Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(4,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.79 |
Dual form | 105.4.q.a.4.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.33013 | + | 2.50000i | 1.53093 | + | 0.883883i | 0.999319 | + | 0.0368954i | \(0.0117469\pi\) |
0.531612 | + | 0.846988i | \(0.321586\pi\) | |||||||
\(3\) | −2.59808 | + | 1.50000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 8.50000 | + | 14.7224i | 1.06250 | + | 1.84030i | ||||
\(5\) | 8.52628 | + | 7.23205i | 0.762614 | + | 0.646854i | ||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(8\) | 45.0000i | 1.98874i | ||||||||
\(9\) | 4.50000 | − | 7.79423i | 0.166667 | − | 0.288675i | ||||
\(10\) | 18.8397 | + | 52.6314i | 0.595765 | + | 1.66435i | ||||
\(11\) | 22.5000 | + | 38.9711i | 0.616728 | + | 1.06820i | 0.990079 | + | 0.140514i | \(0.0448754\pi\) |
−0.373351 | + | 0.927690i | \(0.621791\pi\) | |||||||
\(12\) | −44.1673 | − | 25.5000i | −1.06250 | − | 0.613435i | ||||
\(13\) | − | 37.0000i | − | 0.789381i | −0.918814 | − | 0.394691i | \(-0.870852\pi\) | ||
0.918814 | − | 0.394691i | \(-0.129148\pi\) | |||||||
\(14\) | −42.5000 | − | 82.2724i | −0.811329 | − | 1.57059i | ||||
\(15\) | −33.0000 | − | 6.00000i | −0.568038 | − | 0.103280i | ||||
\(16\) | −44.5000 | + | 77.0763i | −0.695312 | + | 1.20432i | ||||
\(17\) | −50.2295 | + | 29.0000i | −0.716614 | + | 0.413737i | −0.813505 | − | 0.581558i | \(-0.802443\pi\) |
0.0968912 | + | 0.995295i | \(0.469110\pi\) | |||||||
\(18\) | 38.9711 | − | 22.5000i | 0.510310 | − | 0.294628i | ||||
\(19\) | 67.5000 | − | 116.913i | 0.815030 | − | 1.41167i | −0.0942771 | − | 0.995546i | \(-0.530054\pi\) |
0.909307 | − | 0.416127i | \(-0.136613\pi\) | |||||||
\(20\) | −34.0000 | + | 187.000i | −0.380132 | + | 2.09072i | ||||
\(21\) | 55.5000 | + | 2.59808i | 0.576719 | + | 0.0269975i | ||||
\(22\) | 225.000i | 2.18046i | ||||||||
\(23\) | 54.5596 | + | 31.5000i | 0.494629 | + | 0.285574i | 0.726493 | − | 0.687174i | \(-0.241149\pi\) |
−0.231864 | + | 0.972748i | \(0.574482\pi\) | |||||||
\(24\) | −67.5000 | − | 116.913i | −0.574099 | − | 0.994369i | ||||
\(25\) | 20.3949 | + | 123.325i | 0.163159 | + | 0.986600i | ||||
\(26\) | 92.5000 | − | 160.215i | 0.697721 | − | 1.20849i | ||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 14.7224 | − | 314.500i | 0.0993671 | − | 2.12268i | ||||
\(29\) | 184.000 | 1.17820 | 0.589102 | − | 0.808058i | \(-0.299481\pi\) | ||||
0.589102 | + | 0.808058i | \(0.299481\pi\) | |||||||
\(30\) | −127.894 | − | 108.481i | −0.778339 | − | 0.660193i | ||||
\(31\) | −85.0000 | − | 147.224i | −0.492466 | − | 0.852976i | 0.507496 | − | 0.861654i | \(-0.330571\pi\) |
−0.999962 | + | 0.00867760i | \(0.997238\pi\) | |||||||
\(32\) | −73.6122 | + | 42.5000i | −0.406654 | + | 0.234782i | ||||
\(33\) | −116.913 | − | 67.5000i | −0.616728 | − | 0.356068i | ||||
\(34\) | −290.000 | −1.46278 | ||||||||
\(35\) | −60.5910 | − | 197.999i | −0.292622 | − | 0.956228i | ||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | −61.4878 | − | 35.5000i | −0.273204 | − | 0.157734i | 0.357139 | − | 0.934051i | \(-0.383752\pi\) |
−0.630343 | + | 0.776317i | \(0.717086\pi\) | |||||||
\(38\) | 584.567 | − | 337.500i | 2.49551 | − | 1.44078i | ||||
\(39\) | 55.5000 | + | 96.1288i | 0.227875 | + | 0.394691i | ||||
\(40\) | −325.442 | + | 383.683i | −1.28642 | + | 1.51664i | ||||
\(41\) | 247.000 | 0.940852 | 0.470426 | − | 0.882440i | \(-0.344100\pi\) | ||||
0.470426 | + | 0.882440i | \(0.344100\pi\) | |||||||
\(42\) | 233.827 | + | 150.000i | 0.859054 | + | 0.551083i | ||||
\(43\) | − | 242.000i | − | 0.858248i | −0.903246 | − | 0.429124i | \(-0.858822\pi\) | ||
0.903246 | − | 0.429124i | \(-0.141178\pi\) | |||||||
\(44\) | −382.500 | + | 662.509i | −1.31055 | + | 2.26993i | ||||
\(45\) | 94.7365 | − | 33.9115i | 0.313833 | − | 0.112339i | ||||
\(46\) | 157.500 | + | 272.798i | 0.504828 | + | 0.874389i | ||||
\(47\) | −491.036 | − | 283.500i | −1.52394 | − | 0.879845i | −0.999598 | − | 0.0283351i | \(-0.990979\pi\) |
−0.524338 | − | 0.851510i | \(-0.675687\pi\) | |||||||
\(48\) | − | 267.000i | − | 0.802878i | ||||||
\(49\) | 143.000 | + | 311.769i | 0.416910 | + | 0.908948i | ||||
\(50\) | −220.000 | + | 585.000i | −0.622254 | + | 1.65463i | ||||
\(51\) | 87.0000 | − | 150.688i | 0.238871 | − | 0.413737i | ||||
\(52\) | 544.730 | − | 314.500i | 1.45270 | − | 0.838717i | ||||
\(53\) | 38.9711 | − | 22.5000i | 0.101002 | − | 0.0583134i | −0.448648 | − | 0.893708i | \(-0.648094\pi\) |
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(54\) | −67.5000 | + | 116.913i | −0.170103 | + | 0.294628i | ||||
\(55\) | −90.0000 | + | 495.000i | −0.220647 | + | 1.21356i | ||||
\(56\) | 450.000 | − | 701.481i | 1.07382 | − | 1.67392i | ||||
\(57\) | 405.000i | 0.941115i | ||||||||
\(58\) | 796.743 | + | 460.000i | 1.80375 | + | 1.04140i | ||||
\(59\) | −2.00000 | − | 3.46410i | −0.00441318 | − | 0.00764386i | 0.863810 | − | 0.503817i | \(-0.168071\pi\) |
−0.868224 | + | 0.496173i | \(0.834738\pi\) | |||||||
\(60\) | −192.165 | − | 536.840i | −0.413474 | − | 1.15510i | ||||
\(61\) | −131.000 | + | 226.899i | −0.274964 | + | 0.476252i | −0.970126 | − | 0.242601i | \(-0.921999\pi\) |
0.695162 | + | 0.718853i | \(0.255333\pi\) | |||||||
\(62\) | − | 850.000i | − | 1.74113i | ||||||
\(63\) | −148.090 | + | 76.5000i | −0.296153 | + | 0.152986i | ||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 267.586 | − | 315.472i | 0.510615 | − | 0.601993i | ||||
\(66\) | −337.500 | − | 584.567i | −0.629445 | − | 1.09023i | ||||
\(67\) | −756.906 | + | 437.000i | −1.38016 | + | 0.796837i | −0.992178 | − | 0.124830i | \(-0.960161\pi\) |
−0.387983 | + | 0.921666i | \(0.626828\pi\) | |||||||
\(68\) | −853.901 | − | 493.000i | −1.52280 | − | 0.879192i | ||||
\(69\) | −189.000 | −0.329753 | ||||||||
\(70\) | 232.631 | − | 1008.84i | 0.397211 | − | 1.72256i | ||||
\(71\) | −1138.00 | −1.90219 | −0.951097 | − | 0.308893i | \(-0.900042\pi\) | ||||
−0.951097 | + | 0.308893i | \(0.900042\pi\) | |||||||
\(72\) | 350.740 | + | 202.500i | 0.574099 | + | 0.331456i | ||||
\(73\) | −93.5307 | + | 54.0000i | −0.149958 | + | 0.0865784i | −0.573102 | − | 0.819484i | \(-0.694260\pi\) |
0.423143 | + | 0.906063i | \(0.360927\pi\) | |||||||
\(74\) | −177.500 | − | 307.439i | −0.278837 | − | 0.482960i | ||||
\(75\) | −237.975 | − | 289.815i | −0.366386 | − | 0.446200i | ||||
\(76\) | 2295.00 | 3.46388 | ||||||||
\(77\) | 38.9711 | − | 832.500i | 0.0576776 | − | 1.23211i | ||||
\(78\) | 555.000i | 0.805659i | ||||||||
\(79\) | −31.0000 | + | 53.6936i | −0.0441490 | + | 0.0764683i | −0.887256 | − | 0.461278i | \(-0.847391\pi\) |
0.843106 | + | 0.537747i | \(0.180724\pi\) | |||||||
\(80\) | −936.839 | + | 335.347i | −1.30927 | + | 0.468662i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1069.54 | + | 617.500i | 1.44038 | + | 0.831603i | ||||
\(83\) | − | 454.000i | − | 0.600397i | −0.953877 | − | 0.300199i | \(-0.902947\pi\) | ||
0.953877 | − | 0.300199i | \(-0.0970530\pi\) | |||||||
\(84\) | 433.500 | + | 839.179i | 0.563080 | + | 1.09002i | ||||
\(85\) | −638.000 | − | 116.000i | −0.814127 | − | 0.148023i | ||||
\(86\) | 605.000 | − | 1047.89i | 0.758591 | − | 1.31392i | ||||
\(87\) | −478.046 | + | 276.000i | −0.589102 | + | 0.340118i | ||||
\(88\) | −1753.70 | + | 1012.50i | −2.12438 | + | 1.22651i | ||||
\(89\) | −603.000 | + | 1044.43i | −0.718178 | + | 1.24392i | 0.243542 | + | 0.969890i | \(0.421690\pi\) |
−0.961721 | + | 0.274031i | \(0.911643\pi\) | |||||||
\(90\) | 495.000 | + | 90.0000i | 0.579751 | + | 0.105409i | ||||
\(91\) | −370.000 | + | 576.773i | −0.426226 | + | 0.664420i | ||||
\(92\) | 1071.00i | 1.21369i | ||||||||
\(93\) | 441.673 | + | 255.000i | 0.492466 | + | 0.284325i | ||||
\(94\) | −1417.50 | − | 2455.18i | −1.55536 | − | 2.69396i | ||||
\(95\) | 1421.05 | − | 508.673i | 1.53470 | − | 0.549355i | ||||
\(96\) | 127.500 | − | 220.836i | 0.135551 | − | 0.234782i | ||||
\(97\) | 1360.00i | 1.42358i | 0.702393 | + | 0.711789i | \(0.252115\pi\) | ||||
−0.702393 | + | 0.711789i | \(0.747885\pi\) | |||||||
\(98\) | −160.215 | + | 1707.50i | −0.165144 | + | 1.76004i | ||||
\(99\) | 405.000 | 0.411152 | ||||||||
\(100\) | −1642.29 | + | 1348.52i | −1.64229 | + | 1.34852i | ||||
\(101\) | 180.000 | + | 311.769i | 0.177333 | + | 0.307150i | 0.940966 | − | 0.338500i | \(-0.109920\pi\) |
−0.763633 | + | 0.645651i | \(0.776586\pi\) | |||||||
\(102\) | 753.442 | − | 435.000i | 0.731391 | − | 0.422269i | ||||
\(103\) | 131.636 | + | 76.0000i | 0.125927 | + | 0.0727039i | 0.561640 | − | 0.827382i | \(-0.310171\pi\) |
−0.435713 | + | 0.900085i | \(0.643504\pi\) | |||||||
\(104\) | 1665.00 | 1.56987 | ||||||||
\(105\) | 454.419 | + | 423.531i | 0.422350 | + | 0.393642i | ||||
\(106\) | 225.000 | 0.206169 | ||||||||
\(107\) | −308.305 | − | 178.000i | −0.278551 | − | 0.160822i | 0.354216 | − | 0.935164i | \(-0.384748\pi\) |
−0.632767 | + | 0.774342i | \(0.718081\pi\) | |||||||
\(108\) | −397.506 | + | 229.500i | −0.354167 | + | 0.204478i | ||||
\(109\) | −689.000 | − | 1193.38i | −0.605452 | − | 1.04867i | −0.991980 | − | 0.126395i | \(-0.959659\pi\) |
0.386528 | − | 0.922278i | \(-0.373674\pi\) | |||||||
\(110\) | −1627.21 | + | 1918.41i | −1.41044 | + | 1.66285i | ||||
\(111\) | 213.000 | 0.182136 | ||||||||
\(112\) | 1464.45 | − | 756.500i | 1.23551 | − | 0.638237i | ||||
\(113\) | − | 414.000i | − | 0.344653i | −0.985040 | − | 0.172327i | \(-0.944872\pi\) | ||
0.985040 | − | 0.172327i | \(-0.0551285\pi\) | |||||||
\(114\) | −1012.50 | + | 1753.70i | −0.831836 | + | 1.44078i | ||||
\(115\) | 237.381 | + | 663.156i | 0.192486 | + | 0.537735i | ||||
\(116\) | 1564.00 | + | 2708.93i | 1.25184 | + | 2.16826i | ||||
\(117\) | −288.386 | − | 166.500i | −0.227875 | − | 0.131564i | ||||
\(118\) | − | 20.0000i | − | 0.0156030i | ||||||
\(119\) | 1073.00 | + | 50.2295i | 0.826569 | + | 0.0386935i | ||||
\(120\) | 270.000 | − | 1485.00i | 0.205396 | − | 1.12968i | ||||
\(121\) | −347.000 | + | 601.022i | −0.260706 | + | 0.451556i | ||||
\(122\) | −1134.49 | + | 655.000i | −0.841903 | + | 0.486073i | ||||
\(123\) | −641.725 | + | 370.500i | −0.470426 | + | 0.271600i | ||||
\(124\) | 1445.00 | − | 2502.81i | 1.04649 | − | 1.81257i | ||||
\(125\) | −718.000 | + | 1199.00i | −0.513759 | + | 0.857935i | ||||
\(126\) | −832.500 | − | 38.9711i | −0.588611 | − | 0.0275542i | ||||
\(127\) | − | 2323.00i | − | 1.62309i | −0.584287 | − | 0.811547i | \(-0.698626\pi\) | ||
0.584287 | − | 0.811547i | \(-0.301374\pi\) | |||||||
\(128\) | 1831.64 | + | 1057.50i | 1.26481 | + | 0.730240i | ||||
\(129\) | 363.000 | + | 628.734i | 0.247755 | + | 0.429124i | ||||
\(130\) | 1947.36 | − | 697.071i | 1.31381 | − | 0.470286i | ||||
\(131\) | 1140.50 | − | 1975.40i | 0.760656 | − | 1.31749i | −0.181857 | − | 0.983325i | \(-0.558211\pi\) |
0.942513 | − | 0.334170i | \(-0.108456\pi\) | |||||||
\(132\) | − | 2295.00i | − | 1.51329i | ||||||
\(133\) | −2221.36 | + | 1147.50i | −1.44824 | + | 0.748127i | ||||
\(134\) | −4370.00 | −2.81724 | ||||||||
\(135\) | −195.265 | + | 230.210i | −0.124487 | + | 0.146765i | ||||
\(136\) | −1305.00 | − | 2260.33i | −0.822815 | − | 1.42516i | ||||
\(137\) | 530.008 | − | 306.000i | 0.330523 | − | 0.190827i | −0.325550 | − | 0.945525i | \(-0.605550\pi\) |
0.656073 | + | 0.754697i | \(0.272216\pi\) | |||||||
\(138\) | −818.394 | − | 472.500i | −0.504828 | − | 0.291463i | ||||
\(139\) | −800.000 | −0.488166 | −0.244083 | − | 0.969754i | \(-0.578487\pi\) | ||||
−0.244083 | + | 0.969754i | \(0.578487\pi\) | |||||||
\(140\) | 2400.01 | − | 2575.04i | 1.44884 | − | 1.55451i | ||||
\(141\) | 1701.00 | 1.01596 | ||||||||
\(142\) | −4927.68 | − | 2845.00i | −2.91213 | − | 1.68132i | ||||
\(143\) | 1441.93 | − | 832.500i | 0.843220 | − | 0.486833i | ||||
\(144\) | 400.500 | + | 693.686i | 0.231771 | + | 0.401439i | ||||
\(145\) | 1568.84 | + | 1330.70i | 0.898515 | + | 0.762127i | ||||
\(146\) | −540.000 | −0.306101 | ||||||||
\(147\) | −839.179 | − | 595.500i | −0.470845 | − | 0.334123i | ||||
\(148\) | − | 1207.00i | − | 0.670370i | ||||||
\(149\) | 637.000 | − | 1103.32i | 0.350235 | − | 0.606625i | −0.636055 | − | 0.771644i | \(-0.719435\pi\) |
0.986291 | + | 0.165018i | \(0.0527683\pi\) | |||||||
\(150\) | −305.923 | − | 1849.87i | −0.166524 | − | 1.00694i | ||||
\(151\) | 383.000 | + | 663.375i | 0.206411 | + | 0.357515i | 0.950581 | − | 0.310475i | \(-0.100488\pi\) |
−0.744170 | + | 0.667990i | \(0.767155\pi\) | |||||||
\(152\) | 5261.10 | + | 3037.50i | 2.80745 | + | 1.62088i | ||||
\(153\) | 522.000i | 0.275825i | ||||||||
\(154\) | 2250.00 | − | 3507.40i | 1.17734 | − | 1.83529i | ||||
\(155\) | 340.000 | − | 1870.00i | 0.176190 | − | 0.969045i | ||||
\(156\) | −943.500 | + | 1634.19i | −0.484234 | + | 0.838717i | ||||
\(157\) | −116.913 | + | 67.5000i | −0.0594313 | + | 0.0343127i | −0.529421 | − | 0.848359i | \(-0.677591\pi\) |
0.469990 | + | 0.882672i | \(0.344258\pi\) | |||||||
\(158\) | −268.468 | + | 155.000i | −0.135178 | + | 0.0780452i | ||||
\(159\) | −67.5000 | + | 116.913i | −0.0336673 | + | 0.0583134i | ||||
\(160\) | −935.000 | − | 170.000i | −0.461989 | − | 0.0839980i | ||||
\(161\) | −535.500 | − | 1036.63i | −0.262132 | − | 0.507441i | ||||
\(162\) | − | 405.000i | − | 0.196419i | ||||||
\(163\) | 2830.17 | + | 1634.00i | 1.35998 | + | 0.785183i | 0.989620 | − | 0.143707i | \(-0.0459024\pi\) |
0.370356 | + | 0.928890i | \(0.379236\pi\) | |||||||
\(164\) | 2099.50 | + | 3636.44i | 0.999655 | + | 1.73145i | ||||
\(165\) | −508.673 | − | 1421.05i | −0.240001 | − | 0.670475i | ||||
\(166\) | 1135.00 | − | 1965.88i | 0.530681 | − | 0.919167i | ||||
\(167\) | 2529.00i | 1.17186i | 0.810363 | + | 0.585928i | \(0.199270\pi\) | ||||
−0.810363 | + | 0.585928i | \(0.800730\pi\) | |||||||
\(168\) | −116.913 | + | 2497.50i | −0.0536909 | + | 1.14694i | ||||
\(169\) | 828.000 | 0.376878 | ||||||||
\(170\) | −2472.62 | − | 2097.29i | −1.11554 | − | 0.946207i | ||||
\(171\) | −607.500 | − | 1052.22i | −0.271677 | − | 0.470558i | ||||
\(172\) | 3562.83 | − | 2057.00i | 1.57944 | − | 0.911888i | ||||
\(173\) | 272.798 | + | 157.500i | 0.119887 | + | 0.0692168i | 0.558744 | − | 0.829340i | \(-0.311283\pi\) |
−0.438857 | + | 0.898557i | \(0.644617\pi\) | |||||||
\(174\) | −2760.00 | −1.20250 | ||||||||
\(175\) | 915.325 | − | 2126.39i | 0.395383 | − | 0.918516i | ||||
\(176\) | −4005.00 | −1.71527 | ||||||||
\(177\) | 10.3923 | + | 6.00000i | 0.00441318 | + | 0.00254795i | ||||
\(178\) | −5222.13 | + | 3015.00i | −2.19896 | + | 1.26957i | ||||
\(179\) | 38.5000 | + | 66.6840i | 0.0160761 | + | 0.0278447i | 0.873952 | − | 0.486013i | \(-0.161549\pi\) |
−0.857875 | + | 0.513858i | \(0.828216\pi\) | |||||||
\(180\) | 1304.52 | + | 1106.50i | 0.540185 | + | 0.458188i | ||||
\(181\) | −1602.00 | −0.657877 | −0.328938 | − | 0.944351i | \(-0.606691\pi\) | ||||
−0.328938 | + | 0.944351i | \(0.606691\pi\) | |||||||
\(182\) | −3044.08 | + | 1572.50i | −1.23979 | + | 0.640448i | ||||
\(183\) | − | 786.000i | − | 0.317502i | ||||||
\(184\) | −1417.50 | + | 2455.18i | −0.567932 | + | 0.983687i | ||||
\(185\) | −267.524 | − | 747.366i | −0.106318 | − | 0.297013i | ||||
\(186\) | 1275.00 | + | 2208.36i | 0.502621 | + | 0.870565i | ||||
\(187\) | −2260.33 | − | 1305.00i | −0.883911 | − | 0.510326i | ||||
\(188\) | − | 9639.00i | − | 3.73934i | ||||||
\(189\) | 270.000 | − | 420.888i | 0.103913 | − | 0.161985i | ||||
\(190\) | 7425.00 | + | 1350.00i | 2.83508 | + | 0.515470i | ||||
\(191\) | −612.000 | + | 1060.02i | −0.231847 | + | 0.401571i | −0.958352 | − | 0.285591i | \(-0.907810\pi\) |
0.726505 | + | 0.687161i | \(0.241144\pi\) | |||||||
\(192\) | −745.648 | + | 430.500i | −0.280273 | + | 0.161816i | ||||
\(193\) | 3888.45 | − | 2245.00i | 1.45024 | − | 0.837299i | 0.451749 | − | 0.892145i | \(-0.350800\pi\) |
0.998495 | + | 0.0548465i | \(0.0174669\pi\) | |||||||
\(194\) | −3400.00 | + | 5888.97i | −1.25828 | + | 2.17940i | ||||
\(195\) | −222.000 | + | 1221.00i | −0.0815269 | + | 0.448398i | ||||
\(196\) | −3374.50 | + | 4755.35i | −1.22977 | + | 1.73300i | ||||
\(197\) | 2497.00i | 0.903065i | 0.892255 | + | 0.451533i | \(0.149123\pi\) | ||||
−0.892255 | + | 0.451533i | \(0.850877\pi\) | |||||||
\(198\) | 1753.70 | + | 1012.50i | 0.629445 | + | 0.363410i | ||||
\(199\) | 1813.00 | + | 3140.21i | 0.645830 | + | 1.11861i | 0.984109 | + | 0.177565i | \(0.0568218\pi\) |
−0.338279 | + | 0.941046i | \(0.609845\pi\) | |||||||
\(200\) | −5549.62 | + | 917.770i | −1.96209 | + | 0.324481i | ||||
\(201\) | 1311.00 | − | 2270.72i | 0.460054 | − | 0.796837i | ||||
\(202\) | 1800.00i | 0.626968i | ||||||||
\(203\) | −2868.28 | − | 1840.00i | −0.991692 | − | 0.636171i | ||||
\(204\) | 2958.00 | 1.01520 | ||||||||
\(205\) | 2105.99 | + | 1786.32i | 0.717506 | + | 0.608594i | ||||
\(206\) | 380.000 | + | 658.179i | 0.128524 | + | 0.222609i | ||||
\(207\) | 491.036 | − | 283.500i | 0.164876 | − | 0.0951914i | ||||
\(208\) | 2851.82 | + | 1646.50i | 0.950665 | + | 0.548867i | ||||
\(209\) | 6075.00 | 2.01061 | ||||||||
\(210\) | 908.866 | + | 2969.99i | 0.298656 | + | 0.975946i | ||||
\(211\) | −4069.00 | −1.32759 | −0.663795 | − | 0.747915i | \(-0.731055\pi\) | ||||
−0.663795 | + | 0.747915i | \(0.731055\pi\) | |||||||
\(212\) | 662.509 | + | 382.500i | 0.214629 | + | 0.123916i | ||||
\(213\) | 2956.61 | − | 1707.00i | 0.951097 | − | 0.549116i | ||||
\(214\) | −890.000 | − | 1541.53i | −0.284295 | − | 0.492414i | ||||
\(215\) | 1750.16 | − | 2063.36i | 0.555161 | − | 0.654511i | ||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | −147.224 | + | 3145.00i | −0.0460564 | + | 0.983855i | ||||
\(218\) | − | 6890.00i | − | 2.14059i | ||||||
\(219\) | 162.000 | − | 280.592i | 0.0499861 | − | 0.0865784i | ||||
\(220\) | −8052.60 | + | 2882.48i | −2.46776 | + | 0.883349i | ||||
\(221\) | 1073.00 | + | 1858.49i | 0.326596 | + | 0.565681i | ||||
\(222\) | 922.317 | + | 532.500i | 0.278837 | + | 0.160987i | ||||
\(223\) | − | 1368.00i | − | 0.410798i | −0.978678 | − | 0.205399i | \(-0.934151\pi\) | ||
0.978678 | − | 0.205399i | \(-0.0658493\pi\) | |||||||
\(224\) | 1572.50 | + | 73.6122i | 0.469049 | + | 0.0219572i | ||||
\(225\) | 1053.00 | + | 396.000i | 0.312000 | + | 0.117333i | ||||
\(226\) | 1035.00 | − | 1792.67i | 0.304634 | − | 0.527641i | ||||
\(227\) | 81.4064 | − | 47.0000i | 0.0238023 | − | 0.0137423i | −0.488052 | − | 0.872815i | \(-0.662292\pi\) |
0.511854 | + | 0.859072i | \(0.328959\pi\) | |||||||
\(228\) | −5962.58 | + | 3442.50i | −1.73194 | + | 0.999935i | ||||
\(229\) | 1138.00 | − | 1971.07i | 0.328389 | − | 0.568787i | −0.653803 | − | 0.756665i | \(-0.726828\pi\) |
0.982192 | + | 0.187878i | \(0.0601609\pi\) | |||||||
\(230\) | −630.000 | + | 3465.00i | −0.180613 | + | 0.993371i | ||||
\(231\) | 1147.50 | + | 2221.36i | 0.326840 | + | 0.632703i | ||||
\(232\) | 8280.00i | 2.34314i | ||||||||
\(233\) | 2397.16 | + | 1384.00i | 0.674005 | + | 0.389137i | 0.797592 | − | 0.603197i | \(-0.206107\pi\) |
−0.123588 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(234\) | −832.500 | − | 1441.93i | −0.232574 | − | 0.402829i | ||||
\(235\) | −2136.43 | − | 5968.40i | −0.593043 | − | 1.65675i | ||||
\(236\) | 34.0000 | − | 58.8897i | 0.00937801 | − | 0.0162432i | ||||
\(237\) | − | 186.000i | − | 0.0509789i | ||||||
\(238\) | 4520.65 | + | 2900.00i | 1.23122 | + | 0.789828i | ||||
\(239\) | −5076.00 | −1.37380 | −0.686902 | − | 0.726750i | \(-0.741030\pi\) | ||||
−0.686902 | + | 0.726750i | \(0.741030\pi\) | |||||||
\(240\) | 1930.96 | − | 2276.52i | 0.519345 | − | 0.612285i | ||||
\(241\) | −1503.50 | − | 2604.14i | −0.401863 | − | 0.696047i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.993951 | + | 0.109826i | \(0.964970\pi\) | |||||||
\(242\) | −3005.11 | + | 1735.00i | −0.798247 | + | 0.460868i | ||||
\(243\) | 210.444 | + | 121.500i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −4454.00 | −1.16860 | ||||||||
\(245\) | −1035.47 | + | 3692.41i | −0.270016 | + | 0.962856i | ||||
\(246\) | −3705.00 | −0.960253 | ||||||||
\(247\) | −4325.80 | − | 2497.50i | −1.11435 | − | 0.643369i | ||||
\(248\) | 6625.09 | − | 3825.00i | 1.69635 | − | 0.979386i | ||||
\(249\) | 681.000 | + | 1179.53i | 0.173320 | + | 0.300199i | ||||
\(250\) | −6106.53 | + | 3396.82i | −1.54484 | + | 0.859336i | ||||
\(251\) | 6237.00 | 1.56843 | 0.784215 | − | 0.620489i | \(-0.213066\pi\) | ||||
0.784215 | + | 0.620489i | \(0.213066\pi\) | |||||||
\(252\) | −2385.03 | − | 1530.00i | −0.596202 | − | 0.382464i | ||||
\(253\) | 2835.00i | 0.704486i | ||||||||
\(254\) | 5807.50 | − | 10058.9i | 1.43463 | − | 2.48484i | ||||
\(255\) | 1831.57 | − | 655.623i | 0.449794 | − | 0.161007i | ||||
\(256\) | 4139.50 | + | 7169.82i | 1.01062 | + | 1.75045i | ||||
\(257\) | −3815.71 | − | 2203.00i | −0.926137 | − | 0.534706i | −0.0405495 | − | 0.999178i | \(-0.512911\pi\) |
−0.885588 | + | 0.464472i | \(0.846244\pi\) | |||||||
\(258\) | 3630.00i | 0.875945i | ||||||||
\(259\) | 603.500 | + | 1168.27i | 0.144786 | + | 0.280281i | ||||
\(260\) | 6919.00 | + | 1258.00i | 1.65038 | + | 0.300069i | ||||
\(261\) | 828.000 | − | 1434.14i | 0.196367 | − | 0.340118i | ||||
\(262\) | 9877.02 | − | 5702.50i | 2.32902 | − | 1.34466i | ||||
\(263\) | 498.831 | − | 288.000i | 0.116955 | − | 0.0675241i | −0.440381 | − | 0.897811i | \(-0.645157\pi\) |
0.557336 | + | 0.830287i | \(0.311823\pi\) | |||||||
\(264\) | 3037.50 | − | 5261.10i | 0.708126 | − | 1.22651i | ||||
\(265\) | 495.000 | + | 90.0000i | 0.114746 | + | 0.0208629i | ||||
\(266\) | −12487.5 | − | 584.567i | −2.87841 | − | 0.134745i | ||||
\(267\) | − | 3618.00i | − | 0.829281i | ||||||
\(268\) | −12867.4 | − | 7429.00i | −2.93284 | − | 1.69328i | ||||
\(269\) | 259.000 | + | 448.601i | 0.0587045 | + | 0.101679i | 0.893884 | − | 0.448298i | \(-0.147970\pi\) |
−0.835180 | + | 0.549977i | \(0.814636\pi\) | |||||||
\(270\) | −1421.05 | + | 508.673i | −0.320304 | + | 0.114655i | ||||
\(271\) | −1652.00 | + | 2861.35i | −0.370302 | + | 0.641382i | −0.989612 | − | 0.143765i | \(-0.954079\pi\) |
0.619310 | + | 0.785147i | \(0.287412\pi\) | |||||||
\(272\) | − | 5162.00i | − | 1.15071i | ||||||
\(273\) | 96.1288 | − | 2053.50i | 0.0213113 | − | 0.455251i | ||||
\(274\) | 3060.00 | 0.674676 | ||||||||
\(275\) | −4347.23 | + | 3569.62i | −0.953265 | + | 0.782751i | ||||
\(276\) | −1606.50 | − | 2782.54i | −0.350362 | − | 0.606845i | ||||
\(277\) | 3140.21 | − | 1813.00i | 0.681144 | − | 0.393259i | −0.119142 | − | 0.992877i | \(-0.538014\pi\) |
0.800286 | + | 0.599619i | \(0.204681\pi\) | |||||||
\(278\) | −3464.10 | − | 2000.00i | −0.747349 | − | 0.431482i | ||||
\(279\) | −1530.00 | −0.328311 | ||||||||
\(280\) | 8909.97 | − | 2726.60i | 1.90169 | − | 0.581948i | ||||
\(281\) | −5539.00 | −1.17590 | −0.587952 | − | 0.808896i | \(-0.700066\pi\) | ||||
−0.587952 | + | 0.808896i | \(0.700066\pi\) | |||||||
\(282\) | 7365.55 | + | 4252.50i | 1.55536 | + | 0.897988i | ||||
\(283\) | 226.899 | − | 131.000i | 0.0476598 | − | 0.0275164i | −0.475981 | − | 0.879456i | \(-0.657907\pi\) |
0.523641 | + | 0.851939i | \(0.324573\pi\) | |||||||
\(284\) | −9673.00 | − | 16754.1i | −2.02108 | − | 3.50061i | ||||
\(285\) | −2928.98 | + | 3453.14i | −0.608764 | + | 0.717707i | ||||
\(286\) | 8325.00 | 1.72122 | ||||||||
\(287\) | −3850.35 | − | 2470.00i | −0.791913 | − | 0.508012i | ||||
\(288\) | 765.000i | 0.156521i | ||||||||
\(289\) | −774.500 | + | 1341.47i | −0.157643 | + | 0.273046i | ||||
\(290\) | 3466.51 | + | 9684.18i | 0.701933 | + | 1.96095i | ||||
\(291\) | −2040.00 | − | 3533.38i | −0.410952 | − | 0.711789i | ||||
\(292\) | −1590.02 | − | 918.000i | −0.318661 | − | 0.183979i | ||||
\(293\) | 6219.00i | 1.23999i | 0.784605 | + | 0.619996i | \(0.212866\pi\) | ||||
−0.784605 | + | 0.619996i | \(0.787134\pi\) | |||||||
\(294\) | −2145.00 | − | 4676.54i | −0.425507 | − | 0.927691i | ||||
\(295\) | 8.00000 | − | 44.0000i | 0.00157891 | − | 0.00868400i | ||||
\(296\) | 1597.50 | − | 2766.95i | 0.313692 | − | 0.543330i | ||||
\(297\) | −1052.22 | + | 607.500i | −0.205576 | + | 0.118689i | ||||
\(298\) | 5516.58 | − | 3185.00i | 1.07237 | − | 0.619135i | ||||
\(299\) | 1165.50 | − | 2018.71i | 0.225427 | − | 0.390451i | ||||
\(300\) | 2244.00 | − | 5967.00i | 0.431858 | − | 1.14835i | ||||
\(301\) | −2420.00 | + | 3772.41i | −0.463410 | + | 0.722385i | ||||
\(302\) | 3830.00i | 0.729774i | ||||||||
\(303\) | −935.307 | − | 540.000i | −0.177333 | − | 0.102383i | ||||
\(304\) | 6007.50 | + | 10405.3i | 1.13340 | + | 1.96311i | ||||
\(305\) | −2757.89 | + | 987.203i | −0.517758 | + | 0.185335i | ||||
\(306\) | −1305.00 | + | 2260.33i | −0.243797 | + | 0.422269i | ||||
\(307\) | 7066.00i | 1.31361i | 0.754061 | + | 0.656804i | \(0.228092\pi\) | ||||
−0.754061 | + | 0.656804i | \(0.771908\pi\) | |||||||
\(308\) | 12587.7 | − | 6502.50i | 2.32873 | − | 1.20297i | ||||
\(309\) | −456.000 | −0.0839512 | ||||||||
\(310\) | 6147.24 | − | 7247.34i | 1.12626 | − | 1.32781i | ||||
\(311\) | −351.000 | − | 607.950i | −0.0639980 | − | 0.110848i | 0.832251 | − | 0.554399i | \(-0.187052\pi\) |
−0.896249 | + | 0.443551i | \(0.853718\pi\) | |||||||
\(312\) | −4325.80 | + | 2497.50i | −0.784936 | + | 0.453183i | ||||
\(313\) | −3320.34 | − | 1917.00i | −0.599606 | − | 0.346183i | 0.169280 | − | 0.985568i | \(-0.445856\pi\) |
−0.768887 | + | 0.639385i | \(0.779189\pi\) | |||||||
\(314\) | −675.000 | −0.121314 | ||||||||
\(315\) | −1815.91 | − | 418.737i | −0.324810 | − | 0.0748988i | ||||
\(316\) | −1054.00 | −0.187633 | ||||||||
\(317\) | 6406.86 | + | 3699.00i | 1.13516 | + | 0.655383i | 0.945227 | − | 0.326414i | \(-0.105840\pi\) |
0.189930 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(318\) | −584.567 | + | 337.500i | −0.103085 | + | 0.0595159i | ||||
\(319\) | 4140.00 | + | 7170.69i | 0.726632 | + | 1.25856i | ||||
\(320\) | 2447.04 | + | 2075.60i | 0.427481 | + | 0.362592i | ||||
\(321\) | 1068.00 | 0.185701 | ||||||||
\(322\) | 272.798 | − | 5827.50i | 0.0472125 | − | 1.00855i | ||||
\(323\) | 7830.00i | 1.34883i | ||||||||
\(324\) | 688.500 | − | 1192.52i | 0.118056 | − | 0.204478i | ||||
\(325\) | 4563.02 | − | 754.611i | 0.778803 | − | 0.128795i | ||||
\(326\) | 8170.00 | + | 14150.9i | 1.38802 | + | 2.40412i | ||||
\(327\) | 3580.15 | + | 2067.00i | 0.605452 | + | 0.349558i | ||||
\(328\) | 11115.0i | 1.87111i | ||||||||
\(329\) | 4819.50 | + | 9329.69i | 0.807622 | + | 1.56341i | ||||
\(330\) | 1350.00 | − | 7425.00i | 0.225197 | − | 1.23858i | ||||
\(331\) | −3136.50 | + | 5432.58i | −0.520839 | + | 0.902119i | 0.478868 | + | 0.877887i | \(0.341047\pi\) |
−0.999706 | + | 0.0242321i | \(0.992286\pi\) | |||||||
\(332\) | 6683.98 | − | 3859.00i | 1.10491 | − | 0.637922i | ||||
\(333\) | −553.390 | + | 319.500i | −0.0910679 | + | 0.0525781i | ||||
\(334\) | −6322.50 | + | 10950.9i | −1.03578 | + | 1.79403i | ||||
\(335\) | −9614.00 | − | 1748.00i | −1.56797 | − | 0.285085i | ||||
\(336\) | −2670.00 | + | 4162.12i | −0.433513 | + | 0.675780i | ||||
\(337\) | 234.000i | 0.0378243i | 0.999821 | + | 0.0189122i | \(0.00602028\pi\) | ||||
−0.999821 | + | 0.0189122i | \(0.993980\pi\) | |||||||
\(338\) | 3585.35 | + | 2070.00i | 0.576974 | + | 0.333116i | ||||
\(339\) | 621.000 | + | 1075.60i | 0.0994929 | + | 0.172327i | ||||
\(340\) | −3715.20 | − | 10378.9i | −0.592603 | − | 1.65552i | ||||
\(341\) | 3825.00 | − | 6625.09i | 0.607435 | − | 1.05211i | ||||
\(342\) | − | 6075.00i | − | 0.960522i | ||||||
\(343\) | 888.542 | − | 6290.00i | 0.139874 | − | 0.990169i | ||||
\(344\) | 10890.0 | 1.70683 | ||||||||
\(345\) | −1611.47 | − | 1366.86i | −0.251474 | − | 0.213302i | ||||
\(346\) | 787.500 | + | 1363.99i | 0.122359 | + | 0.211932i | ||||
\(347\) | 685.892 | − | 396.000i | 0.106111 | − | 0.0612634i | −0.446005 | − | 0.895030i | \(-0.647154\pi\) |
0.552116 | + | 0.833767i | \(0.313820\pi\) | |||||||
\(348\) | −8126.78 | − | 4692.00i | −1.25184 | − | 0.722752i | ||||
\(349\) | −7264.00 | −1.11413 | −0.557067 | − | 0.830467i | \(-0.688073\pi\) | ||||
−0.557067 | + | 0.830467i | \(0.688073\pi\) | |||||||
\(350\) | 9279.46 | − | 6919.25i | 1.41717 | − | 1.05671i | ||||
\(351\) | 999.000 | 0.151916 | ||||||||
\(352\) | −3312.55 | − | 1912.50i | −0.501589 | − | 0.289593i | ||||
\(353\) | −7205.33 | + | 4160.00i | −1.08641 | + | 0.627236i | −0.932617 | − | 0.360867i | \(-0.882481\pi\) |
−0.153788 | + | 0.988104i | \(0.549147\pi\) | |||||||
\(354\) | 30.0000 | + | 51.9615i | 0.00450419 | + | 0.00780148i | ||||
\(355\) | −9702.91 | − | 8230.07i | −1.45064 | − | 1.23044i | ||||
\(356\) | −20502.0 | −3.05226 | ||||||||
\(357\) | −2863.08 | + | 1479.00i | −0.424455 | + | 0.219263i | ||||
\(358\) | 385.000i | 0.0568377i | ||||||||
\(359\) | 358.000 | − | 620.074i | 0.0526310 | − | 0.0911595i | −0.838510 | − | 0.544887i | \(-0.816573\pi\) |
0.891141 | + | 0.453727i | \(0.149906\pi\) | |||||||
\(360\) | 1526.02 | + | 4263.14i | 0.223412 | + | 0.624132i | ||||
\(361\) | −5683.00 | − | 9843.24i | −0.828546 | − | 1.43508i | ||||
\(362\) | −6936.86 | − | 4005.00i | −1.00716 | − | 0.581487i | ||||
\(363\) | − | 2082.00i | − | 0.301038i | ||||||
\(364\) | −11636.5 | − | 544.730i | −1.67560 | − | 0.0784385i | ||||
\(365\) | −1188.00 | − | 216.000i | −0.170364 | − | 0.0309752i | ||||
\(366\) | 1965.00 | − | 3403.48i | 0.280634 | − | 0.486073i | ||||
\(367\) | 2673.42 | − | 1543.50i | 0.380249 | − | 0.219537i | −0.297678 | − | 0.954666i | \(-0.596212\pi\) |
0.677927 | + | 0.735130i | \(0.262879\pi\) | |||||||
\(368\) | −4855.80 | + | 2803.50i | −0.687843 | + | 0.397126i | ||||
\(369\) | 1111.50 | − | 1925.17i | 0.156809 | − | 0.271600i | ||||
\(370\) | 710.000 | − | 3905.00i | 0.0997598 | − | 0.548679i | ||||
\(371\) | −832.500 | − | 38.9711i | −0.116499 | − | 0.00545359i | ||||
\(372\) | 8670.00i | 1.20838i | ||||||||
\(373\) | 109.119 | + | 63.0000i | 0.0151474 | + | 0.00874535i | 0.507555 | − | 0.861620i | \(-0.330550\pi\) |
−0.492407 | + | 0.870365i | \(0.663883\pi\) | |||||||
\(374\) | −6525.00 | − | 11301.6i | −0.902138 | − | 1.56255i | ||||
\(375\) | 66.9187 | − | 4192.09i | 0.00921511 | − | 0.577277i | ||||
\(376\) | 12757.5 | − | 22096.6i | 1.74978 | − | 3.03071i | ||||
\(377\) | − | 6808.00i | − | 0.930053i | ||||||
\(378\) | 2221.36 | − | 1147.50i | 0.302260 | − | 0.156140i | ||||
\(379\) | 13825.0 | 1.87373 | 0.936864 | − | 0.349695i | \(-0.113715\pi\) | ||||
0.936864 | + | 0.349695i | \(0.113715\pi\) | |||||||
\(380\) | 19567.8 | + | 16597.6i | 2.64160 | + | 2.24062i | ||||
\(381\) | 3484.50 | + | 6035.33i | 0.468547 | + | 0.811547i | ||||
\(382\) | −5300.08 | + | 3060.00i | −0.709883 | + | 0.409851i | ||||
\(383\) | −1632.46 | − | 942.500i | −0.217793 | − | 0.125743i | 0.387135 | − | 0.922023i | \(-0.373465\pi\) |
−0.604928 | + | 0.796280i | \(0.706798\pi\) | |||||||
\(384\) | −6345.00 | −0.843208 | ||||||||
\(385\) | 6352.96 | − | 6816.29i | 0.840979 | − | 0.902312i | ||||
\(386\) | 22450.0 | 2.96030 | ||||||||
\(387\) | −1886.20 | − | 1089.00i | −0.247755 | − | 0.143041i | ||||
\(388\) | −20022.5 | + | 11560.0i | −2.61982 | + | 1.51255i | ||||
\(389\) | 1739.00 | + | 3012.04i | 0.226660 | + | 0.392587i | 0.956816 | − | 0.290694i | \(-0.0938860\pi\) |
−0.730156 | + | 0.683280i | \(0.760553\pi\) | |||||||
\(390\) | −4013.79 | + | 4732.09i | −0.521144 | + | 0.614406i | ||||
\(391\) | −3654.00 | −0.472611 | ||||||||
\(392\) | −14029.6 | + | 6435.00i | −1.80766 | + | 0.829124i | ||||
\(393\) | 6843.00i | 0.878330i | ||||||||
\(394\) | −6242.50 | + | 10812.3i | −0.798205 | + | 1.38253i | ||||
\(395\) | −652.629 | + | 233.613i | −0.0831325 | + | 0.0297578i | ||||
\(396\) | 3442.50 | + | 5962.58i | 0.436849 | + | 0.756644i | ||||
\(397\) | −725.729 | − | 419.000i | −0.0917464 | − | 0.0529698i | 0.453425 | − | 0.891294i | \(-0.350202\pi\) |
−0.545171 | + | 0.838325i | \(0.683535\pi\) | |||||||
\(398\) | 18130.0i | 2.28335i | ||||||||
\(399\) | 4050.00 | − | 6313.33i | 0.508154 | − | 0.792134i | ||||
\(400\) | −10413.0 | − | 3916.00i | −1.30163 | − | 0.489500i | ||||
\(401\) | 6025.50 | − | 10436.5i | 0.750372 | − | 1.29968i | −0.197271 | − | 0.980349i | \(-0.563208\pi\) |
0.947643 | − | 0.319333i | \(-0.103459\pi\) | |||||||
\(402\) | 11353.6 | − | 6555.00i | 1.40862 | − | 0.813268i | ||||
\(403\) | −5447.30 | + | 3145.00i | −0.673323 | + | 0.388743i | ||||
\(404\) | −3060.00 | + | 5300.08i | −0.376833 | + | 0.652695i | ||||
\(405\) | 162.000 | − | 891.000i | 0.0198762 | − | 0.109319i | ||||
\(406\) | −7820.00 | − | 15138.1i | −0.955912 | − | 1.85047i | ||||
\(407\) | − | 3195.00i | − | 0.389116i | ||||||
\(408\) | 6780.98 | + | 3915.00i | 0.822815 | + | 0.475052i | ||||
\(409\) | 2245.00 | + | 3888.45i | 0.271413 | + | 0.470102i | 0.969224 | − | 0.246180i | \(-0.0791756\pi\) |
−0.697811 | + | 0.716282i | \(0.745842\pi\) | |||||||
\(410\) | 4653.42 | + | 13000.0i | 0.560527 | + | 1.56591i | ||||
\(411\) | −918.000 | + | 1590.02i | −0.110174 | + | 0.190827i | ||||
\(412\) | 2584.00i | 0.308992i | ||||||||
\(413\) | −3.46410 | + | 74.0000i | −0.000412730 | + | 0.00881671i | ||||
\(414\) | 2835.00 | 0.336552 | ||||||||
\(415\) | 3283.35 | − | 3870.93i | 0.388370 | − | 0.457871i | ||||
\(416\) | 1572.50 | + | 2723.65i | 0.185332 | + | 0.321005i | ||||
\(417\) | 2078.46 | − | 1200.00i | 0.244083 | − | 0.140921i | ||||
\(418\) | 26305.5 | + | 15187.5i | 3.07810 | + | 1.77714i | ||||
\(419\) | −1395.00 | −0.162650 | −0.0813248 | − | 0.996688i | \(-0.525915\pi\) | ||||
−0.0813248 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(420\) | −2372.84 | + | 10290.2i | −0.275673 | + | 1.19550i | ||||
\(421\) | −10692.0 | −1.23776 | −0.618879 | − | 0.785486i | \(-0.712413\pi\) | ||||
−0.618879 | + | 0.785486i | \(0.712413\pi\) | |||||||
\(422\) | −17619.3 | − | 10172.5i | −2.03245 | − | 1.17343i | ||||
\(423\) | −4419.33 | + | 2551.50i | −0.507979 | + | 0.293282i | ||||
\(424\) | 1012.50 | + | 1753.70i | 0.115970 | + | 0.200866i | ||||
\(425\) | −4600.85 | − | 5603.10i | −0.525115 | − | 0.639506i | ||||
\(426\) | 17070.0 | 1.94142 | ||||||||
\(427\) | 4311.07 | − | 2227.00i | 0.488589 | − | 0.252394i | ||||
\(428\) | − | 6052.00i | − | 0.683492i | ||||||
\(429\) | −2497.50 | + | 4325.80i | −0.281073 | + | 0.486833i | ||||
\(430\) | 12736.8 | − | 4559.22i | 1.42843 | − | 0.511314i | ||||
\(431\) | 4907.00 | + | 8499.17i | 0.548403 | + | 0.949863i | 0.998384 | + | 0.0568243i | \(0.0180975\pi\) |
−0.449981 | + | 0.893038i | \(0.648569\pi\) | |||||||
\(432\) | −2081.06 | − | 1201.50i | −0.231771 | − | 0.133813i | ||||
\(433\) | 9388.00i | 1.04194i | 0.853576 | + | 0.520968i | \(0.174429\pi\) | ||||
−0.853576 | + | 0.520968i | \(0.825571\pi\) | |||||||
\(434\) | −8500.00 | + | 13250.2i | −0.940122 | + | 1.46551i | ||||
\(435\) | −6072.00 | − | 1104.00i | −0.669265 | − | 0.121684i | ||||
\(436\) | 11713.0 | − | 20287.5i | 1.28658 | − | 2.22843i | ||||
\(437\) | 7365.55 | − | 4252.50i | 0.806274 | − | 0.465503i | ||||
\(438\) | 1402.96 | − | 810.000i | 0.153050 | − | 0.0883637i | ||||
\(439\) | 2484.00 | − | 4302.41i | 0.270057 | − | 0.467752i | −0.698819 | − | 0.715298i | \(-0.746291\pi\) |
0.968876 | + | 0.247546i | \(0.0796242\pi\) | |||||||
\(440\) | −22275.0 | − | 4050.00i | −2.41345 | − | 0.438809i | ||||
\(441\) | 3073.50 | + | 288.386i | 0.331876 | + | 0.0311399i | ||||
\(442\) | 10730.0i | 1.15469i | ||||||||
\(443\) | −14166.4 | − | 8179.00i | −1.51934 | − | 0.877192i | −0.999740 | − | 0.0227826i | \(-0.992747\pi\) |
−0.519601 | − | 0.854409i | \(-0.673919\pi\) | |||||||
\(444\) | 1810.50 | + | 3135.88i | 0.193519 | + | 0.335185i | ||||
\(445\) | −12694.7 | + | 4544.15i | −1.35233 | + | 0.484075i | ||||
\(446\) | 3420.00 | − | 5923.61i | 0.363098 | − | 0.628904i | ||||
\(447\) | 3822.00i | 0.404417i | ||||||||
\(448\) | −4473.89 | − | 2870.00i | −0.471811 | − | 0.302667i | ||||
\(449\) | −185.000 | −0.0194447 | −0.00972237 | − | 0.999953i | \(-0.503095\pi\) | ||||
−0.00972237 | + | 0.999953i | \(0.503095\pi\) | |||||||
\(450\) | 3569.62 | + | 4347.23i | 0.373942 | + | 0.455401i | ||||
\(451\) | 5557.50 | + | 9625.87i | 0.580249 | + | 1.00502i | ||||
\(452\) | 6095.09 | − | 3519.00i | 0.634267 | − | 0.366194i | ||||
\(453\) | −1990.13 | − | 1149.00i | −0.206411 | − | 0.119172i | ||||
\(454\) | 470.000 | 0.0485863 | ||||||||
\(455\) | −7325.97 | + | 2241.87i | −0.754829 | + | 0.230990i | ||||
\(456\) | −18225.0 | −1.87163 | ||||||||
\(457\) | 6476.14 | + | 3739.00i | 0.662890 | + | 0.382720i | 0.793377 | − | 0.608730i | \(-0.208321\pi\) |
−0.130487 | + | 0.991450i | \(0.541654\pi\) | |||||||
\(458\) | 9855.37 | − | 5690.00i | 1.00548 | − | 0.580516i | ||||
\(459\) | −783.000 | − | 1356.20i | −0.0796238 | − | 0.137912i | ||||
\(460\) | −7745.53 | + | 9131.65i | −0.785081 | + | 0.925576i | ||||
\(461\) | 2844.00 | 0.287328 | 0.143664 | − | 0.989627i | \(-0.454112\pi\) | ||||
0.143664 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(462\) | −584.567 | + | 12487.5i | −0.0588669 | + | 1.25751i | ||||
\(463\) | − | 16029.0i | − | 1.60892i | −0.594006 | − | 0.804461i | \(-0.702454\pi\) | ||
0.594006 | − | 0.804461i | \(-0.297546\pi\) | |||||||
\(464\) | −8188.00 | + | 14182.0i | −0.819221 | + | 1.41893i | ||||
\(465\) | 1921.65 | + | 5368.40i | 0.191644 | + | 0.535384i | ||||
\(466\) | 6920.00 | + | 11985.8i | 0.687903 | + | 1.19148i | ||||
\(467\) | 8651.59 | + | 4995.00i | 0.857276 | + | 0.494949i | 0.863099 | − | 0.505034i | \(-0.168520\pi\) |
−0.00582297 | + | 0.999983i | \(0.501854\pi\) | |||||||
\(468\) | − | 5661.00i | − | 0.559145i | ||||||
\(469\) | 16169.0 | + | 756.906i | 1.59193 | + | 0.0745217i | ||||
\(470\) | 5670.00 | − | 31185.0i | 0.556463 | − | 3.06055i | ||||
\(471\) | 202.500 | − | 350.740i | 0.0198104 | − | 0.0343127i | ||||
\(472\) | 155.885 | − | 90.0000i | 0.0152016 | − | 0.00877666i | ||||
\(473\) | 9431.02 | − | 5445.00i | 0.916784 | − | 0.529305i | ||||
\(474\) | 465.000 | − | 805.404i | 0.0450594 | − | 0.0780452i | ||||
\(475\) | 15795.0 | + | 5940.00i | 1.52574 | + | 0.573781i | ||||
\(476\) | 8381.00 | + | 16224.1i | 0.807022 | + | 1.56225i | ||||
\(477\) | − | 405.000i | − | 0.0388756i | ||||||
\(478\) | −21979.7 | − | 12690.0i | −2.10320 | − | 1.21428i | ||||
\(479\) | −6840.00 | − | 11847.2i | −0.652458 | − | 1.13009i | −0.982525 | − | 0.186133i | \(-0.940404\pi\) |
0.330066 | − | 0.943958i | \(-0.392929\pi\) | |||||||
\(480\) | 2684.20 | − | 960.827i | 0.255243 | − | 0.0913657i | ||||
\(481\) | −1313.50 | + | 2275.05i | −0.124512 | + | 0.215662i | ||||
\(482\) | − | 15035.0i | − | 1.42080i | ||||||
\(483\) | 2946.22 | + | 1890.00i | 0.277552 | + | 0.178050i | ||||
\(484\) | −11798.0 | −1.10800 | ||||||||
\(485\) | −9835.59 | + | 11595.7i | −0.920848 | + | 1.08564i | ||||
\(486\) | 607.500 | + | 1052.22i | 0.0567012 | + | 0.0982093i | ||||
\(487\) | −3242.40 | + | 1872.00i | −0.301698 | + | 0.174186i | −0.643206 | − | 0.765693i | \(-0.722396\pi\) |
0.341507 | + | 0.939879i | \(0.389063\pi\) | |||||||
\(488\) | −10210.4 | − | 5895.00i | −0.947141 | − | 0.546832i | ||||
\(489\) | −9804.00 | −0.906651 | ||||||||
\(490\) | −13714.8 | + | 13399.9i | −1.26443 | + | 1.23540i | ||||
\(491\) | −7312.00 | −0.672069 | −0.336035 | − | 0.941850i | \(-0.609086\pi\) | ||||
−0.336035 | + | 0.941850i | \(0.609086\pi\) | |||||||
\(492\) | −10909.3 | − | 6298.50i | −0.999655 | − | 0.577151i | ||||
\(493\) | −9242.22 | + | 5336.00i | −0.844318 | + | 0.487467i | ||||
\(494\) | −12487.5 | − | 21629.0i | −1.13733 | − | 1.96991i | ||||
\(495\) | 3453.14 | + | 2928.98i | 0.313550 | + | 0.265955i | ||||
\(496\) | 15130.0 | 1.36967 | ||||||||
\(497\) | 17739.7 | + | 11380.0i | 1.60107 | + | 1.02709i | ||||
\(498\) | 6810.00i | 0.612778i | ||||||||
\(499\) | 9734.00 | − | 16859.8i | 0.873254 | − | 1.51252i | 0.0146426 | − | 0.999893i | \(-0.495339\pi\) |
0.858611 | − | 0.512627i | \(-0.171328\pi\) | |||||||
\(500\) | −23755.2 | − | 379.206i | −2.12473 | − | 0.0339172i | ||||
\(501\) | −3793.50 | − | 6570.53i | −0.338286 | − | 0.585928i | ||||
\(502\) | 27007.0 | + | 15592.5i | 2.40116 | + | 1.38631i | ||||
\(503\) | − | 13392.0i | − | 1.18712i | −0.804791 | − | 0.593558i | \(-0.797723\pi\) | ||
0.804791 | − | 0.593558i | \(-0.202277\pi\) | |||||||
\(504\) | −3442.50 | − | 6664.07i | −0.304248 | − | 0.588970i | ||||
\(505\) | −720.000 | + | 3960.00i | −0.0634447 | + | 0.348946i | ||||
\(506\) | −7087.50 | + | 12275.9i | −0.622683 | + | 1.07852i | ||||
\(507\) | −2151.21 | + | 1242.00i | −0.188439 | + | 0.108795i | ||||
\(508\) | 34200.2 | − | 19745.5i | 2.98699 | − | 1.72454i | ||||
\(509\) | −621.000 | + | 1075.60i | −0.0540773 | + | 0.0936646i | −0.891797 | − | 0.452436i | \(-0.850555\pi\) |
0.837720 | + | 0.546101i | \(0.183888\pi\) | |||||||
\(510\) | 9570.00 | + | 1740.00i | 0.830915 | + | 0.151075i | ||||
\(511\) | 1998.00 | + | 93.5307i | 0.172967 | + | 0.00809698i | ||||
\(512\) | 24475.0i | 2.11260i | ||||||||
\(513\) | 3156.66 | + | 1822.50i | 0.271677 | + | 0.156853i | ||||
\(514\) | −11015.0 | − | 19078.5i | −0.945235 | − | 1.63720i | ||||
\(515\) | 572.728 | + | 1599.99i | 0.0490047 | + | 0.136901i | ||||
\(516\) | −6171.00 | + | 10688.5i | −0.526479 | + | 0.911888i | ||||
\(517\) | − | 25515.0i | − | 2.17050i | ||||||
\(518\) | −307.439 | + | 6567.50i | −0.0260774 | + | 0.557064i | ||||
\(519\) | −945.000 | −0.0799247 | ||||||||
\(520\) | 14196.3 | + | 12041.4i | 1.19721 | + | 1.01548i | ||||
\(521\) | 1019.50 | + | 1765.83i | 0.0857296 | + | 0.148488i | 0.905702 | − | 0.423915i | \(-0.139345\pi\) |
−0.819972 | + | 0.572403i | \(0.806011\pi\) | |||||||
\(522\) | 7170.69 | − | 4140.00i | 0.601250 | − | 0.347132i | ||||
\(523\) | 18806.6 | + | 10858.0i | 1.57238 | + | 0.907815i | 0.995876 | + | 0.0907214i | \(0.0289173\pi\) |
0.576505 | + | 0.817093i | \(0.304416\pi\) | |||||||
\(524\) | 38777.0 | 3.23279 | ||||||||
\(525\) | 811.508 | + | 6897.52i | 0.0674612 | + | 0.573395i | ||||
\(526\) | 2880.00 | 0.238734 | ||||||||
\(527\) | 8539.01 | + | 4930.00i | 0.705816 | + | 0.407503i | ||||
\(528\) | 10405.3 | − | 6007.50i | 0.857637 | − | 0.495157i | ||||
\(529\) | −4099.00 | − | 7099.68i | −0.336895 | − | 0.583519i | ||||
\(530\) | 1918.41 | + | 1627.21i | 0.157227 | + | 0.133361i | ||||
\(531\) | −36.0000 | −0.00294212 | ||||||||
\(532\) | −35775.5 | − | 22950.0i | −2.91554 | − | 1.87032i | ||||
\(533\) | − | 9139.00i | − | 0.742690i | ||||||
\(534\) | 9045.00 | − | 15666.4i | 0.732988 | − | 1.26957i | ||||
\(535\) | −1341.39 | − | 3747.36i | −0.108399 | − | 0.302827i | ||||
\(536\) | −19665.0 | − | 34060.8i | −1.58470 | − | 2.74478i | ||||
\(537\) | −200.052 | − | 115.500i | −0.0160761 | − | 0.00928155i | ||||
\(538\) | 2590.00i | 0.207552i | ||||||||
\(539\) | −8932.50 | + | 12587.7i | −0.713822 | + | 1.00592i | ||||
\(540\) | −5049.00 | − | 918.000i | −0.402360 | − | 0.0731564i | ||||
\(541\) | −2358.00 | + | 4084.18i | −0.187391 | + | 0.324570i | −0.944379 | − | 0.328858i | \(-0.893336\pi\) |
0.756989 | + | 0.653428i | \(0.226670\pi\) | |||||||
\(542\) | −14306.7 | + | 8260.00i | −1.13381 | + | 0.654608i | ||||
\(543\) | 4162.12 | − | 2403.00i | 0.328938 | − | 0.189913i | ||||
\(544\) | 2465.00 | − | 4269.51i | 0.194276 | − | 0.336495i | ||||
\(545\) | 2756.00 | − | 15158.0i | 0.216613 | − | 1.19137i | ||||
\(546\) | 5550.00 | − | 8651.59i | 0.435015 | − | 0.678121i | ||||
\(547\) | 9746.00i | 0.761808i | 0.924615 | + | 0.380904i | \(0.124387\pi\) | ||||
−0.924615 | + | 0.380904i | \(0.875613\pi\) | |||||||
\(548\) | 9010.13 | + | 5202.00i | 0.702361 | + | 0.405508i | ||||
\(549\) | 1179.00 | + | 2042.09i | 0.0916548 | + | 0.158751i | ||||
\(550\) | −27748.1 | + | 4588.85i | −2.15124 | + | 0.355762i | ||||
\(551\) | 12420.0 | − | 21512.1i | 0.960272 | − | 1.66324i | ||||
\(552\) | − | 8505.00i | − | 0.655791i | ||||||
\(553\) | 1020.18 | − | 527.000i | 0.0784491 | − | 0.0405250i | ||||
\(554\) | 18130.0 | 1.39038 | ||||||||
\(555\) | 1816.10 | + | 1540.43i | 0.138899 | + | 0.117815i | ||||
\(556\) | −6800.00 | − | 11777.9i | −0.518677 | − | 0.898374i | ||||
\(557\) | 9925.52 | − | 5730.50i | 0.755041 | − | 0.435923i | −0.0724717 | − | 0.997370i | \(-0.523089\pi\) |
0.827512 | + | 0.561448i | \(0.189755\pi\) | |||||||
\(558\) | −6625.09 | − | 3825.00i | −0.502621 | − | 0.290188i | ||||
\(559\) | −8954.00 | −0.677485 | ||||||||
\(560\) | 17957.3 | + | 4140.84i | 1.35507 | + | 0.312469i | ||||
\(561\) | 7830.00 | 0.589274 | ||||||||
\(562\) | −23984.6 | − | 13847.5i | −1.80023 | − | 1.03936i | ||||
\(563\) | −6344.50 | + | 3663.00i | −0.474936 | + | 0.274204i | −0.718304 | − | 0.695730i | \(-0.755081\pi\) |
0.243368 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(564\) | 14458.5 | + | 25042.9i | 1.07946 | + | 1.86967i | ||||
\(565\) | 2994.07 | − | 3529.88i | 0.222941 | − | 0.262837i | ||||
\(566\) | 1310.00 | 0.0972852 | ||||||||
\(567\) | −70.1481 | + | 1498.50i | −0.00519566 | + | 0.110990i | ||||
\(568\) | − | 51210.0i | − | 3.78296i | ||||||
\(569\) | −985.500 | + | 1706.94i | −0.0726086 | + | 0.125762i | −0.900044 | − | 0.435799i | \(-0.856466\pi\) |
0.827435 | + | 0.561561i | \(0.189799\pi\) | |||||||
\(570\) | −21315.7 | + | 7630.10i | −1.56635 | + | 0.560684i | ||||
\(571\) | 936.000 | + | 1621.20i | 0.0685996 | + | 0.118818i | 0.898285 | − | 0.439413i | \(-0.144814\pi\) |
−0.829685 | + | 0.558231i | \(0.811480\pi\) | |||||||
\(572\) | 24512.8 | + | 14152.5i | 1.79184 | + | 1.03452i | ||||
\(573\) | − | 3672.00i | − | 0.267714i | ||||||
\(574\) | −10497.5 | − | 20321.3i | −0.763340 | − | 1.47769i | ||||
\(575\) | −2772.00 | + | 7371.00i | −0.201044 | + | 0.534595i | ||||
\(576\) | 1291.50 | − | 2236.94i | 0.0934245 | − | 0.161816i | ||||
\(577\) | −9408.50 | + | 5432.00i | −0.678823 | + | 0.391919i | −0.799412 | − | 0.600784i | \(-0.794855\pi\) |
0.120588 | + | 0.992703i | \(0.461522\pi\) | |||||||
\(578\) | −6707.37 | + | 3872.50i | −0.482681 | + | 0.278676i | ||||
\(579\) | −6735.00 | + | 11665.4i | −0.483415 | + | 0.837299i | ||||
\(580\) | −6256.00 | + | 34408.0i | −0.447873 | + | 2.46330i | ||||
\(581\) | −4540.00 | + | 7077.16i | −0.324184 | + | 0.505353i | ||||
\(582\) | − | 20400.0i | − | 1.45293i | ||||||
\(583\) | 1753.70 | + | 1012.50i | 0.124581 | + | 0.0719270i | ||||
\(584\) | −2430.00 | − | 4208.88i | −0.172182 | − | 0.298227i | ||||
\(585\) | −1254.73 | − | 3505.25i | −0.0886779 | − | 0.247734i | ||||
\(586\) | −15547.5 | + | 26929.1i | −1.09601 | + | 1.89834i | ||||
\(587\) | 13914.0i | 0.978351i | 0.872185 | + | 0.489176i | \(0.162702\pi\) | ||||
−0.872185 | + | 0.489176i | \(0.837298\pi\) | |||||||
\(588\) | 1634.19 | − | 17416.5i | 0.114614 | − | 1.22150i | ||||
\(589\) | −22950.0 | −1.60550 | ||||||||
\(590\) | 144.641 | − | 170.526i | 0.0100928 | − | 0.0118990i | ||||
\(591\) | −3745.50 | − | 6487.40i | −0.260693 | − | 0.451533i | ||||
\(592\) | 5472.41 | − | 3159.50i | 0.379924 | − | 0.219349i | ||||
\(593\) | −1664.50 | − | 961.000i | −0.115266 | − | 0.0665490i | 0.441258 | − | 0.897380i | \(-0.354532\pi\) |
−0.556525 | + | 0.830831i | \(0.687866\pi\) | |||||||
\(594\) | −6075.00 | −0.419630 | ||||||||
\(595\) | 8785.44 | + | 8188.26i | 0.605324 | + | 0.564178i | ||||
\(596\) | 21658.0 | 1.48850 | ||||||||
\(597\) | −9420.62 | − | 5439.00i | −0.645830 | − | 0.372870i | ||||
\(598\) | 10093.5 | − | 5827.50i | 0.690226 | − | 0.398502i | ||||
\(599\) | 4714.00 | + | 8164.89i | 0.321551 | + | 0.556942i | 0.980808 | − | 0.194975i | \(-0.0624626\pi\) |
−0.659258 | + | 0.751917i | \(0.729129\pi\) | |||||||
\(600\) | 13041.7 | − | 10708.9i | 0.887375 | − | 0.728646i | ||||
\(601\) | 6274.00 | 0.425827 | 0.212913 | − | 0.977071i | \(-0.431705\pi\) | ||||
0.212913 | + | 0.977071i | \(0.431705\pi\) | |||||||
\(602\) | −19909.9 | + | 10285.0i | −1.34795 | + | 0.696321i | ||||
\(603\) | 7866.00i | 0.531224i | ||||||||
\(604\) | −6511.00 | + | 11277.4i | −0.438624 | + | 0.759719i | ||||
\(605\) | −7305.24 | + | 2614.96i | −0.490909 | + | 0.175724i | ||||
\(606\) | −2700.00 | − | 4676.54i | −0.180990 | − | 0.313484i | ||||
\(607\) | 678.098 | + | 391.500i | 0.0453429 | + | 0.0261787i | 0.522500 | − | 0.852639i | \(-0.324999\pi\) |
−0.477157 | + | 0.878818i | \(0.658333\pi\) | |||||||
\(608\) | 11475.0i | 0.765416i | ||||||||
\(609\) | 10212.0 | + | 478.046i | 0.679493 | + | 0.0318085i | ||||
\(610\) | −14410.0 | − | 2620.00i | −0.956465 | − | 0.173903i | ||||
\(611\) | −10489.5 | + | 18168.3i | −0.694533 | + | 1.20297i | ||||
\(612\) | −7685.11 | + | 4437.00i | −0.507602 | + | 0.293064i | ||||
\(613\) | −16384.3 | + | 9459.50i | −1.07954 | + | 0.623272i | −0.930772 | − | 0.365601i | \(-0.880864\pi\) |
−0.148767 | + | 0.988872i | \(0.547530\pi\) | |||||||
\(614\) | −17665.0 | + | 30596.7i | −1.16108 | + | 2.01104i | ||||
\(615\) | −8151.00 | − | 1482.00i | −0.534439 | − | 0.0971707i | ||||
\(616\) | 37462.5 | + | 1753.70i | 2.45034 | + | 0.114706i | ||||
\(617\) | 2966.00i | 0.193528i | 0.995307 | + | 0.0967639i | \(0.0308492\pi\) | ||||
−0.995307 | + | 0.0967639i | \(0.969151\pi\) | |||||||
\(618\) | −1974.54 | − | 1140.00i | −0.128524 | − | 0.0742031i | ||||
\(619\) | 11727.5 | + | 20312.6i | 0.761499 | + | 1.31896i | 0.942078 | + | 0.335395i | \(0.108870\pi\) |
−0.180578 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(620\) | 30420.9 | − | 10889.4i | 1.97054 | − | 0.705367i | ||||
\(621\) | −850.500 | + | 1473.11i | −0.0549588 | + | 0.0951914i | ||||
\(622\) | − | 3510.00i | − | 0.226267i | ||||||
\(623\) | 19844.1 | − | 10251.0i | 1.27614 | − | 0.659226i | ||||
\(624\) | −9879.00 | −0.633776 | ||||||||
\(625\) | −14793.1 | + | 5030.40i | −0.946758 | + | 0.321945i | ||||
\(626\) | −9585.00 | − | 16601.7i | −0.611971 | − | 1.05996i | ||||
\(627\) | −15783.3 | + | 9112.50i | −1.00530 | + | 0.580412i | ||||
\(628\) | −1987.53 | − | 1147.50i | −0.126291 | − | 0.0729144i | ||||
\(629\) | 4118.00 | 0.261042 | ||||||||
\(630\) | −6816.29 | − | 6352.96i | −0.431059 | − | 0.401759i | ||||
\(631\) | 3970.00 | 0.250465 | 0.125232 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125232 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(632\) | −2416.21 | − | 1395.00i | −0.152075 | − | 0.0878008i | ||||
\(633\) | 10571.6 | − | 6103.50i | 0.663795 | − | 0.383242i | ||||
\(634\) | 18495.0 | + | 32034.3i | 1.15857 | + | 2.00669i | ||||
\(635\) | 16800.1 | − | 19806.5i | 1.04991 | − | 1.23779i | ||||
\(636\) | −2295.00 | −0.143086 | ||||||||
\(637\) | 11535.5 | − | 5291.00i | 0.717506 | − | 0.329101i | ||||
\(638\) | 41400.0i | 2.56903i | ||||||||
\(639\) | −5121.00 | + | 8869.83i | −0.317032 | + | 0.549116i | ||||
\(640\) | 7969.21 | + | 22263.1i | 0.492204 | + | 1.37504i | ||||
\(641\) | −4367.50 | − | 7564.73i | −0.269120 | − | 0.466129i | 0.699515 | − | 0.714618i | \(-0.253399\pi\) |
−0.968635 | + | 0.248489i | \(0.920066\pi\) | |||||||
\(642\) | 4624.58 | + | 2670.00i | 0.284295 | + | 0.164138i | ||||
\(643\) | − | 4150.00i | − | 0.254526i | −0.991869 | − | 0.127263i | \(-0.959381\pi\) | ||
0.991869 | − | 0.127263i | \(-0.0406192\pi\) | |||||||
\(644\) | 10710.0 | − | 16695.2i | 0.655331 | − | 1.02156i | ||||
\(645\) | −1452.00 | + | 7986.00i | −0.0886394 | + | 0.487517i | ||||
\(646\) | −19575.0 | + | 33904.9i | −1.19221 | + | 2.06497i | ||||
\(647\) | 24930.3 | − | 14393.5i | 1.51485 | − | 0.874601i | 0.515005 | − | 0.857187i | \(-0.327790\pi\) |
0.999848 | − | 0.0174139i | \(-0.00554330\pi\) | |||||||
\(648\) | 3156.66 | − | 1822.50i | 0.191366 | − | 0.110485i | ||||
\(649\) | 90.0000 | − | 155.885i | 0.00544347 | − | 0.00942836i | ||||
\(650\) | 21645.0 | + | 8140.00i | 1.30613 | + | 0.491195i | ||||
\(651\) | −4335.00 | − | 8391.79i | −0.260986 | − | 0.505223i | ||||
\(652\) | 55556.0i | 3.33703i | ||||||||
\(653\) | 11702.6 | + | 6756.50i | 0.701314 | + | 0.404904i | 0.807837 | − | 0.589406i | \(-0.200638\pi\) |
−0.106523 | + | 0.994310i | \(0.533972\pi\) | |||||||
\(654\) | 10335.0 | + | 17900.7i | 0.617937 | + | 1.07030i | ||||
\(655\) | 24010.4 | − | 8594.69i | 1.43231 | − | 0.512706i | ||||
\(656\) | −10991.5 | + | 19037.8i | −0.654186 | + | 1.13308i | ||||
\(657\) | 972.000i | 0.0577189i | ||||||||
\(658\) | −2455.18 | + | 52447.5i | −0.145460 | + | 3.10732i | ||||
\(659\) | −29844.0 | −1.76412 | −0.882062 | − | 0.471134i | \(-0.843845\pi\) | ||||
−0.882062 | + | 0.471134i | \(0.843845\pi\) | |||||||
\(660\) | 16597.6 | − | 19567.8i | 0.978877 | − | 1.15405i | ||||
\(661\) | −3996.00 | − | 6921.28i | −0.235138 | − | 0.407271i | 0.724175 | − | 0.689617i | \(-0.242221\pi\) |
−0.959313 | + | 0.282345i | \(0.908888\pi\) | |||||||
\(662\) | −27162.9 | + | 15682.5i | −1.59474 | + | 0.920722i | ||||
\(663\) | −5575.47 | − | 3219.00i | −0.326596 | − | 0.188560i | ||||
\(664\) | 20430.0 | 1.19403 | ||||||||
\(665\) | −27238.7 | − | 6281.05i | −1.58838 | − | 0.366269i | ||||
\(666\) | −3195.00 | −0.185891 | ||||||||
\(667\) | 10039.0 | + | 5796.00i | 0.582774 | + | 0.336465i | ||||
\(668\) | −37233.0 | + | 21496.5i | −2.15657 | + | 1.24510i | ||||
\(669\) | 2052.00 | + | 3554.17i | 0.118587 | + | 0.205399i | ||||
\(670\) | −37259.8 | − | 31604.1i | −2.14847 | − | 1.82235i | ||||
\(671\) | −11790.0 | −0.678313 | ||||||||
\(672\) | −4195.89 | + | 2167.50i | −0.240863 | + | 0.124424i | ||||
\(673\) | − | 24732.0i | − | 1.41657i | −0.705929 | − | 0.708283i | \(-0.749470\pi\) | ||
0.705929 | − | 0.708283i | \(-0.250530\pi\) | |||||||
\(674\) | −585.000 | + | 1013.25i | −0.0334323 | + | 0.0579064i | ||||
\(675\) | −3329.77 | + | 550.662i | −0.189871 | + | 0.0314000i | ||||
\(676\) | 7038.00 | + | 12190.2i | 0.400432 | + | 0.693569i | ||||
\(677\) | 6972.37 | + | 4025.50i | 0.395820 | + | 0.228527i | 0.684679 | − | 0.728845i | \(-0.259943\pi\) |
−0.288859 | + | 0.957372i | \(0.593276\pi\) | |||||||
\(678\) | 6210.00i | 0.351760i | ||||||||
\(679\) | 13600.0 | − | 21200.3i | 0.768660 | − | 1.19822i | ||||
\(680\) | 5220.00 | − | 28710.0i | 0.294379 | − | 1.61909i | ||||
\(681\) | −141.000 | + | 244.219i | −0.00793411 | + | 0.0137423i | ||||
\(682\) | 33125.5 | − | 19125.0i | 1.85988 | − | 1.07380i | ||||
\(683\) | −15834.4 | + | 9142.00i | −0.887096 | + | 0.512165i | −0.872992 | − | 0.487735i | \(-0.837823\pi\) |
−0.0141047 | + | 0.999901i | \(0.504490\pi\) | |||||||
\(684\) | 10327.5 | − | 17887.8i | 0.577313 | − | 0.999935i | ||||
\(685\) | 6732.00 | + | 1224.00i | 0.375499 | + | 0.0682725i | ||||
\(686\) | 19572.5 | − | 25015.1i | 1.08933 | − | 1.39225i | ||||
\(687\) | 6828.00i | 0.379191i | ||||||||
\(688\) | 18652.5 | + | 10769.0i | 1.03360 | + | 0.596750i | ||||
\(689\) | −832.500 | − | 1441.93i | −0.0460315 | − | 0.0797289i | ||||
\(690\) | −3560.71 | − | 9947.33i | −0.196455 | − | 0.548824i | ||||
\(691\) | −5018.00 | + | 8691.43i | −0.276257 | + | 0.478491i | −0.970452 | − | 0.241296i | \(-0.922427\pi\) |
0.694194 | + | 0.719788i | \(0.255761\pi\) | |||||||
\(692\) | 5355.00i | 0.294171i | ||||||||
\(693\) | −6313.33 | − | 4050.00i | −0.346066 | − | 0.222001i | ||||
\(694\) | 3960.00 | 0.216599 | ||||||||
\(695\) | −6821.02 | − | 5785.64i | −0.372282 | − | 0.315772i | ||||
\(696\) | −12420.0 | − | 21512.1i | −0.676406 | − | 1.17157i | ||||
\(697\) | −12406.7 | + | 7163.00i | −0.674227 | + | 0.389265i | ||||
\(698\) | −31454.0 | − | 18160.0i | −1.70566 | − | 0.984765i | ||||
\(699\) | −8304.00 | −0.449336 | ||||||||
\(700\) | 39086.0 | − | 4598.55i | 2.11044 | − | 0.248298i | ||||
\(701\) | 9706.00 | 0.522954 | 0.261477 | − | 0.965210i | \(-0.415790\pi\) | ||||
0.261477 | + | 0.965210i | \(0.415790\pi\) | |||||||
\(702\) | 4325.80 | + | 2497.50i | 0.232574 | + | 0.134276i | ||||
\(703\) | −8300.85 | + | 4792.50i | −0.445338 | + | 0.257116i | ||||
\(704\) | 6457.50 | + | 11184.7i | 0.345705 | + | 0.598778i | ||||
\(705\) | 14503.2 | + | 12301.7i | 0.774783 | + | 0.657177i | ||||
\(706\) | −41600.0 | −2.21762 | ||||||||
\(707\) | 311.769 | − | 6660.00i | 0.0165846 | − | 0.354279i | ||||
\(708\) | 204.000i | 0.0108288i | ||||||||
\(709\) | 13900.0 | − | 24075.5i | 0.736284 | − | 1.27528i | −0.217873 | − | 0.975977i | \(-0.569912\pi\) |
0.954158 | − | 0.299305i | \(-0.0967546\pi\) | |||||||
\(710\) | −21439.6 | − | 59894.5i | −1.13326 | − | 3.16592i | ||||
\(711\) | 279.000 | + | 483.242i | 0.0147163 | + | 0.0254894i | ||||
\(712\) | −46999.2 | − | 27135.0i | −2.47383 | − | 1.42827i | ||||
\(713\) | − | 10710.0i | − | 0.562542i | ||||||
\(714\) | −16095.0 | − | 753.442i | −0.843614 | − | 0.0394914i | ||||
\(715\) | 18315.0 | + | 3330.00i | 0.957961 | + | 0.174175i | ||||
\(716\) | −654.500 | + | 1133.63i | −0.0341618 | + | 0.0591699i | ||||
\(717\) | 13187.8 | − | 7614.00i | 0.686902 | − | 0.396583i | ||||
\(718\) | 3100.37 | − | 1790.00i | 0.161149 | − | 0.0930393i | ||||
\(719\) | 9567.00 | − | 16570.5i | 0.496229 | − | 0.859494i | −0.503761 | − | 0.863843i | \(-0.668051\pi\) |
0.999991 | + | 0.00434852i | \(0.00138418\pi\) | |||||||
\(720\) | −1602.00 | + | 8811.00i | −0.0829209 | + | 0.456065i | ||||
\(721\) | −1292.00 | − | 2501.08i | −0.0667359 | − | 0.129189i | ||||
\(722\) | − | 56830.0i | − | 2.92935i | ||||||
\(723\) | 7812.42 | + | 4510.50i | 0.401863 | + | 0.232016i | ||||
\(724\) | −13617.0 | − | 23585.3i | −0.698994 | − | 1.21069i | ||||
\(725\) | 3752.66 | + | 22691.8i | 0.192235 | + | 1.16242i | ||||
\(726\) | 5205.00 | − | 9015.32i | 0.266082 | − | 0.460868i | ||||
\(727\) | − | 10999.0i | − | 0.561115i | −0.959837 | − | 0.280557i | \(-0.909481\pi\) | ||
0.959837 | − | 0.280557i | \(-0.0905193\pi\) | |||||||
\(728\) | −25954.8 | − | 16650.0i | −1.32136 | − | 0.847651i | ||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −4604.19 | − | 3905.31i | −0.233437 | − | 0.198003i | ||||
\(731\) | 7018.00 | + | 12155.5i | 0.355089 | + | 0.615032i | ||||
\(732\) | 11571.8 | − | 6681.00i | 0.584299 | − | 0.337345i | ||||
\(733\) | 4599.46 | + | 2655.50i | 0.231767 | + | 0.133811i | 0.611387 | − | 0.791332i | \(-0.290612\pi\) |
−0.379620 | + | 0.925142i | \(0.623945\pi\) | |||||||
\(734\) | 15435.0 | 0.776180 | ||||||||
\(735\) | −2848.39 | − | 11146.4i | −0.142945 | − | 0.559375i | ||||
\(736\) | −5355.00 | −0.268190 | ||||||||
\(737\) | −34060.8 | − | 19665.0i | −1.70237 | − | 0.982862i | ||||
\(738\) | 9625.87 | − | 5557.50i | 0.480126 | − | 0.277201i | ||||
\(739\) | 783.500 | + | 1357.06i | 0.0390007 | + | 0.0675512i | 0.884867 | − | 0.465844i | \(-0.154249\pi\) |
−0.845866 | + | 0.533395i | \(0.820916\pi\) | |||||||
\(740\) | 8729.09 | − | 10291.2i | 0.433632 | − | 0.511233i | ||||
\(741\) | 14985.0 | 0.742898 | ||||||||
\(742\) | −3507.40 | − | 2250.00i | −0.173532 | − | 0.111321i | ||||
\(743\) | 29587.0i | 1.46089i | 0.682971 | + | 0.730445i | \(0.260687\pi\) | ||||
−0.682971 | + | 0.730445i | \(0.739313\pi\) | |||||||
\(744\) | −11475.0 | + | 19875.3i | −0.565449 | + | 0.979386i | ||||
\(745\) | 13410.5 | − | 4800.37i | 0.659493 | − | 0.236070i | ||||
\(746\) | 315.000 | + | 545.596i | 0.0154597 | + | 0.0267771i | ||||
\(747\) | −3538.58 | − | 2043.00i | −0.173320 | − | 0.100066i | ||||
\(748\) | − | 44370.0i | − | 2.16889i | ||||||
\(749\) | 3026.00 | + | 5857.80i | 0.147620 | + | 0.285767i | ||||
\(750\) | 10770.0 | − | 17985.0i | 0.524353 | − | 0.875626i | ||||
\(751\) | −14058.0 | + | 24349.2i | −0.683068 | + | 1.18311i | 0.290972 | + | 0.956731i | \(0.406021\pi\) |
−0.974040 | + | 0.226376i | \(0.927312\pi\) | |||||||
\(752\) | 43702.2 | − | 25231.5i | 2.11922 | − | 1.22353i | ||||
\(753\) | −16204.2 | + | 9355.50i | −0.784215 | + | 0.452767i | ||||
\(754\) | 17020.0 | − | 29479.5i | 0.822058 | − | 1.42385i | ||||
\(755\) | −1532.00 | + | 8426.00i | −0.0738479 | + | 0.406164i | ||||
\(756\) | 8491.50 | + | 397.506i | 0.408509 | + | 0.0191232i | ||||
\(757\) | 11870.0i | 0.569911i | 0.958541 | + | 0.284955i | \(0.0919788\pi\) | ||||
−0.958541 | + | 0.284955i | \(0.908021\pi\) | |||||||
\(758\) | 59864.0 | + | 34562.5i | 2.86855 | + | 1.65616i | ||||
\(759\) | −4252.50 | − | 7365.55i | −0.203368 | − | 0.352243i | ||||
\(760\) | 22890.3 | + | 63947.1i | 1.09252 | + | 3.05211i | ||||
\(761\) | −4146.50 | + | 7181.95i | −0.197517 | + | 0.342110i | −0.947723 | − | 0.319095i | \(-0.896621\pi\) |
0.750206 | + | 0.661205i | \(0.229954\pi\) | |||||||
\(762\) | 34845.0i | 1.65656i | ||||||||
\(763\) | −1193.38 | + | 25493.0i | −0.0566230 | + | 1.20958i | ||||
\(764\) | −20808.0 | −0.985350 | ||||||||
\(765\) | −3775.13 | + | 4450.72i | −0.178418 | + | 0.210348i | ||||
\(766\) | −4712.50 | − | 8162.29i | −0.222284 | − | 0.385007i | ||||
\(767\) | −128.172 | + | 74.0000i | −0.00603392 | + | 0.00348368i | ||||
\(768\) | −21509.5 | − | 12418.5i | −1.01062 | − | 0.583482i | ||||
\(769\) | −14283.0 | −0.669777 | −0.334888 | − | 0.942258i | \(-0.608699\pi\) | ||||
−0.334888 | + | 0.942258i | \(0.608699\pi\) | |||||||
\(770\) | 44549.8 | − | 13633.0i | 2.08502 | − | 0.638050i | ||||
\(771\) | 13218.0 | 0.617425 | ||||||||
\(772\) | 66103.7 | + | 38165.0i | 3.08177 | + | 1.77926i | ||||
\(773\) | 14286.8 | − | 8248.50i | 0.664762 | − | 0.383801i | −0.129327 | − | 0.991602i | \(-0.541282\pi\) |
0.794089 | + | 0.607801i | \(0.207948\pi\) | |||||||
\(774\) | −5445.00 | − | 9431.02i | −0.252864 | − | 0.437973i | ||||
\(775\) | 16422.9 | − | 13485.2i | 0.761196 | − | 0.625038i | ||||
\(776\) | −61200.0 | −2.83112 | ||||||||
\(777\) | −3320.34 | − | 2130.00i | −0.153303 | − | 0.0983440i | ||||
\(778\) | 17390.0i | 0.801365i | ||||||||
\(779\) | 16672.5 | − | 28877.6i | 0.766822 | − | 1.32817i | ||||
\(780\) | −19863.1 | + | 7110.12i | −0.911811 | + | 0.326389i | ||||
\(781\) | −25605.0 | − | 44349.2i | −1.17314 | − | 2.03193i | ||||
\(782\) | −15822.3 | − | 9135.00i | −0.723534 | − | 0.417733i | ||||
\(783\) | 4968.00i | 0.226746i | ||||||||
\(784\) | −30393.5 | − | 2851.82i | −1.38454 | − | 0.129912i | ||||
\(785\) | −1485.00 | − | 270.000i | −0.0675184 | − | 0.0122761i | ||||
\(786\) | −17107.5 | + | 29631.1i | −0.776341 | + | 1.34466i | ||||
\(787\) | −35425.6 | + | 20453.0i | −1.60456 | + | 0.926392i | −0.613999 | + | 0.789307i | \(0.710440\pi\) |
−0.990559 | + | 0.137086i | \(0.956226\pi\) | |||||||
\(788\) | −36761.9 | + | 21224.5i | −1.66191 | + | 0.959507i | ||||
\(789\) | −864.000 | + | 1496.49i | −0.0389851 | + | 0.0675241i | ||||
\(790\) | −3410.00 | − | 620.000i | −0.153573 | − | 0.0279223i | ||||
\(791\) | −4140.00 | + | 6453.62i | −0.186095 | + | 0.290094i | ||||
\(792\) | 18225.0i | 0.817673i | ||||||||
\(793\) | 8395.25 | + | 4847.00i | 0.375945 | + | 0.217052i | ||||
\(794\) | −2095.00 | − | 3628.65i | −0.0936382 | − | 0.162186i | ||||
\(795\) | −1421.05 | + | 508.673i | −0.0633954 | + | 0.0226928i | ||||
\(796\) | −30821.0 | + | 53383.5i | −1.37239 | + | 2.37705i | ||||
\(797\) | − | 24134.0i | − | 1.07261i | −0.844024 | − | 0.536305i | \(-0.819820\pi\) | ||
0.844024 | − | 0.536305i | \(-0.180180\pi\) | |||||||
\(798\) | 33320.3 | − | 17212.5i | 1.47810 | − | 0.763554i | ||||
\(799\) | 32886.0 | 1.45610 | ||||||||
\(800\) | −6742.62 | − | 8211.44i | −0.297985 | − | 0.362898i | ||||
\(801\) | 5427.00 | + | 9399.84i | 0.239393 | + | 0.414640i | ||||
\(802\) | 52182.4 | − | 30127.5i | 2.29754 | − | 1.32648i | ||||
\(803\) | −4208.88 | − | 2430.00i | −0.184967 | − | 0.106791i | ||||
\(804\) | 44574.0 | 1.95523 | ||||||||
\(805\) | 2931.16 | − | 12711.4i | 0.128335 | − | 0.556543i | ||||
\(806\) | −31450.0 | −1.37442 | ||||||||
\(807\) | −1345.80 | − | 777.000i | −0.0587045 | − | 0.0338931i | ||||
\(808\) | −14029.6 | + | 8100.00i | −0.610842 | + | 0.352670i | ||||
\(809\) | 17383.5 | + | 30109.1i | 0.755465 | + | 1.30850i | 0.945143 | + | 0.326658i | \(0.105922\pi\) |
−0.189678 | + | 0.981846i | \(0.560744\pi\) | |||||||
\(810\) | 2928.98 | − | 3453.14i | 0.127054 | − | 0.149791i | ||||
\(811\) | 12067.0 | 0.522478 | 0.261239 | − | 0.965274i | \(-0.415869\pi\) | ||||
0.261239 | + | 0.965274i | \(0.415869\pi\) | |||||||
\(812\) | 2708.93 | − | 57868.0i | 0.117075 | − | 2.50095i | ||||
\(813\) | − | 9912.00i | − | 0.427588i | ||||||
\(814\) | 7987.50 | − | 13834.8i | 0.343933 | − | 0.595710i | ||||
\(815\) | 12313.7 | + | 34399.9i | 0.529238 | + | 1.47850i | ||||
\(816\) | 7743.00 | + | 13411.3i | 0.332180 | + | 0.575353i | ||||
\(817\) | −28293.0 | − | 16335.0i | −1.21156 | − | 0.699497i | ||||
\(818\) | 22450.0i | 0.959591i | ||||||||
\(819\) | 2830.50 | + | 5479.34i | 0.120764 | + | 0.233777i | ||||
\(820\) | −8398.00 | + | 46189.0i | −0.357647 | + | 1.96706i | ||||
\(821\) | 16697.0 | − | 28920.1i | 0.709780 | − | 1.22937i | −0.255159 | − | 0.966899i | \(-0.582128\pi\) |
0.964939 | − | 0.262476i | \(-0.0845390\pi\) | |||||||
\(822\) | −7950.11 | + | 4590.00i | −0.337338 | + | 0.194762i | ||||
\(823\) | 10530.9 | − | 6080.00i | 0.446030 | − | 0.257516i | −0.260122 | − | 0.965576i | \(-0.583763\pi\) |
0.706152 | + | 0.708060i | \(0.250429\pi\) | |||||||
\(824\) | −3420.00 | + | 5923.61i | −0.144589 | + | 0.250436i | ||||
\(825\) | 5940.00 | − | 15795.0i | 0.250672 | − | 0.666559i | ||||
\(826\) | −200.000 | + | 311.769i | −0.00842481 | + | 0.0131330i | ||||
\(827\) | 18198.0i | 0.765183i | 0.923918 | + | 0.382592i | \(0.124968\pi\) | ||||
−0.923918 | + | 0.382592i | \(0.875032\pi\) | |||||||
\(828\) | 8347.62 | + | 4819.50i | 0.350362 | + | 0.202282i | ||||
\(829\) | −16623.0 | − | 28791.9i | −0.696430 | − | 1.20625i | −0.969696 | − | 0.244314i | \(-0.921437\pi\) |
0.273266 | − | 0.961939i | \(-0.411896\pi\) | |||||||
\(830\) | 23894.7 | − | 8553.24i | 0.999272 | − | 0.357696i | ||||
\(831\) | −5439.00 | + | 9420.62i | −0.227048 | + | 0.393259i | ||||
\(832\) | − | 10619.0i | − | 0.442485i | ||||||
\(833\) | −16224.1 | − | 11513.0i | −0.674829 | − | 0.478874i | ||||
\(834\) | 12000.0 | 0.498233 | ||||||||
\(835\) | −18289.9 | + | 21563.0i | −0.758020 | + | 0.893673i | ||||
\(836\) | 51637.5 | + | 89438.8i | 2.13627 | + | 3.70013i | ||||
\(837\) | 3975.06 | − | 2295.00i | 0.164155 | − | 0.0947752i | ||||
\(838\) | −6040.53 | − | 3487.50i | −0.249005 | − | 0.143763i | ||||
\(839\) | −23490.0 | −0.966585 | −0.483293 | − | 0.875459i | \(-0.660559\pi\) | ||||
−0.483293 | + | 0.875459i | \(0.660559\pi\) | |||||||
\(840\) | −19058.9 | + | 20448.9i | −0.782850 | + | 0.839944i | ||||
\(841\) | 9467.00 | 0.388167 | ||||||||
\(842\) | −46297.7 | − | 26730.0i | −1.89492 | − | 1.09403i | ||||
\(843\) | 14390.7 | − | 8308.50i | 0.587952 | − | 0.339454i | ||||
\(844\) | −34586.5 | − | 59905.6i | −1.41056 | − | 2.44317i | ||||
\(845\) | 7059.76 | + | 5988.14i | 0.287412 | + | 0.243785i | ||||
\(846\) | −25515.0 | −1.03691 | ||||||||
\(847\) | 11419.4 | − | 5899.00i | 0.463253 | − | 0.239306i | ||||
\(848\) | 4005.00i | 0.162184i | ||||||||
\(849\) | −393.000 | + | 680.696i | −0.0158866 | + | 0.0275164i | ||||
\(850\) | −5914.52 | − | 35764.2i | −0.238666 | − | 1.44318i | ||||
\(851\) | −2236.50 | − | 3873.73i | −0.0900896 | − | 0.156040i | ||||
\(852\) | 50262.4 | + | 29019.0i | 2.02108 | + | 1.16687i | ||||
\(853\) | − | 31491.0i | − | 1.26405i | −0.774950 | − | 0.632023i | \(-0.782225\pi\) | ||
0.774950 | − | 0.632023i | \(-0.217775\pi\) | |||||||
\(854\) | 24235.0 | + | 1134.49i | 0.971083 | + | 0.0454585i | ||||
\(855\) | 2430.00 | − | 13365.0i | 0.0971979 | − | 0.534589i | ||||
\(856\) | 8010.00 | − | 13873.7i | 0.319832 | − | 0.553965i | ||||
\(857\) | −15775.5 | + | 9108.00i | −0.628800 | + | 0.363038i | −0.780287 | − | 0.625421i | \(-0.784927\pi\) |
0.151487 | + | 0.988459i | \(0.451594\pi\) | |||||||
\(858\) | −21629.0 | + | 12487.5i | −0.860608 | + | 0.496872i | ||||
\(859\) | −5458.00 | + | 9453.53i | −0.216792 | + | 0.375495i | −0.953826 | − | 0.300361i | \(-0.902893\pi\) |
0.737033 | + | 0.675856i | \(0.236226\pi\) | |||||||
\(860\) | 45254.0 | + | 8228.00i | 1.79436 | + | 0.326247i | ||||
\(861\) | 13708.5 | + | 641.725i | 0.542607 | + | 0.0254006i | ||||
\(862\) | 49070.0i | 1.93890i | ||||||||
\(863\) | −8706.15 | − | 5026.50i | −0.343408 | − | 0.198267i | 0.318370 | − | 0.947966i | \(-0.396865\pi\) |
−0.661778 | + | 0.749700i | \(0.730198\pi\) | |||||||
\(864\) | −1147.50 | − | 1987.53i | −0.0451837 | − | 0.0782605i | ||||
\(865\) | 1186.90 | + | 3315.78i | 0.0466543 | + | 0.130335i | ||||
\(866\) | −23470.0 | + | 40651.2i | −0.920950 | + | 1.59513i | ||||
\(867\) | − | 4647.00i | − | 0.182030i | ||||||
\(868\) | −47553.5 | + | 24565.0i | −1.85953 | + | 0.960588i | ||||
\(869\) | −2790.00 | −0.108912 | ||||||||
\(870\) | −23532.5 | − | 19960.5i | −0.917043 | − | 0.777843i | ||||
\(871\) | 16169.0 | + | 28005.5i | 0.629008 | + | 1.08947i | ||||
\(872\) | 53702.2 | − | 31005.0i | 2.08554 | − | 1.20408i | ||||
\(873\) | 10600.2 | + | 6120.00i | 0.410952 | + | 0.237263i | ||||
\(874\) | 42525.0 | 1.64580 | ||||||||
\(875\) | 23182.5 | − | 11510.6i | 0.895671 | − | 0.444718i | ||||
\(876\) | 5508.00 | 0.212441 | ||||||||
\(877\) | −13483.1 | − | 7784.50i | −0.519149 | − | 0.299731i | 0.217437 | − | 0.976074i | \(-0.430230\pi\) |
−0.736586 | + | 0.676343i | \(0.763564\pi\) | |||||||
\(878\) | 21512.1 | − | 12420.0i | 0.826876 | − | 0.477397i | ||||
\(879\) | −9328.50 | − | 16157.4i | −0.357955 | − | 0.619996i | ||||
\(880\) | −34147.7 | − | 28964.4i | −1.30809 | − | 1.10953i | ||||
\(881\) | 40117.0 | 1.53414 | 0.767069 | − | 0.641564i | \(-0.221714\pi\) | ||||
0.767069 | + | 0.641564i | \(0.221714\pi\) | |||||||
\(882\) | 12587.7 | + | 8932.50i | 0.480555 | + | 0.341012i | ||||
\(883\) | − | 13572.0i | − | 0.517253i | −0.965977 | − | 0.258626i | \(-0.916730\pi\) | ||
0.965977 | − | 0.258626i | \(-0.0832698\pi\) | |||||||
\(884\) | −18241.0 | + | 31594.3i | −0.694017 | + | 1.20207i | ||||
\(885\) | 45.2154 | + | 126.315i | 0.00171740 | + | 0.00479779i | ||||
\(886\) | −40895.0 | − | 70832.2i | −1.55067 | − | 2.68584i | ||||
\(887\) | 11532.0 | + | 6658.00i | 0.436535 | + | 0.252034i | 0.702127 | − | 0.712052i | \(-0.252234\pi\) |
−0.265592 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(888\) | 9585.00i | 0.362220i | ||||||||
\(889\) | −23230.0 | + | 36212.0i | −0.876388 | + | 1.36615i | ||||
\(890\) | −66330.0 | − | 12060.0i | −2.49819 | − | 0.454216i | ||||
\(891\) | 1822.50 | − | 3156.66i | 0.0685253 | − | 0.118689i | ||||
\(892\) | 20140.3 | − | 11628.0i | 0.755994 | − | 0.436473i | ||||
\(893\) | −66289.9 | + | 38272.5i | −2.48411 | + | 1.43420i | ||||
\(894\) | −9555.00 | + | 16549.7i | −0.357457 | + | 0.619135i | ||||
\(895\) | −154.000 | + | 847.000i | −0.00575157 | + | 0.0316336i | ||||
\(896\) | −17977.5 | − | 34801.2i | −0.670297 | − | 1.29758i | ||||
\(897\) | 6993.00i | 0.260300i | ||||||||
\(898\) | −801.073 | − | 462.500i | −0.0297686 | − | 0.0171869i | ||||
\(899\) | −15640.0 | − | 27089.3i | −0.580226 | − | 1.00498i | ||||
\(900\) | 3120.42 | + | 18868.7i | 0.115571 | + | 0.698842i | ||||
\(901\) | −1305.00 | + | 2260.33i | −0.0482529 | + | 0.0835765i | ||||
\(902\) | 55575.0i | 2.05149i | ||||||||
\(903\) | 628.734 | − | 13431.0i | 0.0231705 | − | 0.494968i | ||||
\(904\) | 18630.0 | 0.685425 | ||||||||
\(905\) | −13659.1 | − | 11585.7i | −0.501706 | − | 0.425551i | ||||
\(906\) | −5745.00 | − | 9950.63i | −0.210668 | − | 0.364887i | ||||
\(907\) | −22267.2 | + | 12856.0i | −0.815184 | + | 0.470647i | −0.848753 | − | 0.528790i | \(-0.822646\pi\) |
0.0335690 | + | 0.999436i | \(0.489313\pi\) | |||||||
\(908\) | 1383.91 | + | 799.000i | 0.0505800 | + | 0.0292024i | ||||
\(909\) | 3240.00 | 0.118222 | ||||||||
\(910\) | −37327.1 | − | 8607.36i | −1.35976 | − | 0.313551i | ||||
\(911\) | 6642.00 | 0.241558 | 0.120779 | − | 0.992679i | \(-0.461461\pi\) | ||||
0.120779 | + | 0.992679i | \(0.461461\pi\) | |||||||
\(912\) | −31215.9 | − | 18022.5i | −1.13340 | − | 0.654369i | ||||
\(913\) | 17692.9 | − | 10215.0i | 0.641347 | − | 0.370282i | ||||
\(914\) | 18695.0 | + | 32380.7i | 0.676560 | + | 1.17184i | ||||
\(915\) | 5684.39 | − | 6701.66i | 0.205377 | − | 0.242131i | ||||
\(916\) | 38692.0 | 1.39565 | ||||||||
\(917\) | −37532.7 | + | 19388.5i | −1.35162 | + | 0.698217i | ||||
\(918\) | − | 7830.00i | − | 0.281513i | ||||||
\(919\) | −3136.00 | + | 5431.71i | −0.112565 | + | 0.194968i | −0.916804 | − | 0.399338i | \(-0.869240\pi\) |
0.804239 | + | 0.594306i | \(0.202573\pi\) | |||||||
\(920\) | −29842.0 | + | 10682.1i | −1.06941 | + | 0.382804i | ||||
\(921\) | −10599.0 | − | 18358.0i | −0.379206 | − | 0.656804i | ||||
\(922\) | 12314.9 | + | 7110.00i | 0.439880 | + | 0.253965i | ||||
\(923\) | 42106.0i | 1.50156i | ||||||||
\(924\) | −22950.0 | + | 35775.5i | −0.817099 | + | 1.27373i | ||||
\(925\) | 3124.00 | − | 8307.00i | 0.111045 | − | 0.295278i | ||||
\(926\) | 40072.5 | − | 69407.6i | 1.42210 | − | 2.46315i | ||||
\(927\) | 1184.72 | − | 684.000i | 0.0419756 | − | 0.0242346i | ||||
\(928\) | −13544.6 | + | 7820.00i | −0.479121 | + | 0.276621i | ||||
\(929\) | −5631.50 | + | 9754.04i | −0.198884 | + | 0.344478i | −0.948167 | − | 0.317773i | \(-0.897065\pi\) |
0.749283 | + | 0.662250i | \(0.230398\pi\) | |||||||
\(930\) | −5100.00 | + | 28050.0i | −0.179823 | + | 0.989028i | ||||
\(931\) | 46102.5 | + | 4325.80i | 1.62293 | + | 0.152280i | ||||
\(932\) | 47056.0i | 1.65383i | ||||||||
\(933\) | 1823.85 | + | 1053.00i | 0.0639980 | + | 0.0369493i | ||||
\(934\) | 24975.0 | + | 43258.0i | 0.874954 | + | 1.51546i | ||||
\(935\) | −9834.35 | − | 27473.6i | −0.343976 | − | 0.960944i | ||||
\(936\) | 7492.50 | − | 12977.4i | 0.261645 | − | 0.453183i | ||||
\(937\) | 35558.0i | 1.23973i | 0.784708 | + | 0.619866i | \(0.212813\pi\) | ||||
−0.784708 | + | 0.619866i | \(0.787187\pi\) | |||||||
\(938\) | 68121.6 | + | 43700.0i | 2.37127 | + | 1.52117i | ||||
\(939\) | 11502.0 | 0.399738 | ||||||||
\(940\) | 69709.7 | − | 82184.8i | 2.41881 | − | 2.85167i | ||||
\(941\) | −13860.0 | − | 24006.2i | −0.480152 | − | 0.831648i | 0.519589 | − | 0.854417i | \(-0.326085\pi\) |
−0.999741 | + | 0.0227688i | \(0.992752\pi\) | |||||||
\(942\) | 1753.70 | − | 1012.50i | 0.0606568 | − | 0.0350202i | ||||
\(943\) | 13476.2 | + | 7780.50i | 0.465372 | + | 0.268683i | ||||
\(944\) | 356.000 | 0.0122742 | ||||||||
\(945\) | 5345.98 | − | 1635.96i | 0.184026 | − | 0.0563150i | ||||
\(946\) | 54450.0 | 1.87138 | ||||||||
\(947\) | 20233.8 | + | 11682.0i | 0.694309 | + | 0.400860i | 0.805224 | − | 0.592970i | \(-0.202045\pi\) |
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(948\) | 2738.37 | − | 1581.00i | 0.0938167 | − | 0.0541651i | ||||
\(949\) | 1998.00 | + | 3460.64i | 0.0683433 | + | 0.118374i | ||||
\(950\) | 53544.4 | + | 65208.5i | 1.82864 | + | 2.22699i | ||||
\(951\) | −22194.0 | −0.756772 | ||||||||
\(952\) | −2260.33 | + | 48285.0i | −0.0769513 | + | 1.64383i | ||||
\(953\) | 7272.00i | 0.247181i | 0.992333 | + | 0.123590i | \(0.0394409\pi\) | ||||
−0.992333 | + | 0.123590i | \(0.960559\pi\) | |||||||
\(954\) | 1012.50 | − | 1753.70i | 0.0343615 | − | 0.0595159i | ||||
\(955\) | −12884.2 | + | 4611.97i | −0.436567 | + | 0.156272i | ||||
\(956\) | −43146.0 | − | 74731.1i | −1.45967 | − | 2.52822i | ||||
\(957\) | −21512.1 | − | 12420.0i | −0.726632 | − | 0.419521i | ||||
\(958\) | − | 68400.0i | − | 2.30679i | ||||||
\(959\) | −11322.0 | − | 530.008i | −0.381237 | − | 0.0178465i | ||||
\(960\) | −9471.00 | − | 1722.00i | −0.318412 | − | 0.0578930i | ||||
\(961\) | 445.500 | − | 771.629i | 0.0149542 | − | 0.0259014i | ||||
\(962\) | −11375.2 | + | 6567.50i | −0.381240 | + | 0.220109i | ||||
\(963\) | −2774.75 | + | 1602.00i | −0.0928504 | + | 0.0536072i | ||||
\(964\) | 25559.5 | − | 44270.4i | 0.853959 | − | 1.47910i | ||||
\(965\) | 49390.0 | + | 8980.00i | 1.64759 | + | 0.299561i | ||||
\(966\) | 8032.50 | + | 15549.5i | 0.267538 | + | 0.517905i | ||||
\(967\) | − | 49040.0i | − | 1.63084i | −0.578871 | − | 0.815419i | \(-0.696507\pi\) | ||
0.578871 | − | 0.815419i | \(-0.303493\pi\) | |||||||
\(968\) | −27046.0 | − | 15615.0i | −0.898027 | − | 0.518476i | ||||
\(969\) | −11745.0 | − | 20342.9i | −0.389374 | − | 0.674416i | ||||
\(970\) | −71578.7 | + | 25622.1i | −2.36933 | + | 0.848118i | ||||
\(971\) | −15815.5 | + | 27393.2i | −0.522702 | + | 0.905346i | 0.476949 | + | 0.878931i | \(0.341743\pi\) |
−0.999651 | + | 0.0264154i | \(0.991591\pi\) | |||||||
\(972\) | 4131.00i | 0.136319i | ||||||||
\(973\) | 12470.8 | + | 8000.00i | 0.410888 | + | 0.263585i | ||||
\(974\) | −18720.0 | −0.615839 | ||||||||
\(975\) | −10723.2 | + | 8805.07i | −0.352222 | + | 0.289218i | ||||
\(976\) | −11659.0 | − | 20194.0i | −0.382372 | − | 0.662288i | ||||
\(977\) | 23647.7 | − | 13653.0i | 0.774367 | − | 0.447081i | −0.0600632 | − | 0.998195i | \(-0.519130\pi\) |
0.834430 | + | 0.551114i | \(0.185797\pi\) | |||||||
\(978\) | −42452.6 | − | 24510.0i | −1.38802 | − | 0.801374i | ||||
\(979\) | −54270.0 | −1.77168 | ||||||||
\(980\) | −63162.8 | + | 16140.8i | −2.05884 | + | 0.526123i | ||||
\(981\) | −12402.0 | −0.403634 | ||||||||
\(982\) | −31661.9 | − | 18280.0i | −1.02889 | − | 0.594031i | ||||
\(983\) | 44731.1 | − | 25825.5i | 1.45137 | − | 0.837951i | 0.452814 | − | 0.891605i | \(-0.350420\pi\) |
0.998560 | + | 0.0536545i | \(0.0170870\pi\) | |||||||
\(984\) | −16672.5 | − | 28877.6i | −0.540142 | − | 0.935554i | ||||
\(985\) | −18058.4 | + | 21290.1i | −0.584152 | + | 0.688690i | ||||
\(986\) | −53360.0 | −1.72346 | ||||||||
\(987\) | −26516.0 | − | 17010.0i | −0.855129 | − | 0.548566i | ||||
\(988\) | − | 84915.0i | − | 2.73432i | ||||||
\(989\) | 7623.00 | − | 13203.4i | 0.245093 | − | 0.424514i | ||||
\(990\) | 7630.10 | + | 21315.7i | 0.244950 | + | 0.684301i | ||||
\(991\) | 18094.0 | + | 31339.7i | 0.579995 | + | 1.00458i | 0.995479 | + | 0.0949801i | \(0.0302788\pi\) |
−0.415484 | + | 0.909600i | \(0.636388\pi\) | |||||||
\(992\) | 12514.1 | + | 7225.00i | 0.400526 | + | 0.231244i | ||||
\(993\) | − | 18819.0i | − | 0.601413i | ||||||
\(994\) | 48365.0 | + | 93626.0i | 1.54330 | + | 2.98756i | ||||
\(995\) | −7252.00 | + | 39886.0i | −0.231059 | + | 1.27083i | ||||
\(996\) | −11577.0 | + | 20052.0i | −0.368305 | + | 0.637922i | ||||
\(997\) | −7553.47 | + | 4361.00i | −0.239941 | + | 0.138530i | −0.615149 | − | 0.788410i | \(-0.710904\pi\) |
0.375209 | + | 0.926940i | \(0.377571\pi\) | |||||||
\(998\) | 84298.9 | − | 48670.0i | 2.67378 | − | 1.54371i | ||||
\(999\) | 958.500 | − | 1660.17i | 0.0303560 | − | 0.0525781i |
(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 | 105.4.q.a.79.2 | yes | 4 | |
5.4 | even | 2 | inner | 105.4.q.a.79.1 | yes | 4 | |
7.4 | even | 3 | inner | 105.4.q.a.4.1 | ✓ | 4 | |
35.4 | even | 6 | inner | 105.4.q.a.4.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.q.a.4.1 | ✓ | 4 | 7.4 | even | 3 | inner | |
105.4.q.a.4.2 | yes | 4 | 35.4 | even | 6 | inner | |
105.4.q.a.79.1 | yes | 4 | 5.4 | even | 2 | inner | |
105.4.q.a.79.2 | yes | 4 | 1.1 | even | 1 | trivial |