Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(2,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.l (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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 18.4 | ||
Character | \(\chi\) | \(=\) | 35.18 |
Dual form | 35.5.l.a.2.4 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.20038 | − | 1.39344i | −1.30009 | − | 0.348359i | −0.458608 | − | 0.888639i | \(-0.651652\pi\) |
−0.841486 | + | 0.540279i | \(0.818319\pi\) | |||||||
\(3\) | 2.56504 | − | 0.687301i | 0.285005 | − | 0.0763668i | −0.113485 | − | 0.993540i | \(-0.536201\pi\) |
0.398489 | + | 0.917173i | \(0.369535\pi\) | |||||||
\(4\) | 11.2458 | + | 6.49278i | 0.702865 | + | 0.405799i | ||||
\(5\) | −19.5926 | − | 15.5283i | −0.783706 | − | 0.621133i | ||||
\(6\) | −14.2969 | −0.397136 | ||||||||
\(7\) | 20.1640 | + | 44.6589i | 0.411510 | + | 0.911405i | ||||
\(8\) | 11.4758 | + | 11.4758i | 0.179309 | + | 0.179309i | ||||
\(9\) | −64.0410 | + | 36.9741i | −0.790630 | + | 0.456470i | ||||
\(10\) | 80.2514 | + | 108.054i | 0.802514 | + | 1.08054i | ||||
\(11\) | −91.3743 | + | 158.265i | −0.755159 | + | 1.30797i | 0.190136 | + | 0.981758i | \(0.439107\pi\) |
−0.945295 | + | 0.326216i | \(0.894226\pi\) | |||||||
\(12\) | 33.3085 | + | 8.92500i | 0.231309 | + | 0.0619791i | ||||
\(13\) | 141.894 | + | 141.894i | 0.839607 | + | 0.839607i | 0.988807 | − | 0.149200i | \(-0.0476699\pi\) |
−0.149200 | + | 0.988807i | \(0.547670\pi\) | |||||||
\(14\) | −42.6310 | − | 260.340i | −0.217505 | − | 1.32827i | ||||
\(15\) | −60.9286 | − | 26.3647i | −0.270794 | − | 0.117177i | ||||
\(16\) | −147.572 | − | 255.602i | −0.576453 | − | 0.998446i | ||||
\(17\) | −110.602 | − | 412.771i | −0.382705 | − | 1.42827i | −0.841753 | − | 0.539863i | \(-0.818476\pi\) |
0.459048 | − | 0.888412i | \(-0.348191\pi\) | |||||||
\(18\) | 384.558 | − | 103.042i | 1.18691 | − | 0.318031i | ||||
\(19\) | −213.281 | + | 123.138i | −0.590805 | + | 0.341101i | −0.765416 | − | 0.643536i | \(-0.777467\pi\) |
0.174611 | + | 0.984638i | \(0.444133\pi\) | |||||||
\(20\) | −119.514 | − | 301.840i | −0.298784 | − | 0.754599i | ||||
\(21\) | 82.4155 | + | 100.693i | 0.186883 | + | 0.228329i | ||||
\(22\) | 695.713 | − | 695.713i | 1.43742 | − | 1.43742i | ||||
\(23\) | −132.073 | + | 492.904i | −0.249666 | + | 0.931766i | 0.721315 | + | 0.692608i | \(0.243538\pi\) |
−0.970981 | + | 0.239158i | \(0.923128\pi\) | |||||||
\(24\) | 37.3231 | + | 21.5485i | 0.0647970 | + | 0.0374106i | ||||
\(25\) | 142.743 | + | 608.481i | 0.228389 | + | 0.973570i | ||||
\(26\) | −540.180 | − | 935.619i | −0.799083 | − | 1.38405i | ||||
\(27\) | −290.953 | + | 290.953i | −0.399112 | + | 0.399112i | ||||
\(28\) | −63.1996 | + | 633.147i | −0.0806118 | + | 0.807585i | ||||
\(29\) | − | 1081.57i | − | 1.28605i | −0.765844 | − | 0.643026i | \(-0.777679\pi\) | ||
0.765844 | − | 0.643026i | \(-0.222321\pi\) | |||||||
\(30\) | 280.114 | + | 222.007i | 0.311238 | + | 0.246674i | ||||
\(31\) | −227.280 | + | 393.660i | −0.236503 | + | 0.409636i | −0.959709 | − | 0.280997i | \(-0.909335\pi\) |
0.723205 | + | 0.690633i | \(0.242668\pi\) | |||||||
\(32\) | 344.058 | + | 1284.04i | 0.335994 | + | 1.25395i | ||||
\(33\) | −125.603 | + | 468.758i | −0.115338 | + | 0.430448i | ||||
\(34\) | 2300.68i | 1.99021i | ||||||||
\(35\) | 298.411 | − | 1188.10i | 0.243601 | − | 0.969876i | ||||
\(36\) | −960.259 | −0.740941 | ||||||||
\(37\) | 72.2086 | + | 19.3482i | 0.0527455 | + | 0.0141331i | 0.285095 | − | 0.958499i | \(-0.407975\pi\) |
−0.232350 | + | 0.972632i | \(0.574641\pi\) | |||||||
\(38\) | 1280.72 | − | 343.169i | 0.886927 | − | 0.237651i | ||||
\(39\) | 461.486 | + | 266.439i | 0.303410 | + | 0.175174i | ||||
\(40\) | −46.6412 | − | 403.039i | −0.0291507 | − | 0.251900i | ||||
\(41\) | −1376.70 | −0.818976 | −0.409488 | − | 0.912315i | \(-0.634293\pi\) | ||||
−0.409488 | + | 0.912315i | \(0.634293\pi\) | |||||||
\(42\) | −288.282 | − | 638.483i | −0.163425 | − | 0.361952i | ||||
\(43\) | −493.766 | − | 493.766i | −0.267045 | − | 0.267045i | 0.560864 | − | 0.827908i | \(-0.310469\pi\) |
−0.827908 | + | 0.560864i | \(0.810469\pi\) | |||||||
\(44\) | −2055.16 | + | 1186.55i | −1.06155 | + | 0.612886i | ||||
\(45\) | 1828.88 | + | 270.029i | 0.903149 | + | 0.133348i | ||||
\(46\) | 1373.66 | − | 2379.25i | 0.649178 | − | 1.12441i | ||||
\(47\) | 826.377 | + | 221.427i | 0.374095 | + | 0.100239i | 0.440968 | − | 0.897523i | \(-0.354635\pi\) |
−0.0668723 | + | 0.997762i | \(0.521302\pi\) | |||||||
\(48\) | −554.204 | − | 554.204i | −0.240540 | − | 0.240540i | ||||
\(49\) | −1587.83 | + | 1801.00i | −0.661319 | + | 0.750104i | ||||
\(50\) | 105.563 | − | 3363.23i | 0.0422251 | − | 1.34529i | ||||
\(51\) | −567.396 | − | 982.759i | −0.218145 | − | 0.377839i | ||||
\(52\) | 674.427 | + | 2517.00i | 0.249418 | + | 0.930841i | ||||
\(53\) | −2893.14 | + | 775.214i | −1.02995 | + | 0.275975i | −0.733944 | − | 0.679210i | \(-0.762323\pi\) |
−0.296009 | + | 0.955185i | \(0.595656\pi\) | |||||||
\(54\) | 1918.49 | − | 1107.64i | 0.657917 | − | 0.379849i | ||||
\(55\) | 4247.85 | − | 1681.94i | 1.40425 | − | 0.556013i | ||||
\(56\) | −281.097 | + | 743.891i | −0.0896356 | + | 0.237210i | ||||
\(57\) | −462.441 | + | 462.441i | −0.142333 | + | 0.142333i | ||||
\(58\) | −1507.10 | + | 5624.57i | −0.448008 | + | 1.67199i | ||||
\(59\) | 1513.47 | + | 873.800i | 0.434779 | + | 0.251020i | 0.701381 | − | 0.712787i | \(-0.252567\pi\) |
−0.266601 | + | 0.963807i | \(0.585901\pi\) | |||||||
\(60\) | −514.012 | − | 692.090i | −0.142781 | − | 0.192247i | ||||
\(61\) | 1639.85 | + | 2840.31i | 0.440702 | + | 0.763318i | 0.997742 | − | 0.0671678i | \(-0.0213963\pi\) |
−0.557040 | + | 0.830486i | \(0.688063\pi\) | |||||||
\(62\) | 1730.48 | − | 1730.48i | 0.450177 | − | 0.450177i | ||||
\(63\) | −2942.54 | − | 2114.45i | −0.741381 | − | 0.532742i | ||||
\(64\) | − | 2434.61i | − | 0.594388i | ||||||
\(65\) | −576.701 | − | 4983.44i | −0.136497 | − | 1.17951i | ||||
\(66\) | 1306.37 | − | 2262.70i | 0.299901 | − | 0.519444i | ||||
\(67\) | −700.989 | − | 2616.13i | −0.156157 | − | 0.582786i | −0.999003 | − | 0.0446321i | \(-0.985788\pi\) |
0.842846 | − | 0.538154i | \(-0.180878\pi\) | |||||||
\(68\) | 1436.23 | − | 5360.07i | 0.310603 | − | 1.15919i | ||||
\(69\) | 1355.09i | 0.284624i | ||||||||
\(70\) | −3207.39 | + | 5762.74i | −0.654569 | + | 1.17607i | ||||
\(71\) | 242.826 | 0.0481701 | 0.0240851 | − | 0.999710i | \(-0.492333\pi\) | ||||
0.0240851 | + | 0.999710i | \(0.492333\pi\) | |||||||
\(72\) | −1159.22 | − | 310.613i | −0.223616 | − | 0.0599177i | ||||
\(73\) | 4723.25 | − | 1265.59i | 0.886330 | − | 0.237491i | 0.213194 | − | 0.977010i | \(-0.431613\pi\) |
0.673136 | + | 0.739519i | \(0.264947\pi\) | |||||||
\(74\) | −348.551 | − | 201.236i | −0.0636507 | − | 0.0367488i | ||||
\(75\) | 784.352 | + | 1462.67i | 0.139440 | + | 0.260031i | ||||
\(76\) | −3198.02 | −0.553674 | ||||||||
\(77\) | −8910.40 | − | 889.421i | −1.50285 | − | 0.150012i | ||||
\(78\) | −2028.64 | − | 2028.64i | −0.333438 | − | 0.333438i | ||||
\(79\) | 3161.63 | − | 1825.37i | 0.506591 | − | 0.292480i | −0.224840 | − | 0.974396i | \(-0.572186\pi\) |
0.731431 | + | 0.681915i | \(0.238853\pi\) | |||||||
\(80\) | −1077.75 | + | 7299.47i | −0.168398 | + | 1.14054i | ||||
\(81\) | 2448.57 | − | 4241.04i | 0.373200 | − | 0.646402i | ||||
\(82\) | 7159.35 | + | 1918.34i | 1.06475 | + | 0.285298i | ||||
\(83\) | 7249.03 | + | 7249.03i | 1.05226 | + | 1.05226i | 0.998557 | + | 0.0537046i | \(0.0171029\pi\) |
0.0537046 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(84\) | 273.052 | + | 1667.48i | 0.0386979 | + | 0.236322i | ||||
\(85\) | −4242.66 | + | 9804.74i | −0.587220 | + | 1.35706i | ||||
\(86\) | 1879.74 | + | 3255.80i | 0.254156 | + | 0.440211i | ||||
\(87\) | −743.364 | − | 2774.27i | −0.0982116 | − | 0.366531i | ||||
\(88\) | −2864.80 | + | 767.620i | −0.369938 | + | 0.0991245i | ||||
\(89\) | 2122.71 | − | 1225.55i | 0.267986 | − | 0.154722i | −0.359986 | − | 0.932958i | \(-0.617219\pi\) |
0.627972 | + | 0.778236i | \(0.283885\pi\) | |||||||
\(90\) | −9134.58 | − | 3952.68i | −1.12773 | − | 0.487985i | ||||
\(91\) | −3475.67 | + | 9197.94i | −0.419716 | + | 1.11073i | ||||
\(92\) | −4685.60 | + | 4685.60i | −0.553591 | + | 0.553591i | ||||
\(93\) | −312.419 | + | 1165.96i | −0.0361220 | + | 0.134809i | ||||
\(94\) | −3988.92 | − | 2303.01i | −0.451440 | − | 0.260639i | ||||
\(95\) | 6090.85 | + | 899.297i | 0.674886 | + | 0.0996451i | ||||
\(96\) | 1765.05 | + | 3057.15i | 0.191520 | + | 0.331722i | ||||
\(97\) | 1798.31 | − | 1798.31i | 0.191126 | − | 0.191126i | −0.605056 | − | 0.796183i | \(-0.706849\pi\) |
0.796183 | + | 0.605056i | \(0.206849\pi\) | |||||||
\(98\) | 10766.9 | − | 7153.34i | 1.12108 | − | 0.744830i | ||||
\(99\) | − | 13513.9i | − | 1.37883i | ||||||
\(100\) | −2345.47 | + | 7769.68i | −0.234547 | + | 0.776968i | ||||
\(101\) | −5538.34 | + | 9592.69i | −0.542922 | + | 0.940368i | 0.455813 | + | 0.890076i | \(0.349349\pi\) |
−0.998735 | + | 0.0502921i | \(0.983985\pi\) | |||||||
\(102\) | 1581.26 | + | 5901.35i | 0.151986 | + | 0.567219i | ||||
\(103\) | 2778.90 | − | 10371.0i | 0.261938 | − | 0.977565i | −0.702160 | − | 0.712019i | \(-0.747781\pi\) |
0.964098 | − | 0.265546i | \(-0.0855523\pi\) | |||||||
\(104\) | 3256.67i | 0.301097i | ||||||||
\(105\) | −51.1432 | − | 3252.62i | −0.00463884 | − | 0.295022i | ||||
\(106\) | 16125.6 | 1.43517 | ||||||||
\(107\) | 6333.07 | + | 1696.94i | 0.553155 | + | 0.148217i | 0.524560 | − | 0.851374i | \(-0.324230\pi\) |
0.0285950 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(108\) | −5161.10 | + | 1382.91i | −0.442481 | + | 0.118562i | ||||
\(109\) | −12516.8 | − | 7226.58i | −1.05351 | − | 0.608246i | −0.129883 | − | 0.991529i | \(-0.541460\pi\) |
−0.923631 | + | 0.383283i | \(0.874793\pi\) | |||||||
\(110\) | −24434.1 | + | 2827.60i | −2.01935 | + | 0.233686i | ||||
\(111\) | 198.516 | 0.0161120 | ||||||||
\(112\) | 8439.27 | − | 11744.4i | 0.672773 | − | 0.936253i | ||||
\(113\) | 6272.31 | + | 6272.31i | 0.491214 | + | 0.491214i | 0.908689 | − | 0.417475i | \(-0.137085\pi\) |
−0.417475 | + | 0.908689i | \(0.637085\pi\) | |||||||
\(114\) | 3049.25 | − | 1760.48i | 0.234630 | − | 0.135464i | ||||
\(115\) | 10241.6 | − | 7606.42i | 0.774415 | − | 0.575155i | ||||
\(116\) | 7022.40 | − | 12163.2i | 0.521879 | − | 0.903920i | ||||
\(117\) | −14333.4 | − | 3840.62i | −1.04707 | − | 0.280562i | ||||
\(118\) | −6653.01 | − | 6653.01i | −0.477809 | − | 0.477809i | ||||
\(119\) | 16203.7 | − | 13262.5i | 1.14425 | − | 0.936548i | ||||
\(120\) | −396.646 | − | 1001.76i | −0.0275449 | − | 0.0695664i | ||||
\(121\) | −9378.01 | − | 16243.2i | −0.640531 | − | 1.10943i | ||||
\(122\) | −4570.06 | − | 17055.7i | −0.307045 | − | 1.14591i | ||||
\(123\) | −3531.29 | + | 946.207i | −0.233412 | + | 0.0625426i | ||||
\(124\) | −5111.90 | + | 2951.36i | −0.332460 | + | 0.191946i | ||||
\(125\) | 6651.98 | − | 14138.3i | 0.425726 | − | 0.904852i | ||||
\(126\) | 12356.0 | + | 15096.2i | 0.778280 | + | 0.950882i | ||||
\(127\) | −5675.98 | + | 5675.98i | −0.351912 | + | 0.351912i | −0.860820 | − | 0.508909i | \(-0.830049\pi\) |
0.508909 | + | 0.860820i | \(0.330049\pi\) | |||||||
\(128\) | 2112.44 | − | 7883.75i | 0.128933 | − | 0.481186i | ||||
\(129\) | −1605.90 | − | 927.164i | −0.0965024 | − | 0.0557157i | ||||
\(130\) | −3945.04 | + | 26719.3i | −0.233434 | + | 1.58103i | ||||
\(131\) | 12680.6 | + | 21963.4i | 0.738917 | + | 1.27984i | 0.952983 | + | 0.303022i | \(0.0979957\pi\) |
−0.214067 | + | 0.976819i | \(0.568671\pi\) | |||||||
\(132\) | −4456.06 | + | 4456.06i | −0.255742 | + | 0.255742i | ||||
\(133\) | −9799.77 | − | 7041.92i | −0.554003 | − | 0.398096i | ||||
\(134\) | 14581.6i | 0.812076i | ||||||||
\(135\) | 10218.5 | − | 1182.53i | 0.560688 | − | 0.0648848i | ||||
\(136\) | 3467.62 | − | 6006.10i | 0.187480 | − | 0.324724i | ||||
\(137\) | 7106.33 | + | 26521.2i | 0.378621 | + | 1.41303i | 0.847982 | + | 0.530025i | \(0.177818\pi\) |
−0.469361 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(138\) | 1888.24 | − | 7047.00i | 0.0991513 | − | 0.370038i | ||||
\(139\) | 10022.6i | 0.518742i | 0.965778 | + | 0.259371i | \(0.0835152\pi\) | ||||
−0.965778 | + | 0.259371i | \(0.916485\pi\) | |||||||
\(140\) | 11069.9 | − | 11423.6i | 0.564793 | − | 0.582838i | ||||
\(141\) | 2271.88 | 0.114274 | ||||||||
\(142\) | −1262.78 | − | 338.362i | −0.0626257 | − | 0.0167805i | ||||
\(143\) | −35422.2 | + | 9491.34i | −1.73222 | + | 0.464147i | ||||
\(144\) | 18901.3 | + | 10912.7i | 0.911522 | + | 0.526268i | ||||
\(145\) | −16795.0 | + | 21190.8i | −0.798809 | + | 1.00789i | ||||
\(146\) | −26326.2 | −1.23504 | ||||||||
\(147\) | −2835.02 | + | 5710.96i | −0.131196 | + | 0.264286i | ||||
\(148\) | 686.422 | + | 686.422i | 0.0313378 | + | 0.0313378i | ||||
\(149\) | −12100.4 | + | 6986.16i | −0.545038 | + | 0.314678i | −0.747118 | − | 0.664691i | \(-0.768563\pi\) |
0.202080 | + | 0.979369i | \(0.435230\pi\) | |||||||
\(150\) | −2040.78 | − | 8699.39i | −0.0907014 | − | 0.386640i | ||||
\(151\) | 4647.32 | − | 8049.39i | 0.203821 | − | 0.353028i | −0.745936 | − | 0.666018i | \(-0.767997\pi\) |
0.949756 | + | 0.312990i | \(0.101331\pi\) | |||||||
\(152\) | −3860.65 | − | 1034.46i | −0.167099 | − | 0.0447740i | ||||
\(153\) | 22344.9 | + | 22344.9i | 0.954543 | + | 0.954543i | ||||
\(154\) | 45098.1 | + | 17041.4i | 1.90159 | + | 0.718561i | ||||
\(155\) | 10565.9 | − | 4183.57i | 0.439787 | − | 0.174134i | ||||
\(156\) | 3459.87 | + | 5992.66i | 0.142171 | + | 0.246247i | ||||
\(157\) | 1034.27 | + | 3859.96i | 0.0419601 | + | 0.156597i | 0.983727 | − | 0.179669i | \(-0.0575026\pi\) |
−0.941767 | + | 0.336266i | \(0.890836\pi\) | |||||||
\(158\) | −18985.2 | + | 5087.07i | −0.760504 | + | 0.203776i | ||||
\(159\) | −6888.22 | + | 3976.91i | −0.272466 | + | 0.157308i | ||||
\(160\) | 13198.0 | − | 30500.4i | 0.515547 | − | 1.19142i | ||||
\(161\) | −24675.7 | + | 4040.67i | −0.951956 | + | 0.155884i | ||||
\(162\) | −18643.1 | + | 18643.1i | −0.710375 | + | 0.710375i | ||||
\(163\) | 5356.47 | − | 19990.6i | 0.201606 | − | 0.752404i | −0.788851 | − | 0.614584i | \(-0.789324\pi\) |
0.990457 | − | 0.137820i | \(-0.0440096\pi\) | |||||||
\(164\) | −15482.1 | − | 8938.61i | −0.575630 | − | 0.332340i | ||||
\(165\) | 9739.92 | − | 7233.79i | 0.357756 | − | 0.265704i | ||||
\(166\) | −27596.6 | − | 47798.7i | −1.00147 | − | 1.73460i | ||||
\(167\) | 4227.71 | − | 4227.71i | 0.151591 | − | 0.151591i | −0.627237 | − | 0.778828i | \(-0.715814\pi\) |
0.778828 | + | 0.627237i | \(0.215814\pi\) | |||||||
\(168\) | −209.749 | + | 2101.31i | −0.00743159 | + | 0.0744512i | ||||
\(169\) | 11706.5i | 0.409879i | ||||||||
\(170\) | 35725.7 | − | 45076.4i | 1.23618 | − | 1.55974i | ||||
\(171\) | 9105.80 | − | 15771.7i | 0.311405 | − | 0.539370i | ||||
\(172\) | −2346.89 | − | 8758.72i | −0.0793298 | − | 0.296063i | ||||
\(173\) | −3486.75 | + | 13012.7i | −0.116501 | + | 0.434787i | −0.999395 | − | 0.0347853i | \(-0.988925\pi\) |
0.882894 | + | 0.469572i | \(0.155592\pi\) | |||||||
\(174\) | 15463.1i | 0.510737i | ||||||||
\(175\) | −24295.8 | + | 18644.1i | −0.793333 | + | 0.608788i | ||||
\(176\) | 53937.2 | 1.74126 | ||||||||
\(177\) | 4482.67 | + | 1201.13i | 0.143084 | + | 0.0383391i | ||||
\(178\) | −12746.6 | + | 3415.45i | −0.402305 | + | 0.107797i | ||||
\(179\) | −52821.8 | − | 30496.7i | −1.64857 | − | 0.951801i | −0.977642 | − | 0.210278i | \(-0.932563\pi\) |
−0.670927 | − | 0.741524i | \(-0.734104\pi\) | |||||||
\(180\) | 18814.0 | + | 14911.2i | 0.580679 | + | 0.460222i | ||||
\(181\) | −35781.9 | −1.09221 | −0.546105 | − | 0.837717i | \(-0.683890\pi\) | ||||
−0.546105 | + | 0.837717i | \(0.683890\pi\) | |||||||
\(182\) | 30891.5 | − | 42989.6i | 0.932602 | − | 1.29784i | ||||
\(183\) | 6158.43 | + | 6158.43i | 0.183894 | + | 0.183894i | ||||
\(184\) | −7172.09 | + | 4140.81i | −0.211841 | + | 0.122306i | ||||
\(185\) | −1114.31 | − | 1500.36i | −0.0325584 | − | 0.0438382i | ||||
\(186\) | 3249.39 | − | 5628.11i | 0.0939240 | − | 0.162681i | ||||
\(187\) | 75433.4 | + | 20212.3i | 2.15715 | + | 0.578007i | ||||
\(188\) | 7855.62 | + | 7855.62i | 0.222262 | + | 0.222262i | ||||
\(189\) | −18860.4 | − | 7126.85i | −0.527991 | − | 0.199514i | ||||
\(190\) | −30421.6 | − | 13163.9i | −0.842703 | − | 0.364651i | ||||
\(191\) | 8873.25 | + | 15368.9i | 0.243229 | + | 0.421286i | 0.961632 | − | 0.274342i | \(-0.0884599\pi\) |
−0.718403 | + | 0.695627i | \(0.755127\pi\) | |||||||
\(192\) | −1673.31 | − | 6244.89i | −0.0453915 | − | 0.169403i | ||||
\(193\) | 31095.8 | − | 8332.09i | 0.834808 | − | 0.223686i | 0.183998 | − | 0.982927i | \(-0.441096\pi\) |
0.650810 | + | 0.759240i | \(0.274429\pi\) | |||||||
\(194\) | −11857.7 | + | 6846.05i | −0.315063 | + | 0.181902i | ||||
\(195\) | −4904.38 | − | 12386.4i | −0.128978 | − | 0.325742i | ||||
\(196\) | −29550.0 | + | 9944.33i | −0.769210 | + | 0.258859i | ||||
\(197\) | −34115.6 | + | 34115.6i | −0.879063 | + | 0.879063i | −0.993438 | − | 0.114375i | \(-0.963514\pi\) |
0.114375 | + | 0.993438i | \(0.463514\pi\) | |||||||
\(198\) | −18830.8 | + | 70277.5i | −0.480328 | + | 1.79261i | ||||
\(199\) | 22489.4 | + | 12984.3i | 0.567900 | + | 0.327877i | 0.756310 | − | 0.654213i | \(-0.227000\pi\) |
−0.188410 | + | 0.982090i | \(0.560333\pi\) | |||||||
\(200\) | −5344.70 | + | 8620.86i | −0.133617 | + | 0.215522i | ||||
\(201\) | −3596.13 | − | 6228.69i | −0.0890110 | − | 0.154172i | ||||
\(202\) | 42168.3 | − | 42168.3i | 1.03343 | − | 1.03343i | ||||
\(203\) | 48301.7 | − | 21808.7i | 1.17211 | − | 0.529223i | ||||
\(204\) | − | 14735.9i | − | 0.354093i | ||||||
\(205\) | 26973.2 | + | 21377.8i | 0.641836 | + | 0.508693i | ||||
\(206\) | −28902.6 | + | 50060.8i | −0.681088 | + | 1.17968i | ||||
\(207\) | −9766.58 | − | 36449.4i | −0.227930 | − | 0.850647i | ||||
\(208\) | 15328.8 | − | 57207.8i | 0.354308 | − | 1.32230i | ||||
\(209\) | − | 45006.4i | − | 1.03034i | ||||||
\(210\) | −4266.35 | + | 16986.1i | −0.0967427 | + | 0.385172i | ||||
\(211\) | −56888.8 | −1.27780 | −0.638899 | − | 0.769291i | \(-0.720610\pi\) | ||||
−0.638899 | + | 0.769291i | \(0.720610\pi\) | |||||||
\(212\) | −37569.1 | − | 10066.6i | −0.835908 | − | 0.223981i | ||||
\(213\) | 622.858 | − | 166.894i | 0.0137287 | − | 0.00367860i | ||||
\(214\) | −30569.7 | − | 17649.5i | −0.667520 | − | 0.385393i | ||||
\(215\) | 2006.82 | + | 17341.5i | 0.0434143 | + | 0.375155i | ||||
\(216\) | −6677.80 | −0.143128 | ||||||||
\(217\) | −22163.3 | − | 2212.30i | −0.470668 | − | 0.0469813i | ||||
\(218\) | 55022.3 | + | 55022.3i | 1.15778 | + | 1.15778i | ||||
\(219\) | 11245.5 | − | 6492.59i | 0.234472 | − | 0.135372i | ||||
\(220\) | 58691.1 | + | 8665.58i | 1.21263 | + | 0.179041i | ||||
\(221\) | 42875.9 | − | 74263.3i | 0.877867 | − | 1.52051i | ||||
\(222\) | −1032.36 | − | 276.620i | −0.0209471 | − | 0.00561277i | ||||
\(223\) | 36204.4 | + | 36204.4i | 0.728034 | + | 0.728034i | 0.970228 | − | 0.242194i | \(-0.0778670\pi\) |
−0.242194 | + | 0.970228i | \(0.577867\pi\) | |||||||
\(224\) | −50406.3 | + | 41256.6i | −1.00459 | + | 0.822238i | ||||
\(225\) | −31639.4 | − | 33690.0i | −0.624977 | − | 0.665481i | ||||
\(226\) | −23878.3 | − | 41358.4i | −0.467505 | − | 0.809743i | ||||
\(227\) | 8759.83 | + | 32692.1i | 0.169998 | + | 0.634442i | 0.997350 | + | 0.0727572i | \(0.0231798\pi\) |
−0.827352 | + | 0.561684i | \(0.810154\pi\) | |||||||
\(228\) | −8203.06 | + | 2198.00i | −0.157800 | + | 0.0422823i | ||||
\(229\) | 24018.6 | − | 13867.1i | 0.458011 | − | 0.264433i | −0.253197 | − | 0.967415i | \(-0.581482\pi\) |
0.711208 | + | 0.702982i | \(0.248149\pi\) | |||||||
\(230\) | −63859.4 | + | 25285.2i | −1.20717 | + | 0.477980i | ||||
\(231\) | −23466.8 | + | 3842.72i | −0.439775 | + | 0.0720137i | ||||
\(232\) | 12411.8 | − | 12411.8i | 0.230600 | − | 0.230600i | ||||
\(233\) | −3708.91 | + | 13841.9i | −0.0683180 | + | 0.254966i | −0.991635 | − | 0.129072i | \(-0.958800\pi\) |
0.923317 | + | 0.384038i | \(0.125467\pi\) | |||||||
\(234\) | 69187.3 | + | 39945.3i | 1.26356 | + | 0.729515i | ||||
\(235\) | −12752.5 | − | 17170.6i | −0.230919 | − | 0.310920i | ||||
\(236\) | 11346.8 | + | 19653.2i | 0.203727 | + | 0.352866i | ||||
\(237\) | 6855.14 | − | 6855.14i | 0.122045 | − | 0.122045i | ||||
\(238\) | −102746. | + | 46390.9i | −1.81389 | + | 0.818991i | ||||
\(239\) | 2378.47i | 0.0416392i | 0.999783 | + | 0.0208196i | \(0.00662756\pi\) | ||||
−0.999783 | + | 0.0208196i | \(0.993372\pi\) | |||||||
\(240\) | 2252.47 | + | 19464.2i | 0.0391053 | + | 0.337920i | ||||
\(241\) | 13602.3 | − | 23559.9i | 0.234196 | − | 0.405639i | −0.724843 | − | 0.688914i | \(-0.758088\pi\) |
0.959039 | + | 0.283275i | \(0.0914210\pi\) | |||||||
\(242\) | 26135.3 | + | 97538.4i | 0.446270 | + | 1.66550i | ||||
\(243\) | 11992.0 | − | 44754.7i | 0.203085 | − | 0.757925i | ||||
\(244\) | 42588.8i | 0.715346i | ||||||||
\(245\) | 59076.2 | − | 10630.1i | 0.984194 | − | 0.177094i | ||||
\(246\) | 19682.5 | 0.325245 | ||||||||
\(247\) | −47735.6 | − | 12790.7i | −0.782435 | − | 0.209653i | ||||
\(248\) | −7125.75 | + | 1909.34i | −0.115858 | + | 0.0310441i | ||||
\(249\) | 23576.3 | + | 13611.8i | 0.380257 | + | 0.219542i | ||||
\(250\) | −54293.6 | + | 64255.4i | −0.868698 | + | 1.02809i | ||||
\(251\) | 2600.65 | 0.0412796 | 0.0206398 | − | 0.999787i | \(-0.493430\pi\) | ||||
0.0206398 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(252\) | −19362.6 | − | 42884.1i | −0.304904 | − | 0.675297i | ||||
\(253\) | −65941.3 | − | 65941.3i | −1.03019 | − | 1.03019i | ||||
\(254\) | 37426.4 | − | 21608.1i | 0.580110 | − | 0.334927i | ||||
\(255\) | −4143.80 | + | 28065.6i | −0.0637263 | + | 0.431612i | ||||
\(256\) | −41447.9 | + | 71789.9i | −0.632445 | + | 1.09543i | ||||
\(257\) | 61575.5 | + | 16499.1i | 0.932270 | + | 0.249801i | 0.692822 | − | 0.721108i | \(-0.256367\pi\) |
0.239448 | + | 0.970909i | \(0.423034\pi\) | |||||||
\(258\) | 7059.32 | + | 7059.32i | 0.106053 | + | 0.106053i | ||||
\(259\) | 591.943 | + | 3614.89i | 0.00882430 | + | 0.0538885i | ||||
\(260\) | 25870.9 | − | 59787.3i | 0.382705 | − | 0.884427i | ||||
\(261\) | 39990.1 | + | 69264.8i | 0.587044 | + | 1.01679i | ||||
\(262\) | −35339.1 | − | 131887.i | −0.514817 | − | 1.92132i | ||||
\(263\) | 37535.5 | − | 10057.6i | 0.542663 | − | 0.145406i | 0.0229337 | − | 0.999737i | \(-0.492699\pi\) |
0.519730 | + | 0.854331i | \(0.326033\pi\) | |||||||
\(264\) | −6820.74 | + | 3937.96i | −0.0978641 | + | 0.0565019i | ||||
\(265\) | 68722.0 | + | 29737.1i | 0.978597 | + | 0.423454i | ||||
\(266\) | 41150.0 | + | 50276.0i | 0.581576 | + | 0.710554i | ||||
\(267\) | 4602.53 | − | 4602.53i | 0.0645615 | − | 0.0645615i | ||||
\(268\) | 9102.75 | − | 33971.9i | 0.126737 | − | 0.472988i | ||||
\(269\) | 507.486 | + | 292.997i | 0.00701325 | + | 0.00404910i | 0.503503 | − | 0.863994i | \(-0.332044\pi\) |
−0.496489 | + | 0.868043i | \(0.665378\pi\) | |||||||
\(270\) | −54788.0 | − | 8089.29i | −0.751550 | − | 0.110964i | ||||
\(271\) | −27894.8 | − | 48315.2i | −0.379826 | − | 0.657878i | 0.611211 | − | 0.791468i | \(-0.290683\pi\) |
−0.991037 | + | 0.133590i | \(0.957349\pi\) | |||||||
\(272\) | −89183.6 | + | 89183.6i | −1.20544 | + | 1.20544i | ||||
\(273\) | −2593.47 | + | 25981.9i | −0.0347982 | + | 0.348615i | ||||
\(274\) | − | 147822.i | − | 1.96897i | ||||||
\(275\) | −109344. | − | 33008.3i | −1.44587 | − | 0.436474i | ||||
\(276\) | −8798.34 | + | 15239.2i | −0.115500 | + | 0.200052i | ||||
\(277\) | 24124.0 | + | 90032.0i | 0.314405 | + | 1.17338i | 0.924542 | + | 0.381080i | \(0.124448\pi\) |
−0.610137 | + | 0.792296i | \(0.708886\pi\) | |||||||
\(278\) | 13965.9 | − | 52121.3i | 0.180708 | − | 0.674413i | ||||
\(279\) | − | 33613.8i | − | 0.431827i | ||||||
\(280\) | 17058.8 | − | 10209.8i | 0.217587 | − | 0.130227i | ||||
\(281\) | 122531. | 1.55180 | 0.775899 | − | 0.630858i | \(-0.217297\pi\) | ||||
0.775899 | + | 0.630858i | \(0.217297\pi\) | |||||||
\(282\) | −11814.6 | − | 3165.72i | −0.148567 | − | 0.0398083i | ||||
\(283\) | −2399.87 | + | 643.044i | −0.0299651 | + | 0.00802912i | −0.273770 | − | 0.961795i | \(-0.588271\pi\) |
0.243805 | + | 0.969824i | \(0.421604\pi\) | |||||||
\(284\) | 2730.78 | + | 1576.61i | 0.0338571 | + | 0.0195474i | ||||
\(285\) | 16241.4 | − | 1879.51i | 0.199955 | − | 0.0231396i | ||||
\(286\) | 197434. | 2.41374 | ||||||||
\(287\) | −27759.7 | − | 61481.8i | −0.337017 | − | 0.746419i | ||||
\(288\) | −69510.1 | − | 69510.1i | −0.838036 | − | 0.838036i | ||||
\(289\) | −85816.2 | + | 49546.0i | −1.02748 | + | 0.593216i | ||||
\(290\) | 116868. | − | 86797.4i | 1.38963 | − | 1.03207i | ||||
\(291\) | 3376.76 | − | 5848.71i | 0.0398762 | − | 0.0690676i | ||||
\(292\) | 61334.1 | + | 16434.4i | 0.719344 | + | 0.192748i | ||||
\(293\) | −110774. | − | 110774.i | −1.29033 | − | 1.29033i | −0.934581 | − | 0.355750i | \(-0.884225\pi\) |
−0.355750 | − | 0.934581i | \(-0.615775\pi\) | |||||||
\(294\) | 22701.0 | − | 25748.7i | 0.262634 | − | 0.297893i | ||||
\(295\) | −16084.2 | − | 40621.6i | −0.184822 | − | 0.466781i | ||||
\(296\) | 606.613 | + | 1050.68i | 0.00692354 | + | 0.0119919i | ||||
\(297\) | −19462.0 | − | 72633.2i | −0.220635 | − | 0.823421i | ||||
\(298\) | 72661.3 | − | 19469.5i | 0.818221 | − | 0.219242i | ||||
\(299\) | −88680.3 | + | 51199.6i | −0.991938 | + | 0.572696i | ||||
\(300\) | −676.133 | + | 21541.6i | −0.00751258 | + | 0.239351i | ||||
\(301\) | 12094.7 | − | 32007.3i | 0.133494 | − | 0.353278i | ||||
\(302\) | −35384.1 | + | 35384.1i | −0.387967 | + | 0.387967i | ||||
\(303\) | −7613.02 | + | 28412.2i | −0.0829223 | + | 0.309470i | ||||
\(304\) | 62948.5 | + | 36343.3i | 0.681143 | + | 0.393258i | ||||
\(305\) | 11976.1 | − | 81113.2i | 0.128741 | − | 0.871951i | ||||
\(306\) | −85065.7 | − | 147338.i | −0.908472 | − | 1.57352i | ||||
\(307\) | −113885. | + | 113885.i | −1.20834 | + | 1.20834i | −0.236781 | + | 0.971563i | \(0.576093\pi\) |
−0.971563 | + | 0.236781i | \(0.923907\pi\) | |||||||
\(308\) | −94430.0 | − | 67855.6i | −0.995425 | − | 0.715293i | ||||
\(309\) | − | 28512.0i | − | 0.298614i | ||||||
\(310\) | −60776.1 | + | 7033.23i | −0.632426 | + | 0.0731866i | ||||
\(311\) | −75362.6 | + | 130532.i | −0.779175 | + | 1.34957i | 0.153243 | + | 0.988188i | \(0.451028\pi\) |
−0.932418 | + | 0.361382i | \(0.882305\pi\) | |||||||
\(312\) | 2238.31 | + | 8353.50i | 0.0229938 | + | 0.0858142i | ||||
\(313\) | −24610.9 | + | 91849.3i | −0.251212 | + | 0.937534i | 0.718947 | + | 0.695064i | \(0.244624\pi\) |
−0.970159 | + | 0.242470i | \(0.922042\pi\) | |||||||
\(314\) | − | 21514.4i | − | 0.218208i | ||||||
\(315\) | 24818.3 | + | 87120.4i | 0.250121 | + | 0.878009i | ||||
\(316\) | 47406.9 | 0.474753 | ||||||||
\(317\) | 84224.1 | + | 22567.8i | 0.838143 | + | 0.224580i | 0.652263 | − | 0.757993i | \(-0.273820\pi\) |
0.185880 | + | 0.982572i | \(0.440486\pi\) | |||||||
\(318\) | 41362.9 | − | 11083.2i | 0.409031 | − | 0.109600i | ||||
\(319\) | 171174. | + | 98827.6i | 1.68212 | + | 0.971174i | ||||
\(320\) | −37805.5 | + | 47700.5i | −0.369194 | + | 0.465825i | ||||
\(321\) | 17410.9 | 0.168971 | ||||||||
\(322\) | 133953. | + | 13371.0i | 1.29194 | + | 0.128959i | ||||
\(323\) | 74416.9 | + | 74416.9i | 0.713290 | + | 0.713290i | ||||
\(324\) | 55072.4 | − | 31796.0i | 0.524619 | − | 0.302889i | ||||
\(325\) | −66085.2 | + | 106594.i | −0.625659 | + | 1.00917i | ||||
\(326\) | −55711.3 | + | 96494.9i | −0.524214 | + | 0.907965i | ||||
\(327\) | −37072.9 | − | 9933.67i | −0.346706 | − | 0.0928996i | ||||
\(328\) | −15798.7 | − | 15798.7i | −0.146850 | − | 0.146850i | ||||
\(329\) | 6774.36 | + | 41369.9i | 0.0625859 | + | 0.382202i | ||||
\(330\) | −60731.1 | + | 24046.5i | −0.557677 | + | 0.220813i | ||||
\(331\) | 91345.3 | + | 158215.i | 0.833740 | + | 1.44408i | 0.895052 | + | 0.445961i | \(0.147138\pi\) |
−0.0613128 | + | 0.998119i | \(0.519529\pi\) | |||||||
\(332\) | 34455.0 | + | 128588.i | 0.312591 | + | 1.16660i | ||||
\(333\) | −5339.70 | + | 1430.77i | −0.0481535 | + | 0.0129027i | ||||
\(334\) | −27876.7 | + | 16094.6i | −0.249890 | + | 0.144274i | ||||
\(335\) | −26889.8 | + | 62142.0i | −0.239606 | + | 0.553727i | ||||
\(336\) | 13575.2 | − | 35925.1i | 0.120245 | − | 0.318214i | ||||
\(337\) | −15879.0 | + | 15879.0i | −0.139818 | + | 0.139818i | −0.773551 | − | 0.633734i | \(-0.781522\pi\) |
0.633734 | + | 0.773551i | \(0.281522\pi\) | |||||||
\(338\) | 16312.3 | − | 60878.4i | 0.142785 | − | 0.532881i | ||||
\(339\) | 20399.7 | + | 11777.8i | 0.177511 | + | 0.102486i | ||||
\(340\) | −111372. | + | 82715.8i | −0.963429 | + | 0.715534i | ||||
\(341\) | −41535.0 | − | 71940.8i | −0.357195 | − | 0.618680i | ||||
\(342\) | −69330.4 | + | 69330.4i | −0.592750 | + | 0.592750i | ||||
\(343\) | −112448. | − | 34595.2i | −0.955789 | − | 0.294055i | ||||
\(344\) | − | 11332.7i | − | 0.0957669i | ||||||
\(345\) | 21042.3 | − | 26549.9i | 0.176789 | − | 0.223061i | ||||
\(346\) | 36264.9 | − | 62812.6i | 0.302924 | − | 0.524680i | ||||
\(347\) | −45694.2 | − | 170533.i | −0.379491 | − | 1.41628i | −0.846670 | − | 0.532118i | \(-0.821396\pi\) |
0.467179 | − | 0.884163i | \(-0.345271\pi\) | |||||||
\(348\) | 9653.00 | − | 36025.5i | 0.0797084 | − | 0.297476i | ||||
\(349\) | − | 89221.1i | − | 0.732515i | −0.930513 | − | 0.366258i | \(-0.880639\pi\) | ||
0.930513 | − | 0.366258i | \(-0.119361\pi\) | |||||||
\(350\) | 152327. | − | 63101.9i | 1.24348 | − | 0.515117i | ||||
\(351\) | −82568.6 | −0.670194 | ||||||||
\(352\) | −234657. | − | 62876.1i | −1.89386 | − | 0.507458i | ||||
\(353\) | 27639.1 | − | 7405.89i | 0.221807 | − | 0.0594330i | −0.146204 | − | 0.989254i | \(-0.546706\pi\) |
0.368011 | + | 0.929821i | \(0.380039\pi\) | |||||||
\(354\) | −21637.9 | − | 12492.6i | −0.172666 | − | 0.0996890i | ||||
\(355\) | −4757.59 | − | 3770.67i | −0.0377512 | − | 0.0299200i | ||||
\(356\) | 31828.9 | 0.251143 | ||||||||
\(357\) | 32447.9 | − | 45155.6i | 0.254596 | − | 0.354303i | ||||
\(358\) | 232198. | + | 232198.i | 1.81173 | + | 1.81173i | ||||
\(359\) | 96601.9 | − | 55773.1i | 0.749543 | − | 0.432749i | −0.0759856 | − | 0.997109i | \(-0.524210\pi\) |
0.825529 | + | 0.564360i | \(0.190877\pi\) | |||||||
\(360\) | 17889.0 | + | 24086.5i | 0.138032 | + | 0.185853i | ||||
\(361\) | −34834.8 | + | 60335.6i | −0.267300 | + | 0.462977i | ||||
\(362\) | 186079. | + | 49859.8i | 1.41998 | + | 0.380481i | ||||
\(363\) | −35219.0 | − | 35219.0i | −0.267278 | − | 0.267278i | ||||
\(364\) | −98807.0 | + | 80871.8i | −0.745736 | + | 0.610371i | ||||
\(365\) | −112193. | − | 48547.9i | −0.842135 | − | 0.364405i | ||||
\(366\) | −23444.8 | − | 40607.6i | −0.175019 | − | 0.303141i | ||||
\(367\) | −49700.3 | − | 185484.i | −0.369000 | − | 1.37713i | −0.861916 | − | 0.507051i | \(-0.830735\pi\) |
0.492915 | − | 0.870077i | \(-0.335931\pi\) | |||||||
\(368\) | 145478. | − | 38980.6i | 1.07424 | − | 0.287842i | ||||
\(369\) | 88165.2 | − | 50902.2i | 0.647507 | − | 0.373838i | ||||
\(370\) | 3704.18 | + | 9355.17i | 0.0270576 | + | 0.0683358i | ||||
\(371\) | −92957.4 | − | 113573.i | −0.675361 | − | 0.825138i | ||||
\(372\) | −11083.8 | + | 11083.8i | −0.0800943 | + | 0.0800943i | ||||
\(373\) | −23398.7 | + | 87325.1i | −0.168180 | + | 0.627655i | 0.829433 | + | 0.558606i | \(0.188663\pi\) |
−0.997613 | + | 0.0690498i | \(0.978003\pi\) | |||||||
\(374\) | −364117. | − | 210223.i | −2.60314 | − | 1.50293i | ||||
\(375\) | 7345.32 | − | 40837.3i | 0.0522334 | − | 0.290398i | ||||
\(376\) | 6942.25 | + | 12024.3i | 0.0491049 | + | 0.0850521i | ||||
\(377\) | 153468. | − | 153468.i | 1.07978 | − | 1.07978i | ||||
\(378\) | 88150.2 | + | 63343.0i | 0.616935 | + | 0.443318i | ||||
\(379\) | 106272.i | 0.739845i | 0.929063 | + | 0.369923i | \(0.120616\pi\) | ||||
−0.929063 | + | 0.369923i | \(0.879384\pi\) | |||||||
\(380\) | 62657.7 | + | 49659.9i | 0.433918 | + | 0.343905i | ||||
\(381\) | −10658.0 | + | 18460.2i | −0.0734221 | + | 0.127171i | ||||
\(382\) | −24728.6 | − | 92288.5i | −0.169462 | − | 0.632442i | ||||
\(383\) | 7977.16 | − | 29771.2i | 0.0543814 | − | 0.202954i | −0.933390 | − | 0.358864i | \(-0.883164\pi\) |
0.987771 | + | 0.155910i | \(0.0498309\pi\) | |||||||
\(384\) | − | 21674.0i | − | 0.146987i | ||||||
\(385\) | 160767. | + | 155790.i | 1.08461 | + | 1.05103i | ||||
\(386\) | −173320. | −1.16325 | ||||||||
\(387\) | 49877.8 | + | 13364.7i | 0.333031 | + | 0.0892355i | ||||
\(388\) | 31899.5 | − | 8547.44i | 0.211895 | − | 0.0567770i | ||||
\(389\) | −168329. | − | 97184.7i | −1.11240 | − | 0.642242i | −0.172947 | − | 0.984931i | \(-0.555329\pi\) |
−0.939449 | + | 0.342689i | \(0.888662\pi\) | |||||||
\(390\) | 8245.04 | + | 71247.6i | 0.0542080 | + | 0.468426i | ||||
\(391\) | 218064. | 1.42637 | ||||||||
\(392\) | −38889.4 | + | 2446.32i | −0.253080 | + | 0.0159199i | ||||
\(393\) | 47621.6 | + | 47621.6i | 0.308332 | + | 0.308332i | ||||
\(394\) | 224952. | − | 129876.i | 1.44909 | − | 0.836635i | ||||
\(395\) | −90289.7 | − | 13331.0i | −0.578687 | − | 0.0854416i | ||||
\(396\) | 87743.0 | − | 151975.i | 0.559528 | − | 0.969131i | ||||
\(397\) | 70827.9 | + | 18978.3i | 0.449390 | + | 0.120414i | 0.476414 | − | 0.879221i | \(-0.341936\pi\) |
−0.0270239 | + | 0.999635i | \(0.508603\pi\) | |||||||
\(398\) | −98860.6 | − | 98860.6i | −0.624104 | − | 0.624104i | ||||
\(399\) | −29976.7 | − | 11327.4i | −0.188295 | − | 0.0711518i | ||||
\(400\) | 134464. | − | 126280.i | 0.840402 | − | 0.789252i | ||||
\(401\) | −17296.7 | − | 29958.7i | −0.107566 | − | 0.186309i | 0.807218 | − | 0.590254i | \(-0.200972\pi\) |
−0.914784 | + | 0.403944i | \(0.867639\pi\) | |||||||
\(402\) | 10022.0 | + | 37402.5i | 0.0620156 | + | 0.231445i | ||||
\(403\) | −88107.3 | + | 23608.3i | −0.542503 | + | 0.145363i | ||||
\(404\) | −124567. | + | 71918.5i | −0.763201 | + | 0.440634i | ||||
\(405\) | −113830. | + | 45071.1i | −0.693980 | + | 0.274782i | ||||
\(406\) | −281576. | + | 46108.4i | −1.70822 | + | 0.279723i | ||||
\(407\) | −9660.16 | + | 9660.16i | −0.0583170 | + | 0.0583170i | ||||
\(408\) | 4766.60 | − | 17789.2i | 0.0286344 | − | 0.106865i | ||||
\(409\) | 189596. | + | 109464.i | 1.13340 | + | 0.654369i | 0.944788 | − | 0.327682i | \(-0.106268\pi\) |
0.188613 | + | 0.982052i | \(0.439601\pi\) | |||||||
\(410\) | −110482. | − | 148758.i | −0.657240 | − | 0.884938i | ||||
\(411\) | 36456.1 | + | 63143.8i | 0.215817 | + | 0.373807i | ||||
\(412\) | 98587.6 | − | 98587.6i | 0.580802 | − | 0.580802i | ||||
\(413\) | −8505.42 | + | 85208.9i | −0.0498650 | + | 0.499557i | ||||
\(414\) | 203159.i | 1.18532i | ||||||||
\(415\) | −29462.4 | − | 254593.i | −0.171069 | − | 1.47826i | ||||
\(416\) | −133378. | + | 231017.i | −0.770719 | + | 1.33492i | ||||
\(417\) | 6888.55 | + | 25708.4i | 0.0396146 | + | 0.147844i | ||||
\(418\) | −62713.6 | + | 234050.i | −0.358929 | + | 1.33954i | ||||
\(419\) | 8790.00i | 0.0500681i | 0.999687 | + | 0.0250340i | \(0.00796942\pi\) | ||||
−0.999687 | + | 0.0250340i | \(0.992031\pi\) | |||||||
\(420\) | 20543.4 | − | 36910.5i | 0.116459 | − | 0.209243i | ||||
\(421\) | 92226.8 | 0.520347 | 0.260173 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260173 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(422\) | 295843. | + | 79270.9i | 1.66126 | + | 0.445132i | ||||
\(423\) | −61109.0 | + | 16374.1i | −0.341527 | + | 0.0915118i | ||||
\(424\) | −42097.1 | − | 24304.8i | −0.234164 | − | 0.135195i | ||||
\(425\) | 235376. | − | 126219.i | 1.30312 | − | 0.698792i | ||||
\(426\) | −3471.65 | −0.0191301 | ||||||||
\(427\) | −93778.9 | + | 130506.i | −0.514339 | + | 0.715771i | ||||
\(428\) | 60202.7 | + | 60202.7i | 0.328646 | + | 0.328646i | ||||
\(429\) | −84336.0 | + | 48691.4i | −0.458246 | + | 0.264568i | ||||
\(430\) | 13728.1 | − | 92978.8i | 0.0742459 | − | 0.502860i | ||||
\(431\) | −81718.8 | + | 141541.i | −0.439914 | + | 0.761953i | −0.997682 | − | 0.0680438i | \(-0.978324\pi\) |
0.557769 | + | 0.829996i | \(0.311658\pi\) | |||||||
\(432\) | 117305. | + | 31431.7i | 0.628561 | + | 0.168422i | ||||
\(433\) | 105552. | + | 105552.i | 0.562977 | + | 0.562977i | 0.930152 | − | 0.367175i | \(-0.119675\pi\) |
−0.367175 | + | 0.930152i | \(0.619675\pi\) | |||||||
\(434\) | 112175. | + | 42387.9i | 0.595546 | + | 0.225041i | ||||
\(435\) | −28515.3 | + | 65898.5i | −0.150695 | + | 0.348255i | ||||
\(436\) | −93841.2 | − | 162538.i | −0.493652 | − | 0.855030i | ||||
\(437\) | −32526.4 | − | 121390.i | −0.170323 | − | 0.635653i | ||||
\(438\) | −67527.8 | + | 18094.0i | −0.351993 | + | 0.0943163i | ||||
\(439\) | −239991. | + | 138559.i | −1.24528 | + | 0.718962i | −0.970164 | − | 0.242449i | \(-0.922049\pi\) |
−0.275115 | + | 0.961411i | \(0.588716\pi\) | |||||||
\(440\) | 68048.8 | + | 29445.8i | 0.351492 | + | 0.152096i | ||||
\(441\) | 35095.7 | − | 174046.i | 0.180458 | − | 0.894927i | ||||
\(442\) | −326452. | + | 326452.i | −1.67099 | + | 1.67099i | ||||
\(443\) | 40763.5 | − | 152132.i | 0.207713 | − | 0.775196i | −0.780892 | − | 0.624666i | \(-0.785235\pi\) |
0.988605 | − | 0.150530i | \(-0.0480982\pi\) | |||||||
\(444\) | 2232.48 | + | 1288.92i | 0.0113246 | + | 0.00653825i | ||||
\(445\) | −60620.3 | − | 8950.42i | −0.306124 | − | 0.0451984i | ||||
\(446\) | −137828. | − | 238725.i | −0.692895 | − | 1.20013i | ||||
\(447\) | −26236.4 | + | 26236.4i | −0.131307 | + | 0.131307i | ||||
\(448\) | 108727. | − | 49091.5i | 0.541729 | − | 0.244597i | ||||
\(449\) | 257522.i | 1.27739i | 0.769461 | + | 0.638693i | \(0.220525\pi\) | ||||
−0.769461 | + | 0.638693i | \(0.779475\pi\) | |||||||
\(450\) | 117592. | + | 219288.i | 0.580702 | + | 1.08290i | ||||
\(451\) | 125795. | − | 217883.i | 0.618458 | − | 1.07120i | ||||
\(452\) | 29812.6 | + | 111262.i | 0.145923 | + | 0.544591i | ||||
\(453\) | 6388.21 | − | 23841.1i | 0.0311303 | − | 0.116180i | ||||
\(454\) | − | 182218.i | − | 0.884054i | ||||||
\(455\) | 210926. | − | 126241.i | 1.01884 | − | 0.609785i | ||||
\(456\) | −10613.7 | −0.0510432 | ||||||||
\(457\) | −129804. | − | 34780.8i | −0.621520 | − | 0.166536i | −0.0657013 | − | 0.997839i | \(-0.520928\pi\) |
−0.555819 | + | 0.831304i | \(0.687595\pi\) | |||||||
\(458\) | −144228. | + | 38645.9i | −0.687575 | + | 0.184235i | ||||
\(459\) | 152277. | + | 87917.0i | 0.722784 | + | 0.417299i | ||||
\(460\) | 164563. | − | 19043.8i | 0.777706 | − | 0.0899990i | ||||
\(461\) | −283986. | −1.33627 | −0.668136 | − | 0.744039i | \(-0.732907\pi\) | ||||
−0.668136 | + | 0.744039i | \(0.732907\pi\) | |||||||
\(462\) | 127391. | + | 12716.0i | 0.596836 | + | 0.0595752i | ||||
\(463\) | −94433.9 | − | 94433.9i | −0.440520 | − | 0.440520i | 0.451667 | − | 0.892187i | \(-0.350830\pi\) |
−0.892187 | + | 0.451667i | \(0.850830\pi\) | |||||||
\(464\) | −276452. | + | 159609.i | −1.28405 | + | 0.741349i | ||||
\(465\) | 24226.6 | − | 17993.0i | 0.112043 | − | 0.0832141i | ||||
\(466\) | 38575.5 | − | 66814.7i | 0.177640 | − | 0.307681i | ||||
\(467\) | −134070. | − | 35923.9i | −0.614748 | − | 0.164721i | −0.0620089 | − | 0.998076i | \(-0.519751\pi\) |
−0.552739 | + | 0.833354i | \(0.686417\pi\) | |||||||
\(468\) | −136255. | − | 136255.i | −0.622099 | − | 0.622099i | ||||
\(469\) | 102699. | − | 84056.9i | 0.466894 | − | 0.382145i | ||||
\(470\) | 42391.7 | + | 107063.i | 0.191905 | + | 0.484668i | ||||
\(471\) | 5305.91 | + | 9190.11i | 0.0239176 | + | 0.0414265i | ||||
\(472\) | 7340.65 | + | 27395.7i | 0.0329496 | + | 0.122970i | ||||
\(473\) | 123263. | − | 33028.3i | 0.550949 | − | 0.147626i | ||||
\(474\) | −45201.5 | + | 26097.1i | −0.201185 | + | 0.116154i | ||||
\(475\) | −105371. | − | 112200.i | −0.467019 | − | 0.497286i | ||||
\(476\) | 268335. | − | 43940.1i | 1.18430 | − | 0.193931i | ||||
\(477\) | 156617. | − | 156617.i | 0.688337 | − | 0.688337i | ||||
\(478\) | 3314.25 | − | 12368.9i | 0.0145054 | − | 0.0541348i | ||||
\(479\) | 362708. | + | 209410.i | 1.58083 | + | 0.912695i | 0.994738 | + | 0.102453i | \(0.0326693\pi\) |
0.586096 | + | 0.810241i | \(0.300664\pi\) | |||||||
\(480\) | 12890.5 | − | 87305.8i | 0.0559482 | − | 0.378931i | ||||
\(481\) | 7500.55 | + | 12991.3i | 0.0324192 | + | 0.0561518i | ||||
\(482\) | −103566. | + | 103566.i | −0.445785 | + | 0.445785i | ||||
\(483\) | −60517.0 | + | 27324.1i | −0.259408 | + | 0.117125i | ||||
\(484\) | − | 243558.i | − | 1.03971i | ||||||
\(485\) | −63158.3 | + | 7308.91i | −0.268502 | + | 0.0310720i | ||||
\(486\) | −124726. | + | 216031.i | −0.528060 | + | 0.914627i | ||||
\(487\) | 25949.6 | + | 96845.3i | 0.109414 | + | 0.408339i | 0.998808 | − | 0.0488018i | \(-0.0155403\pi\) |
−0.889394 | + | 0.457141i | \(0.848874\pi\) | |||||||
\(488\) | −13776.1 | + | 51413.2i | −0.0578479 | + | 0.215891i | ||||
\(489\) | − | 54958.3i | − | 0.229835i | ||||||
\(490\) | −322031. | − | 27038.6i | −1.34124 | − | 0.112614i | ||||
\(491\) | 84408.3 | 0.350124 | 0.175062 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175062 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(492\) | −45855.8 | − | 12287.0i | −0.189437 | − | 0.0507594i | ||||
\(493\) | −446441. | + | 119624.i | −1.83684 | + | 0.492179i | ||||
\(494\) | 230420. | + | 133033.i | 0.944204 | + | 0.545136i | ||||
\(495\) | −209848. | + | 264773.i | −0.856437 | + | 1.08060i | ||||
\(496\) | 134161. | 0.545332 | ||||||||
\(497\) | 4896.33 | + | 10844.3i | 0.0198225 | + | 0.0439025i | ||||
\(498\) | −103639. | − | 103639.i | −0.417891 | − | 0.417891i | ||||
\(499\) | 173842. | − | 100368.i | 0.698158 | − | 0.403082i | −0.108503 | − | 0.994096i | \(-0.534606\pi\) |
0.806661 | + | 0.591015i | \(0.201272\pi\) | |||||||
\(500\) | 166604. | − | 115807.i | 0.666416 | − | 0.463229i | ||||
\(501\) | 7938.55 | − | 13750.0i | 0.0316276 | − | 0.0547805i | ||||
\(502\) | −13524.4 | − | 3623.85i | −0.0536673 | − | 0.0143801i | ||||
\(503\) | 265239. | + | 265239.i | 1.04834 | + | 1.04834i | 0.998771 | + | 0.0495661i | \(0.0157838\pi\) |
0.0495661 | + | 0.998771i | \(0.484216\pi\) | |||||||
\(504\) | −9502.94 | − | 58032.8i | −0.0374108 | − | 0.228461i | ||||
\(505\) | 257469. | − | 101945.i | 1.00958 | − | 0.399745i | ||||
\(506\) | 251035. | + | 434805.i | 0.980466 | + | 1.69822i | ||||
\(507\) | 8045.92 | + | 30027.8i | 0.0313011 | + | 0.116817i | ||||
\(508\) | −100684. | + | 26978.2i | −0.390152 | + | 0.104541i | ||||
\(509\) | −146096. | + | 84348.8i | −0.563902 | + | 0.325569i | −0.754710 | − | 0.656058i | \(-0.772223\pi\) |
0.190808 | + | 0.981627i | \(0.438889\pi\) | |||||||
\(510\) | 60656.9 | − | 140177.i | 0.233206 | − | 0.538936i | ||||
\(511\) | 151759. | + | 185416.i | 0.581184 | + | 0.710076i | ||||
\(512\) | 223239. | − | 223239.i | 0.851588 | − | 0.851588i | ||||
\(513\) | 26227.3 | − | 97881.7i | 0.0996596 | − | 0.371935i | ||||
\(514\) | −297225. | − | 171603.i | −1.12502 | − | 0.649529i | ||||
\(515\) | −215490. | + | 160043.i | −0.812480 | + | 0.603425i | ||||
\(516\) | −12039.8 | − | 20853.5i | −0.0452187 | − | 0.0783211i | ||||
\(517\) | −110554. | + | 110554.i | −0.413611 | + | 0.413611i | ||||
\(518\) | 1958.80 | − | 19623.6i | 0.00730013 | − | 0.0731341i | ||||
\(519\) | 35774.7i | 0.132813i | ||||||||
\(520\) | 50570.6 | − | 63806.8i | 0.187021 | − | 0.235972i | ||||
\(521\) | 253914. | − | 439792.i | 0.935430 | − | 1.62021i | 0.161564 | − | 0.986862i | \(-0.448346\pi\) |
0.773866 | − | 0.633349i | \(-0.218320\pi\) | |||||||
\(522\) | −111447. | − | 415927.i | −0.409005 | − | 1.52643i | ||||
\(523\) | 119575. | − | 446261.i | 0.437157 | − | 1.63149i | −0.298693 | − | 0.954349i | \(-0.596551\pi\) |
0.735850 | − | 0.677144i | \(-0.236783\pi\) | |||||||
\(524\) | 329328.i | 1.19941i | ||||||||
\(525\) | −49505.7 | + | 64521.5i | −0.179612 | + | 0.234092i | ||||
\(526\) | −209213. | −0.756167 | ||||||||
\(527\) | 187629. | + | 50275.1i | 0.675583 | + | 0.181022i | ||||
\(528\) | 138351. | − | 37071.1i | 0.496266 | − | 0.132974i | ||||
\(529\) | 16838.2 | + | 9721.55i | 0.0601707 | + | 0.0347396i | ||||
\(530\) | −315943. | − | 250404.i | −1.12475 | − | 0.891434i | ||||
\(531\) | −129232. | −0.458332 | ||||||||
\(532\) | −64484.9 | − | 142820.i | −0.227842 | − | 0.504622i | ||||
\(533\) | −195345. | − | 195345.i | −0.687618 | − | 0.687618i | ||||
\(534\) | −30348.2 | + | 17521.5i | −0.106427 | + | 0.0614455i | ||||
\(535\) | −97730.9 | − | 131589.i | −0.341448 | − | 0.459741i | ||||
\(536\) | 21977.7 | − | 38066.4i | 0.0764983 | − | 0.132499i | ||||
\(537\) | −156450. | − | 41920.8i | −0.542536 | − | 0.145372i | ||||
\(538\) | −2230.85 | − | 2230.85i | −0.00770735 | − | 0.00770735i | ||||
\(539\) | −139949. | − | 415863.i | −0.481716 | − | 1.43144i | ||||
\(540\) | 122594. | + | 53048.2i | 0.420418 | + | 0.181921i | ||||
\(541\) | −208922. | − | 361863.i | −0.713820 | − | 1.23637i | −0.963413 | − | 0.268022i | \(-0.913630\pi\) |
0.249593 | − | 0.968351i | \(-0.419703\pi\) | |||||||
\(542\) | 77739.3 | + | 290127.i | 0.264632 | + | 0.987619i | ||||
\(543\) | −91782.1 | + | 24592.9i | −0.311285 | + | 0.0834086i | ||||
\(544\) | 491962. | − | 284035.i | 1.66239 | − | 0.959784i | ||||
\(545\) | 133021. | + | 335952.i | 0.447843 | + | 1.13106i | ||||
\(546\) | 49691.2 | − | 131502.i | 0.166684 | − | 0.441110i | ||||
\(547\) | 202388. | − | 202388.i | 0.676412 | − | 0.676412i | −0.282775 | − | 0.959186i | \(-0.591255\pi\) |
0.959186 | + | 0.282775i | \(0.0912548\pi\) | |||||||
\(548\) | −92279.8 | + | 344393.i | −0.307288 | + | 1.14681i | ||||
\(549\) | −210035. | − | 121264.i | −0.696864 | − | 0.402335i | ||||
\(550\) | 522636. | + | 324020.i | 1.72772 | + | 1.07114i | ||||
\(551\) | 133182. | + | 230678.i | 0.438674 | + | 0.759806i | ||||
\(552\) | −15550.7 | + | 15550.7i | −0.0510355 | + | 0.0510355i | ||||
\(553\) | 145270. | + | 104388.i | 0.475035 | + | 0.341351i | ||||
\(554\) | − | 501815.i | − | 1.63502i | ||||||
\(555\) | −3889.46 | − | 3082.62i | −0.0126271 | − | 0.0100077i | ||||
\(556\) | −65074.6 | + | 112713.i | −0.210505 | + | 0.364605i | ||||
\(557\) | 141700. | + | 528833.i | 0.456732 | + | 1.70455i | 0.682947 | + | 0.730468i | \(0.260698\pi\) |
−0.226215 | + | 0.974077i | \(0.572635\pi\) | |||||||
\(558\) | −46838.7 | + | 174805.i | −0.150431 | + | 0.561415i | ||||
\(559\) | − | 140124.i | − | 0.448425i | ||||||
\(560\) | −347718. | + | 99055.4i | −1.10879 | + | 0.315865i | ||||
\(561\) | 207382. | 0.658938 | ||||||||
\(562\) | −637210. | − | 170740.i | −2.01748 | − | 0.540583i | ||||
\(563\) | 437822. | − | 117314.i | 1.38128 | − | 0.370112i | 0.509692 | − | 0.860357i | \(-0.329759\pi\) |
0.871585 | + | 0.490245i | \(0.163093\pi\) | |||||||
\(564\) | 25549.2 | + | 14750.8i | 0.0803190 | + | 0.0463722i | ||||
\(565\) | −25492.7 | − | 220290.i | −0.0798581 | − | 0.690076i | ||||
\(566\) | 13376.3 | 0.0417544 | ||||||||
\(567\) | 238773. | + | 23833.9i | 0.742710 | + | 0.0741361i | ||||
\(568\) | 2786.61 | + | 2786.61i | 0.00863732 | + | 0.00863732i | ||||
\(569\) | −394466. | + | 227745.i | −1.21839 | + | 0.703436i | −0.964573 | − | 0.263817i | \(-0.915018\pi\) |
−0.253814 | + | 0.967253i | \(0.581685\pi\) | |||||||
\(570\) | −87080.2 | − | 12857.2i | −0.268022 | − | 0.0395726i | ||||
\(571\) | −192047. | + | 332635.i | −0.589026 | + | 1.02022i | 0.405334 | + | 0.914169i | \(0.367155\pi\) |
−0.994360 | + | 0.106055i | \(0.966178\pi\) | |||||||
\(572\) | −459977. | − | 123251.i | −1.40587 | − | 0.376701i | ||||
\(573\) | 33323.3 | + | 33323.3i | 0.101494 | + | 0.101494i | ||||
\(574\) | 58690.0 | + | 358410.i | 0.178131 | + | 1.08782i | ||||
\(575\) | −318775. | − | 10005.5i | −0.964160 | − | 0.0302624i | ||||
\(576\) | 90017.7 | + | 155915.i | 0.271321 | + | 0.469941i | ||||
\(577\) | −3056.20 | − | 11405.9i | −0.00917973 | − | 0.0342592i | 0.961184 | − | 0.275908i | \(-0.0889785\pi\) |
−0.970364 | + | 0.241649i | \(0.922312\pi\) | |||||||
\(578\) | 515316. | − | 138078.i | 1.54247 | − | 0.413304i | ||||
\(579\) | 74035.3 | − | 42744.3i | 0.220842 | − | 0.127503i | ||||
\(580\) | −326461. | + | 129262.i | −0.970454 | + | 0.384252i | ||||
\(581\) | −177564. | + | 469903.i | −0.526021 | + | 1.39205i | ||||
\(582\) | −25710.2 | + | 25710.2i | −0.0759031 | + | 0.0759031i | ||||
\(583\) | 141669. | − | 528717.i | 0.416810 | − | 1.55556i | ||||
\(584\) | 68726.5 | + | 39679.2i | 0.201511 | + | 0.116342i | ||||
\(585\) | 221191. | + | 297821.i | 0.646331 | + | 0.870250i | ||||
\(586\) | 421708. | + | 730421.i | 1.22805 | + | 2.12705i | ||||
\(587\) | 218741. | − | 218741.i | 0.634826 | − | 0.634826i | −0.314448 | − | 0.949275i | \(-0.601819\pi\) |
0.949275 | + | 0.314448i | \(0.101819\pi\) | |||||||
\(588\) | −68962.1 | + | 45817.3i | −0.199460 | + | 0.132518i | ||||
\(589\) | − | 111947.i | − | 0.322686i | ||||||
\(590\) | 27040.0 | + | 233660.i | 0.0776788 | + | 0.671244i | ||||
\(591\) | −64060.2 | + | 110956.i | −0.183406 | + | 0.317668i | ||||
\(592\) | −5710.52 | − | 21312.0i | −0.0162942 | − | 0.0608107i | ||||
\(593\) | −4972.04 | + | 18555.9i | −0.0141392 | + | 0.0527682i | −0.972635 | − | 0.232338i | \(-0.925362\pi\) |
0.958496 | + | 0.285107i | \(0.0920290\pi\) | |||||||
\(594\) | 404839.i | 1.14738i | ||||||||
\(595\) | −523418. | + | 8230.06i | −1.47848 | + | 0.0232471i | ||||
\(596\) | −181439. | −0.510784 | ||||||||
\(597\) | 66610.3 | + | 17848.2i | 0.186893 | + | 0.0500778i | ||||
\(598\) | 532514. | − | 142687.i | 1.48912 | − | 0.399008i | ||||
\(599\) | −509004. | − | 293873.i | −1.41862 | − | 0.819043i | −0.422446 | − | 0.906388i | \(-0.638828\pi\) |
−0.996178 | + | 0.0873453i | \(0.972162\pi\) | |||||||
\(600\) | −7784.25 | + | 25786.3i | −0.0216229 | + | 0.0716286i | ||||
\(601\) | −162919. | −0.451048 | −0.225524 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225524 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(602\) | −107497. | + | 149597.i | −0.296623 | + | 0.412790i | ||||
\(603\) | 141621. | + | 141621.i | 0.389487 | + | 0.389487i | ||||
\(604\) | 104526. | − | 60348.1i | 0.286517 | − | 0.165421i | ||||
\(605\) | −68489.4 | + | 463872.i | −0.187117 | + | 1.26732i | ||||
\(606\) | 79181.1 | − | 137146.i | 0.215614 | − | 0.373454i | ||||
\(607\) | −90092.0 | − | 24140.1i | −0.244517 | − | 0.0655181i | 0.134479 | − | 0.990916i | \(-0.457064\pi\) |
−0.378996 | + | 0.925398i | \(0.623731\pi\) | |||||||
\(608\) | −231495. | − | 231495.i | −0.626230 | − | 0.626230i | ||||
\(609\) | 108907. | − | 89138.1i | 0.293643 | − | 0.240342i | ||||
\(610\) | −175307. | + | 405131.i | −0.471128 | + | 1.08877i | ||||
\(611\) | 85838.4 | + | 148677.i | 0.229932 | + | 0.398254i | ||||
\(612\) | 106206. | + | 396368.i | 0.283562 | + | 1.05827i | ||||
\(613\) | −624923. | + | 167448.i | −1.66305 | + | 0.445613i | −0.963224 | − | 0.268700i | \(-0.913406\pi\) |
−0.699826 | + | 0.714313i | \(0.746739\pi\) | |||||||
\(614\) | 750938. | − | 433554.i | 1.99190 | − | 1.15002i | ||||
\(615\) | 83880.3 | + | 36296.3i | 0.221774 | + | 0.0959649i | ||||
\(616\) | −92046.7 | − | 112460.i | −0.242576 | − | 0.296372i | ||||
\(617\) | −125760. | + | 125760.i | −0.330348 | + | 0.330348i | −0.852719 | − | 0.522370i | \(-0.825048\pi\) |
0.522370 | + | 0.852719i | \(0.325048\pi\) | |||||||
\(618\) | −39729.6 | + | 148273.i | −0.104025 | + | 0.388226i | ||||
\(619\) | 511725. | + | 295444.i | 1.33553 | + | 0.771071i | 0.986142 | − | 0.165905i | \(-0.0530546\pi\) |
0.349393 | + | 0.936976i | \(0.386388\pi\) | |||||||
\(620\) | 145985. | + | 21554.3i | 0.379774 | + | 0.0560726i | ||||
\(621\) | −104985. | − | 181839.i | −0.272234 | − | 0.471524i | ||||
\(622\) | 573801. | − | 573801.i | 1.48314 | − | 1.48314i | ||||
\(623\) | 97534.0 | + | 70086.0i | 0.251293 | + | 0.180574i | ||||
\(624\) | − | 157276.i | − | 0.403918i | ||||||
\(625\) | −349874. | + | 173713.i | −0.895677 | + | 0.444705i | ||||
\(626\) | 255972. | − | 443357.i | 0.653197 | − | 1.13137i | ||||
\(627\) | −30933.0 | − | 115443.i | −0.0786840 | − | 0.293653i | ||||
\(628\) | −13430.6 | + | 50123.8i | −0.0340547 | + | 0.127094i | ||||
\(629\) | − | 31945.6i | − | 0.0807439i | ||||||
\(630\) | −7667.53 | − | 487642.i | −0.0193185 | − | 1.22863i | ||||
\(631\) | 424749. | 1.06678 | 0.533389 | − | 0.845870i | \(-0.320918\pi\) | ||||
0.533389 | + | 0.845870i | \(0.320918\pi\) | |||||||
\(632\) | 57229.6 | + | 15334.6i | 0.143280 | + | 0.0383919i | ||||
\(633\) | −145922. | + | 39099.7i | −0.364178 | + | 0.0975813i | ||||
\(634\) | −406550. | − | 234722.i | −1.01143 | − | 0.583949i | ||||
\(635\) | 199346. | − | 23069.0i | 0.494379 | − | 0.0572113i | ||||
\(636\) | −103285. | −0.255342 | ||||||||
\(637\) | −480853. | + | 30247.8i | −1.18504 | + | 0.0745445i | ||||
\(638\) | −752462. | − | 752462.i | −1.84860 | − | 1.84860i | ||||
\(639\) | −15550.8 | + | 8978.25i | −0.0380847 | + | 0.0219882i | ||||
\(640\) | −163810. | + | 121661.i | −0.399926 | + | 0.297023i | ||||
\(641\) | 400493. | − | 693674.i | 0.974718 | − | 1.68826i | 0.293856 | − | 0.955850i | \(-0.405061\pi\) |
0.680862 | − | 0.732411i | \(-0.261605\pi\) | |||||||
\(642\) | −90543.2 | − | 24261.0i | −0.219678 | − | 0.0588624i | ||||
\(643\) | 471886. | + | 471886.i | 1.14134 | + | 1.14134i | 0.988205 | + | 0.153135i | \(0.0489370\pi\) |
0.153135 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(644\) | −303734. | − | 114773.i | −0.732354 | − | 0.276738i | ||||
\(645\) | 17066.4 | + | 43102.4i | 0.0410226 | + | 0.103605i | ||||
\(646\) | −283301. | − | 490691.i | −0.678863 | − | 1.17583i | ||||
\(647\) | 34376.0 | + | 128293.i | 0.0821197 | + | 0.306475i | 0.994753 | − | 0.102304i | \(-0.0326214\pi\) |
−0.912633 | + | 0.408779i | \(0.865955\pi\) | |||||||
\(648\) | 76768.3 | − | 20570.0i | 0.182823 | − | 0.0489874i | ||||
\(649\) | −276584. | + | 159686.i | −0.656655 | + | 0.379120i | ||||
\(650\) | 492200. | − | 462242.i | 1.16497 | − | 1.09407i | ||||
\(651\) | −58370.2 | + | 9558.19i | −0.137730 | + | 0.0225535i | ||||
\(652\) | 190033. | − | 190033.i | 0.447027 | − | 0.447027i | ||||
\(653\) | −136356. | + | 508887.i | −0.319777 | + | 1.19343i | 0.599681 | + | 0.800239i | \(0.295294\pi\) |
−0.919459 | + | 0.393186i | \(0.871373\pi\) | |||||||
\(654\) | 178951. | + | 103318.i | 0.418388 | + | 0.241557i | ||||
\(655\) | 92608.5 | − | 627228.i | 0.215858 | − | 1.46198i | ||||
\(656\) | 203162. | + | 351887.i | 0.472102 | + | 0.817704i | ||||
\(657\) | −255688. | + | 255688.i | −0.592351 | + | 0.592351i | ||||
\(658\) | 22417.1 | − | 224579.i | 0.0517758 | − | 0.518700i | ||||
\(659\) | − | 7796.60i | − | 0.0179529i | −0.999960 | − | 0.00897645i | \(-0.997143\pi\) | ||
0.999960 | − | 0.00897645i | \(-0.00285733\pi\) | |||||||
\(660\) | 156501. | − | 18110.9i | 0.359277 | − | 0.0415768i | ||||
\(661\) | 177819. | − | 307992.i | 0.406982 | − | 0.704914i | −0.587568 | − | 0.809175i | \(-0.699914\pi\) |
0.994550 | + | 0.104261i | \(0.0332477\pi\) | |||||||
\(662\) | −254568. | − | 950060.i | −0.580882 | − | 2.16788i | ||||
\(663\) | 58937.3 | − | 219957.i | 0.134080 | − | 0.500393i | ||||
\(664\) | 166376.i | 0.377359i | ||||||||
\(665\) | 82654.1 | + | 290144.i | 0.186905 | + | 0.656100i | ||||
\(666\) | 29762.1 | 0.0670989 | ||||||||
\(667\) | 533110. | + | 142846.i | 1.19830 | + | 0.321083i | ||||
\(668\) | 74993.8 | − | 20094.5i | 0.168063 | − | 0.0450324i | ||||
\(669\) | 117749. | + | 67982.5i | 0.263091 | + | 0.151896i | ||||
\(670\) | 226428. | − | 285693.i | 0.504407 | − | 0.636428i | ||||
\(671\) | −599361. | −1.33120 | ||||||||
\(672\) | −100938. | + | 140469.i | −0.223521 | + | 0.311059i | ||||
\(673\) | −143492. | − | 143492.i | −0.316810 | − | 0.316810i | 0.530731 | − | 0.847541i | \(-0.321918\pi\) |
−0.847541 | + | 0.530731i | \(0.821918\pi\) | |||||||
\(674\) | 104703. | − | 60450.3i | 0.230483 | − | 0.133070i | ||||
\(675\) | −218571. | − | 135508.i | −0.479716 | − | 0.297411i | ||||
\(676\) | −76008.1 | + | 131650.i | −0.166328 | + | 0.288089i | ||||
\(677\) | −11840.8 | − | 3172.74i | −0.0258347 | − | 0.00692240i | 0.245879 | − | 0.969301i | \(-0.420924\pi\) |
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(678\) | −89674.6 | − | 89674.6i | −0.195079 | − | 0.195079i | ||||
\(679\) | 116571. | + | 44049.3i | 0.252844 | + | 0.0955432i | ||||
\(680\) | −161205. | + | 63829.0i | −0.348626 | + | 0.138039i | ||||
\(681\) | 44938.7 | + | 77836.1i | 0.0969005 | + | 0.167837i | ||||
\(682\) | 115753. | + | 431995.i | 0.248864 | + | 0.928775i | ||||
\(683\) | −480354. | + | 128710.i | −1.02972 | + | 0.275913i | −0.733848 | − | 0.679314i | \(-0.762277\pi\) |
−0.295874 | + | 0.955227i | \(0.595611\pi\) | |||||||
\(684\) | 204805. | − | 118244.i | 0.437751 | − | 0.252736i | ||||
\(685\) | 272598. | − | 629969.i | 0.580953 | − | 1.34257i | ||||
\(686\) | 536563. | + | 336597.i | 1.14018 | + | 0.715256i | ||||
\(687\) | 52077.7 | − | 52077.7i | 0.110341 | − | 0.110341i | ||||
\(688\) | −53341.6 | + | 199074.i | −0.112691 | + | 0.420569i | ||||
\(689\) | −520516. | − | 300520.i | −1.09647 | − | 0.633045i | ||||
\(690\) | −146424. | + | 108748.i | −0.307548 | + | 0.228415i | ||||
\(691\) | 155195. | + | 268805.i | 0.325028 | + | 0.562964i | 0.981518 | − | 0.191370i | \(-0.0612931\pi\) |
−0.656490 | + | 0.754334i | \(0.727960\pi\) | |||||||
\(692\) | −123700. | + | 123700.i | −0.258321 | + | 0.258321i | ||||
\(693\) | 603516. | − | 272494.i | 1.25667 | − | 0.567402i | ||||
\(694\) | 950508.i | 1.97350i | ||||||||
\(695\) | 155634. | − | 196369.i | 0.322207 | − | 0.406541i | ||||
\(696\) | 23306.2 | − | 40367.5i | 0.0481119 | − | 0.0833323i | ||||
\(697\) | 152265. | + | 568262.i | 0.313426 | + | 1.16972i | ||||
\(698\) | −124324. | + | 463983.i | −0.255178 | + | 0.952339i | ||||
\(699\) | 38054.1i | 0.0778838i | ||||||||
\(700\) | −394279. | + | 51921.4i | −0.804651 | + | 0.105962i | ||||
\(701\) | −640845. | −1.30412 | −0.652059 | − | 0.758168i | \(-0.726095\pi\) | ||||
−0.652059 | + | 0.758168i | \(0.726095\pi\) | |||||||
\(702\) | 429388. | + | 115054.i | 0.871315 | + | 0.233468i | ||||
\(703\) | −17783.2 | + | 4764.99i | −0.0359831 | + | 0.00964165i | ||||
\(704\) | 385314. | + | 222461.i | 0.777445 | + | 0.448858i | ||||
\(705\) | −44512.1 | − | 35278.4i | −0.0895570 | − | 0.0709792i | ||||
\(706\) | −154054. | −0.309074 | ||||||||
\(707\) | −540074. | − | 53909.3i | −1.08047 | − | 0.107851i | ||||
\(708\) | 42612.7 | + | 42612.7i | 0.0850104 | + | 0.0850104i | ||||
\(709\) | −508186. | + | 293401.i | −1.01095 | + | 0.583673i | −0.911470 | − | 0.411366i | \(-0.865052\pi\) |
−0.0994815 | + | 0.995039i | \(0.531718\pi\) | |||||||
\(710\) | 19487.1 | + | 26238.3i | 0.0386572 | + | 0.0520498i | ||||
\(711\) | −134983. | + | 233797.i | −0.267017 | + | 0.462487i | ||||
\(712\) | 38423.8 | + | 10295.6i | 0.0757950 | + | 0.0203092i | ||||
\(713\) | −164019. | − | 164019.i | −0.322638 | − | 0.322638i | ||||
\(714\) | −231663. | + | 189612.i | −0.454423 | + | 0.371937i | ||||
\(715\) | 841399. | + | 364086.i | 1.64585 | + | 0.712184i | ||||
\(716\) | −396017. | − | 685921.i | −0.772480 | − | 1.33798i | ||||
\(717\) | 1634.73 | + | 6100.88i | 0.00317985 | + | 0.0118674i | ||||
\(718\) | −580082. | + | 155433.i | −1.12523 | + | 0.301504i | ||||
\(719\) | 851953. | − | 491875.i | 1.64800 | − | 0.951474i | 0.670137 | − | 0.742238i | \(-0.266235\pi\) |
0.977865 | − | 0.209237i | \(-0.0670979\pi\) | |||||||
\(720\) | −200871. | − | 507314.i | −0.387483 | − | 0.978615i | ||||
\(721\) | 519190. | − | 85018.0i | 0.998748 | − | 0.163546i | ||||
\(722\) | 265228. | − | 265228.i | 0.508797 | − | 0.508797i | ||||
\(723\) | 18697.8 | − | 69781.1i | 0.0357696 | − | 0.133494i | ||||
\(724\) | −402397. | − | 232324.i | −0.767676 | − | 0.443218i | ||||
\(725\) | 658115. | − | 154386.i | 1.25206 | − | 0.293720i | ||||
\(726\) | 134076. | + | 232227.i | 0.254378 | + | 0.440595i | ||||
\(727\) | −304919. | + | 304919.i | −0.576920 | + | 0.576920i | −0.934053 | − | 0.357133i | \(-0.883754\pi\) |
0.357133 | + | 0.934053i | \(0.383754\pi\) | |||||||
\(728\) | −145439. | + | 65667.4i | −0.274422 | + | 0.123905i | ||||
\(729\) | 273628.i | 0.514880i | ||||||||
\(730\) | 515800. | + | 408802.i | 0.967911 | + | 0.767126i | ||||
\(731\) | −149201. | + | 258424.i | −0.279214 | + | 0.483613i | ||||
\(732\) | 29271.3 | + | 109242.i | 0.0546286 | + | 0.203877i | ||||
\(733\) | 25537.7 | − | 95307.8i | 0.0475306 | − | 0.177387i | −0.938080 | − | 0.346419i | \(-0.887398\pi\) |
0.985610 | + | 0.169032i | \(0.0540643\pi\) | |||||||
\(734\) | 1.03384e6i | 1.91894i | ||||||||
\(735\) | 144227. | − | 67869.7i | 0.266976 | − | 0.125632i | ||||
\(736\) | −678350. | −1.25227 | ||||||||
\(737\) | 478094. | + | 128105.i | 0.880193 | + | 0.235847i | ||||
\(738\) | −529421. | + | 141858.i | −0.972050 | + | 0.260460i | ||||
\(739\) | 134647. | + | 77738.3i | 0.246551 | + | 0.142346i | 0.618184 | − | 0.786033i | \(-0.287869\pi\) |
−0.371633 | + | 0.928380i | \(0.621202\pi\) | |||||||
\(740\) | −2789.84 | − | 24107.8i | −0.00509467 | − | 0.0440245i | ||||
\(741\) | −131235. | −0.239008 | ||||||||
\(742\) | 325157. | + | 720152.i | 0.590588 | + | 1.30803i | ||||
\(743\) | −10305.6 | − | 10305.6i | −0.0186679 | − | 0.0186679i | 0.697711 | − | 0.716379i | \(-0.254202\pi\) |
−0.716379 | + | 0.697711i | \(0.754202\pi\) | |||||||
\(744\) | −16965.6 | + | 9795.07i | −0.0306494 | + | 0.0176954i | ||||
\(745\) | 345562. | + | 51021.2i | 0.622606 | + | 0.0919260i | ||||
\(746\) | 243364. | − | 421519.i | 0.437299 | − | 0.757424i | ||||
\(747\) | −732261. | − | 196209.i | −1.31228 | − | 0.351623i | ||||
\(748\) | 717077. | + | 717077.i | 1.28163 | + | 1.28163i | ||||
\(749\) | 51916.4 | + | 317045.i | 0.0925425 | + | 0.565141i | ||||
\(750\) | −95102.6 | + | 202134.i | −0.169071 | + | 0.359349i | ||||
\(751\) | −204437. | − | 354095.i | −0.362476 | − | 0.627827i | 0.625891 | − | 0.779910i | \(-0.284735\pi\) |
−0.988368 | + | 0.152083i | \(0.951402\pi\) | |||||||
\(752\) | −65352.9 | − | 243900.i | −0.115566 | − | 0.431297i | ||||
\(753\) | 6670.79 | − | 1787.43i | 0.0117649 | − | 0.00315239i | ||||
\(754\) | −1.01194e6 | + | 584242.i | −1.77996 | + | 1.02766i | ||||
\(755\) | −216047. | + | 85543.8i | −0.379013 | + | 0.150070i | ||||
\(756\) | −165828. | − | 202604.i | −0.290144 | − | 0.354490i | ||||
\(757\) | 227547. | − | 227547.i | 0.397081 | − | 0.397081i | −0.480121 | − | 0.877202i | \(-0.659407\pi\) |
0.877202 | + | 0.480121i | \(0.159407\pi\) | |||||||
\(758\) | 148083. | − | 552655.i | 0.257732 | − | 0.961868i | ||||
\(759\) | −214464. | − | 123821.i | −0.372281 | − | 0.214936i | ||||
\(760\) | 59576.9 | + | 80217.2i | 0.103146 | + | 0.138880i | ||||
\(761\) | −276869. | − | 479550.i | −0.478084 | − | 0.828066i | 0.521600 | − | 0.853190i | \(-0.325335\pi\) |
−0.999684 | + | 0.0251240i | \(0.992002\pi\) | |||||||
\(762\) | 81148.9 | − | 81148.9i | 0.139757 | − | 0.139757i | ||||
\(763\) | 70342.2 | − | 704702.i | 0.120828 | − | 1.21048i | ||||
\(764\) | 230448.i | 0.394809i | ||||||||
\(765\) | −90816.9 | − | 784774.i | −0.155183 | − | 1.34098i | ||||
\(766\) | −82968.4 | + | 143706.i | −0.141402 | + | 0.244915i | ||||
\(767\) | 90764.5 | + | 338738.i | 0.154285 | + | 0.575801i | ||||
\(768\) | −56974.4 | + | 212631.i | −0.0965956 | + | 0.360500i | ||||
\(769\) | − | 1.09700e6i | − | 1.85504i | −0.373774 | − | 0.927520i | \(-0.621936\pi\) | ||
0.373774 | − | 0.927520i | \(-0.378064\pi\) | |||||||
\(770\) | −618966. | − | 1.03418e6i | −1.04396 | − | 1.74428i | ||||
\(771\) | 169284. | 0.284778 | ||||||||
\(772\) | 403796. | + | 108197.i | 0.677529 | + | 0.181543i | ||||
\(773\) | 456971. | − | 122445.i | 0.764768 | − | 0.204919i | 0.144709 | − | 0.989474i | \(-0.453775\pi\) |
0.620059 | + | 0.784555i | \(0.287109\pi\) | |||||||
\(774\) | −240760. | − | 139003.i | −0.401886 | − | 0.232029i | ||||
\(775\) | −271977. | − | 82103.2i | −0.452824 | − | 0.136696i | ||||
\(776\) | 41273.9 | 0.0685412 | ||||||||
\(777\) | 4002.88 | + | 8865.51i | 0.00663026 | + | 0.0146846i | ||||
\(778\) | 739953. | + | 739953.i | 1.22249 | + | 1.22249i | ||||
\(779\) | 293623. | − | 169523.i | 0.483855 | − | 0.279354i | ||||
\(780\) | 25268.1 | − | 171138.i | 0.0415320 | − | 0.281292i | ||||
\(781\) | −22188.0 | + | 38430.8i | −0.0363761 | + | 0.0630053i | ||||
\(782\) | −1.13402e6 | − | 303859.i | −1.85441 | − | 0.496888i | ||||
\(783\) | 314685. | + | 314685.i | 0.513279 | + | 0.513279i | ||||
\(784\) | 694659. | + | 140075.i | 1.13016 | + | 0.227892i | ||||
\(785\) | 39674.5 | − | 91687.3i | 0.0643832 | − | 0.148789i | ||||
\(786\) | −181292. | − | 314008.i | −0.293450 | − | 0.508271i | ||||
\(787\) | −143585. | − | 535866.i | −0.231824 | − | 0.865180i | −0.979555 | − | 0.201178i | \(-0.935523\pi\) |
0.747731 | − | 0.664002i | \(-0.231143\pi\) | |||||||
\(788\) | −605163. | + | 162153.i | −0.974585 | + | 0.261139i | ||||
\(789\) | 89367.5 | − | 51596.3i | 0.143557 | − | 0.0828829i | ||||
\(790\) | 450964. | + | 195139.i | 0.722583 | + | 0.312673i | ||||
\(791\) | −153640. | + | 406589.i | −0.245556 | + | 0.649834i | ||||
\(792\) | 155082. | − | 155082.i | 0.247236 | − | 0.247236i | ||||
\(793\) | −170337. | + | 635705.i | −0.270871 | + | 1.01090i | ||||
\(794\) | −341887. | − | 197388.i | −0.542302 | − | 0.313098i | ||||
\(795\) | 196713. | + | 29044.2i | 0.311243 | + | 0.0459541i | ||||
\(796\) | 168608. | + | 292038.i | 0.266104 | + | 0.460906i | ||||
\(797\) | 717641. | − | 717641.i | 1.12977 | − | 1.12977i | 0.139557 | − | 0.990214i | \(-0.455432\pi\) |
0.990214 | − | 0.139557i | \(-0.0445678\pi\) | |||||||
\(798\) | 140106. | + | 100678.i | 0.220015 | + | 0.158098i | ||||
\(799\) | − | 365595.i | − | 0.572673i | ||||||
\(800\) | −732203. | + | 392641.i | −1.14407 | + | 0.613501i | ||||
\(801\) | −90627.1 | + | 156971.i | −0.141252 | + | 0.244655i | ||||
\(802\) | 48203.6 | + | 179898.i | 0.0749430 | + | 0.279691i | ||||
\(803\) | −231285. | + | 863167.i | −0.358688 | + | 1.33864i | ||||
\(804\) | − | 93395.7i | − | 0.144482i | ||||||
\(805\) | 546206. | + | 304004.i | 0.842878 | + | 0.469124i | ||||
\(806\) | 491088. | 0.755943 | ||||||||
\(807\) | 1503.10 | + | 402.755i | 0.00230803 | + | 0.000618434i | ||||
\(808\) | −173640. | + | 46526.7i | −0.265967 | + | 0.0712655i | ||||
\(809\) | 478893. | + | 276489.i | 0.731715 | + | 0.422456i | 0.819049 | − | 0.573723i | \(-0.194502\pi\) |
−0.0873344 | + | 0.996179i | \(0.527835\pi\) | |||||||
\(810\) | 654763. | − | 75771.6i | 0.997963 | − | 0.115488i | ||||
\(811\) | −819126. | −1.24540 | −0.622700 | − | 0.782461i | \(-0.713964\pi\) | ||||
−0.622700 | + | 0.782461i | \(0.713964\pi\) | |||||||
\(812\) | 684792. | + | 68354.8i | 1.03860 | + | 0.103671i | ||||
\(813\) | −104758. | − | 104758.i | −0.158492 | − | 0.158492i | ||||
\(814\) | 63697.3 | − | 36775.6i | 0.0961329 | − | 0.0555024i | ||||
\(815\) | −415368. | + | 308492.i | −0.625343 | + | 0.464439i | ||||
\(816\) | −167464. | + | 290056.i | −0.251501 | + | 0.435613i | ||||
\(817\) | 166112. | + | 44509.5i | 0.248861 | + | 0.0666820i | ||||
\(818\) | −833442. | − | 833442.i | −1.24557 | − | 1.24557i | ||||
\(819\) | −117500. | − | 717555.i | −0.175175 | − | 1.06976i | ||||
\(820\) | 164534. | + | 415542.i | 0.244697 | + | 0.617999i | ||||
\(821\) | 22394.6 | + | 38788.6i | 0.0332244 | + | 0.0575464i | 0.882159 | − | 0.470951i | \(-0.156089\pi\) |
−0.848935 | + | 0.528497i | \(0.822756\pi\) | |||||||
\(822\) | −101598. | − | 379171.i | −0.150364 | − | 0.561166i | ||||
\(823\) | 578524. | − | 155015.i | 0.854125 | − | 0.228862i | 0.194914 | − | 0.980820i | \(-0.437557\pi\) |
0.659211 | + | 0.751958i | \(0.270890\pi\) | |||||||
\(824\) | 150905. | − | 87125.0i | 0.222254 | − | 0.128318i | ||||
\(825\) | −303159. | − | 9515.35i | −0.445413 | − | 0.0139803i | ||||
\(826\) | 162965. | − | 431267.i | 0.238854 | − | 0.632100i | ||||
\(827\) | −207885. | + | 207885.i | −0.303956 | + | 0.303956i | −0.842560 | − | 0.538603i | \(-0.818952\pi\) |
0.538603 | + | 0.842560i | \(0.318952\pi\) | |||||||
\(828\) | 126825. | − | 473316.i | 0.184988 | − | 0.690383i | ||||
\(829\) | −367785. | − | 212341.i | −0.535161 | − | 0.308975i | 0.207954 | − | 0.978139i | \(-0.433319\pi\) |
−0.743116 | + | 0.669163i | \(0.766653\pi\) | |||||||
\(830\) | −201543. | + | 1.36503e6i | −0.292558 | + | 1.98147i | ||||
\(831\) | 123758. | + | 214355.i | 0.179214 | + | 0.310408i | ||||
\(832\) | 345456. | − | 345456.i | 0.499052 | − | 0.499052i | ||||
\(833\) | 919018. | + | 456216.i | 1.32445 | + | 0.657477i | ||||
\(834\) | − | 143292.i | − | 0.206011i | ||||||
\(835\) | −148481. | + | 17182.8i | −0.212960 | + | 0.0246446i | ||||
\(836\) | 292217. | − | 506135.i | 0.418112 | − | 0.724192i | ||||
\(837\) | −48408.8 | − | 180664.i | −0.0690992 | − | 0.257882i | ||||
\(838\) | 12248.3 | − | 45711.3i | 0.0174417 | − | 0.0650932i | ||||
\(839\) | 311599.i | 0.442661i | 0.975199 | + | 0.221331i | \(0.0710400\pi\) | ||||
−0.975199 | + | 0.221331i | \(0.928960\pi\) | |||||||
\(840\) | 36739.3 | − | 37913.2i | 0.0520682 | − | 0.0537318i | ||||
\(841\) | −462512. | −0.653930 | ||||||||
\(842\) | −479614. | − | 128512.i | −0.676500 | − | 0.181267i | ||||
\(843\) | 314298. | − | 84216.0i | 0.442270 | − | 0.118506i | ||||
\(844\) | −639762. | − | 369367.i | −0.898118 | − | 0.518529i | ||||
\(845\) | 181783. | − | 229362.i | 0.254589 | − | 0.321224i | ||||
\(846\) | 340606. | 0.475896 | ||||||||
\(847\) | 536305. | − | 746339.i | 0.747558 | − | 1.04033i | ||||
\(848\) | 625093. | + | 625093.i | 0.869266 | + | 0.869266i | ||||
\(849\) | −5713.81 | + | 3298.87i | −0.00792703 | + | 0.00457667i | ||||
\(850\) | −1.39992e6 | + | 328406.i | −1.93761 | + | 0.454542i | ||||
\(851\) | −19073.7 | + | 33036.6i | −0.0263375 | + | 0.0456179i | ||||
\(852\) | 8088.16 | + | 2167.22i | 0.0111422 | + | 0.00298554i | ||||
\(853\) | −414829. | − | 414829.i | −0.570126 | − | 0.570126i | 0.362038 | − | 0.932163i | \(-0.382081\pi\) |
−0.932163 | + | 0.362038i | \(0.882081\pi\) | |||||||
\(854\) | 669537. | − | 548004.i | 0.918034 | − | 0.751395i | ||||
\(855\) | −423315. | + | 167612.i | −0.579070 | + | 0.229283i | ||||
\(856\) | 53203.0 | + | 92150.4i | 0.0726087 | + | 0.125762i | ||||
\(857\) | 52634.5 | + | 196434.i | 0.0716652 | + | 0.267458i | 0.992456 | − | 0.122597i | \(-0.0391224\pi\) |
−0.920791 | + | 0.390056i | \(0.872456\pi\) | |||||||
\(858\) | 506427. | − | 135697.i | 0.687927 | − | 0.184329i | ||||
\(859\) | −887266. | + | 512263.i | −1.20245 | + | 0.694236i | −0.961100 | − | 0.276202i | \(-0.910924\pi\) |
−0.241352 | + | 0.970438i | \(0.577591\pi\) | |||||||
\(860\) | −90026.4 | + | 208050.i | −0.121723 | + | 0.281300i | ||||
\(861\) | −113461. | − | 138624.i | −0.153053 | − | 0.186996i | ||||
\(862\) | 622197. | − | 622197.i | 0.837362 | − | 0.837362i | ||||
\(863\) | −137639. | + | 513675.i | −0.184808 | + | 0.689711i | 0.809864 | + | 0.586617i | \(0.199541\pi\) |
−0.994672 | + | 0.103094i | \(0.967126\pi\) | |||||||
\(864\) | −473700. | − | 273491.i | −0.634564 | − | 0.366366i | ||||
\(865\) | 270381. | − | 200811.i | 0.361363 | − | 0.268383i | ||||
\(866\) | −401830. | − | 695990.i | −0.535805 | − | 0.928041i | ||||
\(867\) | −186069. | + | 186069.i | −0.247535 | + | 0.247535i | ||||
\(868\) | −234880. | − | 168780.i | −0.311751 | − | 0.224018i | ||||
\(869\) | 667167.i | 0.883477i | ||||||||
\(870\) | 240116. | − | 302963.i | 0.317236 | − | 0.400268i | ||||
\(871\) | 271746. | − | 470678.i | 0.358201 | − | 0.620422i | ||||
\(872\) | −60709.3 | − | 226570.i | −0.0798403 | − | 0.297968i | ||||
\(873\) | −48674.6 | + | 181656.i | −0.0638667 | + | 0.238354i | ||||
\(874\) | 676597.i | 0.885742i | ||||||||
\(875\) | 765531. | + | 11985.1i | 0.999877 | + | 0.0156540i | ||||
\(876\) | 168620. | 0.219736 | ||||||||
\(877\) | −337723. | − | 90492.7i | −0.439099 | − | 0.117656i | 0.0324955 | − | 0.999472i | \(-0.489655\pi\) |
−0.471594 | + | 0.881816i | \(0.656321\pi\) | |||||||
\(878\) | 1.44112e6 | − | 386147.i | 1.86944 | − | 0.500914i | ||||
\(879\) | −360274. | − | 208004.i | −0.466289 | − | 0.269212i | ||||
\(880\) | −1.05677e6 | − | 837553.i | −1.36463 | − | 1.08155i | ||||
\(881\) | 81328.2 | 0.104783 | 0.0523913 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523913 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(882\) | −425034. | + | 856203.i | −0.546369 | + | 1.10063i | ||||
\(883\) | −563002. | − | 563002.i | −0.722085 | − | 0.722085i | 0.246945 | − | 0.969030i | \(-0.420573\pi\) |
−0.969030 | + | 0.246945i | \(0.920573\pi\) | |||||||
\(884\) | 964351. | − | 556768.i | 1.23404 | − | 0.712475i | ||||
\(885\) | −69175.8 | − | 93141.5i | −0.0883218 | − | 0.118921i | ||||
\(886\) | −423971. | + | 734340.i | −0.540093 | + | 0.935469i | ||||
\(887\) | −890520. | − | 238614.i | −1.13187 | − | 0.303283i | −0.356192 | − | 0.934413i | \(-0.615925\pi\) |
−0.775677 | + | 0.631130i | \(0.782592\pi\) | |||||||
\(888\) | 2278.12 | + | 2278.12i | 0.00288903 | + | 0.00288903i | ||||
\(889\) | −367933. | − | 139033.i | −0.465549 | − | 0.175919i | ||||
\(890\) | 302776. | + | 131016.i | 0.382245 | + | 0.165403i | ||||
\(891\) | 447472. | + | 775044.i | 0.563651 | + | 0.976273i | ||||
\(892\) | 172081. | + | 642216.i | 0.216274 | + | 0.807145i | ||||
\(893\) | −203516. | + | 54531.9i | −0.255209 | + | 0.0683830i | ||||
\(894\) | 172998. | − | 99880.4i | 0.216454 | − | 0.124970i | ||||
\(895\) | 561356. | + | 1.41774e6i | 0.700797 | + | 1.76991i | ||||
\(896\) | 394675. | − | 64628.4i | 0.491613 | − | 0.0805022i | ||||
\(897\) | −192279. | + | 192279.i | −0.238972 | + | 0.238972i | ||||
\(898\) | 358841. | − | 1.33921e6i | 0.444989 | − | 1.66072i | ||||
\(899\) | 425771. | + | 245819.i | 0.526813 | + | 0.304156i | ||||
\(900\) | −137070. | − | 584300.i | −0.169223 | − | 0.721358i | ||||
\(901\) | 639973. | + | 1.10846e6i | 0.788337 | + | 1.36544i | ||||
\(902\) | −957787. | + | 957787.i | −1.17722 | + | 1.17722i | ||||
\(903\) | 9024.86 | − | 90412.8i | 0.0110679 | − | 0.110880i | ||||
\(904\) | 143959.i | 0.176158i | ||||||||
\(905\) | 701062. | + | 555633.i | 0.855971 | + | 0.678407i | ||||
\(906\) | −66442.2 | + | 115081.i | −0.0809446 | + | 0.140200i | ||||
\(907\) | −96015.0 | − | 358333.i | −0.116714 | − | 0.435584i | 0.882695 | − | 0.469946i | \(-0.155727\pi\) |
−0.999409 | + | 0.0343621i | \(0.989060\pi\) | |||||||
\(908\) | −113751. | + | 424526.i | −0.137970 | + | 0.514912i | ||||
\(909\) | − | 819101.i | − | 0.991310i | ||||||
\(910\) | −1.27280e6 | + | 362587.i | −1.53702 | + | 0.437854i | ||||
\(911\) | −99694.8 | −0.120126 | −0.0600628 | − | 0.998195i | \(-0.519130\pi\) | ||||
−0.0600628 | + | 0.998195i | \(0.519130\pi\) | |||||||
\(912\) | 186444. | + | 49957.6i | 0.224161 | + | 0.0600637i | ||||
\(913\) | −1.80964e6 | + | 484892.i | −2.17096 | + | 0.581706i | ||||
\(914\) | 626564. | + | 361747.i | 0.750020 | + | 0.433024i | ||||
\(915\) | −25029.9 | − | 216290.i | −0.0298962 | − | 0.258342i | ||||
\(916\) | 360145. | 0.429226 | ||||||||
\(917\) | −725168. | + | 1.00917e6i | −0.862383 | + | 1.20012i | ||||
\(918\) | −669390. | − | 669390.i | −0.794317 | − | 0.794317i | ||||
\(919\) | 237310. | − | 137011.i | 0.280986 | − | 0.162227i | −0.352884 | − | 0.935667i | \(-0.614799\pi\) |
0.633870 | + | 0.773440i | \(0.281466\pi\) | |||||||
\(920\) | 204820. | + | 30241.1i | 0.241989 | + | 0.0357291i | ||||
\(921\) | −213847. | + | 370394.i | −0.252106 | + | 0.436661i | ||||
\(922\) | 1.47683e6 | + | 395716.i | 1.73728 | + | 0.465502i | ||||
\(923\) | 34455.4 | + | 34455.4i | 0.0404439 | + | 0.0404439i | ||||
\(924\) | −288854. | − | 109151.i | −0.338326 | − | 0.127845i | ||||
\(925\) | −1465.77 | + | 46699.4i | −0.00171310 | + | 0.0545793i | ||||
\(926\) | 359504. | + | 622679.i | 0.419258 | + | 0.726177i | ||||
\(927\) | 205494. | + | 766916.i | 0.239134 | + | 0.892459i | ||||
\(928\) | 1.38878e6 | − | 372123.i | 1.61264 | − | 0.432106i | ||||
\(929\) | 706681. | − | 408002.i | 0.818826 | − | 0.472750i | −0.0311852 | − | 0.999514i | \(-0.509928\pi\) |
0.850012 | + | 0.526764i | \(0.176595\pi\) | |||||||
\(930\) | −151059. | + | 59812.0i | −0.174655 | + | 0.0691548i | ||||
\(931\) | 116882. | − | 579640.i | 0.134849 | − | 0.668742i | ||||
\(932\) | −131582. | + | 131582.i | −0.151483 | + | 0.151483i | ||||
\(933\) | −103594. | + | 386616.i | −0.119006 | + | 0.444137i | ||||
\(934\) | 647155. | + | 373635.i | 0.741848 | + | 0.428306i | ||||
\(935\) | −1.16408e6 | − | 1.56737e6i | −1.33155 | − | 1.79286i | ||||
\(936\) | −120412. | − | 208560.i | −0.137442 | − | 0.238057i | ||||
\(937\) | 179128. | − | 179128.i | 0.204025 | − | 0.204025i | −0.597697 | − | 0.801722i | \(-0.703917\pi\) |
0.801722 | + | 0.597697i | \(0.203917\pi\) | |||||||
\(938\) | −651199. | + | 294024.i | −0.740130 | + | 0.334177i | ||||
\(939\) | 252512.i | 0.286386i | ||||||||
\(940\) | −31927.8 | − | 275897.i | −0.0361337 | − | 0.312242i | ||||
\(941\) | −246028. | + | 426133.i | −0.277847 | + | 0.481245i | −0.970849 | − | 0.239690i | \(-0.922954\pi\) |
0.693003 | + | 0.720935i | \(0.256287\pi\) | |||||||
\(942\) | −14786.9 | − | 55185.5i | −0.0166638 | − | 0.0621903i | ||||
\(943\) | 181825. | − | 678581.i | 0.204471 | − | 0.763094i | ||||
\(944\) | − | 515794.i | − | 0.578805i | ||||||
\(945\) | 258857. | + | 432504.i | 0.289865 | + | 0.484313i | ||||
\(946\) | −687038. | −0.767712 | ||||||||
\(947\) | −696222. | − | 186552.i | −0.776333 | − | 0.208018i | −0.151165 | − | 0.988508i | \(-0.548303\pi\) |
−0.625167 | + | 0.780491i | \(0.714969\pi\) | |||||||
\(948\) | 121601. | − | 32582.8i | 0.135307 | − | 0.0362554i | ||||
\(949\) | 849778. | + | 490620.i | 0.943568 | + | 0.544769i | ||||
\(950\) | 391626. | + | 730311.i | 0.433935 | + | 0.809209i | ||||
\(951\) | 231549. | 0.256025 | ||||||||
\(952\) | 338147. | + | 33753.2i | 0.373105 | + | 0.0372427i | ||||
\(953\) | 286553. | + | 286553.i | 0.315514 | + | 0.315514i | 0.847041 | − | 0.531527i | \(-0.178382\pi\) |
−0.531527 | + | 0.847041i | \(0.678382\pi\) | |||||||
\(954\) | −1.03270e6 | + | 596230.i | −1.13469 | + | 0.655114i | ||||
\(955\) | 64803.0 | − | 438904.i | 0.0710540 | − | 0.481242i | ||||
\(956\) | −15442.9 | + | 26747.9i | −0.0168971 | + | 0.0292667i | ||||
\(957\) | 506994. | + | 135849.i | 0.553578 | + | 0.148331i | ||||
\(958\) | −1.59442e6 | − | 1.59442e6i | −1.73729 | − | 1.73729i | ||||
\(959\) | −1.04111e6 | + | 852133.i | −1.13204 | + | 0.926553i | ||||
\(960\) | −64188.0 | + | 148338.i | −0.0696484 | + | 0.160957i | ||||
\(961\) | 358448. | + | 620851.i | 0.388132 | + | 0.672265i | ||||
\(962\) | −20903.1 | − | 78011.3i | −0.0225871 | − | 0.0842961i | ||||
\(963\) | −468319. | + | 125486.i | −0.504997 | + | 0.135314i | ||||
\(964\) | 305939. | − | 176634.i | 0.329216 | − | 0.190073i | ||||
\(965\) | −738631. | − | 319617.i | −0.793183 | − | 0.343222i | ||||
\(966\) | 352785. | − | 57769.0i | 0.378056 | − | 0.0619071i | ||||
\(967\) | −933227. | + | 933227.i | −0.998009 | + | 0.998009i | −0.999998 | − | 0.00198883i | \(-0.999367\pi\) |
0.00198883 | + | 0.999998i | \(0.499367\pi\) | |||||||
\(968\) | 78783.1 | − | 294023.i | 0.0840780 | − | 0.313784i | ||||
\(969\) | 242029. | + | 139736.i | 0.257763 | + | 0.148819i | ||||
\(970\) | 338631. | + | 49998.0i | 0.359901 | + | 0.0531385i | ||||
\(971\) | 698116. | + | 1.20917e6i | 0.740439 | + | 1.28248i | 0.952296 | + | 0.305177i | \(0.0987157\pi\) |
−0.211856 | + | 0.977301i | \(0.567951\pi\) | |||||||
\(972\) | 425442. | − | 425442.i | 0.450307 | − | 0.450307i | ||||
\(973\) | −447598. | + | 202096.i | −0.472784 | + | 0.213467i | ||||
\(974\) | − | 539791.i | − | 0.568994i | ||||||
\(975\) | −96249.4 | + | 318838.i | −0.101249 | + | 0.335399i | ||||
\(976\) | 483992. | − | 838300.i | 0.508088 | − | 0.880034i | ||||
\(977\) | −374168. | − | 1.39641e6i | −0.391992 | − | 1.46294i | −0.826843 | − | 0.562433i | \(-0.809865\pi\) |
0.434850 | − | 0.900503i | \(-0.356801\pi\) | |||||||
\(978\) | −76580.9 | + | 285804.i | −0.0800650 | + | 0.298807i | ||||
\(979\) | 447935.i | 0.467358i | ||||||||
\(980\) | 733380. | + | 264025.i | 0.763620 | + | 0.274912i | ||||
\(981\) | 1.06878e6 | 1.11059 | ||||||||
\(982\) | −438955. | − | 117618.i | −0.455195 | − | 0.121969i | ||||
\(983\) | −733036. | + | 196416.i | −0.758610 | + | 0.203269i | −0.617334 | − | 0.786701i | \(-0.711787\pi\) |
−0.141276 | + | 0.989970i | \(0.545121\pi\) | |||||||
\(984\) | −51382.7 | − | 29665.8i | −0.0530672 | − | 0.0306384i | ||||
\(985\) | 1.19817e6 | − | 138657.i | 1.23494 | − | 0.142912i | ||||
\(986\) | 2.48835e6 | 2.55951 | ||||||||
\(987\) | 45810.1 | + | 101459.i | 0.0470248 | + | 0.104150i | ||||
\(988\) | −453779. | − | 453779.i | −0.464869 | − | 0.464869i | ||||
\(989\) | 308592. | − | 178166.i | 0.315495 | − | 0.182151i | ||||
\(990\) | 1.46024e6 | − | 1.08451e6i | 1.48988 | − | 1.10653i | ||||
\(991\) | 28543.0 | − | 49438.0i | 0.0290638 | − | 0.0503400i | −0.851128 | − | 0.524959i | \(-0.824081\pi\) |
0.880191 | + | 0.474619i | \(0.157414\pi\) | |||||||
\(992\) | −583673. | − | 156395.i | −0.593125 | − | 0.158927i | ||||
\(993\) | 343046. | + | 343046.i | 0.347899 | + | 0.347899i | ||||
\(994\) | −10351.9 | − | 63217.2i | −0.0104772 | − | 0.0639827i | ||||
\(995\) | −239003. | − | 603618.i | −0.241411 | − | 0.609700i | ||||
\(996\) | 176757. | + | 306152.i | 0.178180 | + | 0.308616i | ||||
\(997\) | 120359. | + | 449187.i | 0.121085 | + | 0.451894i | 0.999670 | − | 0.0256914i | \(-0.00817874\pi\) |
−0.878585 | + | 0.477586i | \(0.841512\pi\) | |||||||
\(998\) | −1.04390e6 | + | 279712.i | −1.04809 | + | 0.280834i | ||||
\(999\) | −26638.7 | + | 15379.9i | −0.0266921 | + | 0.0154107i |
(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 | 35.5.l.a.18.4 | yes | 56 | |
5.2 | odd | 4 | inner | 35.5.l.a.32.11 | yes | 56 | |
7.2 | even | 3 | inner | 35.5.l.a.23.11 | yes | 56 | |
35.2 | odd | 12 | inner | 35.5.l.a.2.4 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.l.a.2.4 | ✓ | 56 | 35.2 | odd | 12 | inner | |
35.5.l.a.18.4 | yes | 56 | 1.1 | even | 1 | trivial | |
35.5.l.a.23.11 | yes | 56 | 7.2 | even | 3 | inner | |
35.5.l.a.32.11 | yes | 56 | 5.2 | odd | 4 | inner |