Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (of order \(2\), degree \(1\), 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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.15 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.64 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.52059i | − | 1.38015i | −0.723739 | − | 0.690074i | \(-0.757578\pi\) | ||
0.723739 | − | 0.690074i | \(-0.242422\pi\) | |||||||
\(3\) | 4.22607 | + | 7.94609i | 0.469563 | + | 0.882899i | ||||
\(4\) | −14.4769 | −0.904807 | ||||||||
\(5\) | 14.8774i | 0.595095i | 0.954707 | + | 0.297547i | \(0.0961686\pi\) | ||||
−0.954707 | + | 0.297547i | \(0.903831\pi\) | |||||||
\(6\) | 43.8671 | − | 23.3304i | 1.21853 | − | 0.648066i | ||||
\(7\) | 83.7732 | 1.70966 | 0.854829 | − | 0.518910i | \(-0.173662\pi\) | ||||
0.854829 | + | 0.518910i | \(0.173662\pi\) | |||||||
\(8\) | − | 8.40835i | − | 0.131381i | ||||||
\(9\) | −45.2807 | + | 67.1614i | −0.559022 | + | 0.829153i | ||||
\(10\) | 82.1318 | 0.821318 | ||||||||
\(11\) | 224.925i | 1.85889i | 0.368964 | + | 0.929444i | \(0.379713\pi\) | ||||
−0.368964 | + | 0.929444i | \(0.620287\pi\) | |||||||
\(12\) | −61.1804 | − | 115.035i | −0.424864 | − | 0.798853i | ||||
\(13\) | −309.676 | −1.83240 | −0.916201 | − | 0.400719i | \(-0.868761\pi\) | ||||
−0.916201 | + | 0.400719i | \(0.868761\pi\) | |||||||
\(14\) | − | 462.478i | − | 2.35958i | ||||||
\(15\) | −118.217 | + | 62.8727i | −0.525409 | + | 0.279434i | ||||
\(16\) | −278.050 | −1.08613 | ||||||||
\(17\) | 375.087i | 1.29788i | 0.760840 | + | 0.648940i | \(0.224787\pi\) | ||||
−0.760840 | + | 0.648940i | \(0.775213\pi\) | |||||||
\(18\) | 370.771 | + | 249.976i | 1.14435 | + | 0.771532i | ||||
\(19\) | −139.347 | −0.386003 | −0.193002 | − | 0.981198i | \(-0.561822\pi\) | ||||
−0.193002 | + | 0.981198i | \(0.561822\pi\) | |||||||
\(20\) | − | 215.378i | − | 0.538446i | ||||||
\(21\) | 354.031 | + | 665.670i | 0.802792 | + | 1.50946i | ||||
\(22\) | 1241.72 | 2.56554 | ||||||||
\(23\) | − | 571.445i | − | 1.08024i | −0.841589 | − | 0.540118i | \(-0.818380\pi\) | ||
0.841589 | − | 0.540118i | \(-0.181620\pi\) | |||||||
\(24\) | 66.8136 | − | 35.5343i | 0.115996 | − | 0.0616914i | ||||
\(25\) | 403.664 | 0.645862 | ||||||||
\(26\) | 1709.59i | 2.52899i | ||||||||
\(27\) | −725.030 | − | 75.9765i | −0.994554 | − | 0.104220i | ||||
\(28\) | −1212.78 | −1.54691 | ||||||||
\(29\) | 607.695i | 0.722586i | 0.932452 | + | 0.361293i | \(0.117665\pi\) | ||||
−0.932452 | + | 0.361293i | \(0.882335\pi\) | |||||||
\(30\) | 347.095 | + | 652.627i | 0.385661 | + | 0.725141i | ||||
\(31\) | 1380.31 | 1.43633 | 0.718166 | − | 0.695872i | \(-0.244982\pi\) | ||||
0.718166 | + | 0.695872i | \(0.244982\pi\) | |||||||
\(32\) | 1400.46i | 1.36764i | ||||||||
\(33\) | −1787.28 | + | 950.549i | −1.64121 | + | 0.872864i | ||||
\(34\) | 2070.70 | 1.79127 | ||||||||
\(35\) | 1246.33i | 1.01741i | ||||||||
\(36\) | 655.525 | − | 972.290i | 0.505807 | − | 0.750223i | ||||
\(37\) | 595.193 | 0.434765 | 0.217382 | − | 0.976087i | \(-0.430248\pi\) | ||||
0.217382 | + | 0.976087i | \(0.430248\pi\) | |||||||
\(38\) | 769.279i | 0.532742i | ||||||||
\(39\) | −1308.71 | − | 2460.71i | −0.860428 | − | 1.61783i | ||||
\(40\) | 125.094 | 0.0781839 | ||||||||
\(41\) | − | 742.104i | − | 0.441466i | −0.975334 | − | 0.220733i | \(-0.929155\pi\) | ||
0.975334 | − | 0.220733i | \(-0.0708449\pi\) | |||||||
\(42\) | 3674.89 | − | 1954.46i | 2.08327 | − | 1.10797i | ||||
\(43\) | 292.877 | 0.158398 | 0.0791988 | − | 0.996859i | \(-0.474764\pi\) | ||||
0.0791988 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(44\) | − | 3256.22i | − | 1.68193i | ||||||
\(45\) | −999.185 | − | 673.658i | −0.493425 | − | 0.332671i | ||||
\(46\) | −3154.71 | −1.49088 | ||||||||
\(47\) | 534.415i | 0.241926i | 0.992657 | + | 0.120963i | \(0.0385983\pi\) | ||||
−0.992657 | + | 0.120963i | \(0.961402\pi\) | |||||||
\(48\) | −1175.06 | − | 2209.41i | −0.510007 | − | 0.958944i | ||||
\(49\) | 4616.95 | 1.92293 | ||||||||
\(50\) | − | 2228.46i | − | 0.891385i | ||||||
\(51\) | −2980.48 | + | 1585.14i | −1.14590 | + | 0.609436i | ||||
\(52\) | 4483.15 | 1.65797 | ||||||||
\(53\) | 3096.79i | 1.10245i | 0.834356 | + | 0.551226i | \(0.185840\pi\) | ||||
−0.834356 | + | 0.551226i | \(0.814160\pi\) | |||||||
\(54\) | −419.435 | + | 4002.59i | −0.143839 | + | 1.37263i | ||||
\(55\) | −3346.30 | −1.10621 | ||||||||
\(56\) | − | 704.395i | − | 0.224616i | ||||||
\(57\) | −588.891 | − | 1107.27i | −0.181253 | − | 0.340802i | ||||
\(58\) | 3354.84 | 0.997276 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | 1711.42 | − | 910.203i | 0.475393 | − | 0.252834i | ||||
\(61\) | −42.3089 | −0.0113703 | −0.00568515 | − | 0.999984i | \(-0.501810\pi\) | ||||
−0.00568515 | + | 0.999984i | \(0.501810\pi\) | |||||||
\(62\) | − | 7620.15i | − | 1.98235i | ||||||
\(63\) | −3793.31 | + | 5626.33i | −0.955736 | + | 1.41757i | ||||
\(64\) | 3282.59 | 0.801415 | ||||||||
\(65\) | − | 4607.16i | − | 1.09045i | ||||||
\(66\) | 5247.59 | + | 9866.83i | 1.20468 | + | 2.26511i | ||||
\(67\) | 1858.73 | 0.414063 | 0.207032 | − | 0.978334i | \(-0.433620\pi\) | ||||
0.207032 | + | 0.978334i | \(0.433620\pi\) | |||||||
\(68\) | − | 5430.11i | − | 1.17433i | ||||||
\(69\) | 4540.75 | − | 2414.96i | 0.953739 | − | 0.507239i | ||||
\(70\) | 6880.45 | 1.40417 | ||||||||
\(71\) | − | 3827.45i | − | 0.759264i | −0.925138 | − | 0.379632i | \(-0.876051\pi\) | ||
0.925138 | − | 0.379632i | \(-0.123949\pi\) | |||||||
\(72\) | 564.717 | + | 380.737i | 0.108935 | + | 0.0734446i | ||||
\(73\) | 8263.85 | 1.55073 | 0.775366 | − | 0.631512i | \(-0.217565\pi\) | ||||
0.775366 | + | 0.631512i | \(0.217565\pi\) | |||||||
\(74\) | − | 3285.82i | − | 0.600040i | ||||||
\(75\) | 1705.91 | + | 3207.55i | 0.303273 | + | 0.570231i | ||||
\(76\) | 2017.32 | 0.349259 | ||||||||
\(77\) | 18842.7i | 3.17806i | ||||||||
\(78\) | −13584.6 | + | 7224.86i | −2.23284 | + | 1.18752i | ||||
\(79\) | −4676.83 | −0.749371 | −0.374686 | − | 0.927152i | \(-0.622249\pi\) | ||||
−0.374686 | + | 0.927152i | \(0.622249\pi\) | |||||||
\(80\) | − | 4136.65i | − | 0.646351i | ||||||
\(81\) | −2460.31 | − | 6082.24i | −0.374990 | − | 0.927029i | ||||
\(82\) | −4096.85 | −0.609288 | ||||||||
\(83\) | − | 3665.27i | − | 0.532047i | −0.963967 | − | 0.266024i | \(-0.914290\pi\) | ||
0.963967 | − | 0.266024i | \(-0.0857099\pi\) | |||||||
\(84\) | −5125.28 | − | 9636.84i | −0.726371 | − | 1.36577i | ||||
\(85\) | −5580.31 | −0.772362 | ||||||||
\(86\) | − | 1616.86i | − | 0.218612i | ||||||
\(87\) | −4828.80 | + | 2568.16i | −0.637971 | + | 0.339300i | ||||
\(88\) | 1891.25 | 0.244222 | ||||||||
\(89\) | − | 2164.68i | − | 0.273283i | −0.990621 | − | 0.136642i | \(-0.956369\pi\) | ||
0.990621 | − | 0.136642i | \(-0.0436309\pi\) | |||||||
\(90\) | −3718.99 | + | 5516.09i | −0.459135 | + | 0.680999i | ||||
\(91\) | −25942.6 | −3.13278 | ||||||||
\(92\) | 8272.75i | 0.977405i | ||||||||
\(93\) | 5833.30 | + | 10968.1i | 0.674448 | + | 1.26814i | ||||
\(94\) | 2950.29 | 0.333894 | ||||||||
\(95\) | − | 2073.12i | − | 0.229709i | ||||||
\(96\) | −11128.2 | + | 5918.45i | −1.20749 | + | 0.642193i | ||||
\(97\) | 5523.27 | 0.587020 | 0.293510 | − | 0.955956i | \(-0.405177\pi\) | ||||
0.293510 | + | 0.955956i | \(0.405177\pi\) | |||||||
\(98\) | − | 25488.3i | − | 2.65393i | ||||||
\(99\) | −15106.3 | − | 10184.8i | −1.54130 | − | 1.03916i | ||||
\(100\) | −5843.81 | −0.584381 | ||||||||
\(101\) | − | 2906.57i | − | 0.284930i | −0.989800 | − | 0.142465i | \(-0.954497\pi\) | ||
0.989800 | − | 0.142465i | \(-0.0455028\pi\) | |||||||
\(102\) | 8750.93 | + | 16454.0i | 0.841112 | + | 1.58151i | ||||
\(103\) | −10723.3 | −1.01077 | −0.505387 | − | 0.862893i | \(-0.668650\pi\) | ||||
−0.505387 | + | 0.862893i | \(0.668650\pi\) | |||||||
\(104\) | 2603.87i | 0.240742i | ||||||||
\(105\) | −9903.41 | + | 5267.05i | −0.898269 | + | 0.477737i | ||||
\(106\) | 17096.1 | 1.52155 | ||||||||
\(107\) | − | 10516.9i | − | 0.918585i | −0.888285 | − | 0.459293i | \(-0.848103\pi\) | ||
0.888285 | − | 0.459293i | \(-0.151897\pi\) | |||||||
\(108\) | 10496.2 | + | 1099.91i | 0.899880 | + | 0.0942991i | ||||
\(109\) | −2290.88 | −0.192819 | −0.0964094 | − | 0.995342i | \(-0.530736\pi\) | ||||
−0.0964094 | + | 0.995342i | \(0.530736\pi\) | |||||||
\(110\) | 18473.5i | 1.52674i | ||||||||
\(111\) | 2515.32 | + | 4729.46i | 0.204149 | + | 0.383853i | ||||
\(112\) | −23293.1 | −1.85691 | ||||||||
\(113\) | − | 9161.51i | − | 0.717481i | −0.933437 | − | 0.358740i | \(-0.883206\pi\) | ||
0.933437 | − | 0.358740i | \(-0.116794\pi\) | |||||||
\(114\) | −6112.76 | + | 3251.02i | −0.470357 | + | 0.250156i | ||||
\(115\) | 8501.59 | 0.642843 | ||||||||
\(116\) | − | 8797.55i | − | 0.653801i | ||||||
\(117\) | 14022.4 | − | 20798.3i | 1.02435 | − | 1.51934i | ||||
\(118\) | −2501.86 | −0.179680 | ||||||||
\(119\) | 31422.3i | 2.21893i | ||||||||
\(120\) | 528.656 | + | 994.010i | 0.0367122 | + | 0.0690285i | ||||
\(121\) | −35950.4 | −2.45546 | ||||||||
\(122\) | 233.570i | 0.0156927i | ||||||||
\(123\) | 5896.83 | − | 3136.18i | 0.389770 | − | 0.207296i | ||||
\(124\) | −19982.7 | −1.29960 | ||||||||
\(125\) | 15303.8i | 0.979444i | ||||||||
\(126\) | 31060.6 | + | 20941.3i | 1.95645 | + | 1.31906i | ||||
\(127\) | 15749.1 | 0.976447 | 0.488223 | − | 0.872719i | \(-0.337645\pi\) | ||||
0.488223 | + | 0.872719i | \(0.337645\pi\) | |||||||
\(128\) | 4285.57i | 0.261571i | ||||||||
\(129\) | 1237.72 | + | 2327.23i | 0.0743777 | + | 0.139849i | ||||
\(130\) | −25434.3 | −1.50499 | ||||||||
\(131\) | − | 17476.7i | − | 1.01839i | −0.860650 | − | 0.509197i | \(-0.829942\pi\) | ||
0.860650 | − | 0.509197i | \(-0.170058\pi\) | |||||||
\(132\) | 25874.3 | − | 13761.0i | 1.48498 | − | 0.789774i | ||||
\(133\) | −11673.6 | −0.659934 | ||||||||
\(134\) | − | 10261.3i | − | 0.571468i | ||||||
\(135\) | 1130.33 | − | 10786.5i | 0.0620209 | − | 0.591854i | ||||
\(136\) | 3153.87 | 0.170516 | ||||||||
\(137\) | 6131.87i | 0.326702i | 0.986568 | + | 0.163351i | \(0.0522303\pi\) | ||||
−0.986568 | + | 0.163351i | \(0.947770\pi\) | |||||||
\(138\) | −13332.0 | − | 25067.6i | −0.700064 | − | 1.31630i | ||||
\(139\) | 32312.4 | 1.67240 | 0.836198 | − | 0.548427i | \(-0.184773\pi\) | ||||
0.836198 | + | 0.548427i | \(0.184773\pi\) | |||||||
\(140\) | − | 18042.9i | − | 0.920558i | ||||||
\(141\) | −4246.51 | + | 2258.47i | −0.213596 | + | 0.113600i | ||||
\(142\) | −21129.8 | −1.04790 | ||||||||
\(143\) | − | 69654.0i | − | 3.40623i | ||||||
\(144\) | 12590.3 | − | 18674.2i | 0.607171 | − | 0.900569i | ||||
\(145\) | −9040.91 | −0.430007 | ||||||||
\(146\) | − | 45621.3i | − | 2.14024i | ||||||
\(147\) | 19511.5 | + | 36686.7i | 0.902936 | + | 1.69775i | ||||
\(148\) | −8616.56 | −0.393378 | ||||||||
\(149\) | 36060.2i | 1.62426i | 0.583476 | + | 0.812131i | \(0.301692\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(150\) | 17707.6 | − | 9417.63i | 0.787003 | − | 0.418561i | ||||
\(151\) | 9345.67 | 0.409880 | 0.204940 | − | 0.978775i | \(-0.434300\pi\) | ||||
0.204940 | + | 0.978775i | \(0.434300\pi\) | |||||||
\(152\) | 1171.68i | 0.0507133i | ||||||||
\(153\) | −25191.4 | − | 16984.2i | −1.07614 | − | 0.725543i | ||||
\(154\) | 104023. | 4.38619 | ||||||||
\(155\) | 20535.4i | 0.854753i | ||||||||
\(156\) | 18946.1 | + | 35623.5i | 0.778521 | + | 1.46382i | ||||
\(157\) | 27677.2 | 1.12285 | 0.561426 | − | 0.827527i | \(-0.310253\pi\) | ||||
0.561426 | + | 0.827527i | \(0.310253\pi\) | |||||||
\(158\) | 25818.8i | 1.03424i | ||||||||
\(159\) | −24607.4 | + | 13087.2i | −0.973354 | + | 0.517670i | ||||
\(160\) | −20835.2 | −0.813876 | ||||||||
\(161\) | − | 47871.8i | − | 1.84683i | ||||||
\(162\) | −33577.5 | + | 13582.4i | −1.27944 | + | 0.517541i | ||||
\(163\) | 22755.5 | 0.856469 | 0.428235 | − | 0.903668i | \(-0.359136\pi\) | ||||
0.428235 | + | 0.903668i | \(0.359136\pi\) | |||||||
\(164\) | 10743.4i | 0.399441i | ||||||||
\(165\) | −14141.7 | − | 26590.0i | −0.519437 | − | 0.976675i | ||||
\(166\) | −20234.5 | −0.734304 | ||||||||
\(167\) | − | 12179.6i | − | 0.436716i | −0.975869 | − | 0.218358i | \(-0.929930\pi\) | ||
0.975869 | − | 0.218358i | \(-0.0700701\pi\) | |||||||
\(168\) | 5597.19 | − | 2976.82i | 0.198313 | − | 0.105471i | ||||
\(169\) | 67338.2 | 2.35770 | ||||||||
\(170\) | 30806.6i | 1.06597i | ||||||||
\(171\) | 6309.75 | − | 9358.76i | 0.215784 | − | 0.320056i | ||||
\(172\) | −4239.96 | −0.143319 | ||||||||
\(173\) | − | 8146.41i | − | 0.272191i | −0.990696 | − | 0.136096i | \(-0.956545\pi\) | ||
0.990696 | − | 0.136096i | \(-0.0434554\pi\) | |||||||
\(174\) | 14177.8 | + | 26657.8i | 0.468284 | + | 0.880494i | ||||
\(175\) | 33816.2 | 1.10420 | ||||||||
\(176\) | − | 62540.4i | − | 2.01900i | ||||||
\(177\) | 3601.07 | − | 1915.20i | 0.114944 | − | 0.0611319i | ||||
\(178\) | −11950.3 | −0.377171 | ||||||||
\(179\) | − | 16581.8i | − | 0.517517i | −0.965942 | − | 0.258759i | \(-0.916687\pi\) | ||
0.965942 | − | 0.258759i | \(-0.0833134\pi\) | |||||||
\(180\) | 14465.1 | + | 9752.49i | 0.446454 | + | 0.301003i | ||||
\(181\) | −27569.2 | −0.841526 | −0.420763 | − | 0.907171i | \(-0.638238\pi\) | ||||
−0.420763 | + | 0.907171i | \(0.638238\pi\) | |||||||
\(182\) | 143218.i | 4.32370i | ||||||||
\(183\) | −178.800 | − | 336.190i | −0.00533907 | − | 0.0100388i | ||||
\(184\) | −4804.91 | −0.141922 | ||||||||
\(185\) | 8854.91i | 0.258726i | ||||||||
\(186\) | 60550.4 | − | 32203.2i | 1.75021 | − | 0.930837i | ||||
\(187\) | −84366.7 | −2.41261 | ||||||||
\(188\) | − | 7736.68i | − | 0.218896i | ||||||
\(189\) | −60738.1 | − | 6364.80i | −1.70035 | − | 0.178181i | ||||
\(190\) | −11444.8 | −0.317032 | ||||||||
\(191\) | − | 15213.9i | − | 0.417037i | −0.978018 | − | 0.208518i | \(-0.933136\pi\) | ||
0.978018 | − | 0.208518i | \(-0.0668641\pi\) | |||||||
\(192\) | 13872.5 | + | 26083.8i | 0.376314 | + | 0.707568i | ||||
\(193\) | −23560.4 | −0.632510 | −0.316255 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316255 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(194\) | − | 30491.7i | − | 0.810174i | ||||||
\(195\) | 36608.9 | − | 19470.2i | 0.962760 | − | 0.512036i | ||||
\(196\) | −66839.2 | −1.73988 | ||||||||
\(197\) | 39153.3i | 1.00887i | 0.863449 | + | 0.504436i | \(0.168300\pi\) | ||||
−0.863449 | + | 0.504436i | \(0.831700\pi\) | |||||||
\(198\) | −56226.0 | + | 83395.7i | −1.43419 | + | 2.12722i | ||||
\(199\) | −71055.1 | −1.79428 | −0.897138 | − | 0.441751i | \(-0.854357\pi\) | ||||
−0.897138 | + | 0.441751i | \(0.854357\pi\) | |||||||
\(200\) | − | 3394.15i | − | 0.0848537i | ||||||
\(201\) | 7855.12 | + | 14769.6i | 0.194429 | + | 0.365576i | ||||
\(202\) | −16046.0 | −0.393245 | ||||||||
\(203\) | 50908.6i | 1.23538i | ||||||||
\(204\) | 43148.1 | − | 22948.0i | 1.03682 | − | 0.551422i | ||||
\(205\) | 11040.6 | 0.262714 | ||||||||
\(206\) | 59198.9i | 1.39502i | ||||||||
\(207\) | 38379.0 | + | 25875.4i | 0.895681 | + | 0.603875i | ||||
\(208\) | 86105.3 | 1.99023 | ||||||||
\(209\) | − | 31342.7i | − | 0.717537i | ||||||
\(210\) | 29077.2 | + | 54672.7i | 0.659348 | + | 1.23974i | ||||
\(211\) | 484.586 | 0.0108844 | 0.00544222 | − | 0.999985i | \(-0.498268\pi\) | ||||
0.00544222 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(212\) | − | 44831.9i | − | 0.997506i | ||||||
\(213\) | 30413.3 | − | 16175.0i | 0.670353 | − | 0.356522i | ||||
\(214\) | −58059.4 | −1.26778 | ||||||||
\(215\) | 4357.24i | 0.0942616i | ||||||||
\(216\) | −638.837 | + | 6096.31i | −0.0136925 | + | 0.130665i | ||||
\(217\) | 115633. | 2.45563 | ||||||||
\(218\) | 12647.0i | 0.266118i | ||||||||
\(219\) | 34923.6 | + | 65665.3i | 0.728166 | + | 1.36914i | ||||
\(220\) | 48444.0 | 1.00091 | ||||||||
\(221\) | − | 116156.i | − | 2.37824i | ||||||
\(222\) | 26109.4 | − | 13886.1i | 0.529774 | − | 0.281756i | ||||
\(223\) | −58515.5 | −1.17669 | −0.588343 | − | 0.808611i | \(-0.700220\pi\) | ||||
−0.588343 | + | 0.808611i | \(0.700220\pi\) | |||||||
\(224\) | 117321.i | 2.33820i | ||||||||
\(225\) | −18278.2 | + | 27110.6i | −0.361051 | + | 0.535519i | ||||
\(226\) | −50577.0 | −0.990229 | ||||||||
\(227\) | − | 44301.3i | − | 0.859734i | −0.902892 | − | 0.429867i | \(-0.858560\pi\) | ||
0.902892 | − | 0.429867i | \(-0.141440\pi\) | |||||||
\(228\) | 8525.32 | + | 16029.8i | 0.163999 | + | 0.308360i | ||||
\(229\) | −29044.0 | −0.553841 | −0.276921 | − | 0.960893i | \(-0.589314\pi\) | ||||
−0.276921 | + | 0.960893i | \(0.589314\pi\) | |||||||
\(230\) | − | 46933.8i | − | 0.887218i | ||||||
\(231\) | −149726. | + | 79630.6i | −2.80591 | + | 1.49230i | ||||
\(232\) | 5109.72 | 0.0949338 | ||||||||
\(233\) | − | 56988.7i | − | 1.04973i | −0.851186 | − | 0.524864i | \(-0.824116\pi\) | ||
0.851186 | − | 0.524864i | \(-0.175884\pi\) | |||||||
\(234\) | −114819. | − | 77411.7i | −2.09692 | − | 1.41376i | ||||
\(235\) | −7950.69 | −0.143969 | ||||||||
\(236\) | 6560.76i | 0.117796i | ||||||||
\(237\) | −19764.6 | − | 37162.5i | −0.351877 | − | 0.661619i | ||||
\(238\) | 173470. | 3.06245 | ||||||||
\(239\) | 37945.5i | 0.664301i | 0.943226 | + | 0.332150i | \(0.107774\pi\) | ||||
−0.943226 | + | 0.332150i | \(0.892226\pi\) | |||||||
\(240\) | 32870.2 | − | 17481.7i | 0.570663 | − | 0.303502i | ||||
\(241\) | −65516.7 | −1.12802 | −0.564011 | − | 0.825767i | \(-0.690742\pi\) | ||||
−0.564011 | + | 0.825767i | \(0.690742\pi\) | |||||||
\(242\) | 198468.i | 3.38890i | ||||||||
\(243\) | 37932.6 | − | 45253.8i | 0.642392 | − | 0.766376i | ||||
\(244\) | 612.502 | 0.0102879 | ||||||||
\(245\) | 68688.1i | 1.14433i | ||||||||
\(246\) | −17313.6 | − | 32554.0i | −0.286099 | − | 0.537940i | ||||
\(247\) | 43152.5 | 0.707314 | ||||||||
\(248\) | − | 11606.2i | − | 0.188706i | ||||||
\(249\) | 29124.6 | − | 15489.7i | 0.469744 | − | 0.249830i | ||||
\(250\) | 84486.1 | 1.35178 | ||||||||
\(251\) | − | 83957.4i | − | 1.33264i | −0.745668 | − | 0.666318i | \(-0.767869\pi\) | ||
0.745668 | − | 0.666318i | \(-0.232131\pi\) | |||||||
\(252\) | 54915.5 | − | 81451.8i | 0.864756 | − | 1.28263i | ||||
\(253\) | 128532. | 2.00804 | ||||||||
\(254\) | − | 86944.4i | − | 1.34764i | ||||||
\(255\) | −23582.8 | − | 44341.7i | −0.362672 | − | 0.681917i | ||||
\(256\) | 76180.4 | 1.16242 | ||||||||
\(257\) | 12693.2i | 0.192178i | 0.995373 | + | 0.0960890i | \(0.0306333\pi\) | ||||
−0.995373 | + | 0.0960890i | \(0.969367\pi\) | |||||||
\(258\) | 12847.7 | − | 6832.94i | 0.193012 | − | 0.102652i | ||||
\(259\) | 49861.2 | 0.743299 | ||||||||
\(260\) | 66697.5i | 0.986649i | ||||||||
\(261\) | −40813.7 | − | 27516.9i | −0.599135 | − | 0.403941i | ||||
\(262\) | −96481.5 | −1.40553 | ||||||||
\(263\) | 48754.8i | 0.704866i | 0.935837 | + | 0.352433i | \(0.114645\pi\) | ||||
−0.935837 | + | 0.352433i | \(0.885355\pi\) | |||||||
\(264\) | 7992.56 | + | 15028.1i | 0.114677 | + | 0.215623i | ||||
\(265\) | −46072.0 | −0.656063 | ||||||||
\(266\) | 64445.0i | 0.910806i | ||||||||
\(267\) | 17200.7 | − | 9148.07i | 0.241282 | − | 0.128324i | ||||
\(268\) | −26908.7 | −0.374647 | ||||||||
\(269\) | − | 67655.3i | − | 0.934970i | −0.884001 | − | 0.467485i | \(-0.845160\pi\) | ||
0.884001 | − | 0.467485i | \(-0.154840\pi\) | |||||||
\(270\) | −59548.1 | − | 6240.09i | −0.816846 | − | 0.0855979i | ||||
\(271\) | 76385.1 | 1.04009 | 0.520044 | − | 0.854140i | \(-0.325916\pi\) | ||||
0.520044 | + | 0.854140i | \(0.325916\pi\) | |||||||
\(272\) | − | 104293.i | − | 1.40967i | ||||||
\(273\) | −109635. | − | 206142.i | −1.47104 | − | 2.76593i | ||||
\(274\) | 33851.5 | 0.450897 | ||||||||
\(275\) | 90794.3i | 1.20059i | ||||||||
\(276\) | −65736.1 | + | 34961.2i | −0.862950 | + | 0.458953i | ||||
\(277\) | 22731.1 | 0.296252 | 0.148126 | − | 0.988969i | \(-0.452676\pi\) | ||||
0.148126 | + | 0.988969i | \(0.452676\pi\) | |||||||
\(278\) | − | 178383.i | − | 2.30815i | ||||||
\(279\) | −62501.7 | + | 92703.8i | −0.802940 | + | 1.19094i | ||||
\(280\) | 10479.5 | 0.133668 | ||||||||
\(281\) | 6215.48i | 0.0787158i | 0.999225 | + | 0.0393579i | \(0.0125312\pi\) | ||||
−0.999225 | + | 0.0393579i | \(0.987469\pi\) | |||||||
\(282\) | 12468.1 | + | 23443.2i | 0.156784 | + | 0.294794i | ||||
\(283\) | −5364.36 | −0.0669800 | −0.0334900 | − | 0.999439i | \(-0.510662\pi\) | ||||
−0.0334900 | + | 0.999439i | \(0.510662\pi\) | |||||||
\(284\) | 55409.6i | 0.686987i | ||||||||
\(285\) | 16473.2 | − | 8761.14i | 0.202810 | − | 0.107863i | ||||
\(286\) | −384531. | −4.70110 | ||||||||
\(287\) | − | 62168.5i | − | 0.754756i | ||||||
\(288\) | −94057.1 | − | 63414.1i | −1.13398 | − | 0.764541i | ||||
\(289\) | −57169.5 | −0.684493 | ||||||||
\(290\) | 49911.1i | 0.593474i | ||||||||
\(291\) | 23341.7 | + | 43888.4i | 0.275643 | + | 0.518279i | ||||
\(292\) | −119635. | −1.40311 | ||||||||
\(293\) | 159220.i | 1.85465i | 0.374258 | + | 0.927324i | \(0.377897\pi\) | ||||
−0.374258 | + | 0.927324i | \(0.622103\pi\) | |||||||
\(294\) | 202532. | − | 107715.i | 2.34315 | − | 1.24618i | ||||
\(295\) | 6742.24 | 0.0774747 | ||||||||
\(296\) | − | 5004.59i | − | 0.0571196i | ||||||
\(297\) | 17089.0 | − | 163078.i | 0.193734 | − | 1.84876i | ||||
\(298\) | 199074. | 2.24172 | ||||||||
\(299\) | 176963.i | 1.97943i | ||||||||
\(300\) | −24696.3 | − | 46435.4i | −0.274403 | − | 0.515949i | ||||
\(301\) | 24535.3 | 0.270806 | ||||||||
\(302\) | − | 51593.6i | − | 0.565695i | ||||||
\(303\) | 23095.9 | − | 12283.4i | 0.251564 | − | 0.133793i | ||||
\(304\) | 38745.5 | 0.419250 | ||||||||
\(305\) | − | 629.445i | − | 0.00676640i | ||||||
\(306\) | −93763.0 | + | 139071.i | −1.00136 | + | 1.48523i | ||||
\(307\) | −20540.8 | −0.217942 | −0.108971 | − | 0.994045i | \(-0.534756\pi\) | ||||
−0.108971 | + | 0.994045i | \(0.534756\pi\) | |||||||
\(308\) | − | 272784.i | − | 2.87553i | ||||||
\(309\) | −45317.4 | − | 85208.3i | −0.474622 | − | 0.892411i | ||||
\(310\) | 113368. | 1.17969 | ||||||||
\(311\) | 123879.i | 1.28079i | 0.768047 | + | 0.640393i | \(0.221229\pi\) | ||||
−0.768047 | + | 0.640393i | \(0.778771\pi\) | |||||||
\(312\) | −20690.6 | + | 11004.1i | −0.212551 | + | 0.113043i | ||||
\(313\) | 21875.0 | 0.223285 | 0.111643 | − | 0.993748i | \(-0.464389\pi\) | ||||
0.111643 | + | 0.993748i | \(0.464389\pi\) | |||||||
\(314\) | − | 152794.i | − | 1.54970i | ||||||
\(315\) | −83704.9 | − | 56434.5i | −0.843587 | − | 0.568753i | ||||
\(316\) | 67706.0 | 0.678036 | ||||||||
\(317\) | 74997.6i | 0.746326i | 0.927766 | + | 0.373163i | \(0.121727\pi\) | ||||
−0.927766 | + | 0.373163i | \(0.878273\pi\) | |||||||
\(318\) | 72249.2 | + | 135847.i | 0.714461 | + | 1.34337i | ||||
\(319\) | −136686. | −1.34321 | ||||||||
\(320\) | 48836.4i | 0.476918i | ||||||||
\(321\) | 83568.1 | − | 44445.0i | 0.811018 | − | 0.431333i | ||||
\(322\) | −264280. | −2.54890 | ||||||||
\(323\) | − | 52267.4i | − | 0.500986i | ||||||
\(324\) | 35617.7 | + | 88052.0i | 0.339293 | + | 0.838782i | ||||
\(325\) | −125005. | −1.18348 | ||||||||
\(326\) | − | 125624.i | − | 1.18205i | ||||||
\(327\) | −9681.41 | − | 18203.5i | −0.0905405 | − | 0.170240i | ||||
\(328\) | −6239.88 | −0.0580000 | ||||||||
\(329\) | 44769.7i | 0.413611i | ||||||||
\(330\) | −146792. | + | 78070.4i | −1.34796 | + | 0.716900i | ||||
\(331\) | 99534.5 | 0.908484 | 0.454242 | − | 0.890878i | \(-0.349910\pi\) | ||||
0.454242 | + | 0.890878i | \(0.349910\pi\) | |||||||
\(332\) | 53061.8i | 0.481400i | ||||||||
\(333\) | −26950.8 | + | 39974.0i | −0.243043 | + | 0.360487i | ||||
\(334\) | −67238.5 | −0.602733 | ||||||||
\(335\) | 27653.0i | 0.246407i | ||||||||
\(336\) | −98438.2 | − | 185089.i | −0.871937 | − | 1.63947i | ||||
\(337\) | 98533.0 | 0.867605 | 0.433802 | − | 0.901008i | \(-0.357172\pi\) | ||||
0.433802 | + | 0.901008i | \(0.357172\pi\) | |||||||
\(338\) | − | 371747.i | − | 3.25397i | ||||||
\(339\) | 72798.2 | − | 38717.1i | 0.633463 | − | 0.336902i | ||||
\(340\) | 80785.7 | 0.698838 | ||||||||
\(341\) | 310468.i | 2.66998i | ||||||||
\(342\) | −51665.9 | − | 34833.5i | −0.441724 | − | 0.297814i | ||||
\(343\) | 185638. | 1.57789 | ||||||||
\(344\) | − | 2462.62i | − | 0.0208104i | ||||||
\(345\) | 35928.3 | + | 67554.4i | 0.301855 | + | 0.567565i | ||||
\(346\) | −44973.0 | −0.375664 | ||||||||
\(347\) | 142395.i | 1.18260i | 0.806453 | + | 0.591299i | \(0.201385\pi\) | ||||
−0.806453 | + | 0.591299i | \(0.798615\pi\) | |||||||
\(348\) | 69906.1 | − | 37179.0i | 0.577240 | − | 0.307001i | ||||
\(349\) | 102446. | 0.841092 | 0.420546 | − | 0.907271i | \(-0.361838\pi\) | ||||
0.420546 | + | 0.907271i | \(0.361838\pi\) | |||||||
\(350\) | − | 186686.i | − | 1.52396i | ||||||
\(351\) | 224524. | + | 23528.1i | 1.82242 | + | 0.190973i | ||||
\(352\) | −315000. | −2.54229 | ||||||||
\(353\) | − | 51077.6i | − | 0.409903i | −0.978772 | − | 0.204952i | \(-0.934296\pi\) | ||
0.978772 | − | 0.204952i | \(-0.0657037\pi\) | |||||||
\(354\) | −10573.0 | − | 19880.0i | −0.0843710 | − | 0.158639i | ||||
\(355\) | 56942.3 | 0.451834 | ||||||||
\(356\) | 31337.9i | 0.247269i | ||||||||
\(357\) | −249684. | + | 132793.i | −1.95909 | + | 1.04193i | ||||
\(358\) | −91541.2 | −0.714250 | ||||||||
\(359\) | − | 204305.i | − | 1.58522i | −0.609726 | − | 0.792612i | \(-0.708721\pi\) | ||
0.609726 | − | 0.792612i | \(-0.291279\pi\) | |||||||
\(360\) | −5664.36 | + | 8401.50i | −0.0437065 | + | 0.0648264i | ||||
\(361\) | −110903. | −0.851001 | ||||||||
\(362\) | 152198.i | 1.16143i | ||||||||
\(363\) | −151929. | − | 285665.i | −1.15299 | − | 2.16793i | ||||
\(364\) | 375568. | 2.83456 | ||||||||
\(365\) | 122944.i | 0.922833i | ||||||||
\(366\) | −1855.97 | + | 987.082i | −0.0138551 | + | 0.00736870i | ||||
\(367\) | 161415. | 1.19843 | 0.599215 | − | 0.800589i | \(-0.295480\pi\) | ||||
0.599215 | + | 0.800589i | \(0.295480\pi\) | |||||||
\(368\) | 158890.i | 1.17328i | ||||||||
\(369\) | 49840.8 | + | 33603.0i | 0.366043 | + | 0.246789i | ||||
\(370\) | 48884.3 | 0.357080 | ||||||||
\(371\) | 259428.i | 1.88482i | ||||||||
\(372\) | −84448.1 | − | 158784.i | −0.610245 | − | 1.14742i | ||||
\(373\) | 183154. | 1.31643 | 0.658216 | − | 0.752829i | \(-0.271311\pi\) | ||||
0.658216 | + | 0.752829i | \(0.271311\pi\) | |||||||
\(374\) | 465754.i | 3.32976i | ||||||||
\(375\) | −121605. | + | 64674.9i | −0.864750 | + | 0.459910i | ||||
\(376\) | 4493.55 | 0.0317844 | ||||||||
\(377\) | − | 188189.i | − | 1.32407i | ||||||
\(378\) | −35137.4 | + | 335310.i | −0.245916 | + | 2.34673i | ||||
\(379\) | 122913. | 0.855694 | 0.427847 | − | 0.903851i | \(-0.359272\pi\) | ||||
0.427847 | + | 0.903851i | \(0.359272\pi\) | |||||||
\(380\) | 30012.4i | 0.207842i | ||||||||
\(381\) | 66556.8 | + | 125144.i | 0.458503 | + | 0.862104i | ||||
\(382\) | −83989.8 | −0.575572 | ||||||||
\(383\) | 207603.i | 1.41526i | 0.706583 | + | 0.707631i | \(0.250236\pi\) | ||||
−0.706583 | + | 0.707631i | \(0.749764\pi\) | |||||||
\(384\) | −34053.5 | + | 18111.1i | −0.230940 | + | 0.122824i | ||||
\(385\) | −280330. | −1.89125 | ||||||||
\(386\) | 130067.i | 0.872957i | ||||||||
\(387\) | −13261.7 | + | 19670.1i | −0.0885477 | + | 0.131336i | ||||
\(388\) | −79959.9 | −0.531139 | ||||||||
\(389\) | − | 155335.i | − | 1.02652i | −0.858232 | − | 0.513262i | \(-0.828437\pi\) | ||
0.858232 | − | 0.513262i | \(-0.171563\pi\) | |||||||
\(390\) | −107487. | − | 202103.i | −0.706685 | − | 1.32875i | ||||
\(391\) | 214342. | 1.40202 | ||||||||
\(392\) | − | 38821.0i | − | 0.252635i | ||||||
\(393\) | 138871. | − | 73857.5i | 0.899140 | − | 0.478200i | ||||
\(394\) | 216150. | 1.39239 | ||||||||
\(395\) | − | 69578.9i | − | 0.445947i | ||||||
\(396\) | 218693. | + | 147444.i | 1.39458 | + | 0.940237i | ||||
\(397\) | −51240.7 | −0.325113 | −0.162557 | − | 0.986699i | \(-0.551974\pi\) | ||||
−0.162557 | + | 0.986699i | \(0.551974\pi\) | |||||||
\(398\) | 392266.i | 2.47636i | ||||||||
\(399\) | −49333.3 | − | 92759.2i | −0.309880 | − | 0.582655i | ||||
\(400\) | −112239. | −0.701491 | ||||||||
\(401\) | − | 38985.7i | − | 0.242447i | −0.992625 | − | 0.121224i | \(-0.961318\pi\) | ||
0.992625 | − | 0.121224i | \(-0.0386818\pi\) | |||||||
\(402\) | 81537.1 | − | 43364.9i | 0.504549 | − | 0.268340i | ||||
\(403\) | −427450. | −2.63194 | ||||||||
\(404\) | 42078.2i | 0.257807i | ||||||||
\(405\) | 90487.7 | − | 36602.9i | 0.551670 | − | 0.223154i | ||||
\(406\) | 281045. | 1.70500 | ||||||||
\(407\) | 133874.i | 0.808179i | ||||||||
\(408\) | 13328.4 | + | 25060.9i | 0.0800681 | + | 0.150549i | ||||
\(409\) | −135878. | −0.812273 | −0.406137 | − | 0.913812i | \(-0.633124\pi\) | ||||
−0.406137 | + | 0.913812i | \(0.633124\pi\) | |||||||
\(410\) | − | 60950.4i | − | 0.362584i | ||||||
\(411\) | −48724.4 | + | 25913.7i | −0.288445 | + | 0.153407i | ||||
\(412\) | 155240. | 0.914555 | ||||||||
\(413\) | − | 37965.0i | − | 0.222578i | ||||||
\(414\) | 142848. | − | 211875.i | 0.833437 | − | 1.23617i | ||||
\(415\) | 54529.6 | 0.316618 | ||||||||
\(416\) | − | 433690.i | − | 2.50607i | ||||||
\(417\) | 136554. | + | 256757.i | 0.785295 | + | 1.47656i | ||||
\(418\) | −173030. | −0.990307 | ||||||||
\(419\) | − | 145521.i | − | 0.828893i | −0.910074 | − | 0.414446i | \(-0.863975\pi\) | ||
0.910074 | − | 0.414446i | \(-0.136025\pi\) | |||||||
\(420\) | 143371. | − | 76250.6i | 0.812760 | − | 0.432260i | ||||
\(421\) | −231179. | −1.30432 | −0.652161 | − | 0.758081i | \(-0.726137\pi\) | ||||
−0.652161 | + | 0.758081i | \(0.726137\pi\) | |||||||
\(422\) | − | 2675.20i | − | 0.0150221i | ||||||
\(423\) | −35892.1 | − | 24198.7i | −0.200594 | − | 0.135242i | ||||
\(424\) | 26038.9 | 0.144841 | ||||||||
\(425\) | 151409.i | 0.838252i | ||||||||
\(426\) | −89295.8 | − | 167899.i | −0.492053 | − | 0.925186i | ||||
\(427\) | −3544.35 | −0.0194393 | ||||||||
\(428\) | 152252.i | 0.831142i | ||||||||
\(429\) | 553477. | − | 294362.i | 3.00736 | − | 1.59944i | ||||
\(430\) | 24054.6 | 0.130095 | ||||||||
\(431\) | 48295.7i | 0.259988i | 0.991515 | + | 0.129994i | \(0.0414958\pi\) | ||||
−0.991515 | + | 0.129994i | \(0.958504\pi\) | |||||||
\(432\) | 201594. | + | 21125.2i | 1.08022 | + | 0.113197i | ||||
\(433\) | −246945. | −1.31712 | −0.658558 | − | 0.752530i | \(-0.728833\pi\) | ||||
−0.658558 | + | 0.752530i | \(0.728833\pi\) | |||||||
\(434\) | − | 638364.i | − | 3.38914i | ||||||
\(435\) | −38207.5 | − | 71839.9i | −0.201915 | − | 0.379653i | ||||
\(436\) | 33164.9 | 0.174464 | ||||||||
\(437\) | 79629.3i | 0.416975i | ||||||||
\(438\) | 362511. | − | 192799.i | 1.88962 | − | 1.00498i | ||||
\(439\) | 285588. | 1.48187 | 0.740937 | − | 0.671575i | \(-0.234382\pi\) | ||||
0.740937 | + | 0.671575i | \(0.234382\pi\) | |||||||
\(440\) | 28136.9i | 0.145335i | ||||||||
\(441\) | −209059. | + | 310081.i | −1.07496 | + | 1.59440i | ||||
\(442\) | −641247. | −3.28232 | ||||||||
\(443\) | 47873.0i | 0.243940i | 0.992534 | + | 0.121970i | \(0.0389212\pi\) | ||||
−0.992534 | + | 0.121970i | \(0.961079\pi\) | |||||||
\(444\) | −36414.1 | − | 68467.9i | −0.184716 | − | 0.347313i | ||||
\(445\) | 32204.7 | 0.162630 | ||||||||
\(446\) | 323040.i | 1.62400i | ||||||||
\(447\) | −286538. | + | 152393.i | −1.43406 | + | 0.762693i | ||||
\(448\) | 274994. | 1.37014 | ||||||||
\(449\) | − | 356568.i | − | 1.76868i | −0.466841 | − | 0.884341i | \(-0.654608\pi\) | ||
0.466841 | − | 0.884341i | \(-0.345392\pi\) | |||||||
\(450\) | 149667. | + | 100906.i | 0.739095 | + | 0.498304i | ||||
\(451\) | 166918. | 0.820636 | ||||||||
\(452\) | 132630.i | 0.649182i | ||||||||
\(453\) | 39495.4 | + | 74261.6i | 0.192464 | + | 0.361883i | ||||
\(454\) | −244569. | −1.18656 | ||||||||
\(455\) | − | 385957.i | − | 1.86430i | ||||||
\(456\) | −9310.29 | + | 4951.60i | −0.0447748 | + | 0.0238131i | ||||
\(457\) | 83662.8 | 0.400590 | 0.200295 | − | 0.979736i | \(-0.435810\pi\) | ||||
0.200295 | + | 0.979736i | \(0.435810\pi\) | |||||||
\(458\) | 160340.i | 0.764383i | ||||||||
\(459\) | 28497.8 | − | 271950.i | 0.135265 | − | 1.29081i | ||||
\(460\) | −123077. | −0.581648 | ||||||||
\(461\) | 105132.i | 0.494692i | 0.968927 | + | 0.247346i | \(0.0795584\pi\) | ||||
−0.968927 | + | 0.247346i | \(0.920442\pi\) | |||||||
\(462\) | 439608. | + | 826576.i | 2.05959 | + | 3.87257i | ||||
\(463\) | 244357. | 1.13989 | 0.569946 | − | 0.821682i | \(-0.306964\pi\) | ||||
0.569946 | + | 0.821682i | \(0.306964\pi\) | |||||||
\(464\) | − | 168969.i | − | 0.784824i | ||||||
\(465\) | −163177. | + | 86784.1i | −0.754661 | + | 0.401360i | ||||
\(466\) | −314611. | −1.44878 | ||||||||
\(467\) | 291275.i | 1.33558i | 0.744351 | + | 0.667789i | \(0.232759\pi\) | ||||
−0.744351 | + | 0.667789i | \(0.767241\pi\) | |||||||
\(468\) | −203000. | + | 301095.i | −0.926841 | + | 1.37471i | ||||
\(469\) | 155712. | 0.707907 | ||||||||
\(470\) | 43892.5i | 0.198698i | ||||||||
\(471\) | 116966. | + | 219925.i | 0.527250 | + | 0.991365i | ||||
\(472\) | −3810.56 | −0.0171043 | ||||||||
\(473\) | 65875.5i | 0.294443i | ||||||||
\(474\) | −205159. | + | 109112.i | −0.913132 | + | 0.485642i | ||||
\(475\) | −56249.5 | −0.249305 | ||||||||
\(476\) | − | 454897.i | − | 2.00770i | ||||||
\(477\) | −207985. | − | 140225.i | −0.914101 | − | 0.616294i | ||||
\(478\) | 209482. | 0.916833 | ||||||||
\(479\) | − | 126030.i | − | 0.549290i | −0.961546 | − | 0.274645i | \(-0.911440\pi\) | ||
0.961546 | − | 0.274645i | \(-0.0885603\pi\) | |||||||
\(480\) | −88051.0 | − | 165559.i | −0.382166 | − | 0.718570i | ||||
\(481\) | −184317. | −0.796664 | ||||||||
\(482\) | 361691.i | 1.55684i | ||||||||
\(483\) | 380393. | − | 202309.i | 1.63057 | − | 0.867204i | ||||
\(484\) | 520451. | 2.22172 | ||||||||
\(485\) | 82171.7i | 0.349332i | ||||||||
\(486\) | −249827. | − | 209410.i | −1.05771 | − | 0.886595i | ||||
\(487\) | 129502. | 0.546031 | 0.273016 | − | 0.962010i | \(-0.411979\pi\) | ||||
0.273016 | + | 0.962010i | \(0.411979\pi\) | |||||||
\(488\) | 355.748i | 0.00149384i | ||||||||
\(489\) | 96166.4 | + | 180818.i | 0.402166 | + | 0.756176i | ||||
\(490\) | 379199. | 1.57934 | ||||||||
\(491\) | 49733.7i | 0.206295i | 0.994666 | + | 0.103147i | \(0.0328913\pi\) | ||||
−0.994666 | + | 0.103147i | \(0.967109\pi\) | |||||||
\(492\) | −85367.9 | + | 45402.2i | −0.352667 | + | 0.187563i | ||||
\(493\) | −227939. | −0.937831 | ||||||||
\(494\) | − | 238227.i | − | 0.976197i | ||||||
\(495\) | 151523. | − | 224742.i | 0.618397 | − | 0.917221i | ||||
\(496\) | −383796. | −1.56004 | ||||||||
\(497\) | − | 320638.i | − | 1.29808i | ||||||
\(498\) | −85512.2 | − | 160785.i | −0.344802 | − | 0.648316i | ||||
\(499\) | 76821.6 | 0.308519 | 0.154260 | − | 0.988030i | \(-0.450701\pi\) | ||||
0.154260 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(500\) | − | 221552.i | − | 0.886208i | ||||||
\(501\) | 96780.1 | − | 51471.7i | 0.385577 | − | 0.205066i | ||||
\(502\) | −463494. | −1.83923 | ||||||||
\(503\) | − | 226728.i | − | 0.896128i | −0.894002 | − | 0.448064i | \(-0.852114\pi\) | ||
0.894002 | − | 0.448064i | \(-0.147886\pi\) | |||||||
\(504\) | 47308.2 | + | 31895.5i | 0.186241 | + | 0.125565i | ||||
\(505\) | 43242.1 | 0.169560 | ||||||||
\(506\) | − | 709575.i | − | 2.77139i | ||||||
\(507\) | 284576. | + | 535076.i | 1.10709 | + | 2.08161i | ||||
\(508\) | −227998. | −0.883496 | ||||||||
\(509\) | 285677.i | 1.10266i | 0.834288 | + | 0.551329i | \(0.185879\pi\) | ||||
−0.834288 | + | 0.551329i | \(0.814121\pi\) | |||||||
\(510\) | −244792. | + | 130191.i | −0.941146 | + | 0.500541i | ||||
\(511\) | 692290. | 2.65122 | ||||||||
\(512\) | − | 351992.i | − | 1.34274i | ||||||
\(513\) | 101031. | + | 10587.1i | 0.383901 | + | 0.0402293i | ||||
\(514\) | 70073.8 | 0.265234 | ||||||||
\(515\) | − | 159535.i | − | 0.601506i | ||||||
\(516\) | −17918.3 | − | 33691.1i | −0.0672974 | − | 0.126537i | ||||
\(517\) | −120203. | −0.449713 | ||||||||
\(518\) | − | 275263.i | − | 1.02586i | ||||||
\(519\) | 64732.1 | − | 34427.2i | 0.240317 | − | 0.127811i | ||||
\(520\) | −38738.7 | −0.143264 | ||||||||
\(521\) | − | 422420.i | − | 1.55621i | −0.628132 | − | 0.778107i | \(-0.716180\pi\) | ||
0.628132 | − | 0.778107i | \(-0.283820\pi\) | |||||||
\(522\) | −151909. | + | 225315.i | −0.557499 | + | 0.826894i | ||||
\(523\) | −293362. | −1.07251 | −0.536254 | − | 0.844056i | \(-0.680161\pi\) | ||||
−0.536254 | + | 0.844056i | \(0.680161\pi\) | |||||||
\(524\) | 253008.i | 0.921450i | ||||||||
\(525\) | 142910. | + | 268707.i | 0.518493 | + | 0.974900i | ||||
\(526\) | 269156. | 0.972818 | ||||||||
\(527\) | 517738.i | 1.86419i | ||||||||
\(528\) | 496952. | − | 264300.i | 1.78257 | − | 0.948045i | ||||
\(529\) | −46708.1 | −0.166909 | ||||||||
\(530\) | 254345.i | 0.905464i | ||||||||
\(531\) | 30436.7 | + | 20520.7i | 0.107947 | + | 0.0727784i | ||||
\(532\) | 168997. | 0.597113 | ||||||||
\(533\) | 229812.i | 0.808943i | ||||||||
\(534\) | −50502.8 | − | 94958.2i | −0.177106 | − | 0.333004i | ||||
\(535\) | 156463. | 0.546645 | ||||||||
\(536\) | − | 15628.9i | − | 0.0543999i | ||||||
\(537\) | 131760. | − | 70075.7i | 0.456916 | − | 0.243007i | ||||
\(538\) | −373497. | −1.29040 | ||||||||
\(539\) | 1.03847e6i | 3.57451i | ||||||||
\(540\) | −16363.7 | + | 156156.i | −0.0561169 | + | 0.535514i | ||||
\(541\) | 298138. | 1.01865 | 0.509323 | − | 0.860576i | \(-0.329896\pi\) | ||||
0.509323 | + | 0.860576i | \(0.329896\pi\) | |||||||
\(542\) | − | 421691.i | − | 1.43547i | ||||||
\(543\) | −116509. | − | 219068.i | −0.395149 | − | 0.742983i | ||||
\(544\) | −525296. | −1.77503 | ||||||||
\(545\) | − | 34082.3i | − | 0.114745i | ||||||
\(546\) | −1.13803e6 | + | 605250.i | −3.81739 | + | 2.03025i | ||||
\(547\) | −174085. | −0.581817 | −0.290908 | − | 0.956751i | \(-0.593957\pi\) | ||||
−0.290908 | + | 0.956751i | \(0.593957\pi\) | |||||||
\(548\) | − | 88770.6i | − | 0.295602i | ||||||
\(549\) | 1915.78 | − | 2841.52i | 0.00635624 | − | 0.00942772i | ||||
\(550\) | 501238. | 1.65698 | ||||||||
\(551\) | − | 84680.7i | − | 0.278921i | ||||||
\(552\) | −20305.9 | − | 38180.3i | −0.0666413 | − | 0.125303i | ||||
\(553\) | −391793. | −1.28117 | ||||||||
\(554\) | − | 125489.i | − | 0.408871i | ||||||
\(555\) | −70361.9 | + | 37421.4i | −0.228429 | + | 0.121488i | ||||
\(556\) | −467783. | −1.51320 | ||||||||
\(557\) | − | 42791.2i | − | 0.137925i | −0.997619 | − | 0.0689626i | \(-0.978031\pi\) | ||
0.997619 | − | 0.0689626i | \(-0.0219689\pi\) | |||||||
\(558\) | 511780. | + | 345046.i | 1.64367 | + | 1.10818i | ||||
\(559\) | −90697.1 | −0.290248 | ||||||||
\(560\) | − | 346540.i | − | 1.10504i | ||||||
\(561\) | −356539. | − | 670385.i | −1.13287 | − | 2.13009i | ||||
\(562\) | 34313.1 | 0.108639 | ||||||||
\(563\) | − | 335794.i | − | 1.05939i | −0.848188 | − | 0.529695i | \(-0.822306\pi\) | ||
0.848188 | − | 0.529695i | \(-0.177694\pi\) | |||||||
\(564\) | 61476.3 | − | 32695.7i | 0.193263 | − | 0.102786i | ||||
\(565\) | 136299. | 0.426969 | ||||||||
\(566\) | 29614.5i | 0.0924423i | ||||||||
\(567\) | −206108. | − | 509529.i | −0.641104 | − | 1.58490i | ||||
\(568\) | −32182.5 | −0.0997525 | ||||||||
\(569\) | 395920.i | 1.22288i | 0.791292 | + | 0.611438i | \(0.209409\pi\) | ||||
−0.791292 | + | 0.611438i | \(0.790591\pi\) | |||||||
\(570\) | −48366.7 | − | 90941.8i | −0.148866 | − | 0.279907i | ||||
\(571\) | 452552. | 1.38802 | 0.694011 | − | 0.719965i | \(-0.255842\pi\) | ||||
0.694011 | + | 0.719965i | \(0.255842\pi\) | |||||||
\(572\) | 1.00837e6i | 3.08198i | ||||||||
\(573\) | 120891. | − | 64295.0i | 0.368201 | − | 0.195825i | ||||
\(574\) | −343207. | −1.04167 | ||||||||
\(575\) | − | 230672.i | − | 0.697684i | ||||||
\(576\) | −148638. | + | 220464.i | −0.448008 | + | 0.664495i | ||||
\(577\) | −294717. | −0.885226 | −0.442613 | − | 0.896713i | \(-0.645948\pi\) | ||||
−0.442613 | + | 0.896713i | \(0.645948\pi\) | |||||||
\(578\) | 315609.i | 0.944701i | ||||||||
\(579\) | −99567.7 | − | 187213.i | −0.297003 | − | 0.558443i | ||||
\(580\) | 130884. | 0.389074 | ||||||||
\(581\) | − | 307052.i | − | 0.909619i | ||||||
\(582\) | 242290. | − | 128860.i | 0.715302 | − | 0.380427i | ||||
\(583\) | −696546. | −2.04933 | ||||||||
\(584\) | − | 69485.4i | − | 0.203736i | ||||||
\(585\) | 309424. | + | 208616.i | 0.904152 | + | 0.609587i | ||||
\(586\) | 878987. | 2.55969 | ||||||||
\(587\) | 252374.i | 0.732432i | 0.930530 | + | 0.366216i | \(0.119347\pi\) | ||||
−0.930530 | + | 0.366216i | \(0.880653\pi\) | |||||||
\(588\) | −282467. | − | 531111.i | −0.816983 | − | 1.53614i | ||||
\(589\) | −192343. | −0.554429 | ||||||||
\(590\) | − | 37221.1i | − | 0.106927i | ||||||
\(591\) | −311116. | + | 165465.i | −0.890733 | + | 0.473729i | ||||
\(592\) | −165493. | −0.472212 | ||||||||
\(593\) | 249978.i | 0.710874i | 0.934700 | + | 0.355437i | \(0.115668\pi\) | ||||
−0.934700 | + | 0.355437i | \(0.884332\pi\) | |||||||
\(594\) | −900285. | − | 94341.6i | −2.55157 | − | 0.267381i | ||||
\(595\) | −467481. | −1.32047 | ||||||||
\(596\) | − | 522041.i | − | 1.46964i | ||||||
\(597\) | −300283. | − | 564610.i | −0.842525 | − | 1.58416i | ||||
\(598\) | 976939. | 2.73190 | ||||||||
\(599\) | − | 527472.i | − | 1.47010i | −0.678014 | − | 0.735049i | \(-0.737159\pi\) | ||
0.678014 | − | 0.735049i | \(-0.262841\pi\) | |||||||
\(600\) | 26970.2 | − | 14343.9i | 0.0749173 | − | 0.0398442i | ||||
\(601\) | 53469.5 | 0.148032 | 0.0740162 | − | 0.997257i | \(-0.476418\pi\) | ||||
0.0740162 | + | 0.997257i | \(0.476418\pi\) | |||||||
\(602\) | − | 135449.i | − | 0.373752i | ||||||
\(603\) | −84164.7 | + | 124835.i | −0.231470 | + | 0.343322i | ||||
\(604\) | −135296. | −0.370862 | ||||||||
\(605\) | − | 534848.i | − | 1.46123i | ||||||
\(606\) | −67811.4 | − | 127503.i | −0.184653 | − | 0.347196i | ||||
\(607\) | −486157. | −1.31947 | −0.659734 | − | 0.751499i | \(-0.729331\pi\) | ||||
−0.659734 | + | 0.751499i | \(0.729331\pi\) | |||||||
\(608\) | − | 195151.i | − | 0.527914i | ||||||
\(609\) | −404524. | + | 215143.i | −1.09071 | + | 0.580086i | ||||
\(610\) | −3474.91 | −0.00933864 | ||||||||
\(611\) | − | 165495.i | − | 0.443306i | ||||||
\(612\) | 364694. | + | 245879.i | 0.973700 | + | 0.656476i | ||||
\(613\) | −28121.3 | −0.0748366 | −0.0374183 | − | 0.999300i | \(-0.511913\pi\) | ||||
−0.0374183 | + | 0.999300i | \(0.511913\pi\) | |||||||
\(614\) | 113398.i | 0.300792i | ||||||||
\(615\) | 46658.1 | + | 87729.3i | 0.123361 | + | 0.231950i | ||||
\(616\) | 158436. | 0.417535 | ||||||||
\(617\) | 81431.3i | 0.213905i | 0.994264 | + | 0.106953i | \(0.0341093\pi\) | ||||
−0.994264 | + | 0.106953i | \(0.965891\pi\) | |||||||
\(618\) | −470400. | + | 250179.i | −1.23166 | + | 0.655048i | ||||
\(619\) | 53438.8 | 0.139468 | 0.0697342 | − | 0.997566i | \(-0.477785\pi\) | ||||
0.0697342 | + | 0.997566i | \(0.477785\pi\) | |||||||
\(620\) | − | 297290.i | − | 0.773386i | ||||||
\(621\) | −43416.4 | + | 414315.i | −0.112582 | + | 1.07435i | ||||
\(622\) | 683885. | 1.76767 | ||||||||
\(623\) | − | 181342.i | − | 0.467221i | ||||||
\(624\) | 363887. | + | 684201.i | 0.934538 | + | 1.75717i | ||||
\(625\) | 24609.5 | 0.0630004 | ||||||||
\(626\) | − | 120763.i | − | 0.308167i | ||||||
\(627\) | 249052. | − | 132456.i | 0.633513 | − | 0.336929i | ||||
\(628\) | −400680. | −1.01596 | ||||||||
\(629\) | 223249.i | 0.564273i | ||||||||
\(630\) | −311552. | + | 462101.i | −0.784963 | + | 1.16427i | ||||
\(631\) | 707294. | 1.77640 | 0.888201 | − | 0.459454i | \(-0.151955\pi\) | ||||
0.888201 | + | 0.459454i | \(0.151955\pi\) | |||||||
\(632\) | 39324.4i | 0.0984528i | ||||||||
\(633\) | 2047.89 | + | 3850.56i | 0.00511092 | + | 0.00960985i | ||||
\(634\) | 414031. | 1.03004 | ||||||||
\(635\) | 234305.i | 0.581078i | ||||||||
\(636\) | 356238. | − | 189463.i | 0.880697 | − | 0.468392i | ||||
\(637\) | −1.42976e6 | −3.52358 | ||||||||
\(638\) | 754588.i | 1.85382i | ||||||||
\(639\) | 257057. | + | 173310.i | 0.629546 | + | 0.424445i | ||||
\(640\) | −63758.0 | −0.155659 | ||||||||
\(641\) | 39907.8i | 0.0971275i | 0.998820 | + | 0.0485637i | \(0.0154644\pi\) | ||||
−0.998820 | + | 0.0485637i | \(0.984536\pi\) | |||||||
\(642\) | −245363. | − | 461345.i | −0.595304 | − | 1.11932i | ||||
\(643\) | 154629. | 0.373999 | 0.186999 | − | 0.982360i | \(-0.440124\pi\) | ||||
0.186999 | + | 0.982360i | \(0.440124\pi\) | |||||||
\(644\) | 693035.i | 1.67103i | ||||||||
\(645\) | −34623.1 | + | 18414.0i | −0.0832235 | + | 0.0442618i | ||||
\(646\) | −288547. | −0.691435 | ||||||||
\(647\) | 658179.i | 1.57230i | 0.618036 | + | 0.786149i | \(0.287928\pi\) | ||||
−0.618036 | + | 0.786149i | \(0.712072\pi\) | |||||||
\(648\) | −51141.6 | + | 20687.1i | −0.121794 | + | 0.0492664i | ||||
\(649\) | 101933. | 0.242007 | ||||||||
\(650\) | 690101.i | 1.63338i | ||||||||
\(651\) | 488674. | + | 918833.i | 1.15307 | + | 2.16808i | ||||
\(652\) | −329430. | −0.774939 | ||||||||
\(653\) | 110641.i | 0.259472i | 0.991549 | + | 0.129736i | \(0.0414129\pi\) | ||||
−0.991549 | + | 0.129736i | \(0.958587\pi\) | |||||||
\(654\) | −100494. | + | 53447.1i | −0.234956 | + | 0.124959i | ||||
\(655\) | 260007. | 0.606041 | ||||||||
\(656\) | 206342.i | 0.479490i | ||||||||
\(657\) | −374193. | + | 555012.i | −0.866893 | + | 1.28579i | ||||
\(658\) | 247155. | 0.570844 | ||||||||
\(659\) | − | 240883.i | − | 0.554672i | −0.960773 | − | 0.277336i | \(-0.910549\pi\) | ||
0.960773 | − | 0.277336i | \(-0.0894515\pi\) | |||||||
\(660\) | 204728. | + | 384941.i | 0.469990 | + | 0.883703i | ||||
\(661\) | −164589. | −0.376701 | −0.188351 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188351 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(662\) | − | 549489.i | − | 1.25384i | ||||||
\(663\) | 922983. | − | 490881.i | 2.09974 | − | 1.11673i | ||||
\(664\) | −30818.9 | −0.0699006 | ||||||||
\(665\) | − | 173672.i | − | 0.392723i | ||||||
\(666\) | 220680. | + | 148784.i | 0.497525 | + | 0.335435i | ||||
\(667\) | 347264. | 0.780564 | ||||||||
\(668\) | 176323.i | 0.395144i | ||||||||
\(669\) | −247290. | − | 464969.i | −0.552528 | − | 1.03890i | ||||
\(670\) | 152661. | 0.340078 | ||||||||
\(671\) | − | 9516.34i | − | 0.0211361i | ||||||
\(672\) | −932247. | + | 495808.i | −2.06439 | + | 1.09793i | ||||
\(673\) | 590080. | 1.30281 | 0.651404 | − | 0.758731i | \(-0.274180\pi\) | ||||
0.651404 | + | 0.758731i | \(0.274180\pi\) | |||||||
\(674\) | − | 543960.i | − | 1.19742i | ||||||
\(675\) | −292668. | − | 30669.0i | −0.642345 | − | 0.0673119i | ||||
\(676\) | −974849. | −2.13326 | ||||||||
\(677\) | − | 605944.i | − | 1.32207i | −0.750355 | − | 0.661036i | \(-0.770117\pi\) | ||
0.750355 | − | 0.661036i | \(-0.229883\pi\) | |||||||
\(678\) | −213741. | − | 401889.i | −0.464975 | − | 0.874273i | ||||
\(679\) | 462702. | 1.00360 | ||||||||
\(680\) | 46921.2i | 0.101473i | ||||||||
\(681\) | 352022. | − | 187220.i | 0.759059 | − | 0.403699i | ||||
\(682\) | 1.71396e6 | 3.68496 | ||||||||
\(683\) | − | 417679.i | − | 0.895367i | −0.894192 | − | 0.447683i | \(-0.852249\pi\) | ||
0.894192 | − | 0.447683i | \(-0.147751\pi\) | |||||||
\(684\) | −91345.6 | + | 135486.i | −0.195243 | + | 0.289589i | ||||
\(685\) | −91226.1 | −0.194419 | ||||||||
\(686\) | − | 1.02483e6i | − | 2.17773i | ||||||
\(687\) | −122742. | − | 230786.i | −0.260063 | − | 0.488986i | ||||
\(688\) | −81434.4 | −0.172041 | ||||||||
\(689\) | − | 959001.i | − | 2.02014i | ||||||
\(690\) | 372940. | − | 198345.i | 0.783324 | − | 0.416604i | ||||
\(691\) | −205400. | −0.430175 | −0.215087 | − | 0.976595i | \(-0.569004\pi\) | ||||
−0.215087 | + | 0.976595i | \(0.569004\pi\) | |||||||
\(692\) | 117935.i | 0.246280i | ||||||||
\(693\) | −1.26550e6 | − | 853213.i | −2.63510 | − | 1.77660i | ||||
\(694\) | 786106. | 1.63216 | ||||||||
\(695\) | 480723.i | 0.995234i | ||||||||
\(696\) | 21594.0 | + | 40602.3i | 0.0445774 | + | 0.0838170i | ||||
\(697\) | 278354. | 0.572970 | ||||||||
\(698\) | − | 565562.i | − | 1.16083i | ||||||
\(699\) | 452837. | − | 240838.i | 0.926804 | − | 0.492913i | ||||
\(700\) | −489555. | −0.999091 | ||||||||
\(701\) | 152513.i | 0.310364i | 0.987886 | + | 0.155182i | \(0.0495965\pi\) | ||||
−0.987886 | + | 0.155182i | \(0.950404\pi\) | |||||||
\(702\) | 129889. | − | 1.23951e6i | 0.263571 | − | 2.51521i | ||||
\(703\) | −82938.5 | −0.167821 | ||||||||
\(704\) | 738339.i | 1.48974i | ||||||||
\(705\) | −33600.1 | − | 63176.9i | −0.0676025 | − | 0.127110i | ||||
\(706\) | −281979. | −0.565727 | ||||||||
\(707\) | − | 243493.i | − | 0.487133i | ||||||
\(708\) | −52132.4 | + | 27726.2i | −0.104002 | + | 0.0553125i | ||||
\(709\) | −444089. | −0.883441 | −0.441720 | − | 0.897153i | \(-0.645632\pi\) | ||||
−0.441720 | + | 0.897153i | \(0.645632\pi\) | |||||||
\(710\) | − | 314355.i | − | 0.623597i | ||||||
\(711\) | 211770. | − | 314102.i | 0.418915 | − | 0.621344i | ||||
\(712\) | −18201.4 | −0.0359041 | ||||||||
\(713\) | − | 788773.i | − | 1.55158i | ||||||
\(714\) | 733093. | + | 1.37840e6i | 1.43801 | + | 2.70384i | ||||
\(715\) | 1.03627e6 | 2.02703 | ||||||||
\(716\) | 240053.i | 0.468253i | ||||||||
\(717\) | −301519. | + | 160360.i | −0.586511 | + | 0.311931i | ||||
\(718\) | −1.12789e6 | −2.18784 | ||||||||
\(719\) | − | 218028.i | − | 0.421749i | −0.977513 | − | 0.210875i | \(-0.932369\pi\) | ||
0.977513 | − | 0.210875i | \(-0.0676312\pi\) | |||||||
\(720\) | 277823. | + | 187310.i | 0.535924 | + | 0.361324i | ||||
\(721\) | −898326. | −1.72808 | ||||||||
\(722\) | 612252.i | 1.17451i | ||||||||
\(723\) | −276878. | − | 520601.i | −0.529677 | − | 0.995930i | ||||
\(724\) | 399117. | 0.761419 | ||||||||
\(725\) | 245305.i | 0.466691i | ||||||||
\(726\) | −1.57704e6 | + | 838737.i | −2.99206 | + | 1.59130i | ||||
\(727\) | 734861. | 1.39039 | 0.695195 | − | 0.718822i | \(-0.255318\pi\) | ||||
0.695195 | + | 0.718822i | \(0.255318\pi\) | |||||||
\(728\) | 218134.i | 0.411586i | ||||||||
\(729\) | 519896. | + | 110170.i | 0.978276 | + | 0.207305i | ||||
\(730\) | 678726. | 1.27365 | ||||||||
\(731\) | 109855.i | 0.205581i | ||||||||
\(732\) | 2588.47 | + | 4867.00i | 0.00483083 | + | 0.00908320i | ||||
\(733\) | −1.04114e6 | −1.93777 | −0.968885 | − | 0.247512i | \(-0.920387\pi\) | ||||
−0.968885 | + | 0.247512i | \(0.920387\pi\) | |||||||
\(734\) | − | 891107.i | − | 1.65401i | ||||||
\(735\) | −545802. | + | 290280.i | −1.01032 | + | 0.537332i | ||||
\(736\) | 800288. | 1.47737 | ||||||||
\(737\) | 418076.i | 0.769697i | ||||||||
\(738\) | 185509. | − | 275150.i | 0.340605 | − | 0.505193i | ||||
\(739\) | −131269. | −0.240365 | −0.120183 | − | 0.992752i | \(-0.538348\pi\) | ||||
−0.120183 | + | 0.992752i | \(0.538348\pi\) | |||||||
\(740\) | − | 128192.i | − | 0.234097i | ||||||
\(741\) | 182365. | + | 342894.i | 0.332128 | + | 0.624487i | ||||
\(742\) | 1.43219e6 | 2.60132 | ||||||||
\(743\) | 629101.i | 1.13957i | 0.821792 | + | 0.569787i | \(0.192974\pi\) | ||||
−0.821792 | + | 0.569787i | \(0.807026\pi\) | |||||||
\(744\) | 92223.7 | − | 49048.4i | 0.166608 | − | 0.0886093i | ||||
\(745\) | −536481. | −0.966589 | ||||||||
\(746\) | − | 1.01112e6i | − | 1.81687i | ||||||
\(747\) | 246165. | + | 165966.i | 0.441149 | + | 0.297426i | ||||
\(748\) | 1.22137e6 | 2.18295 | ||||||||
\(749\) | − | 881033.i | − | 1.57047i | ||||||
\(750\) | 357044. | + | 671334.i | 0.634744 | + | 1.19348i | ||||
\(751\) | −288597. | −0.511696 | −0.255848 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255848 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(752\) | − | 148594.i | − | 0.262764i | ||||||
\(753\) | 667133. | − | 354810.i | 1.17658 | − | 0.625756i | ||||
\(754\) | −1.03891e6 | −1.82741 | ||||||||
\(755\) | 139039.i | 0.243917i | ||||||||
\(756\) | 879300. | + | 92142.6i | 1.53849 | + | 0.161219i | ||||
\(757\) | −764156. | −1.33349 | −0.666746 | − | 0.745285i | \(-0.732313\pi\) | ||||
−0.666746 | + | 0.745285i | \(0.732313\pi\) | |||||||
\(758\) | − | 678550.i | − | 1.18098i | ||||||
\(759\) | 543186. | + | 1.02133e6i | 0.942899 | + | 1.77289i | ||||
\(760\) | −17431.5 | −0.0301792 | ||||||||
\(761\) | − | 390317.i | − | 0.673983i | −0.941508 | − | 0.336991i | \(-0.890591\pi\) | ||
0.941508 | − | 0.336991i | \(-0.109409\pi\) | |||||||
\(762\) | 690868. | − | 367433.i | 1.18983 | − | 0.632802i | ||||
\(763\) | −191914. | −0.329654 | ||||||||
\(764\) | 220251.i | 0.377338i | ||||||||
\(765\) | 252681. | − | 374782.i | 0.431767 | − | 0.640406i | ||||
\(766\) | 1.14609e6 | 1.95327 | ||||||||
\(767\) | 140341.i | 0.238558i | ||||||||
\(768\) | 321943. | + | 605336.i | 0.545829 | + | 1.02630i | ||||
\(769\) | 358531. | 0.606282 | 0.303141 | − | 0.952946i | \(-0.401965\pi\) | ||||
0.303141 | + | 0.952946i | \(0.401965\pi\) | |||||||
\(770\) | 1.54759e6i | 2.61020i | ||||||||
\(771\) | −100861. | + | 53642.2i | −0.169674 | + | 0.0902397i | ||||
\(772\) | 341081. | 0.572299 | ||||||||
\(773\) | − | 239213.i | − | 0.400336i | −0.979762 | − | 0.200168i | \(-0.935851\pi\) | ||
0.979762 | − | 0.200168i | \(-0.0641489\pi\) | |||||||
\(774\) | 108590. | + | 73212.4i | 0.181263 | + | 0.122209i | ||||
\(775\) | 557183. | 0.927672 | ||||||||
\(776\) | − | 46441.6i | − | 0.0771230i | ||||||
\(777\) | 210717. | + | 396202.i | 0.349026 | + | 0.656258i | ||||
\(778\) | −857538. | −1.41675 | ||||||||
\(779\) | 103410.i | 0.170407i | ||||||||
\(780\) | −529984. | + | 281868.i | −0.871112 | + | 0.463294i | ||||
\(781\) | 860890. | 1.41139 | ||||||||
\(782\) | − | 1.18329e6i | − | 1.93499i | ||||||
\(783\) | 46170.6 | − | 440597.i | 0.0753081 | − | 0.718651i | ||||
\(784\) | −1.28374e6 | −2.08855 | ||||||||
\(785\) | 411764.i | 0.668203i | ||||||||
\(786\) | −407737. | − | 766651.i | −0.659987 | − | 1.24095i | ||||
\(787\) | 1.05790e6 | 1.70802 | 0.854011 | − | 0.520256i | \(-0.174163\pi\) | ||||
0.854011 | + | 0.520256i | \(0.174163\pi\) | |||||||
\(788\) | − | 566819.i | − | 0.912835i | ||||||
\(789\) | −387411. | + | 206041.i | −0.622325 | + | 0.330979i | ||||
\(790\) | −384116. | −0.615473 | ||||||||
\(791\) | − | 767489.i | − | 1.22665i | ||||||
\(792\) | −85637.3 | + | 127019.i | −0.136525 | + | 0.202497i | ||||
\(793\) | 13102.0 | 0.0208350 | ||||||||
\(794\) | 282879.i | 0.448704i | ||||||||
\(795\) | −194703. | − | 366093.i | −0.308063 | − | 0.579238i | ||||
\(796\) | 1.02866e6 | 1.62347 | ||||||||
\(797\) | 392415.i | 0.617773i | 0.951099 | + | 0.308887i | \(0.0999564\pi\) | ||||
−0.951099 | + | 0.308887i | \(0.900044\pi\) | |||||||
\(798\) | −512086. | + | 272349.i | −0.804150 | + | 0.427681i | ||||
\(799\) | −200452. | −0.313991 | ||||||||
\(800\) | 565317.i | 0.883308i | ||||||||
\(801\) | 145383. | + | 98018.3i | 0.226594 | + | 0.152771i | ||||
\(802\) | −215224. | −0.334613 | ||||||||
\(803\) | 1.85875e6i | 2.88264i | ||||||||
\(804\) | −113718. | − | 213819.i | −0.175920 | − | 0.330776i | ||||
\(805\) | 712206. | 1.09904 | ||||||||
\(806\) | 2.35978e6i | 3.63246i | ||||||||
\(807\) | 537596. | − | 285916.i | 0.825484 | − | 0.439027i | ||||
\(808\) | −24439.5 | −0.0374343 | ||||||||
\(809\) | − | 51385.0i | − | 0.0785125i | −0.999229 | − | 0.0392563i | \(-0.987501\pi\) | ||
0.999229 | − | 0.0392563i | \(-0.0124989\pi\) | |||||||
\(810\) | −202070. | − | 499545.i | −0.307986 | − | 0.761386i | ||||
\(811\) | −581911. | −0.884739 | −0.442370 | − | 0.896833i | \(-0.645862\pi\) | ||||
−0.442370 | + | 0.896833i | \(0.645862\pi\) | |||||||
\(812\) | − | 736999.i | − | 1.11778i | ||||||
\(813\) | 322808. | + | 606963.i | 0.488386 | + | 0.918292i | ||||
\(814\) | 739064. | 1.11541 | ||||||||
\(815\) | 338542.i | 0.509680i | ||||||||
\(816\) | 828721. | − | 440749.i | 1.24459 | − | 0.661928i | ||||
\(817\) | −40811.7 | −0.0611421 | ||||||||
\(818\) | 750126.i | 1.12106i | ||||||||
\(819\) | 1.17470e6 | − | 1.74234e6i | 1.75129 | − | 2.59755i | ||||
\(820\) | −159833. | −0.237706 | ||||||||
\(821\) | 1.14823e6i | 1.70350i | 0.523947 | + | 0.851751i | \(0.324459\pi\) | ||||
−0.523947 | + | 0.851751i | \(0.675541\pi\) | |||||||
\(822\) | 143059. | + | 268987.i | 0.211724 | + | 0.398097i | ||||
\(823\) | −730019. | −1.07779 | −0.538895 | − | 0.842373i | \(-0.681158\pi\) | ||||
−0.538895 | + | 0.842373i | \(0.681158\pi\) | |||||||
\(824\) | 90165.3i | 0.132796i | ||||||||
\(825\) | −721460. | + | 383702.i | −1.06000 | + | 0.563750i | ||||
\(826\) | −209589. | −0.307191 | ||||||||
\(827\) | − | 254960.i | − | 0.372787i | −0.982475 | − | 0.186394i | \(-0.940320\pi\) | ||
0.982475 | − | 0.186394i | \(-0.0596800\pi\) | |||||||
\(828\) | −555610. | − | 374597.i | −0.810418 | − | 0.546390i | ||||
\(829\) | 418430. | 0.608856 | 0.304428 | − | 0.952535i | \(-0.401535\pi\) | ||||
0.304428 | + | 0.952535i | \(0.401535\pi\) | |||||||
\(830\) | − | 301036.i | − | 0.436980i | ||||||
\(831\) | 96063.1 | + | 180623.i | 0.139109 | + | 0.261560i | ||||
\(832\) | −1.01654e6 | −1.46851 | ||||||||
\(833\) | 1.73176e6i | 2.49573i | ||||||||
\(834\) | 1.41745e6 | − | 753860.i | 2.03787 | − | 1.08382i | ||||
\(835\) | 181200. | 0.259888 | ||||||||
\(836\) | 453746.i | 0.649232i | ||||||||
\(837\) | −1.00077e6 | − | 104871.i | −1.42851 | − | 0.149695i | ||||
\(838\) | −803363. | −1.14399 | ||||||||
\(839\) | 1.14030e6i | 1.61993i | 0.586480 | + | 0.809964i | \(0.300513\pi\) | ||||
−0.586480 | + | 0.809964i | \(0.699487\pi\) | |||||||
\(840\) | 44287.2 | + | 83271.4i | 0.0627654 | + | 0.118015i | ||||
\(841\) | 337988. | 0.477869 | ||||||||
\(842\) | 1.27625e6i | 1.80016i | ||||||||
\(843\) | −49388.7 | + | 26267.0i | −0.0694981 | + | 0.0369620i | ||||
\(844\) | −7015.30 | −0.00984831 | ||||||||
\(845\) | 1.00182e6i | 1.40305i | ||||||||
\(846\) | −133591. | + | 198145.i | −0.186654 | + | 0.276849i | ||||
\(847\) | −3.01168e6 | −4.19800 | ||||||||
\(848\) | − | 861060.i | − | 1.19741i | ||||||
\(849\) | −22670.2 | − | 42625.7i | −0.0314513 | − | 0.0591366i | ||||
\(850\) | 835868. | 1.15691 | ||||||||
\(851\) | − | 340120.i | − | 0.469649i | ||||||
\(852\) | −440290. | + | 234165.i | −0.606540 | + | 0.322583i | ||||
\(853\) | −989362. | −1.35974 | −0.679872 | − | 0.733331i | \(-0.737965\pi\) | ||||
−0.679872 | + | 0.733331i | \(0.737965\pi\) | |||||||
\(854\) | 19566.9i | 0.0268291i | ||||||||
\(855\) | 139234. | + | 93872.4i | 0.190464 | + | 0.128412i | ||||
\(856\) | −88429.7 | −0.120684 | ||||||||
\(857\) | − | 57011.8i | − | 0.0776252i | −0.999247 | − | 0.0388126i | \(-0.987642\pi\) | ||
0.999247 | − | 0.0388126i | \(-0.0123575\pi\) | |||||||
\(858\) | −1.62505e6 | − | 3.05552e6i | −2.20746 | − | 4.15060i | ||||
\(859\) | −840865. | −1.13957 | −0.569783 | − | 0.821795i | \(-0.692973\pi\) | ||||
−0.569783 | + | 0.821795i | \(0.692973\pi\) | |||||||
\(860\) | − | 63079.4i | − | 0.0852886i | ||||||
\(861\) | 493996. | − | 262728.i | 0.666373 | − | 0.354405i | ||||
\(862\) | 266621. | 0.358822 | ||||||||
\(863\) | − | 1.01442e6i | − | 1.36206i | −0.732257 | − | 0.681028i | \(-0.761533\pi\) | ||
0.732257 | − | 0.681028i | \(-0.238467\pi\) | |||||||
\(864\) | 106402. | − | 1.01538e6i | 0.142536 | − | 1.36019i | ||||
\(865\) | 121197. | 0.161979 | ||||||||
\(866\) | 1.36328e6i | 1.81782i | ||||||||
\(867\) | −241602. | − | 454274.i | −0.321412 | − | 0.604338i | ||||
\(868\) | −1.67401e6 | −2.22188 | ||||||||
\(869\) | − | 1.05194e6i | − | 1.39300i | ||||||
\(870\) | −396598. | + | 210928.i | −0.523977 | + | 0.278673i | ||||
\(871\) | −575604. | −0.758731 | ||||||||
\(872\) | 19262.5i | 0.0253326i | ||||||||
\(873\) | −250098. | + | 370950.i | −0.328157 | + | 0.486729i | ||||
\(874\) | 439600. | 0.575487 | ||||||||
\(875\) | 1.28205e6i | 1.67451i | ||||||||
\(876\) | −505586. | − | 950631.i | −0.658850 | − | 1.23881i | ||||
\(877\) | 1.22159e6 | 1.58828 | 0.794139 | − | 0.607736i | \(-0.207922\pi\) | ||||
0.794139 | + | 0.607736i | \(0.207922\pi\) | |||||||
\(878\) | − | 1.57661e6i | − | 2.04520i | ||||||
\(879\) | −1.26517e6 | + | 672873.i | −1.63747 | + | 0.870874i | ||||
\(880\) | 930437. | 1.20149 | ||||||||
\(881\) | 432537.i | 0.557278i | 0.960396 | + | 0.278639i | \(0.0898833\pi\) | ||||
−0.960396 | + | 0.278639i | \(0.910117\pi\) | |||||||
\(882\) | 1.71183e6 | + | 1.15413e6i | 2.20051 | + | 1.48360i | ||||
\(883\) | −1.35107e6 | −1.73283 | −0.866415 | − | 0.499324i | \(-0.833582\pi\) | ||||
−0.866415 | + | 0.499324i | \(0.833582\pi\) | |||||||
\(884\) | 1.68157e6i | 2.15185i | ||||||||
\(885\) | 28493.1 | + | 53574.4i | 0.0363793 | + | 0.0684024i | ||||
\(886\) | 264287. | 0.336674 | ||||||||
\(887\) | − | 1.12995e6i | − | 1.43619i | −0.695946 | − | 0.718094i | \(-0.745015\pi\) | ||
0.695946 | − | 0.718094i | \(-0.254985\pi\) | |||||||
\(888\) | 39767.0 | − | 21149.7i | 0.0504309 | − | 0.0268213i | ||||
\(889\) | 1.31935e6 | 1.66939 | ||||||||
\(890\) | − | 177789.i | − | 0.224453i | ||||||
\(891\) | 1.36805e6 | − | 553386.i | 1.72324 | − | 0.697064i | ||||
\(892\) | 847123. | 1.06467 | ||||||||
\(893\) | − | 74469.2i | − | 0.0933843i | ||||||
\(894\) | 841299. | + | 1.58186e6i | 1.05263 | + | 1.97921i | ||||
\(895\) | 246693. | 0.307972 | ||||||||
\(896\) | 359016.i | 0.447196i | ||||||||
\(897\) | −1.40616e6 | + | 747856.i | −1.74763 | + | 0.929465i | ||||
\(898\) | −1.96847e6 | −2.44104 | ||||||||
\(899\) | 838810.i | 1.03787i | ||||||||
\(900\) | 264612. | − | 392478.i | 0.326681 | − | 0.484541i | ||||
\(901\) | −1.16157e6 | −1.43085 | ||||||||
\(902\) | − | 921486.i | − | 1.13260i | ||||||
\(903\) | 103688. | + | 194960.i | 0.127160 | + | 0.239094i | ||||
\(904\) | −77033.2 | −0.0942630 | ||||||||
\(905\) | − | 410158.i | − | 0.500788i | ||||||
\(906\) | 409968. | − | 218038.i | 0.499451 | − | 0.265629i | ||||
\(907\) | −456693. | −0.555150 | −0.277575 | − | 0.960704i | \(-0.589531\pi\) | ||||
−0.277575 | + | 0.960704i | \(0.589531\pi\) | |||||||
\(908\) | 641345.i | 0.777894i | ||||||||
\(909\) | 195209. | + | 131612.i | 0.236251 | + | 0.159282i | ||||
\(910\) | −2.13071e6 | −2.57301 | ||||||||
\(911\) | 489237.i | 0.589499i | 0.955575 | + | 0.294749i | \(0.0952361\pi\) | ||||
−0.955575 | + | 0.294749i | \(0.904764\pi\) | |||||||
\(912\) | 163741. | + | 307875.i | 0.196864 | + | 0.370156i | ||||
\(913\) | 824413. | 0.989016 | ||||||||
\(914\) | − | 461868.i | − | 0.552873i | ||||||
\(915\) | 5001.63 | − | 2660.07i | 0.00597405 | − | 0.00317725i | ||||
\(916\) | 420467. | 0.501119 | ||||||||
\(917\) | − | 1.46408e6i | − | 1.74111i | ||||||
\(918\) | −1.50132e6 | − | 157325.i | −1.78151 | − | 0.186686i | ||||
\(919\) | 1.17471e6 | 1.39091 | 0.695455 | − | 0.718570i | \(-0.255203\pi\) | ||||
0.695455 | + | 0.718570i | \(0.255203\pi\) | |||||||
\(920\) | − | 71484.4i | − | 0.0844570i | ||||||
\(921\) | −86806.9 | − | 163219.i | −0.102338 | − | 0.192421i | ||||
\(922\) | 580393. | 0.682747 | ||||||||
\(923\) | 1.18527e6i | 1.39128i | ||||||||
\(924\) | 2.16757e6 | − | 1.15280e6i | 2.53880 | − | 1.35024i | ||||
\(925\) | 240258. | 0.280798 | ||||||||
\(926\) | − | 1.34900e6i | − | 1.57322i | ||||||
\(927\) | 485559. | − | 720192.i | 0.565044 | − | 0.838086i | ||||
\(928\) | −851055. | −0.988239 | ||||||||
\(929\) | − | 716985.i | − | 0.830765i | −0.909647 | − | 0.415383i | \(-0.863648\pi\) | ||
0.909647 | − | 0.415383i | \(-0.136352\pi\) | |||||||
\(930\) | 479100. | + | 900831.i | 0.553936 | + | 1.04154i | ||||
\(931\) | −643360. | −0.742257 | ||||||||
\(932\) | 825020.i | 0.949801i | ||||||||
\(933\) | −984354. | + | 523521.i | −1.13081 | + | 0.601410i | ||||
\(934\) | 1.60801e6 | 1.84329 | ||||||||
\(935\) | − | 1.25515e6i | − | 1.43573i | ||||||
\(936\) | −174879. | − | 117905.i | −0.199612 | − | 0.134580i | ||||
\(937\) | −185855. | −0.211687 | −0.105844 | − | 0.994383i | \(-0.533754\pi\) | ||||
−0.105844 | + | 0.994383i | \(0.533754\pi\) | |||||||
\(938\) | − | 859621.i | − | 0.977015i | ||||||
\(939\) | 92445.3 | + | 173821.i | 0.104846 | + | 0.197138i | ||||
\(940\) | 115101. | 0.130264 | ||||||||
\(941\) | 857870.i | 0.968818i | 0.874842 | + | 0.484409i | \(0.160965\pi\) | ||||
−0.874842 | + | 0.484409i | \(0.839035\pi\) | |||||||
\(942\) | 1.21412e6 | − | 645719.i | 1.36823 | − | 0.727682i | ||||
\(943\) | −424072. | −0.476887 | ||||||||
\(944\) | 126009.i | 0.141402i | ||||||||
\(945\) | 94691.4 | − | 903623.i | 0.106034 | − | 1.01187i | ||||
\(946\) | 363672. | 0.406375 | ||||||||
\(947\) | − | 561652.i | − | 0.626279i | −0.949707 | − | 0.313139i | \(-0.898619\pi\) | ||
0.949707 | − | 0.313139i | \(-0.101381\pi\) | |||||||
\(948\) | 286130. | + | 537998.i | 0.318381 | + | 0.598638i | ||||
\(949\) | −2.55912e6 | −2.84157 | ||||||||
\(950\) | 310530.i | 0.344078i | ||||||||
\(951\) | −595938. | + | 316945.i | −0.658931 | + | 0.350447i | ||||
\(952\) | 264210. | 0.291524 | ||||||||
\(953\) | − | 296997.i | − | 0.327014i | −0.986542 | − | 0.163507i | \(-0.947719\pi\) | ||
0.986542 | − | 0.163507i | \(-0.0522806\pi\) | |||||||
\(954\) | −774124. | + | 1.14820e6i | −0.850577 | + | 1.26159i | ||||
\(955\) | 226343. | 0.248176 | ||||||||
\(956\) | − | 549334.i | − | 0.601064i | ||||||
\(957\) | −577644. | − | 1.08612e6i | −0.630720 | − | 1.18592i | ||||
\(958\) | −695757. | −0.758101 | ||||||||
\(959\) | 513687.i | 0.558549i | ||||||||
\(960\) | −388058. | + | 206386.i | −0.421070 | + | 0.223943i | ||||
\(961\) | 981747. | 1.06305 | ||||||||
\(962\) | 1.01754e6i | 1.09951i | ||||||||
\(963\) | 706328. | + | 476212.i | 0.761648 | + | 0.513509i | ||||
\(964\) | 948479. | 1.02064 | ||||||||
\(965\) | − | 350516.i | − | 0.376403i | ||||||
\(966\) | −1.11687e6 | − | 2.10000e6i | −1.19687 | − | 2.25042i | ||||
\(967\) | −437855. | −0.468249 | −0.234125 | − | 0.972207i | \(-0.575222\pi\) | ||||
−0.234125 | + | 0.972207i | \(0.575222\pi\) | |||||||
\(968\) | 302284.i | 0.322600i | ||||||||
\(969\) | 415321. | − | 220885.i | 0.442320 | − | 0.235244i | ||||
\(970\) | 453636. | 0.482130 | ||||||||
\(971\) | − | 391031.i | − | 0.414737i | −0.978263 | − | 0.207368i | \(-0.933510\pi\) | ||
0.978263 | − | 0.207368i | \(-0.0664899\pi\) | |||||||
\(972\) | −549147. | + | 655135.i | −0.581240 | + | 0.693423i | ||||
\(973\) | 2.70691e6 | 2.85923 | ||||||||
\(974\) | − | 714926.i | − | 0.753604i | ||||||
\(975\) | −528279. | − | 993301.i | −0.555718 | − | 1.04489i | ||||
\(976\) | 11764.0 | 0.0123496 | ||||||||
\(977\) | 423993.i | 0.444190i | 0.975025 | + | 0.222095i | \(0.0712896\pi\) | ||||
−0.975025 | + | 0.222095i | \(0.928710\pi\) | |||||||
\(978\) | 998220. | − | 530895.i | 1.04363 | − | 0.555049i | ||||
\(979\) | 486891. | 0.508003 | ||||||||
\(980\) | − | 994392.i | − | 1.03539i | ||||||
\(981\) | 103733. | − | 153859.i | 0.107790 | − | 0.159876i | ||||
\(982\) | 274559. | 0.284717 | ||||||||
\(983\) | − | 1.60421e6i | − | 1.66018i | −0.557632 | − | 0.830088i | \(-0.688290\pi\) | ||
0.557632 | − | 0.830088i | \(-0.311710\pi\) | |||||||
\(984\) | −26370.1 | − | 49582.6i | −0.0272347 | − | 0.0512082i | ||||
\(985\) | −582499. | −0.600375 | ||||||||
\(986\) | 1.25836e6i | 1.29434i | ||||||||
\(987\) | −355744. | + | 189199.i | −0.365177 | + | 0.194216i | ||||
\(988\) | −624715. | −0.639982 | ||||||||
\(989\) | − | 167363.i | − | 0.171107i | ||||||
\(990\) | −1.24071e6 | − | 836495.i | −1.26590 | − | 0.853480i | ||||
\(991\) | 260625. | 0.265381 | 0.132690 | − | 0.991158i | \(-0.457638\pi\) | ||||
0.132690 | + | 0.991158i | \(0.457638\pi\) | |||||||
\(992\) | 1.93308e6i | 1.96439i | ||||||||
\(993\) | 420639. | + | 790910.i | 0.426591 | + | 0.802100i | ||||
\(994\) | −1.77011e6 | −1.79154 | ||||||||
\(995\) | − | 1.05711e6i | − | 1.06776i | ||||||
\(996\) | −421634. | + | 224243.i | −0.425028 | + | 0.226048i | ||||
\(997\) | −1.12829e6 | −1.13509 | −0.567547 | − | 0.823341i | \(-0.692107\pi\) | ||||
−0.567547 | + | 0.823341i | \(0.692107\pi\) | |||||||
\(998\) | − | 424101.i | − | 0.425802i | ||||||
\(999\) | −431533. | − | 45220.7i | −0.432397 | − | 0.0453113i |
(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 | 177.5.b.a.119.15 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.64 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.15 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.64 | yes | 78 | 3.2 | odd | 2 | inner |