Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,5,Mod(43,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.43");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.0897435397\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 57.7 | ||
Character | \(\chi\) | \(=\) | 175.57 |
Dual form | 175.5.g.c.43.7 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0151985 | + | 0.0151985i | 0.00379962 | + | 0.00379962i | 0.709004 | − | 0.705204i | \(-0.249145\pi\) |
−0.705204 | + | 0.709004i | \(0.749145\pi\) | |||||||
\(3\) | −8.40408 | + | 8.40408i | −0.933787 | + | 0.933787i | −0.997940 | − | 0.0641531i | \(-0.979565\pi\) |
0.0641531 | + | 0.997940i | \(0.479565\pi\) | |||||||
\(4\) | − | 15.9995i | − | 0.999971i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.255459 | −0.00709608 | ||||||||
\(7\) | 13.0958 | + | 13.0958i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0.486345 | − | 0.486345i | 0.00759914 | − | 0.00759914i | ||||
\(9\) | − | 60.2572i | − | 0.743916i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 178.541 | 1.47555 | 0.737774 | − | 0.675048i | \(-0.235877\pi\) | ||||
0.737774 | + | 0.675048i | \(0.235877\pi\) | |||||||
\(12\) | 134.461 | + | 134.461i | 0.933760 | + | 0.933760i | ||||
\(13\) | −130.151 | + | 130.151i | −0.770125 | + | 0.770125i | −0.978128 | − | 0.208004i | \(-0.933303\pi\) |
0.208004 | + | 0.978128i | \(0.433303\pi\) | |||||||
\(14\) | 0.398073i | 0.00203098i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −255.978 | −0.999913 | ||||||||
\(17\) | −219.300 | − | 219.300i | −0.758823 | − | 0.758823i | 0.217285 | − | 0.976108i | \(-0.430280\pi\) |
−0.976108 | + | 0.217285i | \(0.930280\pi\) | |||||||
\(18\) | 0.915819 | − | 0.915819i | 0.00282660 | − | 0.00282660i | ||||
\(19\) | 255.173i | 0.706851i | 0.935463 | + | 0.353426i | \(0.114983\pi\) | ||||
−0.935463 | + | 0.353426i | \(0.885017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −220.116 | −0.499130 | ||||||||
\(22\) | 2.71356 | + | 2.71356i | 0.00560653 | + | 0.00560653i | ||||
\(23\) | 54.1585 | − | 54.1585i | 0.102379 | − | 0.102379i | −0.654062 | − | 0.756441i | \(-0.726936\pi\) |
0.756441 | + | 0.654062i | \(0.226936\pi\) | |||||||
\(24\) | 8.17456i | 0.0141920i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.95620 | −0.00585237 | ||||||||
\(27\) | −174.324 | − | 174.324i | −0.239128 | − | 0.239128i | ||||
\(28\) | 209.527 | − | 209.527i | 0.267254 | − | 0.267254i | ||||
\(29\) | − | 438.959i | − | 0.521949i | −0.965346 | − | 0.260975i | \(-0.915956\pi\) | ||
0.965346 | − | 0.260975i | \(-0.0840439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1449.39 | −1.50821 | −0.754103 | − | 0.656757i | \(-0.771928\pi\) | ||||
−0.754103 | + | 0.656757i | \(0.771928\pi\) | |||||||
\(32\) | −11.6720 | − | 11.6720i | −0.0113984 | − | 0.0113984i | ||||
\(33\) | −1500.48 | + | 1500.48i | −1.37785 | + | 1.37785i | ||||
\(34\) | − | 6.66605i | − | 0.00576648i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −964.087 | −0.743895 | ||||||||
\(37\) | −914.326 | − | 914.326i | −0.667879 | − | 0.667879i | 0.289346 | − | 0.957225i | \(-0.406562\pi\) |
−0.957225 | + | 0.289346i | \(0.906562\pi\) | |||||||
\(38\) | −3.87825 | + | 3.87825i | −0.00268577 | + | 0.00268577i | ||||
\(39\) | − | 2187.60i | − | 1.43826i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1734.82 | −1.03202 | −0.516008 | − | 0.856584i | \(-0.672582\pi\) | ||||
−0.516008 | + | 0.856584i | \(0.672582\pi\) | |||||||
\(42\) | −3.34544 | − | 3.34544i | −0.00189651 | − | 0.00189651i | ||||
\(43\) | 103.893 | − | 103.893i | 0.0561885 | − | 0.0561885i | −0.678454 | − | 0.734643i | \(-0.737350\pi\) |
0.734643 | + | 0.678454i | \(0.237350\pi\) | |||||||
\(44\) | − | 2856.58i | − | 1.47551i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.64625 | 0.000778003 | ||||||||
\(47\) | −1422.27 | − | 1422.27i | −0.643851 | − | 0.643851i | 0.307649 | − | 0.951500i | \(-0.400458\pi\) |
−0.951500 | + | 0.307649i | \(0.900458\pi\) | |||||||
\(48\) | 2151.26 | − | 2151.26i | 0.933706 | − | 0.933706i | ||||
\(49\) | 343.000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3686.03 | 1.41716 | ||||||||
\(52\) | 2082.36 | + | 2082.36i | 0.770102 | + | 0.770102i | ||||
\(53\) | −3305.54 | + | 3305.54i | −1.17677 | + | 1.17677i | −0.196204 | + | 0.980563i | \(0.562861\pi\) |
−0.980563 | + | 0.196204i | \(0.937139\pi\) | |||||||
\(54\) | − | 5.29893i | − | 0.00181719i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.7381 | 0.00406191 | ||||||||
\(57\) | −2144.50 | − | 2144.50i | −0.660049 | − | 0.660049i | ||||
\(58\) | 6.67152 | − | 6.67152i | 0.00198321 | − | 0.00198321i | ||||
\(59\) | 4661.12i | 1.33902i | 0.742804 | + | 0.669509i | \(0.233495\pi\) | ||||
−0.742804 | + | 0.669509i | \(0.766505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3974.31 | −1.06808 | −0.534038 | − | 0.845460i | \(-0.679326\pi\) | ||||
−0.534038 | + | 0.845460i | \(0.679326\pi\) | |||||||
\(62\) | −22.0285 | − | 22.0285i | −0.00573061 | − | 0.00573061i | ||||
\(63\) | 789.116 | − | 789.116i | 0.198820 | − | 0.198820i | ||||
\(64\) | 4095.29i | 0.999827i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −45.6100 | −0.0104706 | ||||||||
\(67\) | 3729.40 | + | 3729.40i | 0.830786 | + | 0.830786i | 0.987624 | − | 0.156838i | \(-0.0501302\pi\) |
−0.156838 | + | 0.987624i | \(0.550130\pi\) | |||||||
\(68\) | −3508.69 | + | 3508.69i | −0.758801 | + | 0.758801i | ||||
\(69\) | 910.305i | 0.191200i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1249.55 | −0.247877 | −0.123938 | − | 0.992290i | \(-0.539553\pi\) | ||||
−0.123938 | + | 0.992290i | \(0.539553\pi\) | |||||||
\(72\) | −29.3058 | − | 29.3058i | −0.00565312 | − | 0.00565312i | ||||
\(73\) | 3437.16 | − | 3437.16i | 0.644992 | − | 0.644992i | −0.306786 | − | 0.951779i | \(-0.599254\pi\) |
0.951779 | + | 0.306786i | \(0.0992536\pi\) | |||||||
\(74\) | − | 27.7928i | − | 0.00507538i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4082.66 | 0.706831 | ||||||||
\(77\) | 2338.14 | + | 2338.14i | 0.394357 | + | 0.394357i | ||||
\(78\) | 33.2482 | − | 33.2482i | 0.00546486 | − | 0.00546486i | ||||
\(79\) | − | 11135.9i | − | 1.78431i | −0.451731 | − | 0.892154i | \(-0.649193\pi\) | ||
0.451731 | − | 0.892154i | \(-0.350807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7810.90 | 1.19050 | ||||||||
\(82\) | −26.3666 | − | 26.3666i | −0.00392127 | − | 0.00392127i | ||||
\(83\) | −3632.77 | + | 3632.77i | −0.527329 | + | 0.527329i | −0.919775 | − | 0.392446i | \(-0.871629\pi\) |
0.392446 | + | 0.919775i | \(0.371629\pi\) | |||||||
\(84\) | 3521.76i | 0.499116i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.15802 | 0.000426990 | ||||||||
\(87\) | 3689.05 | + | 3689.05i | 0.487389 | + | 0.487389i | ||||
\(88\) | 86.8327 | − | 86.8327i | 0.0112129 | − | 0.0112129i | ||||
\(89\) | 8157.71i | 1.02988i | 0.857225 | + | 0.514942i | \(0.172186\pi\) | ||||
−0.857225 | + | 0.514942i | \(0.827814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3408.86 | −0.411649 | ||||||||
\(92\) | −866.511 | − | 866.511i | −0.102376 | − | 0.102376i | ||||
\(93\) | 12180.8 | − | 12180.8i | 1.40834 | − | 1.40834i | ||||
\(94\) | − | 43.2326i | − | 0.00489278i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 196.185 | 0.0212874 | ||||||||
\(97\) | −4381.16 | − | 4381.16i | −0.465635 | − | 0.465635i | 0.434862 | − | 0.900497i | \(-0.356797\pi\) |
−0.900497 | + | 0.434862i | \(0.856797\pi\) | |||||||
\(98\) | −5.21308 | + | 5.21308i | −0.000542803 | + | 0.000542803i | ||||
\(99\) | − | 10758.4i | − | 1.09768i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 410.097 | 0.0402016 | 0.0201008 | − | 0.999798i | \(-0.493601\pi\) | ||||
0.0201008 | + | 0.999798i | \(0.493601\pi\) | |||||||
\(102\) | 56.0221 | + | 56.0221i | 0.00538466 | + | 0.00538466i | ||||
\(103\) | 3073.57 | − | 3073.57i | 0.289713 | − | 0.289713i | −0.547254 | − | 0.836967i | \(-0.684327\pi\) |
0.836967 | + | 0.547254i | \(0.184327\pi\) | |||||||
\(104\) | 126.597i | 0.0117046i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.478 | −0.00894254 | ||||||||
\(107\) | −11506.0 | − | 11506.0i | −1.00498 | − | 1.00498i | −0.999988 | − | 0.00499151i | \(-0.998411\pi\) |
−0.00499151 | − | 0.999988i | \(-0.501589\pi\) | |||||||
\(108\) | −2789.11 | + | 2789.11i | −0.239121 | + | 0.239121i | ||||
\(109\) | 13007.3i | 1.09480i | 0.836871 | + | 0.547400i | \(0.184382\pi\) | ||||
−0.836871 | + | 0.547400i | \(0.815618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15368.1 | 1.24731 | ||||||||
\(112\) | −3352.23 | − | 3352.23i | −0.267238 | − | 0.267238i | ||||
\(113\) | 6514.25 | − | 6514.25i | 0.510162 | − | 0.510162i | −0.404414 | − | 0.914576i | \(-0.632525\pi\) |
0.914576 | + | 0.404414i | \(0.132525\pi\) | |||||||
\(114\) | − | 65.1863i | − | 0.00501587i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7023.15 | −0.521934 | ||||||||
\(117\) | 7842.54 | + | 7842.54i | 0.572908 | + | 0.572908i | ||||
\(118\) | −70.8420 | + | 70.8420i | −0.00508777 | + | 0.00508777i | ||||
\(119\) | − | 5743.81i | − | 0.405608i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17236.0 | 1.17724 | ||||||||
\(122\) | −60.4036 | − | 60.4036i | −0.00405829 | − | 0.00405829i | ||||
\(123\) | 14579.6 | − | 14579.6i | 0.963683 | − | 0.963683i | ||||
\(124\) | 23189.5i | 1.50816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 23.9868 | 0.00151088 | ||||||||
\(127\) | −5300.60 | − | 5300.60i | −0.328638 | − | 0.328638i | 0.523430 | − | 0.852068i | \(-0.324652\pi\) |
−0.852068 | + | 0.523430i | \(0.824652\pi\) | |||||||
\(128\) | −248.994 | + | 248.994i | −0.0151974 | + | 0.0151974i | ||||
\(129\) | 1746.24i | 0.104936i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3216.78 | −0.187447 | −0.0937234 | − | 0.995598i | \(-0.529877\pi\) | ||||
−0.0937234 | + | 0.995598i | \(0.529877\pi\) | |||||||
\(132\) | 24006.9 | + | 24006.9i | 1.37781 | + | 1.37781i | ||||
\(133\) | −3341.70 | + | 3341.70i | −0.188914 | + | 0.188914i | ||||
\(134\) | 113.362i | 0.00631335i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −213.311 | −0.0115328 | ||||||||
\(137\) | 9320.99 | + | 9320.99i | 0.496616 | + | 0.496616i | 0.910383 | − | 0.413767i | \(-0.135787\pi\) |
−0.413767 | + | 0.910383i | \(0.635787\pi\) | |||||||
\(138\) | −13.8353 | + | 13.8353i | −0.000726489 | + | 0.000726489i | ||||
\(139\) | − | 10358.2i | − | 0.536111i | −0.963404 | − | 0.268055i | \(-0.913619\pi\) | ||
0.963404 | − | 0.268055i | \(-0.0863810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23905.7 | 1.20244 | ||||||||
\(142\) | −18.9912 | − | 18.9912i | −0.000941838 | − | 0.000941838i | ||||
\(143\) | −23237.3 | + | 23237.3i | −1.13636 | + | 1.13636i | ||||
\(144\) | 15424.5i | 0.743852i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 104.479 | 0.00490146 | ||||||||
\(147\) | −2882.60 | − | 2882.60i | −0.133398 | − | 0.133398i | ||||
\(148\) | −14628.8 | + | 14628.8i | −0.667860 | + | 0.667860i | ||||
\(149\) | − | 3719.04i | − | 0.167517i | −0.996486 | − | 0.0837584i | \(-0.973308\pi\) | ||
0.996486 | − | 0.0837584i | \(-0.0266924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22024.4 | −0.965940 | −0.482970 | − | 0.875637i | \(-0.660442\pi\) | ||||
−0.482970 | + | 0.875637i | \(0.660442\pi\) | |||||||
\(152\) | 124.102 | + | 124.102i | 0.00537146 | + | 0.00537146i | ||||
\(153\) | −13214.4 | + | 13214.4i | −0.564500 | + | 0.564500i | ||||
\(154\) | 71.0725i | 0.00299682i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −35000.6 | −1.43822 | ||||||||
\(157\) | 11748.5 | + | 11748.5i | 0.476634 | + | 0.476634i | 0.904053 | − | 0.427420i | \(-0.140577\pi\) |
−0.427420 | + | 0.904053i | \(0.640577\pi\) | |||||||
\(158\) | 169.248 | − | 169.248i | 0.00677970 | − | 0.00677970i | ||||
\(159\) | − | 55560.0i | − | 2.19770i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1418.50 | 0.0547239 | ||||||||
\(162\) | 118.714 | + | 118.714i | 0.00452347 | + | 0.00452347i | ||||
\(163\) | −5346.78 | + | 5346.78i | −0.201241 | + | 0.201241i | −0.800532 | − | 0.599290i | \(-0.795450\pi\) |
0.599290 | + | 0.800532i | \(0.295450\pi\) | |||||||
\(164\) | 27756.3i | 1.03199i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −110.425 | −0.00400731 | ||||||||
\(167\) | 6998.41 | + | 6998.41i | 0.250938 | + | 0.250938i | 0.821355 | − | 0.570417i | \(-0.193218\pi\) |
−0.570417 | + | 0.821355i | \(0.693218\pi\) | |||||||
\(168\) | −107.052 | + | 107.052i | −0.00379296 | + | 0.00379296i | ||||
\(169\) | − | 5317.59i | − | 0.186184i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15376.0 | 0.525838 | ||||||||
\(172\) | −1662.23 | − | 1662.23i | −0.0561869 | − | 0.0561869i | ||||
\(173\) | 32836.2 | − | 32836.2i | 1.09714 | − | 1.09714i | 0.102392 | − | 0.994744i | \(-0.467350\pi\) |
0.994744 | − | 0.102392i | \(-0.0326496\pi\) | |||||||
\(174\) | 112.136i | 0.00370379i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −45702.6 | −1.47542 | ||||||||
\(177\) | −39172.5 | − | 39172.5i | −1.25036 | − | 1.25036i | ||||
\(178\) | −123.985 | + | 123.985i | −0.00391317 | + | 0.00391317i | ||||
\(179\) | 4157.69i | 0.129761i | 0.997893 | + | 0.0648807i | \(0.0206667\pi\) | ||||
−0.997893 | + | 0.0648807i | \(0.979333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48603.7 | 1.48359 | 0.741793 | − | 0.670629i | \(-0.233976\pi\) | ||||
0.741793 | + | 0.670629i | \(0.233976\pi\) | |||||||
\(182\) | −51.8096 | − | 51.8096i | −0.00156411 | − | 0.00156411i | ||||
\(183\) | 33400.5 | − | 33400.5i | 0.997356 | − | 0.997356i | ||||
\(184\) | − | 52.6794i | − | 0.00155598i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 370.258 | 0.0107023 | ||||||||
\(187\) | −39154.1 | − | 39154.1i | −1.11968 | − | 1.11968i | ||||
\(188\) | −22755.6 | + | 22755.6i | −0.643832 | + | 0.643832i | ||||
\(189\) | − | 4565.83i | − | 0.127819i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −59079.1 | −1.61945 | −0.809724 | − | 0.586811i | \(-0.800383\pi\) | ||||
−0.809724 | + | 0.586811i | \(0.800383\pi\) | |||||||
\(192\) | −34417.2 | − | 34417.2i | −0.933625 | − | 0.933625i | ||||
\(193\) | −41523.8 | + | 41523.8i | −1.11476 | + | 1.11476i | −0.122264 | + | 0.992498i | \(0.539016\pi\) |
−0.992498 | + | 0.122264i | \(0.960984\pi\) | |||||||
\(194\) | − | 133.174i | − | 0.00353848i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5487.84 | 0.142853 | ||||||||
\(197\) | −14556.7 | − | 14556.7i | −0.375085 | − | 0.375085i | 0.494240 | − | 0.869325i | \(-0.335446\pi\) |
−0.869325 | + | 0.494240i | \(0.835446\pi\) | |||||||
\(198\) | 163.512 | − | 163.512i | 0.00417079 | − | 0.00417079i | ||||
\(199\) | − | 68770.5i | − | 1.73658i | −0.496053 | − | 0.868292i | \(-0.665218\pi\) | ||
0.496053 | − | 0.868292i | \(-0.334782\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −62684.3 | −1.55155 | ||||||||
\(202\) | 6.23286 | + | 6.23286i | 0.000152751 | + | 0.000152751i | ||||
\(203\) | 5748.52 | − | 5748.52i | 0.139497 | − | 0.139497i | ||||
\(204\) | − | 58974.7i | − | 1.41712i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 93.4271 | 0.00220160 | ||||||||
\(207\) | −3263.44 | − | 3263.44i | −0.0761614 | − | 0.0761614i | ||||
\(208\) | 33315.8 | − | 33315.8i | 0.770058 | − | 0.770058i | ||||
\(209\) | 45559.0i | 1.04299i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −40600.3 | −0.911935 | −0.455968 | − | 0.889996i | \(-0.650707\pi\) | ||||
−0.455968 | + | 0.889996i | \(0.650707\pi\) | |||||||
\(212\) | 52887.1 | + | 52887.1i | 1.17673 | + | 1.17673i | ||||
\(213\) | 10501.3 | − | 10501.3i | 0.231464 | − | 0.231464i | ||||
\(214\) | − | 349.748i | − | 0.00763708i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −169.563 | −0.00363433 | ||||||||
\(217\) | −18980.9 | − | 18980.9i | −0.403085 | − | 0.403085i | ||||
\(218\) | −197.692 | + | 197.692i | −0.00415983 | + | 0.00415983i | ||||
\(219\) | 57772.4i | 1.20457i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 57084.2 | 1.16878 | ||||||||
\(222\) | 233.573 | + | 233.573i | 0.00473932 | + | 0.00473932i | ||||
\(223\) | −21915.3 | + | 21915.3i | −0.440695 | + | 0.440695i | −0.892246 | − | 0.451550i | \(-0.850871\pi\) |
0.451550 | + | 0.892246i | \(0.350871\pi\) | |||||||
\(224\) | − | 305.708i | − | 0.00609272i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 198.014 | 0.00387685 | ||||||||
\(227\) | 30850.1 | + | 30850.1i | 0.598694 | + | 0.598694i | 0.939965 | − | 0.341271i | \(-0.110857\pi\) |
−0.341271 | + | 0.939965i | \(0.610857\pi\) | |||||||
\(228\) | −34311.0 | + | 34311.0i | −0.660029 | + | 0.660029i | ||||
\(229\) | − | 63623.5i | − | 1.21324i | −0.794992 | − | 0.606620i | \(-0.792525\pi\) | ||
0.794992 | − | 0.606620i | \(-0.207475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −39299.9 | −0.736491 | ||||||||
\(232\) | −213.486 | − | 213.486i | −0.00396636 | − | 0.00396636i | ||||
\(233\) | −29781.5 | + | 29781.5i | −0.548574 | + | 0.548574i | −0.926028 | − | 0.377454i | \(-0.876800\pi\) |
0.377454 | + | 0.926028i | \(0.376800\pi\) | |||||||
\(234\) | 238.390i | 0.00435367i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 74575.8 | 1.33898 | ||||||||
\(237\) | 93586.8 | + | 93586.8i | 1.66616 | + | 1.66616i | ||||
\(238\) | 87.2973 | − | 87.2973i | 0.00154116 | − | 0.00154116i | ||||
\(239\) | 70756.8i | 1.23872i | 0.785108 | + | 0.619359i | \(0.212608\pi\) | ||||
−0.785108 | + | 0.619359i | \(0.787392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12911.9 | 0.222308 | 0.111154 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111154 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(242\) | 261.962 | + | 261.962i | 0.00447308 | + | 0.00447308i | ||||
\(243\) | −51523.2 | + | 51523.2i | −0.872550 | + | 0.872550i | ||||
\(244\) | 63587.2i | 1.06805i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 443.175 | 0.00732326 | ||||||||
\(247\) | −33211.1 | − | 33211.1i | −0.544364 | − | 0.544364i | ||||
\(248\) | −704.901 | + | 704.901i | −0.0114611 | + | 0.0114611i | ||||
\(249\) | − | 61060.2i | − | 0.984826i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −45510.3 | −0.722374 | −0.361187 | − | 0.932494i | \(-0.617628\pi\) | ||||
−0.361187 | + | 0.932494i | \(0.617628\pi\) | |||||||
\(252\) | −12625.5 | − | 12625.5i | −0.198814 | − | 0.198814i | ||||
\(253\) | 9669.53 | − | 9669.53i | 0.151065 | − | 0.151065i | ||||
\(254\) | − | 161.122i | − | 0.00249740i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65517.1 | 0.999711 | ||||||||
\(257\) | 28510.9 | + | 28510.9i | 0.431663 | + | 0.431663i | 0.889194 | − | 0.457530i | \(-0.151266\pi\) |
−0.457530 | + | 0.889194i | \(0.651266\pi\) | |||||||
\(258\) | −26.5403 | + | 26.5403i | −0.000398718 | + | 0.000398718i | ||||
\(259\) | − | 23947.7i | − | 0.356996i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26450.5 | −0.388287 | ||||||||
\(262\) | −48.8902 | − | 48.8902i | −0.000712228 | − | 0.000712228i | ||||
\(263\) | 28724.4 | − | 28724.4i | 0.415279 | − | 0.415279i | −0.468294 | − | 0.883573i | \(-0.655131\pi\) |
0.883573 | + | 0.468294i | \(0.155131\pi\) | |||||||
\(264\) | 1459.50i | 0.0209409i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −101.578 | −0.00143560 | ||||||||
\(267\) | −68558.1 | − | 68558.1i | −0.961692 | − | 0.961692i | ||||
\(268\) | 59668.6 | − | 59668.6i | 0.830762 | − | 0.830762i | ||||
\(269\) | 56575.8i | 0.781855i | 0.920422 | + | 0.390927i | \(0.127846\pi\) | ||||
−0.920422 | + | 0.390927i | \(0.872154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 85972.1 | 1.17063 | 0.585314 | − | 0.810807i | \(-0.300971\pi\) | ||||
0.585314 | + | 0.810807i | \(0.300971\pi\) | |||||||
\(272\) | 56135.9 | + | 56135.9i | 0.758757 | + | 0.758757i | ||||
\(273\) | 28648.4 | − | 28648.4i | 0.384392 | − | 0.384392i | ||||
\(274\) | 283.330i | 0.00377391i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14564.5 | 0.191195 | ||||||||
\(277\) | 52002.6 | + | 52002.6i | 0.677743 | + | 0.677743i | 0.959489 | − | 0.281746i | \(-0.0909135\pi\) |
−0.281746 | + | 0.959489i | \(0.590913\pi\) | |||||||
\(278\) | 157.429 | − | 157.429i | 0.00203702 | − | 0.00203702i | ||||
\(279\) | 87335.9i | 1.12198i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 48758.7 | 0.617503 | 0.308752 | − | 0.951143i | \(-0.400089\pi\) | ||||
0.308752 | + | 0.951143i | \(0.400089\pi\) | |||||||
\(282\) | 363.330 | + | 363.330i | 0.00456881 | + | 0.00456881i | ||||
\(283\) | 80206.3 | − | 80206.3i | 1.00146 | − | 1.00146i | 0.00146510 | − | 0.999999i | \(-0.499534\pi\) |
0.999999 | − | 0.00146510i | \(-0.000466356\pi\) | |||||||
\(284\) | 19992.2i | 0.247870i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −706.345 | −0.00863545 | ||||||||
\(287\) | −22718.8 | − | 22718.8i | −0.275818 | − | 0.275818i | ||||
\(288\) | −703.322 | + | 703.322i | −0.00847948 | + | 0.00847948i | ||||
\(289\) | 12663.7i | 0.151623i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 73639.3 | 0.869608 | ||||||||
\(292\) | −54993.1 | − | 54993.1i | −0.644974 | − | 0.644974i | ||||
\(293\) | 4087.77 | − | 4087.77i | 0.0476159 | − | 0.0476159i | −0.682898 | − | 0.730514i | \(-0.739281\pi\) |
0.730514 | + | 0.682898i | \(0.239281\pi\) | |||||||
\(294\) | − | 87.6224i | − | 0.00101373i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −889.356 | −0.0101506 | ||||||||
\(297\) | −31124.1 | − | 31124.1i | −0.352845 | − | 0.352845i | ||||
\(298\) | 56.5238 | − | 56.5238i | 0.000636501 | − | 0.000636501i | ||||
\(299\) | 14097.6i | 0.157689i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2721.11 | 0.0300340 | ||||||||
\(302\) | −334.738 | − | 334.738i | −0.00367021 | − | 0.00367021i | ||||
\(303\) | −3446.49 | + | 3446.49i | −0.0375398 | + | 0.0375398i | ||||
\(304\) | − | 65318.7i | − | 0.706790i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −401.678 | −0.00428978 | ||||||||
\(307\) | 23151.2 | + | 23151.2i | 0.245639 | + | 0.245639i | 0.819178 | − | 0.573539i | \(-0.194430\pi\) |
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(308\) | 37409.2 | − | 37409.2i | 0.394346 | − | 0.394346i | ||||
\(309\) | 51661.0i | 0.541060i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30470.3 | 0.315033 | 0.157517 | − | 0.987516i | \(-0.449651\pi\) | ||||
0.157517 | + | 0.987516i | \(0.449651\pi\) | |||||||
\(312\) | −1063.93 | − | 1063.93i | −0.0109296 | − | 0.0109296i | ||||
\(313\) | −12110.0 | + | 12110.0i | −0.123610 | + | 0.123610i | −0.766206 | − | 0.642595i | \(-0.777858\pi\) |
0.642595 | + | 0.766206i | \(0.277858\pi\) | |||||||
\(314\) | 357.120i | 0.00362206i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −178169. | −1.78426 | ||||||||
\(317\) | −52830.9 | − | 52830.9i | −0.525738 | − | 0.525738i | 0.393561 | − | 0.919299i | \(-0.371243\pi\) |
−0.919299 | + | 0.393561i | \(0.871243\pi\) | |||||||
\(318\) | 844.429 | − | 844.429i | 0.00835043 | − | 0.00835043i | ||||
\(319\) | − | 78372.4i | − | 0.770161i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 193395. | 1.87687 | ||||||||
\(322\) | 21.5590 | + | 21.5590i | 0.000207930 | + | 0.000207930i | ||||
\(323\) | 55959.4 | − | 55959.4i | 0.536375 | − | 0.536375i | ||||
\(324\) | − | 124971.i | − | 1.19047i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −162.526 | −0.00152928 | ||||||||
\(327\) | −109315. | − | 109315.i | −1.02231 | − | 1.02231i | ||||
\(328\) | −843.720 | + | 843.720i | −0.00784243 | + | 0.00784243i | ||||
\(329\) | − | 37251.4i | − | 0.344153i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −67516.0 | −0.616241 | −0.308121 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308121 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(332\) | 58122.7 | + | 58122.7i | 0.527314 | + | 0.527314i | ||||
\(333\) | −55094.8 | + | 55094.8i | −0.496846 | + | 0.496846i | ||||
\(334\) | 212.730i | 0.00190694i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 56344.9 | 0.499087 | ||||||||
\(337\) | 135510. | + | 135510.i | 1.19320 | + | 1.19320i | 0.976164 | + | 0.217033i | \(0.0696381\pi\) |
0.217033 | + | 0.976164i | \(0.430362\pi\) | |||||||
\(338\) | 80.8194 | − | 80.8194i | 0.000707428 | − | 0.000707428i | ||||
\(339\) | 109493.i | 0.952765i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −258775. | −2.22543 | ||||||||
\(342\) | 233.693 | + | 233.693i | 0.00199799 | + | 0.00199799i | ||||
\(343\) | −4491.86 | + | 4491.86i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 101.055i | − | 0.000853968i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 998.121 | 0.00833741 | ||||||||
\(347\) | 82622.8 | + | 82622.8i | 0.686185 | + | 0.686185i | 0.961387 | − | 0.275202i | \(-0.0887446\pi\) |
−0.275202 | + | 0.961387i | \(0.588745\pi\) | |||||||
\(348\) | 59023.1 | − | 59023.1i | 0.487375 | − | 0.487375i | ||||
\(349\) | 41675.4i | 0.342160i | 0.985257 | + | 0.171080i | \(0.0547256\pi\) | ||||
−0.985257 | + | 0.171080i | \(0.945274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 45376.9 | 0.368316 | ||||||||
\(352\) | −2083.93 | − | 2083.93i | −0.0168189 | − | 0.0168189i | ||||
\(353\) | −76506.9 | + | 76506.9i | −0.613976 | + | 0.613976i | −0.943980 | − | 0.330004i | \(-0.892950\pi\) |
0.330004 | + | 0.943980i | \(0.392950\pi\) | |||||||
\(354\) | − | 1190.72i | − | 0.00950178i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 130520. | 1.02985 | ||||||||
\(357\) | 48271.5 | + | 48271.5i | 0.378751 | + | 0.378751i | ||||
\(358\) | −63.1906 | + | 63.1906i | −0.000493045 | + | 0.000493045i | ||||
\(359\) | 39385.8i | 0.305598i | 0.988257 | + | 0.152799i | \(0.0488287\pi\) | ||||
−0.988257 | + | 0.152799i | \(0.951171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 65207.6 | 0.500361 | ||||||||
\(362\) | 738.704 | + | 738.704i | 0.00563707 | + | 0.00563707i | ||||
\(363\) | −144853. | + | 144853.i | −1.09929 | + | 1.09929i | ||||
\(364\) | 54540.3i | 0.411637i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1015.27 | 0.00757916 | ||||||||
\(367\) | 59666.2 | + | 59666.2i | 0.442992 | + | 0.442992i | 0.893016 | − | 0.450024i | \(-0.148585\pi\) |
−0.450024 | + | 0.893016i | \(0.648585\pi\) | |||||||
\(368\) | −13863.4 | + | 13863.4i | −0.102370 | + | 0.102370i | ||||
\(369\) | 104535.i | 0.767733i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −86577.3 | −0.629008 | ||||||||
\(372\) | −194886. | − | 194886.i | −1.40830 | − | 1.40830i | ||||
\(373\) | 151950. | − | 151950.i | 1.09215 | − | 1.09215i | 0.0968525 | − | 0.995299i | \(-0.469122\pi\) |
0.995299 | − | 0.0968525i | \(-0.0308775\pi\) | |||||||
\(374\) | − | 1190.17i | − | 0.00850872i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1383.42 | −0.00978542 | ||||||||
\(377\) | 57131.0 | + | 57131.0i | 0.401966 | + | 0.401966i | ||||
\(378\) | 69.3937 | − | 69.3937i | 0.000485665 | − | 0.000485665i | ||||
\(379\) | − | 200208.i | − | 1.39381i | −0.717165 | − | 0.696904i | \(-0.754561\pi\) | ||
0.717165 | − | 0.696904i | \(-0.245439\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 89093.4 | 0.613756 | ||||||||
\(382\) | −897.913 | − | 897.913i | −0.00615330 | − | 0.00615330i | ||||
\(383\) | −108161. | + | 108161.i | −0.737351 | + | 0.737351i | −0.972065 | − | 0.234714i | \(-0.924585\pi\) |
0.234714 | + | 0.972065i | \(0.424585\pi\) | |||||||
\(384\) | − | 4185.14i | − | 0.0283823i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1262.20 | −0.00847135 | ||||||||
\(387\) | −6260.27 | − | 6260.27i | −0.0417995 | − | 0.0417995i | ||||
\(388\) | −70096.6 | + | 70096.6i | −0.465622 | + | 0.465622i | ||||
\(389\) | 287702.i | 1.90127i | 0.310317 | + | 0.950633i | \(0.399565\pi\) | ||||
−0.310317 | + | 0.950633i | \(0.600435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23753.9 | −0.155375 | ||||||||
\(392\) | 166.816 | + | 166.816i | 0.00108559 | + | 0.00108559i | ||||
\(393\) | 27034.0 | − | 27034.0i | 0.175035 | − | 0.175035i | ||||
\(394\) | − | 442.480i | − | 0.00285037i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −172129. | −1.09765 | ||||||||
\(397\) | 15821.3 | + | 15821.3i | 0.100383 | + | 0.100383i | 0.755515 | − | 0.655132i | \(-0.227387\pi\) |
−0.655132 | + | 0.755515i | \(0.727387\pi\) | |||||||
\(398\) | 1045.21 | − | 1045.21i | 0.00659837 | − | 0.00659837i | ||||
\(399\) | − | 56167.8i | − | 0.352811i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37856.9 | 0.235427 | 0.117714 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117714 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(402\) | −952.707 | − | 952.707i | −0.00589532 | − | 0.00589532i | ||||
\(403\) | 188639. | − | 188639.i | 1.16151 | − | 1.16151i | ||||
\(404\) | − | 6561.36i | − | 0.0402005i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 174.738 | 0.00106007 | ||||||||
\(407\) | −163245. | − | 163245.i | −0.985488 | − | 0.985488i | ||||
\(408\) | 1792.68 | − | 1792.68i | 0.0107692 | − | 0.0107692i | ||||
\(409\) | − | 16990.5i | − | 0.101569i | −0.998710 | − | 0.0507844i | \(-0.983828\pi\) | ||
0.998710 | − | 0.0507844i | \(-0.0161721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −156669. | −0.927467 | ||||||||
\(412\) | −49175.6 | − | 49175.6i | −0.289705 | − | 0.289705i | ||||
\(413\) | −61041.1 | + | 61041.1i | −0.357868 | + | 0.357868i | ||||
\(414\) | − | 99.1987i | − | 0.000578769i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3038.24 | 0.0175564 | ||||||||
\(417\) | 87051.1 | + | 87051.1i | 0.500613 | + | 0.500613i | ||||
\(418\) | −692.428 | + | 692.428i | −0.00396298 | + | 0.00396298i | ||||
\(419\) | − | 291749.i | − | 1.66181i | −0.556413 | − | 0.830906i | \(-0.687823\pi\) | ||
0.556413 | − | 0.830906i | \(-0.312177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 105749. | 0.596637 | 0.298319 | − | 0.954466i | \(-0.403574\pi\) | ||||
0.298319 | + | 0.954466i | \(0.403574\pi\) | |||||||
\(422\) | −617.063 | − | 617.063i | −0.00346501 | − | 0.00346501i | ||||
\(423\) | −85701.8 | + | 85701.8i | −0.478971 | + | 0.478971i | ||||
\(424\) | 3215.26i | 0.0178848i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 319.208 | 0.00175895 | ||||||||
\(427\) | −52046.8 | − | 52046.8i | −0.285456 | − | 0.285456i | ||||
\(428\) | −184091. | + | 184091.i | −1.00495 | + | 1.00495i | ||||
\(429\) | − | 390577.i | − | 2.12223i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −193428. | −1.04127 | −0.520637 | − | 0.853778i | \(-0.674305\pi\) | ||||
−0.520637 | + | 0.853778i | \(0.674305\pi\) | |||||||
\(432\) | 44623.1 | + | 44623.1i | 0.239107 | + | 0.239107i | ||||
\(433\) | −123647. | + | 123647.i | −0.659488 | + | 0.659488i | −0.955259 | − | 0.295771i | \(-0.904424\pi\) |
0.295771 | + | 0.955259i | \(0.404424\pi\) | |||||||
\(434\) | − | 576.961i | − | 0.00306314i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 208111. | 1.09477 | ||||||||
\(437\) | 13819.8 | + | 13819.8i | 0.0723667 | + | 0.0723667i | ||||
\(438\) | −878.054 | + | 878.054i | −0.00457692 | + | 0.00457692i | ||||
\(439\) | 120323.i | 0.624337i | 0.950027 | + | 0.312168i | \(0.101055\pi\) | ||||
−0.950027 | + | 0.312168i | \(0.898945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20668.2 | 0.106274 | ||||||||
\(442\) | 867.594 | + | 867.594i | 0.00444091 | + | 0.00444091i | ||||
\(443\) | −42476.7 | + | 42476.7i | −0.216443 | + | 0.216443i | −0.806998 | − | 0.590555i | \(-0.798909\pi\) |
0.590555 | + | 0.806998i | \(0.298909\pi\) | |||||||
\(444\) | − | 245883.i | − | 1.24728i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −666.160 | −0.00334895 | ||||||||
\(447\) | 31255.1 | + | 31255.1i | 0.156425 | + | 0.156425i | ||||
\(448\) | −53631.1 | + | 53631.1i | −0.267215 | + | 0.267215i | ||||
\(449\) | − | 58862.3i | − | 0.291974i | −0.989286 | − | 0.145987i | \(-0.953364\pi\) | ||
0.989286 | − | 0.145987i | \(-0.0466358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −309737. | −1.52279 | ||||||||
\(452\) | −104225. | − | 104225.i | −0.510147 | − | 0.510147i | ||||
\(453\) | 185095. | − | 185095.i | 0.901983 | − | 0.901983i | ||||
\(454\) | 937.751i | 0.00454963i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2085.93 | −0.0100316 | ||||||||
\(457\) | −273815. | − | 273815.i | −1.31107 | − | 1.31107i | −0.920629 | − | 0.390438i | \(-0.872324\pi\) |
−0.390438 | − | 0.920629i | \(-0.627676\pi\) | |||||||
\(458\) | 966.981 | − | 966.981i | 0.00460985 | − | 0.00460985i | ||||
\(459\) | 76458.5i | 0.362911i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −361733. | −1.70210 | −0.851052 | − | 0.525082i | \(-0.824035\pi\) | ||||
−0.851052 | + | 0.525082i | \(0.824035\pi\) | |||||||
\(462\) | −597.299 | − | 597.299i | −0.00279839 | − | 0.00279839i | ||||
\(463\) | 16249.5 | − | 16249.5i | 0.0758014 | − | 0.0758014i | −0.668190 | − | 0.743991i | \(-0.732931\pi\) |
0.743991 | + | 0.668190i | \(0.232931\pi\) | |||||||
\(464\) | 112364.i | 0.521904i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −905.269 | −0.00416875 | ||||||||
\(467\) | 188589. | + | 188589.i | 0.864735 | + | 0.864735i | 0.991884 | − | 0.127148i | \(-0.0405824\pi\) |
−0.127148 | + | 0.991884i | \(0.540582\pi\) | |||||||
\(468\) | 125477. | − | 125477.i | 0.572892 | − | 0.572892i | ||||
\(469\) | 97678.9i | 0.444074i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −197471. | −0.890149 | ||||||||
\(472\) | 2266.91 | + | 2266.91i | 0.0101754 | + | 0.0101754i | ||||
\(473\) | 18549.1 | − | 18549.1i | 0.0829088 | − | 0.0829088i | ||||
\(474\) | 2844.76i | 0.0126616i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −91898.3 | −0.405596 | ||||||||
\(477\) | 199183. | + | 199183.i | 0.875416 | + | 0.875416i | ||||
\(478\) | −1075.40 | + | 1075.40i | −0.00470666 | + | 0.00470666i | ||||
\(479\) | 347260.i | 1.51351i | 0.653701 | + | 0.756753i | \(0.273215\pi\) | ||||
−0.653701 | + | 0.756753i | \(0.726785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 238001. | 1.02870 | ||||||||
\(482\) | 196.241 | + | 196.241i | 0.000844689 | + | 0.000844689i | ||||
\(483\) | −11921.2 | + | 11921.2i | −0.0511004 | + | 0.0511004i | ||||
\(484\) | − | 275768.i | − | 1.17721i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1566.15 | −0.00663072 | ||||||||
\(487\) | −35396.5 | − | 35396.5i | −0.149246 | − | 0.149246i | 0.628535 | − | 0.777781i | \(-0.283655\pi\) |
−0.777781 | + | 0.628535i | \(0.783655\pi\) | |||||||
\(488\) | −1932.89 | + | 1932.89i | −0.00811646 | + | 0.00811646i | ||||
\(489\) | − | 89869.6i | − | 0.375833i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −180759. | −0.749785 | −0.374893 | − | 0.927068i | \(-0.622320\pi\) | ||||
−0.374893 | + | 0.927068i | \(0.622320\pi\) | |||||||
\(492\) | −233266. | − | 233266.i | −0.963655 | − | 0.963655i | ||||
\(493\) | −96263.7 | + | 96263.7i | −0.396067 | + | 0.396067i | ||||
\(494\) | − | 1009.52i | − | 0.00413675i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 371010. | 1.50807 | ||||||||
\(497\) | −16363.8 | − | 16363.8i | −0.0662479 | − | 0.0662479i | ||||
\(498\) | 928.023 | − | 928.023i | 0.00374197 | − | 0.00374197i | ||||
\(499\) | − | 186215.i | − | 0.747847i | −0.927460 | − | 0.373923i | \(-0.878012\pi\) | ||
0.927460 | − | 0.373923i | \(-0.121988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −117630. | −0.468645 | ||||||||
\(502\) | −691.687 | − | 691.687i | −0.00274475 | − | 0.00274475i | ||||
\(503\) | 28470.2 | − | 28470.2i | 0.112526 | − | 0.112526i | −0.648602 | − | 0.761128i | \(-0.724646\pi\) |
0.761128 | + | 0.648602i | \(0.224646\pi\) | |||||||
\(504\) | − | 767.565i | − | 0.00302172i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 293.925 | 0.00114798 | ||||||||
\(507\) | 44689.5 | + | 44689.5i | 0.173856 | + | 0.173856i | ||||
\(508\) | −84807.2 | + | 84807.2i | −0.328629 | + | 0.328629i | ||||
\(509\) | 9013.98i | 0.0347921i | 0.999849 | + | 0.0173961i | \(0.00553762\pi\) | ||||
−0.999849 | + | 0.0173961i | \(0.994462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 90024.9 | 0.344763 | ||||||||
\(512\) | 4979.67 | + | 4979.67i | 0.0189959 | + | 0.0189959i | ||||
\(513\) | 44482.9 | − | 44482.9i | 0.169028 | − | 0.169028i | ||||
\(514\) | 866.647i | 0.00328032i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 27939.1 | 0.104933 | ||||||||
\(517\) | −253933. | − | 253933.i | −0.950033 | − | 0.950033i | ||||
\(518\) | 363.969 | − | 363.969i | 0.00135645 | − | 0.00135645i | ||||
\(519\) | 551916.i | 2.04898i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 123697. | 0.455704 | 0.227852 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227852 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(522\) | −402.007 | − | 402.007i | −0.00147534 | − | 0.00147534i | ||||
\(523\) | −82201.1 | + | 82201.1i | −0.300521 | + | 0.300521i | −0.841218 | − | 0.540697i | \(-0.818161\pi\) |
0.540697 | + | 0.841218i | \(0.318161\pi\) | |||||||
\(524\) | 51466.9i | 0.187441i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 873.135 | 0.00315580 | ||||||||
\(527\) | 317850. | + | 317850.i | 1.14446 | + | 1.14446i | ||||
\(528\) | 384089. | − | 384089.i | 1.37773 | − | 1.37773i | ||||
\(529\) | 273975.i | 0.979037i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 280866. | 0.996117 | ||||||||
\(532\) | 53465.6 | + | 53465.6i | 0.188909 | + | 0.188909i | ||||
\(533\) | 225788. | − | 225788.i | 0.794780 | − | 0.794780i | ||||
\(534\) | − | 2083.96i | − | 0.00730814i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3627.55 | 0.0126265 | ||||||||
\(537\) | −34941.5 | − | 34941.5i | −0.121170 | − | 0.121170i | ||||
\(538\) | −859.867 | + | 859.867i | −0.00297075 | + | 0.00297075i | ||||
\(539\) | 61239.7i | 0.210793i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17926.3 | 0.0612484 | 0.0306242 | − | 0.999531i | \(-0.490250\pi\) | ||||
0.0306242 | + | 0.999531i | \(0.490250\pi\) | |||||||
\(542\) | 1306.65 | + | 1306.65i | 0.00444795 | + | 0.00444795i | ||||
\(543\) | −408470. | + | 408470.i | −1.38535 | + | 1.38535i | ||||
\(544\) | 5119.33i | 0.0172988i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 870.825 | 0.00292109 | ||||||||
\(547\) | 336131. | + | 336131.i | 1.12340 | + | 1.12340i | 0.991227 | + | 0.132173i | \(0.0421956\pi\) |
0.132173 | + | 0.991227i | \(0.457804\pi\) | |||||||
\(548\) | 149132. | − | 149132.i | 0.496602 | − | 0.496602i | ||||
\(549\) | 239481.i | 0.794560i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 112011. | 0.368941 | ||||||||
\(552\) | 442.722 | + | 442.722i | 0.00145296 | + | 0.00145296i | ||||
\(553\) | 145833. | − | 145833.i | 0.476876 | − | 0.476876i | ||||
\(554\) | 1580.72i | 0.00515034i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −165726. | −0.536095 | ||||||||
\(557\) | −178158. | − | 178158.i | −0.574241 | − | 0.574241i | 0.359070 | − | 0.933311i | \(-0.383094\pi\) |
−0.933311 | + | 0.359070i | \(0.883094\pi\) | |||||||
\(558\) | −1327.37 | + | 1327.37i | −0.00426309 | + | 0.00426309i | ||||
\(559\) | 27043.4i | 0.0865443i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 658108. | 2.09108 | ||||||||
\(562\) | 741.058 | + | 741.058i | 0.00234628 | + | 0.00234628i | ||||
\(563\) | −289503. | + | 289503.i | −0.913348 | + | 0.913348i | −0.996534 | − | 0.0831863i | \(-0.973490\pi\) |
0.0831863 | + | 0.996534i | \(0.473490\pi\) | |||||||
\(564\) | − | 382480.i | − | 1.20240i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2438.03 | 0.00761037 | ||||||||
\(567\) | 102290. | + | 102290.i | 0.318176 | + | 0.318176i | ||||
\(568\) | −607.711 | + | 607.711i | −0.00188365 | + | 0.00188365i | ||||
\(569\) | 448419.i | 1.38503i | 0.721403 | + | 0.692516i | \(0.243498\pi\) | ||||
−0.721403 | + | 0.692516i | \(0.756502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 403775. | 1.23842 | 0.619209 | − | 0.785226i | \(-0.287453\pi\) | ||||
0.619209 | + | 0.785226i | \(0.287453\pi\) | |||||||
\(572\) | 371787. | + | 371787.i | 1.13632 | + | 1.13632i | ||||
\(573\) | 496506. | − | 496506.i | 1.51222 | − | 1.51222i | ||||
\(574\) | − | 690.584i | − | 0.00209601i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 246771. | 0.743787 | ||||||||
\(577\) | −314392. | − | 314392.i | −0.944321 | − | 0.944321i | 0.0542087 | − | 0.998530i | \(-0.482736\pi\) |
−0.998530 | + | 0.0542087i | \(0.982736\pi\) | |||||||
\(578\) | −192.470 | + | 192.470i | −0.000576112 | + | 0.000576112i | ||||
\(579\) | − | 697938.i | − | 2.08190i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −95148.1 | −0.281869 | ||||||||
\(582\) | 1119.21 | + | 1119.21i | 0.00330418 | + | 0.00330418i | ||||
\(583\) | −590175. | + | 590175.i | −1.73638 | + | 1.73638i | ||||
\(584\) | − | 3343.29i | − | 0.00980277i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 124.256 | 0.000361845 | ||||||||
\(587\) | 56100.9 | + | 56100.9i | 0.162815 | + | 0.162815i | 0.783812 | − | 0.620998i | \(-0.213272\pi\) |
−0.620998 | + | 0.783812i | \(0.713272\pi\) | |||||||
\(588\) | −46120.3 | + | 46120.3i | −0.133394 | + | 0.133394i | ||||
\(589\) | − | 369844.i | − | 1.06608i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 244671. | 0.700500 | ||||||||
\(592\) | 234047. | + | 234047.i | 0.667821 | + | 0.667821i | ||||
\(593\) | 65402.5 | − | 65402.5i | 0.185988 | − | 0.185988i | −0.607971 | − | 0.793959i | \(-0.708016\pi\) |
0.793959 | + | 0.607971i | \(0.208016\pi\) | |||||||
\(594\) | − | 946.078i | − | 0.00268135i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −59502.9 | −0.167512 | ||||||||
\(597\) | 577953. | + | 577953.i | 1.62160 | + | 1.62160i | ||||
\(598\) | −214.262 | + | 214.262i | −0.000599159 | + | 0.000599159i | ||||
\(599\) | − | 519621.i | − | 1.44822i | −0.689687 | − | 0.724108i | \(-0.742252\pi\) | ||
0.689687 | − | 0.724108i | \(-0.257748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −433485. | −1.20012 | −0.600060 | − | 0.799955i | \(-0.704857\pi\) | ||||
−0.600060 | + | 0.799955i | \(0.704857\pi\) | |||||||
\(602\) | 41.3568 | + | 41.3568i | 0.000114118 | + | 0.000114118i | ||||
\(603\) | 224723. | − | 224723.i | 0.618035 | − | 0.618035i | ||||
\(604\) | 352380.i | 0.965913i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −104.763 | −0.000285274 | ||||||||
\(607\) | −374141. | − | 374141.i | −1.01545 | − | 1.01545i | −0.999879 | − | 0.0155710i | \(-0.995043\pi\) |
−0.0155710 | − | 0.999879i | \(-0.504957\pi\) | |||||||
\(608\) | 2978.38 | − | 2978.38i | 0.00805700 | − | 0.00805700i | ||||
\(609\) | 96622.1i | 0.260521i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 370219. | 0.991690 | ||||||||
\(612\) | 211424. | + | 211424.i | 0.564484 | + | 0.564484i | ||||
\(613\) | 152256. | − | 152256.i | 0.405186 | − | 0.405186i | −0.474870 | − | 0.880056i | \(-0.657505\pi\) |
0.880056 | + | 0.474870i | \(0.157505\pi\) | |||||||
\(614\) | 703.727i | 0.00186667i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2274.29 | 0.00599355 | ||||||||
\(617\) | −408731. | − | 408731.i | −1.07366 | − | 1.07366i | −0.997062 | − | 0.0766005i | \(-0.975593\pi\) |
−0.0766005 | − | 0.997062i | \(-0.524407\pi\) | |||||||
\(618\) | −785.169 | + | 785.169i | −0.00205583 | + | 0.00205583i | ||||
\(619\) | 72206.4i | 0.188449i | 0.995551 | + | 0.0942247i | \(0.0300372\pi\) | ||||
−0.995551 | + | 0.0942247i | \(0.969963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18882.3 | −0.0489633 | ||||||||
\(622\) | 463.103 | + | 463.103i | 0.00119701 | + | 0.00119701i | ||||
\(623\) | −106832. | + | 106832.i | −0.275248 | + | 0.275248i | ||||
\(624\) | 559977.i | 1.43814i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −368.107 | −0.000939345 | ||||||||
\(627\) | −382882. | − | 382882.i | −0.973934 | − | 0.973934i | ||||
\(628\) | 187971. | − | 187971.i | 0.476620 | − | 0.476620i | ||||
\(629\) | 401023.i | 1.01360i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −453999. | −1.14024 | −0.570120 | − | 0.821561i | \(-0.693103\pi\) | ||||
−0.570120 | + | 0.821561i | \(0.693103\pi\) | |||||||
\(632\) | −5415.87 | − | 5415.87i | −0.0135592 | − | 0.0135592i | ||||
\(633\) | 341208. | − | 341208.i | 0.851553 | − | 0.851553i | ||||
\(634\) | − | 1605.90i | − | 0.00399521i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −888935. | −2.19764 | ||||||||
\(637\) | −44641.8 | − | 44641.8i | −0.110018 | − | 0.110018i | ||||
\(638\) | 1191.14 | − | 1191.14i | 0.00292632 | − | 0.00292632i | ||||
\(639\) | 75294.2i | 0.184400i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 419719. | 1.02151 | 0.510755 | − | 0.859727i | \(-0.329366\pi\) | ||||
0.510755 | + | 0.859727i | \(0.329366\pi\) | |||||||
\(642\) | 2939.31 | + | 2939.31i | 0.00713141 | + | 0.00713141i | ||||
\(643\) | 291772. | − | 291772.i | 0.705703 | − | 0.705703i | −0.259926 | − | 0.965629i | \(-0.583698\pi\) |
0.965629 | + | 0.259926i | \(0.0836982\pi\) | |||||||
\(644\) | − | 22695.3i | − | 0.0547223i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1701.00 | 0.00407604 | ||||||||
\(647\) | −123334. | − | 123334.i | −0.294628 | − | 0.294628i | 0.544278 | − | 0.838905i | \(-0.316804\pi\) |
−0.838905 | + | 0.544278i | \(0.816804\pi\) | |||||||
\(648\) | 3798.79 | − | 3798.79i | 0.00904681 | − | 0.00904681i | ||||
\(649\) | 832203.i | 1.97579i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 319033. | 0.752791 | ||||||||
\(652\) | 85546.1 | + | 85546.1i | 0.201236 | + | 0.201236i | ||||
\(653\) | −140737. | + | 140737.i | −0.330052 | + | 0.330052i | −0.852606 | − | 0.522554i | \(-0.824979\pi\) |
0.522554 | + | 0.852606i | \(0.324979\pi\) | |||||||
\(654\) | − | 3322.83i | − | 0.00776878i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 444075. | 1.03193 | ||||||||
\(657\) | −207114. | − | 207114.i | −0.479820 | − | 0.479820i | ||||
\(658\) | 566.166 | − | 566.166i | 0.00130765 | − | 0.00130765i | ||||
\(659\) | − | 38660.5i | − | 0.0890218i | −0.999009 | − | 0.0445109i | \(-0.985827\pi\) | ||
0.999009 | − | 0.0445109i | \(-0.0141729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −252816. | −0.578631 | −0.289315 | − | 0.957234i | \(-0.593428\pi\) | ||||
−0.289315 | + | 0.957234i | \(0.593428\pi\) | |||||||
\(662\) | −1026.14 | − | 1026.14i | −0.00234148 | − | 0.00234148i | ||||
\(663\) | −479740. | + | 479740.i | −1.09139 | + | 1.09139i | ||||
\(664\) | 3533.56i | 0.00801449i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1674.71 | −0.00377566 | ||||||||
\(667\) | −23773.4 | − | 23773.4i | −0.0534366 | − | 0.0534366i | ||||
\(668\) | 111971. | − | 111971.i | 0.250931 | − | 0.250931i | ||||
\(669\) | − | 368356.i | − | 0.823031i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −709579. | −1.57600 | ||||||||
\(672\) | 2569.20 | + | 2569.20i | 0.00568930 | + | 0.00568930i | ||||
\(673\) | −322576. | + | 322576.i | −0.712199 | + | 0.712199i | −0.966995 | − | 0.254796i | \(-0.917992\pi\) |
0.254796 | + | 0.966995i | \(0.417992\pi\) | |||||||
\(674\) | 4119.10i | 0.00906740i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −85079.0 | −0.186178 | ||||||||
\(677\) | −105500. | − | 105500.i | −0.230184 | − | 0.230184i | 0.582586 | − | 0.812769i | \(-0.302041\pi\) |
−0.812769 | + | 0.582586i | \(0.802041\pi\) | |||||||
\(678\) | −1664.12 | + | 1664.12i | −0.00362015 | + | 0.00362015i | ||||
\(679\) | − | 114750.i | − | 0.248893i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −518534. | −1.11811 | ||||||||
\(682\) | −3932.99 | − | 3932.99i | −0.00845580 | − | 0.00845580i | ||||
\(683\) | 424431. | − | 424431.i | 0.909841 | − | 0.909841i | −0.0864179 | − | 0.996259i | \(-0.527542\pi\) |
0.996259 | + | 0.0864179i | \(0.0275420\pi\) | |||||||
\(684\) | − | 246009.i | − | 0.525823i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −136.539 | −0.000290141 | ||||||||
\(687\) | 534697. | + | 534697.i | 1.13291 | + | 1.13291i | ||||
\(688\) | −26594.2 | + | 26594.2i | −0.0561836 | + | 0.0561836i | ||||
\(689\) | − | 860439.i | − | 1.81251i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 240516. | 0.503718 | 0.251859 | − | 0.967764i | \(-0.418958\pi\) | ||||
0.251859 | + | 0.967764i | \(0.418958\pi\) | |||||||
\(692\) | −525364. | − | 525364.i | −1.09710 | − | 1.09710i | ||||
\(693\) | 140890. | − | 140890.i | 0.293368 | − | 0.293368i | ||||
\(694\) | 2511.49i | 0.00521449i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3588.30 | 0.00740748 | ||||||||
\(697\) | 380445. | + | 380445.i | 0.783117 | + | 0.783117i | ||||
\(698\) | −633.403 | + | 633.403i | −0.00130008 | + | 0.00130008i | ||||
\(699\) | − | 500573.i | − | 1.02450i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 451921. | 0.919658 | 0.459829 | − | 0.888008i | \(-0.347911\pi\) | ||||
0.459829 | + | 0.888008i | \(0.347911\pi\) | |||||||
\(702\) | 689.661 | + | 689.661i | 0.00139946 | + | 0.00139946i | ||||
\(703\) | 233312. | − | 233312.i | 0.472091 | − | 0.472091i | ||||
\(704\) | 731179.i | 1.47529i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2325.58 | −0.00466576 | ||||||||
\(707\) | 5370.55 | + | 5370.55i | 0.0107443 | + | 0.0107443i | ||||
\(708\) | −626741. | + | 626741.i | −1.25032 | + | 1.25032i | ||||
\(709\) | 567115.i | 1.12818i | 0.825713 | + | 0.564091i | \(0.190773\pi\) | ||||
−0.825713 | + | 0.564091i | \(0.809227\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −671016. | −1.32738 | ||||||||
\(712\) | 3967.46 | + | 3967.46i | 0.00782623 | + | 0.00782623i | ||||
\(713\) | −78496.5 | + | 78496.5i | −0.154409 | + | 0.154409i | ||||
\(714\) | 1467.31i | 0.00287822i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 66521.1 | 0.129758 | ||||||||
\(717\) | −594646. | − | 594646.i | −1.15670 | − | 1.15670i | ||||
\(718\) | −598.605 | + | 598.605i | −0.00116116 | + | 0.00116116i | ||||
\(719\) | − | 316359.i | − | 0.611959i | −0.952038 | − | 0.305979i | \(-0.901016\pi\) | ||
0.952038 | − | 0.305979i | \(-0.0989838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 80501.6 | 0.154858 | ||||||||
\(722\) | 991.057 | + | 991.057i | 0.00190118 | + | 0.00190118i | ||||
\(723\) | −108513. | + | 108513.i | −0.207589 | + | 0.207589i | ||||
\(724\) | − | 777637.i | − | 1.48354i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4403.09 | −0.00835381 | ||||||||
\(727\) | −9776.49 | − | 9776.49i | −0.0184975 | − | 0.0184975i | 0.697798 | − | 0.716295i | \(-0.254164\pi\) |
−0.716295 | + | 0.697798i | \(0.754164\pi\) | |||||||
\(728\) | −1657.88 | + | 1657.88i | −0.00312818 | + | 0.00312818i | ||||
\(729\) | − | 233328.i | − | 0.439047i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45567.2 | −0.0852742 | ||||||||
\(732\) | −534392. | − | 534392.i | −0.997327 | − | 0.997327i | ||||
\(733\) | −160398. | + | 160398.i | −0.298533 | + | 0.298533i | −0.840439 | − | 0.541906i | \(-0.817703\pi\) |
0.541906 | + | 0.840439i | \(0.317703\pi\) | |||||||
\(734\) | 1813.67i | 0.00336641i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1264.28 | −0.00233392 | ||||||||
\(737\) | 665852. | + | 665852.i | 1.22586 | + | 1.22586i | ||||
\(738\) | −1588.78 | + | 1588.78i | −0.00291710 | + | 0.00291710i | ||||
\(739\) | − | 754750.i | − | 1.38202i | −0.722845 | − | 0.691010i | \(-0.757166\pi\) | ||
0.722845 | − | 0.691010i | \(-0.242834\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 558217. | 1.01664 | ||||||||
\(742\) | −1315.85 | − | 1315.85i | −0.00239000 | − | 0.00239000i | ||||
\(743\) | −212897. | + | 212897.i | −0.385649 | + | 0.385649i | −0.873132 | − | 0.487483i | \(-0.837915\pi\) |
0.487483 | + | 0.873132i | \(0.337915\pi\) | |||||||
\(744\) | − | 11848.1i | − | 0.0214044i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4618.82 | 0.00829953 | ||||||||
\(747\) | 218901. | + | 218901.i | 0.392289 | + | 0.392289i | ||||
\(748\) | −626447. | + | 626447.i | −1.11965 | + | 1.11965i | ||||
\(749\) | − | 301361.i | − | 0.537184i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −177487. | −0.314693 | −0.157347 | − | 0.987543i | \(-0.550294\pi\) | ||||
−0.157347 | + | 0.987543i | \(0.550294\pi\) | |||||||
\(752\) | 364069. | + | 364069.i | 0.643795 | + | 0.643795i | ||||
\(753\) | 382472. | − | 382472.i | 0.674543 | − | 0.674543i | ||||
\(754\) | 1736.61i | 0.00305464i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −73051.1 | −0.127815 | ||||||||
\(757\) | 402096. | + | 402096.i | 0.701678 | + | 0.701678i | 0.964771 | − | 0.263093i | \(-0.0847425\pi\) |
−0.263093 | + | 0.964771i | \(0.584742\pi\) | |||||||
\(758\) | 3042.86 | − | 3042.86i | 0.00529594 | − | 0.00529594i | ||||
\(759\) | 162527.i | 0.282125i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 374461. | 0.646603 | 0.323301 | − | 0.946296i | \(-0.395207\pi\) | ||||
0.323301 | + | 0.946296i | \(0.395207\pi\) | |||||||
\(762\) | 1354.09 | + | 1354.09i | 0.00233204 | + | 0.00233204i | ||||
\(763\) | −170341. | + | 170341.i | −0.292597 | + | 0.292597i | ||||
\(764\) | 945238.i | 1.61940i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3287.78 | −0.00560331 | ||||||||
\(767\) | −606650. | − | 606650.i | −1.03121 | − | 1.03121i | ||||
\(768\) | −550611. | + | 550611.i | −0.933517 | + | 0.933517i | ||||
\(769\) | − | 660539.i | − | 1.11698i | −0.829511 | − | 0.558490i | \(-0.811381\pi\) | ||
0.829511 | − | 0.558490i | \(-0.188619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −479217. | −0.806163 | ||||||||
\(772\) | 664361. | + | 664361.i | 1.11473 | + | 1.11473i | ||||
\(773\) | −166751. | + | 166751.i | −0.279067 | + | 0.279067i | −0.832737 | − | 0.553669i | \(-0.813227\pi\) |
0.553669 | + | 0.832737i | \(0.313227\pi\) | |||||||
\(774\) | − | 190.293i | − | 0.000317645i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4261.51 | −0.00707685 | ||||||||
\(777\) | 201258. | + | 201258.i | 0.333359 | + | 0.333359i | ||||
\(778\) | −4372.63 | + | 4372.63i | −0.00722410 | + | 0.00722410i | ||||
\(779\) | − | 442679.i | − | 0.729481i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −223096. | −0.365754 | ||||||||
\(782\) | −361.023 | − | 361.023i | −0.000590366 | − | 0.000590366i | ||||
\(783\) | −76521.2 | + | 76521.2i | −0.124813 | + | 0.124813i | ||||
\(784\) | − | 87800.4i | − | 0.142845i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 821.754 | 0.00133014 | ||||||||
\(787\) | −334297. | − | 334297.i | −0.539738 | − | 0.539738i | 0.383714 | − | 0.923452i | \(-0.374645\pi\) |
−0.923452 | + | 0.383714i | \(0.874645\pi\) | |||||||
\(788\) | −232900. | + | 232900.i | −0.375075 | + | 0.375075i | ||||
\(789\) | 482804.i | 0.775563i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 170619. | 0.272693 | ||||||||
\(792\) | −5232.29 | − | 5232.29i | −0.00834145 | − | 0.00834145i | ||||
\(793\) | 517261. | − | 517261.i | 0.822552 | − | 0.822552i | ||||
\(794\) | 480.919i | 0.000762836i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.10030e6 | −1.73653 | ||||||||
\(797\) | −316482. | − | 316482.i | −0.498232 | − | 0.498232i | 0.412655 | − | 0.910887i | \(-0.364602\pi\) |
−0.910887 | + | 0.412655i | \(0.864602\pi\) | |||||||
\(798\) | 853.666 | − | 853.666i | 0.00134055 | − | 0.00134055i | ||||
\(799\) | 623805.i | 0.977137i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 491561. | 0.766147 | ||||||||
\(802\) | 575.368 | + | 575.368i | 0.000894535 | + | 0.000894535i | ||||
\(803\) | 613676. | − | 613676.i | 0.951718 | − | 0.951718i | ||||
\(804\) | 1.00292e6i | 1.55151i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5734.06 | 0.00882657 | ||||||||
\(807\) | −475468. | − | 475468.i | −0.730086 | − | 0.730086i | ||||
\(808\) | 199.449 | − | 199.449i | 0.000305498 | − | 0.000305498i | ||||
\(809\) | − | 287899.i | − | 0.439889i | −0.975512 | − | 0.219945i | \(-0.929412\pi\) | ||
0.975512 | − | 0.219945i | \(-0.0705877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −265302. | −0.403366 | −0.201683 | − | 0.979451i | \(-0.564641\pi\) | ||||
−0.201683 | + | 0.979451i | \(0.564641\pi\) | |||||||
\(812\) | −91973.7 | − | 91973.7i | −0.139493 | − | 0.139493i | ||||
\(813\) | −722517. | + | 722517.i | −1.09312 | + | 1.09312i | ||||
\(814\) | − | 4962.16i | − | 0.00748897i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −943541. | −1.41703 | ||||||||
\(817\) | 26510.6 | + | 26510.6i | 0.0397169 | + | 0.0397169i | ||||
\(818\) | 258.230 | − | 258.230i | 0.000385923 | − | 0.000385923i | ||||
\(819\) | 205409.i | 0.306232i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −61802.8 | −0.0916899 | −0.0458450 | − | 0.998949i | \(-0.514598\pi\) | ||||
−0.0458450 | + | 0.998949i | \(0.514598\pi\) | |||||||
\(822\) | −2381.13 | − | 2381.13i | −0.00352403 | − | 0.00352403i | ||||
\(823\) | 729615. | − | 729615.i | 1.07719 | − | 1.07719i | 0.0804343 | − | 0.996760i | \(-0.474369\pi\) |
0.996760 | − | 0.0804343i | \(-0.0256307\pi\) | |||||||
\(824\) | − | 2989.63i | − | 0.00440314i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1855.47 | −0.00271952 | ||||||||
\(827\) | −341394. | − | 341394.i | −0.499165 | − | 0.499165i | 0.412013 | − | 0.911178i | \(-0.364826\pi\) |
−0.911178 | + | 0.412013i | \(0.864826\pi\) | |||||||
\(828\) | −52213.5 | + | 52213.5i | −0.0761592 | + | 0.0761592i | ||||
\(829\) | − | 83296.0i | − | 0.121203i | −0.998162 | − | 0.0606017i | \(-0.980698\pi\) | ||
0.998162 | − | 0.0606017i | \(-0.0193019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −874068. | −1.26574 | ||||||||
\(832\) | −533006. | − | 533006.i | −0.769991 | − | 0.769991i | ||||
\(833\) | 75219.8 | − | 75219.8i | 0.108403 | − | 0.108403i | ||||
\(834\) | 2646.09i | 0.00380428i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 728923. | 1.04296 | ||||||||
\(837\) | 252663. | + | 252663.i | 0.360654 | + | 0.360654i | ||||
\(838\) | 4434.15 | − | 4434.15i | 0.00631426 | − | 0.00631426i | ||||
\(839\) | − | 1.16611e6i | − | 1.65659i | −0.560296 | − | 0.828293i | \(-0.689312\pi\) | ||
0.560296 | − | 0.828293i | \(-0.310688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 514596. | 0.727569 | ||||||||
\(842\) | 1607.22 | + | 1607.22i | 0.00226700 | + | 0.00226700i | ||||
\(843\) | −409772. | + | 409772.i | −0.576616 | + | 0.576616i | ||||
\(844\) | 649586.i | 0.911909i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2605.08 | −0.00363982 | ||||||||
\(847\) | 225719. | + | 225719.i | 0.314632 | + | 0.314632i | ||||
\(848\) | 846144. | − | 846144.i | 1.17666 | − | 1.17666i | ||||
\(849\) | 1.34812e6i | 1.87031i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −99037.1 | −0.136754 | ||||||||
\(852\) | −168016. | − | 168016.i | −0.231457 | − | 0.231457i | ||||
\(853\) | 904459. | − | 904459.i | 1.24306 | − | 1.24306i | 0.284330 | − | 0.958726i | \(-0.408229\pi\) |
0.958726 | − | 0.284330i | \(-0.0917712\pi\) | |||||||
\(854\) | − | 1582.07i | − | 0.00216925i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11191.8 | −0.0152739 | ||||||||
\(857\) | 206785. | + | 206785.i | 0.281552 | + | 0.281552i | 0.833728 | − | 0.552176i | \(-0.186202\pi\) |
−0.552176 | + | 0.833728i | \(0.686202\pi\) | |||||||
\(858\) | 5936.19 | − | 5936.19i | 0.00806367 | − | 0.00806367i | ||||
\(859\) | 428256.i | 0.580386i | 0.956968 | + | 0.290193i | \(0.0937195\pi\) | ||||
−0.956968 | + | 0.290193i | \(0.906280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 381862. | 0.515110 | ||||||||
\(862\) | −2939.81 | − | 2939.81i | −0.00395645 | − | 0.00395645i | ||||
\(863\) | −572263. | + | 572263.i | −0.768376 | + | 0.768376i | −0.977821 | − | 0.209444i | \(-0.932835\pi\) |
0.209444 | + | 0.977821i | \(0.432835\pi\) | |||||||
\(864\) | 4069.42i | 0.00545136i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3758.49 | −0.00501161 | ||||||||
\(867\) | −106427. | − | 106427.i | −0.141584 | − | 0.141584i | ||||
\(868\) | −303685. | + | 303685.i | −0.403073 | + | 0.403073i | ||||
\(869\) | − | 1.98821e6i | − | 2.63283i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −970770. | −1.27962 | ||||||||
\(872\) | 6326.04 | + | 6326.04i | 0.00831953 | + | 0.00831953i | ||||
\(873\) | −263997. | + | 263997.i | −0.346394 | + | 0.346394i | ||||
\(874\) | 420.080i | 0.000549933i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 924332. | 1.20454 | ||||||||
\(877\) | −45559.5 | − | 45559.5i | −0.0592352 | − | 0.0592352i | 0.676869 | − | 0.736104i | \(-0.263336\pi\) |
−0.736104 | + | 0.676869i | \(0.763336\pi\) | |||||||
\(878\) | −1828.73 | + | 1828.73i | −0.00237225 | + | 0.00237225i | ||||
\(879\) | 68708.0i | 0.0889261i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −85914.1 | −0.110691 | −0.0553455 | − | 0.998467i | \(-0.517626\pi\) | ||||
−0.0553455 | + | 0.998467i | \(0.517626\pi\) | |||||||
\(882\) | 314.126 | + | 314.126i | 0.000403800 | + | 0.000403800i | ||||
\(883\) | 340402. | − | 340402.i | 0.436586 | − | 0.436586i | −0.454275 | − | 0.890861i | \(-0.650102\pi\) |
0.890861 | + | 0.454275i | \(0.150102\pi\) | |||||||
\(884\) | − | 913321.i | − | 1.16874i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1291.16 | −0.00164480 | ||||||||
\(887\) | −97903.9 | − | 97903.9i | −0.124438 | − | 0.124438i | 0.642145 | − | 0.766583i | \(-0.278045\pi\) |
−0.766583 | + | 0.642145i | \(0.778045\pi\) | |||||||
\(888\) | 7474.22 | − | 7474.22i | 0.00947851 | − | 0.00947851i | ||||
\(889\) | − | 138831.i | − | 0.175664i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.39457e6 | 1.75665 | ||||||||
\(892\) | 350635. | + | 350635.i | 0.440682 | + | 0.440682i | ||||
\(893\) | 362924. | − | 362924.i | 0.455107 | − | 0.455107i | ||||
\(894\) | 950.062i | 0.00118871i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6521.56 | −0.00812335 | ||||||||
\(897\) | −118477. | − | 118477.i | −0.147248 | − | 0.147248i | ||||
\(898\) | 894.619 | − | 894.619i | 0.00110939 | − | 0.00110939i | ||||
\(899\) | 636221.i | 0.787207i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.44981e6 | 1.78591 | ||||||||
\(902\) | −4707.53 | − | 4707.53i | −0.00578602 | − | 0.00578602i | ||||
\(903\) | −22868.4 | + | 22868.4i | −0.0280454 | + | 0.0280454i | ||||
\(904\) | − | 6336.35i | − | 0.00775358i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5626.33 | 0.00685439 | ||||||||
\(907\) | 398218. | + | 398218.i | 0.484068 | + | 0.484068i | 0.906428 | − | 0.422360i | \(-0.138798\pi\) |
−0.422360 | + | 0.906428i | \(0.638798\pi\) | |||||||
\(908\) | 493588. | − | 493588.i | 0.598677 | − | 0.598677i | ||||
\(909\) | − | 24711.3i | − | 0.0299067i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −250366. | −0.301674 | −0.150837 | − | 0.988559i | \(-0.548197\pi\) | ||||
−0.150837 | + | 0.988559i | \(0.548197\pi\) | |||||||
\(912\) | 548944. | + | 548944.i | 0.659991 | + | 0.659991i | ||||
\(913\) | −648600. | + | 648600.i | −0.778100 | + | 0.778100i | ||||
\(914\) | − | 8323.15i | − | 0.00996312i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.01795e6 | −1.21320 | ||||||||
\(917\) | −42126.3 | − | 42126.3i | −0.0500973 | − | 0.0500973i | ||||
\(918\) | −1162.05 | + | 1162.05i | −0.00137893 | + | 0.00137893i | ||||
\(919\) | − | 319536.i | − | 0.378345i | −0.981944 | − | 0.189173i | \(-0.939419\pi\) | ||
0.981944 | − | 0.189173i | \(-0.0605806\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −389129. | −0.458748 | ||||||||
\(922\) | −5497.79 | − | 5497.79i | −0.00646735 | − | 0.00646735i | ||||
\(923\) | 162630. | − | 162630.i | 0.190896 | − | 0.190896i | ||||
\(924\) | 628780.i | 0.736469i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 493.935 | 0.000576034 | ||||||||
\(927\) | −185204. | − | 185204.i | −0.215522 | − | 0.215522i | ||||
\(928\) | −5123.53 | + | 5123.53i | −0.00594940 | + | 0.00594940i | ||||
\(929\) | 318241.i | 0.368744i | 0.982857 | + | 0.184372i | \(0.0590251\pi\) | ||||
−0.982857 | + | 0.184372i | \(0.940975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −87524.4 | −0.100979 | ||||||||
\(932\) | 476491. | + | 476491.i | 0.548558 | + | 0.548558i | ||||
\(933\) | −256075. | + | 256075.i | −0.294174 | + | 0.294174i | ||||
\(934\) | 5732.55i | 0.00657134i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7628.36 | 0.00870722 | ||||||||
\(937\) | 201589. | + | 201589.i | 0.229608 | + | 0.229608i | 0.812529 | − | 0.582921i | \(-0.198090\pi\) |
−0.582921 | + | 0.812529i | \(0.698090\pi\) | |||||||
\(938\) | −1484.57 | + | 1484.57i | −0.00168731 | + | 0.00168731i | ||||
\(939\) | − | 203547.i | − | 0.230851i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −438035. | −0.494686 | −0.247343 | − | 0.968928i | \(-0.579557\pi\) | ||||
−0.247343 | + | 0.968928i | \(0.579557\pi\) | |||||||
\(942\) | −3001.27 | − | 3001.27i | −0.00338223 | − | 0.00338223i | ||||
\(943\) | −93955.1 | + | 93955.1i | −0.105657 | + | 0.105657i | ||||
\(944\) | − | 1.19314e6i | − | 1.33890i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 563.837 | 0.000630045 | ||||||||
\(947\) | −1.20314e6 | − | 1.20314e6i | −1.34158 | − | 1.34158i | −0.894485 | − | 0.447098i | \(-0.852457\pi\) |
−0.447098 | − | 0.894485i | \(-0.647543\pi\) | |||||||
\(948\) | 1.49734e6 | − | 1.49734e6i | 1.66612 | − | 1.66612i | ||||
\(949\) | 894701.i | 0.993449i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 887990. | 0.981855 | ||||||||
\(952\) | −2793.47 | − | 2793.47i | −0.00308227 | − | 0.00308227i | ||||
\(953\) | −323897. | + | 323897.i | −0.356633 | + | 0.356633i | −0.862570 | − | 0.505937i | \(-0.831147\pi\) |
0.505937 | + | 0.862570i | \(0.331147\pi\) | |||||||
\(954\) | 6054.55i | 0.00665250i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.13208e6 | 1.23868 | ||||||||
\(957\) | 658648. | + | 658648.i | 0.719167 | + | 0.719167i | ||||
\(958\) | −5277.83 | + | 5277.83i | −0.00575075 | + | 0.00575075i | ||||
\(959\) | 244132.i | 0.265453i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.17720e6 | 1.27468 | ||||||||
\(962\) | 3617.26 | + | 3617.26i | 0.00390867 | + | 0.00390867i | ||||
\(963\) | −693320. | + | 693320.i | −0.747620 | + | 0.747620i | ||||
\(964\) | − | 206584.i | − | 0.222302i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −362.368 | −0.000388325 | ||||||||
\(967\) | −206662. | − | 206662.i | −0.221008 | − | 0.221008i | 0.587915 | − | 0.808923i | \(-0.299949\pi\) |
−0.808923 | + | 0.587915i | \(0.799949\pi\) | |||||||
\(968\) | 8382.65 | − | 8382.65i | 0.00894603 | − | 0.00894603i | ||||
\(969\) | 940576.i | 1.00172i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 772001. | 0.818803 | 0.409402 | − | 0.912354i | \(-0.365737\pi\) | ||||
0.409402 | + | 0.912354i | \(0.365737\pi\) | |||||||
\(972\) | 824348. | + | 824348.i | 0.872525 | + | 0.872525i | ||||
\(973\) | 135649. | − | 135649.i | 0.143282 | − | 0.143282i | ||||
\(974\) | − | 1075.95i | − | 0.00113416i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.01734e6 | 1.06798 | ||||||||
\(977\) | 433267. | + | 433267.i | 0.453907 | + | 0.453907i | 0.896649 | − | 0.442742i | \(-0.145994\pi\) |
−0.442742 | + | 0.896649i | \(0.645994\pi\) | |||||||
\(978\) | 1365.88 | − | 1365.88i | 0.00142802 | − | 0.00142802i | ||||
\(979\) | 1.45649e6i | 1.51964i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 783784. | 0.814439 | ||||||||
\(982\) | −2747.26 | − | 2747.26i | −0.00284890 | − | 0.00284890i | ||||
\(983\) | −697281. | + | 697281.i | −0.721607 | + | 0.721607i | −0.968933 | − | 0.247325i | \(-0.920448\pi\) |
0.247325 | + | 0.968933i | \(0.420448\pi\) | |||||||
\(984\) | − | 14181.4i | − | 0.0146463i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2926.13 | −0.00300981 | ||||||||
\(987\) | 313064. | + | 313064.i | 0.321365 | + | 0.321365i | ||||
\(988\) | −531362. | + | 531362.i | −0.544348 | + | 0.544348i | ||||
\(989\) | − | 11253.3i | − | 0.0115050i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.67220e6 | 1.70271 | 0.851354 | − | 0.524591i | \(-0.175782\pi\) | ||||
0.851354 | + | 0.524591i | \(0.175782\pi\) | |||||||
\(992\) | 16917.2 | + | 16917.2i | 0.0171912 | + | 0.0171912i | ||||
\(993\) | 567410. | − | 567410.i | 0.575438 | − | 0.575438i | ||||
\(994\) | − | 497.411i | − | 0.000503434i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −976935. | −0.984798 | ||||||||
\(997\) | 387338. | + | 387338.i | 0.389672 | + | 0.389672i | 0.874571 | − | 0.484898i | \(-0.161143\pi\) |
−0.484898 | + | 0.874571i | \(0.661143\pi\) | |||||||
\(998\) | 2830.18 | − | 2830.18i | 0.00284154 | − | 0.00284154i | ||||
\(999\) | 318778.i | 0.319417i |
(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 | 175.5.g.c.57.7 | 24 | ||
5.2 | odd | 4 | 35.5.g.a.8.6 | ✓ | 24 | ||
5.3 | odd | 4 | inner | 175.5.g.c.43.7 | 24 | ||
5.4 | even | 2 | 35.5.g.a.22.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.6 | ✓ | 24 | 5.2 | odd | 4 | ||
35.5.g.a.22.6 | yes | 24 | 5.4 | even | 2 | ||
175.5.g.c.43.7 | 24 | 5.3 | odd | 4 | inner | ||
175.5.g.c.57.7 | 24 | 1.1 | even | 1 | trivial |