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 | 119.64 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.15 |
$q$-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 | \(0.242422\pi\) | ||||
−0.723739 | + | 0.690074i | \(0.757578\pi\) | |||||||
\(3\) | 4.22607 | − | 7.94609i | 0.469563 | − | 0.882899i | ||||
\(4\) | −14.4769 | −0.904807 | ||||||||
\(5\) | − | 14.8774i | − | 0.595095i | −0.954707 | − | 0.297547i | \(-0.903831\pi\) | ||
0.954707 | − | 0.297547i | \(-0.0961686\pi\) | |||||||
\(6\) | 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 | \(-0.620287\pi\) | ||
0.368964 | − | 0.929444i | \(-0.379713\pi\) | |||||||
\(12\) | −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 | \(-0.775213\pi\) | ||
0.760840 | − | 0.648940i | \(-0.224787\pi\) | |||||||
\(18\) | 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 | \(0.181620\pi\) | ||||
−0.841589 | + | 0.540118i | \(0.818380\pi\) | |||||||
\(24\) | 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 | \(-0.882335\pi\) | ||
0.932452 | − | 0.361293i | \(-0.117665\pi\) | |||||||
\(30\) | 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 | \(0.0708449\pi\) | ||||
−0.975334 | + | 0.220733i | \(0.929155\pi\) | |||||||
\(42\) | 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 | \(-0.961402\pi\) | ||
0.992657 | − | 0.120963i | \(-0.0385983\pi\) | |||||||
\(48\) | −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 | \(-0.814160\pi\) | ||
0.834356 | − | 0.551226i | \(-0.185840\pi\) | |||||||
\(54\) | −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 | \(0.123949\pi\) | ||||
−0.925138 | + | 0.379632i | \(0.876051\pi\) | |||||||
\(72\) | 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 | \(0.0857099\pi\) | ||||
−0.963967 | + | 0.266024i | \(0.914290\pi\) | |||||||
\(84\) | −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 | \(0.0436309\pi\) | ||||
−0.990621 | + | 0.136642i | \(0.956369\pi\) | |||||||
\(90\) | −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 | \(0.0455028\pi\) | ||||
−0.989800 | + | 0.142465i | \(0.954497\pi\) | |||||||
\(102\) | 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 | \(0.151897\pi\) | ||||
−0.888285 | + | 0.459293i | \(0.848103\pi\) | |||||||
\(108\) | 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 | \(0.116794\pi\) | ||||
−0.933437 | + | 0.358740i | \(0.883206\pi\) | |||||||
\(114\) | −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 | \(0.170058\pi\) | ||||
−0.860650 | + | 0.509197i | \(0.829942\pi\) | |||||||
\(132\) | 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 | \(-0.947770\pi\) | ||
0.986568 | − | 0.163351i | \(-0.0522303\pi\) | |||||||
\(138\) | −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 | \(-0.698308\pi\) | ||
0.583476 | − | 0.812131i | \(-0.301692\pi\) | |||||||
\(150\) | 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 | \(0.0700701\pi\) | ||||
−0.975869 | + | 0.218358i | \(0.929930\pi\) | |||||||
\(168\) | 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 | \(0.0434554\pi\) | ||||
−0.990696 | + | 0.136096i | \(0.956545\pi\) | |||||||
\(174\) | 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 | \(0.0833134\pi\) | ||||
−0.965942 | + | 0.258759i | \(0.916687\pi\) | |||||||
\(180\) | 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 | \(0.0668641\pi\) | ||||
−0.978018 | + | 0.208518i | \(0.933136\pi\) | |||||||
\(192\) | 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 | \(-0.831700\pi\) | ||
0.863449 | − | 0.504436i | \(-0.168300\pi\) | |||||||
\(198\) | −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 | \(0.141440\pi\) | ||||
−0.902892 | + | 0.429867i | \(0.858560\pi\) | |||||||
\(228\) | 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 | \(0.175884\pi\) | ||||
−0.851186 | + | 0.524864i | \(0.824116\pi\) | |||||||
\(234\) | −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 | \(-0.892226\pi\) | ||
0.943226 | − | 0.332150i | \(-0.107774\pi\) | |||||||
\(240\) | 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 | \(0.232131\pi\) | ||||
−0.745668 | + | 0.666318i | \(0.767869\pi\) | |||||||
\(252\) | 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 | \(-0.969367\pi\) | ||
0.995373 | − | 0.0960890i | \(-0.0306333\pi\) | |||||||
\(258\) | 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 | \(-0.885355\pi\) | ||
0.935837 | − | 0.352433i | \(-0.114645\pi\) | |||||||
\(264\) | 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 | \(0.154840\pi\) | ||||
−0.884001 | + | 0.467485i | \(0.845160\pi\) | |||||||
\(270\) | −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 | \(-0.987469\pi\) | ||
0.999225 | − | 0.0393579i | \(-0.0125312\pi\) | |||||||
\(282\) | 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 | \(-0.622103\pi\) | ||
0.374258 | − | 0.927324i | \(-0.377897\pi\) | |||||||
\(294\) | 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 | \(-0.778771\pi\) | ||
0.768047 | − | 0.640393i | \(-0.221229\pi\) | |||||||
\(312\) | −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 | \(-0.878273\pi\) | ||
0.927766 | − | 0.373163i | \(-0.121727\pi\) | |||||||
\(318\) | 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 | \(-0.798615\pi\) | ||
0.806453 | − | 0.591299i | \(-0.201385\pi\) | |||||||
\(348\) | 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 | \(0.0657037\pi\) | ||||
−0.978772 | + | 0.204952i | \(0.934296\pi\) | |||||||
\(354\) | −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 | \(0.291279\pi\) | ||||
−0.609726 | + | 0.792612i | \(0.708721\pi\) | |||||||
\(360\) | −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 | \(-0.749764\pi\) | ||
0.706583 | − | 0.707631i | \(-0.250236\pi\) | |||||||
\(384\) | −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 | \(0.171563\pi\) | ||||
−0.858232 | + | 0.513262i | \(0.828437\pi\) | |||||||
\(390\) | −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 | \(0.0386818\pi\) | ||||
−0.992625 | + | 0.121224i | \(0.961318\pi\) | |||||||
\(402\) | 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 | \(0.136025\pi\) | ||||
−0.910074 | + | 0.414446i | \(0.863975\pi\) | |||||||
\(420\) | 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 | \(-0.958504\pi\) | ||
0.991515 | − | 0.129994i | \(-0.0414958\pi\) | |||||||
\(432\) | 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 | \(-0.961079\pi\) | ||
0.992534 | − | 0.121970i | \(-0.0389212\pi\) | |||||||
\(444\) | −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 | \(0.345392\pi\) | ||||
−0.466841 | + | 0.884341i | \(0.654608\pi\) | |||||||
\(450\) | 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 | \(-0.920442\pi\) | ||
0.968927 | − | 0.247346i | \(-0.0795584\pi\) | |||||||
\(462\) | 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 | \(-0.767241\pi\) | ||
0.744351 | − | 0.667789i | \(-0.232759\pi\) | |||||||
\(468\) | −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 | \(0.0885603\pi\) | ||||
−0.961546 | + | 0.274645i | \(0.911440\pi\) | |||||||
\(480\) | −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 | \(-0.967109\pi\) | ||
0.994666 | − | 0.103147i | \(-0.0328913\pi\) | |||||||
\(492\) | −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 | \(0.147886\pi\) | ||||
−0.894002 | + | 0.448064i | \(0.852114\pi\) | |||||||
\(504\) | 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 | \(-0.814121\pi\) | ||
0.834288 | − | 0.551329i | \(-0.185879\pi\) | |||||||
\(510\) | −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 | \(0.283820\pi\) | ||||
−0.628132 | + | 0.778107i | \(0.716180\pi\) | |||||||
\(522\) | −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 | \(0.0219689\pi\) | ||||
−0.997619 | + | 0.0689626i | \(0.978031\pi\) | |||||||
\(558\) | 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 | \(0.177694\pi\) | ||||
−0.848188 | + | 0.529695i | \(0.822306\pi\) | |||||||
\(564\) | 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 | \(-0.790591\pi\) | ||
0.791292 | − | 0.611438i | \(-0.209409\pi\) | |||||||
\(570\) | −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 | \(-0.880653\pi\) | ||
0.930530 | − | 0.366216i | \(-0.119347\pi\) | |||||||
\(588\) | −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 | \(-0.884332\pi\) | ||
0.934700 | − | 0.355437i | \(-0.115668\pi\) | |||||||
\(594\) | −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 | \(0.262841\pi\) | ||||
−0.678014 | + | 0.735049i | \(0.737159\pi\) | |||||||
\(600\) | 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 | \(-0.965891\pi\) | ||
0.994264 | − | 0.106953i | \(-0.0341093\pi\) | |||||||
\(618\) | −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 | \(-0.984536\pi\) | ||
0.998820 | − | 0.0485637i | \(-0.0154644\pi\) | |||||||
\(642\) | −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 | \(-0.712072\pi\) | ||
0.618036 | − | 0.786149i | \(-0.287928\pi\) | |||||||
\(648\) | −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 | \(-0.958587\pi\) | ||
0.991549 | − | 0.129736i | \(-0.0414129\pi\) | |||||||
\(654\) | −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 | \(0.0894515\pi\) | ||||
−0.960773 | + | 0.277336i | \(0.910549\pi\) | |||||||
\(660\) | 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 | \(0.229883\pi\) | ||||
−0.750355 | + | 0.661036i | \(0.770117\pi\) | |||||||
\(678\) | −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 | \(0.147751\pi\) | ||||
−0.894192 | + | 0.447683i | \(0.852249\pi\) | |||||||
\(684\) | −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 | \(-0.950404\pi\) | ||
0.987886 | − | 0.155182i | \(-0.0495965\pi\) | |||||||
\(702\) | 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 | \(0.0676312\pi\) | ||||
−0.977513 | + | 0.210875i | \(0.932369\pi\) | |||||||
\(720\) | 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 | \(-0.807026\pi\) | ||
0.821792 | − | 0.569787i | \(-0.192974\pi\) | |||||||
\(744\) | 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 | \(0.109409\pi\) | ||||
−0.941508 | + | 0.336991i | \(0.890591\pi\) | |||||||
\(762\) | 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 | \(0.0641489\pi\) | ||||
−0.979762 | + | 0.200168i | \(0.935851\pi\) | |||||||
\(774\) | 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 | \(-0.900044\pi\) | ||
0.951099 | − | 0.308887i | \(-0.0999564\pi\) | |||||||
\(798\) | −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 | \(0.0124989\pi\) | ||||
−0.999229 | + | 0.0392563i | \(0.987501\pi\) | |||||||
\(810\) | −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 | \(-0.675541\pi\) | ||
0.523947 | − | 0.851751i | \(-0.324459\pi\) | |||||||
\(822\) | 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 | \(0.0596800\pi\) | ||||
−0.982475 | + | 0.186394i | \(0.940320\pi\) | |||||||
\(828\) | −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 | \(-0.699487\pi\) | ||
0.586480 | − | 0.809964i | \(-0.300513\pi\) | |||||||
\(840\) | 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 | \(0.0123575\pi\) | ||||
−0.999247 | + | 0.0388126i | \(0.987642\pi\) | |||||||
\(858\) | −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 | \(0.238467\pi\) | ||||
−0.732257 | + | 0.681028i | \(0.761533\pi\) | |||||||
\(864\) | 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 | \(-0.910117\pi\) | ||
0.960396 | − | 0.278639i | \(-0.0898833\pi\) | |||||||
\(882\) | 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 | \(0.254985\pi\) | ||||
−0.695946 | + | 0.718094i | \(0.745015\pi\) | |||||||
\(888\) | 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 | \(-0.904764\pi\) | ||
0.955575 | − | 0.294749i | \(-0.0952361\pi\) | |||||||
\(912\) | 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 | \(0.136352\pi\) | ||||
−0.909647 | + | 0.415383i | \(0.863648\pi\) | |||||||
\(930\) | 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 | \(-0.839035\pi\) | ||
0.874842 | − | 0.484409i | \(-0.160965\pi\) | |||||||
\(942\) | 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 | \(0.101381\pi\) | ||||
−0.949707 | + | 0.313139i | \(0.898619\pi\) | |||||||
\(948\) | 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 | \(0.0522806\pi\) | ||||
−0.986542 | + | 0.163507i | \(0.947719\pi\) | |||||||
\(954\) | −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 | \(0.0664899\pi\) | ||||
−0.978263 | + | 0.207368i | \(0.933510\pi\) | |||||||
\(972\) | −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 | \(-0.928710\pi\) | ||
0.975025 | − | 0.222095i | \(-0.0712896\pi\) | |||||||
\(978\) | 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 | \(0.311710\pi\) | ||||
−0.557632 | + | 0.830088i | \(0.688290\pi\) | |||||||
\(984\) | −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.119.64 | yes | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.15 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.15 | ✓ | 78 | 3.2 | odd | 2 | inner | |
177.5.b.a.119.64 | yes | 78 | 1.1 | even | 1 | trivial |