Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(6,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, 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("35.6");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 109 x^{10} + 570 x^{9} + 5814 x^{8} - 22512 x^{7} - 151120 x^{6} + 300288 x^{5} + \cdots + 205833600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.10 | ||
Root | \(5.81769 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.6 |
Dual form | 35.5.d.a.6.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.81769 | 1.20442 | 0.602212 | − | 0.798337i | \(-0.294286\pi\) | ||||
0.602212 | + | 0.798337i | \(0.294286\pi\) | |||||||
\(3\) | 14.5704i | 1.61893i | 0.587166 | + | 0.809466i | \(0.300243\pi\) | ||||
−0.587166 | + | 0.809466i | \(0.699757\pi\) | |||||||
\(4\) | 7.21016 | 0.450635 | ||||||||
\(5\) | − | 11.1803i | − | 0.447214i | ||||||
\(6\) | 70.1957i | 1.94988i | ||||||||
\(7\) | 44.8989 | + | 19.6236i | 0.916305 | + | 0.400481i | ||||
\(8\) | −42.3467 | −0.661668 | ||||||||
\(9\) | −131.296 | −1.62094 | ||||||||
\(10\) | − | 53.8634i | − | 0.538634i | ||||||
\(11\) | 201.717 | 1.66708 | 0.833539 | − | 0.552460i | \(-0.186311\pi\) | ||||
0.833539 | + | 0.552460i | \(0.186311\pi\) | |||||||
\(12\) | 105.055i | 0.729548i | ||||||||
\(13\) | − | 258.711i | − | 1.53083i | −0.643535 | − | 0.765416i | \(-0.722533\pi\) | ||
0.643535 | − | 0.765416i | \(-0.277467\pi\) | |||||||
\(14\) | 216.309 | + | 94.5404i | 1.10362 | + | 0.482349i | ||||
\(15\) | 162.902 | 0.724009 | ||||||||
\(16\) | −319.376 | −1.24756 | ||||||||
\(17\) | − | 242.930i | − | 0.840588i | −0.907388 | − | 0.420294i | \(-0.861927\pi\) | ||
0.907388 | − | 0.420294i | \(-0.138073\pi\) | |||||||
\(18\) | −632.545 | −1.95230 | ||||||||
\(19\) | 253.614i | 0.702533i | 0.936276 | + | 0.351266i | \(0.114249\pi\) | ||||
−0.936276 | + | 0.351266i | \(0.885751\pi\) | |||||||
\(20\) | − | 80.6121i | − | 0.201530i | ||||||
\(21\) | −285.923 | + | 654.195i | −0.648352 | + | 1.48344i | ||||
\(22\) | 971.808 | 2.00787 | ||||||||
\(23\) | −323.663 | −0.611840 | −0.305920 | − | 0.952057i | \(-0.598964\pi\) | ||||
−0.305920 | + | 0.952057i | \(0.598964\pi\) | |||||||
\(24\) | − | 617.009i | − | 1.07120i | ||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | − | 1246.39i | − | 1.84377i | ||||||
\(27\) | − | 732.838i | − | 1.00526i | ||||||
\(28\) | 323.729 | + | 141.489i | 0.412919 | + | 0.180471i | ||||
\(29\) | −331.107 | −0.393707 | −0.196853 | − | 0.980433i | \(-0.563072\pi\) | ||||
−0.196853 | + | 0.980433i | \(0.563072\pi\) | |||||||
\(30\) | 784.812 | 0.872013 | ||||||||
\(31\) | 278.747i | 0.290059i | 0.989427 | + | 0.145030i | \(0.0463277\pi\) | ||||
−0.989427 | + | 0.145030i | \(0.953672\pi\) | |||||||
\(32\) | −861.108 | −0.840926 | ||||||||
\(33\) | 2939.09i | 2.69889i | ||||||||
\(34\) | − | 1170.36i | − | 1.01242i | ||||||
\(35\) | 219.398 | − | 501.985i | 0.179101 | − | 0.409784i | ||||
\(36\) | −946.668 | −0.730454 | ||||||||
\(37\) | −322.518 | −0.235587 | −0.117793 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117793 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(38\) | 1221.84i | 0.846147i | ||||||||
\(39\) | 3769.52 | 2.47831 | ||||||||
\(40\) | 473.451i | 0.295907i | ||||||||
\(41\) | 578.646i | 0.344227i | 0.985077 | + | 0.172114i | \(0.0550596\pi\) | ||||
−0.985077 | + | 0.172114i | \(0.944940\pi\) | |||||||
\(42\) | −1377.49 | + | 3151.71i | −0.780891 | + | 1.78668i | ||||
\(43\) | −1524.82 | −0.824674 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(44\) | 1454.41 | 0.751244 | ||||||||
\(45\) | 1467.94i | 0.724908i | ||||||||
\(46\) | −1559.31 | −0.736914 | ||||||||
\(47\) | − | 389.432i | − | 0.176293i | −0.996108 | − | 0.0881467i | \(-0.971906\pi\) | ||
0.996108 | − | 0.0881467i | \(-0.0280944\pi\) | |||||||
\(48\) | − | 4653.44i | − | 2.01972i | ||||||
\(49\) | 1630.83 | + | 1762.16i | 0.679229 | + | 0.733926i | ||||
\(50\) | −602.212 | −0.240885 | ||||||||
\(51\) | 3539.59 | 1.36086 | ||||||||
\(52\) | − | 1865.35i | − | 0.689847i | ||||||
\(53\) | 1071.73 | 0.381535 | 0.190768 | − | 0.981635i | \(-0.438902\pi\) | ||||
0.190768 | + | 0.981635i | \(0.438902\pi\) | |||||||
\(54\) | − | 3530.59i | − | 1.21076i | ||||||
\(55\) | − | 2255.26i | − | 0.745540i | ||||||
\(56\) | −1901.32 | − | 830.995i | −0.606289 | − | 0.264986i | ||||
\(57\) | −3695.26 | −1.13735 | ||||||||
\(58\) | −1595.17 | −0.474190 | ||||||||
\(59\) | 1030.67i | 0.296085i | 0.988981 | + | 0.148042i | \(0.0472972\pi\) | ||||
−0.988981 | + | 0.148042i | \(0.952703\pi\) | |||||||
\(60\) | 1174.55 | 0.326264 | ||||||||
\(61\) | − | 6681.90i | − | 1.79573i | −0.440273 | − | 0.897864i | \(-0.645118\pi\) | ||
0.440273 | − | 0.897864i | \(-0.354882\pi\) | |||||||
\(62\) | 1342.92i | 0.349354i | ||||||||
\(63\) | −5895.07 | − | 2576.51i | −1.48528 | − | 0.649157i | ||||
\(64\) | 961.463 | 0.234732 | ||||||||
\(65\) | −2892.47 | −0.684609 | ||||||||
\(66\) | 14159.6i | 3.25060i | ||||||||
\(67\) | −4053.08 | −0.902892 | −0.451446 | − | 0.892299i | \(-0.649092\pi\) | ||||
−0.451446 | + | 0.892299i | \(0.649092\pi\) | |||||||
\(68\) | − | 1751.57i | − | 0.378799i | ||||||
\(69\) | − | 4715.90i | − | 0.990527i | ||||||
\(70\) | 1056.99 | − | 2418.41i | 0.215713 | − | 0.493553i | ||||
\(71\) | 3210.95 | 0.636967 | 0.318483 | − | 0.947928i | \(-0.396827\pi\) | ||||
0.318483 | + | 0.947928i | \(0.396827\pi\) | |||||||
\(72\) | 5559.97 | 1.07253 | ||||||||
\(73\) | 2238.66i | 0.420091i | 0.977692 | + | 0.210045i | \(0.0673612\pi\) | ||||
−0.977692 | + | 0.210045i | \(0.932639\pi\) | |||||||
\(74\) | −1553.79 | −0.283746 | ||||||||
\(75\) | − | 1821.30i | − | 0.323787i | ||||||
\(76\) | 1828.60i | 0.316586i | ||||||||
\(77\) | 9056.86 | + | 3958.40i | 1.52755 | + | 0.667634i | ||||
\(78\) | 18160.4 | 2.98494 | ||||||||
\(79\) | −5234.87 | −0.838787 | −0.419393 | − | 0.907805i | \(-0.637757\pi\) | ||||
−0.419393 | + | 0.907805i | \(0.637757\pi\) | |||||||
\(80\) | 3570.73i | 0.557927i | ||||||||
\(81\) | 42.7274 | 0.00651233 | ||||||||
\(82\) | 2787.74i | 0.414595i | ||||||||
\(83\) | 3799.88i | 0.551587i | 0.961217 | + | 0.275793i | \(0.0889405\pi\) | ||||
−0.961217 | + | 0.275793i | \(0.911059\pi\) | |||||||
\(84\) | −2061.55 | + | 4716.85i | −0.292170 | + | 0.668488i | ||||
\(85\) | −2716.04 | −0.375923 | ||||||||
\(86\) | −7346.12 | −0.993256 | ||||||||
\(87\) | − | 4824.37i | − | 0.637385i | ||||||
\(88\) | −8542.04 | −1.10305 | ||||||||
\(89\) | 13693.9i | 1.72881i | 0.502799 | + | 0.864403i | \(0.332304\pi\) | ||||
−0.502799 | + | 0.864403i | \(0.667696\pi\) | |||||||
\(90\) | 7072.07i | 0.873095i | ||||||||
\(91\) | 5076.83 | − | 11615.8i | 0.613070 | − | 1.40271i | ||||
\(92\) | −2333.66 | −0.275716 | ||||||||
\(93\) | −4061.45 | −0.469586 | ||||||||
\(94\) | − | 1876.16i | − | 0.212332i | ||||||
\(95\) | 2835.49 | 0.314182 | ||||||||
\(96\) | − | 12546.7i | − | 1.36140i | ||||||
\(97\) | − | 18557.4i | − | 1.97230i | −0.165847 | − | 0.986152i | \(-0.553036\pi\) | ||
0.165847 | − | 0.986152i | \(-0.446964\pi\) | |||||||
\(98\) | 7856.83 | + | 8489.53i | 0.818079 | + | 0.883958i | ||||
\(99\) | −26484.6 | −2.70224 | ||||||||
\(100\) | −901.270 | −0.0901270 | ||||||||
\(101\) | 3882.89i | 0.380639i | 0.981722 | + | 0.190319i | \(0.0609523\pi\) | ||||
−0.981722 | + | 0.190319i | \(0.939048\pi\) | |||||||
\(102\) | 17052.6 | 1.63905 | ||||||||
\(103\) | − | 5551.06i | − | 0.523241i | −0.965171 | − | 0.261620i | \(-0.915743\pi\) | ||
0.965171 | − | 0.261620i | \(-0.0842569\pi\) | |||||||
\(104\) | 10955.6i | 1.01290i | ||||||||
\(105\) | 7314.12 | + | 3196.72i | 0.663413 | + | 0.289952i | ||||
\(106\) | 5163.28 | 0.459530 | ||||||||
\(107\) | −1207.91 | −0.105504 | −0.0527518 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527518 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(108\) | − | 5283.88i | − | 0.453007i | ||||||
\(109\) | 4780.21 | 0.402341 | 0.201170 | − | 0.979556i | \(-0.435526\pi\) | ||||
0.201170 | + | 0.979556i | \(0.435526\pi\) | |||||||
\(110\) | − | 10865.1i | − | 0.897946i | ||||||
\(111\) | − | 4699.22i | − | 0.381399i | ||||||
\(112\) | −14339.7 | − | 6267.31i | −1.14315 | − | 0.499626i | ||||
\(113\) | 17585.2 | 1.37718 | 0.688590 | − | 0.725151i | \(-0.258230\pi\) | ||||
0.688590 | + | 0.725151i | \(0.258230\pi\) | |||||||
\(114\) | −17802.6 | −1.36985 | ||||||||
\(115\) | 3618.66i | 0.273623i | ||||||||
\(116\) | −2387.34 | −0.177418 | ||||||||
\(117\) | 33967.8i | 2.48139i | ||||||||
\(118\) | 4965.45i | 0.356611i | ||||||||
\(119\) | 4767.16 | − | 10907.3i | 0.336640 | − | 0.770235i | ||||
\(120\) | −6898.37 | −0.479053 | ||||||||
\(121\) | 26048.6 | 1.77915 | ||||||||
\(122\) | − | 32191.4i | − | 2.16282i | ||||||
\(123\) | −8431.10 | −0.557281 | ||||||||
\(124\) | 2009.81i | 0.130711i | ||||||||
\(125\) | 1397.54i | 0.0894427i | ||||||||
\(126\) | −28400.6 | − | 12412.8i | −1.78890 | − | 0.781860i | ||||
\(127\) | 12120.0 | 0.751439 | 0.375720 | − | 0.926733i | \(-0.377396\pi\) | ||||
0.375720 | + | 0.926733i | \(0.377396\pi\) | |||||||
\(128\) | 18409.8 | 1.12364 | ||||||||
\(129\) | − | 22217.2i | − | 1.33509i | ||||||
\(130\) | −13935.0 | −0.824559 | ||||||||
\(131\) | 30779.1i | 1.79355i | 0.442486 | + | 0.896776i | \(0.354097\pi\) | ||||
−0.442486 | + | 0.896776i | \(0.645903\pi\) | |||||||
\(132\) | 21191.3i | 1.21621i | ||||||||
\(133\) | −4976.82 | + | 11387.0i | −0.281351 | + | 0.643734i | ||||
\(134\) | −19526.5 | −1.08746 | ||||||||
\(135\) | −8193.37 | −0.449568 | ||||||||
\(136\) | 10287.3i | 0.556190i | ||||||||
\(137\) | −25010.4 | −1.33254 | −0.666268 | − | 0.745712i | \(-0.732109\pi\) | ||||
−0.666268 | + | 0.745712i | \(0.732109\pi\) | |||||||
\(138\) | − | 22719.8i | − | 1.19301i | ||||||
\(139\) | 5006.55i | 0.259125i | 0.991571 | + | 0.129562i | \(0.0413573\pi\) | ||||
−0.991571 | + | 0.129562i | \(0.958643\pi\) | |||||||
\(140\) | 1581.90 | − | 3619.40i | 0.0807091 | − | 0.184663i | ||||
\(141\) | 5674.18 | 0.285407 | ||||||||
\(142\) | 15469.4 | 0.767177 | ||||||||
\(143\) | − | 52186.2i | − | 2.55202i | ||||||
\(144\) | 41932.9 | 2.02223 | ||||||||
\(145\) | 3701.89i | 0.176071i | ||||||||
\(146\) | 10785.2i | 0.505967i | ||||||||
\(147\) | −25675.3 | + | 23761.8i | −1.18818 | + | 1.09963i | ||||
\(148\) | −2325.41 | −0.106164 | ||||||||
\(149\) | 26261.1 | 1.18288 | 0.591439 | − | 0.806350i | \(-0.298560\pi\) | ||||
0.591439 | + | 0.806350i | \(0.298560\pi\) | |||||||
\(150\) | − | 8774.46i | − | 0.389976i | ||||||
\(151\) | 14133.8 | 0.619876 | 0.309938 | − | 0.950757i | \(-0.399692\pi\) | ||||
0.309938 | + | 0.950757i | \(0.399692\pi\) | |||||||
\(152\) | − | 10739.7i | − | 0.464843i | ||||||
\(153\) | 31895.8i | 1.36255i | ||||||||
\(154\) | 43633.2 | + | 19070.4i | 1.83982 | + | 0.804114i | ||||
\(155\) | 3116.48 | 0.129718 | ||||||||
\(156\) | 27178.8 | 1.11682 | ||||||||
\(157\) | 17409.6i | 0.706300i | 0.935567 | + | 0.353150i | \(0.114889\pi\) | ||||
−0.935567 | + | 0.353150i | \(0.885111\pi\) | |||||||
\(158\) | −25220.0 | −1.01025 | ||||||||
\(159\) | 15615.6i | 0.617680i | ||||||||
\(160\) | 9627.49i | 0.376074i | ||||||||
\(161\) | −14532.1 | − | 6351.43i | −0.560632 | − | 0.245030i | ||||
\(162\) | 205.847 | 0.00784360 | ||||||||
\(163\) | −41569.3 | −1.56458 | −0.782290 | − | 0.622915i | \(-0.785948\pi\) | ||||
−0.782290 | + | 0.622915i | \(0.785948\pi\) | |||||||
\(164\) | 4172.13i | 0.155121i | ||||||||
\(165\) | 32860.0 | 1.20698 | ||||||||
\(166\) | 18306.7i | 0.664344i | ||||||||
\(167\) | 16314.1i | 0.584967i | 0.956271 | + | 0.292483i | \(0.0944817\pi\) | ||||
−0.956271 | + | 0.292483i | \(0.905518\pi\) | |||||||
\(168\) | 12107.9 | − | 27703.0i | 0.428994 | − | 0.981542i | ||||
\(169\) | −38370.2 | −1.34345 | ||||||||
\(170\) | −13085.0 | −0.452770 | ||||||||
\(171\) | − | 33298.6i | − | 1.13877i | ||||||
\(172\) | −10994.2 | −0.371627 | ||||||||
\(173\) | 23077.3i | 0.771069i | 0.922693 | + | 0.385535i | \(0.125983\pi\) | ||||
−0.922693 | + | 0.385535i | \(0.874017\pi\) | |||||||
\(174\) | − | 23242.3i | − | 0.767681i | ||||||
\(175\) | −5612.37 | − | 2452.95i | −0.183261 | − | 0.0800963i | ||||
\(176\) | −64423.5 | −2.07979 | ||||||||
\(177\) | −15017.3 | −0.479341 | ||||||||
\(178\) | 65972.9i | 2.08222i | ||||||||
\(179\) | 4029.02 | 0.125746 | 0.0628729 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628729 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(180\) | 10584.1i | 0.326669i | ||||||||
\(181\) | − | 4726.94i | − | 0.144286i | −0.997394 | − | 0.0721428i | \(-0.977016\pi\) | ||
0.997394 | − | 0.0721428i | \(-0.0229837\pi\) | |||||||
\(182\) | 24458.6 | − | 55961.5i | 0.738396 | − | 1.68946i | ||||
\(183\) | 97358.0 | 2.90716 | ||||||||
\(184\) | 13706.1 | 0.404835 | ||||||||
\(185\) | 3605.87i | 0.105358i | ||||||||
\(186\) | −19566.8 | −0.565580 | ||||||||
\(187\) | − | 49003.0i | − | 1.40133i | ||||||
\(188\) | − | 2807.87i | − | 0.0794440i | ||||||
\(189\) | 14380.9 | − | 32903.6i | 0.402590 | − | 0.921128i | ||||
\(190\) | 13660.5 | 0.378408 | ||||||||
\(191\) | 99.8028 | 0.00273575 | 0.00136787 | − | 0.999999i | \(-0.499565\pi\) | ||||
0.00136787 | + | 0.999999i | \(0.499565\pi\) | |||||||
\(192\) | 14008.9i | 0.380015i | ||||||||
\(193\) | −27603.3 | −0.741047 | −0.370524 | − | 0.928823i | \(-0.620822\pi\) | ||||
−0.370524 | + | 0.928823i | \(0.620822\pi\) | |||||||
\(194\) | − | 89403.8i | − | 2.37549i | ||||||
\(195\) | − | 42144.5i | − | 1.10834i | ||||||
\(196\) | 11758.5 | + | 12705.4i | 0.306085 | + | 0.330733i | ||||
\(197\) | −17085.7 | −0.440251 | −0.220125 | − | 0.975472i | \(-0.570647\pi\) | ||||
−0.220125 | + | 0.975472i | \(0.570647\pi\) | |||||||
\(198\) | −127595. | −3.25464 | ||||||||
\(199\) | − | 12618.2i | − | 0.318634i | −0.987227 | − | 0.159317i | \(-0.949071\pi\) | ||
0.987227 | − | 0.159317i | \(-0.0509292\pi\) | |||||||
\(200\) | 5293.34 | 0.132334 | ||||||||
\(201\) | − | 59055.0i | − | 1.46172i | ||||||
\(202\) | 18706.6i | 0.458450i | ||||||||
\(203\) | −14866.4 | − | 6497.52i | −0.360756 | − | 0.157672i | ||||
\(204\) | 25521.0 | 0.613250 | ||||||||
\(205\) | 6469.46 | 0.153943 | ||||||||
\(206\) | − | 26743.3i | − | 0.630203i | ||||||
\(207\) | 42495.8 | 0.991757 | ||||||||
\(208\) | 82626.0i | 1.90981i | ||||||||
\(209\) | 51158.2i | 1.17118i | ||||||||
\(210\) | 35237.2 | + | 15400.8i | 0.799030 | + | 0.349225i | ||||
\(211\) | 27000.1 | 0.606458 | 0.303229 | − | 0.952918i | \(-0.401935\pi\) | ||||
0.303229 | + | 0.952918i | \(0.401935\pi\) | |||||||
\(212\) | 7727.36 | 0.171933 | ||||||||
\(213\) | 46784.8i | 1.03121i | ||||||||
\(214\) | −5819.34 | −0.127071 | ||||||||
\(215\) | 17048.0i | 0.368805i | ||||||||
\(216\) | 31033.3i | 0.665151i | ||||||||
\(217\) | −5470.01 | + | 12515.4i | −0.116163 | + | 0.265783i | ||||
\(218\) | 23029.6 | 0.484588 | ||||||||
\(219\) | −32618.2 | −0.680099 | ||||||||
\(220\) | − | 16260.8i | − | 0.335967i | ||||||
\(221\) | −62848.6 | −1.28680 | ||||||||
\(222\) | − | 22639.4i | − | 0.459366i | ||||||
\(223\) | − | 63568.7i | − | 1.27830i | −0.769081 | − | 0.639152i | \(-0.779286\pi\) | ||
0.769081 | − | 0.639152i | \(-0.220714\pi\) | |||||||
\(224\) | −38662.9 | − | 16898.0i | −0.770545 | − | 0.336775i | ||||
\(225\) | 16412.0 | 0.324189 | ||||||||
\(226\) | 84720.2 | 1.65871 | ||||||||
\(227\) | 74171.9i | 1.43942i | 0.694275 | + | 0.719710i | \(0.255725\pi\) | ||||
−0.694275 | + | 0.719710i | \(0.744275\pi\) | |||||||
\(228\) | −26643.4 | −0.512531 | ||||||||
\(229\) | 79719.2i | 1.52017i | 0.649824 | + | 0.760084i | \(0.274842\pi\) | ||||
−0.649824 | + | 0.760084i | \(0.725158\pi\) | |||||||
\(230\) | 17433.6i | 0.329558i | ||||||||
\(231\) | −57675.5 | + | 131962.i | −1.08085 | + | 2.47300i | ||||
\(232\) | 14021.3 | 0.260503 | ||||||||
\(233\) | 34612.6 | 0.637562 | 0.318781 | − | 0.947828i | \(-0.396727\pi\) | ||||
0.318781 | + | 0.947828i | \(0.396727\pi\) | |||||||
\(234\) | 163646.i | 2.98865i | ||||||||
\(235\) | −4353.98 | −0.0788408 | ||||||||
\(236\) | 7431.30i | 0.133426i | ||||||||
\(237\) | − | 76274.1i | − | 1.35794i | ||||||
\(238\) | 22966.7 | − | 52548.0i | 0.405457 | − | 0.927689i | ||||
\(239\) | 76161.8 | 1.33334 | 0.666671 | − | 0.745352i | \(-0.267719\pi\) | ||||
0.666671 | + | 0.745352i | \(0.267719\pi\) | |||||||
\(240\) | −52027.0 | −0.903246 | ||||||||
\(241\) | − | 57912.8i | − | 0.997103i | −0.866860 | − | 0.498552i | \(-0.833865\pi\) | ||
0.866860 | − | 0.498552i | \(-0.166135\pi\) | |||||||
\(242\) | 125494. | 2.14285 | ||||||||
\(243\) | − | 58737.3i | − | 0.994721i | ||||||
\(244\) | − | 48177.6i | − | 0.809218i | ||||||
\(245\) | 19701.5 | − | 18233.2i | 0.328222 | − | 0.303761i | ||||
\(246\) | −40618.4 | −0.671202 | ||||||||
\(247\) | 65612.7 | 1.07546 | ||||||||
\(248\) | − | 11804.0i | − | 0.191923i | ||||||
\(249\) | −55365.8 | −0.892982 | ||||||||
\(250\) | 6732.93i | 0.107727i | ||||||||
\(251\) | 36981.7i | 0.587002i | 0.955959 | + | 0.293501i | \(0.0948203\pi\) | ||||
−0.955959 | + | 0.293501i | \(0.905180\pi\) | |||||||
\(252\) | −42504.4 | − | 18577.0i | −0.669318 | − | 0.292533i | ||||
\(253\) | −65288.2 | −1.01998 | ||||||||
\(254\) | 58390.3 | 0.905051 | ||||||||
\(255\) | − | 39573.8i | − | 0.608593i | ||||||
\(256\) | 73309.2 | 1.11861 | ||||||||
\(257\) | − | 75229.5i | − | 1.13900i | −0.821993 | − | 0.569498i | \(-0.807138\pi\) | ||
0.821993 | − | 0.569498i | \(-0.192862\pi\) | |||||||
\(258\) | − | 107036.i | − | 1.60801i | ||||||
\(259\) | −14480.7 | − | 6328.97i | −0.215869 | − | 0.0943482i | ||||
\(260\) | −20855.2 | −0.308509 | ||||||||
\(261\) | 43473.2 | 0.638176 | ||||||||
\(262\) | 148284.i | 2.16019i | ||||||||
\(263\) | −31641.9 | −0.457458 | −0.228729 | − | 0.973490i | \(-0.573457\pi\) | ||||
−0.228729 | + | 0.973490i | \(0.573457\pi\) | |||||||
\(264\) | − | 124461.i | − | 1.78577i | ||||||
\(265\) | − | 11982.3i | − | 0.170628i | ||||||
\(266\) | −23976.8 | + | 54859.1i | −0.338866 | + | 0.775328i | ||||
\(267\) | −199525. | −2.79882 | ||||||||
\(268\) | −29223.4 | −0.406875 | ||||||||
\(269\) | − | 79641.8i | − | 1.10062i | −0.834961 | − | 0.550309i | \(-0.814510\pi\) | ||
0.834961 | − | 0.550309i | \(-0.185490\pi\) | |||||||
\(270\) | −39473.2 | −0.541470 | ||||||||
\(271\) | 40912.1i | 0.557075i | 0.960425 | + | 0.278537i | \(0.0898496\pi\) | ||||
−0.960425 | + | 0.278537i | \(0.910150\pi\) | |||||||
\(272\) | 77586.1i | 1.04869i | ||||||||
\(273\) | 169247. | + | 73971.5i | 2.27089 | + | 0.992519i | ||||
\(274\) | −120492. | −1.60494 | ||||||||
\(275\) | −25214.6 | −0.333416 | ||||||||
\(276\) | − | 34002.4i | − | 0.446366i | ||||||
\(277\) | −120604. | −1.57182 | −0.785911 | − | 0.618340i | \(-0.787806\pi\) | ||||
−0.785911 | + | 0.618340i | \(0.787806\pi\) | |||||||
\(278\) | 24120.0i | 0.312096i | ||||||||
\(279\) | − | 36598.4i | − | 0.470169i | ||||||
\(280\) | −9290.81 | + | 21257.4i | −0.118505 | + | 0.271141i | ||||
\(281\) | −48206.6 | −0.610512 | −0.305256 | − | 0.952270i | \(-0.598742\pi\) | ||||
−0.305256 | + | 0.952270i | \(0.598742\pi\) | |||||||
\(282\) | 27336.5 | 0.343751 | ||||||||
\(283\) | − | 45809.5i | − | 0.571982i | −0.958232 | − | 0.285991i | \(-0.907677\pi\) | ||
0.958232 | − | 0.285991i | \(-0.0923228\pi\) | |||||||
\(284\) | 23151.5 | 0.287040 | ||||||||
\(285\) | 41314.3i | 0.508640i | ||||||||
\(286\) | − | 251417.i | − | 3.07371i | ||||||
\(287\) | −11355.1 | + | 25980.6i | −0.137857 | + | 0.315417i | ||||
\(288\) | 113060. | 1.36309 | ||||||||
\(289\) | 24506.0 | 0.293411 | ||||||||
\(290\) | 17834.6i | 0.212064i | ||||||||
\(291\) | 270389. | 3.19303 | ||||||||
\(292\) | 16141.1i | 0.189308i | ||||||||
\(293\) | 73600.8i | 0.857328i | 0.903464 | + | 0.428664i | \(0.141016\pi\) | ||||
−0.903464 | + | 0.428664i | \(0.858984\pi\) | |||||||
\(294\) | −123696. | + | 114477.i | −1.43107 | + | 1.32442i | ||||
\(295\) | 11523.2 | 0.132413 | ||||||||
\(296\) | 13657.6 | 0.155880 | ||||||||
\(297\) | − | 147825.i | − | 1.67585i | ||||||
\(298\) | 126518. | 1.42468 | ||||||||
\(299\) | 83735.1i | 0.936624i | ||||||||
\(300\) | − | 13131.9i | − | 0.145910i | ||||||
\(301\) | −68462.9 | − | 29922.5i | −0.755652 | − | 0.330266i | ||||
\(302\) | 68092.3 | 0.746594 | ||||||||
\(303\) | −56575.3 | −0.616228 | ||||||||
\(304\) | − | 80998.4i | − | 0.876454i | ||||||
\(305\) | −74706.0 | −0.803074 | ||||||||
\(306\) | 153664.i | 1.64108i | ||||||||
\(307\) | − | 4729.94i | − | 0.0501856i | −0.999685 | − | 0.0250928i | \(-0.992012\pi\) | ||
0.999685 | − | 0.0250928i | \(-0.00798812\pi\) | |||||||
\(308\) | 65301.4 | + | 28540.7i | 0.688369 | + | 0.300859i | ||||
\(309\) | 80881.2 | 0.847092 | ||||||||
\(310\) | 15014.3 | 0.156236 | ||||||||
\(311\) | − | 90455.7i | − | 0.935223i | −0.883934 | − | 0.467611i | \(-0.845115\pi\) | ||
0.883934 | − | 0.467611i | \(-0.154885\pi\) | |||||||
\(312\) | −159627. | −1.63982 | ||||||||
\(313\) | − | 108219.i | − | 1.10462i | −0.833638 | − | 0.552312i | \(-0.813746\pi\) | ||
0.833638 | − | 0.552312i | \(-0.186254\pi\) | |||||||
\(314\) | 83874.0i | 0.850684i | ||||||||
\(315\) | −28806.2 | + | 65908.9i | −0.290312 | + | 0.664236i | ||||
\(316\) | −37744.2 | −0.377987 | ||||||||
\(317\) | 117203. | 1.16633 | 0.583163 | − | 0.812356i | \(-0.301815\pi\) | ||||
0.583163 | + | 0.812356i | \(0.301815\pi\) | |||||||
\(318\) | 75231.0i | 0.743948i | ||||||||
\(319\) | −66789.9 | −0.656340 | ||||||||
\(320\) | − | 10749.5i | − | 0.104975i | ||||||
\(321\) | − | 17599.7i | − | 0.170803i | ||||||
\(322\) | −70011.4 | − | 30599.3i | −0.675238 | − | 0.295120i | ||||
\(323\) | 61610.5 | 0.590541 | ||||||||
\(324\) | 308.071 | 0.00293468 | ||||||||
\(325\) | 32338.8i | 0.306167i | ||||||||
\(326\) | −200268. | −1.88442 | ||||||||
\(327\) | 69649.5i | 0.651362i | ||||||||
\(328\) | − | 24503.8i | − | 0.227764i | ||||||
\(329\) | 7642.06 | − | 17485.1i | 0.0706022 | − | 0.161538i | ||||
\(330\) | 158309. | 1.45371 | ||||||||
\(331\) | −59340.4 | −0.541619 | −0.270810 | − | 0.962633i | \(-0.587291\pi\) | ||||
−0.270810 | + | 0.962633i | \(0.587291\pi\) | |||||||
\(332\) | 27397.8i | 0.248564i | ||||||||
\(333\) | 42345.5 | 0.381873 | ||||||||
\(334\) | 78596.5i | 0.704548i | ||||||||
\(335\) | 45314.8i | 0.403785i | ||||||||
\(336\) | 91317.1 | − | 208934.i | 0.808861 | − | 1.85068i | ||||
\(337\) | 157384. | 1.38580 | 0.692902 | − | 0.721032i | \(-0.256332\pi\) | ||||
0.692902 | + | 0.721032i | \(0.256332\pi\) | |||||||
\(338\) | −184856. | −1.61808 | ||||||||
\(339\) | 256223.i | 2.22956i | ||||||||
\(340\) | −19583.1 | −0.169404 | ||||||||
\(341\) | 56227.8i | 0.483551i | ||||||||
\(342\) | − | 160423.i | − | 1.37156i | ||||||
\(343\) | 38642.7 | + | 111122.i | 0.328457 | + | 0.944519i | ||||
\(344\) | 64571.2 | 0.545660 | ||||||||
\(345\) | −52725.4 | −0.442977 | ||||||||
\(346\) | 111180.i | 0.928694i | ||||||||
\(347\) | 165575. | 1.37510 | 0.687551 | − | 0.726136i | \(-0.258686\pi\) | ||||
0.687551 | + | 0.726136i | \(0.258686\pi\) | |||||||
\(348\) | − | 34784.5i | − | 0.287228i | ||||||
\(349\) | − | 187470.i | − | 1.53915i | −0.638558 | − | 0.769574i | \(-0.720469\pi\) | ||
0.638558 | − | 0.769574i | \(-0.279531\pi\) | |||||||
\(350\) | −27038.7 | − | 11817.6i | −0.220724 | − | 0.0964698i | ||||
\(351\) | −189593. | −1.53889 | ||||||||
\(352\) | −173700. | −1.40189 | ||||||||
\(353\) | − | 132192.i | − | 1.06085i | −0.847731 | − | 0.530426i | \(-0.822032\pi\) | ||
0.847731 | − | 0.530426i | \(-0.177968\pi\) | |||||||
\(354\) | −72348.6 | −0.577329 | ||||||||
\(355\) | − | 35899.5i | − | 0.284860i | ||||||
\(356\) | 98735.1i | 0.779061i | ||||||||
\(357\) | 158924. | + | 69459.4i | 1.24696 | + | 0.544998i | ||||
\(358\) | 19410.6 | 0.151451 | ||||||||
\(359\) | −216123. | −1.67692 | −0.838459 | − | 0.544965i | \(-0.816543\pi\) | ||||
−0.838459 | + | 0.544965i | \(0.816543\pi\) | |||||||
\(360\) | − | 62162.4i | − | 0.479648i | ||||||
\(361\) | 66000.8 | 0.506448 | ||||||||
\(362\) | − | 22772.9i | − | 0.173781i | ||||||
\(363\) | 379538.i | 2.88033i | ||||||||
\(364\) | 36604.8 | − | 83752.1i | 0.276271 | − | 0.632110i | ||||
\(365\) | 25029.0 | 0.187870 | ||||||||
\(366\) | 469041. | 3.50145 | ||||||||
\(367\) | 36676.9i | 0.272308i | 0.990688 | + | 0.136154i | \(0.0434742\pi\) | ||||
−0.990688 | + | 0.136154i | \(0.956526\pi\) | |||||||
\(368\) | 103370. | 0.763309 | ||||||||
\(369\) | − | 75974.1i | − | 0.557973i | ||||||
\(370\) | 17372.0i | 0.126895i | ||||||||
\(371\) | 48119.6 | + | 21031.2i | 0.349602 | + | 0.152798i | ||||
\(372\) | −29283.7 | −0.211612 | ||||||||
\(373\) | −250019. | −1.79703 | −0.898517 | − | 0.438940i | \(-0.855354\pi\) | ||||
−0.898517 | + | 0.438940i | \(0.855354\pi\) | |||||||
\(374\) | − | 236081.i | − | 1.68779i | ||||||
\(375\) | −20362.7 | −0.144802 | ||||||||
\(376\) | 16491.2i | 0.116648i | ||||||||
\(377\) | 85661.1i | 0.602699i | ||||||||
\(378\) | 69282.8 | − | 158520.i | 0.484888 | − | 1.10943i | ||||
\(379\) | 159502. | 1.11042 | 0.555211 | − | 0.831710i | \(-0.312638\pi\) | ||||
0.555211 | + | 0.831710i | \(0.312638\pi\) | |||||||
\(380\) | 20444.4 | 0.141582 | ||||||||
\(381\) | 176593.i | 1.21653i | ||||||||
\(382\) | 480.819 | 0.00329500 | ||||||||
\(383\) | − | 237902.i | − | 1.62181i | −0.585178 | − | 0.810905i | \(-0.698975\pi\) | ||
0.585178 | − | 0.810905i | \(-0.301025\pi\) | |||||||
\(384\) | 268238.i | 1.81910i | ||||||||
\(385\) | 44256.3 | − | 101259.i | 0.298575 | − | 0.683142i | ||||
\(386\) | −132984. | −0.892534 | ||||||||
\(387\) | 200203. | 1.33675 | ||||||||
\(388\) | − | 133802.i | − | 0.888789i | ||||||
\(389\) | −487.890 | −0.00322420 | −0.00161210 | − | 0.999999i | \(-0.500513\pi\) | ||||
−0.00161210 | + | 0.999999i | \(0.500513\pi\) | |||||||
\(390\) | − | 203039.i | − | 1.33491i | ||||||
\(391\) | 78627.5i | 0.514305i | ||||||||
\(392\) | −69060.3 | − | 74621.6i | −0.449424 | − | 0.485615i | ||||
\(393\) | −448464. | −2.90364 | ||||||||
\(394\) | −82313.6 | −0.530248 | ||||||||
\(395\) | 58527.6i | 0.375117i | ||||||||
\(396\) | −190959. | −1.21772 | ||||||||
\(397\) | 213503.i | 1.35464i | 0.735689 | + | 0.677319i | \(0.236858\pi\) | ||||
−0.735689 | + | 0.677319i | \(0.763142\pi\) | |||||||
\(398\) | − | 60790.7i | − | 0.383770i | ||||||
\(399\) | −165913. | − | 72514.3i | −1.04216 | − | 0.455489i | ||||
\(400\) | 39922.0 | 0.249513 | ||||||||
\(401\) | −195733. | −1.21724 | −0.608619 | − | 0.793463i | \(-0.708276\pi\) | ||||
−0.608619 | + | 0.793463i | \(0.708276\pi\) | |||||||
\(402\) | − | 284509.i | − | 1.76053i | ||||||
\(403\) | 72114.8 | 0.444032 | ||||||||
\(404\) | 27996.3i | 0.171529i | ||||||||
\(405\) | − | 477.707i | − | 0.00291240i | ||||||
\(406\) | −71621.6 | − | 31303.0i | −0.434502 | − | 0.189904i | ||||
\(407\) | −65057.3 | −0.392742 | ||||||||
\(408\) | −149890. | −0.900434 | ||||||||
\(409\) | − | 61109.4i | − | 0.365310i | −0.983177 | − | 0.182655i | \(-0.941531\pi\) | ||
0.983177 | − | 0.182655i | \(-0.0584692\pi\) | |||||||
\(410\) | 31167.9 | 0.185413 | ||||||||
\(411\) | − | 364411.i | − | 2.15729i | ||||||
\(412\) | − | 40024.1i | − | 0.235791i | ||||||
\(413\) | −20225.5 | + | 46276.0i | −0.118576 | + | 0.271304i | ||||
\(414\) | 204732. | 1.19450 | ||||||||
\(415\) | 42484.0 | 0.246677 | ||||||||
\(416\) | 222778.i | 1.28732i | ||||||||
\(417\) | −72947.4 | −0.419506 | ||||||||
\(418\) | 246464.i | 1.41059i | ||||||||
\(419\) | − | 131493.i | − | 0.748988i | −0.927229 | − | 0.374494i | \(-0.877816\pi\) | ||
0.927229 | − | 0.374494i | \(-0.122184\pi\) | |||||||
\(420\) | 52736.0 | + | 23048.9i | 0.298957 | + | 0.130663i | ||||
\(421\) | −35202.6 | −0.198615 | −0.0993073 | − | 0.995057i | \(-0.531663\pi\) | ||||
−0.0993073 | + | 0.995057i | \(0.531663\pi\) | |||||||
\(422\) | 130078. | 0.730432 | ||||||||
\(423\) | 51131.0i | 0.285761i | ||||||||
\(424\) | −45384.4 | −0.252449 | ||||||||
\(425\) | 30366.3i | 0.168118i | ||||||||
\(426\) | 225395.i | 1.24201i | ||||||||
\(427\) | 131123. | − | 300010.i | 0.719156 | − | 1.64543i | ||||
\(428\) | −8709.23 | −0.0475436 | ||||||||
\(429\) | 760374. | 4.13155 | ||||||||
\(430\) | 82132.1i | 0.444198i | ||||||||
\(431\) | 285348. | 1.53610 | 0.768052 | − | 0.640388i | \(-0.221226\pi\) | ||||
0.768052 | + | 0.640388i | \(0.221226\pi\) | |||||||
\(432\) | 234051.i | 1.25413i | ||||||||
\(433\) | − | 255078.i | − | 1.36050i | −0.732982 | − | 0.680248i | \(-0.761872\pi\) | ||
0.732982 | − | 0.680248i | \(-0.238128\pi\) | |||||||
\(434\) | −26352.8 | + | 60295.5i | −0.139910 | + | 0.320115i | ||||
\(435\) | −53938.1 | −0.285047 | ||||||||
\(436\) | 34466.1 | 0.181309 | ||||||||
\(437\) | − | 82085.6i | − | 0.429837i | ||||||
\(438\) | −157145. | −0.819127 | ||||||||
\(439\) | 190309.i | 0.987482i | 0.869609 | + | 0.493741i | \(0.164371\pi\) | ||||
−0.869609 | + | 0.493741i | \(0.835629\pi\) | |||||||
\(440\) | 95502.9i | 0.493300i | ||||||||
\(441\) | −214122. | − | 231365.i | −1.10099 | − | 1.18965i | ||||
\(442\) | −302785. | −1.54985 | ||||||||
\(443\) | 119088. | 0.606822 | 0.303411 | − | 0.952860i | \(-0.401875\pi\) | ||||
0.303411 | + | 0.952860i | \(0.401875\pi\) | |||||||
\(444\) | − | 33882.1i | − | 0.171872i | ||||||
\(445\) | 153102. | 0.773146 | ||||||||
\(446\) | − | 306255.i | − | 1.53962i | ||||||
\(447\) | 382634.i | 1.91500i | ||||||||
\(448\) | 43168.7 | + | 18867.4i | 0.215086 | + | 0.0940059i | ||||
\(449\) | 170376. | 0.845114 | 0.422557 | − | 0.906336i | \(-0.361133\pi\) | ||||
0.422557 | + | 0.906336i | \(0.361133\pi\) | |||||||
\(450\) | 79068.2 | 0.390460 | ||||||||
\(451\) | 116722.i | 0.573854i | ||||||||
\(452\) | 126792. | 0.620606 | ||||||||
\(453\) | 205935.i | 1.00354i | ||||||||
\(454\) | 357337.i | 1.73367i | ||||||||
\(455\) | −129869. | − | 56760.7i | −0.627311 | − | 0.274173i | ||||
\(456\) | 156482. | 0.752550 | ||||||||
\(457\) | −341751. | −1.63635 | −0.818176 | − | 0.574967i | \(-0.805015\pi\) | ||||
−0.818176 | + | 0.574967i | \(0.805015\pi\) | |||||||
\(458\) | 384062.i | 1.83093i | ||||||||
\(459\) | −178028. | −0.845013 | ||||||||
\(460\) | 26091.2i | 0.123304i | ||||||||
\(461\) | 220317.i | 1.03668i | 0.855174 | + | 0.518342i | \(0.173450\pi\) | ||||
−0.855174 | + | 0.518342i | \(0.826550\pi\) | |||||||
\(462\) | −277863. | + | 635752.i | −1.30181 | + | 2.97854i | ||||
\(463\) | 334907. | 1.56229 | 0.781145 | − | 0.624349i | \(-0.214636\pi\) | ||||
0.781145 | + | 0.624349i | \(0.214636\pi\) | |||||||
\(464\) | 105748. | 0.491174 | ||||||||
\(465\) | 45408.4i | 0.210005i | ||||||||
\(466\) | 166753. | 0.767895 | ||||||||
\(467\) | − | 331727.i | − | 1.52106i | −0.649302 | − | 0.760531i | \(-0.724939\pi\) | ||
0.649302 | − | 0.760531i | \(-0.275061\pi\) | |||||||
\(468\) | 244913.i | 1.11820i | ||||||||
\(469\) | −181979. | − | 79536.0i | −0.827324 | − | 0.361591i | ||||
\(470\) | −20976.2 | −0.0949577 | ||||||||
\(471\) | −253665. | −1.14345 | ||||||||
\(472\) | − | 43645.5i | − | 0.195910i | ||||||
\(473\) | −307582. | −1.37480 | ||||||||
\(474\) | − | 367465.i | − | 1.63553i | ||||||
\(475\) | − | 31701.8i | − | 0.140507i | ||||||
\(476\) | 34372.0 | − | 78643.4i | 0.151702 | − | 0.347095i | ||||
\(477\) | −140715. | −0.618447 | ||||||||
\(478\) | 366924. | 1.60591 | ||||||||
\(479\) | − | 339790.i | − | 1.48095i | −0.672085 | − | 0.740474i | \(-0.734601\pi\) | ||
0.672085 | − | 0.740474i | \(-0.265399\pi\) | |||||||
\(480\) | −140276. | −0.608838 | ||||||||
\(481\) | 83439.0i | 0.360644i | ||||||||
\(482\) | − | 279006.i | − | 1.20093i | ||||||
\(483\) | 92542.9 | − | 211739.i | 0.396688 | − | 0.907625i | ||||
\(484\) | 187814. | 0.801748 | ||||||||
\(485\) | −207478. | −0.882041 | ||||||||
\(486\) | − | 282978.i | − | 1.19807i | ||||||
\(487\) | 74140.1 | 0.312605 | 0.156302 | − | 0.987709i | \(-0.450043\pi\) | ||||
0.156302 | + | 0.987709i | \(0.450043\pi\) | |||||||
\(488\) | 282957.i | 1.18818i | ||||||||
\(489\) | − | 605681.i | − | 2.53295i | ||||||
\(490\) | 94915.8 | − | 87842.1i | 0.395318 | − | 0.365856i | ||||
\(491\) | −1259.76 | −0.00522547 | −0.00261273 | − | 0.999997i | \(-0.500832\pi\) | ||||
−0.00261273 | + | 0.999997i | \(0.500832\pi\) | |||||||
\(492\) | −60789.6 | −0.251130 | ||||||||
\(493\) | 80436.0i | 0.330945i | ||||||||
\(494\) | 316102. | 1.29531 | ||||||||
\(495\) | 296107.i | 1.20848i | ||||||||
\(496\) | − | 89025.1i | − | 0.361867i | ||||||
\(497\) | 144168. | + | 63010.4i | 0.583656 | + | 0.255093i | ||||
\(498\) | −266735. | −1.07553 | ||||||||
\(499\) | −77913.9 | −0.312906 | −0.156453 | − | 0.987685i | \(-0.550006\pi\) | ||||
−0.156453 | + | 0.987685i | \(0.550006\pi\) | |||||||
\(500\) | 10076.5i | 0.0403060i | ||||||||
\(501\) | −237703. | −0.947022 | ||||||||
\(502\) | 178166.i | 0.706998i | ||||||||
\(503\) | − | 221665.i | − | 0.876116i | −0.898947 | − | 0.438058i | \(-0.855666\pi\) | ||
0.898947 | − | 0.438058i | \(-0.144334\pi\) | |||||||
\(504\) | 249637. | + | 109107.i | 0.982760 | + | 0.429527i | ||||
\(505\) | 43412.1 | 0.170227 | ||||||||
\(506\) | −314539. | −1.22849 | ||||||||
\(507\) | − | 559069.i | − | 2.17495i | ||||||
\(508\) | 87386.9 | 0.338625 | ||||||||
\(509\) | 339130.i | 1.30897i | 0.756074 | + | 0.654486i | \(0.227115\pi\) | ||||
−0.756074 | + | 0.654486i | \(0.772885\pi\) | |||||||
\(510\) | − | 190654.i | − | 0.733004i | ||||||
\(511\) | −43930.6 | + | 100514.i | −0.168239 | + | 0.384931i | ||||
\(512\) | 58624.9 | 0.223636 | ||||||||
\(513\) | 185858. | 0.706231 | ||||||||
\(514\) | − | 362433.i | − | 1.37183i | ||||||
\(515\) | −62062.8 | −0.234000 | ||||||||
\(516\) | − | 160190.i | − | 0.601639i | ||||||
\(517\) | − | 78554.9i | − | 0.293895i | ||||||
\(518\) | −69763.7 | − | 30491.0i | −0.259998 | − | 0.113635i | ||||
\(519\) | −336246. | −1.24831 | ||||||||
\(520\) | 122487. | 0.452984 | ||||||||
\(521\) | 342794.i | 1.26287i | 0.775430 | + | 0.631433i | \(0.217533\pi\) | ||||
−0.775430 | + | 0.631433i | \(0.782467\pi\) | |||||||
\(522\) | 209441. | 0.768634 | ||||||||
\(523\) | 174970.i | 0.639676i | 0.947472 | + | 0.319838i | \(0.103628\pi\) | ||||
−0.947472 | + | 0.319838i | \(0.896372\pi\) | |||||||
\(524\) | 221923.i | 0.808237i | ||||||||
\(525\) | 35740.4 | − | 81774.4i | 0.129670 | − | 0.296687i | ||||
\(526\) | −152441. | −0.550973 | ||||||||
\(527\) | 67716.0 | 0.243820 | ||||||||
\(528\) | − | 938675.i | − | 3.36703i | ||||||
\(529\) | −175083. | −0.625652 | ||||||||
\(530\) | − | 57727.2i | − | 0.205508i | ||||||
\(531\) | − | 135323.i | − | 0.479936i | ||||||
\(532\) | −35883.7 | + | 82102.2i | −0.126787 | + | 0.290089i | ||||
\(533\) | 149702. | 0.526954 | ||||||||
\(534\) | −961251. | −3.37097 | ||||||||
\(535\) | 13504.8i | 0.0471826i | ||||||||
\(536\) | 171635. | 0.597414 | ||||||||
\(537\) | 58704.4i | 0.203574i | ||||||||
\(538\) | − | 383690.i | − | 1.32561i | ||||||
\(539\) | 328965. | + | 355456.i | 1.13233 | + | 1.22351i | ||||
\(540\) | −59075.6 | −0.202591 | ||||||||
\(541\) | 316083. | 1.07996 | 0.539978 | − | 0.841679i | \(-0.318433\pi\) | ||||
0.539978 | + | 0.841679i | \(0.318433\pi\) | |||||||
\(542\) | 197102.i | 0.670954i | ||||||||
\(543\) | 68873.4 | 0.233589 | ||||||||
\(544\) | 209189.i | 0.706873i | ||||||||
\(545\) | − | 53444.4i | − | 0.179932i | ||||||
\(546\) | 815382. | + | 356372.i | 2.73511 | + | 1.19541i | ||||
\(547\) | 94365.5 | 0.315383 | 0.157692 | − | 0.987488i | \(-0.449595\pi\) | ||||
0.157692 | + | 0.987488i | \(0.449595\pi\) | |||||||
\(548\) | −180329. | −0.600488 | ||||||||
\(549\) | 877310.i | 2.91077i | ||||||||
\(550\) | −121476. | −0.401574 | ||||||||
\(551\) | − | 83973.6i | − | 0.276592i | ||||||
\(552\) | 199703.i | 0.655400i | ||||||||
\(553\) | −235040. | − | 102727.i | −0.768584 | − | 0.335918i | ||||
\(554\) | −581035. | −1.89314 | ||||||||
\(555\) | −52538.9 | −0.170567 | ||||||||
\(556\) | 36098.1i | 0.116771i | ||||||||
\(557\) | −135243. | −0.435916 | −0.217958 | − | 0.975958i | \(-0.569940\pi\) | ||||
−0.217958 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(558\) | − | 176320.i | − | 0.566283i | ||||||
\(559\) | 394488.i | 1.26244i | ||||||||
\(560\) | −70070.6 | + | 160322.i | −0.223439 | + | 0.511231i | ||||
\(561\) | 713993. | 2.26865 | ||||||||
\(562\) | −232245. | −0.735315 | ||||||||
\(563\) | 243317.i | 0.767637i | 0.923408 | + | 0.383819i | \(0.125391\pi\) | ||||
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(564\) | 40911.8 | 0.128614 | ||||||||
\(565\) | − | 196609.i | − | 0.615894i | ||||||
\(566\) | − | 220696.i | − | 0.688909i | ||||||
\(567\) | 1918.41 | + | 838.465i | 0.00596728 | + | 0.00260807i | ||||
\(568\) | −135973. | −0.421460 | ||||||||
\(569\) | 139613. | 0.431222 | 0.215611 | − | 0.976479i | \(-0.430826\pi\) | ||||
0.215611 | + | 0.976479i | \(0.430826\pi\) | |||||||
\(570\) | 199039.i | 0.612617i | ||||||||
\(571\) | −548346. | −1.68183 | −0.840915 | − | 0.541167i | \(-0.817983\pi\) | ||||
−0.840915 | + | 0.541167i | \(0.817983\pi\) | |||||||
\(572\) | − | 376271.i | − | 1.15003i | ||||||
\(573\) | 1454.17i | 0.00442899i | ||||||||
\(574\) | −54705.4 | + | 125166.i | −0.166038 | + | 0.379896i | ||||
\(575\) | 40457.9 | 0.122368 | ||||||||
\(576\) | −126237. | −0.380487 | ||||||||
\(577\) | 445087.i | 1.33688i | 0.743764 | + | 0.668442i | \(0.233038\pi\) | ||||
−0.743764 | + | 0.668442i | \(0.766962\pi\) | |||||||
\(578\) | 118062. | 0.353391 | ||||||||
\(579\) | − | 402190.i | − | 1.19971i | ||||||
\(580\) | 26691.3i | 0.0793438i | ||||||||
\(581\) | −74567.3 | + | 170611.i | −0.220900 | + | 0.505422i | ||||
\(582\) | 1.30265e6 | 3.84575 | ||||||||
\(583\) | 216186. | 0.636049 | ||||||||
\(584\) | − | 94800.1i | − | 0.277961i | ||||||
\(585\) | 379771. | 1.10971 | ||||||||
\(586\) | 354586.i | 1.03259i | ||||||||
\(587\) | − | 143426.i | − | 0.416248i | −0.978102 | − | 0.208124i | \(-0.933264\pi\) | ||
0.978102 | − | 0.208124i | \(-0.0667358\pi\) | |||||||
\(588\) | −185123. | + | 171327.i | −0.535434 | + | 0.495530i | ||||
\(589\) | −70694.2 | −0.203776 | ||||||||
\(590\) | 55515.4 | 0.159481 | ||||||||
\(591\) | − | 248945.i | − | 0.712736i | ||||||
\(592\) | 103005. | 0.293909 | ||||||||
\(593\) | − | 299727.i | − | 0.852347i | −0.904642 | − | 0.426173i | \(-0.859861\pi\) | ||
0.904642 | − | 0.426173i | \(-0.140139\pi\) | |||||||
\(594\) | − | 712178.i | − | 2.01844i | ||||||
\(595\) | −121947. | − | 53298.5i | −0.344460 | − | 0.150550i | ||||
\(596\) | 189346. | 0.533046 | ||||||||
\(597\) | 183852. | 0.515847 | ||||||||
\(598\) | 403410.i | 1.12809i | ||||||||
\(599\) | −439671. | −1.22539 | −0.612694 | − | 0.790320i | \(-0.709914\pi\) | ||||
−0.612694 | + | 0.790320i | \(0.709914\pi\) | |||||||
\(600\) | 77126.1i | 0.214239i | ||||||||
\(601\) | 188484.i | 0.521827i | 0.965362 | + | 0.260913i | \(0.0840237\pi\) | ||||
−0.965362 | + | 0.260913i | \(0.915976\pi\) | |||||||
\(602\) | −329833. | − | 144157.i | −0.910125 | − | 0.397781i | ||||
\(603\) | 532155. | 1.46354 | ||||||||
\(604\) | 101907. | 0.279338 | ||||||||
\(605\) | − | 291232.i | − | 0.795661i | ||||||
\(606\) | −272562. | −0.742200 | ||||||||
\(607\) | 10230.2i | 0.0277656i | 0.999904 | + | 0.0138828i | \(0.00441917\pi\) | ||||
−0.999904 | + | 0.0138828i | \(0.995581\pi\) | |||||||
\(608\) | − | 218389.i | − | 0.590778i | ||||||
\(609\) | 94671.4 | − | 216609.i | 0.255261 | − | 0.584039i | ||||
\(610\) | −359910. | −0.967241 | ||||||||
\(611\) | −100750. | −0.269876 | ||||||||
\(612\) | 229974.i | 0.614011i | ||||||||
\(613\) | 436819. | 1.16247 | 0.581233 | − | 0.813737i | \(-0.302571\pi\) | ||||
0.581233 | + | 0.813737i | \(0.302571\pi\) | |||||||
\(614\) | − | 22787.4i | − | 0.0604447i | ||||||
\(615\) | 94262.5i | 0.249223i | ||||||||
\(616\) | −383528. | − | 167625.i | −1.01073 | − | 0.441752i | ||||
\(617\) | 26556.4 | 0.0697588 | 0.0348794 | − | 0.999392i | \(-0.488895\pi\) | ||||
0.0348794 | + | 0.999392i | \(0.488895\pi\) | |||||||
\(618\) | 389661. | 1.02026 | ||||||||
\(619\) | 510737.i | 1.33296i | 0.745525 | + | 0.666478i | \(0.232199\pi\) | ||||
−0.745525 | + | 0.666478i | \(0.767801\pi\) | |||||||
\(620\) | 22470.4 | 0.0584557 | ||||||||
\(621\) | 237193.i | 0.615061i | ||||||||
\(622\) | − | 435788.i | − | 1.12640i | ||||||
\(623\) | −268723. | + | 614841.i | −0.692355 | + | 1.58411i | ||||
\(624\) | −1.20389e6 | −3.09185 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | − | 521365.i | − | 1.33043i | ||||||
\(627\) | −745395. | −1.89606 | ||||||||
\(628\) | 125526.i | 0.318284i | ||||||||
\(629\) | 78349.4i | 0.198032i | ||||||||
\(630\) | −138779. | + | 317529.i | −0.349659 | + | 0.800022i | ||||
\(631\) | −3641.38 | −0.00914550 | −0.00457275 | − | 0.999990i | \(-0.501456\pi\) | ||||
−0.00457275 | + | 0.999990i | \(0.501456\pi\) | |||||||
\(632\) | 221680. | 0.554998 | ||||||||
\(633\) | 393403.i | 0.981815i | ||||||||
\(634\) | 564647. | 1.40475 | ||||||||
\(635\) | − | 135505.i | − | 0.336054i | ||||||
\(636\) | 112591.i | 0.278348i | ||||||||
\(637\) | 455889. | − | 421913.i | 1.12352 | − | 1.03979i | ||||
\(638\) | −321773. | −0.790512 | ||||||||
\(639\) | −421586. | −1.03249 | ||||||||
\(640\) | − | 205827.i | − | 0.502508i | ||||||
\(641\) | 330651. | 0.804736 | 0.402368 | − | 0.915478i | \(-0.368187\pi\) | ||||
0.402368 | + | 0.915478i | \(0.368187\pi\) | |||||||
\(642\) | − | 84790.0i | − | 0.205719i | ||||||
\(643\) | 75104.8i | 0.181654i | 0.995867 | + | 0.0908272i | \(0.0289511\pi\) | ||||
−0.995867 | + | 0.0908272i | \(0.971049\pi\) | |||||||
\(644\) | −104779. | − | 45794.9i | −0.252640 | − | 0.110419i | ||||
\(645\) | −248396. | −0.597071 | ||||||||
\(646\) | 296821. | 0.711261 | ||||||||
\(647\) | 381648.i | 0.911706i | 0.890055 | + | 0.455853i | \(0.150666\pi\) | ||||
−0.890055 | + | 0.455853i | \(0.849334\pi\) | |||||||
\(648\) | −1809.37 | −0.00430900 | ||||||||
\(649\) | 207903.i | 0.493596i | ||||||||
\(650\) | 155799.i | 0.368754i | ||||||||
\(651\) | −182355. | − | 79700.3i | −0.430284 | − | 0.188061i | ||||
\(652\) | −299722. | −0.705055 | ||||||||
\(653\) | 462477. | 1.08458 | 0.542292 | − | 0.840190i | \(-0.317557\pi\) | ||||
0.542292 | + | 0.840190i | \(0.317557\pi\) | |||||||
\(654\) | 335550.i | 0.784516i | ||||||||
\(655\) | 344121. | 0.802100 | ||||||||
\(656\) | − | 184806.i | − | 0.429445i | ||||||
\(657\) | − | 293929.i | − | 0.680943i | ||||||
\(658\) | 36817.1 | − | 84237.8i | 0.0850350 | − | 0.194561i | ||||
\(659\) | −187187. | −0.431028 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(660\) | 236926. | 0.543907 | ||||||||
\(661\) | − | 95871.7i | − | 0.219426i | −0.993963 | − | 0.109713i | \(-0.965007\pi\) | ||
0.993963 | − | 0.109713i | \(-0.0349931\pi\) | |||||||
\(662\) | −285884. | −0.652339 | ||||||||
\(663\) | − | 915729.i | − | 2.08324i | ||||||
\(664\) | − | 160913.i | − | 0.364967i | ||||||
\(665\) | 127311. | + | 55642.6i | 0.287887 | + | 0.125824i | ||||
\(666\) | 204008. | 0.459936 | ||||||||
\(667\) | 107167. | 0.240885 | ||||||||
\(668\) | 117628.i | 0.263607i | ||||||||
\(669\) | 926221. | 2.06949 | ||||||||
\(670\) | 218313.i | 0.486328i | ||||||||
\(671\) | − | 1.34785e6i | − | 2.99362i | ||||||
\(672\) | 246211. | − | 563333.i | 0.545217 | − | 1.24746i | ||||
\(673\) | −118770. | −0.262226 | −0.131113 | − | 0.991367i | \(-0.541855\pi\) | ||||
−0.131113 | + | 0.991367i | \(0.541855\pi\) | |||||||
\(674\) | 758230. | 1.66909 | ||||||||
\(675\) | 91604.7i | 0.201053i | ||||||||
\(676\) | −276656. | −0.605405 | ||||||||
\(677\) | 340700.i | 0.743352i | 0.928363 | + | 0.371676i | \(0.121217\pi\) | ||||
−0.928363 | + | 0.371676i | \(0.878783\pi\) | |||||||
\(678\) | 1.23441e6i | 2.68534i | ||||||||
\(679\) | 364163. | − | 833208.i | 0.789871 | − | 1.80723i | ||||
\(680\) | 115015. | 0.248736 | ||||||||
\(681\) | −1.08071e6 | −2.33032 | ||||||||
\(682\) | 270888.i | 0.582401i | ||||||||
\(683\) | −148626. | −0.318605 | −0.159303 | − | 0.987230i | \(-0.550925\pi\) | ||||
−0.159303 | + | 0.987230i | \(0.550925\pi\) | |||||||
\(684\) | − | 240089.i | − | 0.513168i | ||||||
\(685\) | 279624.i | 0.595928i | ||||||||
\(686\) | 186168. | + | 535350.i | 0.395601 | + | 1.13760i | ||||
\(687\) | −1.16154e6 | −2.46105 | ||||||||
\(688\) | 486992. | 1.02883 | ||||||||
\(689\) | − | 277269.i | − | 0.584066i | ||||||
\(690\) | −254015. | −0.533532 | ||||||||
\(691\) | 68328.5i | 0.143102i | 0.997437 | + | 0.0715510i | \(0.0227949\pi\) | ||||
−0.997437 | + | 0.0715510i | \(0.977205\pi\) | |||||||
\(692\) | 166391.i | 0.347471i | ||||||||
\(693\) | −1.18913e6 | − | 519724.i | −2.47607 | − | 1.08220i | ||||
\(694\) | 797688. | 1.65620 | ||||||||
\(695\) | 55974.9 | 0.115884 | ||||||||
\(696\) | 204296.i | 0.421737i | ||||||||
\(697\) | 140570. | 0.289353 | ||||||||
\(698\) | − | 903171.i | − | 1.85378i | ||||||
\(699\) | 504319.i | 1.03217i | ||||||||
\(700\) | −40466.1 | − | 17686.2i | −0.0825838 | − | 0.0360942i | ||||
\(701\) | −8208.96 | −0.0167052 | −0.00835261 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835261 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(702\) | −913401. | −1.85348 | ||||||||
\(703\) | − | 81795.3i | − | 0.165507i | ||||||
\(704\) | 193943. | 0.391317 | ||||||||
\(705\) | − | 63439.2i | − | 0.127638i | ||||||
\(706\) | − | 636859.i | − | 1.27772i | ||||||
\(707\) | −76196.3 | + | 174338.i | −0.152439 | + | 0.348781i | ||||
\(708\) | −108277. | −0.216008 | ||||||||
\(709\) | −678427. | −1.34962 | −0.674808 | − | 0.737993i | \(-0.735774\pi\) | ||||
−0.674808 | + | 0.737993i | \(0.735774\pi\) | |||||||
\(710\) | − | 172953.i | − | 0.343092i | ||||||
\(711\) | 687319. | 1.35962 | ||||||||
\(712\) | − | 579891.i | − | 1.14390i | ||||||
\(713\) | − | 90220.1i | − | 0.177470i | ||||||
\(714\) | 765645. | + | 334634.i | 1.50187 | + | 0.656408i | ||||
\(715\) | −583460. | −1.14130 | ||||||||
\(716\) | 29049.9 | 0.0566655 | ||||||||
\(717\) | 1.10971e6i | 2.15859i | ||||||||
\(718\) | −1.04121e6 | −2.01972 | ||||||||
\(719\) | − | 589061.i | − | 1.13947i | −0.821829 | − | 0.569735i | \(-0.807046\pi\) | ||
0.821829 | − | 0.569735i | \(-0.192954\pi\) | |||||||
\(720\) | − | 468824.i | − | 0.904368i | ||||||
\(721\) | 108932. | − | 249237.i | 0.209548 | − | 0.479448i | ||||
\(722\) | 317972. | 0.609978 | ||||||||
\(723\) | 843812. | 1.61424 | ||||||||
\(724\) | − | 34082.0i | − | 0.0650201i | ||||||
\(725\) | 41388.4 | 0.0787414 | ||||||||
\(726\) | 1.82850e6i | 3.46913i | ||||||||
\(727\) | 705964.i | 1.33571i | 0.744289 | + | 0.667857i | \(0.232788\pi\) | ||||
−0.744289 | + | 0.667857i | \(0.767212\pi\) | |||||||
\(728\) | −214987. | + | 491893.i | −0.405649 | + | 0.928128i | ||||
\(729\) | 859286. | 1.61690 | ||||||||
\(730\) | 120582. | 0.226275 | ||||||||
\(731\) | 370425.i | 0.693211i | ||||||||
\(732\) | 701967. | 1.31007 | ||||||||
\(733\) | 318582.i | 0.592944i | 0.955042 | + | 0.296472i | \(0.0958101\pi\) | ||||
−0.955042 | + | 0.296472i | \(0.904190\pi\) | |||||||
\(734\) | 176698.i | 0.327974i | ||||||||
\(735\) | 265665. | + | 287059.i | 0.491768 | + | 0.531369i | ||||
\(736\) | 278709. | 0.514512 | ||||||||
\(737\) | −817573. | −1.50519 | ||||||||
\(738\) | − | 366020.i | − | 0.672035i | ||||||
\(739\) | −547274. | −1.00211 | −0.501055 | − | 0.865415i | \(-0.667055\pi\) | ||||
−0.501055 | + | 0.865415i | \(0.667055\pi\) | |||||||
\(740\) | 25998.9i | 0.0474779i | ||||||||
\(741\) | 956003.i | 1.74110i | ||||||||
\(742\) | 231826. | + | 101322.i | 0.421069 | + | 0.184033i | ||||
\(743\) | 233435. | 0.422851 | 0.211426 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211426 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(744\) | 171989. | 0.310710 | ||||||||
\(745\) | − | 293608.i | − | 0.528999i | ||||||
\(746\) | −1.20452e6 | −2.16439 | ||||||||
\(747\) | − | 498910.i | − | 0.894090i | ||||||
\(748\) | − | 353320.i | − | 0.631487i | ||||||
\(749\) | −54233.9 | − | 23703.5i | −0.0966734 | − | 0.0422522i | ||||
\(750\) | −98101.4 | −0.174403 | ||||||||
\(751\) | 495140. | 0.877906 | 0.438953 | − | 0.898510i | \(-0.355349\pi\) | ||||
0.438953 | + | 0.898510i | \(0.355349\pi\) | |||||||
\(752\) | 124375.i | 0.219937i | ||||||||
\(753\) | −538838. | −0.950316 | ||||||||
\(754\) | 412689.i | 0.725905i | ||||||||
\(755\) | − | 158021.i | − | 0.277217i | ||||||
\(756\) | 103689. | − | 237241.i | 0.181421 | − | 0.415093i | ||||
\(757\) | 124849. | 0.217868 | 0.108934 | − | 0.994049i | \(-0.465256\pi\) | ||||
0.108934 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(758\) | 768432. | 1.33742 | ||||||||
\(759\) | − | 951275.i | − | 1.65129i | ||||||
\(760\) | −120074. | −0.207884 | ||||||||
\(761\) | 892015.i | 1.54029i | 0.637868 | + | 0.770146i | \(0.279817\pi\) | ||||
−0.637868 | + | 0.770146i | \(0.720183\pi\) | |||||||
\(762\) | 850769.i | 1.46522i | ||||||||
\(763\) | 214626. | + | 93804.9i | 0.368667 | + | 0.161130i | ||||
\(764\) | 719.595 | 0.00123282 | ||||||||
\(765\) | 356606. | 0.609349 | ||||||||
\(766\) | − | 1.14614e6i | − | 1.95335i | ||||||
\(767\) | 266645. | 0.453256 | ||||||||
\(768\) | 1.06814e6i | 1.81095i | ||||||||
\(769\) | − | 105869.i | − | 0.179026i | −0.995986 | − | 0.0895132i | \(-0.971469\pi\) | ||
0.995986 | − | 0.0895132i | \(-0.0285311\pi\) | |||||||
\(770\) | 213213. | − | 487834.i | 0.359611 | − | 0.822792i | ||||
\(771\) | 1.09612e6 | 1.84396 | ||||||||
\(772\) | −199024. | −0.333942 | ||||||||
\(773\) | − | 255665.i | − | 0.427870i | −0.976848 | − | 0.213935i | \(-0.931372\pi\) | ||
0.976848 | − | 0.213935i | \(-0.0686281\pi\) | |||||||
\(774\) | 964519. | 1.61001 | ||||||||
\(775\) | − | 34843.4i | − | 0.0580118i | ||||||
\(776\) | 785845.i | 1.30501i | ||||||||
\(777\) | 92215.6 | − | 210990.i | 0.152743 | − | 0.349478i | ||||
\(778\) | −2350.50 | −0.00388331 | ||||||||
\(779\) | −146753. | −0.241831 | ||||||||
\(780\) | − | 303869.i | − | 0.499455i | ||||||
\(781\) | 647702. | 1.06187 | ||||||||
\(782\) | 378803.i | 0.619441i | ||||||||
\(783\) | 242648.i | 0.395779i | ||||||||
\(784\) | −520848. | − | 562791.i | −0.847381 | − | 0.915619i | ||||
\(785\) | 194645. | 0.315867 | ||||||||
\(786\) | −2.16056e6 | −3.49721 | ||||||||
\(787\) | − | 754940.i | − | 1.21889i | −0.792830 | − | 0.609443i | \(-0.791393\pi\) | ||
0.792830 | − | 0.609443i | \(-0.208607\pi\) | |||||||
\(788\) | −123191. | −0.198392 | ||||||||
\(789\) | − | 461035.i | − | 0.740594i | ||||||
\(790\) | 281968.i | 0.451799i | ||||||||
\(791\) | 789557. | + | 345085.i | 1.26192 | + | 0.551535i | ||||
\(792\) | 1.12154e6 | 1.78798 | ||||||||
\(793\) | −1.72868e6 | −2.74896 | ||||||||
\(794\) | 1.02859e6i | 1.63156i | ||||||||
\(795\) | 174587. | 0.276235 | ||||||||
\(796\) | − | 90979.5i | − | 0.143588i | ||||||
\(797\) | − | 360915.i | − | 0.568183i | −0.958797 | − | 0.284091i | \(-0.908308\pi\) | ||
0.958797 | − | 0.284091i | \(-0.0916919\pi\) | |||||||
\(798\) | −799319. | − | 349351.i | −1.25520 | − | 0.548601i | ||||
\(799\) | −94604.8 | −0.148190 | ||||||||
\(800\) | 107639. | 0.168185 | ||||||||
\(801\) | − | 1.79796e6i | − | 2.80230i | ||||||
\(802\) | −942981. | −1.46607 | ||||||||
\(803\) | 451576.i | 0.700325i | ||||||||
\(804\) | − | 425796.i | − | 0.658703i | ||||||
\(805\) | −71011.2 | + | 162474.i | −0.109581 | + | 0.250722i | ||||
\(806\) | 347427. | 0.534802 | ||||||||
\(807\) | 1.16041e6 | 1.78183 | ||||||||
\(808\) | − | 164428.i | − | 0.251856i | ||||||
\(809\) | 52604.1 | 0.0803754 | 0.0401877 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401877 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(810\) | − | 2301.44i | − | 0.00350776i | ||||||
\(811\) | 284790.i | 0.432996i | 0.976283 | + | 0.216498i | \(0.0694634\pi\) | ||||
−0.976283 | + | 0.216498i | \(0.930537\pi\) | |||||||
\(812\) | −107189. | − | 46848.2i | −0.162569 | − | 0.0710527i | ||||
\(813\) | −596106. | −0.901867 | ||||||||
\(814\) | −313426. | −0.473027 | ||||||||
\(815\) | 464759.i | 0.699701i | ||||||||
\(816\) | −1.13046e6 | −1.69775 | ||||||||
\(817\) | − | 386716.i | − | 0.579360i | ||||||
\(818\) | − | 294407.i | − | 0.439988i | ||||||
\(819\) | −666570. | + | 1.52512e6i | −0.993751 | + | 2.27371i | ||||
\(820\) | 46645.8 | 0.0693722 | ||||||||
\(821\) | −459269. | −0.681366 | −0.340683 | − | 0.940178i | \(-0.610658\pi\) | ||||
−0.340683 | + | 0.940178i | \(0.610658\pi\) | |||||||
\(822\) | − | 1.75562e6i | − | 2.59829i | ||||||
\(823\) | −750048. | −1.10736 | −0.553680 | − | 0.832729i | \(-0.686777\pi\) | ||||
−0.553680 | + | 0.832729i | \(0.686777\pi\) | |||||||
\(824\) | 235069.i | 0.346212i | ||||||||
\(825\) | − | 367386.i | − | 0.539778i | ||||||
\(826\) | −97440.0 | + | 222944.i | −0.142816 | + | 0.326764i | ||||
\(827\) | −892076. | −1.30434 | −0.652170 | − | 0.758072i | \(-0.726141\pi\) | ||||
−0.652170 | + | 0.758072i | \(0.726141\pi\) | |||||||
\(828\) | 306402. | 0.446921 | ||||||||
\(829\) | − | 965908.i | − | 1.40549i | −0.711443 | − | 0.702743i | \(-0.751958\pi\) | ||
0.711443 | − | 0.702743i | \(-0.248042\pi\) | |||||||
\(830\) | 204675. | 0.297104 | ||||||||
\(831\) | − | 1.75725e6i | − | 2.54467i | ||||||
\(832\) | − | 248741.i | − | 0.359336i | ||||||
\(833\) | 428081. | − | 396177.i | 0.616930 | − | 0.570952i | ||||
\(834\) | −351438. | −0.505262 | ||||||||
\(835\) | 182398. | 0.261605 | ||||||||
\(836\) | 368859.i | 0.527774i | ||||||||
\(837\) | 204276. | 0.291586 | ||||||||
\(838\) | − | 633493.i | − | 0.902098i | ||||||
\(839\) | 1.19914e6i | 1.70351i | 0.523938 | + | 0.851757i | \(0.324463\pi\) | ||||
−0.523938 | + | 0.851757i | \(0.675537\pi\) | |||||||
\(840\) | −309729. | − | 135371.i | −0.438959 | − | 0.191852i | ||||
\(841\) | −597649. | −0.844995 | ||||||||
\(842\) | −169595. | −0.239216 | ||||||||
\(843\) | − | 702389.i | − | 0.988377i | ||||||
\(844\) | 194675. | 0.273291 | ||||||||
\(845\) | 428992.i | 0.600809i | ||||||||
\(846\) | 246334.i | 0.344178i | ||||||||
\(847\) | 1.16955e6 | + | 511166.i | 1.63025 | + | 0.712517i | ||||
\(848\) | −342286. | −0.475989 | ||||||||
\(849\) | 667462. | 0.926000 | ||||||||
\(850\) | 146295.i | 0.202485i | ||||||||
\(851\) | 104387. | 0.144141 | ||||||||
\(852\) | 337326.i | 0.464698i | ||||||||
\(853\) | 517748.i | 0.711575i | 0.934567 | + | 0.355787i | \(0.115787\pi\) | ||||
−0.934567 | + | 0.355787i | \(0.884213\pi\) | |||||||
\(854\) | 631710. | − | 1.44536e6i | 0.866168 | − | 1.98180i | ||||
\(855\) | −372290. | −0.509271 | ||||||||
\(856\) | 51151.0 | 0.0698083 | ||||||||
\(857\) | − | 1446.87i | − | 0.00197001i | −1.00000 | 0.000985004i | \(-0.999686\pi\) | |||
1.00000 | 0.000985004i | \(-0.000313536\pi\) | ||||||||
\(858\) | 3.66325e6 | 4.97613 | ||||||||
\(859\) | − | 217289.i | − | 0.294477i | −0.989101 | − | 0.147239i | \(-0.952961\pi\) | ||
0.989101 | − | 0.147239i | \(-0.0470385\pi\) | |||||||
\(860\) | 122919.i | 0.166197i | ||||||||
\(861\) | −378547. | − | 165448.i | −0.510639 | − | 0.223181i | ||||
\(862\) | 1.37472e6 | 1.85012 | ||||||||
\(863\) | 608808. | 0.817446 | 0.408723 | − | 0.912658i | \(-0.365974\pi\) | ||||
0.408723 | + | 0.912658i | \(0.365974\pi\) | |||||||
\(864\) | 631053.i | 0.845353i | ||||||||
\(865\) | 258012. | 0.344833 | ||||||||
\(866\) | − | 1.22889e6i | − | 1.63861i | ||||||
\(867\) | 357062.i | 0.475013i | ||||||||
\(868\) | −39439.7 | + | 90238.3i | −0.0523473 | + | 0.119771i | ||||
\(869\) | −1.05596e6 | −1.39832 | ||||||||
\(870\) | −259857. | −0.343317 | ||||||||
\(871\) | 1.04858e6i | 1.38218i | ||||||||
\(872\) | −202426. | −0.266216 | ||||||||
\(873\) | 2.43652e6i | 3.19699i | ||||||||
\(874\) | − | 395463.i | − | 0.517706i | ||||||
\(875\) | −27424.8 | + | 62748.2i | −0.0358202 | + | 0.0819568i | ||||
\(876\) | −235183. | −0.306477 | ||||||||
\(877\) | 461213. | 0.599657 | 0.299828 | − | 0.953993i | \(-0.403071\pi\) | ||||
0.299828 | + | 0.953993i | \(0.403071\pi\) | |||||||
\(878\) | 916848.i | 1.18935i | ||||||||
\(879\) | −1.07239e6 | −1.38796 | ||||||||
\(880\) | 720276.i | 0.930109i | ||||||||
\(881\) | − | 468049.i | − | 0.603031i | −0.953461 | − | 0.301515i | \(-0.902508\pi\) | ||
0.953461 | − | 0.301515i | \(-0.0974925\pi\) | |||||||
\(882\) | −1.03157e6 | − | 1.11464e6i | −1.32606 | − | 1.43284i | ||||
\(883\) | −1.35057e6 | −1.73218 | −0.866092 | − | 0.499884i | \(-0.833376\pi\) | ||||
−0.866092 | + | 0.499884i | \(0.833376\pi\) | |||||||
\(884\) | −453149. | −0.579877 | ||||||||
\(885\) | 167898.i | 0.214368i | ||||||||
\(886\) | 573730. | 0.730870 | ||||||||
\(887\) | 417192.i | 0.530259i | 0.964213 | + | 0.265130i | \(0.0854148\pi\) | ||||
−0.964213 | + | 0.265130i | \(0.914585\pi\) | |||||||
\(888\) | 198997.i | 0.252360i | ||||||||
\(889\) | 544174. | + | 237837.i | 0.688547 | + | 0.300937i | ||||
\(890\) | 737599. | 0.931195 | ||||||||
\(891\) | 8618.82 | 0.0108566 | ||||||||
\(892\) | − | 458341.i | − | 0.576048i | ||||||
\(893\) | 98765.5 | 0.123852 | ||||||||
\(894\) | 1.84341e6i | 2.30647i | ||||||||
\(895\) | − | 45045.8i | − | 0.0562352i | ||||||
\(896\) | 826579. | + | 361266.i | 1.02960 | + | 0.449998i | ||||
\(897\) | −1.22005e6 | −1.51633 | ||||||||
\(898\) | 820819. | 1.01788 | ||||||||
\(899\) | − | 92295.2i | − | 0.114198i | ||||||
\(900\) | 118334. | 0.146091 | ||||||||
\(901\) | − | 260356.i | − | 0.320714i | ||||||
\(902\) | 562333.i | 0.691163i | ||||||||
\(903\) | 435982. | − | 997531.i | 0.534679 | − | 1.22335i | ||||
\(904\) | −744676. | −0.911236 | ||||||||
\(905\) | −52848.8 | −0.0645265 | ||||||||
\(906\) | 992132.i | 1.20868i | ||||||||
\(907\) | −207532. | −0.252273 | −0.126137 | − | 0.992013i | \(-0.540258\pi\) | ||||
−0.126137 | + | 0.992013i | \(0.540258\pi\) | |||||||
\(908\) | 534792.i | 0.648654i | ||||||||
\(909\) | − | 509810.i | − | 0.616993i | ||||||
\(910\) | −625669. | − | 273456.i | −0.755548 | − | 0.330221i | ||||
\(911\) | 1.34881e6 | 1.62522 | 0.812612 | − | 0.582805i | \(-0.198045\pi\) | ||||
0.812612 | + | 0.582805i | \(0.198045\pi\) | |||||||
\(912\) | 1.18018e6 | 1.41892 | ||||||||
\(913\) | 766499.i | 0.919538i | ||||||||
\(914\) | −1.64645e6 | −1.97086 | ||||||||
\(915\) | − | 1.08850e6i | − | 1.30012i | ||||||
\(916\) | 574788.i | 0.685042i | ||||||||
\(917\) | −603997. | + | 1.38195e6i | −0.718284 | + | 1.64344i | ||||
\(918\) | −857686. | −1.01775 | ||||||||
\(919\) | 352887. | 0.417835 | 0.208918 | − | 0.977933i | \(-0.433006\pi\) | ||||
0.208918 | + | 0.977933i | \(0.433006\pi\) | |||||||
\(920\) | − | 153239.i | − | 0.181048i | ||||||
\(921\) | 68917.1 | 0.0812471 | ||||||||
\(922\) | 1.06142e6i | 1.24861i | ||||||||
\(923\) | − | 830707.i | − | 0.975089i | ||||||
\(924\) | −415850. | + | 951467.i | −0.487071 | + | 1.11442i | ||||
\(925\) | 40314.8 | 0.0471174 | ||||||||
\(926\) | 1.61348e6 | 1.88166 | ||||||||
\(927\) | 728834.i | 0.848143i | ||||||||
\(928\) | 285119. | 0.331078 | ||||||||
\(929\) | − | 382601.i | − | 0.443317i | −0.975124 | − | 0.221658i | \(-0.928853\pi\) | ||
0.975124 | − | 0.221658i | \(-0.0711470\pi\) | |||||||
\(930\) | 218764.i | 0.252935i | ||||||||
\(931\) | −446908. | + | 413602.i | −0.515607 | + | 0.477181i | ||||
\(932\) | 249563. | 0.287308 | ||||||||
\(933\) | 1.31797e6 | 1.51406 | ||||||||
\(934\) | − | 1.59816e6i | − | 1.83200i | ||||||
\(935\) | −547870. | −0.626693 | ||||||||
\(936\) | − | 1.43842e6i | − | 1.64186i | ||||||
\(937\) | − | 1.43975e6i | − | 1.63987i | −0.572460 | − | 0.819933i | \(-0.694011\pi\) | ||
0.572460 | − | 0.819933i | \(-0.305989\pi\) | |||||||
\(938\) | −876719. | − | 383180.i | −0.996448 | − | 0.435509i | ||||
\(939\) | 1.57679e6 | 1.78831 | ||||||||
\(940\) | −31392.9 | −0.0355284 | ||||||||
\(941\) | − | 829098.i | − | 0.936326i | −0.883642 | − | 0.468163i | \(-0.844916\pi\) | ||
0.883642 | − | 0.468163i | \(-0.155084\pi\) | |||||||
\(942\) | −1.22208e6 | −1.37720 | ||||||||
\(943\) | − | 187286.i | − | 0.210612i | ||||||
\(944\) | − | 329171.i | − | 0.369384i | ||||||
\(945\) | −367874. | − | 160783.i | −0.411941 | − | 0.180044i | ||||
\(946\) | −1.48183e6 | −1.65584 | ||||||||
\(947\) | −1.43840e6 | −1.60391 | −0.801957 | − | 0.597382i | \(-0.796208\pi\) | ||||
−0.801957 | + | 0.597382i | \(0.796208\pi\) | |||||||
\(948\) | − | 549948.i | − | 0.611935i | ||||||
\(949\) | 579167. | 0.643089 | ||||||||
\(950\) | − | 152729.i | − | 0.169229i | ||||||
\(951\) | 1.70769e6i | 1.88820i | ||||||||
\(952\) | −201874. | + | 461889.i | −0.222744 | + | 0.509640i | ||||
\(953\) | 1.38772e6 | 1.52797 | 0.763985 | − | 0.645235i | \(-0.223240\pi\) | ||||
0.763985 | + | 0.645235i | \(0.223240\pi\) | |||||||
\(954\) | −677919. | −0.744871 | ||||||||
\(955\) | − | 1115.83i | − | 0.00122346i | ||||||
\(956\) | 549139. | 0.600851 | ||||||||
\(957\) | − | 973154.i | − | 1.06257i | ||||||
\(958\) | − | 1.63700e6i | − | 1.78369i | ||||||
\(959\) | −1.12294e6 | − | 490793.i | −1.22101 | − | 0.533656i | ||||
\(960\) | 156624. | 0.169948 | ||||||||
\(961\) | 845821. | 0.915866 | ||||||||
\(962\) | 401983.i | 0.434368i | ||||||||
\(963\) | 158594. | 0.171015 | ||||||||
\(964\) | − | 417560.i | − | 0.449330i | ||||||
\(965\) | 308614.i | 0.331406i | ||||||||
\(966\) | 445843. | − | 1.02009e6i | 0.477780 | − | 1.09316i | ||||
\(967\) | 1.67888e6 | 1.79542 | 0.897711 | − | 0.440586i | \(-0.145229\pi\) | ||||
0.897711 | + | 0.440586i | \(0.145229\pi\) | |||||||
\(968\) | −1.10307e6 | −1.17721 | ||||||||
\(969\) | 897690.i | 0.956046i | ||||||||
\(970\) | −999565. | −1.06235 | ||||||||
\(971\) | − | 9746.54i | − | 0.0103374i | −0.999987 | − | 0.00516871i | \(-0.998355\pi\) | ||
0.999987 | − | 0.00516871i | \(-0.00164526\pi\) | |||||||
\(972\) | − | 423505.i | − | 0.448256i | ||||||
\(973\) | −98246.5 | + | 224789.i | −0.103775 | + | 0.237437i | ||||
\(974\) | 357184. | 0.376508 | ||||||||
\(975\) | −471190. | −0.495663 | ||||||||
\(976\) | 2.13404e6i | 2.24028i | ||||||||
\(977\) | 1.26088e6 | 1.32095 | 0.660473 | − | 0.750850i | \(-0.270356\pi\) | ||||
0.660473 | + | 0.750850i | \(0.270356\pi\) | |||||||
\(978\) | − | 2.91799e6i | − | 3.05074i | ||||||
\(979\) | 2.76228e6i | 2.88206i | ||||||||
\(980\) | 142051. | − | 131465.i | 0.147908 | − | 0.136885i | ||||
\(981\) | −627624. | −0.652171 | ||||||||
\(982\) | −6069.14 | −0.00629368 | ||||||||
\(983\) | − | 1.04613e6i | − | 1.08263i | −0.840819 | − | 0.541316i | \(-0.817926\pi\) | ||
0.840819 | − | 0.541316i | \(-0.182074\pi\) | |||||||
\(984\) | 357029. | 0.368735 | ||||||||
\(985\) | 191024.i | 0.196886i | ||||||||
\(986\) | 387516.i | 0.398598i | ||||||||
\(987\) | 254765. | + | 111348.i | 0.261520 | + | 0.114300i | ||||
\(988\) | 473078. | 0.484640 | ||||||||
\(989\) | 493529. | 0.504568 | ||||||||
\(990\) | 1.42655e6i | 1.45552i | ||||||||
\(991\) | −587932. | −0.598659 | −0.299330 | − | 0.954150i | \(-0.596763\pi\) | ||||
−0.299330 | + | 0.954150i | \(0.596763\pi\) | |||||||
\(992\) | − | 240031.i | − | 0.243918i | ||||||
\(993\) | − | 864612.i | − | 0.876845i | ||||||
\(994\) | 694558. | + | 303565.i | 0.702968 | + | 0.307240i | ||||
\(995\) | −141076. | −0.142497 | ||||||||
\(996\) | −399196. | −0.402409 | ||||||||
\(997\) | − | 480094.i | − | 0.482988i | −0.970402 | − | 0.241494i | \(-0.922363\pi\) | ||
0.970402 | − | 0.241494i | \(-0.0776374\pi\) | |||||||
\(998\) | −375365. | −0.376871 | ||||||||
\(999\) | 236354.i | 0.236827i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 35.5.d.a.6.10 | yes | 12 | |
3.2 | odd | 2 | 315.5.h.a.181.4 | 12 | |||
4.3 | odd | 2 | 560.5.f.b.321.2 | 12 | |||
5.2 | odd | 4 | 175.5.c.d.174.2 | 24 | |||
5.3 | odd | 4 | 175.5.c.d.174.23 | 24 | |||
5.4 | even | 2 | 175.5.d.i.76.3 | 12 | |||
7.6 | odd | 2 | inner | 35.5.d.a.6.9 | ✓ | 12 | |
21.20 | even | 2 | 315.5.h.a.181.3 | 12 | |||
28.27 | even | 2 | 560.5.f.b.321.11 | 12 | |||
35.13 | even | 4 | 175.5.c.d.174.1 | 24 | |||
35.27 | even | 4 | 175.5.c.d.174.24 | 24 | |||
35.34 | odd | 2 | 175.5.d.i.76.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.d.a.6.9 | ✓ | 12 | 7.6 | odd | 2 | inner | |
35.5.d.a.6.10 | yes | 12 | 1.1 | even | 1 | trivial | |
175.5.c.d.174.1 | 24 | 35.13 | even | 4 | |||
175.5.c.d.174.2 | 24 | 5.2 | odd | 4 | |||
175.5.c.d.174.23 | 24 | 5.3 | odd | 4 | |||
175.5.c.d.174.24 | 24 | 35.27 | even | 4 | |||
175.5.d.i.76.3 | 12 | 5.4 | even | 2 | |||
175.5.d.i.76.4 | 12 | 35.34 | odd | 2 | |||
315.5.h.a.181.3 | 12 | 21.20 | even | 2 | |||
315.5.h.a.181.4 | 12 | 3.2 | odd | 2 | |||
560.5.f.b.321.2 | 12 | 4.3 | odd | 2 | |||
560.5.f.b.321.11 | 12 | 28.27 | even | 2 |