) | −19.9454 | − | 34.5464i | −0.809557 | − | 1.40219i | −0.913171 | − | 0.407576i | \(-0.866374\pi\) |
0.103614 | − | 0.994618i | \(-0.466959\pi\) | |||||||
\(608\) | −6.88052 | + | 11.9174i | −0.279042 | + | 0.483315i | ||||
\(609\) | 25.4613 | − | 44.1003i | 1.03175 | − | 1.78704i | ||||
\(610\) | −10.4775 | −0.424223 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 13.4461 | 0.543528 | ||||||||
\(613\) | 0.172736 | − | 0.299187i | 0.00697673 | − | 0.0120841i | −0.862516 | − | 0.506030i | \(-0.831113\pi\) |
0.869493 | + | 0.493946i | \(0.164446\pi\) | |||||||
\(614\) | −3.92763 | + | 6.80286i | −0.158506 | + | 0.274541i | ||||
\(615\) | −0.378725 | − | 0.655970i | −0.0152716 | − | 0.0264513i | ||||
\(616\) | 11.3258 | 0.456328 | ||||||||
\(617\) | −19.3425 | − | 33.5022i | −0.778700 | − | 1.34875i | −0.932691 | − | 0.360676i | \(-0.882546\pi\) |
0.153991 | − | 0.988072i | \(-0.450787\pi\) | |||||||
\(618\) | −47.7121 | − | 82.6398i | −1.91926 | − | 3.32426i | ||||
\(619\) | 14.8971 | 0.598764 | 0.299382 | − | 0.954133i | \(-0.403219\pi\) | ||||
0.299382 | + | 0.954133i | \(0.403219\pi\) | |||||||
\(620\) | −3.09479 | − | 5.36033i | −0.124290 | − | 0.215276i | ||||
\(621\) | 10.7440 | − | 18.6091i | 0.431141 | − | 0.746758i | ||||
\(622\) | 3.96859 | − | 6.87381i | 0.159126 | − | 0.275615i | ||||
\(623\) | −23.9644 | −0.960113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −44.1123 | + | 76.4047i | −1.76308 | + | 3.05374i | ||||
\(627\) | 8.66397 | − | 15.0064i | 0.346006 | − | 0.599299i | ||||
\(628\) | −5.12019 | − | 8.86842i | −0.204318 | − | 0.353889i | ||||
\(629\) | 0.482694 | 0.0192463 | ||||||||
\(630\) | 11.8648 | + | 20.5505i | 0.472706 | + | 0.818750i | ||||
\(631\) | 19.4225 | + | 33.6408i | 0.773198 | + | 1.33922i | 0.935802 | + | 0.352526i | \(0.114677\pi\) |
−0.162604 | + | 0.986691i | \(0.551989\pi\) | |||||||
\(632\) | −51.8053 | −2.06071 | ||||||||
\(633\) | −15.0581 | − | 26.0814i | −0.598506 | − | 1.03664i | ||||
\(634\) | 17.0140 | − | 29.4691i | 0.675713 | − | 1.17037i | ||||
\(635\) | 0.744750 | − | 1.28994i | 0.0295545 | − | 0.0511899i | ||||
\(636\) | 83.5470 | 3.31285 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25.2326 | 0.998967 | ||||||||
\(639\) | −24.3683 | + | 42.2072i | −0.963996 | + | 1.66969i | ||||
\(640\) | −8.44391 | + | 14.6253i | −0.333775 | + | 0.578115i | ||||
\(641\) | −18.5908 | − | 32.2003i | −0.734293 | − | 1.27183i | −0.955033 | − | 0.296501i | \(-0.904180\pi\) |
0.220739 | − | 0.975333i | \(-0.429153\pi\) | |||||||
\(642\) | 51.9397 | 2.04990 | ||||||||
\(643\) | −4.55189 | − | 7.88410i | −0.179509 | − | 0.310918i | 0.762204 | − | 0.647337i | \(-0.224118\pi\) |
−0.941712 | + | 0.336419i | \(0.890784\pi\) | |||||||
\(644\) | −15.3753 | − | 26.6307i | −0.605870 | − | 1.04940i | ||||
\(645\) | 1.80144 | 0.0709316 | ||||||||
\(646\) | −4.55783 | − | 7.89439i | −0.179325 | − | 0.310601i | ||||
\(647\) | 9.56118 | − | 16.5605i | 0.375889 | − | 0.651059i | −0.614571 | − | 0.788862i | \(-0.710671\pi\) |
0.990460 | + | 0.137803i | \(0.0440041\pi\) | |||||||
\(648\) | −2.60486 | + | 4.51175i | −0.102329 | + | 0.177238i | ||||
\(649\) | 0.792455 | 0.0311066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.88525 | 0.309047 | ||||||||
\(652\) | −33.7843 | + | 58.5161i | −1.32309 | + | 2.29167i | ||||
\(653\) | −17.3162 | + | 29.9926i | −0.677636 | + | 1.17370i | 0.298055 | + | 0.954549i | \(0.403662\pi\) |
−0.975691 | + | 0.219152i | \(0.929671\pi\) | |||||||
\(654\) | 35.5399 | + | 61.5570i | 1.38972 | + | 2.40707i | ||||
\(655\) | −4.12676 | −0.161246 | ||||||||
\(656\) | −0.725758 | − | 1.25705i | −0.0283361 | − | 0.0490796i | ||||
\(657\) | 9.27453 | + | 16.0640i | 0.361834 | + | 0.626714i | ||||
\(658\) | −44.9114 | −1.75083 | ||||||||
\(659\) | 3.34926 | + | 5.80109i | 0.130469 | + | 0.225978i | 0.923857 | − | 0.382737i | \(-0.125018\pi\) |
−0.793389 | + | 0.608715i | \(0.791685\pi\) | |||||||
\(660\) | −6.38994 | + | 11.0677i | −0.248728 | + | 0.430809i | ||||
\(661\) | −3.01379 | + | 5.22004i | −0.117223 | + | 0.203036i | −0.918666 | − | 0.395035i | \(-0.870732\pi\) |
0.801443 | + | 0.598071i | \(0.204066\pi\) | |||||||
\(662\) | −71.8604 | −2.79294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.4492 | 1.10404 | ||||||||
\(665\) | 5.46039 | − | 9.45767i | 0.211745 | − | 0.366753i | ||||
\(666\) | −4.71706 | + | 8.17018i | −0.182782 | + | 0.316588i | ||||
\(667\) | −18.0491 | − | 31.2620i | −0.698865 | − | 1.21047i | ||||
\(668\) | −60.8479 | −2.35428 | ||||||||
\(669\) | 30.1614 | + | 52.2411i | 1.16611 | + | 2.01976i | ||||
\(670\) | 10.1003 | + | 17.4942i | 0.390209 | + | 0.675861i | ||||
\(671\) | 4.48990 | 0.173330 | ||||||||
\(672\) | 6.46481 | + | 11.1974i | 0.249386 | + | 0.431948i | ||||
\(673\) | −11.6784 | + | 20.2276i | −0.450169 | + | 0.779715i | −0.998396 | − | 0.0566140i | \(-0.981970\pi\) |
0.548227 | + | 0.836329i | \(0.315303\pi\) | |||||||
\(674\) | −14.6603 | + | 25.3923i | −0.564692 | + | 0.978075i | ||||
\(675\) | −5.62828 | −0.216633 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.4042 | −1.74503 | −0.872513 | − | 0.488590i | \(-0.837511\pi\) | ||||
−0.872513 | + | 0.488590i | \(0.837511\pi\) | |||||||
\(678\) | −23.5901 | + | 40.8593i | −0.905973 | + | 1.56919i | ||||
\(679\) | 4.02148 | − | 6.96540i | 0.154330 | − | 0.267308i | ||||
\(680\) | 1.77124 | + | 3.06787i | 0.0679239 | + | 0.117648i | ||||
\(681\) | −44.3408 | −1.69914 | ||||||||
\(682\) | 1.95360 | + | 3.38374i | 0.0748073 | + | 0.129570i | ||||
\(683\) | 12.7489 | + | 22.0817i | 0.487823 | + | 0.844934i | 0.999902 | − | 0.0140045i | \(-0.00445791\pi\) |
−0.512079 | + | 0.858938i | \(0.671125\pi\) | |||||||
\(684\) | 120.945 | 4.62445 | ||||||||
\(685\) | −10.0548 | − | 17.4155i | −0.384175 | − | 0.665411i | ||||
\(686\) | 24.6523 | − | 42.6991i | 0.941230 | − | 1.63026i | ||||
\(687\) | −10.7715 | + | 18.6567i | −0.410957 | + | 0.711798i | ||||
\(688\) | 3.45214 | 0.131612 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 26.9327 | 1.02531 | ||||||||
\(691\) | 3.29815 | − | 5.71257i | 0.125468 | − | 0.217316i | −0.796448 | − | 0.604707i | \(-0.793290\pi\) |
0.921916 | + | 0.387391i | \(0.126624\pi\) | |||||||
\(692\) | 51.4683 | − | 89.1457i | 1.95653 | − | 3.38881i | ||||
\(693\) | −5.08438 | − | 8.80641i | −0.193140 | − | 0.334528i | ||||
\(694\) | 4.74090 | 0.179962 | ||||||||
\(695\) | 10.4126 | + | 18.0352i | 0.394974 | + | 0.684115i | ||||
\(696\) | 74.2892 | + | 128.673i | 2.81593 | + | 4.87733i | ||||
\(697\) | 0.170754 | 0.00646778 | ||||||||
\(698\) | 12.8133 | + | 22.1933i | 0.484990 | + | 0.840028i | ||||
\(699\) | −26.9327 | + | 46.6487i | −1.01869 | + | 1.76442i | ||||
\(700\) | −4.02720 | + | 6.97531i | −0.152214 | + | 0.263642i | ||||
\(701\) | 29.2474 | 1.10466 | 0.552329 | − | 0.833626i | \(-0.313739\pi\) | ||||
0.552329 | + | 0.833626i | \(0.313739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.34174 | 0.163752 | ||||||||
\(704\) | 2.58966 | − | 4.48542i | 0.0976015 | − | 0.169051i | ||||
\(705\) | 13.3513 | − | 23.1252i | 0.502841 | − | 0.870946i | ||||
\(706\) | −0.998937 | − | 1.73021i | −0.0375955 | − | 0.0651173i | ||||
\(707\) | −29.0499 | −1.09253 | ||||||||
\(708\) | 4.42792 | + | 7.66938i | 0.166411 | + | 0.288233i | ||||
\(709\) | −5.46673 | − | 9.46865i | −0.205307 | − | 0.355603i | 0.744923 | − | 0.667150i | \(-0.232486\pi\) |
−0.950231 | + | 0.311548i | \(0.899153\pi\) | |||||||
\(710\) | −24.3683 | −0.914527 | ||||||||
\(711\) | 23.2566 | + | 40.2815i | 0.872189 | + | 1.51068i | ||||
\(712\) | 34.9608 | − | 60.5538i | 1.31021 | − | 2.26935i | ||||
\(713\) | 2.79486 | − | 4.84084i | 0.104668 | − | 0.181291i | ||||
\(714\) | −8.56490 | −0.320533 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0152 | 0.598516 | ||||||||
\(717\) | 18.0260 | − | 31.2220i | 0.673194 | − | 1.16601i | ||||
\(718\) | −10.1476 | + | 17.5762i | −0.378706 | + | 0.655938i | ||||
\(719\) | −8.02989 | − | 13.9082i | −0.299464 | − | 0.518688i | 0.676549 | − | 0.736398i | \(-0.263475\pi\) |
−0.976014 | + | 0.217710i | \(0.930141\pi\) | |||||||
\(720\) | −27.0370 | −1.00761 | ||||||||
\(721\) | 12.8858 | + | 22.3189i | 0.479893 | + | 0.831199i | ||||
\(722\) | −17.2894 | − | 29.9461i | −0.643444 | − | 1.11448i | ||||
\(723\) | −73.2966 | −2.72593 | ||||||||
\(724\) | 17.9416 | + | 31.0758i | 0.666796 | + | 1.15492i | ||||
\(725\) | −4.72756 | + | 8.18837i | −0.175577 | + | 0.304108i | ||||
\(726\) | −34.7655 | + | 60.2156i | −1.29027 | + | 2.23481i | ||||
\(727\) | 51.3754 | 1.90541 | 0.952704 | − | 0.303900i | \(-0.0982889\pi\) | ||||
0.952704 | + | 0.303900i | \(0.0982889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0532 | −1.59456 | ||||||||
\(730\) | −4.63726 | + | 8.03198i | −0.171633 | + | 0.297277i | ||||
\(731\) | −0.203052 | + | 0.351697i | −0.00751016 | + | 0.0130080i | ||||
\(732\) | 25.0877 | + | 43.4532i | 0.927268 | + | 1.60608i | ||||
\(733\) | −9.82358 | −0.362842 | −0.181421 | − | 0.983406i | \(-0.558070\pi\) | ||||
−0.181421 | + | 0.983406i | \(0.558070\pi\) | |||||||
\(734\) | 25.6120 | + | 44.3613i | 0.945357 | + | 1.63741i | ||||
\(735\) | 4.76346 | + | 8.25055i | 0.175703 | + | 0.304326i | ||||
\(736\) | 9.16560 | 0.337848 | ||||||||
\(737\) | −4.32824 | − | 7.49673i | −0.159433 | − | 0.276146i | ||||
\(738\) | −1.66867 | + | 2.89022i | −0.0614246 | + | 0.106390i | ||||
\(739\) | −24.5421 | + | 42.5082i | −0.902797 | + | 1.56369i | −0.0789487 | + | 0.996879i | \(0.525156\pi\) |
−0.823848 | + | 0.566811i | \(0.808177\pi\) | |||||||
\(740\) | −3.20216 | −0.117714 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.2386 | −1.22023 | ||||||||
\(743\) | −20.4188 | + | 35.3663i | −0.749091 | + | 1.29746i | 0.199167 | + | 0.979966i | \(0.436176\pi\) |
−0.948259 | + | 0.317499i | \(0.897157\pi\) | |||||||
\(744\) | −11.5035 | + | 19.9247i | −0.421739 | + | 0.730473i | ||||
\(745\) | 6.68388 | + | 11.5768i | 0.244878 | + | 0.424142i | ||||
\(746\) | −44.4346 | −1.62687 | ||||||||
\(747\) | −12.7715 | − | 22.1208i | −0.467283 | − | 0.809358i | ||||
\(748\) | −1.44050 | − | 2.49503i | −0.0526700 | − | 0.0912272i | ||||
\(749\) | −14.0276 | −0.512557 | ||||||||
\(750\) | −3.52720 | − | 6.10929i | −0.128795 | − | 0.223080i | ||||
\(751\) | 1.36340 | − | 2.36148i | 0.0497512 | − | 0.0861716i | −0.840077 | − | 0.542467i | \(-0.817490\pi\) |
0.889829 | + | 0.456295i | \(0.150824\pi\) | |||||||
\(752\) | 25.5855 | − | 44.3154i | 0.933006 | − | 1.61601i | ||||
\(753\) | −21.5175 | −0.784142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.2984 | −0.665946 | ||||||||
\(756\) | 22.6662 | − | 39.2590i | 0.824362 | − | 1.42784i | ||||
\(757\) | −7.40301 | + | 12.8224i | −0.269067 | + | 0.466038i | −0.968621 | − | 0.248542i | \(-0.920049\pi\) |
0.699554 | + | 0.714580i | \(0.253382\pi\) | |||||||
\(758\) | −2.55234 | − | 4.42078i | −0.0927051 | − | 0.160570i | ||||
\(759\) | −11.5413 | −0.418924 | ||||||||
\(760\) | 15.9319 | + | 27.5949i | 0.577911 | + | 1.00097i | ||||
\(761\) | 5.68445 | + | 9.84575i | 0.206061 | + | 0.356908i | 0.950470 | − | 0.310815i | \(-0.100602\pi\) |
−0.744409 | + | 0.667724i | \(0.767269\pi\) | |||||||
\(762\) | −10.5075 | −0.380647 | ||||||||
\(763\) | −9.59843 | − | 16.6250i | −0.347486 | − | 0.601864i | ||||
\(764\) | 11.5055 | − | 19.9281i | 0.416255 | − | 0.720975i | ||||
\(765\) | 1.59030 | − | 2.75447i | 0.0574972 | − | 0.0995882i | ||||
\(766\) | −19.7275 | −0.712784 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 91.7512 | 3.31078 | ||||||||
\(769\) | 10.5281 | − | 18.2352i | 0.379654 | − | 0.657579i | −0.611358 | − | 0.791354i | \(-0.709377\pi\) |
0.991012 | + | 0.133775i | \(0.0427098\pi\) | |||||||
\(770\) | 2.54219 | − | 4.40320i | 0.0916142 | − | 0.158680i | ||||
\(771\) | 0.474602 | + | 0.822034i | 0.0170924 | + | 0.0296048i | ||||
\(772\) | 51.3970 | 1.84982 | ||||||||
\(773\) | −7.04144 | − | 12.1961i | −0.253263 | − | 0.438664i | 0.711159 | − | 0.703031i | \(-0.248170\pi\) |
−0.964422 | + | 0.264367i | \(0.914837\pi\) | |||||||
\(774\) | −3.96859 | − | 6.87381i | −0.142648 | − | 0.247074i | ||||
\(775\) | −1.46410 | −0.0525921 | ||||||||
\(776\) | 11.7336 | + | 20.3231i | 0.421210 | + | 0.729558i | ||||
\(777\) | 2.03971 | − | 3.53288i | 0.0731741 | − | 0.126741i | ||||
\(778\) | 11.4940 | − | 19.9081i | 0.412078 | − | 0.713740i | ||||
\(779\) | 1.53590 | 0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4425 | 0.373660 | ||||||||
\(782\) | −3.03576 | + | 5.25809i | −0.108558 | + | 0.188029i | ||||
\(783\) | 26.6080 | − | 46.0864i | 0.950893 | − | 1.64699i | ||||
\(784\) | 9.12832 | + | 15.8107i | 0.326011 | + | 0.564668i | ||||
\(785\) | −2.42229 | −0.0864552 | ||||||||
\(786\) | 14.5559 | + | 25.2116i | 0.519192 | + | 0.899267i | ||||
\(787\) | −16.5121 | − | 28.5998i | −0.588593 | − | 1.01947i | −0.994417 | − | 0.105522i | \(-0.966349\pi\) |
0.405823 | − | 0.913951i | \(-0.366985\pi\) | |||||||
\(788\) | −18.5095 | −0.659374 | ||||||||
\(789\) | −7.59839 | − | 13.1608i | −0.270510 | − | 0.468537i | ||||
\(790\) | −11.6283 | + | 20.1408i | −0.413716 | + | 0.716576i | ||||
\(791\) | 6.37109 | − | 11.0350i | 0.226530 | − | 0.392361i | ||||
\(792\) | 29.6697 | 1.05427 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.8574 | −0.562758 | ||||||||
\(795\) | 9.88124 | − | 17.1148i | 0.350451 | − | 0.606999i | ||||
\(796\) | −44.0454 | + | 76.2890i | −1.56115 | + | 2.70399i | ||||
\(797\) | 8.47079 | + | 14.6718i | 0.300051 | + | 0.519703i | 0.976147 | − | 0.217110i | \(-0.0696630\pi\) |
−0.676096 | + | 0.736813i | \(0.736330\pi\) | |||||||
\(798\) | −77.0395 | −2.72717 | ||||||||
\(799\) | 3.00984 | + | 5.21319i | 0.106480 | + | 0.184429i | ||||
\(800\) | −1.20036 | − | 2.07908i | −0.0424391 | − | 0.0735067i | ||||
\(801\) | −62.7787 | −2.21817 | ||||||||
\(802\) | −5.20213 | − | 9.01036i | −0.183694 | − | 0.318167i | ||||
\(803\) | 1.98719 | − | 3.44191i | 0.0701263 | − | 0.121462i | ||||
\(804\) | 48.3689 | − | 83.7774i | 1.70584 | − | 2.95460i | ||||
\(805\) | −7.27382 | −0.256369 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.70425 | 0.130396 | ||||||||
\(808\) | 42.3798 | − | 73.4039i | 1.49092 | − | 2.58234i | ||||
\(809\) | 25.8818 | − | 44.8285i | 0.909954 | − | 1.57609i | 0.0958292 | − | 0.995398i | \(-0.469450\pi\) |
0.814125 | − | 0.580689i | \(-0.197217\pi\) | |||||||
\(810\) | 1.16938 | + | 2.02543i | 0.0410878 | + | 0.0711662i | ||||
\(811\) | 22.6699 | 0.796047 | 0.398023 | − | 0.917375i | \(-0.369696\pi\) | ||||
0.398023 | + | 0.917375i | \(0.369696\pi\) | |||||||
\(812\) | −38.0776 | − | 65.9524i | −1.33626 | − | 2.31448i | ||||
\(813\) | −16.4597 | − | 28.5091i | −0.577267 | − | 0.999856i | ||||
\(814\) | 2.02138 | 0.0708494 | ||||||||
\(815\) | 7.99144 | + | 13.8416i | 0.279928 | + | 0.484849i | ||||
\(816\) | 4.87932 | − | 8.45123i | 0.170810 | − | 0.295852i | ||||
\(817\) | −1.82641 | + | 3.16344i | −0.0638981 | + | 0.110675i | ||||
\(818\) | 25.3745 | 0.887198 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13277 | −0.0395581 | ||||||||
\(821\) | −14.3315 | + | 24.8230i | −0.500174 | + | 0.866328i | 0.499826 | + | 0.866126i | \(0.333397\pi\) |
−1.00000 | 0.000201482i | \(0.999936\pi\) | ||||||||
\(822\) | −70.9307 | + | 122.856i | −2.47399 | + | 4.28508i | ||||
\(823\) | 12.9164 | + | 22.3718i | 0.450236 | + | 0.779831i | 0.998400 | − | 0.0565391i | \(-0.0180066\pi\) |
−0.548165 | + | 0.836371i | \(0.684673\pi\) | |||||||
\(824\) | −75.1946 | −2.61953 | ||||||||
\(825\) | 1.51150 | + | 2.61799i | 0.0526235 | + | 0.0911466i | ||||
\(826\) | −1.76162 | − | 3.05121i | −0.0612945 | − | 0.106165i | ||||
\(827\) | −16.0820 | −0.559227 | −0.279613 | − | 0.960113i | \(-0.590206\pi\) | ||||
−0.279613 | + | 0.960113i | \(0.590206\pi\) | |||||||
\(828\) | −40.2780 | − | 69.7635i | −1.39976 | − | 2.42445i | ||||
\(829\) | 11.2909 | − | 19.5564i | 0.392149 | − | 0.679222i | −0.600584 | − | 0.799562i | \(-0.705065\pi\) |
0.992733 | + | 0.120340i | \(0.0383984\pi\) | |||||||
\(830\) | 6.38573 | − | 11.0604i | 0.221652 | − | 0.383912i | ||||
\(831\) | 57.4304 | 1.99224 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.14768 | −0.0744128 | ||||||||
\(834\) | 73.4549 | − | 127.228i | 2.54354 | − | 4.40553i | ||||
\(835\) | −7.19658 | + | 12.4648i | −0.249048 | + | 0.431364i | ||||
\(836\) | −12.9570 | − | 22.4422i | −0.448128 | − | 0.776181i | ||||
\(837\) | 8.24037 | 0.284829 | ||||||||
\(838\) | −35.6744 | − | 61.7898i | −1.23235 | − | 2.13449i | ||||
\(839\) | 8.92198 | + | 15.4533i | 0.308021 | + | 0.533508i | 0.977929 | − | 0.208936i | \(-0.0670000\pi\) |
−0.669908 | + | 0.742444i | \(0.733667\pi\) | |||||||
\(840\) | 29.9387 | 1.03298 | ||||||||
\(841\) | −30.1996 | − | 52.3073i | −1.04137 | − | 1.80370i | ||||
\(842\) | −2.51793 | + | 4.36118i | −0.0867736 | + | 0.150296i | ||||
\(843\) | −16.7835 | + | 29.0698i | −0.578053 | + | 1.00122i | ||||
\(844\) | −45.0390 | −1.55031 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −117.653 | −4.04498 | ||||||||
\(847\) | 9.38927 | − | 16.2627i | 0.322619 | − | 0.558793i | ||||
\(848\) | 18.9356 | − | 32.7975i | 0.650252 | − | 1.12627i | ||||
\(849\) | −32.0169 | − | 55.4550i | −1.09882 | − | 1.90321i | ||||
\(850\) | 1.59030 | 0.0545467 | ||||||||
\(851\) | −1.44591 | − | 2.50440i | −0.0495653 | − | 0.0858497i | ||||
\(852\) | 58.3482 | + | 101.062i | 1.99898 | + | 3.46233i | ||||
\(853\) | 19.7936 | 0.677720 | 0.338860 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338860 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(854\) | −9.98097 | − | 17.2875i | −0.341542 | − | 0.591568i | ||||
\(855\) | 14.3044 | − | 24.7759i | 0.489199 | − | 0.847318i | ||||
\(856\) | 20.4643 | − | 35.4452i | 0.699456 | − | 1.21149i | ||||
\(857\) | −11.7302 | −0.400696 | −0.200348 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200348 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37452 | 0.183376 | 0.0916882 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916882 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(860\) | 1.34703 | − | 2.33313i | 0.0459335 | − | 0.0795591i | ||||
\(861\) | 0.721551 | − | 1.24976i | 0.0245904 | − | 0.0425918i | ||||
\(862\) | 25.7191 | + | 44.5467i | 0.875995 | + | 1.51727i | ||||
\(863\) | −25.3234 | −0.862017 | −0.431008 | − | 0.902348i | \(-0.641842\pi\) | ||||
−0.431008 | + | 0.902348i | \(0.641842\pi\) | |||||||
\(864\) | 6.75596 | + | 11.7017i | 0.229842 | + | 0.398099i | ||||
\(865\) | −12.1745 | − | 21.0868i | −0.413944 | − | 0.716973i | ||||
\(866\) | 73.4567 | 2.49616 | ||||||||
\(867\) | −23.4541 | − | 40.6237i | −0.796544 | − | 1.37965i | ||||
\(868\) | 5.89623 | − | 10.2126i | 0.200131 | − | 0.346637i | ||||
\(869\) | 4.98302 | − | 8.63084i | 0.169037 | − | 0.292781i | ||||
\(870\) | 66.7001 | 2.26135 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 56.0112 | 1.89678 | ||||||||
\(873\) | 10.5349 | − | 18.2470i | 0.356553 | − | 0.617567i | ||||
\(874\) | −27.3060 | + | 47.2954i | −0.923640 | + | 1.59979i | ||||
\(875\) | 0.952606 | + | 1.64996i | 0.0322040 | + | 0.0557789i | ||||
\(876\) | 44.4144 | 1.50062 | ||||||||
\(877\) | −10.3458 | − | 17.9194i | −0.349352 | − | 0.605095i | 0.636783 | − | 0.771043i | \(-0.280265\pi\) |
−0.986134 | + | 0.165949i | \(0.946931\pi\) | |||||||
\(878\) | −21.1520 | − | 36.6363i | −0.713845 | − | 1.23642i | ||||
\(879\) | −52.6151 | −1.77466 | ||||||||
\(880\) | 2.89651 | + | 5.01691i | 0.0976414 | + | 0.169120i | ||||
\(881\) | −24.1997 | + | 41.9150i | −0.815307 | + | 1.41215i | 0.0937999 | + | 0.995591i | \(0.470099\pi\) |
−0.909107 | + | 0.416562i | \(0.863235\pi\) | |||||||
\(882\) | 20.9879 | − | 36.3521i | 0.706699 | − | 1.22404i | ||||
\(883\) | 45.8550 | 1.54314 | 0.771572 | − | 0.636142i | \(-0.219471\pi\) | ||||
0.771572 | + | 0.636142i | \(0.219471\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.09479 | 0.0704155 | ||||||||
\(886\) | 30.1207 | − | 52.1705i | 1.01192 | − | 1.75270i | ||||
\(887\) | 0.541169 | − | 0.937332i | 0.0181707 | − | 0.0314725i | −0.856797 | − | 0.515654i | \(-0.827549\pi\) |
0.874968 | + | 0.484181i | \(0.160882\pi\) | |||||||
\(888\) | 5.95131 | + | 10.3080i | 0.199713 | + | 0.345913i | ||||
\(889\) | 2.83781 | 0.0951772 | ||||||||
\(890\) | −15.6947 | − | 27.1840i | −0.526086 | − | 0.911208i | ||||
\(891\) | −0.501109 | − | 0.867947i | −0.0167878 | − | 0.0290773i | ||||
\(892\) | 90.2133 | 3.02056 | ||||||||
\(893\) | 27.0729 | + | 46.8916i | 0.905959 | + | 1.56917i | ||||
\(894\) | 47.1507 | − | 81.6675i | 1.57696 | − | 2.73137i | ||||
\(895\) | 1.89414 | − | 3.28075i | 0.0633142 | − | 0.109663i | ||||
\(896\) | −32.1749 | −1.07489 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.0637 | −1.73739 | ||||||||
\(899\) | 6.92163 | − | 11.9886i | 0.230849 | − | 0.399842i | ||||
\(900\) | −10.5499 | + | 18.2730i | −0.351663 | + | 0.609099i | ||||
\(901\) | 2.22756 | + | 3.85824i | 0.0742107 | + | 0.128537i | ||||
\(902\) | 0.715068 | 0.0238092 | ||||||||
\(903\) | 1.71606 | + | 2.97231i | 0.0571070 | + | 0.0989122i | ||||
\(904\) | 18.5891 | + | 32.1973i | 0.618264 | + | 1.07086i | ||||
\(905\) | 8.48794 | 0.282149 | ||||||||
\(906\) | 64.5420 | + | 111.790i | 2.14426 | + | 3.71397i | ||||
\(907\) | 22.7653 | − | 39.4307i | 0.755910 | − | 1.30928i | −0.189010 | − | 0.981975i | \(-0.560528\pi\) |
0.944920 | − | 0.327300i | \(-0.106139\pi\) | |||||||
\(908\) | −33.1560 | + | 57.4279i | −1.10032 | + | 1.90581i | ||||
\(909\) | −76.1009 | −2.52411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7417 | 1.31670 | 0.658350 | − | 0.752712i | \(-0.271255\pi\) | ||||
0.658350 | + | 0.752712i | \(0.271255\pi\) | |||||||
\(912\) | 43.8885 | − | 76.0171i | 1.45329 | − | 2.51718i | ||||
\(913\) | −2.73645 | + | 4.73967i | −0.0905632 | + | 0.156860i | ||||
\(914\) | 38.1387 | + | 66.0582i | 1.26152 | + | 2.18501i | ||||
\(915\) | 11.8687 | 0.392365 | ||||||||
\(916\) | 16.1088 | + | 27.9012i | 0.532250 | + | 0.921883i | ||||
\(917\) | −3.93118 | − | 6.80900i | −0.129819 | − | 0.224853i | ||||
\(918\) | −8.95062 | −0.295415 | ||||||||
\(919\) | −23.4969 | − | 40.6978i | −0.775091 | − | 1.34250i | −0.934743 | − | 0.355323i | \(-0.884371\pi\) |
0.159653 | − | 0.987173i | \(-0.448963\pi\) | |||||||
\(920\) | 10.6115 | − | 18.3797i | 0.349851 | − | 0.605960i | ||||
\(921\) | 4.44911 | − | 7.70608i | 0.146603 | − | 0.253924i | ||||
\(922\) | 11.6745 | 0.384481 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.3484 | −0.801002 | ||||||||
\(925\) | −0.378725 | + | 0.655970i | −0.0124524 | + | 0.0215682i | ||||
\(926\) | 17.4700 | − | 30.2589i | 0.574099 | − | 0.994369i | ||||
\(927\) | 33.7565 | + | 58.4680i | 1.10871 | + | 1.92034i | ||||
\(928\) | 22.6991 | 0.745134 | ||||||||
\(929\) | 7.61066 | + | 13.1821i | 0.249698 | + | 0.432489i | 0.963442 | − | 0.267917i | \(-0.0863354\pi\) |
−0.713744 | + | 0.700406i | \(0.753002\pi\) | |||||||
\(930\) | 5.16418 | + | 8.94462i | 0.169340 | + | 0.293306i | ||||
\(931\) | −19.3180 | −0.633121 | ||||||||
\(932\) | 40.2780 | + | 69.7635i | 1.31935 | + | 2.28518i | ||||
\(933\) | −4.49551 | + | 7.78645i | −0.147176 | + | 0.254917i | ||||
\(934\) | 8.71564 | − | 15.0959i | 0.285184 | − | 0.493954i | ||||
\(935\) | −0.681482 | −0.0222869 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.07285 | 0.198392 | 0.0991958 | − | 0.995068i | \(-0.468373\pi\) | ||||
0.0991958 | + | 0.995068i | \(0.468373\pi\) | |||||||
\(938\) | −19.2432 | + | 33.3302i | −0.628313 | + | 1.08827i | ||||
\(939\) | 49.9691 | − | 86.5490i | 1.63068 | − | 2.82442i | ||||
\(940\) | −19.9670 | − | 34.5839i | −0.651253 | − | 1.12800i | ||||
\(941\) | −0.0496576 | −0.00161879 | −0.000809396 | − | 1.00000i | \(-0.500258\pi\) | ||||
−0.000809396 | 1.00000i | \(0.500258\pi\) | ||||||||
\(942\) | 8.54390 | + | 14.7985i | 0.278375 | + | 0.482160i | ||||
\(943\) | −0.511495 | − | 0.885936i | −0.0166566 | − | 0.0288500i | ||||
\(944\) | 4.01429 | 0.130654 | ||||||||
\(945\) | −5.36153 | − | 9.28645i | −0.174411 | − | 0.302088i | ||||
\(946\) | −0.850322 | + | 1.47280i | −0.0276464 | + | 0.0478849i | ||||
\(947\) | 9.32907 | − | 16.1584i | 0.303154 | − | 0.525078i | −0.673695 | − | 0.739010i | \(-0.735294\pi\) |
0.976849 | + | 0.213932i | \(0.0686270\pi\) | |||||||
\(948\) | 111.372 | 3.61720 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14.3044 | 0.464095 | ||||||||
\(951\) | −19.2730 | + | 33.3818i | −0.624969 | + | 1.08248i | ||||
\(952\) | −3.37458 | + | 5.84495i | −0.109371 | + | 0.189436i | ||||
\(953\) | 0.764764 | + | 1.32461i | 0.0247731 | + | 0.0429083i | 0.878146 | − | 0.478392i | \(-0.158780\pi\) |
−0.853373 | + | 0.521301i | \(0.825447\pi\) | |||||||
\(954\) | −87.0739 | −2.81912 | ||||||||
\(955\) | −2.72155 | − | 4.71386i | −0.0880673 | − | 0.152537i | ||||
\(956\) | −26.9581 | − | 46.6927i | −0.871886 | − | 1.51015i | ||||
\(957\) | −28.5827 | −0.923948 | ||||||||
\(958\) | 20.3244 | + | 35.2028i | 0.656650 | + | 1.13735i | ||||
\(959\) | 19.1566 | − | 33.1802i | 0.618598 | − | 1.07144i | ||||
\(960\) | 6.84555 | − | 11.8568i | 0.220939 | − | 0.382678i | ||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.7475 | −1.18417 | ||||||||
\(964\) | −54.8078 | + | 94.9299i | −1.76524 | + | 3.05749i | ||||
\(965\) | 6.07880 | − | 10.5288i | 0.195683 | − | 0.338934i | ||||
\(966\) | 25.6562 | + | 44.4379i | 0.825475 | + | 1.42976i | ||||
\(967\) | 32.1716 | 1.03457 | 0.517285 | − | 0.855813i | \(-0.326943\pi\) | ||||
0.517285 | + | 0.855813i | \(0.326943\pi\) | |||||||
\(968\) | 27.3953 | + | 47.4501i | 0.880519 | + | 1.52510i | ||||
\(969\) | 5.16297 | + | 8.94253i | 0.165859 | + | 0.287276i | ||||
\(970\) | 10.5349 | 0.338256 | ||||||||
\(971\) | 8.62705 | + | 14.9425i | 0.276855 | + | 0.479527i | 0.970601 | − | 0.240692i | \(-0.0773745\pi\) |
−0.693746 | + | 0.720219i | \(0.744041\pi\) | |||||||
\(972\) | −30.0908 | + | 52.1188i | −0.965164 | + | 1.67171i | ||||
\(973\) | −19.8383 | + | 34.3609i | −0.635986 | + | 1.10156i | ||||
\(974\) | 50.0122 | 1.60249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7442 | 0.728023 | ||||||||
\(977\) | −7.86142 | + | 13.6164i | −0.251509 | + | 0.435626i | −0.963942 | − | 0.266114i | \(-0.914260\pi\) |
0.712432 | + | 0.701741i | \(0.247593\pi\) | |||||||
\(978\) | 56.3748 | − | 97.6440i | 1.80267 | − | 3.12231i | ||||
\(979\) | 6.72557 | + | 11.6490i | 0.214950 | + | 0.372304i | ||||
\(980\) | 14.2476 | 0.455122 | ||||||||
\(981\) | −25.1447 | − | 43.5518i | −0.802807 | − | 1.39050i | ||||
\(982\) | 19.7124 | + | 34.1429i | 0.629049 | + | 1.08954i | ||||
\(983\) | 38.5356 | 1.22910 | 0.614548 | − | 0.788880i | \(-0.289338\pi\) | ||||
0.614548 | + | 0.788880i | \(0.289338\pi\) | |||||||
\(984\) | 2.10529 | + | 3.64647i | 0.0671141 | + | 0.116245i | ||||
\(985\) | −2.18915 | + | 3.79172i | −0.0697521 | + | 0.120814i | ||||
\(986\) | −7.51821 | + | 13.0219i | −0.239429 | + | 0.414703i | ||||
\(987\) | 50.8743 | 1.61935 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.43298 | 0.0773642 | ||||||||
\(990\) | 6.65968 | − | 11.5349i | 0.211659 | − | 0.366604i | ||||
\(991\) | −4.29571 | + | 7.44040i | −0.136458 | + | 0.236352i | −0.926153 | − | 0.377147i | \(-0.876905\pi\) |
0.789696 | + | 0.613499i | \(0.210238\pi\) | |||||||
\(992\) | 1.75745 | + | 3.04399i | 0.0557991 | + | 0.0966468i | ||||
\(993\) | 81.4014 | 2.58320 | ||||||||
\(994\) | −23.2134 | − | 40.2068i | −0.736285 | − | 1.27528i | ||||
\(995\) | 10.4186 | + | 18.0456i | 0.330293 | + | 0.572085i | ||||
\(996\) | −61.1606 | −1.93795 | ||||||||
\(997\) | 10.2687 | + | 17.7859i | 0.325213 | + | 0.563285i | 0.981555 | − | 0.191178i | \(-0.0612308\pi\) |
−0.656343 | + | 0.754463i | \(0.727897\pi\) | |||||||
\(998\) | −1.55534 | + | 2.69393i | −0.0492335 | + | 0.0852750i | ||||
\(999\) | 2.13157 | − | 3.69198i | 0.0674398 | − | 0.116809i |
(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 | 845.2.e.m.191.1 | 8 | ||
13.2 | odd | 12 | 65.2.m.a.36.1 | ✓ | 8 | ||
13.3 | even | 3 | inner | 845.2.e.m.146.1 | 8 | ||
13.4 | even | 6 | 845.2.a.l.1.1 | 4 | |||
13.5 | odd | 4 | 845.2.m.g.316.4 | 8 | |||
13.6 | odd | 12 | 845.2.c.g.506.1 | 8 | |||
13.7 | odd | 12 | 845.2.c.g.506.8 | 8 | |||
13.8 | odd | 4 | 65.2.m.a.56.1 | yes | 8 | ||
13.9 | even | 3 | 845.2.a.m.1.4 | 4 | |||
13.10 | even | 6 | 845.2.e.n.146.4 | 8 | |||
13.11 | odd | 12 | 845.2.m.g.361.4 | 8 | |||
13.12 | even | 2 | 845.2.e.n.191.4 | 8 | |||
39.2 | even | 12 | 585.2.bu.c.361.4 | 8 | |||
39.8 | even | 4 | 585.2.bu.c.316.4 | 8 | |||
39.17 | odd | 6 | 7605.2.a.cj.1.4 | 4 | |||
39.35 | odd | 6 | 7605.2.a.cf.1.1 | 4 | |||
52.15 | even | 12 | 1040.2.da.b.881.1 | 8 | |||
52.47 | even | 4 | 1040.2.da.b.641.1 | 8 | |||
65.2 | even | 12 | 325.2.m.b.49.1 | 8 | |||
65.4 | even | 6 | 4225.2.a.bl.1.4 | 4 | |||
65.8 | even | 4 | 325.2.m.b.199.1 | 8 | |||
65.9 | even | 6 | 4225.2.a.bi.1.1 | 4 | |||
65.28 | even | 12 | 325.2.m.c.49.4 | 8 | |||
65.34 | odd | 4 | 325.2.n.d.251.4 | 8 | |||
65.47 | even | 4 | 325.2.m.c.199.4 | 8 | |||
65.54 | odd | 12 | 325.2.n.d.101.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.1 | ✓ | 8 | 13.2 | odd | 12 | ||
65.2.m.a.56.1 | yes | 8 | 13.8 | odd | 4 | ||
325.2.m.b.49.1 | 8 | 65.2 | even | 12 | |||
325.2.m.b.199.1 | 8 | 65.8 | even | 4 | |||
325.2.m.c.49.4 | 8 | 65.28 | even | 12 | |||
325.2.m.c.199.4 | 8 | 65.47 | even | 4 | |||
325.2.n.d.101.4 | 8 | 65.54 | odd | 12 | |||
325.2.n.d.251.4 | 8 | 65.34 | odd | 4 | |||
585.2.bu.c.316.4 | 8 | 39.8 | even | 4 | |||
585.2.bu.c.361.4 | 8 | 39.2 | even | 12 | |||
845.2.a.l.1.1 | 4 | 13.4 | even | 6 | |||
845.2.a.m.1.4 | 4 | 13.9 | even | 3 | |||
845.2.c.g.506.1 | 8 | 13.6 | odd | 12 | |||
845.2.c.g.506.8 | 8 | 13.7 | odd | 12 | |||
845.2.e.m.146.1 | 8 | 13.3 | even | 3 | inner | ||
845.2.e.m.191.1 | 8 | 1.1 | even | 1 | trivial | ||
845.2.e.n.146.4 | 8 | 13.10 | even | 6 | |||
845.2.e.n.191.4 | 8 | 13.12 | even | 2 | |||
845.2.m.g.316.4 | 8 | 13.5 | odd | 4 | |||
845.2.m.g.361.4 | 8 | 13.11 | odd | 12 | |||
1040.2.da.b.641.1 | 8 | 52.47 | even | 4 | |||
1040.2.da.b.881.1 | 8 | 52.15 | even | 12 | |||
4225.2.a.bi.1.1 | 4 | 65.9 | even | 6 | |||
4225.2.a.bl.1.4 | 4 | 65.4 | even | 6 | |||
7605.2.a.cf.1.1 | 4 | 39.35 | odd | 6 | |||
7605.2.a.cj.1.4 | 4 | 39.17 | odd | 6 |