Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,3,Mod(93,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.93");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.p (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.53680925261\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 207.4 | ||
Root | \(4.90868 + 1.31528i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.207 |
Dual form | 350.3.p.e.93.4 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.183013 | + | 0.683013i | ||||
\(3\) | 1.31528 | + | 4.90868i | 0.438426 | + | 1.63623i | 0.732733 | + | 0.680516i | \(0.238244\pi\) |
−0.294308 | + | 0.955711i | \(0.595089\pi\) | |||||||
\(4\) | −1.73205 | − | 1.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.18681 | −1.19780 | ||||||||
\(7\) | 0.145113 | + | 6.99850i | 0.0207304 | + | 0.999785i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −14.5710 | + | 8.41254i | −1.61899 | + | 0.934727i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.474367 | − | 0.821627i | 0.0431242 | − | 0.0746934i | −0.843658 | − | 0.536882i | \(-0.819602\pi\) |
0.886782 | + | 0.462188i | \(0.152936\pi\) | |||||||
\(12\) | 2.63055 | − | 9.81736i | 0.219213 | − | 0.818113i | ||||
\(13\) | −0.862338 | + | 0.862338i | −0.0663337 | + | 0.0663337i | −0.739495 | − | 0.673162i | \(-0.764936\pi\) |
0.673162 | + | 0.739495i | \(0.264936\pi\) | |||||||
\(14\) | −9.61324 | − | 2.36340i | −0.686660 | − | 0.168814i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −29.3872 | + | 7.87429i | −1.72866 | + | 0.463193i | −0.979874 | − | 0.199617i | \(-0.936030\pi\) |
−0.748787 | + | 0.662810i | \(0.769364\pi\) | |||||||
\(18\) | −6.15841 | − | 22.9835i | −0.342134 | − | 1.27686i | ||||
\(19\) | 20.9123 | − | 12.0737i | 1.10065 | − | 0.635459i | 0.164256 | − | 0.986418i | \(-0.447478\pi\) |
0.936391 | + | 0.350959i | \(0.114144\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −34.1625 | + | 9.91727i | −1.62679 | + | 0.472251i | ||||
\(22\) | 0.948733 | + | 0.948733i | 0.0431242 | + | 0.0431242i | ||||
\(23\) | 5.47452 | + | 1.46689i | 0.238023 | + | 0.0637780i | 0.375858 | − | 0.926677i | \(-0.377348\pi\) |
−0.137836 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(24\) | 12.4479 | + | 7.18681i | 0.518663 | + | 0.299450i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.862338 | − | 1.49361i | −0.0331669 | − | 0.0574467i | ||||
\(27\) | −28.1187 | − | 28.1187i | −1.04143 | − | 1.04143i | ||||
\(28\) | 6.74715 | − | 12.2669i | 0.240970 | − | 0.438102i | ||||
\(29\) | − | 7.33636i | − | 0.252978i | −0.991968 | − | 0.126489i | \(-0.959629\pi\) | ||
0.991968 | − | 0.126489i | \(-0.0403708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.5316 | + | 40.7579i | −0.759083 | + | 1.31477i | 0.184235 | + | 0.982882i | \(0.441019\pi\) |
−0.943319 | + | 0.331889i | \(0.892314\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 4.65703 | + | 1.24785i | 0.141122 | + | 0.0378135i | ||||
\(34\) | − | 43.0259i | − | 1.26547i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 33.6502 | 0.934727 | ||||||||
\(37\) | 2.13074 | − | 7.95202i | 0.0575875 | − | 0.214919i | −0.931136 | − | 0.364672i | \(-0.881181\pi\) |
0.988723 | + | 0.149753i | \(0.0478477\pi\) | |||||||
\(38\) | 8.83857 | + | 32.9860i | 0.232594 | + | 0.868053i | ||||
\(39\) | −5.36716 | − | 3.09873i | −0.137619 | − | 0.0794546i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.3601 | 1.30147 | 0.650733 | − | 0.759306i | \(-0.274462\pi\) | ||||
0.650733 | + | 0.759306i | \(0.274462\pi\) | |||||||
\(42\) | −1.04290 | − | 50.2968i | −0.0248308 | − | 1.19754i | ||||
\(43\) | 33.0776 | − | 33.0776i | 0.769247 | − | 0.769247i | −0.208727 | − | 0.977974i | \(-0.566932\pi\) |
0.977974 | + | 0.208727i | \(0.0669319\pi\) | |||||||
\(44\) | −1.64325 | + | 0.948733i | −0.0373467 | + | 0.0215621i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00763 | + | 6.94142i | −0.0871224 | + | 0.150900i | ||||
\(47\) | 7.87429 | − | 29.3872i | 0.167538 | − | 0.625260i | −0.830165 | − | 0.557518i | \(-0.811754\pi\) |
0.997703 | − | 0.0677424i | \(-0.0215796\pi\) | |||||||
\(48\) | −14.3736 | + | 14.3736i | −0.299450 | + | 0.299450i | ||||
\(49\) | −48.9579 | + | 2.03114i | −0.999141 | + | 0.0414518i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −77.3047 | − | 133.896i | −1.51578 | − | 2.62541i | ||||
\(52\) | 2.35595 | − | 0.631275i | 0.0453068 | − | 0.0121399i | ||||
\(53\) | −3.48276 | − | 12.9978i | −0.0657125 | − | 0.245242i | 0.925255 | − | 0.379346i | \(-0.123851\pi\) |
−0.990967 | + | 0.134104i | \(0.957184\pi\) | |||||||
\(54\) | 48.7030 | − | 28.1187i | 0.901907 | − | 0.520717i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14.2872 | + | 13.7068i | 0.255129 | + | 0.244764i | ||||
\(57\) | 86.7715 | + | 86.7715i | 1.52231 | + | 1.52231i | ||||
\(58\) | 10.0217 | + | 2.68529i | 0.172787 | + | 0.0462982i | ||||
\(59\) | 43.5119 | + | 25.1216i | 0.737490 | + | 0.425790i | 0.821156 | − | 0.570704i | \(-0.193330\pi\) |
−0.0836659 | + | 0.996494i | \(0.526663\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.7478 | + | 39.4004i | 0.372915 | + | 0.645909i | 0.990013 | − | 0.140978i | \(-0.0450248\pi\) |
−0.617097 | + | 0.786887i | \(0.711691\pi\) | |||||||
\(62\) | −47.0632 | − | 47.0632i | −0.759083 | − | 0.759083i | ||||
\(63\) | −60.9896 | − | 100.754i | −0.968089 | − | 1.59927i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.40918 | + | 5.90487i | −0.0516542 | + | 0.0894678i | ||||
\(67\) | −65.9999 | + | 17.6846i | −0.985073 | + | 0.263949i | −0.715180 | − | 0.698941i | \(-0.753655\pi\) |
−0.269893 | + | 0.962890i | \(0.586988\pi\) | |||||||
\(68\) | 58.7745 | + | 15.7486i | 0.864331 | + | 0.231597i | ||||
\(69\) | 28.8020i | 0.417421i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9203 | −0.167892 | −0.0839460 | − | 0.996470i | \(-0.526752\pi\) | ||||
−0.0839460 | + | 0.996470i | \(0.526752\pi\) | |||||||
\(72\) | −12.3168 | + | 45.9670i | −0.171067 | + | 0.638430i | ||||
\(73\) | 14.2554 | + | 53.2017i | 0.195279 | + | 0.728791i | 0.992194 | + | 0.124700i | \(0.0397969\pi\) |
−0.796916 | + | 0.604091i | \(0.793536\pi\) | |||||||
\(74\) | 10.0828 | + | 5.82128i | 0.136253 | + | 0.0786660i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48.2949 | −0.635459 | ||||||||
\(77\) | 5.81899 | + | 3.20062i | 0.0755713 | + | 0.0415665i | ||||
\(78\) | 6.19746 | − | 6.19746i | 0.0794546 | − | 0.0794546i | ||||
\(79\) | −61.4002 | + | 35.4495i | −0.777218 | + | 0.448727i | −0.835444 | − | 0.549576i | \(-0.814789\pi\) |
0.0582252 | + | 0.998303i | \(0.481456\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.3289 | − | 43.8709i | 0.312702 | − | 0.541616i | ||||
\(82\) | −19.5312 | + | 72.8913i | −0.238185 | + | 0.888918i | ||||
\(83\) | −85.7452 | + | 85.7452i | −1.03307 | + | 1.03307i | −0.0336406 | + | 0.999434i | \(0.510710\pi\) |
−0.999434 | + | 0.0336406i | \(0.989290\pi\) | |||||||
\(84\) | 69.0885 | + | 16.9853i | 0.822482 | + | 0.202206i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 33.0776 | + | 57.2921i | 0.384624 | + | 0.666188i | ||||
\(87\) | 36.0118 | − | 9.64934i | 0.413929 | − | 0.110912i | ||||
\(88\) | −0.694521 | − | 2.59199i | −0.00789228 | − | 0.0294544i | ||||
\(89\) | −135.750 | + | 78.3752i | −1.52528 | + | 0.880621i | −0.525729 | + | 0.850652i | \(0.676207\pi\) |
−0.999551 | + | 0.0299681i | \(0.990459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.16021 | − | 5.90994i | −0.0676946 | − | 0.0649443i | ||||
\(92\) | −8.01526 | − | 8.01526i | −0.0871224 | − | 0.0871224i | ||||
\(93\) | −231.018 | − | 61.9011i | −2.48406 | − | 0.665603i | ||||
\(94\) | 37.2615 | + | 21.5130i | 0.396399 | + | 0.228861i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.3736 | − | 24.8958i | −0.149725 | − | 0.259332i | ||||
\(97\) | 87.1790 | + | 87.1790i | 0.898753 | + | 0.898753i | 0.995326 | − | 0.0965731i | \(-0.0307882\pi\) |
−0.0965731 | + | 0.995326i | \(0.530788\pi\) | |||||||
\(98\) | 15.1452 | − | 67.6212i | 0.154543 | − | 0.690012i | ||||
\(99\) | 15.9625i | 0.161238i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 25.2261 | − | 43.6929i | 0.249763 | − | 0.432603i | −0.713697 | − | 0.700455i | \(-0.752980\pi\) |
0.963460 | + | 0.267852i | \(0.0863138\pi\) | |||||||
\(102\) | 211.200 | − | 56.5910i | 2.07059 | − | 0.554813i | ||||
\(103\) | 139.636 | + | 37.4152i | 1.35569 | + | 0.363255i | 0.862230 | − | 0.506517i | \(-0.169067\pi\) |
0.493455 | + | 0.869771i | \(0.335734\pi\) | |||||||
\(104\) | 3.44935i | 0.0331669i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.0302 | 0.179530 | ||||||||
\(107\) | 1.79591 | − | 6.70244i | 0.0167842 | − | 0.0626397i | −0.957026 | − | 0.290003i | \(-0.906344\pi\) |
0.973810 | + | 0.227363i | \(0.0730104\pi\) | |||||||
\(108\) | 20.5843 | + | 76.8217i | 0.190595 | + | 0.711312i | ||||
\(109\) | 42.3291 | + | 24.4387i | 0.388340 | + | 0.224208i | 0.681441 | − | 0.731873i | \(-0.261354\pi\) |
−0.293100 | + | 0.956082i | \(0.594687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41.8364 | 0.376905 | ||||||||
\(112\) | −23.9533 | + | 14.4997i | −0.213869 | + | 0.129461i | ||||
\(113\) | 8.29274 | − | 8.29274i | 0.0733871 | − | 0.0733871i | −0.669461 | − | 0.742848i | \(-0.733475\pi\) |
0.742848 | + | 0.669461i | \(0.233475\pi\) | |||||||
\(114\) | −150.293 | + | 86.7715i | −1.31836 | + | 0.761153i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.33636 | + | 12.7069i | −0.0632445 | + | 0.109543i | ||||
\(117\) | 5.31063 | − | 19.8196i | 0.0453900 | − | 0.169398i | ||||
\(118\) | −50.2432 | + | 50.2432i | −0.425790 | + | 0.425790i | ||||
\(119\) | −59.3726 | − | 204.524i | −0.498930 | − | 1.71869i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.0500 | + | 104.010i | 0.496281 | + | 0.859583i | ||||
\(122\) | −62.1483 | + | 16.6526i | −0.509412 | + | 0.136497i | ||||
\(123\) | 70.1834 | + | 261.928i | 0.570596 | + | 2.12949i | ||||
\(124\) | 81.5158 | − | 47.0632i | 0.657385 | − | 0.379542i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 159.956 | − | 46.4348i | 1.26949 | − | 0.368530i | ||||
\(127\) | 80.3440 | + | 80.3440i | 0.632630 | + | 0.632630i | 0.948727 | − | 0.316097i | \(-0.102373\pi\) |
−0.316097 | + | 0.948727i | \(0.602373\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 205.874 | + | 118.861i | 1.59592 | + | 0.921405i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5429 | − | 21.7250i | −0.0957475 | − | 0.165840i | 0.814173 | − | 0.580623i | \(-0.197191\pi\) |
−0.909920 | + | 0.414783i | \(0.863857\pi\) | |||||||
\(132\) | −6.81836 | − | 6.81836i | −0.0516542 | − | 0.0516542i | ||||
\(133\) | 87.5325 | + | 144.603i | 0.658139 | + | 1.08724i | ||||
\(134\) | − | 96.6305i | − | 0.721123i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −43.0259 | + | 74.5231i | −0.316367 | + | 0.547964i | ||||
\(137\) | −66.0647 | + | 17.7020i | −0.482224 | + | 0.129212i | −0.491738 | − | 0.870743i | \(-0.663638\pi\) |
0.00951399 | + | 0.999955i | \(0.496972\pi\) | |||||||
\(138\) | −39.3443 | − | 10.5423i | −0.285104 | − | 0.0763933i | ||||
\(139\) | − | 67.3054i | − | 0.484212i | −0.970250 | − | 0.242106i | \(-0.922162\pi\) | ||
0.970250 | − | 0.242106i | \(-0.0778381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 154.609 | 1.09652 | ||||||||
\(142\) | 4.36314 | − | 16.2835i | 0.0307264 | − | 0.114672i | ||||
\(143\) | 0.299456 | + | 1.11758i | 0.00209410 | + | 0.00781528i | ||||
\(144\) | −58.2838 | − | 33.6502i | −0.404749 | − | 0.233682i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −77.8927 | −0.533512 | ||||||||
\(147\) | −74.3634 | − | 237.647i | −0.505873 | − | 1.61665i | ||||
\(148\) | −11.6426 | + | 11.6426i | −0.0786660 | + | 0.0786660i | ||||
\(149\) | 51.9776 | − | 30.0093i | 0.348843 | − | 0.201404i | −0.315333 | − | 0.948981i | \(-0.602116\pi\) |
0.664175 | + | 0.747577i | \(0.268783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.9018 | + | 41.3992i | −0.158290 | + | 0.274167i | −0.934252 | − | 0.356613i | \(-0.883932\pi\) |
0.775962 | + | 0.630780i | \(0.217265\pi\) | |||||||
\(152\) | 17.6771 | − | 65.9720i | 0.116297 | − | 0.434026i | ||||
\(153\) | 361.957 | − | 361.957i | 2.36573 | − | 2.36573i | ||||
\(154\) | −6.50203 | + | 6.77738i | −0.0422210 | + | 0.0440089i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.19746 | + | 10.7343i | 0.0397273 | + | 0.0688097i | ||||
\(157\) | 101.024 | − | 27.0694i | 0.643466 | − | 0.172416i | 0.0776933 | − | 0.996977i | \(-0.475245\pi\) |
0.565773 | + | 0.824561i | \(0.308578\pi\) | |||||||
\(158\) | −25.9508 | − | 96.8497i | −0.164246 | − | 0.612973i | ||||
\(159\) | 59.2214 | − | 34.1915i | 0.372462 | − | 0.215041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.47163 | + | 38.5263i | −0.0588300 | + | 0.239294i | ||||
\(162\) | 50.6578 | + | 50.6578i | 0.312702 | + | 0.312702i | ||||
\(163\) | −39.7089 | − | 10.6400i | −0.243613 | − | 0.0652759i | 0.134946 | − | 0.990853i | \(-0.456914\pi\) |
−0.378559 | + | 0.925577i | \(0.623580\pi\) | |||||||
\(164\) | −92.4225 | − | 53.3601i | −0.563552 | − | 0.325367i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −85.7452 | − | 148.515i | −0.516537 | − | 0.894669i | ||||
\(167\) | −26.4354 | − | 26.4354i | −0.158296 | − | 0.158296i | 0.623515 | − | 0.781811i | \(-0.285704\pi\) |
−0.781811 | + | 0.623515i | \(0.785704\pi\) | |||||||
\(168\) | −48.4905 | + | 88.1596i | −0.288634 | + | 0.524759i | ||||
\(169\) | 167.513i | 0.991200i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −203.141 | + | 351.851i | −1.18796 | + | 2.05761i | ||||
\(172\) | −90.3698 | + | 24.2145i | −0.525406 | + | 0.140782i | ||||
\(173\) | −242.480 | − | 64.9724i | −1.40162 | − | 0.375563i | −0.522693 | − | 0.852521i | \(-0.675073\pi\) |
−0.878926 | + | 0.476958i | \(0.841739\pi\) | |||||||
\(174\) | 52.7250i | 0.303017i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.79493 | 0.0215621 | ||||||||
\(177\) | −66.0838 | + | 246.628i | −0.373355 | + | 1.39338i | ||||
\(178\) | −57.3746 | − | 214.125i | −0.322329 | − | 1.20295i | ||||
\(179\) | 46.8192 | + | 27.0311i | 0.261560 | + | 0.151012i | 0.625046 | − | 0.780588i | \(-0.285080\pi\) |
−0.363486 | + | 0.931600i | \(0.618414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 201.453 | 1.11300 | 0.556501 | − | 0.830847i | \(-0.312143\pi\) | ||||
0.556501 | + | 0.830847i | \(0.312143\pi\) | |||||||
\(182\) | 10.3279 | − | 6.25181i | 0.0567468 | − | 0.0343506i | ||||
\(183\) | −163.484 | + | 163.484i | −0.893357 | + | 0.893357i | ||||
\(184\) | 13.8828 | − | 8.01526i | 0.0754502 | − | 0.0435612i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 169.117 | − | 292.919i | 0.909231 | − | 1.57483i | ||||
\(187\) | −7.47060 | + | 27.8807i | −0.0399497 | + | 0.149094i | ||||
\(188\) | −43.0259 | + | 43.0259i | −0.228861 | + | 0.228861i | ||||
\(189\) | 192.708 | − | 200.869i | 1.01962 | − | 1.06280i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −87.8707 | − | 152.197i | −0.460056 | − | 0.796841i | 0.538907 | − | 0.842365i | \(-0.318837\pi\) |
−0.998963 | + | 0.0455246i | \(0.985504\pi\) | |||||||
\(192\) | 39.2694 | − | 10.5222i | 0.204528 | − | 0.0548032i | ||||
\(193\) | 13.5073 | + | 50.4101i | 0.0699862 | + | 0.261192i | 0.992050 | − | 0.125846i | \(-0.0401647\pi\) |
−0.922064 | + | 0.387039i | \(0.873498\pi\) | |||||||
\(194\) | −150.998 | + | 87.1790i | −0.778343 | + | 0.449376i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 86.8287 | + | 45.4398i | 0.443003 | + | 0.231836i | ||||
\(197\) | 62.8178 | + | 62.8178i | 0.318872 | + | 0.318872i | 0.848334 | − | 0.529462i | \(-0.177606\pi\) |
−0.529462 | + | 0.848334i | \(0.677606\pi\) | |||||||
\(198\) | −21.8052 | − | 5.84269i | −0.110127 | − | 0.0295085i | ||||
\(199\) | 22.4632 | + | 12.9692i | 0.112881 | + | 0.0651717i | 0.555377 | − | 0.831598i | \(-0.312574\pi\) |
−0.442497 | + | 0.896770i | \(0.645907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −173.616 | − | 300.712i | −0.863762 | − | 1.49608i | ||||
\(202\) | 50.4522 | + | 50.4522i | 0.249763 | + | 0.249763i | ||||
\(203\) | 51.3435 | − | 1.06460i | 0.252924 | − | 0.00524432i | ||||
\(204\) | 309.219i | 1.51578i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −102.220 | + | 177.051i | −0.496215 | + | 0.859470i | ||||
\(207\) | −92.1093 | + | 24.6806i | −0.444973 | + | 0.119230i | ||||
\(208\) | −4.71190 | − | 1.26255i | −0.0226534 | − | 0.00606996i | ||||
\(209\) | − | 22.9095i | − | 0.109615i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −223.675 | −1.06007 | −0.530036 | − | 0.847975i | \(-0.677822\pi\) | ||||
−0.530036 | + | 0.847975i | \(0.677822\pi\) | |||||||
\(212\) | −6.96552 | + | 25.9957i | −0.0328562 | + | 0.122621i | ||||
\(213\) | −15.6785 | − | 58.5131i | −0.0736081 | − | 0.274709i | ||||
\(214\) | 8.49836 | + | 4.90653i | 0.0397119 | + | 0.0229277i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −112.475 | −0.520717 | ||||||||
\(217\) | −288.659 | − | 158.771i | −1.33022 | − | 0.731664i | ||||
\(218\) | −48.8774 | + | 48.8774i | −0.224208 | + | 0.224208i | ||||
\(219\) | −242.400 | + | 139.950i | −1.10685 | + | 0.639041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.5514 | − | 32.1320i | 0.0839432 | − | 0.145394i | ||||
\(222\) | −15.3132 | + | 57.1496i | −0.0689784 | + | 0.257431i | ||||
\(223\) | 131.856 | − | 131.856i | 0.591282 | − | 0.591282i | −0.346696 | − | 0.937978i | \(-0.612696\pi\) |
0.937978 | + | 0.346696i | \(0.112696\pi\) | |||||||
\(224\) | −11.0394 | − | 38.0280i | −0.0492831 | − | 0.169768i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.29274 | + | 14.3634i | 0.0366935 | + | 0.0635551i | ||||
\(227\) | 366.184 | − | 98.1186i | 1.61314 | − | 0.432241i | 0.664166 | − | 0.747585i | \(-0.268787\pi\) |
0.948977 | + | 0.315344i | \(0.102120\pi\) | |||||||
\(228\) | −63.5211 | − | 237.064i | −0.278601 | − | 1.03975i | ||||
\(229\) | 39.8456 | − | 23.0049i | 0.173998 | − | 0.100458i | −0.410471 | − | 0.911873i | \(-0.634636\pi\) |
0.584470 | + | 0.811415i | \(0.301303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.05726 | + | 32.7733i | −0.0348799 | + | 0.141876i | ||||
\(232\) | −14.6727 | − | 14.6727i | −0.0632445 | − | 0.0632445i | ||||
\(233\) | 100.854 | + | 27.0237i | 0.432849 | + | 0.115981i | 0.468663 | − | 0.883377i | \(-0.344736\pi\) |
−0.0358143 | + | 0.999358i | \(0.511402\pi\) | |||||||
\(234\) | 25.1302 | + | 14.5089i | 0.107394 | + | 0.0620039i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −50.2432 | − | 87.0238i | −0.212895 | − | 0.368745i | ||||
\(237\) | −254.768 | − | 254.768i | −1.07497 | − | 1.07497i | ||||
\(238\) | 301.117 | − | 6.24360i | 1.26520 | − | 0.0262336i | ||||
\(239\) | − | 4.00351i | − | 0.0167511i | −0.999965 | − | 0.00837554i | \(-0.997334\pi\) | ||
0.999965 | − | 0.00837554i | \(-0.00266605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 148.899 | − | 257.901i | 0.617839 | − | 1.07013i | −0.372041 | − | 0.928216i | \(-0.621342\pi\) |
0.989879 | − | 0.141912i | \(-0.0453249\pi\) | |||||||
\(242\) | −164.060 | + | 43.9596i | −0.677932 | + | 0.181651i | ||||
\(243\) | −97.0348 | − | 26.0004i | −0.399320 | − | 0.106998i | ||||
\(244\) | − | 90.9914i | − | 0.372915i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −383.489 | −1.55890 | ||||||||
\(247\) | −7.62184 | + | 28.4451i | −0.0308577 | + | 0.115162i | ||||
\(248\) | 34.4526 | + | 128.579i | 0.138922 | + | 0.518463i | ||||
\(249\) | −533.674 | − | 308.117i | −2.14327 | − | 1.23742i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 300.624 | 1.19770 | 0.598852 | − | 0.800860i | \(-0.295624\pi\) | ||||
0.598852 | + | 0.800860i | \(0.295624\pi\) | |||||||
\(252\) | 4.88306 | + | 235.501i | 0.0193772 | + | 0.934526i | ||||
\(253\) | 3.80217 | − | 3.80217i | 0.0150283 | − | 0.0150283i | ||||
\(254\) | −139.160 | + | 80.3440i | −0.547873 | + | 0.316315i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 85.5296 | − | 319.201i | 0.332800 | − | 1.24203i | −0.573435 | − | 0.819251i | \(-0.694389\pi\) |
0.906235 | − | 0.422775i | \(-0.138944\pi\) | |||||||
\(258\) | −237.723 | + | 237.723i | −0.921405 | + | 0.921405i | ||||
\(259\) | 55.9614 | + | 13.7580i | 0.216067 | + | 0.0531198i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 61.7175 | + | 106.898i | 0.236465 | + | 0.409570i | ||||
\(262\) | 34.2679 | − | 9.18206i | 0.130794 | − | 0.0350460i | ||||
\(263\) | −97.9751 | − | 365.648i | −0.372529 | − | 1.39030i | −0.856922 | − | 0.515446i | \(-0.827626\pi\) |
0.484393 | − | 0.874851i | \(-0.339041\pi\) | |||||||
\(264\) | 11.8097 | − | 6.81836i | 0.0447339 | − | 0.0258271i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −229.570 | + | 66.6434i | −0.863044 | + | 0.250539i | ||||
\(267\) | −563.268 | − | 563.268i | −2.10962 | − | 2.10962i | ||||
\(268\) | 132.000 | + | 35.3692i | 0.492536 | + | 0.131975i | ||||
\(269\) | 125.485 | + | 72.4489i | 0.466488 | + | 0.269327i | 0.714768 | − | 0.699361i | \(-0.246532\pi\) |
−0.248280 | + | 0.968688i | \(0.579865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 165.311 | + | 286.326i | 0.610002 | + | 1.05655i | 0.991239 | + | 0.132078i | \(0.0421648\pi\) |
−0.381237 | + | 0.924477i | \(0.624502\pi\) | |||||||
\(272\) | −86.0518 | − | 86.0518i | −0.316367 | − | 0.316367i | ||||
\(273\) | 20.9076 | − | 38.0117i | 0.0765846 | − | 0.139237i | ||||
\(274\) | − | 96.7254i | − | 0.353012i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 28.8020 | − | 49.8866i | 0.104355 | − | 0.180749i | ||||
\(277\) | 75.9189 | − | 20.3424i | 0.274075 | − | 0.0734383i | −0.119163 | − | 0.992875i | \(-0.538021\pi\) |
0.393239 | + | 0.919436i | \(0.371355\pi\) | |||||||
\(278\) | 91.9409 | + | 24.6355i | 0.330723 | + | 0.0886169i | ||||
\(279\) | − | 791.842i | − | 2.83814i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −342.866 | −1.22016 | −0.610081 | − | 0.792339i | \(-0.708863\pi\) | ||||
−0.610081 | + | 0.792339i | \(0.708863\pi\) | |||||||
\(282\) | −56.5910 | + | 211.200i | −0.200677 | + | 0.748938i | ||||
\(283\) | 24.0385 | + | 89.7129i | 0.0849417 | + | 0.317007i | 0.995303 | − | 0.0968072i | \(-0.0308630\pi\) |
−0.910361 | + | 0.413814i | \(0.864196\pi\) | |||||||
\(284\) | 20.6466 | + | 11.9203i | 0.0726994 | + | 0.0419730i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.63626 | −0.00572118 | ||||||||
\(287\) | 7.74323 | + | 373.441i | 0.0269799 | + | 1.30119i | ||||
\(288\) | 67.3004 | − | 67.3004i | 0.233682 | − | 0.233682i | ||||
\(289\) | 551.324 | − | 318.307i | 1.90770 | − | 1.10141i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −313.269 | + | 542.598i | −1.07653 | + | 1.86460i | ||||
\(292\) | 28.5107 | − | 106.403i | 0.0976394 | − | 0.364395i | ||||
\(293\) | 345.276 | − | 345.276i | 1.17842 | − | 1.17842i | 0.198270 | − | 0.980147i | \(-0.436468\pi\) |
0.980147 | − | 0.198270i | \(-0.0635323\pi\) | |||||||
\(294\) | 351.851 | − | 14.5974i | 1.19677 | − | 0.0496510i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.6426 | − | 20.1655i | −0.0393330 | − | 0.0681267i | ||||
\(297\) | −36.4416 | + | 9.76451i | −0.122699 | + | 0.0328771i | ||||
\(298\) | 21.9683 | + | 81.9868i | 0.0737191 | + | 0.275124i | ||||
\(299\) | −5.98585 | + | 3.45593i | −0.0200196 | + | 0.0115583i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 236.294 | + | 226.694i | 0.785029 | + | 0.753135i | ||||
\(302\) | −47.8037 | − | 47.8037i | −0.158290 | − | 0.158290i | ||||
\(303\) | 247.654 | + | 66.3586i | 0.817339 | + | 0.219005i | ||||
\(304\) | 83.6492 | + | 48.2949i | 0.275162 | + | 0.158865i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 361.957 | + | 626.929i | 1.18287 | + | 2.04879i | ||||
\(307\) | 344.100 | + | 344.100i | 1.12085 | + | 1.12085i | 0.991614 | + | 0.129233i | \(0.0412517\pi\) |
0.129233 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(308\) | −6.87816 | − | 11.3626i | −0.0223317 | − | 0.0368917i | ||||
\(309\) | 734.638i | 2.37747i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 165.159 | − | 286.064i | 0.531059 | − | 0.919821i | −0.468284 | − | 0.883578i | \(-0.655128\pi\) |
0.999343 | − | 0.0362433i | \(-0.0115391\pi\) | |||||||
\(312\) | −16.9318 | + | 4.53685i | −0.0542685 | + | 0.0145412i | ||||
\(313\) | 82.7090 | + | 22.1618i | 0.264246 | + | 0.0708045i | 0.388509 | − | 0.921445i | \(-0.372990\pi\) |
−0.124263 | + | 0.992249i | \(0.539657\pi\) | |||||||
\(314\) | 147.910i | 0.471050i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 141.798 | 0.448727 | ||||||||
\(317\) | 45.6055 | − | 170.202i | 0.143866 | − | 0.536915i | −0.855937 | − | 0.517080i | \(-0.827019\pi\) |
0.999803 | − | 0.0198354i | \(-0.00631421\pi\) | |||||||
\(318\) | 25.0299 | + | 93.4129i | 0.0787104 | + | 0.293751i | ||||
\(319\) | −6.02775 | − | 3.48012i | −0.0188958 | − | 0.0109095i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.2623 | 0.109851 | ||||||||
\(322\) | −49.1610 | − | 27.0401i | −0.152674 | − | 0.0839754i | ||||
\(323\) | −519.483 | + | 519.483i | −1.60831 | + | 1.60831i | ||||
\(324\) | −87.7419 | + | 50.6578i | −0.270808 | + | 0.156351i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.0689 | − | 50.3489i | 0.0891685 | − | 0.154444i | ||||
\(327\) | −64.2873 | + | 239.924i | −0.196597 | + | 0.733711i | ||||
\(328\) | 106.720 | − | 106.720i | 0.325367 | − | 0.325367i | ||||
\(329\) | 206.809 | + | 50.8437i | 0.628599 | + | 0.154540i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160.736 | − | 278.404i | −0.485608 | − | 0.841098i | 0.514255 | − | 0.857637i | \(-0.328069\pi\) |
−0.999863 | + | 0.0165391i | \(0.994735\pi\) | |||||||
\(332\) | 234.260 | − | 62.7698i | 0.705603 | − | 0.189066i | ||||
\(333\) | 35.8498 | + | 133.793i | 0.107657 | + | 0.401782i | ||||
\(334\) | 45.7874 | − | 26.4354i | 0.137088 | − | 0.0791479i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −102.679 | − | 98.5079i | −0.305594 | − | 0.293178i | ||||
\(337\) | 77.9872 | + | 77.9872i | 0.231416 | + | 0.231416i | 0.813284 | − | 0.581868i | \(-0.197678\pi\) |
−0.581868 | + | 0.813284i | \(0.697678\pi\) | |||||||
\(338\) | −228.827 | − | 61.3139i | −0.677002 | − | 0.181402i | ||||
\(339\) | 51.6137 | + | 29.7992i | 0.152253 | + | 0.0879031i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.3252 | + | 38.6684i | 0.0654698 | + | 0.113397i | ||||
\(342\) | −406.283 | − | 406.283i | −1.18796 | − | 1.18796i | ||||
\(343\) | −21.3193 | − | 342.337i | −0.0621555 | − | 0.998066i | ||||
\(344\) | − | 132.311i | − | 0.384624i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 177.508 | − | 307.453i | 0.513028 | − | 0.888591i | ||||
\(347\) | −325.624 | + | 87.2508i | −0.938398 | + | 0.251443i | −0.695432 | − | 0.718592i | \(-0.744787\pi\) |
−0.242966 | + | 0.970035i | \(0.578120\pi\) | |||||||
\(348\) | −72.0237 | − | 19.2987i | −0.206965 | − | 0.0554560i | ||||
\(349\) | − | 287.505i | − | 0.823797i | −0.911230 | − | 0.411899i | \(-0.864866\pi\) | ||
0.911230 | − | 0.411899i | \(-0.135134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 48.4957 | 0.138164 | ||||||||
\(352\) | −1.38904 | + | 5.18397i | −0.00394614 | + | 0.0147272i | ||||
\(353\) | −42.9263 | − | 160.203i | −0.121604 | − | 0.453834i | 0.878092 | − | 0.478493i | \(-0.158817\pi\) |
−0.999696 | + | 0.0246589i | \(0.992150\pi\) | |||||||
\(354\) | −312.712 | − | 180.544i | −0.883366 | − | 0.510012i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 313.501 | 0.880621 | ||||||||
\(357\) | 925.851 | − | 560.447i | 2.59342 | − | 1.56988i | ||||
\(358\) | −54.0621 | + | 54.0621i | −0.151012 | + | 0.151012i | ||||
\(359\) | −324.332 | + | 187.253i | −0.903432 | + | 0.521597i | −0.878312 | − | 0.478088i | \(-0.841330\pi\) |
−0.0251201 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 111.049 | − | 192.343i | 0.307616 | − | 0.532806i | ||||
\(362\) | −73.7371 | + | 275.191i | −0.203694 | + | 0.760195i | ||||
\(363\) | −431.567 | + | 431.567i | −1.18889 | + | 1.18889i | ||||
\(364\) | 4.75986 | + | 16.3965i | 0.0130765 | + | 0.0450454i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −163.484 | − | 283.163i | −0.446678 | − | 0.773670i | ||||
\(367\) | 31.5361 | − | 8.45008i | 0.0859295 | − | 0.0230247i | −0.215598 | − | 0.976482i | \(-0.569170\pi\) |
0.301528 | + | 0.953457i | \(0.402503\pi\) | |||||||
\(368\) | 5.86758 | + | 21.8981i | 0.0159445 | + | 0.0595057i | ||||
\(369\) | −777.508 | + | 448.895i | −2.10707 | + | 1.21652i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 90.4599 | − | 26.2602i | 0.243827 | − | 0.0707823i | ||||
\(372\) | 338.234 | + | 338.234i | 0.909231 | + | 0.909231i | ||||
\(373\) | 711.719 | + | 190.704i | 1.90809 | + | 0.511272i | 0.994513 | + | 0.104614i | \(0.0333606\pi\) |
0.913580 | + | 0.406658i | \(0.133306\pi\) | |||||||
\(374\) | −35.3512 | − | 20.4101i | −0.0945221 | − | 0.0545723i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −43.0259 | − | 74.5231i | −0.114431 | − | 0.198200i | ||||
\(377\) | 6.32643 | + | 6.32643i | 0.0167810 | + | 0.0167810i | ||||
\(378\) | 203.856 | + | 336.767i | 0.539301 | + | 0.890919i | ||||
\(379\) | − | 287.166i | − | 0.757693i | −0.925460 | − | 0.378846i | \(-0.876321\pi\) | ||
0.925460 | − | 0.378846i | \(-0.123679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −288.708 | + | 500.057i | −0.757764 | + | 1.31249i | ||||
\(382\) | 240.067 | − | 64.3258i | 0.628448 | − | 0.168392i | ||||
\(383\) | −441.247 | − | 118.232i | −1.15208 | − | 0.308699i | −0.368283 | − | 0.929714i | \(-0.620054\pi\) |
−0.783799 | + | 0.621014i | \(0.786721\pi\) | |||||||
\(384\) | 57.4944i | 0.149725i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −73.8055 | −0.191206 | ||||||||
\(387\) | −203.706 | + | 760.240i | −0.526371 | + | 1.96444i | ||||
\(388\) | −63.8195 | − | 238.178i | −0.164483 | − | 0.613860i | ||||
\(389\) | 470.416 | + | 271.595i | 1.20930 | + | 0.698187i | 0.962605 | − | 0.270907i | \(-0.0873237\pi\) |
0.246690 | + | 0.969094i | \(0.420657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −172.432 | −0.441002 | ||||||||
\(392\) | −93.8535 | + | 101.978i | −0.239422 | + | 0.260148i | ||||
\(393\) | 90.1435 | − | 90.1435i | 0.229373 | − | 0.229373i | ||||
\(394\) | −108.804 | + | 62.8178i | −0.276151 | + | 0.159436i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.9625 | − | 27.6479i | 0.0403094 | − | 0.0698179i | ||||
\(397\) | −165.368 | + | 617.160i | −0.416543 | + | 1.55456i | 0.365182 | + | 0.930936i | \(0.381007\pi\) |
−0.781725 | + | 0.623623i | \(0.785660\pi\) | |||||||
\(398\) | −25.9383 | + | 25.9383i | −0.0651717 | + | 0.0651717i | ||||
\(399\) | −594.678 | + | 619.861i | −1.49042 | + | 1.55354i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −223.636 | − | 387.349i | −0.557696 | − | 0.965958i | −0.997688 | − | 0.0679566i | \(-0.978352\pi\) |
0.439992 | − | 0.898002i | \(-0.354981\pi\) | |||||||
\(402\) | 474.328 | − | 127.096i | 1.17992 | − | 0.316159i | ||||
\(403\) | −14.8549 | − | 55.4393i | −0.0368608 | − | 0.137566i | ||||
\(404\) | −87.3858 | + | 50.4522i | −0.216302 | + | 0.124882i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.3388 | + | 70.5262i | −0.0427063 | + | 0.173710i | ||||
\(407\) | −5.52284 | − | 5.52284i | −0.0135696 | − | 0.0135696i | ||||
\(408\) | −422.401 | − | 113.182i | −1.03530 | − | 0.277407i | ||||
\(409\) | −19.9762 | − | 11.5333i | −0.0488417 | − | 0.0281988i | 0.475380 | − | 0.879780i | \(-0.342310\pi\) |
−0.524222 | + | 0.851582i | \(0.675644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −173.787 | − | 301.007i | −0.422839 | − | 0.732378i | ||||
\(412\) | −204.441 | − | 204.441i | −0.496215 | − | 0.496215i | ||||
\(413\) | −169.499 | + | 308.163i | −0.410410 | + | 0.746158i | ||||
\(414\) | − | 134.857i | − | 0.325743i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.44935 | − | 5.97446i | 0.00829172 | − | 0.0143617i | ||||
\(417\) | 330.381 | − | 88.5253i | 0.792280 | − | 0.212291i | ||||
\(418\) | 31.2949 | + | 8.38545i | 0.0748682 | + | 0.0200609i | ||||
\(419\) | 502.792i | 1.19998i | 0.800007 | + | 0.599990i | \(0.204829\pi\) | ||||
−0.800007 | + | 0.599990i | \(0.795171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 48.4897 | 0.115177 | 0.0575887 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575887 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(422\) | 81.8708 | − | 305.546i | 0.194007 | − | 0.724043i | ||||
\(423\) | 132.486 | + | 494.443i | 0.313205 | + | 1.16890i | ||||
\(424\) | −32.9612 | − | 19.0302i | −0.0777387 | − | 0.0448824i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 85.6691 | 0.201101 | ||||||||
\(427\) | −272.443 | + | 164.918i | −0.638039 | + | 0.386225i | ||||
\(428\) | −9.81306 | + | 9.81306i | −0.0229277 | + | 0.0229277i | ||||
\(429\) | −5.09200 | + | 2.93987i | −0.0118695 | + | 0.00685284i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 185.726 | − | 321.686i | 0.430918 | − | 0.746372i | −0.566035 | − | 0.824381i | \(-0.691523\pi\) |
0.996953 | + | 0.0780097i | \(0.0248565\pi\) | |||||||
\(432\) | 41.1686 | − | 153.643i | 0.0952977 | − | 0.355656i | ||||
\(433\) | −449.707 | + | 449.707i | −1.03858 | + | 1.03858i | −0.0393595 | + | 0.999225i | \(0.512532\pi\) |
−0.999225 | + | 0.0393595i | \(0.987468\pi\) | |||||||
\(434\) | 322.542 | − | 336.201i | 0.743184 | − | 0.774656i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.8774 | − | 84.6582i | −0.112104 | − | 0.194170i | ||||
\(437\) | 132.196 | − | 35.4217i | 0.302507 | − | 0.0810566i | ||||
\(438\) | −102.450 | − | 382.350i | −0.233905 | − | 0.872946i | ||||
\(439\) | 508.790 | − | 293.750i | 1.15897 | − | 0.669134i | 0.207917 | − | 0.978147i | \(-0.433332\pi\) |
0.951058 | + | 0.309012i | \(0.0999984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 696.276 | − | 441.456i | 1.57886 | − | 1.00103i | ||||
\(442\) | 37.1029 | + | 37.1029i | 0.0839432 | + | 0.0839432i | ||||
\(443\) | 4.58686 | + | 1.22904i | 0.0103541 | + | 0.00277437i | 0.263992 | − | 0.964525i | \(-0.414961\pi\) |
−0.253638 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(444\) | −72.4628 | − | 41.8364i | −0.163205 | − | 0.0942262i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 131.856 | + | 228.381i | 0.295641 | + | 0.512065i | ||||
\(447\) | 215.671 | + | 215.671i | 0.482485 | + | 0.482485i | ||||
\(448\) | 55.9880 | − | 1.16090i | 0.124973 | − | 0.00259130i | ||||
\(449\) | − | 40.6375i | − | 0.0905067i | −0.998976 | − | 0.0452533i | \(-0.985590\pi\) | ||
0.998976 | − | 0.0452533i | \(-0.0144095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3123 | − | 43.8421i | 0.0561248 | − | 0.0972109i | ||||
\(452\) | −22.6562 | + | 6.07071i | −0.0501243 | + | 0.0134308i | ||||
\(453\) | −234.653 | − | 62.8750i | −0.517997 | − | 0.138797i | ||||
\(454\) | 536.130i | 1.18090i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 347.086 | 0.761153 | ||||||||
\(457\) | −85.0810 | + | 317.526i | −0.186173 | + | 0.694806i | 0.808204 | + | 0.588903i | \(0.200440\pi\) |
−0.994376 | + | 0.105903i | \(0.966227\pi\) | |||||||
\(458\) | 16.8407 | + | 62.8505i | 0.0367702 | + | 0.137228i | ||||
\(459\) | 1047.75 | + | 604.916i | 2.28267 | + | 1.31790i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 64.7559 | 0.140468 | 0.0702341 | − | 0.997531i | \(-0.477625\pi\) | ||||
0.0702341 | + | 0.997531i | \(0.477625\pi\) | |||||||
\(462\) | −41.8199 | − | 23.0023i | −0.0905194 | − | 0.0497884i | ||||
\(463\) | 604.400 | − | 604.400i | 1.30540 | − | 1.30540i | 0.380701 | − | 0.924698i | \(-0.375683\pi\) |
0.924698 | − | 0.380701i | \(-0.124317\pi\) | |||||||
\(464\) | 25.4139 | − | 14.6727i | 0.0547713 | − | 0.0316222i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −73.8301 | + | 127.877i | −0.158434 | + | 0.274415i | ||||
\(467\) | 92.4995 | − | 345.213i | 0.198072 | − | 0.739214i | −0.793379 | − | 0.608729i | \(-0.791680\pi\) |
0.991450 | − | 0.130485i | \(-0.0416535\pi\) | |||||||
\(468\) | −29.0178 | + | 29.0178i | −0.0620039 | + | 0.0620039i | ||||
\(469\) | −133.343 | − | 459.334i | −0.284314 | − | 0.979389i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 265.750 | + | 460.292i | 0.564224 | + | 0.977265i | ||||
\(472\) | 137.267 | − | 36.7806i | 0.290820 | − | 0.0779250i | ||||
\(473\) | −11.4866 | − | 42.8684i | −0.0242845 | − | 0.0906309i | ||||
\(474\) | 441.272 | − | 254.768i | 0.930953 | − | 0.537486i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −101.687 | + | 413.618i | −0.213629 | + | 0.868946i | ||||
\(477\) | 160.092 | + | 160.092i | 0.335623 | + | 0.335623i | ||||
\(478\) | 5.46889 | + | 1.46539i | 0.0114412 | + | 0.00306566i | ||||
\(479\) | 508.668 | + | 293.679i | 1.06194 | + | 0.613109i | 0.925967 | − | 0.377604i | \(-0.123252\pi\) |
0.135969 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.01992 | + | 8.69475i | 0.0104364 | + | 0.0180764i | ||||
\(482\) | 297.798 | + | 297.798i | 0.617839 | + | 0.617839i | ||||
\(483\) | −201.571 | + | 4.17954i | −0.417331 | + | 0.00865329i | ||||
\(484\) | − | 240.200i | − | 0.496281i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 71.0344 | − | 123.035i | 0.146161 | − | 0.253159i | ||||
\(487\) | 549.440 | − | 147.222i | 1.12821 | − | 0.302304i | 0.354010 | − | 0.935242i | \(-0.384818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(488\) | 124.297 | + | 33.3052i | 0.254706 | + | 0.0682483i | ||||
\(489\) | − | 208.913i | − | 0.427224i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 485.037 | 0.987856 | 0.493928 | − | 0.869503i | \(-0.335561\pi\) | ||||
0.493928 | + | 0.869503i | \(0.335561\pi\) | |||||||
\(492\) | 140.367 | − | 523.856i | 0.285298 | − | 1.06475i | ||||
\(493\) | 57.7686 | + | 215.595i | 0.117178 | + | 0.437313i | ||||
\(494\) | −36.0669 | − | 20.8233i | −0.0730100 | − | 0.0421523i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −188.253 | −0.379542 | ||||||||
\(497\) | −1.72979 | − | 83.4244i | −0.00348046 | − | 0.167856i | ||||
\(498\) | 616.234 | − | 616.234i | 1.23742 | − | 1.23742i | ||||
\(499\) | −500.231 | + | 288.808i | −1.00247 | + | 0.578774i | −0.908977 | − | 0.416846i | \(-0.863135\pi\) |
−0.0934891 | + | 0.995620i | \(0.529802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 94.9930 | − | 164.533i | 0.189607 | − | 0.328409i | ||||
\(502\) | −110.036 | + | 410.660i | −0.219195 | + | 0.818047i | ||||
\(503\) | 417.802 | − | 417.802i | 0.830620 | − | 0.830620i | −0.156981 | − | 0.987602i | \(-0.550176\pi\) |
0.987602 | + | 0.156981i | \(0.0501763\pi\) | |||||||
\(504\) | −323.487 | − | 79.5288i | −0.641840 | − | 0.157795i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.80217 | + | 6.58555i | 0.00751417 | + | 0.0130149i | ||||
\(507\) | −822.266 | + | 220.326i | −1.62183 | + | 0.434567i | ||||
\(508\) | −58.8159 | − | 219.504i | −0.115779 | − | 0.432094i | ||||
\(509\) | −136.905 | + | 79.0420i | −0.268968 | + | 0.155289i | −0.628419 | − | 0.777875i | \(-0.716297\pi\) |
0.359451 | + | 0.933164i | \(0.382964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −370.263 | + | 107.486i | −0.724586 | + | 0.210345i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −927.523 | − | 248.529i | −1.80804 | − | 0.484462i | ||||
\(514\) | 404.730 | + | 233.671i | 0.787413 | + | 0.454613i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −237.723 | − | 411.748i | −0.460703 | − | 0.797960i | ||||
\(517\) | −20.4101 | − | 20.4101i | −0.0394779 | − | 0.0394779i | ||||
\(518\) | −39.2771 | + | 71.4089i | −0.0758245 | + | 0.137855i | ||||
\(519\) | − | 1275.71i | − | 2.45802i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 58.2493 | − | 100.891i | 0.111803 | − | 0.193648i | −0.804694 | − | 0.593689i | \(-0.797671\pi\) |
0.916497 | + | 0.400041i | \(0.131004\pi\) | |||||||
\(522\) | −168.615 | + | 45.1803i | −0.323018 | + | 0.0865523i | ||||
\(523\) | −244.396 | − | 65.4858i | −0.467297 | − | 0.125212i | 0.0174845 | − | 0.999847i | \(-0.494434\pi\) |
−0.484782 | + | 0.874635i | \(0.661101\pi\) | |||||||
\(524\) | 50.1717i | 0.0957475i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 535.346 | 1.01777 | ||||||||
\(527\) | 370.589 | − | 1383.06i | 0.703205 | − | 2.62440i | ||||
\(528\) | 4.99139 | + | 18.6281i | 0.00945338 | + | 0.0352805i | ||||
\(529\) | −430.309 | − | 248.439i | −0.813438 | − | 0.469639i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −845.347 | −1.59199 | ||||||||
\(532\) | −7.00819 | − | 337.991i | −0.0131733 | − | 0.635322i | ||||
\(533\) | −46.0145 | + | 46.0145i | −0.0863311 | + | 0.0863311i | ||||
\(534\) | 975.608 | − | 563.268i | 1.82698 | − | 1.05481i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −96.6305 | + | 167.369i | −0.180281 | + | 0.312256i | ||||
\(537\) | −71.1067 | + | 265.374i | −0.132415 | + | 0.494178i | ||||
\(538\) | −144.898 | + | 144.898i | −0.269327 | + | 0.269327i | ||||
\(539\) | −21.5551 | + | 41.1886i | −0.0399910 | + | 0.0764167i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 420.568 | + | 728.445i | 0.777390 | + | 1.34648i | 0.933442 | + | 0.358730i | \(0.116790\pi\) |
−0.156052 | + | 0.987749i | \(0.549877\pi\) | |||||||
\(542\) | −451.637 | + | 121.016i | −0.833279 | + | 0.223276i | ||||
\(543\) | 264.967 | + | 988.871i | 0.487969 | + | 1.82112i | ||||
\(544\) | 149.046 | − | 86.0518i | 0.273982 | − | 0.158183i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 44.2722 | + | 42.4736i | 0.0810846 | + | 0.0777904i | ||||
\(547\) | −228.297 | − | 228.297i | −0.417362 | − | 0.417362i | 0.466931 | − | 0.884294i | \(-0.345360\pi\) |
−0.884294 | + | 0.466931i | \(0.845360\pi\) | |||||||
\(548\) | 132.129 | + | 35.4040i | 0.241112 | + | 0.0646058i | ||||
\(549\) | −662.916 | − | 382.734i | −1.20750 | − | 0.697148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −88.5771 | − | 153.420i | −0.160757 | − | 0.278439i | ||||
\(552\) | 57.6041 | + | 57.6041i | 0.104355 | + | 0.104355i | ||||
\(553\) | −257.003 | − | 424.565i | −0.464743 | − | 0.767749i | ||||
\(554\) | 111.153i | 0.200637i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −67.3054 | + | 116.576i | −0.121053 | + | 0.209670i | ||||
\(557\) | −925.810 | + | 248.070i | −1.66214 | + | 0.445368i | −0.962974 | − | 0.269595i | \(-0.913110\pi\) |
−0.699162 | + | 0.714963i | \(0.746443\pi\) | |||||||
\(558\) | 1081.68 | + | 289.834i | 1.93849 | + | 0.519416i | ||||
\(559\) | 57.0482i | 0.102054i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −146.683 | −0.261467 | ||||||||
\(562\) | 125.497 | − | 468.363i | 0.223305 | − | 0.833386i | ||||
\(563\) | 240.016 | + | 895.754i | 0.426317 | + | 1.59104i | 0.761030 | + | 0.648717i | \(0.224694\pi\) |
−0.334713 | + | 0.942320i | \(0.608639\pi\) | |||||||
\(564\) | −267.791 | − | 154.609i | −0.474807 | − | 0.274130i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −131.349 | −0.232065 | ||||||||
\(567\) | 310.706 | + | 170.898i | 0.547982 | + | 0.301407i | ||||
\(568\) | −23.8407 | + | 23.8407i | −0.0419730 | + | 0.0419730i | ||||
\(569\) | −391.524 | + | 226.046i | −0.688091 | + | 0.397270i | −0.802897 | − | 0.596118i | \(-0.796709\pi\) |
0.114805 | + | 0.993388i | \(0.463376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −195.371 | + | 338.393i | −0.342157 | + | 0.592633i | −0.984833 | − | 0.173505i | \(-0.944491\pi\) |
0.642676 | + | 0.766138i | \(0.277824\pi\) | |||||||
\(572\) | 0.598912 | − | 2.23517i | 0.00104705 | − | 0.00390764i | ||||
\(573\) | 631.510 | − | 631.510i | 1.10211 | − | 1.10211i | ||||
\(574\) | −512.964 | − | 126.111i | −0.893665 | − | 0.219706i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 67.3004 | + | 116.568i | 0.116841 | + | 0.202374i | ||||
\(577\) | −438.134 | + | 117.398i | −0.759330 | + | 0.203462i | −0.617653 | − | 0.786451i | \(-0.711916\pi\) |
−0.141677 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(578\) | 233.017 | + | 869.631i | 0.403144 | + | 1.50455i | ||||
\(579\) | −229.681 | + | 132.606i | −0.396686 | + | 0.229027i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −612.530 | − | 587.645i | −1.05427 | − | 1.01144i | ||||
\(582\) | −626.539 | − | 626.539i | −1.07653 | − | 1.07653i | ||||
\(583\) | −12.3315 | − | 3.30421i | −0.0211518 | − | 0.00566760i | ||||
\(584\) | 134.914 | + | 77.8927i | 0.231017 | + | 0.133378i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 345.276 | + | 598.036i | 0.589209 | + | 1.02054i | ||||
\(587\) | 132.759 | + | 132.759i | 0.226165 | + | 0.226165i | 0.811088 | − | 0.584924i | \(-0.198876\pi\) |
−0.584924 | + | 0.811088i | \(0.698876\pi\) | |||||||
\(588\) | −108.846 | + | 485.980i | −0.185112 | + | 0.826497i | ||||
\(589\) | 1136.45i | 1.92946i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −225.730 | + | 390.975i | −0.381946 | + | 0.661549i | ||||
\(592\) | 31.8081 | − | 8.52295i | 0.0537299 | − | 0.0143969i | ||||
\(593\) | 132.343 | + | 35.4612i | 0.223176 | + | 0.0597997i | 0.368674 | − | 0.929559i | \(-0.379812\pi\) |
−0.145498 | + | 0.989358i | \(0.546479\pi\) | |||||||
\(594\) | − | 53.3543i | − | 0.0898220i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −120.037 | −0.201404 | ||||||||
\(597\) | −34.1161 | + | 127.323i | −0.0571458 | + | 0.213271i | ||||
\(598\) | −2.52992 | − | 9.44178i | −0.00423063 | − | 0.0157889i | ||||
\(599\) | −533.617 | − | 308.084i | −0.890847 | − | 0.514331i | −0.0166277 | − | 0.999862i | \(-0.505293\pi\) |
−0.874220 | + | 0.485531i | \(0.838626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −660.812 | −1.09952 | −0.549760 | − | 0.835322i | \(-0.685281\pi\) | ||||
−0.549760 | + | 0.835322i | \(0.685281\pi\) | |||||||
\(602\) | −396.159 | + | 239.808i | −0.658071 | + | 0.398351i | ||||
\(603\) | 812.909 | − | 812.909i | 1.34811 | − | 1.34811i | ||||
\(604\) | 82.7984 | − | 47.8037i | 0.137083 | − | 0.0791451i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −181.295 | + | 314.012i | −0.299167 | + | 0.518172i | ||||
\(607\) | 100.052 | − | 373.398i | 0.164830 | − | 0.615153i | −0.833232 | − | 0.552924i | \(-0.813512\pi\) |
0.998062 | − | 0.0622299i | \(-0.0198212\pi\) | |||||||
\(608\) | −96.5897 | + | 96.5897i | −0.158865 | + | 0.158865i | ||||
\(609\) | 72.7567 | + | 250.628i | 0.119469 | + | 0.411541i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5514 | + | 32.1320i | 0.0303624 | + | 0.0525893i | ||||
\(612\) | −988.886 | + | 264.971i | −1.61583 | + | 0.432959i | ||||
\(613\) | 13.3884 | + | 49.9662i | 0.0218408 | + | 0.0815109i | 0.975986 | − | 0.217833i | \(-0.0698988\pi\) |
−0.954145 | + | 0.299344i | \(0.903232\pi\) | |||||||
\(614\) | −595.999 | + | 344.100i | −0.970683 | + | 0.560424i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.0392 | − | 5.23673i | 0.0292845 | − | 0.00850119i | ||||
\(617\) | 616.887 | + | 616.887i | 0.999816 | + | 0.999816i | 1.00000 | 0.000183933i | \(-5.85476e-5\pi\) | |
−0.000183933 | 1.00000i | \(0.500059\pi\) | ||||||||
\(618\) | −1003.53 | − | 268.896i | −1.62384 | − | 0.435107i | ||||
\(619\) | −449.823 | − | 259.705i | −0.726693 | − | 0.419556i | 0.0905183 | − | 0.995895i | \(-0.471148\pi\) |
−0.817211 | + | 0.576339i | \(0.804481\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −112.689 | − | 195.184i | −0.181464 | − | 0.314305i | ||||
\(622\) | 330.319 | + | 330.319i | 0.531059 | + | 0.531059i | ||||
\(623\) | −568.208 | − | 938.672i | −0.912051 | − | 1.50670i | ||||
\(624\) | − | 24.7898i | − | 0.0397273i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −60.5472 | + | 104.871i | −0.0967208 | + | 0.167525i | ||||
\(627\) | 112.455 | − | 30.1323i | 0.179354 | − | 0.0480579i | ||||
\(628\) | −202.048 | − | 54.1387i | −0.321733 | − | 0.0862081i | ||||
\(629\) | 250.466i | 0.398197i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −427.140 | −0.676925 | −0.338463 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338463 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(632\) | −51.9016 | + | 193.699i | −0.0821228 | + | 0.306486i | ||||
\(633\) | −294.195 | − | 1097.95i | −0.464763 | − | 1.73452i | ||||
\(634\) | 215.808 | + | 124.597i | 0.340390 | + | 0.196525i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −136.766 | −0.215041 | ||||||||
\(637\) | 40.4667 | − | 43.9698i | 0.0635271 | − | 0.0690264i | ||||
\(638\) | 6.96025 | − | 6.96025i | 0.0109095 | − | 0.0109095i | ||||
\(639\) | 173.691 | − | 100.280i | 0.271816 | − | 0.156933i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −135.063 | + | 233.937i | −0.210707 | + | 0.364956i | −0.951936 | − | 0.306297i | \(-0.900910\pi\) |
0.741229 | + | 0.671252i | \(0.234243\pi\) | |||||||
\(642\) | −12.9069 | + | 48.1692i | −0.0201042 | + | 0.0750298i | ||||
\(643\) | −192.668 | + | 192.668i | −0.299639 | + | 0.299639i | −0.840872 | − | 0.541234i | \(-0.817957\pi\) |
0.541234 | + | 0.840872i | \(0.317957\pi\) | |||||||
\(644\) | 54.9316 | − | 57.2579i | 0.0852976 | − | 0.0889097i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −519.483 | − | 899.770i | −0.804153 | − | 1.39283i | ||||
\(647\) | 237.128 | − | 63.5381i | 0.366503 | − | 0.0982042i | −0.0708670 | − | 0.997486i | \(-0.522577\pi\) |
0.437370 | + | 0.899282i | \(0.355910\pi\) | |||||||
\(648\) | −37.0841 | − | 138.400i | −0.0572285 | − | 0.213580i | ||||
\(649\) | 41.2812 | − | 23.8337i | 0.0636074 | − | 0.0367237i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 399.691 | − | 1625.76i | 0.613964 | − | 2.49733i | ||||
\(652\) | 58.1379 | + | 58.1379i | 0.0891685 | + | 0.0891685i | ||||
\(653\) | −440.504 | − | 118.033i | −0.674585 | − | 0.180755i | −0.0947659 | − | 0.995500i | \(-0.530210\pi\) |
−0.579819 | + | 0.814745i | \(0.696877\pi\) | |||||||
\(654\) | −304.211 | − | 175.636i | −0.465154 | − | 0.268557i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 106.720 | + | 184.845i | 0.162683 | + | 0.281776i | ||||
\(657\) | −655.276 | − | 655.276i | −0.997376 | − | 0.997376i | ||||
\(658\) | −145.151 | + | 263.896i | −0.220595 | + | 0.401058i | ||||
\(659\) | − | 973.026i | − | 1.47652i | −0.674517 | − | 0.738259i | \(-0.735648\pi\) | ||
0.674517 | − | 0.738259i | \(-0.264352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 152.550 | − | 264.224i | 0.230787 | − | 0.399734i | −0.727253 | − | 0.686369i | \(-0.759203\pi\) |
0.958040 | + | 0.286635i | \(0.0925367\pi\) | |||||||
\(662\) | 439.140 | − | 117.667i | 0.663353 | − | 0.177745i | ||||
\(663\) | 182.126 | + | 48.8006i | 0.274700 | + | 0.0736057i | ||||
\(664\) | 342.981i | 0.516537i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −195.887 | −0.294125 | ||||||||
\(667\) | 10.7617 | − | 40.1631i | 0.0161344 | − | 0.0602145i | ||||
\(668\) | 19.3520 | + | 72.2228i | 0.0289701 | + | 0.108118i | ||||
\(669\) | 820.666 | + | 473.811i | 1.22670 | + | 0.708238i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.1633 | 0.0643268 | ||||||||
\(672\) | 172.148 | − | 104.206i | 0.256172 | − | 0.155069i | ||||
\(673\) | −567.081 | + | 567.081i | −0.842616 | + | 0.842616i | −0.989198 | − | 0.146582i | \(-0.953173\pi\) |
0.146582 | + | 0.989198i | \(0.453173\pi\) | |||||||
\(674\) | −135.078 | + | 77.9872i | −0.200412 | + | 0.115708i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 167.513 | − | 290.141i | 0.247800 | − | 0.429202i | ||||
\(677\) | −103.404 | + | 385.908i | −0.152738 | + | 0.570027i | 0.846550 | + | 0.532309i | \(0.178676\pi\) |
−0.999288 | + | 0.0377179i | \(0.987991\pi\) | |||||||
\(678\) | −59.5983 | + | 59.5983i | −0.0879031 | + | 0.0879031i | ||||
\(679\) | −597.471 | + | 622.773i | −0.879928 | + | 0.917191i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 963.266 | + | 1668.42i | 1.41449 | + | 2.44996i | ||||
\(682\) | −60.9936 | + | 16.3432i | −0.0894334 | + | 0.0239636i | ||||
\(683\) | −246.473 | − | 919.851i | −0.360869 | − | 1.34678i | −0.872936 | − | 0.487835i | \(-0.837787\pi\) |
0.512067 | − | 0.858945i | \(-0.328880\pi\) | |||||||
\(684\) | 703.702 | − | 406.283i | 1.02880 | − | 0.593980i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 475.444 | + | 96.1812i | 0.693067 | + | 0.140206i | ||||
\(687\) | 165.332 | + | 165.332i | 0.240657 | + | 0.240657i | ||||
\(688\) | 180.740 | + | 48.4290i | 0.262703 | + | 0.0703910i | ||||
\(689\) | 14.2119 | + | 8.20522i | 0.0206268 | + | 0.0119089i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 235.417 | + | 407.754i | 0.340690 | + | 0.590093i | 0.984561 | − | 0.175042i | \(-0.0560060\pi\) |
−0.643871 | + | 0.765134i | \(0.722673\pi\) | |||||||
\(692\) | 355.016 | + | 355.016i | 0.513028 | + | 0.513028i | ||||
\(693\) | −111.714 | + | 2.31636i | −0.161203 | + | 0.00334251i | ||||
\(694\) | − | 476.747i | − | 0.686955i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 52.7250 | − | 91.3224i | 0.0757543 | − | 0.131210i | ||||
\(697\) | −1568.11 | + | 420.173i | −2.24980 | + | 0.602831i | ||||
\(698\) | 392.740 | + | 105.234i | 0.562664 | + | 0.150765i | ||||
\(699\) | 530.602i | 0.759088i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1335.50 | −1.90514 | −0.952569 | − | 0.304322i | \(-0.901570\pi\) | ||||
−0.952569 | + | 0.304322i | \(0.901570\pi\) | |||||||
\(702\) | −17.7506 | + | 66.2463i | −0.0252858 | + | 0.0943679i | ||||
\(703\) | −51.4518 | − | 192.021i | −0.0731890 | − | 0.273145i | ||||
\(704\) | −6.57302 | − | 3.79493i | −0.00933667 | − | 0.00539053i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 234.554 | 0.332229 | ||||||||
\(707\) | 309.445 | + | 170.204i | 0.437688 | + | 0.240742i | ||||
\(708\) | 361.088 | − | 361.088i | 0.510012 | − | 0.510012i | ||||
\(709\) | 1150.06 | − | 663.986i | 1.62208 | − | 0.936510i | 0.635722 | − | 0.771918i | \(-0.280703\pi\) |
0.986362 | − | 0.164592i | \(-0.0526307\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 596.440 | − | 1033.06i | 0.838875 | − | 1.45297i | ||||
\(712\) | −114.749 | + | 428.250i | −0.161165 | + | 0.601475i | ||||
\(713\) | −188.612 | + | 188.612i | −0.264532 | + | 0.264532i | ||||
\(714\) | 426.700 | + | 1469.87i | 0.597618 | + | 2.05865i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −54.0621 | − | 93.6384i | −0.0755058 | − | 0.130780i | ||||
\(717\) | 19.6519 | − | 5.26572i | 0.0274086 | − | 0.00734410i | ||||
\(718\) | −137.079 | − | 511.585i | −0.190918 | − | 0.712515i | ||||
\(719\) | 244.147 | − | 140.958i | 0.339564 | − | 0.196048i | −0.320515 | − | 0.947243i | \(-0.603856\pi\) |
0.660079 | + | 0.751196i | \(0.270523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −241.588 | + | 982.668i | −0.335073 | + | 1.36292i | ||||
\(722\) | 222.098 | + | 222.098i | 0.307616 | + | 0.307616i | ||||
\(723\) | 1461.80 | + | 391.687i | 2.02185 | + | 0.541753i | ||||
\(724\) | −348.928 | − | 201.453i | −0.481944 | − | 0.278251i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −431.567 | − | 747.497i | −0.594445 | − | 1.02961i | ||||
\(727\) | −830.098 | − | 830.098i | −1.14181 | − | 1.14181i | −0.988118 | − | 0.153694i | \(-0.950883\pi\) |
−0.153694 | − | 0.988118i | \(-0.549117\pi\) | |||||||
\(728\) | −24.1403 | + | 0.500544i | −0.0331597 | + | 0.000687561i | ||||
\(729\) | − | 966.430i | − | 1.32569i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −711.598 | + | 1232.52i | −0.973458 | + | 1.68608i | ||||
\(732\) | 446.647 | − | 119.679i | 0.610174 | − | 0.163496i | ||||
\(733\) | 1152.36 | + | 308.773i | 1.57211 | + | 0.421245i | 0.936472 | − | 0.350743i | \(-0.114071\pi\) |
0.635637 | + | 0.771988i | \(0.280737\pi\) | |||||||
\(734\) | 46.1721i | 0.0629048i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.0610 | −0.0435612 | ||||||||
\(737\) | −16.7780 | + | 62.6163i | −0.0227652 | + | 0.0849610i | ||||
\(738\) | −328.614 | − | 1226.40i | −0.445276 | − | 1.66179i | ||||
\(739\) | −491.205 | − | 283.597i | −0.664688 | − | 0.383758i | 0.129373 | − | 0.991596i | \(-0.458704\pi\) |
−0.794061 | + | 0.607838i | \(0.792037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −149.653 | −0.201960 | ||||||||
\(742\) | 2.76151 | + | 133.182i | 0.00372172 | + | 0.179491i | ||||
\(743\) | 121.240 | − | 121.240i | 0.163176 | − | 0.163176i | −0.620796 | − | 0.783972i | \(-0.713190\pi\) |
0.783972 | + | 0.620796i | \(0.213190\pi\) | |||||||
\(744\) | −585.838 | + | 338.234i | −0.787417 | + | 0.454615i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −521.014 | + | 902.423i | −0.698411 | + | 1.20968i | ||||
\(747\) | 528.054 | − | 1970.72i | 0.706900 | − | 2.63819i | ||||
\(748\) | 40.8201 | − | 40.8201i | 0.0545723 | − | 0.0545723i | ||||
\(749\) | 47.1676 | + | 11.5961i | 0.0629741 | + | 0.0154821i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −499.516 | − | 865.187i | −0.665135 | − | 1.15205i | −0.979249 | − | 0.202662i | \(-0.935041\pi\) |
0.314114 | − | 0.949385i | \(-0.398293\pi\) | |||||||
\(752\) | 117.549 | − | 31.4972i | 0.156315 | − | 0.0418845i | ||||
\(753\) | 395.404 | + | 1475.67i | 0.525104 | + | 1.95972i | ||||
\(754\) | −10.9577 | + | 6.32643i | −0.0145327 | + | 0.00839048i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −534.649 | + | 155.207i | −0.707208 | + | 0.205300i | ||||
\(757\) | −290.904 | − | 290.904i | −0.384285 | − | 0.384285i | 0.488358 | − | 0.872643i | \(-0.337596\pi\) |
−0.872643 | + | 0.488358i | \(0.837596\pi\) | |||||||
\(758\) | 392.275 | + | 105.110i | 0.517514 | + | 0.138667i | ||||
\(759\) | 23.6645 | + | 13.6627i | 0.0311786 | + | 0.0180010i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 185.178 | + | 320.737i | 0.243335 | + | 0.421468i | 0.961662 | − | 0.274237i | \(-0.0884253\pi\) |
−0.718327 | + | 0.695705i | \(0.755092\pi\) | |||||||
\(762\) | −577.416 | − | 577.416i | −0.757764 | − | 0.757764i | ||||
\(763\) | −164.892 | + | 299.786i | −0.216110 | + | 0.392905i | ||||
\(764\) | 351.483i | 0.460056i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 323.016 | − | 559.479i | 0.421691 | − | 0.730391i | ||||
\(767\) | −59.1853 | + | 15.8587i | −0.0771647 | + | 0.0206762i | ||||
\(768\) | −78.5389 | − | 21.0444i | −0.102264 | − | 0.0274016i | ||||
\(769\) | − | 615.359i | − | 0.800207i | −0.916470 | − | 0.400103i | \(-0.868974\pi\) | ||
0.916470 | − | 0.400103i | \(-0.131026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1679.35 | 2.17814 | ||||||||
\(772\) | 27.0147 | − | 100.820i | 0.0349931 | − | 0.130596i | ||||
\(773\) | 218.298 | + | 814.698i | 0.282403 | + | 1.05394i | 0.950716 | + | 0.310063i | \(0.100350\pi\) |
−0.668313 | + | 0.743880i | \(0.732983\pi\) | |||||||
\(774\) | −963.945 | − | 556.534i | −1.24541 | − | 0.719036i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 348.716 | 0.449376 | ||||||||
\(777\) | 6.07099 | + | 292.792i | 0.00781337 | + | 0.376824i | ||||
\(778\) | −543.189 | + | 543.189i | −0.698187 | + | 0.698187i | ||||
\(779\) | 1115.88 | − | 644.255i | 1.43246 | − | 0.827029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.65461 | + | 9.79407i | −0.00724021 | + | 0.0125404i | ||||
\(782\) | 63.1144 | − | 235.546i | 0.0807090 | − | 0.301210i | ||||
\(783\) | −206.289 | + | 206.289i | −0.263460 | + | 0.263460i | ||||
\(784\) | −104.952 | − | 165.533i | −0.133867 | − | 0.211139i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 90.1435 | + | 156.133i | 0.114686 | + | 0.198643i | ||||
\(787\) | 440.137 | − | 117.934i | 0.559259 | − | 0.149853i | 0.0318931 | − | 0.999491i | \(-0.489846\pi\) |
0.527366 | + | 0.849638i | \(0.323180\pi\) | |||||||
\(788\) | −45.9858 | − | 171.622i | −0.0583577 | − | 0.217794i | ||||
\(789\) | 1665.99 | − | 961.857i | 2.11151 | − | 1.21908i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.2401 | + | 56.8333i | 0.0748927 | + | 0.0718500i | ||||
\(792\) | 31.9250 | + | 31.9250i | 0.0403094 | + | 0.0403094i | ||||
\(793\) | −53.5928 | − | 14.3602i | −0.0675824 | − | 0.0181086i | ||||
\(794\) | −782.528 | − | 451.793i | −0.985551 | − | 0.569008i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.9383 | − | 44.9265i | −0.0325858 | − | 0.0564403i | ||||
\(797\) | 1040.82 | + | 1040.82i | 1.30592 | + | 1.30592i | 0.924331 | + | 0.381592i | \(0.124624\pi\) |
0.381592 | + | 0.924331i | \(0.375376\pi\) | |||||||
\(798\) | −629.079 | − | 1039.23i | −0.788319 | − | 1.30229i | ||||
\(799\) | 925.614i | 1.15847i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1318.67 | − | 2284.00i | 1.64628 | − | 2.85144i | ||||
\(802\) | 610.985 | − | 163.713i | 0.761827 | − | 0.204131i | ||||
\(803\) | 50.4742 | + | 13.5245i | 0.0628571 | + | 0.0168425i | ||||
\(804\) | 694.465i | 0.863762i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 81.1687 | 0.100706 | ||||||||
\(807\) | −190.581 | + | 711.257i | −0.236160 | + | 0.881360i | ||||
\(808\) | −36.9336 | − | 137.838i | −0.0457099 | − | 0.170592i | ||||
\(809\) | 192.279 | + | 111.012i | 0.237674 | + | 0.137221i | 0.614107 | − | 0.789222i | \(-0.289516\pi\) |
−0.376433 | + | 0.926444i | \(0.622850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1418.65 | 1.74926 | 0.874632 | − | 0.484788i | \(-0.161103\pi\) | ||||
0.874632 | + | 0.484788i | \(0.161103\pi\) | |||||||
\(812\) | −89.9941 | − | 49.4996i | −0.110830 | − | 0.0609600i | ||||
\(813\) | −1188.06 | + | 1188.06i | −1.46132 | + | 1.46132i | ||||
\(814\) | 9.56585 | − | 5.52284i | 0.0117517 | − | 0.00678482i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 309.219 | − | 535.583i | 0.378945 | − | 0.656351i | ||||
\(817\) | 292.359 | − | 1091.10i | 0.357845 | − | 1.33549i | ||||
\(818\) | 23.0666 | − | 23.0666i | 0.0281988 | − | 0.0281988i | ||||
\(819\) | 139.478 | + | 34.2904i | 0.170302 | + | 0.0418686i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 192.277 | + | 333.033i | 0.234198 | + | 0.405643i | 0.959039 | − | 0.283273i | \(-0.0914202\pi\) |
−0.724841 | + | 0.688916i | \(0.758087\pi\) | |||||||
\(822\) | 474.794 | − | 127.221i | 0.577608 | − | 0.154770i | ||||
\(823\) | −17.2796 | − | 64.4885i | −0.0209959 | − | 0.0783578i | 0.954633 | − | 0.297785i | \(-0.0962478\pi\) |
−0.975629 | + | 0.219427i | \(0.929581\pi\) | |||||||
\(824\) | 354.102 | − | 204.441i | 0.429735 | − | 0.248108i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −358.918 | − | 344.336i | −0.434525 | − | 0.416872i | ||||
\(827\) | −595.969 | − | 595.969i | −0.720639 | − | 0.720639i | 0.248096 | − | 0.968735i | \(-0.420195\pi\) |
−0.968735 | + | 0.248096i | \(0.920195\pi\) | |||||||
\(828\) | 184.219 | + | 49.3612i | 0.222486 | + | 0.0596150i | ||||
\(829\) | −609.282 | − | 351.769i | −0.734960 | − | 0.424329i | 0.0852739 | − | 0.996358i | \(-0.472823\pi\) |
−0.820234 | + | 0.572028i | \(0.806157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 199.709 | + | 345.905i | 0.240323 | + | 0.416252i | ||||
\(832\) | 6.89871 | + | 6.89871i | 0.00829172 | + | 0.00829172i | ||||
\(833\) | 1422.74 | − | 445.198i | 1.70798 | − | 0.534451i | ||||
\(834\) | 483.711i | 0.579989i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.9095 | + | 39.6804i | −0.0274037 | + | 0.0474645i | ||||
\(837\) | 1807.74 | − | 484.381i | 2.15978 | − | 0.578711i | ||||
\(838\) | −686.826 | − | 184.035i | −0.819602 | − | 0.219612i | ||||
\(839\) | 3.00042i | 0.00357618i | 0.999998 | + | 0.00178809i | \(0.000569167\pi\) | ||||
−0.999998 | + | 0.00178809i | \(0.999431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 787.178 | 0.936002 | ||||||||
\(842\) | −17.7485 | + | 66.2382i | −0.0210789 | + | 0.0786677i | ||||
\(843\) | −450.963 | − | 1683.02i | −0.534950 | − | 1.99646i | ||||
\(844\) | 387.417 | + | 223.675i | 0.459025 | + | 0.265018i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −723.915 | −0.855691 | ||||||||
\(847\) | −719.197 | + | 435.352i | −0.849110 | + | 0.513993i | ||||
\(848\) | 38.0603 | − | 38.0603i | 0.0448824 | − | 0.0448824i | ||||
\(849\) | −408.755 | + | 235.995i | −0.481454 | + | 0.277968i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.3295 | − | 40.4079i | 0.0274143 | − | 0.0474829i | ||||
\(852\) | −31.3571 | + | 117.026i | −0.0368041 | + | 0.137355i | ||||
\(853\) | −657.357 | + | 657.357i | −0.770641 | + | 0.770641i | −0.978219 | − | 0.207577i | \(-0.933442\pi\) |
0.207577 | + | 0.978219i | \(0.433442\pi\) | |||||||
\(854\) | −125.561 | − | 432.528i | −0.147027 | − | 0.506473i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.81306 | − | 16.9967i | −0.0114639 | − | 0.0198560i | ||||
\(857\) | −1022.44 | + | 273.963i | −1.19305 | + | 0.319677i | −0.800091 | − | 0.599879i | \(-0.795216\pi\) |
−0.392960 | + | 0.919556i | \(0.628549\pi\) | |||||||
\(858\) | −2.15213 | − | 8.03187i | −0.00250831 | − | 0.00936115i | ||||
\(859\) | −747.383 | + | 431.502i | −0.870062 | + | 0.502331i | −0.867369 | − | 0.497666i | \(-0.834191\pi\) |
−0.00269328 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1822.92 | + | 529.187i | −2.11721 | + | 0.614619i | ||||
\(862\) | 371.451 | + | 371.451i | 0.430918 | + | 0.430918i | ||||
\(863\) | 1176.48 | + | 315.238i | 1.36325 | + | 0.365282i | 0.865009 | − | 0.501757i | \(-0.167313\pi\) |
0.498241 | + | 0.867039i | \(0.333980\pi\) | |||||||
\(864\) | 194.812 | + | 112.475i | 0.225477 | + | 0.130179i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −449.707 | − | 778.916i | −0.519292 | − | 0.899441i | ||||
\(867\) | 2287.61 | + | 2287.61i | 2.63854 | + | 2.63854i | ||||
\(868\) | 341.200 | + | 563.658i | 0.393088 | + | 0.649376i | ||||
\(869\) | 67.2641i | 0.0774041i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.6641 | − | 72.1644i | 0.0478348 | − | 0.0828523i | ||||
\(872\) | 133.536 | − | 35.7808i | 0.153137 | − | 0.0410330i | ||||
\(873\) | −2003.68 | − | 536.884i | −2.29516 | − | 0.614988i | ||||
\(874\) | 193.548i | 0.221451i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 559.800 | 0.639041 | ||||||||
\(877\) | 350.753 | − | 1309.03i | 0.399946 | − | 1.49262i | −0.413244 | − | 0.910620i | \(-0.635604\pi\) |
0.813190 | − | 0.581999i | \(-0.197729\pi\) | |||||||
\(878\) | 215.040 | + | 802.540i | 0.244920 | + | 0.914055i | ||||
\(879\) | 2148.98 | + | 1240.72i | 2.44481 | + | 1.41151i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 906.106 | 1.02850 | 0.514248 | − | 0.857641i | \(-0.328071\pi\) | ||||
0.514248 | + | 0.857641i | \(0.328071\pi\) | |||||||
\(882\) | 348.185 | + | 1112.71i | 0.394768 | + | 1.26158i | ||||
\(883\) | 479.615 | − | 479.615i | 0.543166 | − | 0.543166i | −0.381290 | − | 0.924455i | \(-0.624520\pi\) |
0.924455 | + | 0.381290i | \(0.124520\pi\) | |||||||
\(884\) | −64.2641 | + | 37.1029i | −0.0726969 | + | 0.0419716i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.35781 | + | 5.81590i | −0.00378986 | + | 0.00656422i | ||||
\(887\) | −99.6947 | + | 372.066i | −0.112395 | + | 0.419465i | −0.999079 | − | 0.0429116i | \(-0.986337\pi\) |
0.886683 | + | 0.462377i | \(0.153003\pi\) | |||||||
\(888\) | 83.6729 | − | 83.6729i | 0.0942262 | − | 0.0942262i | ||||
\(889\) | −550.628 | + | 573.946i | −0.619379 | + | 0.645608i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.0304 | − | 41.6218i | −0.0269701 | − | 0.0467136i | ||||
\(892\) | −360.237 | + | 96.5252i | −0.403853 | + | 0.108212i | ||||
\(893\) | −190.144 | − | 709.626i | −0.212927 | − | 0.794654i | ||||
\(894\) | −373.553 | + | 215.671i | −0.417844 | + | 0.241242i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.9072 | + | 76.9059i | −0.0211018 | + | 0.0858325i | ||||
\(897\) | −24.8371 | − | 24.8371i | −0.0276891 | − | 0.0276891i | ||||
\(898\) | 55.5119 | + | 14.8744i | 0.0618172 | + | 0.0165639i | ||||
\(899\) | 299.015 | + | 172.636i | 0.332608 | + | 0.192031i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 204.697 | + | 354.546i | 0.227189 | + | 0.393503i | ||||
\(902\) | 50.6245 | + | 50.6245i | 0.0561248 | + | 0.0561248i | ||||
\(903\) | −801.975 | + | 1458.05i | −0.888123 | + | 1.61468i | ||||
\(904\) | − | 33.1710i | − | 0.0366935i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 171.778 | − | 297.528i | 0.189600 | − | 0.328397i | ||||
\(907\) | 790.213 | − | 211.737i | 0.871238 | − | 0.233448i | 0.204615 | − | 0.978842i | \(-0.434406\pi\) |
0.666623 | + | 0.745395i | \(0.267739\pi\) | |||||||
\(908\) | −732.367 | − | 196.237i | −0.806572 | − | 0.216120i | ||||
\(909\) | 848.863i | 0.933843i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 719.634 | 0.789939 | 0.394969 | − | 0.918694i | \(-0.370755\pi\) | ||||
0.394969 | + | 0.918694i | \(0.370755\pi\) | |||||||
\(912\) | −127.042 | + | 474.128i | −0.139301 | + | 0.519877i | ||||
\(913\) | 29.7759 | + | 111.125i | 0.0326133 | + | 0.121714i | ||||
\(914\) | −402.607 | − | 232.446i | −0.440490 | − | 0.254317i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −92.0195 | −0.100458 | ||||||||
\(917\) | 150.222 | − | 90.9341i | 0.163819 | − | 0.0991648i | ||||
\(918\) | −1209.83 | + | 1209.83i | −1.31790 | + | 1.31790i | ||||
\(919\) | 395.313 | − | 228.234i | 0.430156 | − | 0.248351i | −0.269257 | − | 0.963068i | \(-0.586778\pi\) |
0.699413 | + | 0.714718i | \(0.253445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1236.49 | + | 2141.66i | −1.34255 | + | 2.32537i | ||||
\(922\) | −23.7023 | + | 88.4582i | −0.0257075 | + | 0.0959416i | ||||
\(923\) | 10.2794 | − | 10.2794i | 0.0111369 | − | 0.0111369i | ||||
\(924\) | 46.7288 | − | 48.7077i | 0.0505723 | − | 0.0527140i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 604.400 | + | 1046.85i | 0.652700 | + | 1.13051i | ||||
\(927\) | −2349.38 | + | 629.515i | −2.53439 | + | 0.679088i | ||||
\(928\) | 10.7412 | + | 40.0866i | 0.0115745 | + | 0.0431968i | ||||
\(929\) | −260.770 | + | 150.556i | −0.280700 | + | 0.162062i | −0.633740 | − | 0.773546i | \(-0.718481\pi\) |
0.353040 | + | 0.935608i | \(0.385148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −999.298 | + | 633.579i | −1.07336 | + | 0.680536i | ||||
\(932\) | −147.660 | − | 147.660i | −0.158434 | − | 0.158434i | ||||
\(933\) | 1621.43 | + | 434.461i | 1.73787 | + | 0.465660i | ||||
\(934\) | 437.712 | + | 252.713i | 0.468643 | + | 0.270571i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −29.0178 | − | 50.2604i | −0.0310020 | − | 0.0536970i | ||||
\(937\) | −201.407 | − | 201.407i | −0.214949 | − | 0.214949i | 0.591417 | − | 0.806366i | \(-0.298569\pi\) |
−0.806366 | + | 0.591417i | \(0.798569\pi\) | |||||||
\(938\) | 676.268 | − | 14.0223i | 0.720968 | − | 0.0149491i | ||||
\(939\) | 435.141i | 0.463409i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 235.272 | − | 407.502i | 0.250023 | − | 0.433052i | −0.713509 | − | 0.700646i | \(-0.752895\pi\) |
0.963532 | + | 0.267594i | \(0.0862285\pi\) | |||||||
\(942\) | −726.041 | + | 194.542i | −0.770745 | + | 0.206520i | ||||
\(943\) | 292.121 | + | 78.2737i | 0.309779 | + | 0.0830050i | ||||
\(944\) | 200.973i | 0.212895i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.7637 | 0.0663464 | ||||||||
\(947\) | −73.4049 | + | 273.951i | −0.0775131 | + | 0.289283i | −0.993791 | − | 0.111259i | \(-0.964512\pi\) |
0.916278 | + | 0.400542i | \(0.131178\pi\) | |||||||
\(948\) | 186.503 | + | 696.040i | 0.196733 | + | 0.734219i | ||||
\(949\) | −58.1708 | − | 33.5849i | −0.0612970 | − | 0.0353898i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 895.451 | 0.941589 | ||||||||
\(952\) | −527.793 | − | 290.302i | −0.554404 | − | 0.304940i | ||||
\(953\) | −627.876 | + | 627.876i | −0.658842 | + | 0.658842i | −0.955106 | − | 0.296264i | \(-0.904259\pi\) |
0.296264 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(954\) | −277.288 | + | 160.092i | −0.290658 | + | 0.167811i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.00351 | + | 6.93428i | −0.00418777 | + | 0.00725343i | ||||
\(957\) | 9.15465 | − | 34.1656i | 0.00956599 | − | 0.0357008i | ||||
\(958\) | −587.359 | + | 587.359i | −0.613109 | + | 0.613109i | ||||
\(959\) | −133.474 | − | 459.785i | −0.139180 | − | 0.479442i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −626.971 | − | 1085.94i | −0.652415 | − | 1.13002i | ||||
\(962\) | −13.7147 | + | 3.67483i | −0.0142564 | + | 0.00381999i | ||||
\(963\) | 30.2164 | + | 112.769i | 0.0313774 | + | 0.117102i | ||||
\(964\) | −515.802 | + | 297.798i | −0.535064 | + | 0.308919i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 68.0708 | − | 276.881i | 0.0704666 | − | 0.286626i | ||||
\(967\) | 929.872 | + | 929.872i | 0.961604 | + | 0.961604i | 0.999290 | − | 0.0376852i | \(-0.0119984\pi\) |
−0.0376852 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(968\) | 328.119 | + | 87.9192i | 0.338966 | + | 0.0908257i | ||||
\(969\) | −3233.24 | − | 1866.71i | −3.33667 | − | 1.92643i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −628.982 | − | 1089.43i | −0.647767 | − | 1.12196i | −0.983655 | − | 0.180063i | \(-0.942370\pi\) |
0.335888 | − | 0.941902i | \(-0.390964\pi\) | |||||||
\(972\) | 142.069 | + | 142.069i | 0.146161 | + | 0.146161i | ||||
\(973\) | 471.037 | − | 9.76686i | 0.484108 | − | 0.0100379i | ||||
\(974\) | 804.435i | 0.825909i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −90.9914 | + | 157.602i | −0.0932289 | + | 0.161477i | ||||
\(977\) | 182.799 | − | 48.9808i | 0.187102 | − | 0.0501339i | −0.164051 | − | 0.986452i | \(-0.552456\pi\) |
0.351153 | + | 0.936318i | \(0.385790\pi\) | |||||||
\(978\) | 285.380 | + | 76.4674i | 0.291800 | + | 0.0781875i | ||||
\(979\) | 148.714i | 0.151904i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −822.367 | −0.838295 | ||||||||
\(982\) | −177.536 | + | 662.573i | −0.180790 | + | 0.674718i | ||||
\(983\) | −363.301 | − | 1355.86i | −0.369583 | − | 1.37930i | −0.861100 | − | 0.508436i | \(-0.830224\pi\) |
0.491516 | − | 0.870868i | \(-0.336443\pi\) | |||||||
\(984\) | 664.222 | + | 383.489i | 0.675023 | + | 0.389725i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −315.654 | −0.320135 | ||||||||
\(987\) | 22.4358 | + | 1082.03i | 0.0227313 | + | 1.09629i | ||||
\(988\) | 41.6465 | − | 41.6465i | 0.0421523 | − | 0.0421523i | ||||
\(989\) | 229.606 | − | 132.563i | 0.232159 | − | 0.134037i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 258.071 | − | 446.992i | 0.260414 | − | 0.451051i | −0.705938 | − | 0.708274i | \(-0.749474\pi\) |
0.966352 | + | 0.257223i | \(0.0828075\pi\) | |||||||
\(992\) | 68.9052 | − | 257.158i | 0.0694609 | − | 0.259232i | ||||
\(993\) | 1155.18 | − | 1155.18i | 1.16332 | − | 1.16332i | ||||
\(994\) | 114.593 | + | 28.1725i | 0.115285 | + | 0.0283426i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 616.234 | + | 1067.35i | 0.618709 | + | 1.07164i | ||||
\(997\) | 1276.18 | − | 341.950i | 1.28002 | − | 0.342979i | 0.446155 | − | 0.894955i | \(-0.352793\pi\) |
0.833860 | + | 0.551976i | \(0.186126\pi\) | |||||||
\(998\) | −211.422 | − | 789.039i | −0.211846 | − | 0.790620i | ||||
\(999\) | −283.514 | + | 163.687i | −0.283798 | + | 0.163851i |
(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 | 350.3.p.e.207.4 | 16 | ||
5.2 | odd | 4 | 70.3.l.c.53.4 | yes | 16 | ||
5.3 | odd | 4 | inner | 350.3.p.e.193.1 | 16 | ||
5.4 | even | 2 | 70.3.l.c.67.1 | yes | 16 | ||
7.2 | even | 3 | inner | 350.3.p.e.107.1 | 16 | ||
35.2 | odd | 12 | 70.3.l.c.23.1 | ✓ | 16 | ||
35.4 | even | 6 | 490.3.f.o.197.1 | 8 | |||
35.9 | even | 6 | 70.3.l.c.37.4 | yes | 16 | ||
35.17 | even | 12 | 490.3.f.p.393.4 | 8 | |||
35.23 | odd | 12 | inner | 350.3.p.e.93.4 | 16 | ||
35.24 | odd | 6 | 490.3.f.p.197.4 | 8 | |||
35.32 | odd | 12 | 490.3.f.o.393.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.3.l.c.23.1 | ✓ | 16 | 35.2 | odd | 12 | ||
70.3.l.c.37.4 | yes | 16 | 35.9 | even | 6 | ||
70.3.l.c.53.4 | yes | 16 | 5.2 | odd | 4 | ||
70.3.l.c.67.1 | yes | 16 | 5.4 | even | 2 | ||
350.3.p.e.93.4 | 16 | 35.23 | odd | 12 | inner | ||
350.3.p.e.107.1 | 16 | 7.2 | even | 3 | inner | ||
350.3.p.e.193.1 | 16 | 5.3 | odd | 4 | inner | ||
350.3.p.e.207.4 | 16 | 1.1 | even | 1 | trivial | ||
490.3.f.o.197.1 | 8 | 35.4 | even | 6 | |||
490.3.f.o.393.1 | 8 | 35.32 | odd | 12 | |||
490.3.f.p.197.4 | 8 | 35.24 | odd | 6 | |||
490.3.f.p.393.4 | 8 | 35.17 | even | 12 |