Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,4,Mod(37,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(4.24813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8248384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(-0.641412 - 1.89436i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.37 |
Dual form | 72.4.d.d.37.3 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25295 | + | 2.53577i | −0.442983 | + | 0.896530i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.86025 | − | 6.35436i | −0.607532 | − | 0.794295i | ||||
\(5\) | − | 9.15486i | − | 0.818836i | −0.912347 | − | 0.409418i | \(-0.865732\pi\) | ||
0.912347 | − | 0.409418i | \(-0.134268\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.4175 | 1.48040 | 0.740202 | − | 0.672385i | \(-0.234730\pi\) | ||||
0.740202 | + | 0.672385i | \(0.234730\pi\) | |||||||
\(8\) | 22.2028 | − | 4.36281i | 0.981236 | − | 0.192811i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 23.2146 | + | 11.4705i | 0.734111 | + | 0.362730i | ||||
\(11\) | − | 20.5252i | − | 0.562598i | −0.959620 | − | 0.281299i | \(-0.909235\pi\) | ||
0.959620 | − | 0.281299i | \(-0.0907652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.0471i | 0.683713i | 0.939752 | + | 0.341857i | \(0.111056\pi\) | ||||
−0.939752 | + | 0.341857i | \(0.888944\pi\) | |||||||
\(14\) | −34.3526 | + | 69.5243i | −0.655794 | + | 1.32723i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.7559 | + | 61.7676i | −0.261810 | + | 0.965119i | ||||
\(17\) | 111.764 | 1.59452 | 0.797258 | − | 0.603639i | \(-0.206283\pi\) | ||||
0.797258 | + | 0.603639i | \(0.206283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 129.764i | − | 1.56684i | −0.621494 | − | 0.783419i | \(-0.713474\pi\) | ||
0.621494 | − | 0.783419i | \(-0.286526\pi\) | |||||||
\(20\) | −58.1733 | + | 44.4950i | −0.650397 | + | 0.497469i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 52.0471 | + | 25.7169i | 0.504386 | + | 0.249221i | ||||
\(23\) | −9.16510 | −0.0830893 | −0.0415447 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415447 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 41.1885 | 0.329508 | ||||||||
\(26\) | −81.2641 | − | 40.1533i | −0.612970 | − | 0.302874i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −133.256 | − | 174.220i | −0.899392 | − | 1.17588i | ||||
\(29\) | − | 41.0606i | − | 0.262923i | −0.991321 | − | 0.131461i | \(-0.958033\pi\) | ||
0.991321 | − | 0.131461i | \(-0.0419669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −187.606 | −1.08694 | −0.543468 | − | 0.839430i | \(-0.682889\pi\) | ||||
−0.543468 | + | 0.839430i | \(0.682889\pi\) | |||||||
\(32\) | −135.634 | − | 119.880i | −0.749281 | − | 0.662252i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −140.034 | + | 283.408i | −0.706344 | + | 1.42953i | ||||
\(35\) | − | 251.003i | − | 1.21221i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114.127i | 0.507093i | 0.967323 | + | 0.253546i | \(0.0815970\pi\) | ||||
−0.967323 | + | 0.253546i | \(0.918403\pi\) | |||||||
\(38\) | 329.052 | + | 162.587i | 1.40472 | + | 0.694083i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −39.9409 | − | 203.264i | −0.157880 | − | 0.803471i | ||||
\(41\) | −282.915 | −1.07766 | −0.538828 | − | 0.842416i | \(-0.681133\pi\) | ||||
−0.538828 | + | 0.842416i | \(0.681133\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 89.3870i | − | 0.317009i | −0.987358 | − | 0.158505i | \(-0.949333\pi\) | ||
0.987358 | − | 0.158505i | \(-0.0506673\pi\) | |||||||
\(44\) | −130.424 | + | 99.7576i | −0.446869 | + | 0.341796i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.4834 | − | 23.2406i | 0.0368072 | − | 0.0744921i | ||||
\(47\) | 54.6464 | 0.169596 | 0.0847978 | − | 0.996398i | \(-0.472976\pi\) | ||||
0.0847978 | + | 0.996398i | \(0.472976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 408.717 | 1.19159 | ||||||||
\(50\) | −51.6070 | + | 104.445i | −0.145967 | + | 0.295414i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 203.639 | − | 155.757i | 0.543070 | − | 0.415378i | ||||
\(53\) | 726.878i | 1.88386i | 0.335815 | + | 0.941928i | \(0.390988\pi\) | ||||
−0.335815 | + | 0.941928i | \(0.609012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −187.905 | −0.460675 | ||||||||
\(56\) | 608.745 | − | 119.617i | 1.45262 | − | 0.285438i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 104.120 | + | 51.4467i | 0.235718 | + | 0.116470i | ||||
\(59\) | 216.579i | 0.477900i | 0.971032 | + | 0.238950i | \(0.0768033\pi\) | ||||
−0.971032 | + | 0.238950i | \(0.923197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 754.222i | 1.58309i | 0.611114 | + | 0.791543i | \(0.290722\pi\) | ||||
−0.611114 | + | 0.791543i | \(0.709278\pi\) | |||||||
\(62\) | 235.060 | − | 475.726i | 0.481495 | − | 0.974471i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 473.932 | − | 193.734i | 0.925648 | − | 0.378386i | ||||
\(65\) | 293.387 | 0.559849 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 379.433i | − | 0.691868i | −0.938259 | − | 0.345934i | \(-0.887562\pi\) | ||
0.938259 | − | 0.345934i | \(-0.112438\pi\) | |||||||
\(68\) | −543.202 | − | 710.189i | −0.968719 | − | 1.26652i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 636.486 | + | 314.493i | 1.08678 | + | 0.536987i | ||||
\(71\) | −302.080 | −0.504933 | −0.252467 | − | 0.967606i | \(-0.581242\pi\) | ||||
−0.252467 | + | 0.967606i | \(0.581242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −504.396 | −0.808700 | −0.404350 | − | 0.914604i | \(-0.632502\pi\) | ||||
−0.404350 | + | 0.914604i | \(0.632502\pi\) | |||||||
\(74\) | −289.401 | − | 142.995i | −0.454624 | − | 0.224634i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −824.568 | + | 630.686i | −1.24453 | + | 0.951904i | ||||
\(77\) | − | 562.748i | − | 0.832872i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 301.780 | 0.429784 | 0.214892 | − | 0.976638i | \(-0.431060\pi\) | ||||
0.214892 | + | 0.976638i | \(0.431060\pi\) | |||||||
\(80\) | 565.474 | + | 153.398i | 0.790274 | + | 0.214380i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 354.477 | − | 717.408i | 0.477384 | − | 0.966151i | ||||
\(83\) | 599.003i | 0.792158i | 0.918216 | + | 0.396079i | \(0.129629\pi\) | ||||
−0.918216 | + | 0.396079i | \(0.870371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1023.18i | − | 1.30565i | ||||||
\(86\) | 226.665 | + | 111.997i | 0.284208 | + | 0.140430i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −89.5475 | − | 455.717i | −0.108475 | − | 0.552041i | ||||
\(89\) | 277.528 | 0.330538 | 0.165269 | − | 0.986248i | \(-0.447151\pi\) | ||||
0.165269 | + | 0.986248i | \(0.447151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 878.651i | 1.01217i | ||||||||
\(92\) | 44.5447 | + | 58.2383i | 0.0504794 | + | 0.0659975i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −68.4689 | + | 138.571i | −0.0751280 | + | 0.152048i | ||||
\(95\) | −1187.97 | −1.28298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −765.905 | −0.801710 | −0.400855 | − | 0.916141i | \(-0.631287\pi\) | ||||
−0.400855 | + | 0.916141i | \(0.631287\pi\) | |||||||
\(98\) | −512.100 | + | 1036.41i | −0.527856 | + | 1.06830i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −200.187 | − | 261.727i | −0.200187 | − | 0.261727i | ||||
\(101\) | − | 201.253i | − | 0.198272i | −0.995074 | − | 0.0991360i | \(-0.968392\pi\) | ||
0.995074 | − | 0.0991360i | \(-0.0316079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 682.440 | 0.652843 | 0.326421 | − | 0.945224i | \(-0.394157\pi\) | ||||
0.326421 | + | 0.945224i | \(0.394157\pi\) | |||||||
\(104\) | 139.816 | + | 711.537i | 0.131827 | + | 0.670884i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1843.20 | − | 910.739i | −1.68893 | − | 0.834517i | ||||
\(107\) | − | 457.252i | − | 0.413123i | −0.978434 | − | 0.206562i | \(-0.933773\pi\) | ||
0.978434 | − | 0.206562i | \(-0.0662274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 625.812i | 0.549926i | 0.961455 | + | 0.274963i | \(0.0886655\pi\) | ||||
−0.961455 | + | 0.274963i | \(0.911334\pi\) | |||||||
\(110\) | 235.435 | − | 476.484i | 0.204071 | − | 0.413009i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −459.403 | + | 1693.51i | −0.387585 | + | 1.42877i | ||||
\(113\) | −981.151 | −0.816805 | −0.408402 | − | 0.912802i | \(-0.633914\pi\) | ||||
−0.408402 | + | 0.912802i | \(0.633914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.9052i | 0.0680365i | ||||||||
\(116\) | −260.914 | + | 199.565i | −0.208838 | + | 0.159734i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −549.193 | − | 271.361i | −0.428452 | − | 0.211702i | ||||
\(119\) | 3064.29 | 2.36053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 909.717 | 0.683484 | ||||||||
\(122\) | −1912.53 | − | 944.999i | −1.41928 | − | 0.701280i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 911.813 | + | 1192.12i | 0.660348 | + | 0.863349i | ||||
\(125\) | − | 1521.43i | − | 1.08865i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −808.055 | −0.564593 | −0.282296 | − | 0.959327i | \(-0.591096\pi\) | ||||
−0.282296 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(128\) | −102.547 | + | 1444.52i | −0.0708121 | + | 0.997490i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −367.598 | + | 743.962i | −0.248004 | + | 0.501921i | ||||
\(131\) | − | 1110.85i | − | 0.740884i | −0.928856 | − | 0.370442i | \(-0.879206\pi\) | ||
0.928856 | − | 0.370442i | \(-0.120794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3557.80i | − | 2.31955i | ||||||
\(134\) | 962.155 | + | 475.409i | 0.620280 | + | 0.306486i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2481.48 | − | 487.606i | 1.56460 | − | 0.307440i | ||||
\(137\) | 466.765 | 0.291084 | 0.145542 | − | 0.989352i | \(-0.453507\pi\) | ||||
0.145542 | + | 0.989352i | \(0.453507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 351.773i | 0.214654i | 0.994224 | + | 0.107327i | \(0.0342292\pi\) | ||||
−0.994224 | + | 0.107327i | \(0.965771\pi\) | |||||||
\(140\) | −1594.96 | + | 1219.94i | −0.962850 | + | 0.736454i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 378.489 | − | 766.005i | 0.223677 | − | 0.452688i | ||||
\(143\) | 657.773 | 0.384656 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −375.904 | −0.215291 | ||||||||
\(146\) | 631.981 | − | 1279.03i | 0.358240 | − | 0.725023i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 725.207 | − | 554.688i | 0.402781 | − | 0.308075i | ||||
\(149\) | 1290.49i | 0.709540i | 0.934954 | + | 0.354770i | \(0.115441\pi\) | ||||
−0.934954 | + | 0.354770i | \(0.884559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1175.51 | 0.633521 | 0.316761 | − | 0.948505i | \(-0.397405\pi\) | ||||
0.316761 | + | 0.948505i | \(0.397405\pi\) | |||||||
\(152\) | −566.136 | − | 2881.13i | −0.302103 | − | 1.53744i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1427.00 | + | 705.093i | 0.746694 | + | 0.368948i | ||||
\(155\) | 1717.51i | 0.890022i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1092.09i | − | 0.555148i | −0.960704 | − | 0.277574i | \(-0.910470\pi\) | ||
0.960704 | − | 0.277574i | \(-0.0895303\pi\) | |||||||
\(158\) | −378.115 | + | 765.246i | −0.190387 | + | 0.385314i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1097.49 | + | 1241.71i | −0.542276 | + | 0.613538i | ||||
\(161\) | −251.284 | −0.123006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3626.97i | 1.74286i | 0.490519 | + | 0.871430i | \(0.336807\pi\) | ||||
−0.490519 | + | 0.871430i | \(0.663193\pi\) | |||||||
\(164\) | 1375.04 | + | 1797.75i | 0.654711 | + | 0.855978i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1518.93 | − | 750.518i | −0.710193 | − | 0.350913i | ||||
\(167\) | −45.8012 | −0.0212228 | −0.0106114 | − | 0.999944i | \(-0.503378\pi\) | ||||
−0.0106114 | + | 0.999944i | \(0.503378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1169.98 | 0.532536 | ||||||||
\(170\) | 2594.56 | + | 1281.99i | 1.17055 | + | 0.578379i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −567.998 | + | 434.444i | −0.251799 | + | 0.192593i | ||||
\(173\) | − | 2455.02i | − | 1.07891i | −0.842014 | − | 0.539455i | \(-0.818630\pi\) | ||
0.842014 | − | 0.539455i | \(-0.181370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1129.28 | 0.487805 | ||||||||
\(176\) | 1267.79 | + | 343.917i | 0.542974 | + | 0.147294i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −347.728 | + | 703.747i | −0.146423 | + | 0.296338i | ||||
\(179\) | 1026.28i | 0.428533i | 0.976775 | + | 0.214267i | \(0.0687362\pi\) | ||||
−0.976775 | + | 0.214267i | \(0.931264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3699.05i | 1.51905i | 0.650477 | + | 0.759526i | \(0.274569\pi\) | ||||
−0.650477 | + | 0.759526i | \(0.725431\pi\) | |||||||
\(182\) | −2228.06 | − | 1100.90i | −0.907442 | − | 0.448375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −203.491 | + | 39.9856i | −0.0815302 | + | 0.0160205i | ||||
\(185\) | 1044.82 | 0.415226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2293.98i | − | 0.897071i | ||||||
\(188\) | −265.595 | − | 347.243i | −0.103035 | − | 0.134709i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1488.46 | − | 3012.42i | 0.568340 | − | 1.15023i | ||||
\(191\) | −5108.93 | −1.93544 | −0.967721 | − | 0.252023i | \(-0.918904\pi\) | ||||
−0.967721 | + | 0.252023i | \(0.918904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1414.13 | −0.527417 | −0.263709 | − | 0.964602i | \(-0.584946\pi\) | ||||
−0.263709 | + | 0.964602i | \(0.584946\pi\) | |||||||
\(194\) | 959.638 | − | 1942.16i | 0.355144 | − | 0.718757i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1986.47 | − | 2597.13i | −0.723931 | − | 0.946477i | ||||
\(197\) | 2816.66i | 1.01867i | 0.860567 | + | 0.509337i | \(0.170109\pi\) | ||||
−0.860567 | + | 0.509337i | \(0.829891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −948.556 | −0.337896 | −0.168948 | − | 0.985625i | \(-0.554037\pi\) | ||||
−0.168948 | + | 0.985625i | \(0.554037\pi\) | |||||||
\(200\) | 914.502 | − | 179.698i | 0.323325 | − | 0.0635328i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 510.332 | + | 252.160i | 0.177757 | + | 0.0878311i | ||||
\(203\) | − | 1125.78i | − | 0.389232i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2590.05i | 0.882424i | ||||||||
\(206\) | −855.060 | + | 1730.51i | −0.289198 | + | 0.585293i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1979.48 | − | 536.977i | −0.659865 | − | 0.179003i | ||||
\(209\) | −2663.43 | −0.881499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4487.28i | − | 1.46406i | −0.681271 | − | 0.732032i | \(-0.738572\pi\) | ||
0.681271 | − | 0.732032i | \(-0.261428\pi\) | |||||||
\(212\) | 4618.85 | − | 3532.81i | 1.49634 | − | 1.14450i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1159.49 | + | 572.912i | 0.370377 | + | 0.183007i | ||||
\(215\) | −818.326 | −0.259578 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5143.68 | −1.60910 | ||||||||
\(218\) | −1586.91 | − | 784.108i | −0.493025 | − | 0.243608i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 913.267 | + | 1194.02i | 0.279875 | + | 0.365912i | ||||
\(221\) | 3581.72i | 1.09019i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4590.98 | −1.37863 | −0.689315 | − | 0.724462i | \(-0.742088\pi\) | ||||
−0.689315 | + | 0.724462i | \(0.742088\pi\) | |||||||
\(224\) | −3718.75 | − | 3286.82i | −1.10924 | − | 0.980401i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1229.33 | − | 2487.97i | 0.361831 | − | 0.732290i | ||||
\(227\) | 2897.47i | 0.847189i | 0.905852 | + | 0.423594i | \(0.139232\pi\) | ||||
−0.905852 | + | 0.423594i | \(0.860768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 34.6293i | − | 0.00999288i | −0.999988 | − | 0.00499644i | \(-0.998410\pi\) | ||
0.999988 | − | 0.00499644i | \(-0.00159042\pi\) | |||||||
\(230\) | −212.764 | − | 105.129i | −0.0609968 | − | 0.0301390i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −179.140 | − | 911.662i | −0.0506944 | − | 0.257989i | ||||
\(233\) | 1054.02 | 0.296355 | 0.148178 | − | 0.988961i | \(-0.452659\pi\) | ||||
0.148178 | + | 0.988961i | \(0.452659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 500.280i | − | 0.138871i | ||||||
\(236\) | 1376.22 | − | 1052.63i | 0.379594 | − | 0.290340i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3839.38 | + | 7770.32i | −1.04567 | + | 2.11628i | ||||
\(239\) | 654.700 | 0.177192 | 0.0885962 | − | 0.996068i | \(-0.471762\pi\) | ||||
0.0885962 | + | 0.996068i | \(0.471762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3194.00 | 0.853707 | 0.426854 | − | 0.904321i | \(-0.359622\pi\) | ||||
0.426854 | + | 0.904321i | \(0.359622\pi\) | |||||||
\(242\) | −1139.83 | + | 2306.83i | −0.302772 | + | 0.612764i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4792.60 | − | 3665.71i | 1.25744 | − | 0.961774i | ||||
\(245\) | − | 3741.74i | − | 0.975719i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4158.57 | 1.07127 | ||||||||
\(248\) | −4165.38 | + | 818.490i | −1.06654 | + | 0.209573i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3858.00 | + | 1906.27i | 0.976006 | + | 0.482253i | ||||
\(251\) | − | 5042.90i | − | 1.26815i | −0.773273 | − | 0.634074i | \(-0.781382\pi\) | ||
0.773273 | − | 0.634074i | \(-0.218618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 188.115i | 0.0467459i | ||||||||
\(254\) | 1012.45 | − | 2049.04i | 0.250105 | − | 0.506174i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3534.48 | − | 2069.94i | −0.862911 | − | 0.505356i | ||||
\(257\) | 5166.64 | 1.25403 | 0.627016 | − | 0.779007i | \(-0.284276\pi\) | ||||
0.627016 | + | 0.779007i | \(0.284276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3129.08i | 0.750702i | ||||||||
\(260\) | −1425.94 | − | 1864.29i | −0.340126 | − | 0.444685i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2816.87 | + | 1391.84i | 0.664225 | + | 0.328199i | ||||
\(263\) | 7366.11 | 1.72705 | 0.863524 | − | 0.504308i | \(-0.168252\pi\) | ||||
0.863524 | + | 0.504308i | \(0.168252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6654.47 | 1.54257 | ||||||||
\(266\) | 9021.76 | + | 4457.73i | 2.07955 | + | 1.02752i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2411.06 | + | 1844.14i | −0.549548 | + | 0.420332i | ||||
\(269\) | 7877.80i | 1.78557i | 0.450484 | + | 0.892784i | \(0.351251\pi\) | ||||
−0.450484 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5399.92 | −1.21041 | −0.605206 | − | 0.796069i | \(-0.706909\pi\) | ||||
−0.605206 | + | 0.796069i | \(0.706909\pi\) | |||||||
\(272\) | −1872.70 | + | 6903.40i | −0.417461 | + | 1.53890i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −584.832 | + | 1183.61i | −0.128945 | + | 0.260965i | ||||
\(275\) | − | 845.402i | − | 0.185381i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4416.07i | 0.957892i | 0.877844 | + | 0.478946i | \(0.158981\pi\) | ||||
−0.877844 | + | 0.478946i | \(0.841019\pi\) | |||||||
\(278\) | −892.014 | − | 440.752i | −0.192444 | − | 0.0950883i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1095.08 | − | 5572.98i | −0.233727 | − | 1.18946i | ||||
\(281\) | −8068.94 | −1.71300 | −0.856499 | − | 0.516148i | \(-0.827365\pi\) | ||||
−0.856499 | + | 0.516148i | \(0.827365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5241.13i | − | 1.10089i | −0.834870 | − | 0.550447i | \(-0.814457\pi\) | ||
0.834870 | − | 0.550447i | \(-0.185543\pi\) | |||||||
\(284\) | 1468.18 | + | 1919.52i | 0.306763 | + | 0.401066i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −824.154 | + | 1667.96i | −0.170396 | + | 0.344855i | ||||
\(287\) | −7756.81 | −1.59537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7578.21 | 1.54248 | ||||||||
\(290\) | 470.987 | − | 953.206i | 0.0953701 | − | 0.193014i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2451.49 | + | 3205.11i | 0.491311 | + | 0.642346i | ||||
\(293\) | − | 6372.75i | − | 1.27065i | −0.772246 | − | 0.635324i | \(-0.780867\pi\) | ||
0.772246 | − | 0.635324i | \(-0.219133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1982.75 | 0.391322 | ||||||||
\(296\) | 497.916 | + | 2533.95i | 0.0977730 | + | 0.497577i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3272.40 | − | 1616.92i | −0.636124 | − | 0.314314i | ||||
\(299\) | − | 293.715i | − | 0.0568093i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2450.76i | − | 0.469301i | ||||||
\(302\) | −1472.85 | + | 2980.83i | −0.280639 | + | 0.567971i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8015.22 | + | 2174.31i | 1.51219 | + | 0.410214i | ||||
\(305\) | 6904.79 | 1.29629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3810.22i | − | 0.708342i | −0.935181 | − | 0.354171i | \(-0.884763\pi\) | ||
0.935181 | − | 0.354171i | \(-0.115237\pi\) | |||||||
\(308\) | −3575.91 | + | 2735.10i | −0.661546 | + | 0.505996i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4355.20 | − | 2151.94i | −0.797932 | − | 0.394265i | ||||
\(311\) | 8106.73 | 1.47810 | 0.739052 | − | 0.673648i | \(-0.235274\pi\) | ||||
0.739052 | + | 0.673648i | \(0.235274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −559.983 | −0.101125 | −0.0505625 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505625 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(314\) | 2769.29 | + | 1368.33i | 0.497707 | + | 0.245921i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1466.73 | − | 1917.62i | −0.261108 | − | 0.341376i | ||||
\(317\) | − | 5828.98i | − | 1.03277i | −0.856357 | − | 0.516385i | \(-0.827277\pi\) | ||
0.856357 | − | 0.516385i | \(-0.172723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −842.776 | −0.147920 | ||||||||
\(320\) | −1773.60 | − | 4338.78i | −0.309836 | − | 0.757953i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 314.845 | − | 637.197i | 0.0544895 | − | 0.110278i | ||||
\(323\) | − | 14503.0i | − | 2.49835i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1319.97i | 0.225289i | ||||||||
\(326\) | −9197.16 | − | 4544.40i | −1.56253 | − | 0.772058i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6281.52 | + | 1234.31i | −1.05744 | + | 0.207784i | ||||
\(329\) | 1498.26 | 0.251070 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2847.98i | 0.472928i | 0.971640 | + | 0.236464i | \(0.0759885\pi\) | ||||
−0.971640 | + | 0.236464i | \(0.924011\pi\) | |||||||
\(332\) | 3806.28 | − | 2911.31i | 0.629207 | − | 0.481261i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 57.3864 | − | 116.141i | 0.00940133 | − | 0.0190269i | ||||
\(335\) | −3473.66 | −0.566526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10127.8 | −1.63707 | −0.818537 | − | 0.574454i | \(-0.805214\pi\) | ||||
−0.818537 | + | 0.574454i | \(0.805214\pi\) | |||||||
\(338\) | −1465.92 | + | 2966.80i | −0.235904 | + | 0.477434i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6501.69 | + | 4972.94i | −1.03707 | + | 0.793222i | ||||
\(341\) | 3850.65i | 0.611508i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1801.78 | 0.283636 | ||||||||
\(344\) | −389.979 | − | 1984.65i | −0.0611228 | − | 0.311061i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6225.36 | + | 3076.00i | 0.967276 | + | 0.477939i | ||||
\(347\) | 10148.2i | 1.56999i | 0.619505 | + | 0.784993i | \(0.287333\pi\) | ||||
−0.619505 | + | 0.784993i | \(0.712667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9515.96i | − | 1.45954i | −0.683695 | − | 0.729768i | \(-0.739628\pi\) | ||
0.683695 | − | 0.729768i | \(-0.260372\pi\) | |||||||
\(350\) | −1414.93 | + | 2863.60i | −0.216089 | + | 0.437332i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2460.57 | + | 2783.92i | −0.372582 | + | 0.421544i | ||||
\(353\) | −2813.56 | −0.424223 | −0.212111 | − | 0.977245i | \(-0.568034\pi\) | ||||
−0.212111 | + | 0.977245i | \(0.568034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2765.50i | 0.413457i | ||||||||
\(356\) | −1348.86 | − | 1763.51i | −0.200813 | − | 0.262545i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2602.40 | − | 1285.87i | −0.384193 | − | 0.189833i | ||||
\(359\) | 2427.25 | 0.356839 | 0.178419 | − | 0.983955i | \(-0.442902\pi\) | ||||
0.178419 | + | 0.983955i | \(0.442902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9979.71 | −1.45498 | ||||||||
\(362\) | −9379.95 | − | 4634.71i | −1.36188 | − | 0.672915i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5583.27 | − | 4270.47i | 0.803963 | − | 0.614926i | ||||
\(365\) | 4617.67i | 0.662192i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5021.46 | 0.714219 | 0.357109 | − | 0.934063i | \(-0.383762\pi\) | ||||
0.357109 | + | 0.934063i | \(0.383762\pi\) | |||||||
\(368\) | 153.569 | − | 566.106i | 0.0217536 | − | 0.0801911i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1309.10 | + | 2649.42i | −0.183938 | + | 0.372262i | ||||
\(371\) | 19929.1i | 2.78887i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3182.40i | 0.441765i | 0.975300 | + | 0.220882i | \(0.0708937\pi\) | ||||
−0.975300 | + | 0.220882i | \(0.929106\pi\) | |||||||
\(374\) | 5817.00 | + | 2874.23i | 0.804251 | + | 0.397387i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1213.30 | − | 238.412i | 0.166413 | − | 0.0326999i | ||||
\(377\) | 1315.87 | 0.179764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5868.93i | 0.795426i | 0.917510 | + | 0.397713i | \(0.130196\pi\) | ||||
−0.917510 | + | 0.397713i | \(0.869804\pi\) | |||||||
\(380\) | 5773.85 | + | 7548.81i | 0.779453 | + | 1.01907i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6401.22 | − | 12955.1i | 0.857368 | − | 1.73518i | ||||
\(383\) | −7350.18 | −0.980618 | −0.490309 | − | 0.871549i | \(-0.663116\pi\) | ||||
−0.490309 | + | 0.871549i | \(0.663116\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5151.88 | −0.681985 | ||||||||
\(386\) | 1771.83 | − | 3585.92i | 0.233637 | − | 0.472846i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3722.49 | + | 4866.84i | 0.487064 | + | 0.636795i | ||||
\(389\) | − | 13009.1i | − | 1.69560i | −0.530317 | − | 0.847800i | \(-0.677927\pi\) | ||
0.530317 | − | 0.847800i | \(-0.322073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1024.33 | −0.132487 | ||||||||
\(392\) | 9074.67 | − | 1783.15i | 1.16923 | − | 0.229752i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7142.41 | − | 3529.13i | −0.913272 | − | 0.451256i | ||||
\(395\) | − | 2762.76i | − | 0.351923i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4877.88i | − | 0.616659i | −0.951280 | − | 0.308330i | \(-0.900230\pi\) | ||
0.951280 | − | 0.308330i | \(-0.0997700\pi\) | |||||||
\(398\) | 1188.49 | − | 2405.32i | 0.149682 | − | 0.302934i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −690.149 | + | 2544.12i | −0.0862686 | + | 0.318015i | ||||
\(401\) | −5552.33 | −0.691446 | −0.345723 | − | 0.938337i | \(-0.612366\pi\) | ||||
−0.345723 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6012.23i | − | 0.743153i | ||||||
\(404\) | −1278.84 | + | 978.143i | −0.157486 | + | 0.120456i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2854.71 | + | 1410.54i | 0.348958 | + | 0.172423i | ||||
\(407\) | 2342.49 | 0.285289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6989.27 | 0.844981 | 0.422491 | − | 0.906367i | \(-0.361156\pi\) | ||||
0.422491 | + | 0.906367i | \(0.361156\pi\) | |||||||
\(410\) | −6567.77 | − | 3245.19i | −0.791119 | − | 0.390899i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3316.83 | − | 4336.47i | −0.396623 | − | 0.518550i | ||||
\(413\) | 5938.03i | 0.707485i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5483.79 | 0.648647 | ||||||||
\(416\) | 3841.83 | − | 4346.69i | 0.452791 | − | 0.512293i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3337.13 | − | 6753.85i | 0.390489 | − | 0.790291i | ||||
\(419\) | − | 10461.0i | − | 1.21970i | −0.792518 | − | 0.609849i | \(-0.791230\pi\) | ||
0.792518 | − | 0.609849i | \(-0.208770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4648.55i | 0.538139i | 0.963121 | + | 0.269070i | \(0.0867162\pi\) | ||||
−0.963121 | + | 0.269070i | \(0.913284\pi\) | |||||||
\(422\) | 11378.7 | + | 5622.32i | 1.31258 | + | 0.648555i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3171.23 | + | 16138.8i | 0.363228 | + | 1.84851i | ||||
\(425\) | 4603.40 | 0.525406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20678.8i | 2.34360i | ||||||||
\(428\) | −2905.54 | + | 2222.36i | −0.328142 | + | 0.250986i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1025.32 | − | 2075.09i | 0.114989 | − | 0.232720i | ||||
\(431\) | −12490.7 | −1.39595 | −0.697975 | − | 0.716122i | \(-0.745915\pi\) | ||||
−0.697975 | + | 0.716122i | \(0.745915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9446.37 | 1.04842 | 0.524208 | − | 0.851590i | \(-0.324362\pi\) | ||||
0.524208 | + | 0.851590i | \(0.324362\pi\) | |||||||
\(434\) | 6444.75 | − | 13043.2i | 0.712806 | − | 1.44261i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3976.64 | − | 3041.60i | 0.436803 | − | 0.334097i | ||||
\(437\) | 1189.30i | 0.130188i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2793.60 | 0.303716 | 0.151858 | − | 0.988402i | \(-0.451474\pi\) | ||||
0.151858 | + | 0.988402i | \(0.451474\pi\) | |||||||
\(440\) | −4172.03 | + | 819.795i | −0.452031 | + | 0.0888232i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9082.41 | − | 4487.70i | −0.977390 | − | 0.482937i | ||||
\(443\) | 7601.37i | 0.815241i | 0.913151 | + | 0.407621i | \(0.133641\pi\) | ||||
−0.913151 | + | 0.407621i | \(0.866359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2540.73i | − | 0.270657i | ||||||
\(446\) | 5752.25 | − | 11641.7i | 0.610710 | − | 1.23598i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12994.0 | − | 5311.68i | 1.37033 | − | 0.560164i | ||||
\(449\) | −10708.8 | −1.12557 | −0.562785 | − | 0.826603i | \(-0.690270\pi\) | ||||
−0.562785 | + | 0.826603i | \(0.690270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5806.89i | 0.606287i | ||||||||
\(452\) | 4768.64 | + | 6234.59i | 0.496235 | + | 0.648784i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7347.32 | − | 3630.37i | −0.759530 | − | 0.375290i | ||||
\(455\) | 8043.92 | 0.828802 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 233.840 | 0.0239356 | 0.0119678 | − | 0.999928i | \(-0.496190\pi\) | ||||
0.0119678 | + | 0.999928i | \(0.496190\pi\) | |||||||
\(458\) | 87.8120 | + | 43.3887i | 0.00895892 | + | 0.00442668i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 533.164 | − | 407.801i | 0.0540411 | − | 0.0413343i | ||||
\(461\) | 981.307i | 0.0991410i | 0.998771 | + | 0.0495705i | \(0.0157853\pi\) | ||||
−0.998771 | + | 0.0495705i | \(0.984215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14082.7 | −1.41356 | −0.706782 | − | 0.707431i | \(-0.749854\pi\) | ||||
−0.706782 | + | 0.707431i | \(0.749854\pi\) | |||||||
\(464\) | 2536.22 | + | 688.006i | 0.253752 | + | 0.0688359i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1320.62 | + | 2672.74i | −0.131280 | + | 0.265692i | ||||
\(467\) | 9286.49i | 0.920188i | 0.887870 | + | 0.460094i | \(0.152184\pi\) | ||||
−0.887870 | + | 0.460094i | \(0.847816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10403.1i | − | 1.02424i | ||||||
\(470\) | 1268.59 | + | 626.824i | 0.124502 | + | 0.0615175i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 944.892 | + | 4808.66i | 0.0921444 | + | 0.468933i | ||||
\(473\) | −1834.68 | −0.178349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5344.79i | − | 0.516286i | ||||||
\(476\) | −14893.2 | − | 19471.6i | −1.43409 | − | 1.87496i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −820.303 | + | 1660.17i | −0.0784933 | + | 0.158858i | ||||
\(479\) | 19409.3 | 1.85143 | 0.925715 | − | 0.378222i | \(-0.123464\pi\) | ||||
0.925715 | + | 0.378222i | \(0.123464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3657.46 | −0.346706 | ||||||||
\(482\) | −4001.90 | + | 8099.24i | −0.378178 | + | 0.765374i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4421.46 | − | 5780.67i | −0.415238 | − | 0.542888i | ||||
\(485\) | 7011.76i | 0.656469i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12124.8 | 1.12818 | 0.564091 | − | 0.825712i | \(-0.309227\pi\) | ||||
0.564091 | + | 0.825712i | \(0.309227\pi\) | |||||||
\(488\) | 3290.53 | + | 16745.9i | 0.305236 | + | 1.55338i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9488.20 | + | 4688.20i | 0.874762 | + | 0.432227i | ||||
\(491\) | − | 5100.69i | − | 0.468820i | −0.972138 | − | 0.234410i | \(-0.924684\pi\) | ||
0.972138 | − | 0.234410i | \(-0.0753159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4589.10i | − | 0.419235i | ||||||
\(494\) | −5210.46 | + | 10545.2i | −0.474554 | + | 0.960424i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3143.50 | − | 11588.0i | 0.284571 | − | 1.04902i | ||||
\(497\) | −8282.26 | −0.747505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 85.2797i | 0.00765058i | 0.999993 | + | 0.00382529i | \(0.00121763\pi\) | ||||
−0.999993 | + | 0.00382529i | \(0.998782\pi\) | |||||||
\(500\) | −9667.74 | + | 7394.55i | −0.864709 | + | 0.661389i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12787.6 | + | 6318.48i | 1.13693 | + | 0.561768i | ||||
\(503\) | 12287.2 | 1.08918 | 0.544592 | − | 0.838701i | \(-0.316684\pi\) | ||||
0.544592 | + | 0.838701i | \(0.316684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1842.45 | −0.162352 | ||||||||
\(506\) | −477.017 | − | 235.698i | −0.0419091 | − | 0.0207076i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3927.35 | + | 5134.67i | 0.343008 | + | 0.448453i | ||||
\(509\) | − | 450.441i | − | 0.0392248i | −0.999808 | − | 0.0196124i | \(-0.993757\pi\) | ||
0.999808 | − | 0.0196124i | \(-0.00624322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13829.2 | −1.19720 | ||||||||
\(512\) | 9677.40 | − | 6369.11i | 0.835322 | − | 0.549761i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6473.52 | + | 13101.4i | −0.555515 | + | 1.12428i | ||||
\(515\) | − | 6247.64i | − | 0.534571i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1121.63i | − | 0.0954141i | ||||||
\(518\) | −7934.63 | − | 3920.57i | −0.673026 | − | 0.332548i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6514.02 | − | 1279.99i | 0.549344 | − | 0.107945i | ||||
\(521\) | 15088.1 | 1.26876 | 0.634378 | − | 0.773023i | \(-0.281256\pi\) | ||||
0.634378 | + | 0.773023i | \(0.281256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17719.4i | − | 1.48149i | −0.671789 | − | 0.740743i | \(-0.734474\pi\) | ||
0.671789 | − | 0.740743i | \(-0.265526\pi\) | |||||||
\(524\) | −7058.77 | + | 5399.04i | −0.588481 | + | 0.450111i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9229.33 | + | 18678.7i | −0.765053 | + | 1.54835i | ||||
\(527\) | −20967.6 | −1.73314 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12083.0 | −0.993096 | ||||||||
\(530\) | −8337.69 | + | 16874.2i | −0.683332 | + | 1.38296i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22607.6 | + | 17291.8i | −1.84241 | + | 1.40920i | ||||
\(533\) | − | 9066.62i | − | 0.736808i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4186.08 | −0.338280 | ||||||||
\(536\) | −1655.40 | − | 8424.50i | −0.133400 | − | 0.678886i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19976.3 | − | 9870.46i | −1.60082 | − | 0.790977i | ||||
\(539\) | − | 8388.98i | − | 0.670388i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12244.5i | 0.973074i | 0.873660 | + | 0.486537i | \(0.161740\pi\) | ||||
−0.873660 | + | 0.486537i | \(0.838260\pi\) | |||||||
\(542\) | 6765.80 | − | 13692.9i | 0.536192 | − | 1.08517i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15159.0 | − | 13398.3i | −1.19474 | − | 1.05597i | ||||
\(545\) | 5729.22 | 0.450299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7822.46i | 0.611452i | 0.952119 | + | 0.305726i | \(0.0988992\pi\) | ||||
−0.952119 | + | 0.305726i | \(0.901101\pi\) | |||||||
\(548\) | −2268.60 | − | 2966.00i | −0.176843 | − | 0.231206i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2143.74 | + | 1059.24i | 0.166199 | + | 0.0821205i | ||||
\(551\) | −5328.19 | −0.411957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8274.05 | 0.636254 | ||||||||
\(554\) | −11198.1 | − | 5533.10i | −0.858779 | − | 0.424330i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2235.29 | − | 1709.70i | 0.170499 | − | 0.130409i | ||||
\(557\) | − | 16555.5i | − | 1.25938i | −0.776845 | − | 0.629692i | \(-0.783181\pi\) | ||
0.776845 | − | 0.629692i | \(-0.216819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2864.60 | 0.216743 | ||||||||
\(560\) | 15503.9 | + | 4205.77i | 1.16992 | + | 0.317368i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10109.9 | − | 20461.0i | 0.758830 | − | 1.53575i | ||||
\(563\) | − | 12580.7i | − | 0.941766i | −0.882196 | − | 0.470883i | \(-0.843935\pi\) | ||
0.882196 | − | 0.470883i | \(-0.156065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8982.30i | 0.668829i | ||||||||
\(566\) | 13290.3 | + | 6566.86i | 0.986985 | + | 0.487678i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6707.03 | + | 1317.92i | −0.495459 | + | 0.0973567i | ||||
\(569\) | −2657.93 | −0.195828 | −0.0979141 | − | 0.995195i | \(-0.531217\pi\) | ||||
−0.0979141 | + | 0.995195i | \(0.531217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17669.0i | − | 1.29496i | −0.762081 | − | 0.647481i | \(-0.775822\pi\) | ||
0.762081 | − | 0.647481i | \(-0.224178\pi\) | |||||||
\(572\) | −3196.94 | − | 4179.73i | −0.233691 | − | 0.305530i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9718.86 | − | 19669.5i | 0.706721 | − | 1.43029i | ||||
\(575\) | −377.497 | −0.0273786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14617.7 | 1.05467 | 0.527334 | − | 0.849658i | \(-0.323192\pi\) | ||||
0.527334 | + | 0.849658i | \(0.323192\pi\) | |||||||
\(578\) | −9495.08 | + | 19216.6i | −0.683293 | + | 1.38288i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1826.99 | + | 2388.63i | 0.130796 | + | 0.171004i | ||||
\(581\) | 16423.1i | 1.17271i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14919.3 | 1.05985 | ||||||||
\(584\) | −11199.0 | + | 2200.59i | −0.793525 | + | 0.155926i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16159.8 | + | 7984.70i | 1.13917 | + | 0.562876i | ||||
\(587\) | − | 4096.53i | − | 0.288044i | −0.989574 | − | 0.144022i | \(-0.953996\pi\) | ||
0.989574 | − | 0.144022i | \(-0.0460036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24344.5i | 1.70305i | ||||||||
\(590\) | −2484.27 | + | 5027.79i | −0.173349 | + | 0.350832i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7049.38 | − | 1912.30i | −0.489405 | − | 0.132762i | ||||
\(593\) | 21988.3 | 1.52269 | 0.761343 | − | 0.648349i | \(-0.224540\pi\) | ||||
0.761343 | + | 0.648349i | \(0.224540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 28053.1i | − | 1.93288i | ||||||
\(596\) | 8200.27 | − | 6272.13i | 0.563584 | − | 0.431068i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 744.794 | + | 368.009i | 0.0509312 | + | 0.0251656i | ||||
\(599\) | −20767.7 | −1.41660 | −0.708302 | − | 0.705909i | \(-0.750539\pi\) | ||||
−0.708302 | + | 0.705909i | \(0.750539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5382.61 | 0.365326 | 0.182663 | − | 0.983176i | \(-0.441528\pi\) | ||||
0.182663 | + | 0.983176i | \(0.441528\pi\) | |||||||
\(602\) | 6214.57 | + | 3070.67i | 0.420743 | + | 0.207893i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5713.28 | − | 7469.62i | −0.384884 | − | 0.503203i | ||||
\(605\) | − | 8328.33i | − | 0.559661i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11165.4 | 0.746607 | 0.373304 | − | 0.927709i | \(-0.378225\pi\) | ||||
0.373304 | + | 0.927709i | \(0.378225\pi\) | |||||||
\(608\) | −15556.2 | + | 17600.5i | −1.03764 | + | 1.17400i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8651.33 | + | 17509.0i | −0.574233 | + | 1.16216i | ||||
\(611\) | 1751.26i | 0.115955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16413.5i | − | 1.08146i | −0.841195 | − | 0.540731i | \(-0.818148\pi\) | ||
0.841195 | − | 0.540731i | \(-0.181852\pi\) | |||||||
\(614\) | 9661.85 | + | 4774.00i | 0.635050 | + | 0.313784i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2455.17 | − | 12494.6i | −0.160587 | − | 0.817243i | ||||
\(617\) | 51.5882 | 0.00336607 | 0.00168303 | − | 0.999999i | \(-0.499464\pi\) | ||||
0.00168303 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6349.55i | 0.412294i | 0.978521 | + | 0.206147i | \(0.0660925\pi\) | ||||
−0.978521 | + | 0.206147i | \(0.933907\pi\) | |||||||
\(620\) | 10913.7 | − | 8347.52i | 0.706941 | − | 0.540717i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10157.3 | + | 20556.8i | −0.654775 | + | 1.32516i | ||||
\(623\) | 7609.11 | 0.489330 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8779.94 | −0.561916 | ||||||||
\(626\) | 701.629 | − | 1419.99i | 0.0447967 | − | 0.0906616i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6939.53 | + | 5307.83i | −0.440951 | + | 0.337270i | ||||
\(629\) | 12755.3i | 0.808567i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13379.1 | −0.844078 | −0.422039 | − | 0.906578i | \(-0.638685\pi\) | ||||
−0.422039 | + | 0.906578i | \(0.638685\pi\) | |||||||
\(632\) | 6700.38 | − | 1316.61i | 0.421720 | − | 0.0828671i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14780.9 | + | 7303.39i | 0.925909 | + | 0.457500i | ||||
\(635\) | 7397.63i | 0.462309i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13098.2i | 0.814709i | ||||||||
\(638\) | 1055.95 | − | 2137.09i | 0.0655260 | − | 0.132615i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13224.4 | + | 938.802i | 0.816780 | + | 0.0579835i | ||||
\(641\) | 20406.3 | 1.25741 | 0.628705 | − | 0.777644i | \(-0.283585\pi\) | ||||
0.628705 | + | 0.777644i | \(0.283585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19415.1i | 1.19076i | 0.803446 | + | 0.595378i | \(0.202998\pi\) | ||||
−0.803446 | + | 0.595378i | \(0.797002\pi\) | |||||||
\(644\) | 1221.30 | + | 1596.75i | 0.0747299 | + | 0.0977029i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36776.2 | + | 18171.4i | 2.23984 | + | 1.10673i | ||||
\(647\) | 8167.12 | 0.496264 | 0.248132 | − | 0.968726i | \(-0.420183\pi\) | ||||
0.248132 | + | 0.968726i | \(0.420183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4445.31 | 0.268866 | ||||||||
\(650\) | −3347.15 | − | 1653.86i | −0.201978 | − | 0.0997993i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23047.1 | − | 17628.0i | 1.38435 | − | 1.05884i | ||||
\(653\) | − | 7444.93i | − | 0.446160i | −0.974800 | − | 0.223080i | \(-0.928389\pi\) | ||
0.974800 | − | 0.223080i | \(-0.0716111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10169.7 | −0.606662 | ||||||||
\(656\) | 4740.49 | − | 17475.0i | 0.282142 | − | 1.04007i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1877.24 | + | 3799.25i | −0.111220 | + | 0.225092i | ||||
\(659\) | 23780.4i | 1.40569i | 0.711342 | + | 0.702846i | \(0.248088\pi\) | ||||
−0.711342 | + | 0.702846i | \(0.751912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2528.90i | 0.148809i | 0.997228 | + | 0.0744046i | \(0.0237056\pi\) | ||||
−0.997228 | + | 0.0744046i | \(0.976294\pi\) | |||||||
\(662\) | −7221.82 | − | 3568.36i | −0.423994 | − | 0.209499i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2613.34 | + | 13299.6i | 0.152737 | + | 0.777294i | ||||
\(665\) | −32571.2 | −1.89933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 376.324i | 0.0218461i | ||||||||
\(668\) | 222.605 | + | 291.037i | 0.0128935 | + | 0.0168571i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4352.31 | − | 8808.40i | 0.250962 | − | 0.507908i | ||||
\(671\) | 15480.5 | 0.890640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16733.7 | 0.958447 | 0.479224 | − | 0.877693i | \(-0.340918\pi\) | ||||
0.479224 | + | 0.877693i | \(0.340918\pi\) | |||||||
\(674\) | 12689.5 | − | 25681.6i | 0.725196 | − | 1.46769i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5686.41 | − | 7434.49i | −0.323532 | − | 0.422991i | ||||
\(677\) | 24191.5i | 1.37335i | 0.726966 | + | 0.686673i | \(0.240930\pi\) | ||||
−0.726966 | + | 0.686673i | \(0.759070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20999.2 | −1.18685 | ||||||||
\(680\) | −4463.96 | − | 22717.6i | −0.251743 | − | 1.28115i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9764.35 | − | 4824.65i | −0.548235 | − | 0.270888i | ||||
\(683\) | − | 13965.2i | − | 0.782376i | −0.920311 | − | 0.391188i | \(-0.872064\pi\) | ||
0.920311 | − | 0.391188i | \(-0.127936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4273.17i | − | 0.238350i | ||||||
\(686\) | −2257.54 | + | 4568.91i | −0.125646 | + | 0.254288i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5521.23 | + | 1497.76i | 0.305952 | + | 0.0829962i | ||||
\(689\) | −23294.4 | −1.28802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8685.63i | − | 0.478172i | −0.970998 | − | 0.239086i | \(-0.923152\pi\) | ||
0.970998 | − | 0.239086i | \(-0.0768479\pi\) | |||||||
\(692\) | −15600.1 | + | 11932.0i | −0.856974 | + | 0.655472i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25733.5 | − | 12715.2i | −1.40754 | − | 0.695477i | ||||
\(695\) | 3220.43 | 0.175767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31619.7 | −1.71834 | ||||||||
\(698\) | 24130.3 | + | 11923.0i | 1.30852 | + | 0.646550i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5488.61 | − | 7175.88i | −0.296357 | − | 0.387461i | ||||
\(701\) | 25942.2i | 1.39775i | 0.715243 | + | 0.698876i | \(0.246316\pi\) | ||||
−0.715243 | + | 0.698876i | \(0.753684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14809.6 | 0.794532 | ||||||||
\(704\) | −3976.42 | − | 9727.53i | −0.212879 | − | 0.520767i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3525.24 | − | 7134.54i | 0.187924 | − | 0.380329i | ||||
\(707\) | − | 5517.86i | − | 0.293522i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5487.75i | − | 0.290687i | −0.989381 | − | 0.145343i | \(-0.953571\pi\) | ||
0.989381 | − | 0.145343i | \(-0.0464287\pi\) | |||||||
\(710\) | −7012.66 | − | 3465.02i | −0.370677 | − | 0.183155i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6161.91 | − | 1210.80i | 0.324336 | − | 0.0637314i | ||||
\(713\) | 1719.43 | 0.0903128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6021.82i | − | 0.314970i | ||||||
\(716\) | 6521.33 | − | 4987.96i | 0.340382 | − | 0.260348i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3041.21 | + | 6154.94i | −0.158074 | + | 0.319917i | ||||
\(719\) | −17141.2 | −0.889094 | −0.444547 | − | 0.895756i | \(-0.646635\pi\) | ||||
−0.444547 | + | 0.895756i | \(0.646635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18710.8 | 0.966470 | ||||||||
\(722\) | 12504.0 | − | 25306.3i | 0.644532 | − | 1.30443i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23505.1 | − | 17978.3i | 1.20658 | − | 0.922873i | ||||
\(725\) | − | 1691.23i | − | 0.0866352i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15946.4 | −0.813508 | −0.406754 | − | 0.913538i | \(-0.633339\pi\) | ||||
−0.406754 | + | 0.913538i | \(0.633339\pi\) | |||||||
\(728\) | 3833.39 | + | 19508.5i | 0.195158 | + | 0.993179i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11709.4 | − | 5785.69i | −0.593675 | − | 0.293340i | ||||
\(731\) | − | 9990.26i | − | 0.505476i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15914.2i | 0.801917i | 0.916096 | + | 0.400958i | \(0.131323\pi\) | ||||
−0.916096 | + | 0.400958i | \(0.868677\pi\) | |||||||
\(734\) | −6291.62 | + | 12733.3i | −0.316387 | + | 0.640318i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1243.10 | + | 1098.72i | 0.0622572 | + | 0.0550261i | ||||
\(737\) | −7787.94 | −0.389243 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13555.4i | 0.674755i | 0.941369 | + | 0.337377i | \(0.109540\pi\) | ||||
−0.941369 | + | 0.337377i | \(0.890460\pi\) | |||||||
\(740\) | −5078.09 | − | 6639.17i | −0.252263 | − | 0.329812i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −50535.7 | − | 24970.1i | −2.50030 | − | 1.23542i | ||||
\(743\) | 1772.73 | 0.0875303 | 0.0437652 | − | 0.999042i | \(-0.486065\pi\) | ||||
0.0437652 | + | 0.999042i | \(0.486065\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11814.3 | 0.580997 | ||||||||
\(746\) | −8069.82 | − | 3987.37i | −0.396055 | − | 0.195694i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14576.8 | + | 11149.3i | −0.712539 | + | 0.544999i | ||||
\(749\) | − | 12536.7i | − | 0.611589i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1006.65 | −0.0489124 | −0.0244562 | − | 0.999701i | \(-0.507785\pi\) | ||||
−0.0244562 | + | 0.999701i | \(0.507785\pi\) | |||||||
\(752\) | −915.647 | + | 3375.38i | −0.0444019 | + | 0.163680i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1648.72 | + | 3336.75i | −0.0796324 | + | 0.161164i | ||||
\(755\) | − | 10761.6i | − | 0.518750i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28774.0i | − | 1.38152i | −0.723086 | − | 0.690758i | \(-0.757277\pi\) | ||
0.723086 | − | 0.690758i | \(-0.242723\pi\) | |||||||
\(758\) | −14882.2 | − | 7353.45i | −0.713123 | − | 0.352360i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −26376.3 | + | 5182.90i | −1.25891 | + | 0.247373i | ||||
\(761\) | −18393.5 | −0.876166 | −0.438083 | − | 0.898934i | \(-0.644342\pi\) | ||||
−0.438083 | + | 0.898934i | \(0.644342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17158.2i | 0.814112i | ||||||||
\(764\) | 24830.7 | + | 32464.0i | 1.17584 | + | 1.53731i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9209.38 | − | 18638.4i | 0.434397 | − | 0.879153i | ||||
\(767\) | −6940.72 | −0.326747 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14672.2 | −0.688027 | −0.344014 | − | 0.938965i | \(-0.611787\pi\) | ||||
−0.344014 | + | 0.938965i | \(0.611787\pi\) | |||||||
\(770\) | 6455.03 | − | 13064.0i | 0.302108 | − | 0.611420i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6873.05 | + | 8985.92i | 0.320423 | + | 0.418925i | ||||
\(773\) | − | 16256.4i | − | 0.756405i | −0.925723 | − | 0.378202i | \(-0.876542\pi\) | ||
0.925723 | − | 0.378202i | \(-0.123458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7727.21 | −0.358154 | ||||||||
\(776\) | −17005.3 | + | 3341.50i | −0.786667 | + | 0.154578i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32988.1 | + | 16299.7i | 1.52016 | + | 0.751122i | ||||
\(779\) | 36712.2i | 1.68851i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6200.24i | 0.284074i | ||||||||
\(782\) | 1283.43 | − | 2597.46i | 0.0586896 | − | 0.118779i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6848.40 | + | 25245.5i | −0.311971 | + | 1.15003i | ||||
\(785\) | −9997.92 | −0.454575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23988.3i | 1.08652i | 0.839565 | + | 0.543259i | \(0.182810\pi\) | ||||
−0.839565 | + | 0.543259i | \(0.817190\pi\) | |||||||
\(788\) | 17898.1 | − | 13689.7i | 0.809129 | − | 0.618877i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7005.72 | + | 3461.59i | 0.315509 | + | 0.155896i | ||||
\(791\) | −26900.7 | −1.20920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24170.6 | −1.08238 | ||||||||
\(794\) | 12369.2 | + | 6111.72i | 0.552853 | + | 0.273170i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4610.22 | + | 6027.47i | 0.205283 | + | 0.268389i | ||||
\(797\) | − | 32966.9i | − | 1.46518i | −0.680672 | − | 0.732589i | \(-0.738312\pi\) | ||
0.680672 | − | 0.732589i | \(-0.261688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6107.50 | 0.270423 | ||||||||
\(800\) | −5586.58 | − | 4937.70i | −0.246894 | − | 0.218218i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6956.76 | − | 14079.4i | 0.306299 | − | 0.619902i | ||||
\(803\) | 10352.8i | 0.454973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2300.47i | 0.100721i | ||||||||
\(806\) | 15245.6 | + | 7533.00i | 0.666259 | + | 0.329204i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −878.031 | − | 4468.40i | −0.0382290 | − | 0.194552i | ||||
\(809\) | 41700.3 | 1.81224 | 0.906122 | − | 0.423017i | \(-0.139029\pi\) | ||||
0.906122 | + | 0.423017i | \(0.139029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5981.80i | − | 0.259000i | −0.991579 | − | 0.129500i | \(-0.958663\pi\) | ||
0.991579 | − | 0.129500i | \(-0.0413373\pi\) | |||||||
\(812\) | −7153.60 | + | 5471.56i | −0.309165 | + | 0.236471i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2935.01 | + | 5940.00i | −0.126378 | + | 0.255770i | ||||
\(815\) | 33204.4 | 1.42712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11599.2 | −0.496702 | ||||||||
\(818\) | −8757.18 | + | 17723.2i | −0.374312 | + | 0.757551i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16458.1 | − | 12588.3i | 0.700905 | − | 0.536100i | ||||
\(821\) | 9846.06i | 0.418550i | 0.977857 | + | 0.209275i | \(0.0671104\pi\) | ||||
−0.977857 | + | 0.209275i | \(0.932890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47001.9 | 1.99074 | 0.995372 | − | 0.0960935i | \(-0.0306348\pi\) | ||||
0.995372 | + | 0.0960935i | \(0.0306348\pi\) | |||||||
\(824\) | 15152.1 | − | 2977.36i | 0.640593 | − | 0.125875i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15057.5 | − | 7440.03i | −0.634282 | − | 0.313404i | ||||
\(827\) | 21727.4i | 0.913587i | 0.889573 | + | 0.456794i | \(0.151002\pi\) | ||||
−0.889573 | + | 0.456794i | \(0.848998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 22772.3i | − | 0.954058i | −0.878888 | − | 0.477029i | \(-0.841714\pi\) | ||
0.878888 | − | 0.477029i | \(-0.158286\pi\) | |||||||
\(830\) | −6870.89 | + | 13905.6i | −0.287340 | + | 0.581532i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6208.61 | + | 15188.2i | 0.258708 | + | 0.632878i | ||||
\(833\) | 45679.8 | 1.90002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 419.304i | 0.0173780i | ||||||||
\(836\) | 12945.0 | + | 16924.4i | 0.535539 | + | 0.700171i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26526.7 | + | 13107.1i | 1.09350 | + | 0.540306i | ||||
\(839\) | −11010.4 | −0.453064 | −0.226532 | − | 0.974004i | \(-0.572739\pi\) | ||||
−0.226532 | + | 0.974004i | \(0.572739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22703.0 | 0.930872 | ||||||||
\(842\) | −11787.7 | − | 5824.39i | −0.482458 | − | 0.238387i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28513.8 | + | 21809.3i | −1.16290 | + | 0.889465i | ||||
\(845\) | − | 10711.0i | − | 0.436059i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24942.1 | 1.01183 | ||||||||
\(848\) | −44897.5 | − | 12179.5i | −1.81815 | − | 0.493213i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5767.81 | + | 11673.2i | −0.232746 | + | 0.471042i | ||||
\(851\) | − | 1045.99i | − | 0.0421340i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38177.4i | − | 1.53244i | −0.642579 | − | 0.766219i | \(-0.722136\pi\) | ||
0.642579 | − | 0.766219i | \(-0.277864\pi\) | |||||||
\(854\) | −52436.8 | − | 25909.5i | −2.10111 | − | 1.03818i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1994.90 | − | 10152.3i | −0.0796547 | − | 0.405372i | ||||
\(857\) | −8848.01 | −0.352675 | −0.176337 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176337 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4347.66i | − | 0.172690i | −0.996265 | − | 0.0863448i | \(-0.972481\pi\) | ||
0.996265 | − | 0.0863448i | \(-0.0275187\pi\) | |||||||
\(860\) | 3977.27 | + | 5199.94i | 0.157702 | + | 0.206182i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15650.1 | − | 31673.5i | 0.618382 | − | 1.25151i | ||||
\(863\) | 33669.9 | 1.32808 | 0.664042 | − | 0.747695i | \(-0.268839\pi\) | ||||
0.664042 | + | 0.747695i | \(0.268839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22475.3 | −0.883450 | ||||||||
\(866\) | −11835.8 | + | 23953.8i | −0.464430 | + | 0.939936i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24999.6 | + | 32684.8i | 0.977582 | + | 1.27810i | ||||
\(869\) | − | 6194.10i | − | 0.241796i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12159.7 | 0.473039 | ||||||||
\(872\) | 2730.30 | + | 13894.8i | 0.106032 | + | 0.539607i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3015.79 | − | 1490.13i | −0.116717 | − | 0.0576709i | ||||
\(875\) | − | 41713.8i | − | 1.61164i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 50102.0i | − | 1.92910i | −0.263892 | − | 0.964552i | \(-0.585006\pi\) | ||
0.263892 | − | 0.964552i | \(-0.414994\pi\) | |||||||
\(878\) | −3500.23 | + | 7083.93i | −0.134541 | + | 0.272291i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3148.51 | − | 11606.5i | 0.120609 | − | 0.444606i | ||||
\(881\) | −18716.9 | −0.715766 | −0.357883 | − | 0.933766i | \(-0.616501\pi\) | ||||
−0.357883 | + | 0.933766i | \(0.616501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7514.19i | 0.286379i | 0.989695 | + | 0.143189i | \(0.0457358\pi\) | ||||
−0.989695 | + | 0.143189i | \(0.954264\pi\) | |||||||
\(884\) | 22759.5 | − | 17408.1i | 0.865934 | − | 0.662326i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19275.3 | − | 9524.10i | −0.730888 | − | 0.361138i | ||||
\(887\) | 15544.6 | 0.588429 | 0.294215 | − | 0.955739i | \(-0.404942\pi\) | ||||
0.294215 | + | 0.955739i | \(0.404942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22154.8 | −0.835825 | ||||||||
\(890\) | 6442.71 | + | 3183.40i | 0.242652 | + | 0.119896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22313.3 | + | 29172.7i | 0.837562 | + | 1.09504i | ||||
\(893\) | − | 7091.14i | − | 0.265729i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9395.42 | 0.350898 | ||||||||
\(896\) | −2811.57 | + | 39605.0i | −0.104830 | + | 1.47669i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13417.6 | − | 27155.1i | 0.498609 | − | 1.00911i | ||||
\(899\) | 7703.21i | 0.285780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 81238.8i | 3.00384i | ||||||||
\(902\) | −14724.9 | − | 7275.71i | −0.543555 | − | 0.268575i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21784.3 | + | 4280.58i | −0.801478 | + | 0.157489i | ||||
\(905\) | 33864.3 | 1.24385 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8713.10i | 0.318979i | 0.987200 | + | 0.159489i | \(0.0509848\pi\) | ||||
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(908\) | 18411.6 | − | 14082.4i | 0.672918 | − | 0.514694i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10078.6 | + | 20397.5i | −0.367145 | + | 0.743046i | ||||
\(911\) | −1975.97 | −0.0718627 | −0.0359313 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359313 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12294.6 | 0.445666 | ||||||||
\(914\) | −292.988 | + | 592.964i | −0.0106031 | + | 0.0214590i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −220.047 | + | 168.307i | −0.00793730 | + | 0.00607099i | ||||
\(917\) | − | 30456.8i | − | 1.09681i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18430.5 | −0.661552 | −0.330776 | − | 0.943709i | \(-0.607311\pi\) | ||||
−0.330776 | + | 0.943709i | \(0.607311\pi\) | |||||||
\(920\) | 366.063 | + | 1862.93i | 0.0131182 | + | 0.0667599i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2488.37 | − | 1229.52i | −0.0888829 | − | 0.0439178i | ||||
\(923\) | − | 9680.79i | − | 0.345230i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4700.74i | 0.167091i | ||||||||
\(926\) | 17644.9 | − | 35710.6i | 0.626185 | − | 1.26730i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4922.36 | + | 5569.23i | −0.174121 | + | 0.197003i | ||||
\(929\) | −12506.8 | −0.441697 | −0.220848 | − | 0.975308i | \(-0.570883\pi\) | ||||
−0.220848 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 53036.7i | − | 1.86703i | ||||||
\(932\) | −5122.78 | − | 6697.59i | −0.180045 | − | 0.235394i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23548.4 | − | 11635.5i | −0.824976 | − | 0.407628i | ||||
\(935\) | −21001.0 | −0.734554 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39267.5 | 1.36906 | 0.684532 | − | 0.728982i | \(-0.260006\pi\) | ||||
0.684532 | + | 0.728982i | \(0.260006\pi\) | |||||||
\(938\) | 26379.9 | + | 13034.5i | 0.918265 | + | 0.453723i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3178.96 | + | 2431.49i | −0.110305 | + | 0.0843685i | ||||
\(941\) | 23727.2i | 0.821981i | 0.911640 | + | 0.410991i | \(0.134817\pi\) | ||||
−0.911640 | + | 0.410991i | \(0.865183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2592.94 | 0.0895418 | ||||||||
\(944\) | −13377.5 | − | 3628.96i | −0.461231 | − | 0.125119i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2298.76 | − | 4652.34i | 0.0790054 | − | 0.159895i | ||||
\(947\) | − | 23399.8i | − | 0.802948i | −0.915870 | − | 0.401474i | \(-0.868498\pi\) | ||
0.915870 | − | 0.401474i | \(-0.131502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 16164.4i | − | 0.552919i | ||||||
\(950\) | 13553.2 | + | 6696.73i | 0.462866 | + | 0.228706i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 68035.8 | − | 13368.9i | 2.31623 | − | 0.455135i | ||||
\(953\) | −41497.1 | −1.41052 | −0.705258 | − | 0.708950i | \(-0.749169\pi\) | ||||
−0.705258 | + | 0.708950i | \(0.749169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46771.6i | 1.58481i | ||||||||
\(956\) | −3182.01 | − | 4160.20i | −0.107650 | − | 0.140743i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24318.8 | + | 49217.6i | −0.820152 | + | 1.65986i | ||||
\(959\) | 12797.5 | 0.430921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5405.00 | 0.181431 | ||||||||
\(962\) | 4582.59 | − | 9274.46i | 0.153585 | − | 0.310832i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15523.6 | − | 20295.8i | −0.518654 | − | 0.678096i | ||||
\(965\) | 12946.2i | 0.431868i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49123.6 | −1.63362 | −0.816808 | − | 0.576909i | \(-0.804259\pi\) | ||||
−0.816808 | + | 0.576909i | \(0.804259\pi\) | |||||||
\(968\) | 20198.3 | − | 3968.92i | 0.670659 | − | 0.131783i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17780.2 | − | 8785.35i | −0.588544 | − | 0.290805i | ||||
\(971\) | 20346.8i | 0.672462i | 0.941780 | + | 0.336231i | \(0.109152\pi\) | ||||
−0.941780 | + | 0.336231i | \(0.890848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9644.71i | 0.317775i | ||||||||
\(974\) | −15191.7 | + | 30745.6i | −0.499766 | + | 1.01145i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46586.5 | − | 12637.6i | −1.52787 | − | 0.414468i | ||||
\(977\) | −40602.1 | −1.32955 | −0.664777 | − | 0.747042i | \(-0.731474\pi\) | ||||
−0.664777 | + | 0.747042i | \(0.731474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5696.32i | − | 0.185960i | ||||||
\(980\) | −23776.4 | + | 18185.8i | −0.775009 | + | 0.592781i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12934.2 | + | 6390.89i | 0.420312 | + | 0.207680i | ||||
\(983\) | −50425.9 | −1.63615 | −0.818075 | − | 0.575112i | \(-0.804959\pi\) | ||||
−0.818075 | + | 0.575112i | \(0.804959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25786.2 | 0.834127 | ||||||||
\(986\) | 11636.9 | + | 5749.89i | 0.375856 | + | 0.185714i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20211.7 | − | 26425.0i | −0.650829 | − | 0.850903i | ||||
\(989\) | 819.241i | 0.0263401i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8511.62 | −0.272836 | −0.136418 | − | 0.990651i | \(-0.543559\pi\) | ||||
−0.136418 | + | 0.990651i | \(0.543559\pi\) | |||||||
\(992\) | 25445.8 | + | 22490.3i | 0.814421 | + | 0.719826i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10377.2 | − | 21001.9i | 0.331132 | − | 0.670161i | ||||
\(995\) | 8683.90i | 0.276681i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 25302.1i | − | 0.803738i | −0.915697 | − | 0.401869i | \(-0.868361\pi\) | ||
0.915697 | − | 0.401869i | \(-0.131639\pi\) | |||||||
\(998\) | −216.250 | − | 106.851i | −0.00685898 | − | 0.00338908i | ||||
\(999\) | 0 | 0 |
(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 | 72.4.d.d.37.4 | 6 | ||
3.2 | odd | 2 | 24.4.d.a.13.3 | ✓ | 6 | ||
4.3 | odd | 2 | 288.4.d.d.145.2 | 6 | |||
8.3 | odd | 2 | 288.4.d.d.145.5 | 6 | |||
8.5 | even | 2 | inner | 72.4.d.d.37.3 | 6 | ||
12.11 | even | 2 | 96.4.d.a.49.6 | 6 | |||
16.3 | odd | 4 | 2304.4.a.bw.1.1 | 3 | |||
16.5 | even | 4 | 2304.4.a.bt.1.3 | 3 | |||
16.11 | odd | 4 | 2304.4.a.bu.1.3 | 3 | |||
16.13 | even | 4 | 2304.4.a.bv.1.1 | 3 | |||
24.5 | odd | 2 | 24.4.d.a.13.4 | yes | 6 | ||
24.11 | even | 2 | 96.4.d.a.49.1 | 6 | |||
48.5 | odd | 4 | 768.4.a.r.1.1 | 3 | |||
48.11 | even | 4 | 768.4.a.t.1.1 | 3 | |||
48.29 | odd | 4 | 768.4.a.s.1.3 | 3 | |||
48.35 | even | 4 | 768.4.a.q.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.d.a.13.3 | ✓ | 6 | 3.2 | odd | 2 | ||
24.4.d.a.13.4 | yes | 6 | 24.5 | odd | 2 | ||
72.4.d.d.37.3 | 6 | 8.5 | even | 2 | inner | ||
72.4.d.d.37.4 | 6 | 1.1 | even | 1 | trivial | ||
96.4.d.a.49.1 | 6 | 24.11 | even | 2 | |||
96.4.d.a.49.6 | 6 | 12.11 | even | 2 | |||
288.4.d.d.145.2 | 6 | 4.3 | odd | 2 | |||
288.4.d.d.145.5 | 6 | 8.3 | odd | 2 | |||
768.4.a.q.1.3 | 3 | 48.35 | even | 4 | |||
768.4.a.r.1.1 | 3 | 48.5 | odd | 4 | |||
768.4.a.s.1.3 | 3 | 48.29 | odd | 4 | |||
768.4.a.t.1.1 | 3 | 48.11 | even | 4 | |||
2304.4.a.bt.1.3 | 3 | 16.5 | even | 4 | |||
2304.4.a.bu.1.3 | 3 | 16.11 | odd | 4 | |||
2304.4.a.bv.1.1 | 3 | 16.13 | even | 4 | |||
2304.4.a.bw.1.1 | 3 | 16.3 | odd | 4 |