Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not 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: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.3.d.b.74.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23607 | −1.11803 | −0.559017 | − | 0.829156i | \(-0.688821\pi\) | ||||
−0.559017 | + | 0.829156i | \(0.688821\pi\) | |||||||
\(3\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(4\) | 1.00000 | 0.250000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.00000 | + | 4.47214i | 0.833333 | + | 0.745356i | ||||
\(7\) | 6.00000i | 0.857143i | 0.903508 | + | 0.428571i | \(0.140983\pi\) | ||||
−0.903508 | + | 0.428571i | \(0.859017\pi\) | |||||||
\(8\) | 6.70820 | 0.838525 | ||||||||
\(9\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214i | 0.406558i | 0.979121 | + | 0.203279i | \(0.0651598\pi\) | ||||
−0.979121 | + | 0.203279i | \(0.934840\pi\) | |||||||
\(12\) | −2.23607 | − | 2.00000i | −0.186339 | − | 0.166667i | ||||
\(13\) | 16.0000i | 1.23077i | 0.788227 | + | 0.615385i | \(0.210999\pi\) | ||||
−0.788227 | + | 0.615385i | \(0.789001\pi\) | |||||||
\(14\) | − | 13.4164i | − | 0.958315i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.0000 | −1.18750 | ||||||||
\(17\) | 4.47214 | 0.263067 | 0.131533 | − | 0.991312i | \(-0.458010\pi\) | ||||
0.131533 | + | 0.991312i | \(0.458010\pi\) | |||||||
\(18\) | −2.23607 | − | 20.0000i | −0.124226 | − | 1.11111i | ||||
\(19\) | 2.00000 | 0.105263 | 0.0526316 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526316 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000 | − | 13.4164i | 0.571429 | − | 0.638877i | ||||
\(22\) | − | 10.0000i | − | 0.454545i | ||||||
\(23\) | −13.4164 | −0.583322 | −0.291661 | − | 0.956522i | \(-0.594208\pi\) | ||||
−0.291661 | + | 0.956522i | \(0.594208\pi\) | |||||||
\(24\) | −15.0000 | − | 13.4164i | −0.625000 | − | 0.559017i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 35.7771i | − | 1.37604i | ||||||
\(27\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(28\) | 6.00000i | 0.214286i | ||||||||
\(29\) | 31.3050i | 1.07948i | 0.841831 | + | 0.539741i | \(0.181478\pi\) | ||||
−0.841831 | + | 0.539741i | \(0.818522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.0000 | −0.580645 | −0.290323 | − | 0.956929i | \(-0.593763\pi\) | ||||
−0.290323 | + | 0.956929i | \(0.593763\pi\) | |||||||
\(32\) | 15.6525 | 0.489140 | ||||||||
\(33\) | 8.94427 | − | 10.0000i | 0.271039 | − | 0.303030i | ||||
\(34\) | −10.0000 | −0.294118 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | + | 8.94427i | 0.0277778 | + | 0.248452i | ||||
\(37\) | 16.0000i | 0.432432i | 0.976346 | + | 0.216216i | \(0.0693716\pi\) | ||||
−0.976346 | + | 0.216216i | \(0.930628\pi\) | |||||||
\(38\) | −4.47214 | −0.117688 | ||||||||
\(39\) | 32.0000 | − | 35.7771i | 0.820513 | − | 0.917361i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.6099i | 1.52707i | 0.645766 | + | 0.763535i | \(0.276538\pi\) | ||||
−0.645766 | + | 0.763535i | \(0.723462\pi\) | |||||||
\(42\) | −26.8328 | + | 30.0000i | −0.638877 | + | 0.714286i | ||||
\(43\) | 16.0000i | 0.372093i | 0.982541 | + | 0.186047i | \(0.0595675\pi\) | ||||
−0.982541 | + | 0.186047i | \(0.940432\pi\) | |||||||
\(44\) | 4.47214i | 0.101639i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.0000 | 0.652174 | ||||||||
\(47\) | −49.1935 | −1.04667 | −0.523335 | − | 0.852127i | \(-0.675312\pi\) | ||||
−0.523335 | + | 0.852127i | \(0.675312\pi\) | |||||||
\(48\) | 42.4853 | + | 38.0000i | 0.885110 | + | 0.791667i | ||||
\(49\) | 13.0000 | 0.265306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0000 | − | 8.94427i | −0.196078 | − | 0.175378i | ||||
\(52\) | 16.0000i | 0.307692i | ||||||||
\(53\) | −4.47214 | −0.0843799 | −0.0421900 | − | 0.999110i | \(-0.513433\pi\) | ||||
−0.0421900 | + | 0.999110i | \(0.513433\pi\) | |||||||
\(54\) | −35.0000 | + | 49.1935i | −0.648148 | + | 0.910991i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 40.2492i | 0.718736i | ||||||||
\(57\) | −4.47214 | − | 4.00000i | −0.0784585 | − | 0.0701754i | ||||
\(58\) | − | 70.0000i | − | 1.20690i | ||||||
\(59\) | − | 4.47214i | − | 0.0757989i | −0.999282 | − | 0.0378995i | \(-0.987933\pi\) | ||
0.999282 | − | 0.0378995i | \(-0.0120667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 82.0000 | 1.34426 | 0.672131 | − | 0.740432i | \(-0.265379\pi\) | ||||
0.672131 | + | 0.740432i | \(0.265379\pi\) | |||||||
\(62\) | 40.2492 | 0.649181 | ||||||||
\(63\) | −53.6656 | + | 6.00000i | −0.851835 | + | 0.0952381i | ||||
\(64\) | 41.0000 | 0.640625 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.0000 | + | 22.3607i | −0.303030 | + | 0.338798i | ||||
\(67\) | − | 24.0000i | − | 0.358209i | −0.983830 | − | 0.179104i | \(-0.942680\pi\) | ||
0.983830 | − | 0.179104i | \(-0.0573200\pi\) | |||||||
\(68\) | 4.47214 | 0.0657667 | ||||||||
\(69\) | 30.0000 | + | 26.8328i | 0.434783 | + | 0.388881i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.220i | − | 1.76366i | −0.471568 | − | 0.881830i | \(-0.656312\pi\) | ||
0.471568 | − | 0.881830i | \(-0.343688\pi\) | |||||||
\(72\) | 6.70820 | + | 60.0000i | 0.0931695 | + | 0.833333i | ||||
\(73\) | − | 74.0000i | − | 1.01370i | −0.862035 | − | 0.506849i | \(-0.830810\pi\) | ||
0.862035 | − | 0.506849i | \(-0.169190\pi\) | |||||||
\(74\) | − | 35.7771i | − | 0.483474i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.0263158 | ||||||||
\(77\) | −26.8328 | −0.348478 | ||||||||
\(78\) | −71.5542 | + | 80.0000i | −0.917361 | + | 1.02564i | ||||
\(79\) | −138.000 | −1.74684 | −0.873418 | − | 0.486972i | \(-0.838101\pi\) | ||||
−0.873418 | + | 0.486972i | \(0.838101\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | − | 140.000i | − | 1.70732i | ||||||
\(83\) | 93.9149 | 1.13150 | 0.565752 | − | 0.824575i | \(-0.308586\pi\) | ||||
0.565752 | + | 0.824575i | \(0.308586\pi\) | |||||||
\(84\) | 12.0000 | − | 13.4164i | 0.142857 | − | 0.159719i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 35.7771i | − | 0.416013i | ||||||
\(87\) | 62.6099 | − | 70.0000i | 0.719654 | − | 0.804598i | ||||
\(88\) | 30.0000i | 0.340909i | ||||||||
\(89\) | − | 107.331i | − | 1.20597i | −0.797753 | − | 0.602985i | \(-0.793978\pi\) | ||
0.797753 | − | 0.602985i | \(-0.206022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.0000 | −1.05495 | ||||||||
\(92\) | −13.4164 | −0.145831 | ||||||||
\(93\) | 40.2492 | + | 36.0000i | 0.432787 | + | 0.387097i | ||||
\(94\) | 110.000 | 1.17021 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −35.0000 | − | 31.3050i | −0.364583 | − | 0.326093i | ||||
\(97\) | 166.000i | 1.71134i | 0.517522 | + | 0.855670i | \(0.326855\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(98\) | −29.0689 | −0.296621 | ||||||||
\(99\) | −40.0000 | + | 4.47214i | −0.404040 | + | 0.0451731i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.0820i | 0.664179i | 0.943248 | + | 0.332089i | \(0.107754\pi\) | ||||
−0.943248 | + | 0.332089i | \(0.892246\pi\) | |||||||
\(102\) | 22.3607 | + | 20.0000i | 0.219222 | + | 0.196078i | ||||
\(103\) | 26.0000i | 0.252427i | 0.992003 | + | 0.126214i | \(0.0402825\pi\) | ||||
−0.992003 | + | 0.126214i | \(0.959718\pi\) | |||||||
\(104\) | 107.331i | 1.03203i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.0943396 | ||||||||
\(107\) | 201.246 | 1.88080 | 0.940402 | − | 0.340064i | \(-0.110449\pi\) | ||||
0.940402 | + | 0.340064i | \(0.110449\pi\) | |||||||
\(108\) | 15.6525 | − | 22.0000i | 0.144930 | − | 0.203704i | ||||
\(109\) | −38.0000 | −0.348624 | −0.174312 | − | 0.984690i | \(-0.555770\pi\) | ||||
−0.174312 | + | 0.984690i | \(0.555770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.0000 | − | 35.7771i | 0.288288 | − | 0.322316i | ||||
\(112\) | − | 114.000i | − | 1.01786i | ||||||
\(113\) | −31.3050 | −0.277035 | −0.138517 | − | 0.990360i | \(-0.544234\pi\) | ||||
−0.138517 | + | 0.990360i | \(0.544234\pi\) | |||||||
\(114\) | 10.0000 | + | 8.94427i | 0.0877193 | + | 0.0784585i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 31.3050i | 0.269870i | ||||||||
\(117\) | −143.108 | + | 16.0000i | −1.22315 | + | 0.136752i | ||||
\(118\) | 10.0000i | 0.0847458i | ||||||||
\(119\) | 26.8328i | 0.225486i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.000 | 0.834711 | ||||||||
\(122\) | −183.358 | −1.50293 | ||||||||
\(123\) | 125.220 | − | 140.000i | 1.01805 | − | 1.13821i | ||||
\(124\) | −18.0000 | −0.145161 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 120.000 | − | 13.4164i | 0.952381 | − | 0.106479i | ||||
\(127\) | 26.0000i | 0.204724i | 0.994747 | + | 0.102362i | \(0.0326401\pi\) | ||||
−0.994747 | + | 0.102362i | \(0.967360\pi\) | |||||||
\(128\) | −154.289 | −1.20538 | ||||||||
\(129\) | 32.0000 | − | 35.7771i | 0.248062 | − | 0.277342i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4164i | 0.102415i | 0.998688 | + | 0.0512077i | \(0.0163070\pi\) | ||||
−0.998688 | + | 0.0512077i | \(0.983693\pi\) | |||||||
\(132\) | 8.94427 | − | 10.0000i | 0.0677596 | − | 0.0757576i | ||||
\(133\) | 12.0000i | 0.0902256i | ||||||||
\(134\) | 53.6656i | 0.400490i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.0000 | 0.220588 | ||||||||
\(137\) | −120.748 | −0.881370 | −0.440685 | − | 0.897662i | \(-0.645264\pi\) | ||||
−0.440685 | + | 0.897662i | \(0.645264\pi\) | |||||||
\(138\) | −67.0820 | − | 60.0000i | −0.486102 | − | 0.434783i | ||||
\(139\) | 82.0000 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 110.000 | + | 98.3870i | 0.780142 | + | 0.697780i | ||||
\(142\) | 280.000i | 1.97183i | ||||||||
\(143\) | −71.5542 | −0.500379 | ||||||||
\(144\) | −19.0000 | − | 169.941i | −0.131944 | − | 1.18015i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 165.469i | 1.13335i | ||||||||
\(147\) | −29.0689 | − | 26.0000i | −0.197748 | − | 0.176871i | ||||
\(148\) | 16.0000i | 0.108108i | ||||||||
\(149\) | 111.803i | 0.750358i | 0.926952 | + | 0.375179i | \(0.122419\pi\) | ||||
−0.926952 | + | 0.375179i | \(0.877581\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −158.000 | −1.04636 | −0.523179 | − | 0.852223i | \(-0.675254\pi\) | ||||
−0.523179 | + | 0.852223i | \(0.675254\pi\) | |||||||
\(152\) | 13.4164 | 0.0882658 | ||||||||
\(153\) | 4.47214 | + | 40.0000i | 0.0292296 | + | 0.261438i | ||||
\(154\) | 60.0000 | 0.389610 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 32.0000 | − | 35.7771i | 0.205128 | − | 0.229340i | ||||
\(157\) | − | 164.000i | − | 1.04459i | −0.852766 | − | 0.522293i | \(-0.825077\pi\) | ||
0.852766 | − | 0.522293i | \(-0.174923\pi\) | |||||||
\(158\) | 308.577 | 1.95302 | ||||||||
\(159\) | 10.0000 | + | 8.94427i | 0.0628931 | + | 0.0562533i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 80.4984i | − | 0.499990i | ||||||
\(162\) | 176.649 | − | 40.0000i | 1.09043 | − | 0.246914i | ||||
\(163\) | 236.000i | 1.44785i | 0.689877 | + | 0.723926i | \(0.257664\pi\) | ||||
−0.689877 | + | 0.723926i | \(0.742336\pi\) | |||||||
\(164\) | 62.6099i | 0.381768i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −210.000 | −1.26506 | ||||||||
\(167\) | 93.9149 | 0.562364 | 0.281182 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281182 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(168\) | 80.4984 | − | 90.0000i | 0.479157 | − | 0.535714i | ||||
\(169\) | −87.0000 | −0.514793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 17.8885i | 0.0116959 | + | 0.104611i | ||||
\(172\) | 16.0000i | 0.0930233i | ||||||||
\(173\) | −13.4164 | −0.0775515 | −0.0387757 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387757 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(174\) | −140.000 | + | 156.525i | −0.804598 | + | 0.899568i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 84.9706i | − | 0.482787i | ||||||
\(177\) | −8.94427 | + | 10.0000i | −0.0505326 | + | 0.0564972i | ||||
\(178\) | 240.000i | 1.34831i | ||||||||
\(179\) | − | 192.302i | − | 1.07431i | −0.843483 | − | 0.537156i | \(-0.819499\pi\) | ||
0.843483 | − | 0.537156i | \(-0.180501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.0110497 | 0.00552486 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552486 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | 214.663 | 1.17946 | ||||||||
\(183\) | −183.358 | − | 164.000i | −1.00195 | − | 0.896175i | ||||
\(184\) | −90.0000 | −0.489130 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −90.0000 | − | 80.4984i | −0.483871 | − | 0.432787i | ||||
\(187\) | 20.0000i | 0.106952i | ||||||||
\(188\) | −49.1935 | −0.261668 | ||||||||
\(189\) | 132.000 | + | 93.9149i | 0.698413 | + | 0.496904i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 205.718i | − | 1.07706i | −0.842607 | − | 0.538529i | \(-0.818980\pi\) | ||
0.842607 | − | 0.538529i | \(-0.181020\pi\) | |||||||
\(192\) | −91.6788 | − | 82.0000i | −0.477494 | − | 0.427083i | ||||
\(193\) | − | 214.000i | − | 1.10881i | −0.832248 | − | 0.554404i | \(-0.812946\pi\) | ||
0.832248 | − | 0.554404i | \(-0.187054\pi\) | |||||||
\(194\) | − | 371.187i | − | 1.91334i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0000 | 0.0663265 | ||||||||
\(197\) | −93.9149 | −0.476725 | −0.238363 | − | 0.971176i | \(-0.576611\pi\) | ||||
−0.238363 | + | 0.971176i | \(0.576611\pi\) | |||||||
\(198\) | 89.4427 | − | 10.0000i | 0.451731 | − | 0.0505051i | ||||
\(199\) | 242.000 | 1.21608 | 0.608040 | − | 0.793906i | \(-0.291956\pi\) | ||||
0.608040 | + | 0.793906i | \(0.291956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −48.0000 | + | 53.6656i | −0.238806 | + | 0.266993i | ||||
\(202\) | − | 150.000i | − | 0.742574i | ||||||
\(203\) | −187.830 | −0.925270 | ||||||||
\(204\) | −10.0000 | − | 8.94427i | −0.0490196 | − | 0.0438445i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 58.1378i | − | 0.282222i | ||||||
\(207\) | −13.4164 | − | 120.000i | −0.0648136 | − | 0.579710i | ||||
\(208\) | − | 304.000i | − | 1.46154i | ||||||
\(209\) | 8.94427i | 0.0427956i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.00947867 | 0.00473934 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00473934 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(212\) | −4.47214 | −0.0210950 | ||||||||
\(213\) | −250.440 | + | 280.000i | −1.17577 | + | 1.31455i | ||||
\(214\) | −450.000 | −2.10280 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 105.000 | − | 147.580i | 0.486111 | − | 0.683243i | ||||
\(217\) | − | 108.000i | − | 0.497696i | ||||||
\(218\) | 84.9706 | 0.389773 | ||||||||
\(219\) | −148.000 | + | 165.469i | −0.675799 | + | 0.755566i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 71.5542i | 0.323775i | ||||||||
\(222\) | −71.5542 | + | 80.0000i | −0.322316 | + | 0.360360i | ||||
\(223\) | 86.0000i | 0.385650i | 0.981233 | + | 0.192825i | \(0.0617650\pi\) | ||||
−0.981233 | + | 0.192825i | \(0.938235\pi\) | |||||||
\(224\) | 93.9149i | 0.419263i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 70.0000 | 0.309735 | ||||||||
\(227\) | −58.1378 | −0.256114 | −0.128057 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128057 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(228\) | −4.47214 | − | 4.00000i | −0.0196146 | − | 0.0175439i | ||||
\(229\) | 282.000 | 1.23144 | 0.615721 | − | 0.787965i | \(-0.288865\pi\) | ||||
0.615721 | + | 0.787965i | \(0.288865\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 60.0000 | + | 53.6656i | 0.259740 | + | 0.232319i | ||||
\(232\) | 210.000i | 0.905172i | ||||||||
\(233\) | 362.243 | 1.55469 | 0.777346 | − | 0.629074i | \(-0.216566\pi\) | ||||
0.777346 | + | 0.629074i | \(0.216566\pi\) | |||||||
\(234\) | 320.000 | − | 35.7771i | 1.36752 | − | 0.152894i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 4.47214i | − | 0.0189497i | ||||||
\(237\) | 308.577 | + | 276.000i | 1.30201 | + | 1.16456i | ||||
\(238\) | − | 60.0000i | − | 0.252101i | ||||||
\(239\) | 250.440i | 1.04786i | 0.851760 | + | 0.523932i | \(0.175536\pi\) | ||||
−0.851760 | + | 0.523932i | \(0.824464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 262.000 | 1.08714 | 0.543568 | − | 0.839365i | \(-0.317073\pi\) | ||||
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(242\) | −225.843 | −0.933235 | ||||||||
\(243\) | 212.426 | + | 118.000i | 0.874183 | + | 0.485597i | ||||
\(244\) | 82.0000 | 0.336066 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −280.000 | + | 313.050i | −1.13821 | + | 1.27256i | ||||
\(247\) | 32.0000i | 0.129555i | ||||||||
\(248\) | −120.748 | −0.486886 | ||||||||
\(249\) | −210.000 | − | 187.830i | −0.843373 | − | 0.754336i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 469.574i | 1.87081i | 0.353573 | + | 0.935407i | \(0.384967\pi\) | ||||
−0.353573 | + | 0.935407i | \(0.615033\pi\) | |||||||
\(252\) | −53.6656 | + | 6.00000i | −0.212959 | + | 0.0238095i | ||||
\(253\) | − | 60.0000i | − | 0.237154i | ||||||
\(254\) | − | 58.1378i | − | 0.228889i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 181.000 | 0.707031 | ||||||||
\(257\) | 201.246 | 0.783059 | 0.391529 | − | 0.920166i | \(-0.371946\pi\) | ||||
0.391529 | + | 0.920166i | \(0.371946\pi\) | |||||||
\(258\) | −71.5542 | + | 80.0000i | −0.277342 | + | 0.310078i | ||||
\(259\) | −96.0000 | −0.370656 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −280.000 | + | 31.3050i | −1.07280 | + | 0.119942i | ||||
\(262\) | − | 30.0000i | − | 0.114504i | ||||||
\(263\) | 58.1378 | 0.221056 | 0.110528 | − | 0.993873i | \(-0.464746\pi\) | ||||
0.110528 | + | 0.993873i | \(0.464746\pi\) | |||||||
\(264\) | 60.0000 | − | 67.0820i | 0.227273 | − | 0.254099i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 26.8328i | − | 0.100875i | ||||||
\(267\) | −214.663 | + | 240.000i | −0.803979 | + | 0.898876i | ||||
\(268\) | − | 24.0000i | − | 0.0895522i | ||||||
\(269\) | 371.187i | 1.37988i | 0.723867 | + | 0.689939i | \(0.242363\pi\) | ||||
−0.723867 | + | 0.689939i | \(0.757637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 82.0000 | 0.302583 | 0.151292 | − | 0.988489i | \(-0.451657\pi\) | ||||
0.151292 | + | 0.988489i | \(0.451657\pi\) | |||||||
\(272\) | −84.9706 | −0.312392 | ||||||||
\(273\) | 214.663 | + | 192.000i | 0.786310 | + | 0.703297i | ||||
\(274\) | 270.000 | 0.985401 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 30.0000 | + | 26.8328i | 0.108696 | + | 0.0972203i | ||||
\(277\) | − | 24.0000i | − | 0.0866426i | −0.999061 | − | 0.0433213i | \(-0.986206\pi\) | ||
0.999061 | − | 0.0433213i | \(-0.0137939\pi\) | |||||||
\(278\) | −183.358 | −0.659560 | ||||||||
\(279\) | −18.0000 | − | 160.997i | −0.0645161 | − | 0.577050i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 187.830i | − | 0.668433i | −0.942496 | − | 0.334217i | \(-0.891528\pi\) | ||
0.942496 | − | 0.334217i | \(-0.108472\pi\) | |||||||
\(282\) | −245.967 | − | 220.000i | −0.872225 | − | 0.780142i | ||||
\(283\) | − | 144.000i | − | 0.508834i | −0.967095 | − | 0.254417i | \(-0.918116\pi\) | ||
0.967095 | − | 0.254417i | \(-0.0818836\pi\) | |||||||
\(284\) | − | 125.220i | − | 0.440915i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 160.000 | 0.559441 | ||||||||
\(287\) | −375.659 | −1.30892 | ||||||||
\(288\) | 15.6525 | + | 140.000i | 0.0543489 | + | 0.486111i | ||||
\(289\) | −269.000 | −0.930796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 332.000 | − | 371.187i | 1.14089 | − | 1.27556i | ||||
\(292\) | − | 74.0000i | − | 0.253425i | ||||||
\(293\) | −469.574 | −1.60264 | −0.801321 | − | 0.598234i | \(-0.795869\pi\) | ||||
−0.801321 | + | 0.598234i | \(0.795869\pi\) | |||||||
\(294\) | 65.0000 | + | 58.1378i | 0.221088 | + | 0.197748i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 107.331i | 0.362606i | ||||||||
\(297\) | 98.3870 | + | 70.0000i | 0.331269 | + | 0.235690i | ||||
\(298\) | − | 250.000i | − | 0.838926i | ||||||
\(299\) | − | 214.663i | − | 0.717935i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −96.0000 | −0.318937 | ||||||||
\(302\) | 353.299 | 1.16986 | ||||||||
\(303\) | 134.164 | − | 150.000i | 0.442786 | − | 0.495050i | ||||
\(304\) | −38.0000 | −0.125000 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.0000 | − | 89.4427i | −0.0326797 | − | 0.292296i | ||||
\(307\) | − | 184.000i | − | 0.599349i | −0.954042 | − | 0.299674i | \(-0.903122\pi\) | ||
0.954042 | − | 0.299674i | \(-0.0968780\pi\) | |||||||
\(308\) | −26.8328 | −0.0871195 | ||||||||
\(309\) | 52.0000 | − | 58.1378i | 0.168285 | − | 0.188148i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160.997i | 0.517675i | 0.965921 | + | 0.258837i | \(0.0833394\pi\) | ||||
−0.965921 | + | 0.258837i | \(0.916661\pi\) | |||||||
\(312\) | 214.663 | − | 240.000i | 0.688021 | − | 0.769231i | ||||
\(313\) | − | 394.000i | − | 1.25879i | −0.777087 | − | 0.629393i | \(-0.783304\pi\) | ||
0.777087 | − | 0.629393i | \(-0.216696\pi\) | |||||||
\(314\) | 366.715i | 1.16788i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −138.000 | −0.436709 | ||||||||
\(317\) | 451.686 | 1.42488 | 0.712438 | − | 0.701735i | \(-0.247591\pi\) | ||||
0.712438 | + | 0.701735i | \(0.247591\pi\) | |||||||
\(318\) | −22.3607 | − | 20.0000i | −0.0703166 | − | 0.0628931i | ||||
\(319\) | −140.000 | −0.438871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −450.000 | − | 402.492i | −1.40187 | − | 1.25387i | ||||
\(322\) | 180.000i | 0.559006i | ||||||||
\(323\) | 8.94427 | 0.0276912 | ||||||||
\(324\) | −79.0000 | + | 17.8885i | −0.243827 | + | 0.0552116i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 527.712i | − | 1.61875i | ||||||
\(327\) | 84.9706 | + | 76.0000i | 0.259849 | + | 0.232416i | ||||
\(328\) | 420.000i | 1.28049i | ||||||||
\(329\) | − | 295.161i | − | 0.897146i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −198.000 | −0.598187 | −0.299094 | − | 0.954224i | \(-0.596684\pi\) | ||||
−0.299094 | + | 0.954224i | \(0.596684\pi\) | |||||||
\(332\) | 93.9149 | 0.282876 | ||||||||
\(333\) | −143.108 | + | 16.0000i | −0.429755 | + | 0.0480480i | ||||
\(334\) | −210.000 | −0.628743 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −228.000 | + | 254.912i | −0.678571 | + | 0.758666i | ||||
\(337\) | − | 394.000i | − | 1.16914i | −0.811343 | − | 0.584570i | \(-0.801263\pi\) | ||
0.811343 | − | 0.584570i | \(-0.198737\pi\) | |||||||
\(338\) | 194.538 | 0.575556 | ||||||||
\(339\) | 70.0000 | + | 62.6099i | 0.206490 | + | 0.184690i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 80.4984i | − | 0.236066i | ||||||
\(342\) | −4.47214 | − | 40.0000i | −0.0130764 | − | 0.116959i | ||||
\(343\) | 372.000i | 1.08455i | ||||||||
\(344\) | 107.331i | 0.312009i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.0000 | 0.0867052 | ||||||||
\(347\) | −183.358 | −0.528408 | −0.264204 | − | 0.964467i | \(-0.585109\pi\) | ||||
−0.264204 | + | 0.964467i | \(0.585109\pi\) | |||||||
\(348\) | 62.6099 | − | 70.0000i | 0.179914 | − | 0.201149i | ||||
\(349\) | 362.000 | 1.03725 | 0.518625 | − | 0.855002i | \(-0.326444\pi\) | ||||
0.518625 | + | 0.855002i | \(0.326444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 352.000 | + | 250.440i | 1.00285 | + | 0.713503i | ||||
\(352\) | 70.0000i | 0.198864i | ||||||||
\(353\) | 308.577 | 0.874157 | 0.437078 | − | 0.899423i | \(-0.356013\pi\) | ||||
0.437078 | + | 0.899423i | \(0.356013\pi\) | |||||||
\(354\) | 20.0000 | − | 22.3607i | 0.0564972 | − | 0.0631658i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 107.331i | − | 0.301492i | ||||||
\(357\) | 53.6656 | − | 60.0000i | 0.150324 | − | 0.168067i | ||||
\(358\) | 430.000i | 1.20112i | ||||||||
\(359\) | − | 295.161i | − | 0.822175i | −0.911596 | − | 0.411088i | \(-0.865149\pi\) | ||
0.911596 | − | 0.411088i | \(-0.134851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | −4.47214 | −0.0123540 | ||||||||
\(363\) | −225.843 | − | 202.000i | −0.622157 | − | 0.556474i | ||||
\(364\) | −96.0000 | −0.263736 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 410.000 | + | 366.715i | 1.12022 | + | 1.00195i | ||||
\(367\) | 186.000i | 0.506812i | 0.967360 | + | 0.253406i | \(0.0815509\pi\) | ||||
−0.967360 | + | 0.253406i | \(0.918449\pi\) | |||||||
\(368\) | 254.912 | 0.692695 | ||||||||
\(369\) | −560.000 | + | 62.6099i | −1.51762 | + | 0.169675i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 26.8328i | − | 0.0723256i | ||||||
\(372\) | 40.2492 | + | 36.0000i | 0.108197 | + | 0.0967742i | ||||
\(373\) | − | 44.0000i | − | 0.117962i | −0.998259 | − | 0.0589812i | \(-0.981215\pi\) | ||
0.998259 | − | 0.0589812i | \(-0.0187852\pi\) | |||||||
\(374\) | − | 44.7214i | − | 0.119576i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −330.000 | −0.877660 | ||||||||
\(377\) | −500.879 | −1.32859 | ||||||||
\(378\) | −295.161 | − | 210.000i | −0.780849 | − | 0.555556i | ||||
\(379\) | 362.000 | 0.955145 | 0.477573 | − | 0.878592i | \(-0.341517\pi\) | ||||
0.477573 | + | 0.878592i | \(0.341517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.0000 | − | 58.1378i | 0.136483 | − | 0.152593i | ||||
\(382\) | 460.000i | 1.20419i | ||||||||
\(383\) | 362.243 | 0.945804 | 0.472902 | − | 0.881115i | \(-0.343206\pi\) | ||||
0.472902 | + | 0.881115i | \(0.343206\pi\) | |||||||
\(384\) | 345.000 | + | 308.577i | 0.898438 | + | 0.803587i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 478.519i | 1.23969i | ||||||||
\(387\) | −143.108 | + | 16.0000i | −0.369789 | + | 0.0413437i | ||||
\(388\) | 166.000i | 0.427835i | ||||||||
\(389\) | − | 442.741i | − | 1.13815i | −0.822285 | − | 0.569076i | \(-0.807301\pi\) | ||
0.822285 | − | 0.569076i | \(-0.192699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −60.0000 | −0.153453 | ||||||||
\(392\) | 87.2067 | 0.222466 | ||||||||
\(393\) | 26.8328 | − | 30.0000i | 0.0682769 | − | 0.0763359i | ||||
\(394\) | 210.000 | 0.532995 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −40.0000 | + | 4.47214i | −0.101010 | + | 0.0112933i | ||||
\(397\) | − | 124.000i | − | 0.312343i | −0.987730 | − | 0.156171i | \(-0.950085\pi\) | ||
0.987730 | − | 0.156171i | \(-0.0499152\pi\) | |||||||
\(398\) | −541.128 | −1.35962 | ||||||||
\(399\) | 24.0000 | − | 26.8328i | 0.0601504 | − | 0.0672502i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 268.328i | − | 0.669148i | −0.942370 | − | 0.334574i | \(-0.891408\pi\) | ||
0.942370 | − | 0.334574i | \(-0.108592\pi\) | |||||||
\(402\) | 107.331 | − | 120.000i | 0.266993 | − | 0.298507i | ||||
\(403\) | − | 288.000i | − | 0.714640i | ||||||
\(404\) | 67.0820i | 0.166045i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 420.000 | 1.03448 | ||||||||
\(407\) | −71.5542 | −0.175809 | ||||||||
\(408\) | −67.0820 | − | 60.0000i | −0.164417 | − | 0.147059i | ||||
\(409\) | −458.000 | −1.11980 | −0.559902 | − | 0.828559i | \(-0.689161\pi\) | ||||
−0.559902 | + | 0.828559i | \(0.689161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 270.000 | + | 241.495i | 0.656934 | + | 0.587580i | ||||
\(412\) | 26.0000i | 0.0631068i | ||||||||
\(413\) | 26.8328 | 0.0649705 | ||||||||
\(414\) | 30.0000 | + | 268.328i | 0.0724638 | + | 0.648136i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 250.440i | 0.602018i | ||||||||
\(417\) | −183.358 | − | 164.000i | −0.439706 | − | 0.393285i | ||||
\(418\) | − | 20.0000i | − | 0.0478469i | ||||||
\(419\) | 594.794i | 1.41956i | 0.704425 | + | 0.709778i | \(0.251205\pi\) | ||||
−0.704425 | + | 0.709778i | \(0.748795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 562.000 | 1.33492 | 0.667458 | − | 0.744647i | \(-0.267382\pi\) | ||||
0.667458 | + | 0.744647i | \(0.267382\pi\) | |||||||
\(422\) | −4.47214 | −0.0105975 | ||||||||
\(423\) | −49.1935 | − | 440.000i | −0.116297 | − | 1.04019i | ||||
\(424\) | −30.0000 | −0.0707547 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 560.000 | − | 626.099i | 1.31455 | − | 1.46972i | ||||
\(427\) | 492.000i | 1.15222i | ||||||||
\(428\) | 201.246 | 0.470201 | ||||||||
\(429\) | 160.000 | + | 143.108i | 0.372960 | + | 0.333586i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 348.827i | 0.809342i | 0.914462 | + | 0.404671i | \(0.132614\pi\) | ||||
−0.914462 | + | 0.404671i | \(0.867386\pi\) | |||||||
\(432\) | −297.397 | + | 418.000i | −0.688419 | + | 0.967593i | ||||
\(433\) | 226.000i | 0.521940i | 0.965347 | + | 0.260970i | \(0.0840424\pi\) | ||||
−0.965347 | + | 0.260970i | \(0.915958\pi\) | |||||||
\(434\) | 241.495i | 0.556441i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.0000 | −0.0871560 | ||||||||
\(437\) | −26.8328 | −0.0614023 | ||||||||
\(438\) | 330.938 | − | 370.000i | 0.755566 | − | 0.844749i | ||||
\(439\) | 2.00000 | 0.00455581 | 0.00227790 | − | 0.999997i | \(-0.499275\pi\) | ||||
0.00227790 | + | 0.999997i | \(0.499275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | + | 116.276i | 0.0294785 | + | 0.263663i | ||||
\(442\) | − | 160.000i | − | 0.361991i | ||||||
\(443\) | −201.246 | −0.454280 | −0.227140 | − | 0.973862i | \(-0.572938\pi\) | ||||
−0.227140 | + | 0.973862i | \(0.572938\pi\) | |||||||
\(444\) | 32.0000 | − | 35.7771i | 0.0720721 | − | 0.0805790i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 192.302i | − | 0.431170i | ||||||
\(447\) | 223.607 | − | 250.000i | 0.500239 | − | 0.559284i | ||||
\(448\) | 246.000i | 0.549107i | ||||||||
\(449\) | − | 313.050i | − | 0.697215i | −0.937269 | − | 0.348607i | \(-0.886655\pi\) | ||
0.937269 | − | 0.348607i | \(-0.113345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −280.000 | −0.620843 | ||||||||
\(452\) | −31.3050 | −0.0692587 | ||||||||
\(453\) | 353.299 | + | 316.000i | 0.779909 | + | 0.697572i | ||||
\(454\) | 130.000 | 0.286344 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.0000 | − | 26.8328i | −0.0657895 | − | 0.0588439i | ||||
\(457\) | − | 334.000i | − | 0.730853i | −0.930840 | − | 0.365427i | \(-0.880923\pi\) | ||
0.930840 | − | 0.365427i | \(-0.119077\pi\) | |||||||
\(458\) | −630.571 | −1.37679 | ||||||||
\(459\) | 70.0000 | − | 98.3870i | 0.152505 | − | 0.214351i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 93.9149i | 0.203720i | 0.994799 | + | 0.101860i | \(0.0324794\pi\) | ||||
−0.994799 | + | 0.101860i | \(0.967521\pi\) | |||||||
\(462\) | −134.164 | − | 120.000i | −0.290398 | − | 0.259740i | ||||
\(463\) | 366.000i | 0.790497i | 0.918574 | + | 0.395248i | \(0.129341\pi\) | ||||
−0.918574 | + | 0.395248i | \(0.870659\pi\) | |||||||
\(464\) | − | 594.794i | − | 1.28188i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −810.000 | −1.73820 | ||||||||
\(467\) | 451.686 | 0.967207 | 0.483604 | − | 0.875287i | \(-0.339328\pi\) | ||||
0.483604 | + | 0.875287i | \(0.339328\pi\) | |||||||
\(468\) | −143.108 | + | 16.0000i | −0.305787 | + | 0.0341880i | ||||
\(469\) | 144.000 | 0.307036 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −328.000 | + | 366.715i | −0.696391 | + | 0.778588i | ||||
\(472\) | − | 30.0000i | − | 0.0635593i | ||||||
\(473\) | −71.5542 | −0.151277 | ||||||||
\(474\) | −690.000 | − | 617.155i | −1.45570 | − | 1.30201i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.8328i | 0.0563715i | ||||||||
\(477\) | −4.47214 | − | 40.0000i | −0.00937555 | − | 0.0838574i | ||||
\(478\) | − | 560.000i | − | 1.17155i | ||||||
\(479\) | 590.322i | 1.23240i | 0.787588 | + | 0.616202i | \(0.211330\pi\) | ||||
−0.787588 | + | 0.616202i | \(0.788670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −256.000 | −0.532225 | ||||||||
\(482\) | −585.850 | −1.21546 | ||||||||
\(483\) | −160.997 | + | 180.000i | −0.333327 | + | 0.372671i | ||||
\(484\) | 101.000 | 0.208678 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −475.000 | − | 263.856i | −0.977366 | − | 0.542914i | ||||
\(487\) | 886.000i | 1.81930i | 0.415374 | + | 0.909651i | \(0.363651\pi\) | ||||
−0.415374 | + | 0.909651i | \(0.636349\pi\) | |||||||
\(488\) | 550.073 | 1.12720 | ||||||||
\(489\) | 472.000 | − | 527.712i | 0.965235 | − | 1.07917i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 406.964i | − | 0.828848i | −0.910084 | − | 0.414424i | \(-0.863983\pi\) | ||
0.910084 | − | 0.414424i | \(-0.136017\pi\) | |||||||
\(492\) | 125.220 | − | 140.000i | 0.254512 | − | 0.284553i | ||||
\(493\) | 140.000i | 0.283976i | ||||||||
\(494\) | − | 71.5542i | − | 0.144847i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 342.000 | 0.689516 | ||||||||
\(497\) | 751.319 | 1.51171 | ||||||||
\(498\) | 469.574 | + | 420.000i | 0.942920 | + | 0.843373i | ||||
\(499\) | 2.00000 | 0.00400802 | 0.00200401 | − | 0.999998i | \(-0.499362\pi\) | ||||
0.00200401 | + | 0.999998i | \(0.499362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −210.000 | − | 187.830i | −0.419162 | − | 0.374910i | ||||
\(502\) | − | 1050.00i | − | 2.09163i | ||||||
\(503\) | 219.135 | 0.435655 | 0.217828 | − | 0.975987i | \(-0.430103\pi\) | ||||
0.217828 | + | 0.975987i | \(0.430103\pi\) | |||||||
\(504\) | −360.000 | + | 40.2492i | −0.714286 | + | 0.0798596i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 134.164i | 0.265146i | ||||||||
\(507\) | 194.538 | + | 174.000i | 0.383704 | + | 0.343195i | ||||
\(508\) | 26.0000i | 0.0511811i | ||||||||
\(509\) | 800.512i | 1.57272i | 0.617771 | + | 0.786358i | \(0.288036\pi\) | ||||
−0.617771 | + | 0.786358i | \(0.711964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 444.000 | 0.868885 | ||||||||
\(512\) | 212.426 | 0.414895 | ||||||||
\(513\) | 31.3050 | − | 44.0000i | 0.0610233 | − | 0.0857700i | ||||
\(514\) | −450.000 | −0.875486 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 32.0000 | − | 35.7771i | 0.0620155 | − | 0.0693354i | ||||
\(517\) | − | 220.000i | − | 0.425532i | ||||||
\(518\) | 214.663 | 0.414406 | ||||||||
\(519\) | 30.0000 | + | 26.8328i | 0.0578035 | + | 0.0517010i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 527.712i | − | 1.01288i | −0.862274 | − | 0.506441i | \(-0.830961\pi\) | ||
0.862274 | − | 0.506441i | \(-0.169039\pi\) | |||||||
\(522\) | 626.099 | − | 70.0000i | 1.19942 | − | 0.134100i | ||||
\(523\) | 376.000i | 0.718929i | 0.933159 | + | 0.359465i | \(0.117041\pi\) | ||||
−0.933159 | + | 0.359465i | \(0.882959\pi\) | |||||||
\(524\) | 13.4164i | 0.0256038i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −130.000 | −0.247148 | ||||||||
\(527\) | −80.4984 | −0.152748 | ||||||||
\(528\) | −169.941 | + | 190.000i | −0.321858 | + | 0.359848i | ||||
\(529\) | −349.000 | −0.659735 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.0000 | − | 4.47214i | 0.0753296 | − | 0.00842210i | ||||
\(532\) | 12.0000i | 0.0225564i | ||||||||
\(533\) | −1001.76 | −1.87947 | ||||||||
\(534\) | 480.000 | − | 536.656i | 0.898876 | − | 1.00497i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 160.997i | − | 0.300367i | ||||||
\(537\) | −384.604 | + | 430.000i | −0.716208 | + | 0.800745i | ||||
\(538\) | − | 830.000i | − | 1.54275i | ||||||
\(539\) | 58.1378i | 0.107862i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −198.000 | −0.365989 | −0.182994 | − | 0.983114i | \(-0.558579\pi\) | ||||
−0.182994 | + | 0.983114i | \(0.558579\pi\) | |||||||
\(542\) | −183.358 | −0.338298 | ||||||||
\(543\) | −4.47214 | − | 4.00000i | −0.00823598 | − | 0.00736648i | ||||
\(544\) | 70.0000 | 0.128676 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −480.000 | − | 429.325i | −0.879121 | − | 0.786310i | ||||
\(547\) | − | 1024.00i | − | 1.87203i | −0.351961 | − | 0.936015i | \(-0.614485\pi\) | ||
0.351961 | − | 0.936015i | \(-0.385515\pi\) | |||||||
\(548\) | −120.748 | −0.220342 | ||||||||
\(549\) | 82.0000 | + | 733.430i | 0.149362 | + | 1.33594i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 62.6099i | 0.113630i | ||||||||
\(552\) | 201.246 | + | 180.000i | 0.364576 | + | 0.326087i | ||||
\(553\) | − | 828.000i | − | 1.49729i | ||||||
\(554\) | 53.6656i | 0.0968694i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 82.0000 | 0.147482 | ||||||||
\(557\) | 67.0820 | 0.120435 | 0.0602173 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602173 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(558\) | 40.2492 | + | 360.000i | 0.0721312 | + | 0.645161i | ||||
\(559\) | −256.000 | −0.457961 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | − | 44.7214i | 0.0713012 | − | 0.0797172i | ||||
\(562\) | 420.000i | 0.747331i | ||||||||
\(563\) | −254.912 | −0.452774 | −0.226387 | − | 0.974037i | \(-0.572691\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(564\) | 110.000 | + | 98.3870i | 0.195035 | + | 0.174445i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 321.994i | 0.568894i | ||||||||
\(567\) | −107.331 | − | 474.000i | −0.189297 | − | 0.835979i | ||||
\(568\) | − | 840.000i | − | 1.47887i | ||||||
\(569\) | − | 858.650i | − | 1.50905i | −0.656271 | − | 0.754526i | \(-0.727867\pi\) | ||
0.656271 | − | 0.754526i | \(-0.272133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 962.000 | 1.68476 | 0.842382 | − | 0.538881i | \(-0.181153\pi\) | ||||
0.842382 | + | 0.538881i | \(0.181153\pi\) | |||||||
\(572\) | −71.5542 | −0.125095 | ||||||||
\(573\) | −411.437 | + | 460.000i | −0.718039 | + | 0.802792i | ||||
\(574\) | 840.000 | 1.46341 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 41.0000 | + | 366.715i | 0.0711806 | + | 0.636658i | ||||
\(577\) | 886.000i | 1.53553i | 0.640732 | + | 0.767764i | \(0.278631\pi\) | ||||
−0.640732 | + | 0.767764i | \(0.721369\pi\) | |||||||
\(578\) | 601.502 | 1.04066 | ||||||||
\(579\) | −428.000 | + | 478.519i | −0.739206 | + | 0.826457i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 563.489i | 0.969861i | ||||||||
\(582\) | −742.375 | + | 830.000i | −1.27556 | + | 1.42612i | ||||
\(583\) | − | 20.0000i | − | 0.0343053i | ||||||
\(584\) | − | 496.407i | − | 0.850012i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1050.00 | 1.79181 | ||||||||
\(587\) | −657.404 | −1.11994 | −0.559969 | − | 0.828513i | \(-0.689187\pi\) | ||||
−0.559969 | + | 0.828513i | \(0.689187\pi\) | |||||||
\(588\) | −29.0689 | − | 26.0000i | −0.0494369 | − | 0.0442177i | ||||
\(589\) | −36.0000 | −0.0611205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 210.000 | + | 187.830i | 0.355330 | + | 0.317817i | ||||
\(592\) | − | 304.000i | − | 0.513514i | ||||||
\(593\) | 111.803 | 0.188539 | 0.0942693 | − | 0.995547i | \(-0.469949\pi\) | ||||
0.0942693 | + | 0.995547i | \(0.469949\pi\) | |||||||
\(594\) | −220.000 | − | 156.525i | −0.370370 | − | 0.263510i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 111.803i | 0.187590i | ||||||||
\(597\) | −541.128 | − | 484.000i | −0.906413 | − | 0.810720i | ||||
\(598\) | 480.000i | 0.802676i | ||||||||
\(599\) | − | 223.607i | − | 0.373300i | −0.982426 | − | 0.186650i | \(-0.940237\pi\) | ||
0.982426 | − | 0.186650i | \(-0.0597631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.00332779 | 0.00166389 | − | 0.999999i | \(-0.499470\pi\) | ||||
0.00166389 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(602\) | 214.663 | 0.356582 | ||||||||
\(603\) | 214.663 | − | 24.0000i | 0.355991 | − | 0.0398010i | ||||
\(604\) | −158.000 | −0.261589 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −300.000 | + | 335.410i | −0.495050 | + | 0.553482i | ||||
\(607\) | 506.000i | 0.833608i | 0.908996 | + | 0.416804i | \(0.136850\pi\) | ||||
−0.908996 | + | 0.416804i | \(0.863150\pi\) | |||||||
\(608\) | 31.3050 | 0.0514884 | ||||||||
\(609\) | 420.000 | + | 375.659i | 0.689655 | + | 0.616846i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 787.096i | − | 1.28821i | ||||||
\(612\) | 4.47214 | + | 40.0000i | 0.00730741 | + | 0.0653595i | ||||
\(613\) | 556.000i | 0.907015i | 0.891253 | + | 0.453507i | \(0.149827\pi\) | ||||
−0.891253 | + | 0.453507i | \(0.850173\pi\) | |||||||
\(614\) | 411.437i | 0.670092i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −180.000 | −0.292208 | ||||||||
\(617\) | 93.9149 | 0.152212 | 0.0761060 | − | 0.997100i | \(-0.475751\pi\) | ||||
0.0761060 | + | 0.997100i | \(0.475751\pi\) | |||||||
\(618\) | −116.276 | + | 130.000i | −0.188148 | + | 0.210356i | ||||
\(619\) | 802.000 | 1.29564 | 0.647819 | − | 0.761794i | \(-0.275681\pi\) | ||||
0.647819 | + | 0.761794i | \(0.275681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −210.000 | + | 295.161i | −0.338164 | + | 0.475299i | ||||
\(622\) | − | 360.000i | − | 0.578778i | ||||||
\(623\) | 643.988 | 1.03369 | ||||||||
\(624\) | −608.000 | + | 679.765i | −0.974359 | + | 1.08937i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 881.011i | 1.40737i | ||||||||
\(627\) | 17.8885 | − | 20.0000i | 0.0285304 | − | 0.0318979i | ||||
\(628\) | − | 164.000i | − | 0.261146i | ||||||
\(629\) | 71.5542i | 0.113759i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −698.000 | −1.10618 | −0.553090 | − | 0.833121i | \(-0.686552\pi\) | ||||
−0.553090 | + | 0.833121i | \(0.686552\pi\) | |||||||
\(632\) | −925.732 | −1.46477 | ||||||||
\(633\) | −4.47214 | − | 4.00000i | −0.00706499 | − | 0.00631912i | ||||
\(634\) | −1010.00 | −1.59306 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.0000 | + | 8.94427i | 0.0157233 | + | 0.0140633i | ||||
\(637\) | 208.000i | 0.326531i | ||||||||
\(638\) | 313.050 | 0.490673 | ||||||||
\(639\) | 1120.00 | − | 125.220i | 1.75274 | − | 0.195962i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 912.316i | 1.42327i | 0.702550 | + | 0.711635i | \(0.252045\pi\) | ||||
−0.702550 | + | 0.711635i | \(0.747955\pi\) | |||||||
\(642\) | 1006.23 | + | 900.000i | 1.56734 | + | 1.40187i | ||||
\(643\) | 156.000i | 0.242613i | 0.992615 | + | 0.121306i | \(0.0387084\pi\) | ||||
−0.992615 | + | 0.121306i | \(0.961292\pi\) | |||||||
\(644\) | − | 80.4984i | − | 0.124998i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.0000 | −0.0309598 | ||||||||
\(647\) | 755.791 | 1.16815 | 0.584073 | − | 0.811701i | \(-0.301458\pi\) | ||||
0.584073 | + | 0.811701i | \(0.301458\pi\) | |||||||
\(648\) | −529.948 | + | 120.000i | −0.817821 | + | 0.185185i | ||||
\(649\) | 20.0000 | 0.0308166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −216.000 | + | 241.495i | −0.331797 | + | 0.370961i | ||||
\(652\) | 236.000i | 0.361963i | ||||||||
\(653\) | 487.463 | 0.746497 | 0.373249 | − | 0.927731i | \(-0.378244\pi\) | ||||
0.373249 | + | 0.927731i | \(0.378244\pi\) | |||||||
\(654\) | −190.000 | − | 169.941i | −0.290520 | − | 0.259849i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1189.59i | − | 1.81340i | ||||||
\(657\) | 661.876 | − | 74.0000i | 1.00742 | − | 0.112633i | ||||
\(658\) | 660.000i | 1.00304i | ||||||||
\(659\) | − | 406.964i | − | 0.617548i | −0.951135 | − | 0.308774i | \(-0.900081\pi\) | ||
0.951135 | − | 0.308774i | \(-0.0999187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 682.000 | 1.03177 | 0.515885 | − | 0.856658i | \(-0.327463\pi\) | ||||
0.515885 | + | 0.856658i | \(0.327463\pi\) | |||||||
\(662\) | 442.741 | 0.668794 | ||||||||
\(663\) | 143.108 | − | 160.000i | 0.215850 | − | 0.241327i | ||||
\(664\) | 630.000 | 0.948795 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 320.000 | − | 35.7771i | 0.480480 | − | 0.0537194i | ||||
\(667\) | − | 420.000i | − | 0.629685i | ||||||
\(668\) | 93.9149 | 0.140591 | ||||||||
\(669\) | 172.000 | − | 192.302i | 0.257100 | − | 0.287447i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 366.715i | 0.546520i | ||||||||
\(672\) | 187.830 | − | 210.000i | 0.279508 | − | 0.312500i | ||||
\(673\) | − | 894.000i | − | 1.32838i | −0.747564 | − | 0.664190i | \(-0.768777\pi\) | ||
0.747564 | − | 0.664190i | \(-0.231223\pi\) | |||||||
\(674\) | 881.011i | 1.30714i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −87.0000 | −0.128698 | ||||||||
\(677\) | −550.073 | −0.812515 | −0.406258 | − | 0.913759i | \(-0.633166\pi\) | ||||
−0.406258 | + | 0.913759i | \(0.633166\pi\) | |||||||
\(678\) | −156.525 | − | 140.000i | −0.230862 | − | 0.206490i | ||||
\(679\) | −996.000 | −1.46686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 130.000 | + | 116.276i | 0.190896 | + | 0.170742i | ||||
\(682\) | 180.000i | 0.263930i | ||||||||
\(683\) | −442.741 | −0.648231 | −0.324115 | − | 0.946018i | \(-0.605067\pi\) | ||||
−0.324115 | + | 0.946018i | \(0.605067\pi\) | |||||||
\(684\) | 2.00000 | + | 17.8885i | 0.00292398 | + | 0.0261528i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 831.817i | − | 1.21256i | ||||||
\(687\) | −630.571 | − | 564.000i | −0.917862 | − | 0.820961i | ||||
\(688\) | − | 304.000i | − | 0.441860i | ||||||
\(689\) | − | 71.5542i | − | 0.103852i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −758.000 | −1.09696 | −0.548480 | − | 0.836163i | \(-0.684793\pi\) | ||||
−0.548480 | + | 0.836163i | \(0.684793\pi\) | |||||||
\(692\) | −13.4164 | −0.0193879 | ||||||||
\(693\) | −26.8328 | − | 240.000i | −0.0387198 | − | 0.346320i | ||||
\(694\) | 410.000 | 0.590778 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 420.000 | − | 469.574i | 0.603448 | − | 0.674676i | ||||
\(697\) | 280.000i | 0.401722i | ||||||||
\(698\) | −809.457 | −1.15968 | ||||||||
\(699\) | −810.000 | − | 724.486i | −1.15880 | − | 1.03646i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 782.624i | − | 1.11644i | −0.829693 | − | 0.558220i | \(-0.811485\pi\) | ||
0.829693 | − | 0.558220i | \(-0.188515\pi\) | |||||||
\(702\) | −787.096 | − | 560.000i | −1.12122 | − | 0.797721i | ||||
\(703\) | 32.0000i | 0.0455192i | ||||||||
\(704\) | 183.358i | 0.260451i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −690.000 | −0.977337 | ||||||||
\(707\) | −402.492 | −0.569296 | ||||||||
\(708\) | −8.94427 | + | 10.0000i | −0.0126332 | + | 0.0141243i | ||||
\(709\) | 2.00000 | 0.00282087 | 0.00141044 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00141044 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −138.000 | − | 1234.31i | −0.194093 | − | 1.73602i | ||||
\(712\) | − | 720.000i | − | 1.01124i | ||||||
\(713\) | 241.495 | 0.338703 | ||||||||
\(714\) | −120.000 | + | 134.164i | −0.168067 | + | 0.187905i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 192.302i | − | 0.268578i | ||||||
\(717\) | 500.879 | − | 560.000i | 0.698576 | − | 0.781032i | ||||
\(718\) | 660.000i | 0.919220i | ||||||||
\(719\) | − | 858.650i | − | 1.19423i | −0.802156 | − | 0.597114i | \(-0.796314\pi\) | ||
0.802156 | − | 0.597114i | \(-0.203686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −156.000 | −0.216366 | ||||||||
\(722\) | 798.276 | 1.10565 | ||||||||
\(723\) | −585.850 | − | 524.000i | −0.810304 | − | 0.724758i | ||||
\(724\) | 2.00000 | 0.00276243 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 505.000 | + | 451.686i | 0.695592 | + | 0.622157i | ||||
\(727\) | − | 674.000i | − | 0.927098i | −0.886071 | − | 0.463549i | \(-0.846576\pi\) | ||
0.886071 | − | 0.463549i | \(-0.153424\pi\) | |||||||
\(728\) | −643.988 | −0.884598 | ||||||||
\(729\) | −239.000 | − | 688.709i | −0.327846 | − | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 71.5542i | 0.0978853i | ||||||||
\(732\) | −183.358 | − | 164.000i | −0.250488 | − | 0.224044i | ||||
\(733\) | 656.000i | 0.894952i | 0.894296 | + | 0.447476i | \(0.147677\pi\) | ||||
−0.894296 | + | 0.447476i | \(0.852323\pi\) | |||||||
\(734\) | − | 415.909i | − | 0.566633i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −210.000 | −0.285326 | ||||||||
\(737\) | 107.331 | 0.145633 | ||||||||
\(738\) | 1252.20 | − | 140.000i | 1.69675 | − | 0.189702i | ||||
\(739\) | −598.000 | −0.809202 | −0.404601 | − | 0.914493i | \(-0.632590\pi\) | ||||
−0.404601 | + | 0.914493i | \(0.632590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 64.0000 | − | 71.5542i | 0.0863698 | − | 0.0965643i | ||||
\(742\) | 60.0000i | 0.0808625i | ||||||||
\(743\) | −782.624 | −1.05333 | −0.526665 | − | 0.850073i | \(-0.676558\pi\) | ||||
−0.526665 | + | 0.850073i | \(0.676558\pi\) | |||||||
\(744\) | 270.000 | + | 241.495i | 0.362903 | + | 0.324591i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 98.3870i | 0.131886i | ||||||||
\(747\) | 93.9149 | + | 840.000i | 0.125723 | + | 1.12450i | ||||
\(748\) | 20.0000i | 0.0267380i | ||||||||
\(749\) | 1207.48i | 1.61212i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −338.000 | −0.450067 | −0.225033 | − | 0.974351i | \(-0.572249\pi\) | ||||
−0.225033 | + | 0.974351i | \(0.572249\pi\) | |||||||
\(752\) | 934.676 | 1.24292 | ||||||||
\(753\) | 939.149 | − | 1050.00i | 1.24721 | − | 1.39442i | ||||
\(754\) | 1120.00 | 1.48541 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 132.000 | + | 93.9149i | 0.174603 | + | 0.124226i | ||||
\(757\) | 656.000i | 0.866579i | 0.901255 | + | 0.433289i | \(0.142647\pi\) | ||||
−0.901255 | + | 0.433289i | \(0.857353\pi\) | |||||||
\(758\) | −809.457 | −1.06788 | ||||||||
\(759\) | −120.000 | + | 134.164i | −0.158103 | + | 0.176764i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 295.161i | 0.387859i | 0.981015 | + | 0.193930i | \(0.0621234\pi\) | ||||
−0.981015 | + | 0.193930i | \(0.937877\pi\) | |||||||
\(762\) | −116.276 | + | 130.000i | −0.152593 | + | 0.170604i | ||||
\(763\) | − | 228.000i | − | 0.298820i | ||||||
\(764\) | − | 205.718i | − | 0.269265i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −810.000 | −1.05744 | ||||||||
\(767\) | 71.5542 | 0.0932910 | ||||||||
\(768\) | −404.728 | − | 362.000i | −0.526990 | − | 0.471354i | ||||
\(769\) | 82.0000 | 0.106632 | 0.0533160 | − | 0.998578i | \(-0.483021\pi\) | ||||
0.0533160 | + | 0.998578i | \(0.483021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −450.000 | − | 402.492i | −0.583658 | − | 0.522039i | ||||
\(772\) | − | 214.000i | − | 0.277202i | ||||||
\(773\) | 1059.90 | 1.37115 | 0.685573 | − | 0.728004i | \(-0.259552\pi\) | ||||
0.685573 | + | 0.728004i | \(0.259552\pi\) | |||||||
\(774\) | 320.000 | − | 35.7771i | 0.413437 | − | 0.0462236i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1113.56i | 1.43500i | ||||||||
\(777\) | 214.663 | + | 192.000i | 0.276271 | + | 0.247104i | ||||
\(778\) | 990.000i | 1.27249i | ||||||||
\(779\) | 125.220i | 0.160744i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 560.000 | 0.717029 | ||||||||
\(782\) | 134.164 | 0.171565 | ||||||||
\(783\) | 688.709 | + | 490.000i | 0.879577 | + | 0.625798i | ||||
\(784\) | −247.000 | −0.315051 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −60.0000 | + | 67.0820i | −0.0763359 | + | 0.0853461i | ||||
\(787\) | 536.000i | 0.681067i | 0.940232 | + | 0.340534i | \(0.110608\pi\) | ||||
−0.940232 | + | 0.340534i | \(0.889392\pi\) | |||||||
\(788\) | −93.9149 | −0.119181 | ||||||||
\(789\) | −130.000 | − | 116.276i | −0.164766 | − | 0.147371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 187.830i | − | 0.237459i | ||||||
\(792\) | −268.328 | + | 30.0000i | −0.338798 | + | 0.0378788i | ||||
\(793\) | 1312.00i | 1.65448i | ||||||||
\(794\) | 277.272i | 0.349210i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 242.000 | 0.304020 | ||||||||
\(797\) | −406.964 | −0.510620 | −0.255310 | − | 0.966859i | \(-0.582178\pi\) | ||||
−0.255310 | + | 0.966859i | \(0.582178\pi\) | |||||||
\(798\) | −53.6656 | + | 60.0000i | −0.0672502 | + | 0.0751880i | ||||
\(799\) | −220.000 | −0.275344 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 960.000 | − | 107.331i | 1.19850 | − | 0.133997i | ||||
\(802\) | 600.000i | 0.748130i | ||||||||
\(803\) | 330.938 | 0.412127 | ||||||||
\(804\) | −48.0000 | + | 53.6656i | −0.0597015 | + | 0.0667483i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 643.988i | 0.798992i | ||||||||
\(807\) | 742.375 | − | 830.000i | 0.919919 | − | 1.02850i | ||||
\(808\) | 450.000i | 0.556931i | ||||||||
\(809\) | 1091.20i | 1.34883i | 0.738354 | + | 0.674414i | \(0.235603\pi\) | ||||
−0.738354 | + | 0.674414i | \(0.764397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −558.000 | −0.688039 | −0.344020 | − | 0.938962i | \(-0.611789\pi\) | ||||
−0.344020 | + | 0.938962i | \(0.611789\pi\) | |||||||
\(812\) | −187.830 | −0.231317 | ||||||||
\(813\) | −183.358 | − | 164.000i | −0.225532 | − | 0.201722i | ||||
\(814\) | 160.000 | 0.196560 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 190.000 | + | 169.941i | 0.232843 | + | 0.208261i | ||||
\(817\) | 32.0000i | 0.0391677i | ||||||||
\(818\) | 1024.12 | 1.25198 | ||||||||
\(819\) | −96.0000 | − | 858.650i | −0.117216 | − | 1.04841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 389.076i | 0.473905i | 0.971521 | + | 0.236952i | \(0.0761485\pi\) | ||||
−0.971521 | + | 0.236952i | \(0.923851\pi\) | |||||||
\(822\) | −603.738 | − | 540.000i | −0.734475 | − | 0.656934i | ||||
\(823\) | − | 214.000i | − | 0.260024i | −0.991512 | − | 0.130012i | \(-0.958498\pi\) | ||
0.991512 | − | 0.130012i | \(-0.0415016\pi\) | |||||||
\(824\) | 174.413i | 0.211667i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −60.0000 | −0.0726392 | ||||||||
\(827\) | 31.3050 | 0.0378536 | 0.0189268 | − | 0.999821i | \(-0.493975\pi\) | ||||
0.0189268 | + | 0.999821i | \(0.493975\pi\) | |||||||
\(828\) | −13.4164 | − | 120.000i | −0.0162034 | − | 0.144928i | ||||
\(829\) | −318.000 | −0.383595 | −0.191797 | − | 0.981435i | \(-0.561432\pi\) | ||||
−0.191797 | + | 0.981435i | \(0.561432\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.0000 | + | 53.6656i | −0.0577617 | + | 0.0645796i | ||||
\(832\) | 656.000i | 0.788462i | ||||||||
\(833\) | 58.1378 | 0.0697932 | ||||||||
\(834\) | 410.000 | + | 366.715i | 0.491607 | + | 0.439706i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.94427i | 0.0106989i | ||||||||
\(837\) | −281.745 | + | 396.000i | −0.336612 | + | 0.473118i | ||||
\(838\) | − | 1330.00i | − | 1.58711i | ||||||
\(839\) | − | 62.6099i | − | 0.0746244i | −0.999304 | − | 0.0373122i | \(-0.988120\pi\) | ||
0.999304 | − | 0.0373122i | \(-0.0118796\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −139.000 | −0.165279 | ||||||||
\(842\) | −1256.67 | −1.49248 | ||||||||
\(843\) | −375.659 | + | 420.000i | −0.445622 | + | 0.498221i | ||||
\(844\) | 2.00000 | 0.00236967 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 110.000 | + | 983.870i | 0.130024 | + | 1.16297i | ||||
\(847\) | 606.000i | 0.715466i | ||||||||
\(848\) | 84.9706 | 0.100201 | ||||||||
\(849\) | −288.000 | + | 321.994i | −0.339223 | + | 0.379262i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 214.663i | − | 0.252247i | ||||||
\(852\) | −250.440 | + | 280.000i | −0.293943 | + | 0.328638i | ||||
\(853\) | − | 684.000i | − | 0.801876i | −0.916105 | − | 0.400938i | \(-0.868684\pi\) | ||
0.916105 | − | 0.400938i | \(-0.131316\pi\) | |||||||
\(854\) | − | 1100.15i | − | 1.28823i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1350.00 | 1.57710 | ||||||||
\(857\) | −1498.17 | −1.74815 | −0.874076 | − | 0.485790i | \(-0.838532\pi\) | ||||
−0.874076 | + | 0.485790i | \(0.838532\pi\) | |||||||
\(858\) | −357.771 | − | 320.000i | −0.416982 | − | 0.372960i | ||||
\(859\) | 842.000 | 0.980210 | 0.490105 | − | 0.871664i | \(-0.336959\pi\) | ||||
0.490105 | + | 0.871664i | \(0.336959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 840.000 | + | 751.319i | 0.975610 | + | 0.872612i | ||||
\(862\) | − | 780.000i | − | 0.904872i | ||||||
\(863\) | −1015.17 | −1.17633 | −0.588166 | − | 0.808740i | \(-0.700150\pi\) | ||||
−0.588166 | + | 0.808740i | \(0.700150\pi\) | |||||||
\(864\) | 245.000 | − | 344.354i | 0.283565 | − | 0.398558i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 505.351i | − | 0.583547i | ||||||
\(867\) | 601.502 | + | 538.000i | 0.693774 | + | 0.620531i | ||||
\(868\) | − | 108.000i | − | 0.124424i | ||||||
\(869\) | − | 617.155i | − | 0.710190i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 384.000 | 0.440873 | ||||||||
\(872\) | −254.912 | −0.292330 | ||||||||
\(873\) | −1484.75 | + | 166.000i | −1.70074 | + | 0.190149i | ||||
\(874\) | 60.0000 | 0.0686499 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −148.000 | + | 165.469i | −0.168950 | + | 0.188892i | ||||
\(877\) | 156.000i | 0.177879i | 0.996037 | + | 0.0889396i | \(0.0283478\pi\) | ||||
−0.996037 | + | 0.0889396i | \(0.971652\pi\) | |||||||
\(878\) | −4.47214 | −0.00509355 | ||||||||
\(879\) | 1050.00 | + | 939.149i | 1.19454 | + | 1.06843i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 125.220i | 0.142134i | 0.997472 | + | 0.0710669i | \(0.0226404\pi\) | ||||
−0.997472 | + | 0.0710669i | \(0.977360\pi\) | |||||||
\(882\) | −29.0689 | − | 260.000i | −0.0329579 | − | 0.294785i | ||||
\(883\) | − | 964.000i | − | 1.09173i | −0.837872 | − | 0.545866i | \(-0.816201\pi\) | ||
0.837872 | − | 0.545866i | \(-0.183799\pi\) | |||||||
\(884\) | 71.5542i | 0.0809436i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 450.000 | 0.507901 | ||||||||
\(887\) | 952.565 | 1.07392 | 0.536959 | − | 0.843608i | \(-0.319573\pi\) | ||||
0.536959 | + | 0.843608i | \(0.319573\pi\) | |||||||
\(888\) | 214.663 | − | 240.000i | 0.241737 | − | 0.270270i | ||||
\(889\) | −156.000 | −0.175478 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −80.0000 | − | 353.299i | −0.0897868 | − | 0.396519i | ||||
\(892\) | 86.0000i | 0.0964126i | ||||||||
\(893\) | −98.3870 | −0.110176 | ||||||||
\(894\) | −500.000 | + | 559.017i | −0.559284 | + | 0.625299i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 925.732i | − | 1.03318i | ||||||
\(897\) | −429.325 | + | 480.000i | −0.478623 | + | 0.535117i | ||||
\(898\) | 700.000i | 0.779510i | ||||||||
\(899\) | − | 563.489i | − | 0.626795i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | −0.0221976 | ||||||||
\(902\) | 626.099 | 0.694123 | ||||||||
\(903\) | 214.663 | + | 192.000i | 0.237722 | + | 0.212625i | ||||
\(904\) | −210.000 | −0.232301 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −790.000 | − | 706.597i | −0.871965 | − | 0.779909i | ||||
\(907\) | − | 1284.00i | − | 1.41566i | −0.706385 | − | 0.707828i | \(-0.749675\pi\) | ||
0.706385 | − | 0.707828i | \(-0.250325\pi\) | |||||||
\(908\) | −58.1378 | −0.0640284 | ||||||||
\(909\) | −600.000 | + | 67.0820i | −0.660066 | + | 0.0737976i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 62.6099i | − | 0.0687266i | −0.999409 | − | 0.0343633i | \(-0.989060\pi\) | ||
0.999409 | − | 0.0343633i | \(-0.0109403\pi\) | |||||||
\(912\) | 84.9706 | + | 76.0000i | 0.0931695 | + | 0.0833333i | ||||
\(913\) | 420.000i | 0.460022i | ||||||||
\(914\) | 746.847i | 0.817119i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 282.000 | 0.307860 | ||||||||
\(917\) | −80.4984 | −0.0877846 | ||||||||
\(918\) | −156.525 | + | 220.000i | −0.170506 | + | 0.239651i | ||||
\(919\) | −418.000 | −0.454842 | −0.227421 | − | 0.973797i | \(-0.573029\pi\) | ||||
−0.227421 | + | 0.973797i | \(0.573029\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −368.000 | + | 411.437i | −0.399566 | + | 0.446728i | ||||
\(922\) | − | 210.000i | − | 0.227766i | ||||||
\(923\) | 2003.52 | 2.17066 | ||||||||
\(924\) | 60.0000 | + | 53.6656i | 0.0649351 | + | 0.0580797i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 818.401i | − | 0.883802i | ||||||
\(927\) | −232.551 | + | 26.0000i | −0.250864 | + | 0.0280475i | ||||
\(928\) | 490.000i | 0.528017i | ||||||||
\(929\) | − | 169.941i | − | 0.182929i | −0.995808 | − | 0.0914646i | \(-0.970845\pi\) | ||
0.995808 | − | 0.0914646i | \(-0.0291548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.0000 | 0.0279270 | ||||||||
\(932\) | 362.243 | 0.388673 | ||||||||
\(933\) | 321.994 | − | 360.000i | 0.345117 | − | 0.385852i | ||||
\(934\) | −1010.00 | −1.08137 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −960.000 | + | 107.331i | −1.02564 | + | 0.114670i | ||||
\(937\) | − | 534.000i | − | 0.569904i | −0.958542 | − | 0.284952i | \(-0.908022\pi\) | ||
0.958542 | − | 0.284952i | \(-0.0919777\pi\) | |||||||
\(938\) | −321.994 | −0.343277 | ||||||||
\(939\) | −788.000 | + | 881.011i | −0.839191 | + | 0.938244i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 129.692i | 0.137824i | 0.997623 | + | 0.0689118i | \(0.0219527\pi\) | ||||
−0.997623 | + | 0.0689118i | \(0.978047\pi\) | |||||||
\(942\) | 733.430 | − | 820.000i | 0.778588 | − | 0.870488i | ||||
\(943\) | − | 840.000i | − | 0.890774i | ||||||
\(944\) | 84.9706i | 0.0900112i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 160.000 | 0.169133 | ||||||||
\(947\) | 1516.05 | 1.60090 | 0.800451 | − | 0.599398i | \(-0.204593\pi\) | ||||
0.800451 | + | 0.599398i | \(0.204593\pi\) | |||||||
\(948\) | 308.577 | + | 276.000i | 0.325504 | + | 0.291139i | ||||
\(949\) | 1184.00 | 1.24763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1010.00 | − | 903.371i | −1.06204 | − | 0.949917i | ||||
\(952\) | 180.000i | 0.189076i | ||||||||
\(953\) | −406.964 | −0.427035 | −0.213518 | − | 0.976939i | \(-0.568492\pi\) | ||||
−0.213518 | + | 0.976939i | \(0.568492\pi\) | |||||||
\(954\) | 10.0000 | + | 89.4427i | 0.0104822 | + | 0.0937555i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 250.440i | 0.261966i | ||||||||
\(957\) | 313.050 | + | 280.000i | 0.327115 | + | 0.292581i | ||||
\(958\) | − | 1320.00i | − | 1.37787i | ||||||
\(959\) | − | 724.486i | − | 0.755460i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −637.000 | −0.662851 | ||||||||
\(962\) | 572.433 | 0.595045 | ||||||||
\(963\) | 201.246 | + | 1800.00i | 0.208978 | + | 1.86916i | ||||
\(964\) | 262.000 | 0.271784 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 360.000 | − | 402.492i | 0.372671 | − | 0.416659i | ||||
\(967\) | − | 674.000i | − | 0.697001i | −0.937309 | − | 0.348501i | \(-0.886691\pi\) | ||
0.937309 | − | 0.348501i | \(-0.113309\pi\) | |||||||
\(968\) | 677.529 | 0.699926 | ||||||||
\(969\) | −20.0000 | − | 17.8885i | −0.0206398 | − | 0.0184608i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1328.22i | 1.36789i | 0.729532 | + | 0.683947i | \(0.239738\pi\) | ||||
−0.729532 | + | 0.683947i | \(0.760262\pi\) | |||||||
\(972\) | 212.426 | + | 118.000i | 0.218546 | + | 0.121399i | ||||
\(973\) | 492.000i | 0.505653i | ||||||||
\(974\) | − | 1981.16i | − | 2.03404i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1558.00 | −1.59631 | ||||||||
\(977\) | −371.187 | −0.379926 | −0.189963 | − | 0.981791i | \(-0.560837\pi\) | ||||
−0.189963 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(978\) | −1055.42 | + | 1180.00i | −1.07917 | + | 1.20654i | ||||
\(979\) | 480.000 | 0.490296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.0000 | − | 339.882i | −0.0387360 | − | 0.346465i | ||||
\(982\) | 910.000i | 0.926680i | ||||||||
\(983\) | −442.741 | −0.450398 | −0.225199 | − | 0.974313i | \(-0.572303\pi\) | ||||
−0.225199 | + | 0.974313i | \(0.572303\pi\) | |||||||
\(984\) | 840.000 | − | 939.149i | 0.853659 | − | 0.954419i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 313.050i | − | 0.317494i | ||||||
\(987\) | −590.322 | + | 660.000i | −0.598097 | + | 0.668693i | ||||
\(988\) | 32.0000i | 0.0323887i | ||||||||
\(989\) | − | 214.663i | − | 0.217050i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 962.000 | 0.970737 | 0.485368 | − | 0.874310i | \(-0.338686\pi\) | ||||
0.485368 | + | 0.874310i | \(0.338686\pi\) | |||||||
\(992\) | −281.745 | −0.284017 | ||||||||
\(993\) | 442.741 | + | 396.000i | 0.445862 | + | 0.398792i | ||||
\(994\) | −1680.00 | −1.69014 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −210.000 | − | 187.830i | −0.210843 | − | 0.188584i | ||||
\(997\) | − | 24.0000i | − | 0.0240722i | −0.999928 | − | 0.0120361i | \(-0.996169\pi\) | ||
0.999928 | − | 0.0120361i | \(-0.00383130\pi\) | |||||||
\(998\) | −4.47214 | −0.00448110 | ||||||||
\(999\) | 352.000 | + | 250.440i | 0.352352 | + | 0.250690i |
(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 | 75.3.d.b.74.1 | 4 | ||
3.2 | odd | 2 | inner | 75.3.d.b.74.3 | 4 | ||
4.3 | odd | 2 | 1200.3.c.f.449.4 | 4 | |||
5.2 | odd | 4 | 15.3.c.a.11.1 | ✓ | 2 | ||
5.3 | odd | 4 | 75.3.c.e.26.2 | 2 | |||
5.4 | even | 2 | inner | 75.3.d.b.74.4 | 4 | ||
12.11 | even | 2 | 1200.3.c.f.449.2 | 4 | |||
15.2 | even | 4 | 15.3.c.a.11.2 | yes | 2 | ||
15.8 | even | 4 | 75.3.c.e.26.1 | 2 | |||
15.14 | odd | 2 | inner | 75.3.d.b.74.2 | 4 | ||
20.3 | even | 4 | 1200.3.l.g.401.2 | 2 | |||
20.7 | even | 4 | 240.3.l.b.161.1 | 2 | |||
20.19 | odd | 2 | 1200.3.c.f.449.1 | 4 | |||
40.27 | even | 4 | 960.3.l.b.641.2 | 2 | |||
40.37 | odd | 4 | 960.3.l.c.641.1 | 2 | |||
45.2 | even | 12 | 405.3.i.b.296.2 | 4 | |||
45.7 | odd | 12 | 405.3.i.b.296.1 | 4 | |||
45.22 | odd | 12 | 405.3.i.b.26.2 | 4 | |||
45.32 | even | 12 | 405.3.i.b.26.1 | 4 | |||
60.23 | odd | 4 | 1200.3.l.g.401.1 | 2 | |||
60.47 | odd | 4 | 240.3.l.b.161.2 | 2 | |||
60.59 | even | 2 | 1200.3.c.f.449.3 | 4 | |||
120.77 | even | 4 | 960.3.l.c.641.2 | 2 | |||
120.107 | odd | 4 | 960.3.l.b.641.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.c.a.11.1 | ✓ | 2 | 5.2 | odd | 4 | ||
15.3.c.a.11.2 | yes | 2 | 15.2 | even | 4 | ||
75.3.c.e.26.1 | 2 | 15.8 | even | 4 | |||
75.3.c.e.26.2 | 2 | 5.3 | odd | 4 | |||
75.3.d.b.74.1 | 4 | 1.1 | even | 1 | trivial | ||
75.3.d.b.74.2 | 4 | 15.14 | odd | 2 | inner | ||
75.3.d.b.74.3 | 4 | 3.2 | odd | 2 | inner | ||
75.3.d.b.74.4 | 4 | 5.4 | even | 2 | inner | ||
240.3.l.b.161.1 | 2 | 20.7 | even | 4 | |||
240.3.l.b.161.2 | 2 | 60.47 | odd | 4 | |||
405.3.i.b.26.1 | 4 | 45.32 | even | 12 | |||
405.3.i.b.26.2 | 4 | 45.22 | odd | 12 | |||
405.3.i.b.296.1 | 4 | 45.7 | odd | 12 | |||
405.3.i.b.296.2 | 4 | 45.2 | even | 12 | |||
960.3.l.b.641.1 | 2 | 120.107 | odd | 4 | |||
960.3.l.b.641.2 | 2 | 40.27 | even | 4 | |||
960.3.l.c.641.1 | 2 | 40.37 | odd | 4 | |||
960.3.l.c.641.2 | 2 | 120.77 | even | 4 | |||
1200.3.c.f.449.1 | 4 | 20.19 | odd | 2 | |||
1200.3.c.f.449.2 | 4 | 12.11 | even | 2 | |||
1200.3.c.f.449.3 | 4 | 60.59 | even | 2 | |||
1200.3.c.f.449.4 | 4 | 4.3 | odd | 2 | |||
1200.3.l.g.401.1 | 2 | 60.23 | odd | 4 | |||
1200.3.l.g.401.2 | 2 | 20.3 | even | 4 |