Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(91,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (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: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.17 | ||
Character | \(\chi\) | \(=\) | 230.91 |
Dual form | 230.5.d.a.91.32 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | 0.707107 | ||||||||
\(3\) | 17.4598 | 1.93998 | 0.969988 | − | 0.243154i | \(-0.0781819\pi\) | ||||
0.969988 | + | 0.243154i | \(0.0781819\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | 49.3837 | 1.37177 | ||||||||
\(7\) | − | 69.3646i | − | 1.41560i | −0.706411 | − | 0.707802i | \(-0.749687\pi\) | ||
0.706411 | − | 0.707802i | \(-0.250313\pi\) | |||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | 223.844 | 2.76351 | ||||||||
\(10\) | 31.6228i | 0.316228i | ||||||||
\(11\) | 62.8983i | 0.519821i | 0.965633 | + | 0.259910i | \(0.0836930\pi\) | ||||
−0.965633 | + | 0.259910i | \(0.916307\pi\) | |||||||
\(12\) | 139.678 | 0.969988 | ||||||||
\(13\) | −93.8132 | −0.555108 | −0.277554 | − | 0.960710i | \(-0.589524\pi\) | ||||
−0.277554 | + | 0.960710i | \(0.589524\pi\) | |||||||
\(14\) | − | 196.193i | − | 1.00098i | ||||||
\(15\) | 195.206i | 0.867583i | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − | 294.893i | − | 1.02039i | −0.860059 | − | 0.510195i | \(-0.829573\pi\) | ||
0.860059 | − | 0.510195i | \(-0.170427\pi\) | |||||||
\(18\) | 633.126 | 1.95409 | ||||||||
\(19\) | 108.705i | 0.301121i | 0.988601 | + | 0.150560i | \(0.0481078\pi\) | ||||
−0.988601 | + | 0.150560i | \(0.951892\pi\) | |||||||
\(20\) | 89.4427i | 0.223607i | ||||||||
\(21\) | − | 1211.09i | − | 2.74624i | ||||||
\(22\) | 177.903i | 0.367569i | ||||||||
\(23\) | −94.8175 | + | 520.433i | −0.179239 | + | 0.983806i | ||||
\(24\) | 395.070 | 0.685885 | ||||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | −265.344 | −0.392520 | ||||||||
\(27\) | 2494.02 | 3.42116 | ||||||||
\(28\) | − | 554.917i | − | 0.707802i | ||||||
\(29\) | 365.974 | 0.435165 | 0.217583 | − | 0.976042i | \(-0.430183\pi\) | ||||
0.217583 | + | 0.976042i | \(0.430183\pi\) | |||||||
\(30\) | 552.127i | 0.613474i | ||||||||
\(31\) | −501.410 | −0.521759 | −0.260879 | − | 0.965371i | \(-0.584012\pi\) | ||||
−0.260879 | + | 0.965371i | \(0.584012\pi\) | |||||||
\(32\) | 181.019 | 0.176777 | ||||||||
\(33\) | 1098.19i | 1.00844i | ||||||||
\(34\) | − | 834.082i | − | 0.721525i | ||||||
\(35\) | 775.520 | 0.633077 | ||||||||
\(36\) | 1790.75 | 1.38175 | ||||||||
\(37\) | 1893.15i | 1.38287i | 0.722437 | + | 0.691437i | \(0.243022\pi\) | ||||
−0.722437 | + | 0.691437i | \(0.756978\pi\) | |||||||
\(38\) | 307.463i | 0.212924i | ||||||||
\(39\) | −1637.96 | −1.07690 | ||||||||
\(40\) | 252.982i | 0.158114i | ||||||||
\(41\) | −2682.34 | −1.59568 | −0.797841 | − | 0.602868i | \(-0.794025\pi\) | ||||
−0.797841 | + | 0.602868i | \(0.794025\pi\) | |||||||
\(42\) | − | 3425.48i | − | 1.94188i | ||||||
\(43\) | − | 606.856i | − | 0.328208i | −0.986443 | − | 0.164104i | \(-0.947527\pi\) | ||
0.986443 | − | 0.164104i | \(-0.0524732\pi\) | |||||||
\(44\) | 503.186i | 0.259910i | ||||||||
\(45\) | 2502.65i | 1.23588i | ||||||||
\(46\) | −268.184 | + | 1472.01i | −0.126741 | + | 0.695656i | ||||
\(47\) | −1816.05 | −0.822113 | −0.411056 | − | 0.911610i | \(-0.634840\pi\) | ||||
−0.411056 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(48\) | 1117.43 | 0.484994 | ||||||||
\(49\) | −2410.45 | −1.00394 | ||||||||
\(50\) | −353.553 | −0.141421 | ||||||||
\(51\) | − | 5148.76i | − | 1.97953i | ||||||
\(52\) | −750.506 | −0.277554 | ||||||||
\(53\) | − | 866.268i | − | 0.308390i | −0.988040 | − | 0.154195i | \(-0.950722\pi\) | ||
0.988040 | − | 0.154195i | \(-0.0492784\pi\) | |||||||
\(54\) | 7054.16 | 2.41912 | ||||||||
\(55\) | −703.224 | −0.232471 | ||||||||
\(56\) | − | 1569.54i | − | 0.500492i | ||||||
\(57\) | 1897.96i | 0.584167i | ||||||||
\(58\) | 1035.13 | 0.307708 | ||||||||
\(59\) | 4425.54 | 1.27134 | 0.635671 | − | 0.771960i | \(-0.280723\pi\) | ||||
0.635671 | + | 0.771960i | \(0.280723\pi\) | |||||||
\(60\) | 1561.65i | 0.433792i | ||||||||
\(61\) | 552.555i | 0.148496i | 0.997240 | + | 0.0742482i | \(0.0236557\pi\) | ||||
−0.997240 | + | 0.0742482i | \(0.976344\pi\) | |||||||
\(62\) | −1418.20 | −0.368939 | ||||||||
\(63\) | − | 15526.8i | − | 3.91203i | ||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | − | 1048.86i | − | 0.248252i | ||||||
\(66\) | 3106.15i | 0.713074i | ||||||||
\(67\) | 6584.19i | 1.46674i | 0.679830 | + | 0.733370i | \(0.262054\pi\) | ||||
−0.679830 | + | 0.733370i | \(0.737946\pi\) | |||||||
\(68\) | − | 2359.14i | − | 0.510195i | ||||||
\(69\) | −1655.49 | + | 9086.65i | −0.347720 | + | 1.90856i | ||||
\(70\) | 2193.50 | 0.447653 | ||||||||
\(71\) | −7800.85 | −1.54748 | −0.773740 | − | 0.633503i | \(-0.781616\pi\) | ||||
−0.773740 | + | 0.633503i | \(0.781616\pi\) | |||||||
\(72\) | 5065.01 | 0.977047 | ||||||||
\(73\) | 2030.45 | 0.381019 | 0.190509 | − | 0.981685i | \(-0.438986\pi\) | ||||
0.190509 | + | 0.981685i | \(0.438986\pi\) | |||||||
\(74\) | 5354.65i | 0.977840i | ||||||||
\(75\) | −2182.47 | −0.387995 | ||||||||
\(76\) | 869.636i | 0.150560i | ||||||||
\(77\) | 4362.91 | 0.735860 | ||||||||
\(78\) | −4632.84 | −0.761480 | ||||||||
\(79\) | 11883.7i | 1.90413i | 0.305891 | + | 0.952066i | \(0.401046\pi\) | ||||
−0.305891 | + | 0.952066i | \(0.598954\pi\) | |||||||
\(80\) | 715.542i | 0.111803i | ||||||||
\(81\) | 25413.7 | 3.87346 | ||||||||
\(82\) | −7586.81 | −1.12832 | ||||||||
\(83\) | − | 9302.52i | − | 1.35034i | −0.737660 | − | 0.675172i | \(-0.764069\pi\) | ||
0.737660 | − | 0.675172i | \(-0.235931\pi\) | |||||||
\(84\) | − | 9688.73i | − | 1.37312i | ||||||
\(85\) | 3297.00 | 0.456332 | ||||||||
\(86\) | − | 1716.45i | − | 0.232078i | ||||||
\(87\) | 6389.82 | 0.844210 | ||||||||
\(88\) | 1423.23i | 0.183784i | ||||||||
\(89\) | − | 11080.9i | − | 1.39892i | −0.714669 | − | 0.699462i | \(-0.753423\pi\) | ||
0.714669 | − | 0.699462i | \(-0.246577\pi\) | |||||||
\(90\) | 7078.57i | 0.873897i | ||||||||
\(91\) | 6507.32i | 0.785813i | ||||||||
\(92\) | −758.540 | + | 4163.47i | −0.0896196 | + | 0.491903i | ||||
\(93\) | −8754.51 | −1.01220 | ||||||||
\(94\) | −5136.56 | −0.581321 | ||||||||
\(95\) | −1215.35 | −0.134665 | ||||||||
\(96\) | 3160.56 | 0.342942 | ||||||||
\(97\) | − | 9252.99i | − | 0.983419i | −0.870759 | − | 0.491710i | \(-0.836372\pi\) | ||
0.870759 | − | 0.491710i | \(-0.163628\pi\) | |||||||
\(98\) | −6817.78 | −0.709889 | ||||||||
\(99\) | 14079.4i | 1.43653i | ||||||||
\(100\) | −1000.00 | −0.100000 | ||||||||
\(101\) | −4885.92 | −0.478965 | −0.239482 | − | 0.970901i | \(-0.576978\pi\) | ||||
−0.239482 | + | 0.970901i | \(0.576978\pi\) | |||||||
\(102\) | − | 14562.9i | − | 1.39974i | ||||||
\(103\) | − | 8790.26i | − | 0.828567i | −0.910148 | − | 0.414283i | \(-0.864032\pi\) | ||
0.910148 | − | 0.414283i | \(-0.135968\pi\) | |||||||
\(104\) | −2122.75 | −0.196260 | ||||||||
\(105\) | 13540.4 | 1.22815 | ||||||||
\(106\) | − | 2450.18i | − | 0.218065i | ||||||
\(107\) | − | 22541.8i | − | 1.96889i | −0.175698 | − | 0.984444i | \(-0.556218\pi\) | ||
0.175698 | − | 0.984444i | \(-0.443782\pi\) | |||||||
\(108\) | 19952.2 | 1.71058 | ||||||||
\(109\) | − | 5212.01i | − | 0.438684i | −0.975648 | − | 0.219342i | \(-0.929609\pi\) | ||
0.975648 | − | 0.219342i | \(-0.0703911\pi\) | |||||||
\(110\) | −1989.02 | −0.164382 | ||||||||
\(111\) | 33054.1i | 2.68274i | ||||||||
\(112\) | − | 4439.33i | − | 0.353901i | ||||||
\(113\) | 13202.4i | 1.03395i | 0.856002 | + | 0.516973i | \(0.172941\pi\) | ||||
−0.856002 | + | 0.516973i | \(0.827059\pi\) | |||||||
\(114\) | 5368.23i | 0.413068i | ||||||||
\(115\) | −5818.62 | − | 1060.09i | −0.439971 | − | 0.0801582i | ||||
\(116\) | 2927.79 | 0.217583 | ||||||||
\(117\) | −20999.5 | −1.53404 | ||||||||
\(118\) | 12517.3 | 0.898975 | ||||||||
\(119\) | −20455.1 | −1.44447 | ||||||||
\(120\) | 4417.01i | 0.306737i | ||||||||
\(121\) | 10684.8 | 0.729787 | ||||||||
\(122\) | 1562.86i | 0.105003i | ||||||||
\(123\) | −46833.1 | −3.09558 | ||||||||
\(124\) | −4011.28 | −0.260879 | ||||||||
\(125\) | − | 1397.54i | − | 0.0894427i | ||||||
\(126\) | − | 43916.6i | − | 2.76622i | ||||||
\(127\) | −16087.6 | −0.997430 | −0.498715 | − | 0.866766i | \(-0.666195\pi\) | ||||
−0.498715 | + | 0.866766i | \(0.666195\pi\) | |||||||
\(128\) | 1448.15 | 0.0883883 | ||||||||
\(129\) | − | 10595.6i | − | 0.636715i | ||||||
\(130\) | − | 2966.63i | − | 0.175540i | ||||||
\(131\) | −21055.6 | −1.22695 | −0.613473 | − | 0.789716i | \(-0.710228\pi\) | ||||
−0.613473 | + | 0.789716i | \(0.710228\pi\) | |||||||
\(132\) | 8785.52i | 0.504220i | ||||||||
\(133\) | 7540.25 | 0.426268 | ||||||||
\(134\) | 18622.9i | 1.03714i | ||||||||
\(135\) | 27884.0i | 1.52999i | ||||||||
\(136\) | − | 6672.66i | − | 0.360762i | ||||||
\(137\) | 34815.7i | 1.85496i | 0.373875 | + | 0.927479i | \(0.378029\pi\) | ||||
−0.373875 | + | 0.927479i | \(0.621971\pi\) | |||||||
\(138\) | −4682.44 | + | 25700.9i | −0.245875 | + | 1.34955i | ||||
\(139\) | 13204.2 | 0.683409 | 0.341705 | − | 0.939807i | \(-0.388996\pi\) | ||||
0.341705 | + | 0.939807i | \(0.388996\pi\) | |||||||
\(140\) | 6204.16 | 0.316539 | ||||||||
\(141\) | −31707.8 | −1.59488 | ||||||||
\(142\) | −22064.1 | −1.09423 | ||||||||
\(143\) | − | 5900.69i | − | 0.288556i | ||||||
\(144\) | 14326.0 | 0.690876 | ||||||||
\(145\) | 4091.71i | 0.194612i | ||||||||
\(146\) | 5742.98 | 0.269421 | ||||||||
\(147\) | −42085.9 | −1.94761 | ||||||||
\(148\) | 15145.2i | 0.691437i | ||||||||
\(149\) | 3486.31i | 0.157034i | 0.996913 | + | 0.0785169i | \(0.0250184\pi\) | ||||
−0.996913 | + | 0.0785169i | \(0.974982\pi\) | |||||||
\(150\) | −6172.96 | −0.274354 | ||||||||
\(151\) | −33962.4 | −1.48951 | −0.744757 | − | 0.667336i | \(-0.767435\pi\) | ||||
−0.744757 | + | 0.667336i | \(0.767435\pi\) | |||||||
\(152\) | 2459.70i | 0.106462i | ||||||||
\(153\) | − | 66009.9i | − | 2.81985i | ||||||
\(154\) | 12340.2 | 0.520332 | ||||||||
\(155\) | − | 5605.94i | − | 0.233338i | ||||||
\(156\) | −13103.7 | −0.538448 | ||||||||
\(157\) | 1022.17i | 0.0414690i | 0.999785 | + | 0.0207345i | \(0.00660047\pi\) | ||||
−0.999785 | + | 0.0207345i | \(0.993400\pi\) | |||||||
\(158\) | 33612.2i | 1.34643i | ||||||||
\(159\) | − | 15124.8i | − | 0.598269i | ||||||
\(160\) | 2023.86i | 0.0790569i | ||||||||
\(161\) | 36099.6 | + | 6576.98i | 1.39268 | + | 0.253732i | ||||
\(162\) | 71880.9 | 2.73895 | ||||||||
\(163\) | 11549.3 | 0.434691 | 0.217346 | − | 0.976095i | \(-0.430260\pi\) | ||||
0.217346 | + | 0.976095i | \(0.430260\pi\) | |||||||
\(164\) | −21458.7 | −0.797841 | ||||||||
\(165\) | −12278.1 | −0.450988 | ||||||||
\(166\) | − | 26311.5i | − | 0.954838i | ||||||
\(167\) | 41559.9 | 1.49019 | 0.745095 | − | 0.666958i | \(-0.232404\pi\) | ||||
0.745095 | + | 0.666958i | \(0.232404\pi\) | |||||||
\(168\) | − | 27403.9i | − | 0.970942i | ||||||
\(169\) | −19760.1 | −0.691855 | ||||||||
\(170\) | 9325.32 | 0.322676 | ||||||||
\(171\) | 24332.8i | 0.832148i | ||||||||
\(172\) | − | 4854.85i | − | 0.164104i | ||||||
\(173\) | 31791.6 | 1.06223 | 0.531117 | − | 0.847299i | \(-0.321773\pi\) | ||||
0.531117 | + | 0.847299i | \(0.321773\pi\) | |||||||
\(174\) | 18073.2 | 0.596946 | ||||||||
\(175\) | 8670.58i | 0.283121i | ||||||||
\(176\) | 4025.49i | 0.129955i | ||||||||
\(177\) | 77269.0 | 2.46637 | ||||||||
\(178\) | − | 31341.5i | − | 0.989189i | ||||||
\(179\) | −28774.4 | −0.898050 | −0.449025 | − | 0.893519i | \(-0.648229\pi\) | ||||
−0.449025 | + | 0.893519i | \(0.648229\pi\) | |||||||
\(180\) | 20021.2i | 0.617939i | ||||||||
\(181\) | 55583.7i | 1.69664i | 0.529481 | + | 0.848322i | \(0.322387\pi\) | ||||
−0.529481 | + | 0.848322i | \(0.677613\pi\) | |||||||
\(182\) | 18405.5i | 0.555654i | ||||||||
\(183\) | 9647.49i | 0.288079i | ||||||||
\(184\) | −2145.48 | + | 11776.1i | −0.0633706 | + | 0.347828i | ||||
\(185\) | −21166.1 | −0.618440 | ||||||||
\(186\) | −24761.5 | −0.715733 | ||||||||
\(187\) | 18548.2 | 0.530420 | ||||||||
\(188\) | −14528.4 | −0.411056 | ||||||||
\(189\) | − | 172997.i | − | 4.84300i | ||||||
\(190\) | −3437.54 | −0.0952227 | ||||||||
\(191\) | − | 9119.25i | − | 0.249973i | −0.992158 | − | 0.124986i | \(-0.960111\pi\) | ||
0.992158 | − | 0.124986i | \(-0.0398887\pi\) | |||||||
\(192\) | 8939.41 | 0.242497 | ||||||||
\(193\) | 1202.93 | 0.0322944 | 0.0161472 | − | 0.999870i | \(-0.494860\pi\) | ||||
0.0161472 | + | 0.999870i | \(0.494860\pi\) | |||||||
\(194\) | − | 26171.4i | − | 0.695382i | ||||||
\(195\) | − | 18312.9i | − | 0.481602i | ||||||
\(196\) | −19283.6 | −0.501968 | ||||||||
\(197\) | −69432.6 | −1.78908 | −0.894542 | − | 0.446984i | \(-0.852498\pi\) | ||||
−0.894542 | + | 0.446984i | \(0.852498\pi\) | |||||||
\(198\) | 39822.6i | 1.01578i | ||||||||
\(199\) | − | 17511.6i | − | 0.442201i | −0.975251 | − | 0.221101i | \(-0.929035\pi\) | ||
0.975251 | − | 0.221101i | \(-0.0709649\pi\) | |||||||
\(200\) | −2828.43 | −0.0707107 | ||||||||
\(201\) | 114959.i | 2.84544i | ||||||||
\(202\) | −13819.5 | −0.338679 | ||||||||
\(203\) | − | 25385.6i | − | 0.616022i | ||||||
\(204\) | − | 41190.1i | − | 0.989766i | ||||||
\(205\) | − | 29989.5i | − | 0.713611i | ||||||
\(206\) | − | 24862.6i | − | 0.585885i | ||||||
\(207\) | −21224.3 | + | 116496.i | −0.495328 | + | 2.71875i | ||||
\(208\) | −6004.05 | −0.138777 | ||||||||
\(209\) | −6837.33 | −0.156529 | ||||||||
\(210\) | 38298.1 | 0.868437 | ||||||||
\(211\) | 43957.8 | 0.987350 | 0.493675 | − | 0.869646i | \(-0.335653\pi\) | ||||
0.493675 | + | 0.869646i | \(0.335653\pi\) | |||||||
\(212\) | − | 6930.14i | − | 0.154195i | ||||||
\(213\) | −136201. | −3.00207 | ||||||||
\(214\) | − | 63757.8i | − | 1.39221i | ||||||
\(215\) | 6784.86 | 0.146779 | ||||||||
\(216\) | 56433.3 | 1.20956 | ||||||||
\(217\) | 34780.1i | 0.738604i | ||||||||
\(218\) | − | 14741.8i | − | 0.310197i | ||||||
\(219\) | 35451.2 | 0.739167 | ||||||||
\(220\) | −5625.79 | −0.116235 | ||||||||
\(221\) | 27664.8i | 0.566426i | ||||||||
\(222\) | 93491.0i | 1.89698i | ||||||||
\(223\) | 33778.7 | 0.679255 | 0.339628 | − | 0.940560i | \(-0.389699\pi\) | ||||
0.339628 | + | 0.940560i | \(0.389699\pi\) | |||||||
\(224\) | − | 12556.3i | − | 0.250246i | ||||||
\(225\) | −27980.5 | −0.552701 | ||||||||
\(226\) | 37342.2i | 0.731110i | ||||||||
\(227\) | 25376.5i | 0.492471i | 0.969210 | + | 0.246236i | \(0.0791937\pi\) | ||||
−0.969210 | + | 0.246236i | \(0.920806\pi\) | |||||||
\(228\) | 15183.7i | 0.292083i | ||||||||
\(229\) | − | 84049.3i | − | 1.60274i | −0.598168 | − | 0.801370i | \(-0.704105\pi\) | ||
0.598168 | − | 0.801370i | \(-0.295895\pi\) | |||||||
\(230\) | −16457.5 | − | 2998.39i | −0.311107 | − | 0.0566804i | ||||
\(231\) | 76175.5 | 1.42755 | ||||||||
\(232\) | 8281.04 | 0.153854 | ||||||||
\(233\) | 32229.2 | 0.593661 | 0.296830 | − | 0.954930i | \(-0.404070\pi\) | ||||
0.296830 | + | 0.954930i | \(0.404070\pi\) | |||||||
\(234\) | −59395.6 | −1.08473 | ||||||||
\(235\) | − | 20304.0i | − | 0.367660i | ||||||
\(236\) | 35404.3 | 0.635671 | ||||||||
\(237\) | 207487.i | 3.69397i | ||||||||
\(238\) | −57855.8 | −1.02139 | ||||||||
\(239\) | 30122.2 | 0.527340 | 0.263670 | − | 0.964613i | \(-0.415067\pi\) | ||||
0.263670 | + | 0.964613i | \(0.415067\pi\) | |||||||
\(240\) | 12493.2i | 0.216896i | ||||||||
\(241\) | − | 15549.4i | − | 0.267719i | −0.991000 | − | 0.133859i | \(-0.957263\pi\) | ||
0.991000 | − | 0.133859i | \(-0.0427370\pi\) | |||||||
\(242\) | 30221.2 | 0.516037 | ||||||||
\(243\) | 241703. | 4.09325 | ||||||||
\(244\) | 4420.44i | 0.0742482i | ||||||||
\(245\) | − | 26949.6i | − | 0.448973i | ||||||
\(246\) | −132464. | −2.18891 | ||||||||
\(247\) | − | 10197.9i | − | 0.167154i | ||||||
\(248\) | −11345.6 | −0.184470 | ||||||||
\(249\) | − | 162420.i | − | 2.61964i | ||||||
\(250\) | − | 3952.85i | − | 0.0632456i | ||||||
\(251\) | − | 59069.3i | − | 0.937593i | −0.883306 | − | 0.468796i | \(-0.844688\pi\) | ||
0.883306 | − | 0.468796i | \(-0.155312\pi\) | |||||||
\(252\) | − | 124215.i | − | 1.95601i | ||||||
\(253\) | −32734.4 | − | 5963.86i | −0.511402 | − | 0.0931722i | ||||
\(254\) | −45502.5 | −0.705290 | ||||||||
\(255\) | 57564.9 | 0.885273 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 99291.1 | 1.50329 | 0.751647 | − | 0.659566i | \(-0.229260\pi\) | ||||
0.751647 | + | 0.659566i | \(0.229260\pi\) | |||||||
\(258\) | − | 29968.8i | − | 0.450225i | ||||||
\(259\) | 131318. | 1.95760 | ||||||||
\(260\) | − | 8390.91i | − | 0.124126i | ||||||
\(261\) | 81921.0 | 1.20258 | ||||||||
\(262\) | −59554.3 | −0.867581 | ||||||||
\(263\) | − | 37218.4i | − | 0.538080i | −0.963129 | − | 0.269040i | \(-0.913294\pi\) | ||
0.963129 | − | 0.269040i | \(-0.0867063\pi\) | |||||||
\(264\) | 24849.2i | 0.356537i | ||||||||
\(265\) | 9685.17 | 0.137916 | ||||||||
\(266\) | 21327.0 | 0.301417 | ||||||||
\(267\) | − | 193470.i | − | 2.71388i | ||||||
\(268\) | 52673.6i | 0.733370i | ||||||||
\(269\) | −10708.0 | −0.147981 | −0.0739905 | − | 0.997259i | \(-0.523573\pi\) | ||||
−0.0739905 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(270\) | 78868.0i | 1.08186i | ||||||||
\(271\) | −18835.5 | −0.256471 | −0.128236 | − | 0.991744i | \(-0.540931\pi\) | ||||
−0.128236 | + | 0.991744i | \(0.540931\pi\) | |||||||
\(272\) | − | 18873.1i | − | 0.255097i | ||||||
\(273\) | 113616.i | 1.52446i | ||||||||
\(274\) | 98473.7i | 1.31165i | ||||||||
\(275\) | − | 7862.29i | − | 0.103964i | ||||||
\(276\) | −13243.9 | + | 72693.2i | −0.173860 | + | 0.954279i | ||||
\(277\) | 27259.2 | 0.355266 | 0.177633 | − | 0.984097i | \(-0.443156\pi\) | ||||
0.177633 | + | 0.984097i | \(0.443156\pi\) | |||||||
\(278\) | 37347.0 | 0.483243 | ||||||||
\(279\) | −112238. | −1.44188 | ||||||||
\(280\) | 17548.0 | 0.223827 | ||||||||
\(281\) | − | 19178.1i | − | 0.242881i | −0.992599 | − | 0.121440i | \(-0.961249\pi\) | ||
0.992599 | − | 0.121440i | \(-0.0387513\pi\) | |||||||
\(282\) | −89683.1 | −1.12775 | ||||||||
\(283\) | − | 60935.5i | − | 0.760848i | −0.924812 | − | 0.380424i | \(-0.875778\pi\) | ||
0.924812 | − | 0.380424i | \(-0.124222\pi\) | |||||||
\(284\) | −62406.8 | −0.773740 | ||||||||
\(285\) | −21219.8 | −0.261247 | ||||||||
\(286\) | − | 16689.7i | − | 0.204040i | ||||||
\(287\) | 186060.i | 2.25885i | ||||||||
\(288\) | 40520.1 | 0.488523 | ||||||||
\(289\) | −3440.69 | −0.0411955 | ||||||||
\(290\) | 11573.1i | 0.137611i | ||||||||
\(291\) | − | 161555.i | − | 1.90781i | ||||||
\(292\) | 16243.6 | 0.190509 | ||||||||
\(293\) | 69688.9i | 0.811761i | 0.913926 | + | 0.405880i | \(0.133035\pi\) | ||||
−0.913926 | + | 0.405880i | \(0.866965\pi\) | |||||||
\(294\) | −119037. | −1.37717 | ||||||||
\(295\) | 49479.1i | 0.568562i | ||||||||
\(296\) | 42837.2i | 0.488920i | ||||||||
\(297\) | 156870.i | 1.77839i | ||||||||
\(298\) | 9860.76i | 0.111040i | ||||||||
\(299\) | 8895.14 | − | 48823.5i | 0.0994970 | − | 0.546118i | ||||
\(300\) | −17459.8 | −0.193998 | ||||||||
\(301\) | −42094.3 | −0.464612 | ||||||||
\(302\) | −96060.2 | −1.05325 | ||||||||
\(303\) | −85307.1 | −0.929180 | ||||||||
\(304\) | 6957.09i | 0.0752801i | ||||||||
\(305\) | −6177.75 | −0.0664096 | ||||||||
\(306\) | − | 186704.i | − | 1.99394i | ||||||
\(307\) | 148352. | 1.57405 | 0.787024 | − | 0.616923i | \(-0.211621\pi\) | ||||
0.787024 | + | 0.616923i | \(0.211621\pi\) | |||||||
\(308\) | 34903.3 | 0.367930 | ||||||||
\(309\) | − | 153476.i | − | 1.60740i | ||||||
\(310\) | − | 15856.0i | − | 0.164995i | ||||||
\(311\) | 134338. | 1.38892 | 0.694460 | − | 0.719531i | \(-0.255643\pi\) | ||||
0.694460 | + | 0.719531i | \(0.255643\pi\) | |||||||
\(312\) | −37062.8 | −0.380740 | ||||||||
\(313\) | 23016.1i | 0.234933i | 0.993077 | + | 0.117466i | \(0.0374773\pi\) | ||||
−0.993077 | + | 0.117466i | \(0.962523\pi\) | |||||||
\(314\) | 2891.13i | 0.0293230i | ||||||||
\(315\) | 173595. | 1.74951 | ||||||||
\(316\) | 95069.5i | 0.952066i | ||||||||
\(317\) | 111202. | 1.10661 | 0.553305 | − | 0.832979i | \(-0.313366\pi\) | ||||
0.553305 | + | 0.832979i | \(0.313366\pi\) | |||||||
\(318\) | − | 42779.5i | − | 0.423040i | ||||||
\(319\) | 23019.1i | 0.226208i | ||||||||
\(320\) | 5724.33i | 0.0559017i | ||||||||
\(321\) | − | 393575.i | − | 3.81960i | ||||||
\(322\) | 102105. | + | 18602.5i | 0.984773 | + | 0.179415i | ||||
\(323\) | 32056.2 | 0.307260 | ||||||||
\(324\) | 203310. | 1.93673 | ||||||||
\(325\) | 11726.7 | 0.111022 | ||||||||
\(326\) | 32666.4 | 0.307373 | ||||||||
\(327\) | − | 91000.5i | − | 0.851037i | ||||||
\(328\) | −60694.4 | −0.564159 | ||||||||
\(329\) | 125969.i | 1.16379i | ||||||||
\(330\) | −34727.8 | −0.318896 | ||||||||
\(331\) | −82063.9 | −0.749025 | −0.374512 | − | 0.927222i | \(-0.622190\pi\) | ||||
−0.374512 | + | 0.927222i | \(0.622190\pi\) | |||||||
\(332\) | − | 74420.2i | − | 0.675172i | ||||||
\(333\) | 423771.i | 3.82158i | ||||||||
\(334\) | 117549. | 1.05372 | ||||||||
\(335\) | −73613.5 | −0.655946 | ||||||||
\(336\) | − | 77509.8i | − | 0.686559i | ||||||
\(337\) | 3251.27i | 0.0286281i | 0.999898 | + | 0.0143141i | \(0.00455646\pi\) | ||||
−0.999898 | + | 0.0143141i | \(0.995444\pi\) | |||||||
\(338\) | −55890.0 | −0.489216 | ||||||||
\(339\) | 230512.i | 2.00583i | ||||||||
\(340\) | 26376.0 | 0.228166 | ||||||||
\(341\) | − | 31537.8i | − | 0.271221i | ||||||
\(342\) | 68823.7i | 0.588418i | ||||||||
\(343\) | 655.389i | 0.00557071i | ||||||||
\(344\) | − | 13731.6i | − | 0.116039i | ||||||
\(345\) | −101592. | − | 18509.0i | −0.853533 | − | 0.155505i | ||||
\(346\) | 89920.2 | 0.751113 | ||||||||
\(347\) | 32147.5 | 0.266986 | 0.133493 | − | 0.991050i | \(-0.457381\pi\) | ||||
0.133493 | + | 0.991050i | \(0.457381\pi\) | |||||||
\(348\) | 51118.6 | 0.422105 | ||||||||
\(349\) | 198530. | 1.62995 | 0.814975 | − | 0.579496i | \(-0.196751\pi\) | ||||
0.814975 | + | 0.579496i | \(0.196751\pi\) | |||||||
\(350\) | 24524.1i | 0.200197i | ||||||||
\(351\) | −233972. | −1.89911 | ||||||||
\(352\) | 11385.8i | 0.0918922i | ||||||||
\(353\) | −31094.6 | −0.249537 | −0.124768 | − | 0.992186i | \(-0.539819\pi\) | ||||
−0.124768 | + | 0.992186i | \(0.539819\pi\) | |||||||
\(354\) | 218550. | 1.74399 | ||||||||
\(355\) | − | 87216.1i | − | 0.692054i | ||||||
\(356\) | − | 88647.1i | − | 0.699462i | ||||||
\(357\) | −357142. | −2.80223 | ||||||||
\(358\) | −81386.3 | −0.635017 | ||||||||
\(359\) | − | 211521.i | − | 1.64121i | −0.571495 | − | 0.820606i | \(-0.693636\pi\) | ||
0.571495 | − | 0.820606i | \(-0.306364\pi\) | |||||||
\(360\) | 56628.5i | 0.436949i | ||||||||
\(361\) | 118504. | 0.909326 | ||||||||
\(362\) | 157215.i | 1.19971i | ||||||||
\(363\) | 186554. | 1.41577 | ||||||||
\(364\) | 52058.5i | 0.392906i | ||||||||
\(365\) | 22701.1i | 0.170397i | ||||||||
\(366\) | 27287.2i | 0.203703i | ||||||||
\(367\) | 36290.1i | 0.269436i | 0.990884 | + | 0.134718i | \(0.0430129\pi\) | ||||
−0.990884 | + | 0.134718i | \(0.956987\pi\) | |||||||
\(368\) | −6068.32 | + | 33307.7i | −0.0448098 | + | 0.245951i | ||||
\(369\) | −600426. | −4.40967 | ||||||||
\(370\) | −59866.8 | −0.437303 | ||||||||
\(371\) | −60088.3 | −0.436558 | ||||||||
\(372\) | −70036.1 | −0.506100 | ||||||||
\(373\) | − | 133203.i | − | 0.957409i | −0.877976 | − | 0.478705i | \(-0.841107\pi\) | ||
0.877976 | − | 0.478705i | \(-0.158893\pi\) | |||||||
\(374\) | 52462.4 | 0.375063 | ||||||||
\(375\) | − | 24400.8i | − | 0.173517i | ||||||
\(376\) | −41092.4 | −0.290661 | ||||||||
\(377\) | −34333.2 | −0.241564 | ||||||||
\(378\) | − | 489309.i | − | 3.42452i | ||||||
\(379\) | 228349.i | 1.58972i | 0.606792 | + | 0.794861i | \(0.292456\pi\) | ||||
−0.606792 | + | 0.794861i | \(0.707544\pi\) | |||||||
\(380\) | −9722.83 | −0.0673326 | ||||||||
\(381\) | −280885. | −1.93499 | ||||||||
\(382\) | − | 25793.1i | − | 0.176757i | ||||||
\(383\) | − | 74510.6i | − | 0.507949i | −0.967211 | − | 0.253975i | \(-0.918262\pi\) | ||
0.967211 | − | 0.253975i | \(-0.0817380\pi\) | |||||||
\(384\) | 25284.5 | 0.171471 | ||||||||
\(385\) | 48778.9i | 0.329087i | ||||||||
\(386\) | 3402.41 | 0.0228356 | ||||||||
\(387\) | − | 135841.i | − | 0.907004i | ||||||
\(388\) | − | 74023.9i | − | 0.491710i | ||||||
\(389\) | 41483.3i | 0.274141i | 0.990561 | + | 0.137070i | \(0.0437687\pi\) | ||||
−0.990561 | + | 0.137070i | \(0.956231\pi\) | |||||||
\(390\) | − | 51796.8i | − | 0.340544i | ||||||
\(391\) | 153472. | + | 27961.0i | 1.00387 | + | 0.182894i | ||||
\(392\) | −54542.2 | −0.354945 | ||||||||
\(393\) | −367626. | −2.38024 | ||||||||
\(394\) | −196385. | −1.26507 | ||||||||
\(395\) | −132864. | −0.851554 | ||||||||
\(396\) | 112635.i | 0.718263i | ||||||||
\(397\) | −5511.87 | −0.0349718 | −0.0174859 | − | 0.999847i | \(-0.505566\pi\) | ||||
−0.0174859 | + | 0.999847i | \(0.505566\pi\) | |||||||
\(398\) | − | 49530.3i | − | 0.312683i | ||||||
\(399\) | 131651. | 0.826949 | ||||||||
\(400\) | −8000.00 | −0.0500000 | ||||||||
\(401\) | 207005.i | 1.28733i | 0.765306 | + | 0.643667i | \(0.222588\pi\) | ||||
−0.765306 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(402\) | 325152.i | 2.01203i | ||||||||
\(403\) | 47038.9 | 0.289632 | ||||||||
\(404\) | −39087.4 | −0.239482 | ||||||||
\(405\) | 284134.i | 1.73226i | ||||||||
\(406\) | − | 71801.4i | − | 0.435593i | ||||||
\(407\) | −119076. | −0.718846 | ||||||||
\(408\) | − | 116503.i | − | 0.699870i | ||||||
\(409\) | −83511.1 | −0.499226 | −0.249613 | − | 0.968346i | \(-0.580303\pi\) | ||||
−0.249613 | + | 0.968346i | \(0.580303\pi\) | |||||||
\(410\) | − | 84823.1i | − | 0.504599i | ||||||
\(411\) | 607875.i | 3.59857i | ||||||||
\(412\) | − | 70322.1i | − | 0.414283i | ||||||
\(413\) | − | 306976.i | − | 1.79972i | ||||||
\(414\) | −60031.5 | + | 329500.i | −0.350250 | + | 1.92245i | ||||
\(415\) | 104005. | 0.603892 | ||||||||
\(416\) | −16982.0 | −0.0981301 | ||||||||
\(417\) | 230542. | 1.32580 | ||||||||
\(418\) | −19338.9 | −0.110682 | ||||||||
\(419\) | 188064.i | 1.07122i | 0.844467 | + | 0.535608i | \(0.179917\pi\) | ||||
−0.844467 | + | 0.535608i | \(0.820083\pi\) | |||||||
\(420\) | 108323. | 0.614077 | ||||||||
\(421\) | − | 117145.i | − | 0.660938i | −0.943817 | − | 0.330469i | \(-0.892793\pi\) | ||
0.943817 | − | 0.330469i | \(-0.107207\pi\) | |||||||
\(422\) | 124331. | 0.698162 | ||||||||
\(423\) | −406511. | −2.27191 | ||||||||
\(424\) | − | 19601.4i | − | 0.109032i | ||||||
\(425\) | 36861.6i | 0.204078i | ||||||||
\(426\) | −385235. | −2.12279 | ||||||||
\(427\) | 38327.8 | 0.210212 | ||||||||
\(428\) | − | 180334.i | − | 0.984444i | ||||||
\(429\) | − | 103025.i | − | 0.559792i | ||||||
\(430\) | 19190.5 | 0.103788 | ||||||||
\(431\) | − | 202900.i | − | 1.09226i | −0.837700 | − | 0.546131i | \(-0.816100\pi\) | ||
0.837700 | − | 0.546131i | \(-0.183900\pi\) | |||||||
\(432\) | 159618. | 0.855289 | ||||||||
\(433\) | − | 95101.1i | − | 0.507236i | −0.967305 | − | 0.253618i | \(-0.918379\pi\) | ||
0.967305 | − | 0.253618i | \(-0.0816205\pi\) | |||||||
\(434\) | 98373.0i | 0.522272i | ||||||||
\(435\) | 71440.4i | 0.377542i | ||||||||
\(436\) | − | 41696.1i | − | 0.219342i | ||||||
\(437\) | −56573.4 | − | 10307.1i | −0.296244 | − | 0.0539726i | ||||
\(438\) | 100271. | 0.522670 | ||||||||
\(439\) | −40253.8 | −0.208871 | −0.104435 | − | 0.994532i | \(-0.533304\pi\) | ||||
−0.104435 | + | 0.994532i | \(0.533304\pi\) | |||||||
\(440\) | −15912.1 | −0.0821908 | ||||||||
\(441\) | −539564. | −2.77438 | ||||||||
\(442\) | 78247.9i | 0.400524i | ||||||||
\(443\) | 233288. | 1.18873 | 0.594367 | − | 0.804194i | \(-0.297403\pi\) | ||||
0.594367 | + | 0.804194i | \(0.297403\pi\) | |||||||
\(444\) | 264432.i | 1.34137i | ||||||||
\(445\) | 123888. | 0.625618 | ||||||||
\(446\) | 95540.6 | 0.480306 | ||||||||
\(447\) | 60870.1i | 0.304642i | ||||||||
\(448\) | − | 35514.7i | − | 0.176951i | ||||||
\(449\) | −279358. | −1.38570 | −0.692850 | − | 0.721082i | \(-0.743645\pi\) | ||||
−0.692850 | + | 0.721082i | \(0.743645\pi\) | |||||||
\(450\) | −79140.8 | −0.390819 | ||||||||
\(451\) | − | 168715.i | − | 0.829468i | ||||||
\(452\) | 105620.i | 0.516973i | ||||||||
\(453\) | −592976. | −2.88962 | ||||||||
\(454\) | 71775.7i | 0.348230i | ||||||||
\(455\) | −72754.0 | −0.351426 | ||||||||
\(456\) | 42945.9i | 0.206534i | ||||||||
\(457\) | 273520.i | 1.30966i | 0.755778 | + | 0.654828i | \(0.227259\pi\) | ||||
−0.755778 | + | 0.654828i | \(0.772741\pi\) | |||||||
\(458\) | − | 237727.i | − | 1.13331i | ||||||
\(459\) | − | 735469.i | − | 3.49091i | ||||||
\(460\) | −46549.0 | − | 8480.74i | −0.219986 | − | 0.0400791i | ||||
\(461\) | −201691. | −0.949042 | −0.474521 | − | 0.880244i | \(-0.657379\pi\) | ||||
−0.474521 | + | 0.880244i | \(0.657379\pi\) | |||||||
\(462\) | 215457. | 1.00943 | ||||||||
\(463\) | 179802. | 0.838749 | 0.419375 | − | 0.907813i | \(-0.362249\pi\) | ||||
0.419375 | + | 0.907813i | \(0.362249\pi\) | |||||||
\(464\) | 23422.3 | 0.108791 | ||||||||
\(465\) | − | 97878.4i | − | 0.452669i | ||||||
\(466\) | 91158.1 | 0.419781 | ||||||||
\(467\) | − | 304288.i | − | 1.39525i | −0.716465 | − | 0.697623i | \(-0.754241\pi\) | ||
0.716465 | − | 0.697623i | \(-0.245759\pi\) | |||||||
\(468\) | −167996. | −0.767022 | ||||||||
\(469\) | 456710. | 2.07632 | ||||||||
\(470\) | − | 57428.4i | − | 0.259975i | ||||||
\(471\) | 17846.8i | 0.0804488i | ||||||||
\(472\) | 100139. | 0.449487 | ||||||||
\(473\) | 38170.2 | 0.170609 | ||||||||
\(474\) | 586861.i | 2.61203i | ||||||||
\(475\) | − | 13588.1i | − | 0.0602241i | ||||||
\(476\) | −163641. | −0.722234 | ||||||||
\(477\) | − | 193909.i | − | 0.852238i | ||||||
\(478\) | 85198.4 | 0.372886 | ||||||||
\(479\) | 146012.i | 0.636381i | 0.948027 | + | 0.318191i | \(0.103075\pi\) | ||||
−0.948027 | + | 0.318191i | \(0.896925\pi\) | |||||||
\(480\) | 35336.1i | 0.153369i | ||||||||
\(481\) | − | 177603.i | − | 0.767644i | ||||||
\(482\) | − | 43980.2i | − | 0.189306i | ||||||
\(483\) | 630292. | + | 114833.i | 2.70176 | + | 0.492233i | ||||
\(484\) | 85478.4 | 0.364893 | ||||||||
\(485\) | 103452. | 0.439798 | ||||||||
\(486\) | 683638. | 2.89437 | ||||||||
\(487\) | 304198. | 1.28262 | 0.641311 | − | 0.767281i | \(-0.278391\pi\) | ||||
0.641311 | + | 0.767281i | \(0.278391\pi\) | |||||||
\(488\) | 12502.9i | 0.0525014i | ||||||||
\(489\) | 201648. | 0.843290 | ||||||||
\(490\) | − | 76225.1i | − | 0.317472i | ||||||
\(491\) | 71274.4 | 0.295645 | 0.147823 | − | 0.989014i | \(-0.452774\pi\) | ||||
0.147823 | + | 0.989014i | \(0.452774\pi\) | |||||||
\(492\) | −374665. | −1.54779 | ||||||||
\(493\) | − | 107923.i | − | 0.444038i | ||||||
\(494\) | − | 28844.1i | − | 0.118196i | ||||||
\(495\) | −157412. | −0.642434 | ||||||||
\(496\) | −32090.2 | −0.130440 | ||||||||
\(497\) | 541103.i | 2.19062i | ||||||||
\(498\) | − | 459393.i | − | 1.85236i | ||||||
\(499\) | 317321. | 1.27438 | 0.637188 | − | 0.770708i | \(-0.280097\pi\) | ||||
0.637188 | + | 0.770708i | \(0.280097\pi\) | |||||||
\(500\) | − | 11180.3i | − | 0.0447214i | ||||||
\(501\) | 725627. | 2.89093 | ||||||||
\(502\) | − | 167073.i | − | 0.662978i | ||||||
\(503\) | 374840.i | 1.48153i | 0.671766 | + | 0.740764i | \(0.265536\pi\) | ||||
−0.671766 | + | 0.740764i | \(0.734464\pi\) | |||||||
\(504\) | − | 351332.i | − | 1.38311i | ||||||
\(505\) | − | 54626.3i | − | 0.214200i | ||||||
\(506\) | −92586.7 | − | 16868.3i | −0.361616 | − | 0.0658827i | ||||
\(507\) | −345007. | −1.34218 | ||||||||
\(508\) | −128700. | −0.498715 | ||||||||
\(509\) | −482427. | −1.86207 | −0.931036 | − | 0.364929i | \(-0.881093\pi\) | ||||
−0.931036 | + | 0.364929i | \(0.881093\pi\) | |||||||
\(510\) | 162818. | 0.625983 | ||||||||
\(511\) | − | 140841.i | − | 0.539372i | ||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | 271112.i | 1.03018i | ||||||||
\(514\) | 280838. | 1.06299 | ||||||||
\(515\) | 98278.1 | 0.370546 | ||||||||
\(516\) | − | 84764.6i | − | 0.318357i | ||||||
\(517\) | − | 114226.i | − | 0.427351i | ||||||
\(518\) | 371423. | 1.38423 | ||||||||
\(519\) | 555074. | 2.06071 | ||||||||
\(520\) | − | 23733.1i | − | 0.0877702i | ||||||
\(521\) | − | 114785.i | − | 0.422873i | −0.977392 | − | 0.211437i | \(-0.932186\pi\) | ||
0.977392 | − | 0.211437i | \(-0.0678142\pi\) | |||||||
\(522\) | 231708. | 0.850353 | ||||||||
\(523\) | − | 122797.i | − | 0.448937i | −0.974481 | − | 0.224469i | \(-0.927935\pi\) | ||
0.974481 | − | 0.224469i | \(-0.0720646\pi\) | |||||||
\(524\) | −168445. | −0.613473 | ||||||||
\(525\) | 151386.i | 0.549248i | ||||||||
\(526\) | − | 105270.i | − | 0.380480i | ||||||
\(527\) | 147862.i | 0.532397i | ||||||||
\(528\) | 70284.2i | 0.252110i | ||||||||
\(529\) | −261860. | − | 98692.3i | −0.935747 | − | 0.352673i | ||||
\(530\) | 27393.8 | 0.0975215 | ||||||||
\(531\) | 990631. | 3.51336 | ||||||||
\(532\) | 60322.0 | 0.213134 | ||||||||
\(533\) | 251639. | 0.885775 | ||||||||
\(534\) | − | 547215.i | − | 1.91900i | ||||||
\(535\) | 252025. | 0.880514 | ||||||||
\(536\) | 148983.i | 0.518571i | ||||||||
\(537\) | −502395. | −1.74219 | ||||||||
\(538\) | −30286.9 | −0.104638 | ||||||||
\(539\) | − | 151613.i | − | 0.521866i | ||||||
\(540\) | 223072.i | 0.764994i | ||||||||
\(541\) | 171718. | 0.586706 | 0.293353 | − | 0.956004i | \(-0.405229\pi\) | ||||
0.293353 | + | 0.956004i | \(0.405229\pi\) | |||||||
\(542\) | −53274.9 | −0.181353 | ||||||||
\(543\) | 970480.i | 3.29145i | ||||||||
\(544\) | − | 53381.3i | − | 0.180381i | ||||||
\(545\) | 58272.0 | 0.196186 | ||||||||
\(546\) | 321355.i | 1.07795i | ||||||||
\(547\) | 283125. | 0.946245 | 0.473122 | − | 0.880997i | \(-0.343127\pi\) | ||||
0.473122 | + | 0.880997i | \(0.343127\pi\) | |||||||
\(548\) | 278526.i | 0.927479i | ||||||||
\(549\) | 123686.i | 0.410371i | ||||||||
\(550\) | − | 22237.9i | − | 0.0735137i | ||||||
\(551\) | 39783.0i | 0.131037i | ||||||||
\(552\) | −37459.5 | + | 205607.i | −0.122937 | + | 0.674777i | ||||
\(553\) | 824308. | 2.69550 | ||||||||
\(554\) | 77100.6 | 0.251211 | ||||||||
\(555\) | −369556. | −1.19976 | ||||||||
\(556\) | 105633. | 0.341705 | ||||||||
\(557\) | − | 265207.i | − | 0.854821i | −0.904058 | − | 0.427411i | \(-0.859426\pi\) | ||
0.904058 | − | 0.427411i | \(-0.140574\pi\) | |||||||
\(558\) | −317456. | −1.01957 | ||||||||
\(559\) | 56931.1i | 0.182191i | ||||||||
\(560\) | 49633.3 | 0.158269 | ||||||||
\(561\) | 323848. | 1.02900 | ||||||||
\(562\) | − | 54243.9i | − | 0.171743i | ||||||
\(563\) | 297822.i | 0.939594i | 0.882774 | + | 0.469797i | \(0.155673\pi\) | ||||
−0.882774 | + | 0.469797i | \(0.844327\pi\) | |||||||
\(564\) | −253662. | −0.797439 | ||||||||
\(565\) | −147608. | −0.462394 | ||||||||
\(566\) | − | 172352.i | − | 0.538001i | ||||||
\(567\) | − | 1.76281e6i | − | 5.48328i | ||||||
\(568\) | −176513. | −0.547117 | ||||||||
\(569\) | 6160.11i | 0.0190267i | 0.999955 | + | 0.00951336i | \(0.00302824\pi\) | ||||
−0.999955 | + | 0.00951336i | \(0.996972\pi\) | |||||||
\(570\) | −60018.7 | −0.184730 | ||||||||
\(571\) | 111470.i | 0.341888i | 0.985281 | + | 0.170944i | \(0.0546817\pi\) | ||||
−0.985281 | + | 0.170944i | \(0.945318\pi\) | |||||||
\(572\) | − | 47205.5i | − | 0.144278i | ||||||
\(573\) | − | 159220.i | − | 0.484941i | ||||||
\(574\) | 526256.i | 1.59725i | ||||||||
\(575\) | 11852.2 | − | 65054.1i | 0.0358478 | − | 0.196761i | ||||
\(576\) | 114608. | 0.345438 | ||||||||
\(577\) | −356286. | −1.07015 | −0.535077 | − | 0.844803i | \(-0.679718\pi\) | ||||
−0.535077 | + | 0.844803i | \(0.679718\pi\) | |||||||
\(578\) | −9731.73 | −0.0291296 | ||||||||
\(579\) | 21002.9 | 0.0626503 | ||||||||
\(580\) | 32733.7i | 0.0973059i | ||||||||
\(581\) | −645266. | −1.91155 | ||||||||
\(582\) | − | 456947.i | − | 1.34902i | ||||||
\(583\) | 54486.8 | 0.160308 | ||||||||
\(584\) | 45943.8 | 0.134711 | ||||||||
\(585\) | − | 234782.i | − | 0.686045i | ||||||
\(586\) | 197110.i | 0.574002i | ||||||||
\(587\) | 21337.8 | 0.0619262 | 0.0309631 | − | 0.999521i | \(-0.490143\pi\) | ||||
0.0309631 | + | 0.999521i | \(0.490143\pi\) | |||||||
\(588\) | −336687. | −0.973805 | ||||||||
\(589\) | − | 54505.5i | − | 0.157112i | ||||||
\(590\) | 139948.i | 0.402034i | ||||||||
\(591\) | −1.21228e6 | −3.47078 | ||||||||
\(592\) | 121162.i | 0.345718i | ||||||||
\(593\) | −470676. | −1.33848 | −0.669241 | − | 0.743045i | \(-0.733381\pi\) | ||||
−0.669241 | + | 0.743045i | \(0.733381\pi\) | |||||||
\(594\) | 443695.i | 1.25751i | ||||||||
\(595\) | − | 228695.i | − | 0.645986i | ||||||
\(596\) | 27890.4i | 0.0785169i | ||||||||
\(597\) | − | 305749.i | − | 0.857859i | ||||||
\(598\) | 25159.2 | − | 138094.i | 0.0703550 | − | 0.386164i | ||||
\(599\) | −241014. | −0.671721 | −0.335860 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335860 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(600\) | −49383.7 | −0.137177 | ||||||||
\(601\) | 355329. | 0.983743 | 0.491872 | − | 0.870668i | \(-0.336313\pi\) | ||||
0.491872 | + | 0.870668i | \(0.336313\pi\) | |||||||
\(602\) | −119061. | −0.328530 | ||||||||
\(603\) | 1.47383e6i | 4.05334i | ||||||||
\(604\) | −271699. | −0.744757 | ||||||||
\(605\) | 119460.i | 0.326370i | ||||||||
\(606\) | −241285. | −0.657030 | ||||||||
\(607\) | −226640. | −0.615119 | −0.307559 | − | 0.951529i | \(-0.599512\pi\) | ||||
−0.307559 | + | 0.951529i | \(0.599512\pi\) | |||||||
\(608\) | 19677.6i | 0.0532311i | ||||||||
\(609\) | − | 443228.i | − | 1.19507i | ||||||
\(610\) | −17473.3 | −0.0469587 | ||||||||
\(611\) | 170369. | 0.456361 | ||||||||
\(612\) | − | 528079.i | − | 1.40993i | ||||||
\(613\) | − | 297657.i | − | 0.792127i | −0.918223 | − | 0.396064i | \(-0.870376\pi\) | ||
0.918223 | − | 0.396064i | \(-0.129624\pi\) | |||||||
\(614\) | 419604. | 1.11302 | ||||||||
\(615\) | − | 523610.i | − | 1.38439i | ||||||
\(616\) | 98721.5 | 0.260166 | ||||||||
\(617\) | 614052.i | 1.61300i | 0.591234 | + | 0.806500i | \(0.298641\pi\) | ||||
−0.591234 | + | 0.806500i | \(0.701359\pi\) | |||||||
\(618\) | − | 434096.i | − | 1.13660i | ||||||
\(619\) | 622814.i | 1.62546i | 0.582638 | + | 0.812732i | \(0.302021\pi\) | ||||
−0.582638 | + | 0.812732i | \(0.697979\pi\) | |||||||
\(620\) | − | 44847.5i | − | 0.116669i | ||||||
\(621\) | −236477. | + | 1.29797e6i | −0.613205 | + | 3.36575i | ||||
\(622\) | 379965. | 0.982115 | ||||||||
\(623\) | −768621. | −1.98032 | ||||||||
\(624\) | −104829. | −0.269224 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 65099.5i | 0.166123i | ||||||||
\(627\) | −119378. | −0.303662 | ||||||||
\(628\) | 8177.35i | 0.0207345i | ||||||||
\(629\) | 558277. | 1.41107 | ||||||||
\(630\) | 491002. | 1.23709 | ||||||||
\(631\) | − | 655660.i | − | 1.64672i | −0.567519 | − | 0.823360i | \(-0.692097\pi\) | ||
0.567519 | − | 0.823360i | \(-0.307903\pi\) | |||||||
\(632\) | 268897.i | 0.673213i | ||||||||
\(633\) | 767494. | 1.91544 | ||||||||
\(634\) | 314527. | 0.782491 | ||||||||
\(635\) | − | 179864.i | − | 0.446064i | ||||||
\(636\) | − | 120999.i | − | 0.299135i | ||||||
\(637\) | 226132. | 0.557292 | ||||||||
\(638\) | 65107.9i | 0.159953i | ||||||||
\(639\) | −1.74617e6 | −4.27647 | ||||||||
\(640\) | 16190.9i | 0.0395285i | ||||||||
\(641\) | − | 703980.i | − | 1.71334i | −0.515863 | − | 0.856671i | \(-0.672529\pi\) | ||
0.515863 | − | 0.856671i | \(-0.327471\pi\) | |||||||
\(642\) | − | 1.11320e6i | − | 2.70086i | ||||||
\(643\) | − | 303481.i | − | 0.734023i | −0.930217 | − | 0.367011i | \(-0.880381\pi\) | ||
0.930217 | − | 0.367011i | \(-0.119619\pi\) | |||||||
\(644\) | 288797. | + | 52615.8i | 0.696340 | + | 0.126866i | ||||
\(645\) | 118462. | 0.284748 | ||||||||
\(646\) | 90668.5 | 0.217266 | ||||||||
\(647\) | −463400. | −1.10700 | −0.553500 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553500 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(648\) | 575047. | 1.36947 | ||||||||
\(649\) | 278359.i | 0.660870i | ||||||||
\(650\) | 33168.0 | 0.0785041 | ||||||||
\(651\) | 607253.i | 1.43287i | ||||||||
\(652\) | 92394.5 | 0.217346 | ||||||||
\(653\) | −580918. | −1.36235 | −0.681175 | − | 0.732121i | \(-0.738531\pi\) | ||||
−0.681175 | + | 0.732121i | \(0.738531\pi\) | |||||||
\(654\) | − | 257388.i | − | 0.601774i | ||||||
\(655\) | − | 235409.i | − | 0.548707i | ||||||
\(656\) | −171670. | −0.398920 | ||||||||
\(657\) | 454504. | 1.05295 | ||||||||
\(658\) | 356295.i | 0.822921i | ||||||||
\(659\) | − | 846482.i | − | 1.94916i | −0.224046 | − | 0.974579i | \(-0.571926\pi\) | ||
0.224046 | − | 0.974579i | \(-0.428074\pi\) | |||||||
\(660\) | −98225.1 | −0.225494 | ||||||||
\(661\) | − | 14348.8i | − | 0.0328407i | −0.999865 | − | 0.0164203i | \(-0.994773\pi\) | ||
0.999865 | − | 0.0164203i | \(-0.00522699\pi\) | |||||||
\(662\) | −232112. | −0.529640 | ||||||||
\(663\) | 483022.i | 1.09885i | ||||||||
\(664\) | − | 210492.i | − | 0.477419i | ||||||
\(665\) | 84302.5i | 0.190633i | ||||||||
\(666\) | 1.19861e6i | 2.70226i | ||||||||
\(667\) | −34700.7 | + | 190465.i | −0.0779986 | + | 0.428118i | ||||
\(668\) | 332479. | 0.745095 | ||||||||
\(669\) | 589769. | 1.31774 | ||||||||
\(670\) | −208211. | −0.463824 | ||||||||
\(671\) | −34754.8 | −0.0771915 | ||||||||
\(672\) | − | 219231.i | − | 0.485471i | ||||||
\(673\) | 201489. | 0.444857 | 0.222428 | − | 0.974949i | \(-0.428602\pi\) | ||||
0.222428 | + | 0.974949i | \(0.428602\pi\) | |||||||
\(674\) | 9195.97i | 0.0202431i | ||||||||
\(675\) | −311753. | −0.684231 | ||||||||
\(676\) | −158081. | −0.345928 | ||||||||
\(677\) | 127799.i | 0.278836i | 0.990234 | + | 0.139418i | \(0.0445232\pi\) | ||||
−0.990234 | + | 0.139418i | \(0.955477\pi\) | |||||||
\(678\) | 651986.i | 1.41833i | ||||||||
\(679\) | −641830. | −1.39213 | ||||||||
\(680\) | 74602.6 | 0.161338 | ||||||||
\(681\) | 443069.i | 0.955382i | ||||||||
\(682\) | − | 89202.5i | − | 0.191782i | ||||||
\(683\) | −840247. | −1.80122 | −0.900608 | − | 0.434632i | \(-0.856878\pi\) | ||||
−0.900608 | + | 0.434632i | \(0.856878\pi\) | |||||||
\(684\) | 194663.i | 0.416074i | ||||||||
\(685\) | −389252. | −0.829563 | ||||||||
\(686\) | 1853.72i | 0.00393909i | ||||||||
\(687\) | − | 1.46748e6i | − | 3.10928i | ||||||
\(688\) | − | 38838.8i | − | 0.0820519i | ||||||
\(689\) | 81267.4i | 0.171190i | ||||||||
\(690\) | −287345. | − | 52351.3i | −0.603539 | − | 0.109959i | ||||
\(691\) | 304935. | 0.638632 | 0.319316 | − | 0.947648i | \(-0.396547\pi\) | ||||
0.319316 | + | 0.947648i | \(0.396547\pi\) | |||||||
\(692\) | 254333. | 0.531117 | ||||||||
\(693\) | 976612. | 2.03355 | ||||||||
\(694\) | 90926.8 | 0.188787 | ||||||||
\(695\) | 147627.i | 0.305630i | ||||||||
\(696\) | 144585. | 0.298473 | ||||||||
\(697\) | 791003.i | 1.62822i | ||||||||
\(698\) | 561526. | 1.15255 | ||||||||
\(699\) | 562716. | 1.15169 | ||||||||
\(700\) | 69364.6i | 0.141560i | ||||||||
\(701\) | − | 68580.5i | − | 0.139561i | −0.997562 | − | 0.0697806i | \(-0.977770\pi\) | ||
0.997562 | − | 0.0697806i | \(-0.0222299\pi\) | |||||||
\(702\) | −661774. | −1.34287 | ||||||||
\(703\) | −205794. | −0.416412 | ||||||||
\(704\) | 32203.9i | 0.0649776i | ||||||||
\(705\) | − | 354504.i | − | 0.713251i | ||||||
\(706\) | −87948.7 | −0.176449 | ||||||||
\(707\) | 338910.i | 0.678025i | ||||||||
\(708\) | 618152. | 1.23319 | ||||||||
\(709\) | − | 883225.i | − | 1.75703i | −0.477716 | − | 0.878514i | \(-0.658535\pi\) | ||
0.477716 | − | 0.878514i | \(-0.341465\pi\) | |||||||
\(710\) | − | 246684.i | − | 0.489356i | ||||||
\(711\) | 2.66009e6i | 5.26208i | ||||||||
\(712\) | − | 250732.i | − | 0.494595i | ||||||
\(713\) | 47542.5 | − | 260950.i | 0.0935196 | − | 0.513309i | ||||
\(714\) | −1.01015e6 | −1.98148 | ||||||||
\(715\) | 65971.7 | 0.129046 | ||||||||
\(716\) | −230195. | −0.449025 | ||||||||
\(717\) | 525927. | 1.02303 | ||||||||
\(718\) | − | 598272.i | − | 1.16051i | ||||||
\(719\) | 612080. | 1.18400 | 0.591998 | − | 0.805939i | \(-0.298339\pi\) | ||||
0.591998 | + | 0.805939i | \(0.298339\pi\) | |||||||
\(720\) | 160170.i | 0.308969i | ||||||||
\(721\) | −609733. | −1.17292 | ||||||||
\(722\) | 335181. | 0.642991 | ||||||||
\(723\) | − | 271488.i | − | 0.519367i | ||||||
\(724\) | 444670.i | 0.848322i | ||||||||
\(725\) | −45746.7 | −0.0870330 | ||||||||
\(726\) | 527655. | 1.00110 | ||||||||
\(727\) | 516461.i | 0.977166i | 0.872517 | + | 0.488583i | \(0.162486\pi\) | ||||
−0.872517 | + | 0.488583i | \(0.837514\pi\) | |||||||
\(728\) | 147244.i | 0.277827i | ||||||||
\(729\) | 2.16156e6 | 4.06736 | ||||||||
\(730\) | 64208.4i | 0.120489i | ||||||||
\(731\) | −178957. | −0.334900 | ||||||||
\(732\) | 77179.9i | 0.144040i | ||||||||
\(733\) | 758127.i | 1.41102i | 0.708698 | + | 0.705512i | \(0.249283\pi\) | ||||
−0.708698 | + | 0.705512i | \(0.750717\pi\) | |||||||
\(734\) | 102644.i | 0.190520i | ||||||||
\(735\) | − | 470535.i | − | 0.870998i | ||||||
\(736\) | −17163.8 | + | 94208.5i | −0.0316853 | + | 0.173914i | ||||
\(737\) | −414135. | −0.762441 | ||||||||
\(738\) | −1.69826e6 | −3.11811 | ||||||||
\(739\) | 641756. | 1.17512 | 0.587558 | − | 0.809182i | \(-0.300089\pi\) | ||||
0.587558 | + | 0.809182i | \(0.300089\pi\) | |||||||
\(740\) | −169329. | −0.309220 | ||||||||
\(741\) | − | 178053.i | − | 0.324275i | ||||||
\(742\) | −169955. | −0.308693 | ||||||||
\(743\) | 338378.i | 0.612950i | 0.951879 | + | 0.306475i | \(0.0991495\pi\) | ||||
−0.951879 | + | 0.306475i | \(0.900850\pi\) | |||||||
\(744\) | −198092. | −0.357866 | ||||||||
\(745\) | −38978.1 | −0.0702276 | ||||||||
\(746\) | − | 376756.i | − | 0.676990i | ||||||
\(747\) | − | 2.08231e6i | − | 3.73168i | ||||||
\(748\) | 148386. | 0.265210 | ||||||||
\(749\) | −1.56360e6 | −2.78717 | ||||||||
\(750\) | − | 69015.8i | − | 0.122695i | ||||||
\(751\) | 415430.i | 0.736577i | 0.929712 | + | 0.368288i | \(0.120056\pi\) | ||||
−0.929712 | + | 0.368288i | \(0.879944\pi\) | |||||||
\(752\) | −116227. | −0.205528 | ||||||||
\(753\) | − | 1.03134e6i | − | 1.81891i | ||||||
\(754\) | −97108.9 | −0.170811 | ||||||||
\(755\) | − | 379711.i | − | 0.666131i | ||||||
\(756\) | − | 1.38398e6i | − | 2.42150i | ||||||
\(757\) | − | 163552.i | − | 0.285407i | −0.989766 | − | 0.142703i | \(-0.954421\pi\) | ||
0.989766 | − | 0.142703i | \(-0.0455795\pi\) | |||||||
\(758\) | 645869.i | 1.12410i | ||||||||
\(759\) | −571535. | − | 104128.i | −0.992108 | − | 0.180752i | ||||
\(760\) | −27500.3 | −0.0476113 | ||||||||
\(761\) | −715636. | −1.23573 | −0.617864 | − | 0.786285i | \(-0.712002\pi\) | ||||
−0.617864 | + | 0.786285i | \(0.712002\pi\) | |||||||
\(762\) | −794463. | −1.36824 | ||||||||
\(763\) | −361529. | −0.621003 | ||||||||
\(764\) | − | 72954.0i | − | 0.124986i | ||||||
\(765\) | 738013. | 1.26108 | ||||||||
\(766\) | − | 210748.i | − | 0.359174i | ||||||
\(767\) | −415174. | −0.705732 | ||||||||
\(768\) | 71515.3 | 0.121248 | ||||||||
\(769\) | 896493.i | 1.51598i | 0.652264 | + | 0.757991i | \(0.273819\pi\) | ||||
−0.652264 | + | 0.757991i | \(0.726181\pi\) | |||||||
\(770\) | 137967.i | 0.232699i | ||||||||
\(771\) | 1.73360e6 | 2.91635 | ||||||||
\(772\) | 9623.46 | 0.0161472 | ||||||||
\(773\) | 171722.i | 0.287387i | 0.989622 | + | 0.143694i | \(0.0458980\pi\) | ||||
−0.989622 | + | 0.143694i | \(0.954102\pi\) | |||||||
\(774\) | − | 384216.i | − | 0.641348i | ||||||
\(775\) | 62676.3 | 0.104352 | ||||||||
\(776\) | − | 209371.i | − | 0.347691i | ||||||
\(777\) | 2.29278e6 | 3.79770 | ||||||||
\(778\) | 117332.i | 0.193847i | ||||||||
\(779\) | − | 291583.i | − | 0.480493i | ||||||
\(780\) | − | 146503.i | − | 0.240801i | ||||||
\(781\) | − | 490660.i | − | 0.804412i | ||||||
\(782\) | 434084. | + | 79085.6i | 0.709840 | + | 0.129325i | ||||
\(783\) | 912748. | 1.48877 | ||||||||
\(784\) | −154269. | −0.250984 | ||||||||
\(785\) | −11428.2 | −0.0185455 | ||||||||
\(786\) | −1.03980e6 | −1.68309 | ||||||||
\(787\) | 160006.i | 0.258337i | 0.991623 | + | 0.129169i | \(0.0412308\pi\) | ||||
−0.991623 | + | 0.129169i | \(0.958769\pi\) | |||||||
\(788\) | −555460. | −0.894542 | ||||||||
\(789\) | − | 649826.i | − | 1.04386i | ||||||
\(790\) | −375795. | −0.602140 | ||||||||
\(791\) | 915782. | 1.46366 | ||||||||
\(792\) | 318580.i | 0.507889i | ||||||||
\(793\) | − | 51837.0i | − | 0.0824315i | ||||||
\(794\) | −15589.9 | −0.0247288 | ||||||||
\(795\) | 169101. | 0.267554 | ||||||||
\(796\) | − | 140093.i | − | 0.221101i | ||||||
\(797\) | 442182.i | 0.696121i | 0.937472 | + | 0.348060i | \(0.113160\pi\) | ||||
−0.937472 | + | 0.348060i | \(0.886840\pi\) | |||||||
\(798\) | 372365. | 0.584741 | ||||||||
\(799\) | 535539.i | 0.838875i | ||||||||
\(800\) | −22627.4 | −0.0353553 | ||||||||
\(801\) | − | 2.48039e6i | − | 3.86594i | ||||||
\(802\) | 585497.i | 0.910282i | ||||||||
\(803\) | 127712.i | 0.198061i | ||||||||
\(804\) | 919669.i | 1.42272i | ||||||||
\(805\) | −73532.9 | + | 403606.i | −0.113472 | + | 0.622825i | ||||
\(806\) | 133046. | 0.204801 | ||||||||
\(807\) | −186960. | −0.287079 | ||||||||
\(808\) | −110556. | −0.169340 | ||||||||
\(809\) | −146806. | −0.224309 | −0.112154 | − | 0.993691i | \(-0.535775\pi\) | ||||
−0.112154 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(810\) | 803653.i | 1.22489i | ||||||||
\(811\) | −505788. | −0.769001 | −0.384500 | − | 0.923125i | \(-0.625626\pi\) | ||||
−0.384500 | + | 0.923125i | \(0.625626\pi\) | |||||||
\(812\) | − | 203085.i | − | 0.308011i | ||||||
\(813\) | −328864. | −0.497548 | ||||||||
\(814\) | −336798. | −0.508301 | ||||||||
\(815\) | 129125.i | 0.194400i | ||||||||
\(816\) | − | 329521.i | − | 0.494883i | ||||||
\(817\) | 65968.0 | 0.0988301 | ||||||||
\(818\) | −236205. | −0.353006 | ||||||||
\(819\) | 1.45662e6i | 2.17160i | ||||||||
\(820\) | − | 239916.i | − | 0.356805i | ||||||
\(821\) | 79249.8 | 0.117574 | 0.0587870 | − | 0.998271i | \(-0.481277\pi\) | ||||
0.0587870 | + | 0.998271i | \(0.481277\pi\) | |||||||
\(822\) | 1.71933e6i | 2.54458i | ||||||||
\(823\) | 740309. | 1.09298 | 0.546491 | − | 0.837465i | \(-0.315963\pi\) | ||||
0.546491 | + | 0.837465i | \(0.315963\pi\) | |||||||
\(824\) | − | 198901.i | − | 0.292943i | ||||||
\(825\) | − | 137274.i | − | 0.201688i | ||||||
\(826\) | − | 868259.i | − | 1.27259i | ||||||
\(827\) | 274955.i | 0.402023i | 0.979589 | + | 0.201011i | \(0.0644228\pi\) | ||||
−0.979589 | + | 0.201011i | \(0.935577\pi\) | |||||||
\(828\) | −169795. | + | 931966.i | −0.247664 | + | 1.35938i | ||||
\(829\) | −885762. | −1.28887 | −0.644433 | − | 0.764661i | \(-0.722907\pi\) | ||||
−0.644433 | + | 0.764661i | \(0.722907\pi\) | |||||||
\(830\) | 294172. | 0.427016 | ||||||||
\(831\) | 475939. | 0.689207 | ||||||||
\(832\) | −48032.4 | −0.0693885 | ||||||||
\(833\) | 710824.i | 1.02441i | ||||||||
\(834\) | 652070. | 0.937480 | ||||||||
\(835\) | 464654.i | 0.666433i | ||||||||
\(836\) | −54698.6 | −0.0782643 | ||||||||
\(837\) | −1.25053e6 | −1.78502 | ||||||||
\(838\) | 531924.i | 0.757464i | ||||||||
\(839\) | − | 78938.5i | − | 0.112141i | −0.998427 | − | 0.0560706i | \(-0.982143\pi\) | ||
0.998427 | − | 0.0560706i | \(-0.0178572\pi\) | |||||||
\(840\) | 306384. | 0.434218 | ||||||||
\(841\) | −573344. | −0.810631 | ||||||||
\(842\) | − | 331337.i | − | 0.467354i | ||||||
\(843\) | − | 334845.i | − | 0.471183i | ||||||
\(844\) | 351663. | 0.493675 | ||||||||
\(845\) | − | 220924.i | − | 0.309407i | ||||||
\(846\) | −1.14979e6 | −1.60648 | ||||||||
\(847\) | − | 741147.i | − | 1.03309i | ||||||
\(848\) | − | 55441.1i | − | 0.0770975i | ||||||
\(849\) | − | 1.06392e6i | − | 1.47603i | ||||||
\(850\) | 104260.i | 0.144305i | ||||||||
\(851\) | −985260. | − | 179504.i | −1.36048 | − | 0.247865i | ||||
\(852\) | −1.08961e6 | −1.50104 | ||||||||
\(853\) | −173285. | −0.238156 | −0.119078 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119078 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(854\) | 108407. | 0.148642 | ||||||||
\(855\) | −272050. | −0.372148 | ||||||||
\(856\) | − | 510063.i | − | 0.696107i | ||||||
\(857\) | 550193. | 0.749124 | 0.374562 | − | 0.927202i | \(-0.377793\pi\) | ||||
0.374562 | + | 0.927202i | \(0.377793\pi\) | |||||||
\(858\) | − | 291398.i | − | 0.395833i | ||||||
\(859\) | 175899. | 0.238384 | 0.119192 | − | 0.992871i | \(-0.461970\pi\) | ||||
0.119192 | + | 0.992871i | \(0.461970\pi\) | |||||||
\(860\) | 54278.8 | 0.0733895 | ||||||||
\(861\) | 3.24856e6i | 4.38212i | ||||||||
\(862\) | − | 573887.i | − | 0.772346i | ||||||
\(863\) | −1.28923e6 | −1.73105 | −0.865524 | − | 0.500867i | \(-0.833015\pi\) | ||||
−0.865524 | + | 0.500867i | \(0.833015\pi\) | |||||||
\(864\) | 451466. | 0.604781 | ||||||||
\(865\) | 355441.i | 0.475045i | ||||||||
\(866\) | − | 268987.i | − | 0.358670i | ||||||
\(867\) | −60073.6 | −0.0799182 | ||||||||
\(868\) | 278241.i | 0.369302i | ||||||||
\(869\) | −747464. | −0.989807 | ||||||||
\(870\) | 202064.i | 0.266963i | ||||||||
\(871\) | − | 617684.i | − | 0.814199i | ||||||
\(872\) | − | 117934.i | − | 0.155098i | ||||||
\(873\) | − | 2.07123e6i | − | 2.71768i | ||||||
\(874\) | −160014. | − | 29152.9i | −0.209476 | − | 0.0381644i | ||||
\(875\) | −96940.0 | −0.126615 | ||||||||
\(876\) | 283610. | 0.369584 | ||||||||
\(877\) | −988741. | −1.28553 | −0.642767 | − | 0.766062i | \(-0.722214\pi\) | ||||
−0.642767 | + | 0.766062i | \(0.722214\pi\) | |||||||
\(878\) | −113855. | −0.147694 | ||||||||
\(879\) | 1.21675e6i | 1.57480i | ||||||||
\(880\) | −45006.4 | −0.0581177 | ||||||||
\(881\) | − | 963126.i | − | 1.24088i | −0.784252 | − | 0.620442i | \(-0.786953\pi\) | ||
0.784252 | − | 0.620442i | \(-0.213047\pi\) | |||||||
\(882\) | −1.52612e6 | −1.96178 | ||||||||
\(883\) | −821811. | −1.05402 | −0.527012 | − | 0.849858i | \(-0.676688\pi\) | ||||
−0.527012 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(884\) | 221319.i | 0.283213i | ||||||||
\(885\) | 863894.i | 1.10300i | ||||||||
\(886\) | 659838. | 0.840562 | ||||||||
\(887\) | −163425. | −0.207717 | −0.103858 | − | 0.994592i | \(-0.533119\pi\) | ||||
−0.103858 | + | 0.994592i | \(0.533119\pi\) | |||||||
\(888\) | 747928.i | 0.948492i | ||||||||
\(889\) | 1.11591e6i | 1.41197i | ||||||||
\(890\) | 350408. | 0.442379 | ||||||||
\(891\) | 1.59848e6i | 2.01350i | ||||||||
\(892\) | 270230. | 0.339628 | ||||||||
\(893\) | − | 197412.i | − | 0.247555i | ||||||
\(894\) | 172167.i | 0.215414i | ||||||||
\(895\) | − | 321708.i | − | 0.401620i | ||||||
\(896\) | − | 100451.i | − | 0.125123i | ||||||
\(897\) | 155307. | − | 852448.i | 0.193022 | − | 1.05946i | ||||
\(898\) | −790145. | −0.979838 | ||||||||
\(899\) | −183503. | −0.227051 | ||||||||
\(900\) | −223844. | −0.276351 | ||||||||
\(901\) | −255456. | −0.314678 | ||||||||
\(902\) | − | 477197.i | − | 0.586523i | ||||||
\(903\) | −734958. | −0.901336 | ||||||||
\(904\) | 298737.i | 0.365555i | ||||||||
\(905\) | −621445. | −0.758762 | ||||||||
\(906\) | −1.67719e6 | −2.04327 | ||||||||
\(907\) | 778506.i | 0.946341i | 0.880971 | + | 0.473170i | \(0.156890\pi\) | ||||
−0.880971 | + | 0.473170i | \(0.843110\pi\) | |||||||
\(908\) | 203012.i | 0.246236i | ||||||||
\(909\) | −1.09368e6 | −1.32362 | ||||||||
\(910\) | −205779. | −0.248496 | ||||||||
\(911\) | − | 631880.i | − | 0.761374i | −0.924704 | − | 0.380687i | \(-0.875688\pi\) | ||
0.924704 | − | 0.380687i | \(-0.124312\pi\) | |||||||
\(912\) | 121469.i | 0.146042i | ||||||||
\(913\) | 585113. | 0.701937 | ||||||||
\(914\) | 773632.i | 0.926066i | ||||||||
\(915\) | −107862. | −0.128833 | ||||||||
\(916\) | − | 672395.i | − | 0.801370i | ||||||
\(917\) | 1.46051e6i | 1.73687i | ||||||||
\(918\) | − | 2.08022e6i | − | 2.46845i | ||||||
\(919\) | − | 329548.i | − | 0.390201i | −0.980783 | − | 0.195100i | \(-0.937497\pi\) | ||
0.980783 | − | 0.195100i | \(-0.0625032\pi\) | |||||||
\(920\) | −131660. | − | 23987.1i | −0.155553 | − | 0.0283402i | ||||
\(921\) | 2.59020e6 | 3.05361 | ||||||||
\(922\) | −570469. | −0.671074 | ||||||||
\(923\) | 731822. | 0.859018 | ||||||||
\(924\) | 609404. | 0.713775 | ||||||||
\(925\) | − | 236644.i | − | 0.276575i | ||||||
\(926\) | 508556. | 0.593085 | ||||||||
\(927\) | − | 1.96765e6i | − | 2.28975i | ||||||
\(928\) | 66248.3 | 0.0769271 | ||||||||
\(929\) | 392594. | 0.454896 | 0.227448 | − | 0.973790i | \(-0.426962\pi\) | ||||
0.227448 | + | 0.973790i | \(0.426962\pi\) | |||||||
\(930\) | − | 276842.i | − | 0.320085i | ||||||
\(931\) | − | 262027.i | − | 0.302306i | ||||||
\(932\) | 257834. | 0.296830 | ||||||||
\(933\) | 2.34551e6 | 2.69447 | ||||||||
\(934\) | − | 860656.i | − | 0.986588i | ||||||
\(935\) | 207376.i | 0.237211i | ||||||||
\(936\) | −475165. | −0.542366 | ||||||||
\(937\) | 432138.i | 0.492202i | 0.969244 | + | 0.246101i | \(0.0791496\pi\) | ||||
−0.969244 | + | 0.246101i | \(0.920850\pi\) | |||||||
\(938\) | 1.29177e6 | 1.46818 | ||||||||
\(939\) | 401857.i | 0.455764i | ||||||||
\(940\) | − | 162432.i | − | 0.183830i | ||||||
\(941\) | 35467.3i | 0.0400543i | 0.999799 | + | 0.0200272i | \(0.00637527\pi\) | ||||
−0.999799 | + | 0.0200272i | \(0.993625\pi\) | |||||||
\(942\) | 50478.5i | 0.0568859i | ||||||||
\(943\) | 254333. | − | 1.39598e6i | 0.286009 | − | 1.56984i | ||||
\(944\) | 283235. | 0.317836 | ||||||||
\(945\) | 1.93416e6 | 2.16586 | ||||||||
\(946\) | 107962. | 0.120639 | ||||||||
\(947\) | 552193. | 0.615731 | 0.307865 | − | 0.951430i | \(-0.400385\pi\) | ||||
0.307865 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(948\) | 1.65989e6i | 1.84699i | ||||||||
\(949\) | −190483. | −0.211507 | ||||||||
\(950\) | − | 38432.9i | − | 0.0425849i | ||||||
\(951\) | 1.94156e6 | 2.14680 | ||||||||
\(952\) | −462846. | −0.510697 | ||||||||
\(953\) | 894272.i | 0.984654i | 0.870410 | + | 0.492327i | \(0.163854\pi\) | ||||
−0.870410 | + | 0.492327i | \(0.836146\pi\) | |||||||
\(954\) | − | 548457.i | − | 0.602623i | ||||||
\(955\) | 101956. | 0.111791 | ||||||||
\(956\) | 240977. | 0.263670 | ||||||||
\(957\) | 401909.i | 0.438838i | ||||||||
\(958\) | 412984.i | 0.449989i | ||||||||
\(959\) | 2.41498e6 | 2.62589 | ||||||||
\(960\) | 99945.6i | 0.108448i | ||||||||
\(961\) | −672109. | −0.727768 | ||||||||
\(962\) | − | 502337.i | − | 0.542806i | ||||||
\(963\) | − | 5.04585e6i | − | 5.44103i | ||||||
\(964\) | − | 124395.i | − | 0.133859i | ||||||
\(965\) | 13449.2i | 0.0144425i | ||||||||
\(966\) | 1.78273e6 | + | 324796.i | 1.91044 | + | 0.348062i | ||||
\(967\) | 984833. | 1.05320 | 0.526599 | − | 0.850114i | \(-0.323467\pi\) | ||||
0.526599 | + | 0.850114i | \(0.323467\pi\) | |||||||
\(968\) | 241770. | 0.258019 | ||||||||
\(969\) | 559694. | 0.596078 | ||||||||
\(970\) | 292605. | 0.310984 | ||||||||
\(971\) | − | 358995.i | − | 0.380758i | −0.981711 | − | 0.190379i | \(-0.939028\pi\) | ||
0.981711 | − | 0.190379i | \(-0.0609718\pi\) | |||||||
\(972\) | 1.93362e6 | 2.04663 | ||||||||
\(973\) | − | 915901.i | − | 0.967437i | ||||||
\(974\) | 860403. | 0.906951 | ||||||||
\(975\) | 204745. | 0.215379 | ||||||||
\(976\) | 35363.5i | 0.0371241i | ||||||||
\(977\) | − | 31385.8i | − | 0.0328810i | −0.999865 | − | 0.0164405i | \(-0.994767\pi\) | ||
0.999865 | − | 0.0164405i | \(-0.00523340\pi\) | |||||||
\(978\) | 570348. | 0.596296 | ||||||||
\(979\) | 696969. | 0.727190 | ||||||||
\(980\) | − | 215597.i | − | 0.224487i | ||||||
\(981\) | − | 1.16668e6i | − | 1.21231i | ||||||
\(982\) | 201594. | 0.209053 | ||||||||
\(983\) | 1.50797e6i | 1.56058i | 0.625416 | + | 0.780292i | \(0.284929\pi\) | ||||
−0.625416 | + | 0.780292i | \(0.715071\pi\) | |||||||
\(984\) | −1.05971e6 | −1.09445 | ||||||||
\(985\) | − | 776280.i | − | 0.800103i | ||||||
\(986\) | − | 305252.i | − | 0.313982i | ||||||
\(987\) | 2.19940e6i | 2.25772i | ||||||||
\(988\) | − | 81583.4i | − | 0.0835772i | ||||||
\(989\) | 315828. | + | 57540.6i | 0.322893 | + | 0.0588277i | ||||
\(990\) | −445230. | −0.454270 | ||||||||
\(991\) | −1.10604e6 | −1.12622 | −0.563110 | − | 0.826382i | \(-0.690395\pi\) | ||||
−0.563110 | + | 0.826382i | \(0.690395\pi\) | |||||||
\(992\) | −90764.9 | −0.0922348 | ||||||||
\(993\) | −1.43282e6 | −1.45309 | ||||||||
\(994\) | 1.53047e6i | 1.54900i | ||||||||
\(995\) | 195786. | 0.197758 | ||||||||
\(996\) | − | 1.29936e6i | − | 1.30982i | ||||||
\(997\) | −960399. | −0.966187 | −0.483094 | − | 0.875569i | \(-0.660487\pi\) | ||||
−0.483094 | + | 0.875569i | \(0.660487\pi\) | |||||||
\(998\) | 897519. | 0.901120 | ||||||||
\(999\) | 4.72157e6i | 4.73103i |
(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 | 230.5.d.a.91.17 | ✓ | 32 | |
23.22 | odd | 2 | inner | 230.5.d.a.91.32 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.5.d.a.91.17 | ✓ | 32 | 1.1 | even | 1 | trivial | |
230.5.d.a.91.32 | yes | 32 | 23.22 | odd | 2 | inner |