Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 74 x^{14} + 4007 x^{12} + 91050 x^{10} + 1502189 x^{8} + 12598332 x^{6} + 74261084 x^{4} + 22070000 x^{2} + 6250000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.5 | ||
Root | \(0.272818 + 0.472535i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.z.226.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.979925 | + | 1.69728i | 0.346456 | + | 0.600079i | 0.985617 | − | 0.168994i | \(-0.0540517\pi\) |
−0.639161 | + | 0.769073i | \(0.720718\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.07949 | − | 3.60179i | 0.259937 | − | 0.450224i | ||||
\(5\) | −5.94483 | − | 10.2967i | −0.531722 | − | 0.920969i | −0.999314 | − | 0.0370251i | \(-0.988212\pi\) |
0.467593 | − | 0.883944i | \(-0.345121\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 23.8298 | 1.05314 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.6510 | − | 20.1801i | 0.368436 | − | 0.638150i | ||||
\(11\) | 18.2065 | − | 31.5346i | 0.499043 | − | 0.864367i | −0.500957 | − | 0.865472i | \(-0.667018\pi\) |
0.999999 | + | 0.00110512i | \(0.000351770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.964525 | −0.0205778 | −0.0102889 | − | 0.999947i | \(-0.503275\pi\) | ||||
−0.0102889 | + | 0.999947i | \(0.503275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.71545 | + | 11.6315i | 0.104929 | + | 0.181742i | ||||
\(17\) | −49.1257 | + | 85.0882i | −0.700866 | + | 1.21394i | 0.267296 | + | 0.963614i | \(0.413870\pi\) |
−0.968163 | + | 0.250322i | \(0.919464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −53.0004 | − | 91.7994i | −0.639954 | − | 1.10843i | −0.985442 | − | 0.170010i | \(-0.945620\pi\) |
0.345488 | − | 0.938423i | \(-0.387713\pi\) | |||||||
\(20\) | −49.4490 | −0.552856 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 71.3640 | 0.691585 | ||||||||
\(23\) | 27.1816 | + | 47.0800i | 0.246424 | + | 0.426820i | 0.962531 | − | 0.271171i | \(-0.0874110\pi\) |
−0.716107 | + | 0.697991i | \(0.754078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.18202 | + | 14.1717i | −0.0654562 | + | 0.113373i | ||||
\(26\) | −0.945162 | − | 1.63707i | −0.00712929 | − | 0.0123483i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −229.725 | −1.47099 | −0.735497 | − | 0.677528i | \(-0.763051\pi\) | ||||
−0.735497 | + | 0.677528i | \(0.763051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 63.8645 | − | 110.616i | 0.370013 | − | 0.640881i | −0.619554 | − | 0.784954i | \(-0.712687\pi\) |
0.989567 | + | 0.144073i | \(0.0460200\pi\) | |||||||
\(32\) | 82.1579 | − | 142.302i | 0.453863 | − | 0.786113i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −192.558 | −0.971277 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −155.908 | − | 270.040i | −0.692732 | − | 1.19985i | −0.970939 | − | 0.239326i | \(-0.923073\pi\) |
0.278207 | − | 0.960521i | \(-0.410260\pi\) | |||||||
\(38\) | 103.873 | − | 179.913i | 0.443432 | − | 0.768046i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −141.664 | − | 245.369i | −0.559976 | − | 0.969908i | ||||
\(41\) | −419.919 | −1.59952 | −0.799760 | − | 0.600320i | \(-0.795040\pi\) | ||||
−0.799760 | + | 0.600320i | \(0.795040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 523.180 | 1.85545 | 0.927723 | − | 0.373270i | \(-0.121763\pi\) | ||||
0.927723 | + | 0.373270i | \(0.121763\pi\) | |||||||
\(44\) | −75.7207 | − | 131.152i | −0.259439 | − | 0.449362i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −53.2719 | + | 92.2697i | −0.170750 | + | 0.295748i | ||||
\(47\) | −135.164 | − | 234.111i | −0.419483 | − | 0.726566i | 0.576404 | − | 0.817165i | \(-0.304455\pi\) |
−0.995887 | + | 0.0905985i | \(0.971122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −32.0711 | −0.0907107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00572 | + | 3.47402i | −0.00534892 | + | 0.00926460i | ||||
\(53\) | −125.541 | + | 217.443i | −0.325366 | + | 0.563550i | −0.981586 | − | 0.191019i | \(-0.938821\pi\) |
0.656221 | + | 0.754569i | \(0.272154\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −432.938 | −1.06141 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −225.113 | − | 389.907i | −0.509634 | − | 0.882712i | ||||
\(59\) | −204.015 | + | 353.364i | −0.450177 | + | 0.779729i | −0.998397 | − | 0.0566051i | \(-0.981972\pi\) |
0.548220 | + | 0.836334i | \(0.315306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −430.273 | − | 745.255i | −0.903128 | − | 1.56426i | −0.823411 | − | 0.567446i | \(-0.807932\pi\) |
−0.0797171 | − | 0.996818i | \(-0.525402\pi\) | |||||||
\(62\) | 250.329 | 0.512772 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 429.481 | 0.838831 | ||||||||
\(65\) | 5.73394 | + | 9.93147i | 0.0109417 | + | 0.0189515i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −253.180 | + | 438.520i | −0.461654 | + | 0.799609i | −0.999044 | − | 0.0437257i | \(-0.986077\pi\) |
0.537389 | + | 0.843334i | \(0.319411\pi\) | |||||||
\(68\) | 204.313 | + | 353.881i | 0.364362 | + | 0.631093i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 523.702 | 0.875380 | 0.437690 | − | 0.899126i | \(-0.355797\pi\) | ||||
0.437690 | + | 0.899126i | \(0.355797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 314.982 | − | 545.565i | 0.505012 | − | 0.874706i | −0.494972 | − | 0.868909i | \(-0.664822\pi\) |
0.999983 | − | 0.00579655i | \(-0.00184511\pi\) | |||||||
\(74\) | 305.556 | − | 529.239i | 0.480002 | − | 0.831388i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −440.856 | −0.665391 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −159.774 | − | 276.737i | −0.227544 | − | 0.394118i | 0.729535 | − | 0.683943i | \(-0.239736\pi\) |
−0.957080 | + | 0.289825i | \(0.906403\pi\) | |||||||
\(80\) | 79.8444 | − | 138.295i | 0.111586 | − | 0.193273i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −411.489 | − | 712.720i | −0.554163 | − | 0.959838i | ||||
\(83\) | 1309.16 | 1.73131 | 0.865654 | − | 0.500643i | \(-0.166903\pi\) | ||||
0.865654 | + | 0.500643i | \(0.166903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1168.18 | 1.49066 | ||||||||
\(86\) | 512.677 | + | 887.982i | 0.642830 | + | 1.11341i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 433.857 | − | 751.463i | 0.525561 | − | 0.910298i | ||||
\(89\) | 174.290 | + | 301.880i | 0.207581 | + | 0.359542i | 0.950952 | − | 0.309338i | \(-0.100107\pi\) |
−0.743371 | + | 0.668880i | \(0.766774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 226.096 | 0.256219 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 264.901 | − | 458.822i | 0.290665 | − | 0.503446i | ||||
\(95\) | −630.157 | + | 1091.46i | −0.680555 | + | 1.17876i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 161.996 | 0.169569 | 0.0847844 | − | 0.996399i | \(-0.472980\pi\) | ||||
0.0847844 | + | 0.996399i | \(0.472980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 34.0289 | + | 58.9399i | 0.0340289 | + | 0.0589399i | ||||
\(101\) | 109.171 | − | 189.090i | 0.107554 | − | 0.186289i | −0.807225 | − | 0.590244i | \(-0.799032\pi\) |
0.914779 | + | 0.403955i | \(0.132365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −115.545 | − | 200.130i | −0.110534 | − | 0.191451i | 0.805452 | − | 0.592661i | \(-0.201923\pi\) |
−0.915986 | + | 0.401211i | \(0.868589\pi\) | |||||||
\(104\) | −22.9844 | −0.0216712 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −492.083 | −0.450899 | ||||||||
\(107\) | −932.562 | − | 1615.25i | −0.842563 | − | 1.45936i | −0.887721 | − | 0.460381i | \(-0.847713\pi\) |
0.0451586 | − | 0.998980i | \(-0.485621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −300.502 | + | 520.485i | −0.264063 | + | 0.457371i | −0.967318 | − | 0.253567i | \(-0.918396\pi\) |
0.703255 | + | 0.710938i | \(0.251729\pi\) | |||||||
\(110\) | −424.247 | − | 734.818i | −0.367731 | − | 0.636928i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 475.349 | 0.395727 | 0.197863 | − | 0.980230i | \(-0.436600\pi\) | ||||
0.197863 | + | 0.980230i | \(0.436600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 323.180 | − | 559.765i | 0.262058 | − | 0.453899i | ||||
\(116\) | −477.711 | + | 827.420i | −0.382365 | + | 0.662276i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −799.676 | −0.623865 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54607 | + | 4.40992i | 0.00191290 | + | 0.00331324i | ||||
\(122\) | 843.270 | − | 1460.59i | 0.625788 | − | 1.08390i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −265.612 | − | 460.053i | −0.192360 | − | 0.333177i | ||||
\(125\) | −1291.64 | −0.924226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29.0876 | −0.0203237 | −0.0101619 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101619 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(128\) | −236.404 | − | 409.463i | −0.163245 | − | 0.282748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.2377 | + | 19.4642i | −0.00758160 | + | 0.0131317i | ||||
\(131\) | 1057.63 | + | 1831.87i | 0.705387 | + | 1.22177i | 0.966552 | + | 0.256472i | \(0.0825603\pi\) |
−0.261164 | + | 0.965294i | \(0.584106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −992.389 | −0.639771 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1170.65 | + | 2027.63i | −0.738109 | + | 1.27844i | ||||
\(137\) | 88.6708 | − | 153.582i | 0.0552968 | − | 0.0957768i | −0.837052 | − | 0.547123i | \(-0.815723\pi\) |
0.892349 | + | 0.451347i | \(0.149056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2369.18 | 1.44569 | 0.722846 | − | 0.691009i | \(-0.242834\pi\) | ||||
0.722846 | + | 0.691009i | \(0.242834\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 513.189 | + | 888.869i | 0.303281 | + | 0.525297i | ||||
\(143\) | −17.5606 | + | 30.4159i | −0.0102692 | + | 0.0177868i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1365.67 | + | 2365.42i | 0.782159 | + | 1.35474i | ||||
\(146\) | 1234.63 | 0.699857 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1296.84 | −0.720266 | ||||||||
\(149\) | 745.517 | + | 1291.27i | 0.409900 | + | 0.709968i | 0.994878 | − | 0.101081i | \(-0.0322301\pi\) |
−0.584978 | + | 0.811049i | \(0.698897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −205.230 | + | 355.469i | −0.110605 | + | 0.191574i | −0.916014 | − | 0.401145i | \(-0.868612\pi\) |
0.805409 | + | 0.592719i | \(0.201946\pi\) | |||||||
\(152\) | −1262.99 | − | 2187.56i | −0.673960 | − | 1.16733i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1518.65 | −0.786975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −226.750 | + | 392.743i | −0.115265 | + | 0.199645i | −0.917886 | − | 0.396845i | \(-0.870105\pi\) |
0.802621 | + | 0.596490i | \(0.203438\pi\) | |||||||
\(158\) | 313.133 | − | 542.363i | 0.157668 | − | 0.273089i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1953.66 | −0.965314 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −374.083 | − | 647.931i | −0.179757 | − | 0.311349i | 0.762040 | − | 0.647530i | \(-0.224198\pi\) |
−0.941797 | + | 0.336181i | \(0.890865\pi\) | |||||||
\(164\) | −873.219 | + | 1512.46i | −0.415774 | + | 0.720142i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1282.87 | + | 2222.00i | 0.599821 | + | 1.03892i | ||||
\(167\) | −518.269 | −0.240149 | −0.120074 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120074 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.07 | −0.999577 | ||||||||
\(170\) | 1144.72 | + | 1982.72i | 0.516449 | + | 0.894516i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1087.95 | − | 1884.38i | 0.482299 | − | 0.835366i | ||||
\(173\) | 656.742 | + | 1137.51i | 0.288620 | + | 0.499904i | 0.973480 | − | 0.228770i | \(-0.0734704\pi\) |
−0.684861 | + | 0.728674i | \(0.740137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 489.060 | 0.209456 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −341.583 | + | 591.639i | −0.143836 | + | 0.249131i | ||||
\(179\) | 2066.57 | − | 3579.41i | 0.862921 | − | 1.49462i | −0.00617538 | − | 0.999981i | \(-0.501966\pi\) |
0.869097 | − | 0.494642i | \(-0.164701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3714.04 | 1.52521 | 0.762603 | − | 0.646867i | \(-0.223921\pi\) | ||||
0.762603 | + | 0.646867i | \(0.223921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 647.733 | + | 1121.91i | 0.259519 | + | 0.449500i | ||||
\(185\) | −1853.69 | + | 3210.69i | −0.736682 | + | 1.27597i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1788.81 | + | 3098.32i | 0.699524 | + | 1.21161i | ||||
\(188\) | −1124.29 | −0.436156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2470.03 | −0.943129 | ||||||||
\(191\) | −1534.19 | − | 2657.29i | −0.581203 | − | 1.00667i | −0.995337 | − | 0.0964578i | \(-0.969249\pi\) |
0.414134 | − | 0.910216i | \(-0.364085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1044.77 | + | 1809.59i | −0.389657 | + | 0.674906i | −0.992403 | − | 0.123027i | \(-0.960740\pi\) |
0.602746 | + | 0.797933i | \(0.294073\pi\) | |||||||
\(194\) | 158.744 | + | 274.952i | 0.0587481 | + | 0.101755i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3729.89 | 1.34895 | 0.674476 | − | 0.738297i | \(-0.264370\pi\) | ||||
0.674476 | + | 0.738297i | \(0.264370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1054.42 | + | 1826.31i | −0.375608 | + | 0.650573i | −0.990418 | − | 0.138103i | \(-0.955900\pi\) |
0.614809 | + | 0.788676i | \(0.289233\pi\) | |||||||
\(200\) | −194.976 | + | 337.708i | −0.0689344 | + | 0.119398i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 427.918 | 0.149051 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2496.35 | + | 4323.80i | 0.850499 | + | 1.47311i | ||||
\(206\) | 226.451 | − | 392.225i | 0.0765903 | − | 0.132658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.47722 | − | 11.2189i | −0.00215920 | − | 0.00373985i | ||||
\(209\) | −3859.81 | −1.27746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1546.53 | −0.504584 | −0.252292 | − | 0.967651i | \(-0.581184\pi\) | ||||
−0.252292 | + | 0.967651i | \(0.581184\pi\) | |||||||
\(212\) | 522.124 | + | 904.345i | 0.169149 | + | 0.292975i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1827.68 | − | 3165.64i | 0.583821 | − | 1.01121i | ||||
\(215\) | −3110.22 | − | 5387.05i | −0.986581 | − | 1.70881i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1177.88 | −0.365945 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −900.293 | + | 1559.35i | −0.275899 | + | 0.477871i | ||||
\(221\) | 47.3829 | − | 82.0697i | 0.0144223 | − | 0.0249801i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4860.40 | 1.45954 | 0.729768 | − | 0.683695i | \(-0.239628\pi\) | ||||
0.729768 | + | 0.683695i | \(0.239628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 465.807 | + | 806.801i | 0.137102 | + | 0.237467i | ||||
\(227\) | 350.471 | − | 607.034i | 0.102474 | − | 0.177490i | −0.810229 | − | 0.586113i | \(-0.800658\pi\) |
0.912703 | + | 0.408623i | \(0.133991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1847.12 | + | 3199.30i | 0.533018 | + | 0.923214i | 0.999256 | + | 0.0385550i | \(0.0122755\pi\) |
−0.466239 | + | 0.884659i | \(0.654391\pi\) | |||||||
\(230\) | 1266.77 | 0.363167 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5474.29 | −1.54916 | ||||||||
\(233\) | 172.161 | + | 298.192i | 0.0484062 | + | 0.0838420i | 0.889213 | − | 0.457493i | \(-0.151252\pi\) |
−0.840807 | + | 0.541335i | \(0.817919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1607.06 | + | 2783.50i | −0.446097 | + | 0.772662i | ||||
\(236\) | 848.494 | + | 1469.64i | 0.234035 | + | 0.405361i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6144.21 | −1.66291 | −0.831456 | − | 0.555590i | \(-0.812492\pi\) | ||||
−0.831456 | + | 0.555590i | \(0.812492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2813.06 | − | 4872.36i | 0.751888 | − | 1.30231i | −0.195019 | − | 0.980799i | \(-0.562477\pi\) |
0.946907 | − | 0.321508i | \(-0.104190\pi\) | |||||||
\(242\) | −4.98991 | + | 8.64277i | −0.00132547 | + | 0.00229578i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3579.00 | −0.939025 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51.1202 | + | 88.5429i | 0.0131688 | + | 0.0228091i | ||||
\(248\) | 1521.88 | − | 2635.97i | 0.389674 | − | 0.674936i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1265.71 | − | 2192.28i | −0.320203 | − | 0.554608i | ||||
\(251\) | 520.460 | 0.130881 | 0.0654405 | − | 0.997856i | \(-0.479155\pi\) | ||||
0.0654405 | + | 0.997856i | \(0.479155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1979.53 | 0.491905 | ||||||||
\(254\) | −28.5037 | − | 49.3699i | −0.00704127 | − | 0.0121958i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2181.24 | − | 3778.02i | 0.532530 | − | 0.922368i | ||||
\(257\) | 2004.75 | + | 3472.33i | 0.486587 | + | 0.842794i | 0.999881 | − | 0.0154192i | \(-0.00490827\pi\) |
−0.513294 | + | 0.858213i | \(0.671575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 47.6948 | 0.0113766 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2072.80 | + | 3590.20i | −0.488771 | + | 0.846576i | ||||
\(263\) | −1792.60 | + | 3104.87i | −0.420290 | + | 0.727963i | −0.995968 | − | 0.0897135i | \(-0.971405\pi\) |
0.575678 | + | 0.817677i | \(0.304738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2985.28 | 0.692016 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1052.97 | + | 1823.80i | 0.240002 | + | 0.415695i | ||||
\(269\) | 2754.59 | − | 4771.10i | 0.624352 | − | 1.08141i | −0.364314 | − | 0.931276i | \(-0.618697\pi\) |
0.988666 | − | 0.150133i | \(-0.0479700\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2909.95 | + | 5040.18i | 0.652276 | + | 1.12977i | 0.982569 | + | 0.185896i | \(0.0595189\pi\) |
−0.330294 | + | 0.943878i | \(0.607148\pi\) | |||||||
\(272\) | −1319.60 | −0.294165 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 347.563 | 0.0766316 | ||||||||
\(275\) | 297.932 | + | 516.034i | 0.0653308 | + | 0.113156i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 575.226 | − | 996.320i | 0.124772 | − | 0.216112i | −0.796872 | − | 0.604149i | \(-0.793513\pi\) |
0.921644 | + | 0.388037i | \(0.126847\pi\) | |||||||
\(278\) | 2321.62 | + | 4021.16i | 0.500868 | + | 0.867529i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 895.631 | 0.190138 | 0.0950692 | − | 0.995471i | \(-0.469693\pi\) | ||||
0.0950692 | + | 0.995471i | \(0.469693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −61.2251 | + | 106.045i | −0.0128603 | + | 0.0222746i | −0.872384 | − | 0.488821i | \(-0.837427\pi\) |
0.859524 | + | 0.511096i | \(0.170760\pi\) | |||||||
\(284\) | 1089.04 | − | 1886.27i | 0.227544 | − | 0.394117i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −68.8324 | −0.0142313 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2370.16 | − | 4105.24i | −0.482427 | − | 0.835588i | ||||
\(290\) | −2676.52 | + | 4635.86i | −0.541967 | + | 0.938715i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1310.01 | − | 2269.00i | −0.262542 | − | 0.454736i | ||||
\(293\) | 7601.77 | 1.51570 | 0.757850 | − | 0.652429i | \(-0.226250\pi\) | ||||
0.757850 | + | 0.652429i | \(0.226250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4851.33 | 0.957475 | ||||||||
\(296\) | −3715.25 | − | 6435.01i | −0.729543 | − | 1.26360i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1461.10 | + | 2530.70i | −0.284025 | + | 0.491945i | ||||
\(299\) | −26.2174 | − | 45.4098i | −0.00507087 | − | 0.00878300i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −804.441 | −0.153279 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 711.844 | − | 1232.95i | 0.134299 | − | 0.232613i | ||||
\(305\) | −5115.80 | + | 8860.82i | −0.960426 | + | 1.66351i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3539.05 | −0.657929 | −0.328964 | − | 0.944342i | \(-0.606700\pi\) | ||||
−0.328964 | + | 0.944342i | \(0.606700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1488.17 | − | 2577.58i | −0.272652 | − | 0.472247i | ||||
\(311\) | −1947.47 | + | 3373.11i | −0.355083 | + | 0.615021i | −0.987132 | − | 0.159907i | \(-0.948881\pi\) |
0.632049 | + | 0.774928i | \(0.282214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4341.29 | − | 7519.33i | −0.783975 | − | 1.35788i | −0.929610 | − | 0.368546i | \(-0.879856\pi\) |
0.145635 | − | 0.989338i | \(-0.453478\pi\) | |||||||
\(314\) | −888.792 | −0.159737 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1329.00 | −0.236589 | ||||||||
\(317\) | 4247.76 | + | 7357.34i | 0.752612 | + | 1.30356i | 0.946553 | + | 0.322549i | \(0.104540\pi\) |
−0.193941 | + | 0.981013i | \(0.562127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4182.48 | + | 7244.28i | −0.734088 | + | 1.27148i | ||||
\(320\) | −2553.19 | − | 4422.26i | −0.446025 | − | 0.772537i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10414.7 | 1.79409 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.89177 | − | 13.6689i | 0.00134694 | − | 0.00233297i | ||||
\(326\) | 733.147 | − | 1269.85i | 0.124556 | − | 0.215737i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10006.6 | −1.68451 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −635.355 | − | 1100.47i | −0.105505 | − | 0.182741i | 0.808439 | − | 0.588580i | \(-0.200313\pi\) |
−0.913945 | + | 0.405839i | \(0.866979\pi\) | |||||||
\(332\) | 2722.38 | − | 4715.30i | 0.450031 | − | 0.779476i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −507.865 | − | 879.647i | −0.0832010 | − | 0.144108i | ||||
\(335\) | 6020.44 | 0.981886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4695.47 | 0.758986 | 0.379493 | − | 0.925195i | \(-0.376098\pi\) | ||||
0.379493 | + | 0.925195i | \(0.376098\pi\) | |||||||
\(338\) | −2151.98 | − | 3727.34i | −0.346309 | − | 0.599825i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2429.21 | − | 4207.52i | 0.387478 | − | 0.671132i | ||||
\(341\) | −2325.50 | − | 4027.88i | −0.369304 | − | 0.639654i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12467.3 | 1.95404 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1287.12 | + | 2229.35i | −0.199988 | + | 0.346389i | ||||
\(347\) | 3256.98 | − | 5641.26i | 0.503874 | − | 0.872735i | −0.496116 | − | 0.868256i | \(-0.665241\pi\) |
0.999990 | − | 0.00447854i | \(-0.00142557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7184.75 | 1.10198 | 0.550990 | − | 0.834512i | \(-0.314250\pi\) | ||||
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2991.62 | − | 5181.63i | −0.452994 | − | 0.784608i | ||||
\(353\) | 3034.27 | − | 5255.52i | 0.457502 | − | 0.792416i | −0.541326 | − | 0.840813i | \(-0.682078\pi\) |
0.998828 | + | 0.0483961i | \(0.0154110\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3113.32 | − | 5392.43i | −0.465459 | − | 0.806198i | ||||
\(356\) | 1449.74 | 0.215832 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8100.34 | 1.19586 | ||||||||
\(359\) | 871.857 | + | 1510.10i | 0.128175 | + | 0.222006i | 0.922970 | − | 0.384873i | \(-0.125755\pi\) |
−0.794795 | + | 0.606879i | \(0.792421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2188.59 | + | 3790.75i | −0.319083 | + | 0.552668i | ||||
\(362\) | 3639.48 | + | 6303.76i | 0.528416 | + | 0.915244i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7490.06 | −1.07410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4500.06 | − | 7794.33i | 0.640058 | − | 1.10861i | −0.345361 | − | 0.938470i | \(-0.612244\pi\) |
0.985419 | − | 0.170143i | \(-0.0544230\pi\) | |||||||
\(368\) | −365.074 | + | 632.326i | −0.0517141 | + | 0.0895714i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7265.91 | −1.02091 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2635.88 | − | 4565.47i | −0.365899 | − | 0.633757i | 0.623021 | − | 0.782205i | \(-0.285905\pi\) |
−0.988920 | + | 0.148449i | \(0.952572\pi\) | |||||||
\(374\) | −3505.81 | + | 6072.24i | −0.484708 | + | 0.839540i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3220.93 | − | 5578.82i | −0.441774 | − | 0.765174i | ||||
\(377\) | 221.575 | 0.0302698 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10480.0 | 1.42037 | 0.710185 | − | 0.704015i | \(-0.248611\pi\) | ||||
0.710185 | + | 0.704015i | \(0.248611\pi\) | |||||||
\(380\) | 2620.82 | + | 4539.39i | 0.353803 | + | 0.612804i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3006.78 | − | 5207.89i | 0.402723 | − | 0.697536i | ||||
\(383\) | 687.014 | + | 1189.94i | 0.0916574 | + | 0.158755i | 0.908209 | − | 0.418518i | \(-0.137450\pi\) |
−0.816551 | + | 0.577273i | \(0.804117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4095.17 | −0.539996 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 336.869 | − | 583.475i | 0.0440772 | − | 0.0763439i | ||||
\(389\) | 949.135 | − | 1643.95i | 0.123710 | − | 0.214271i | −0.797518 | − | 0.603295i | \(-0.793854\pi\) |
0.921228 | + | 0.389024i | \(0.127188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5341.26 | −0.690842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3655.01 | + | 6330.66i | 0.467352 | + | 0.809478i | ||||
\(395\) | −1899.66 | + | 3290.31i | −0.241980 | + | 0.419123i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2786.15 | − | 4825.75i | −0.352224 | − | 0.610070i | 0.634415 | − | 0.772993i | \(-0.281241\pi\) |
−0.986639 | + | 0.162923i | \(0.947908\pi\) | |||||||
\(398\) | −4133.02 | −0.520527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −219.784 | −0.0274730 | ||||||||
\(401\) | −2858.19 | − | 4950.53i | −0.355938 | − | 0.616503i | 0.631340 | − | 0.775506i | \(-0.282505\pi\) |
−0.987278 | + | 0.159003i | \(0.949172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −61.5989 | + | 106.692i | −0.00761404 | + | 0.0131879i | ||||
\(404\) | −454.042 | − | 786.423i | −0.0559144 | − | 0.0968466i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11354.2 | −1.38281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5174.27 | − | 8962.09i | 0.625553 | − | 1.08349i | −0.362881 | − | 0.931835i | \(-0.618207\pi\) |
0.988434 | − | 0.151653i | \(-0.0484597\pi\) | |||||||
\(410\) | −4892.46 | + | 8474.00i | −0.589321 | + | 1.02073i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −961.103 | −0.114927 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7782.71 | − | 13480.0i | −0.920574 | − | 1.59448i | ||||
\(416\) | −79.2433 | + | 137.253i | −0.00933948 | + | 0.0161765i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3782.33 | − | 6551.18i | −0.442583 | − | 0.766576i | ||||
\(419\) | −3251.80 | −0.379142 | −0.189571 | − | 0.981867i | \(-0.560710\pi\) | ||||
−0.189571 | + | 0.981867i | \(0.560710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3708.63 | 0.429329 | 0.214664 | − | 0.976688i | \(-0.431134\pi\) | ||||
0.214664 | + | 0.976688i | \(0.431134\pi\) | |||||||
\(422\) | −1515.48 | − | 2624.89i | −0.174816 | − | 0.302790i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2991.62 | + | 5181.63i | −0.342655 | + | 0.593496i | ||||
\(425\) | −803.895 | − | 1392.39i | −0.0917521 | − | 0.158919i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7757.03 | −0.876052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6095.55 | − | 10557.8i | 0.683613 | − | 1.18405i | ||||
\(431\) | 2074.37 | − | 3592.92i | 0.231831 | − | 0.401542i | −0.726516 | − | 0.687149i | \(-0.758862\pi\) |
0.958347 | + | 0.285607i | \(0.0921952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1985.64 | −0.220378 | −0.110189 | − | 0.993911i | \(-0.535146\pi\) | ||||
−0.110189 | + | 0.993911i | \(0.535146\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1249.79 | + | 2164.69i | 0.137280 | + | 0.237775i | ||||
\(437\) | 2881.28 | − | 4990.52i | 0.315401 | − | 0.546290i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3457.21 | − | 5988.07i | −0.375863 | − | 0.651013i | 0.614593 | − | 0.788844i | \(-0.289320\pi\) |
−0.990456 | + | 0.137831i | \(0.955987\pi\) | |||||||
\(440\) | −10316.8 | −1.11781 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 185.727 | 0.0199867 | ||||||||
\(443\) | 2118.73 | + | 3669.76i | 0.227233 | + | 0.393579i | 0.956987 | − | 0.290131i | \(-0.0936989\pi\) |
−0.729754 | + | 0.683710i | \(0.760366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2072.25 | − | 3589.25i | 0.220751 | − | 0.382352i | ||||
\(446\) | 4762.82 | + | 8249.45i | 0.505664 | + | 0.875836i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2097.02 | 0.220411 | 0.110206 | − | 0.993909i | \(-0.464849\pi\) | ||||
0.110206 | + | 0.993909i | \(0.464849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7645.26 | + | 13242.0i | −0.798228 | + | 1.38257i | ||||
\(452\) | 988.487 | − | 1712.11i | 0.102864 | − | 0.178166i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1373.74 | 0.142011 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9338.14 | + | 16174.1i | 0.955842 | + | 1.65557i | 0.732429 | + | 0.680844i | \(0.238387\pi\) |
0.223414 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(458\) | −3620.08 | + | 6270.16i | −0.369334 | + | 0.639706i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1344.10 | − | 2328.06i | −0.136237 | − | 0.235970i | ||||
\(461\) | −13879.5 | −1.40224 | −0.701121 | − | 0.713043i | \(-0.747317\pi\) | ||||
−0.701121 | + | 0.713043i | \(0.747317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4780.89 | 0.479885 | 0.239942 | − | 0.970787i | \(-0.422871\pi\) | ||||
0.239942 | + | 0.970787i | \(0.422871\pi\) | |||||||
\(464\) | −1542.70 | − | 2672.04i | −0.154350 | − | 0.267342i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −337.410 | + | 584.411i | −0.0335412 | + | 0.0580951i | ||||
\(467\) | −4188.09 | − | 7253.99i | −0.414993 | − | 0.718789i | 0.580435 | − | 0.814307i | \(-0.302883\pi\) |
−0.995428 | + | 0.0955176i | \(0.969549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6299.17 | −0.618211 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4861.62 | + | 8420.58i | −0.474098 | + | 0.821162i | ||||
\(473\) | 9525.28 | − | 16498.3i | 0.925947 | − | 1.60379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1734.60 | 0.167556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6020.87 | − | 10428.4i | −0.576126 | − | 0.997879i | ||||
\(479\) | 8505.68 | − | 14732.3i | 0.811346 | − | 1.40529i | −0.100577 | − | 0.994929i | \(-0.532069\pi\) |
0.911922 | − | 0.410363i | \(-0.134598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 150.377 | + | 260.461i | 0.0142549 | + | 0.0246902i | ||||
\(482\) | 11026.3 | 1.04198 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.1781 | 0.00198893 | ||||||||
\(485\) | −963.037 | − | 1668.03i | −0.0901635 | − | 0.156168i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3008.83 | + | 5211.44i | −0.279965 | + | 0.484913i | −0.971376 | − | 0.237548i | \(-0.923656\pi\) |
0.691411 | + | 0.722462i | \(0.256990\pi\) | |||||||
\(488\) | −10253.3 | − | 17759.3i | −0.951118 | − | 1.64739i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12306.6 | 1.13113 | 0.565567 | − | 0.824702i | \(-0.308657\pi\) | ||||
0.565567 | + | 0.824702i | \(0.308657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11285.4 | − | 19546.9i | 1.03097 | − | 1.78569i | ||||
\(494\) | −100.188 | + | 173.531i | −0.00912484 | + | 0.0158047i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1715.51 | 0.155300 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4282.96 | − | 7418.31i | −0.384232 | − | 0.665509i | 0.607430 | − | 0.794373i | \(-0.292200\pi\) |
−0.991662 | + | 0.128864i | \(0.958867\pi\) | |||||||
\(500\) | −2685.97 | + | 4652.23i | −0.240240 | + | 0.416108i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 510.012 | + | 883.366i | 0.0453445 | + | 0.0785390i | ||||
\(503\) | −10520.4 | −0.932568 | −0.466284 | − | 0.884635i | \(-0.654408\pi\) | ||||
−0.466284 | + | 0.884635i | \(0.654408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2596.02 | −0.228755 | ||||||||
\(506\) | 1939.79 | + | 3359.82i | 0.170423 | + | 0.295182i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −60.4876 | + | 104.768i | −0.00528288 | + | 0.00915022i | ||||
\(509\) | −2722.71 | − | 4715.86i | −0.237096 | − | 0.410662i | 0.722784 | − | 0.691074i | \(-0.242862\pi\) |
−0.959880 | + | 0.280412i | \(0.909529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4767.35 | 0.411502 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3929.01 | + | 6805.24i | −0.337162 | + | 0.583981i | ||||
\(515\) | −1373.79 | + | 2379.48i | −0.117547 | + | 0.203597i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9843.46 | −0.837360 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 136.639 | + | 236.665i | 0.0115231 | + | 0.0199585i | ||||
\(521\) | −11108.9 | + | 19241.3i | −0.934149 | + | 1.61799i | −0.158005 | + | 0.987438i | \(0.550506\pi\) |
−0.776144 | + | 0.630555i | \(0.782827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11054.9 | + | 19147.7i | 0.924281 | + | 1.60090i | 0.792713 | + | 0.609595i | \(0.208668\pi\) |
0.131568 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(524\) | 8797.36 | 0.733425 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7026.44 | −0.582447 | ||||||||
\(527\) | 6274.77 | + | 10868.2i | 0.518659 | + | 0.898344i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4605.82 | − | 7977.51i | 0.378550 | − | 0.655668i | ||||
\(530\) | 2925.35 | + | 5066.86i | 0.239753 | + | 0.415265i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 405.022 | 0.0329146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11087.8 | + | 19204.7i | −0.896018 | + | 1.55195i | ||||
\(536\) | −6033.22 | + | 10449.8i | −0.486186 | + | 0.842098i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10797.2 | 0.865241 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4315.67 | + | 7474.96i | 0.342967 | + | 0.594036i | 0.984982 | − | 0.172656i | \(-0.0552348\pi\) |
−0.642015 | + | 0.766692i | \(0.721901\pi\) | |||||||
\(542\) | −5703.06 | + | 9877.99i | −0.451969 | + | 0.782834i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8072.12 | + | 13981.3i | 0.636194 | + | 1.10192i | ||||
\(545\) | 7145.74 | 0.561633 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17846.7 | −1.39501 | −0.697505 | − | 0.716580i | \(-0.745707\pi\) | ||||
−0.697505 | + | 0.716580i | \(0.745707\pi\) | |||||||
\(548\) | −368.781 | − | 638.747i | −0.0287473 | − | 0.0497918i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −583.902 | + | 1011.35i | −0.0452685 | + | 0.0784073i | ||||
\(551\) | 12175.5 | + | 21088.6i | 0.941369 | + | 1.63050i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2254.71 | 0.172913 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4926.70 | − | 8533.29i | 0.375789 | − | 0.650885i | ||||
\(557\) | 7851.64 | − | 13599.4i | 0.597279 | − | 1.03452i | −0.395942 | − | 0.918276i | \(-0.629582\pi\) |
0.993221 | − | 0.116242i | \(-0.0370849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −504.620 | −0.0381810 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 877.651 | + | 1520.14i | 0.0658745 | + | 0.114098i | ||||
\(563\) | 336.839 | − | 583.423i | 0.0252151 | − | 0.0436738i | −0.853143 | − | 0.521678i | \(-0.825306\pi\) |
0.878358 | + | 0.478004i | \(0.158640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2825.87 | − | 4894.55i | −0.210417 | − | 0.364452i | ||||
\(566\) | −239.984 | −0.0178221 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12479.7 | 0.921896 | ||||||||
\(569\) | −7593.10 | − | 13151.6i | −0.559436 | − | 0.968972i | −0.997544 | − | 0.0700496i | \(-0.977684\pi\) |
0.438107 | − | 0.898923i | \(-0.355649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1263.33 | + | 2188.15i | −0.0925898 | + | 0.160370i | −0.908600 | − | 0.417667i | \(-0.862848\pi\) |
0.816010 | + | 0.578037i | \(0.196181\pi\) | |||||||
\(572\) | 73.0345 | + | 126.499i | 0.00533868 | + | 0.00924687i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −889.603 | −0.0645200 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10840.2 | + | 18775.8i | −0.782119 | + | 1.35467i | 0.148586 | + | 0.988900i | \(0.452528\pi\) |
−0.930705 | + | 0.365771i | \(0.880805\pi\) | |||||||
\(578\) | 4645.17 | − | 8045.66i | 0.334279 | − | 0.578989i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11359.6 | 0.813248 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4571.33 | + | 7917.77i | 0.324743 | + | 0.562471i | ||||
\(584\) | 7505.95 | − | 13000.7i | 0.531847 | − | 0.921186i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7449.16 | + | 12902.3i | 0.525123 | + | 0.909540i | ||||
\(587\) | 17458.1 | 1.22755 | 0.613776 | − | 0.789481i | \(-0.289650\pi\) | ||||
0.613776 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13539.4 | −0.947165 | ||||||||
\(590\) | 4753.94 | + | 8234.06i | 0.331723 | + | 0.574561i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2093.98 | − | 3626.88i | 0.145375 | − | 0.251797i | ||||
\(593\) | 2743.50 | + | 4751.88i | 0.189987 | + | 0.329066i | 0.945245 | − | 0.326360i | \(-0.105822\pi\) |
−0.755259 | + | 0.655427i | \(0.772489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6201.20 | 0.426193 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 51.3821 | − | 88.9964i | 0.00351366 | − | 0.00608584i | ||||
\(599\) | −11498.6 | + | 19916.2i | −0.784343 | + | 1.35852i | 0.145048 | + | 0.989425i | \(0.453666\pi\) |
−0.929391 | + | 0.369097i | \(0.879667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18027.1 | 1.22353 | 0.611764 | − | 0.791040i | \(-0.290460\pi\) | ||||
0.611764 | + | 0.791040i | \(0.290460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 853.551 | + | 1478.39i | 0.0575008 | + | 0.0995943i | ||||
\(605\) | 30.2719 | − | 52.4324i | 0.00203426 | − | 0.00352344i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5142.56 | + | 8907.18i | 0.343872 | + | 0.595604i | 0.985148 | − | 0.171707i | \(-0.0549281\pi\) |
−0.641276 | + | 0.767310i | \(0.721595\pi\) | |||||||
\(608\) | −17417.6 | −1.16181 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20052.4 | −1.33098 | ||||||||
\(611\) | 130.369 | + | 225.806i | 0.00863203 | + | 0.0149511i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 798.464 | − | 1382.98i | 0.0526096 | − | 0.0911224i | −0.838521 | − | 0.544869i | \(-0.816579\pi\) |
0.891131 | + | 0.453746i | \(0.149913\pi\) | |||||||
\(614\) | −3468.00 | − | 6006.75i | −0.227943 | − | 0.394809i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5850.74 | −0.381753 | −0.190877 | − | 0.981614i | \(-0.561133\pi\) | ||||
−0.190877 | + | 0.981614i | \(0.561133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 860.808 | − | 1490.96i | 0.0558947 | − | 0.0968124i | −0.836724 | − | 0.547625i | \(-0.815532\pi\) |
0.892619 | + | 0.450812i | \(0.148866\pi\) | |||||||
\(620\) | −3158.03 | + | 5469.87i | −0.204564 | + | 0.354315i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7633.48 | −0.492082 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8701.36 | + | 15071.2i | 0.556887 | + | 0.964557i | ||||
\(626\) | 8508.27 | − | 14736.8i | 0.543225 | − | 0.940894i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 943.051 | + | 1633.41i | 0.0599233 | + | 0.103790i | ||||
\(629\) | 30636.3 | 1.94205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19533.5 | −1.23235 | −0.616177 | − | 0.787608i | \(-0.711319\pi\) | ||||
−0.616177 | + | 0.787608i | \(0.711319\pi\) | |||||||
\(632\) | −3807.38 | − | 6594.58i | −0.239636 | − | 0.415061i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8324.97 | + | 14419.3i | −0.521493 | + | 0.903253i | ||||
\(635\) | 172.921 | + | 299.508i | 0.0108066 | + | 0.0187175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16394.1 | −1.01732 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2810.76 | + | 4868.38i | −0.173602 | + | 0.300687i | ||||
\(641\) | −11748.1 | + | 20348.3i | −0.723903 | + | 1.25384i | 0.235521 | + | 0.971869i | \(0.424320\pi\) |
−0.959424 | + | 0.281967i | \(0.909013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1537.40 | −0.0942913 | −0.0471456 | − | 0.998888i | \(-0.515012\pi\) | ||||
−0.0471456 | + | 0.998888i | \(0.515012\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10205.7 | + | 17676.7i | 0.621573 | + | 1.07660i | ||||
\(647\) | 14136.5 | − | 24485.1i | 0.858985 | − | 1.48781i | −0.0139128 | − | 0.999903i | \(-0.504429\pi\) |
0.872898 | − | 0.487903i | \(-0.162238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7428.79 | + | 12867.0i | 0.449315 | + | 0.778236i | ||||
\(650\) | 30.9333 | 0.00186662 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3111.62 | −0.186902 | ||||||||
\(653\) | −1334.48 | − | 2311.39i | −0.0799730 | − | 0.138517i | 0.823265 | − | 0.567657i | \(-0.192150\pi\) |
−0.903238 | + | 0.429140i | \(0.858817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12574.9 | − | 21780.3i | 0.750140 | − | 1.29928i | ||||
\(656\) | −2819.94 | − | 4884.29i | −0.167836 | − | 0.290700i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6343.74 | 0.374988 | 0.187494 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187494 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4204.58 | − | 7282.54i | 0.247412 | − | 0.428529i | −0.715395 | − | 0.698720i | \(-0.753753\pi\) |
0.962807 | + | 0.270191i | \(0.0870867\pi\) | |||||||
\(662\) | 1245.20 | − | 2156.75i | 0.0731059 | − | 0.126623i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31196.9 | 1.82331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6244.29 | − | 10815.4i | −0.362489 | − | 0.627849i | ||||
\(668\) | −1077.74 | + | 1866.70i | −0.0624235 | + | 0.108121i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5899.58 | + | 10218.4i | 0.340180 | + | 0.589209i | ||||
\(671\) | −31335.1 | −1.80280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15326.7 | −0.877862 | −0.438931 | − | 0.898521i | \(-0.644643\pi\) | ||||
−0.438931 | + | 0.898521i | \(0.644643\pi\) | |||||||
\(674\) | 4601.20 | + | 7969.52i | 0.262955 | + | 0.455452i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4566.71 | + | 7909.78i | −0.259827 | + | 0.450033i | ||||
\(677\) | −6505.81 | − | 11268.4i | −0.369333 | − | 0.639704i | 0.620128 | − | 0.784500i | \(-0.287081\pi\) |
−0.989461 | + | 0.144797i | \(0.953747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 27837.4 | 1.56987 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4557.63 | − | 7894.04i | 0.255895 | − | 0.443223i | ||||
\(683\) | −8736.00 | + | 15131.2i | −0.489420 | + | 0.847700i | −0.999926 | − | 0.0121740i | \(-0.996125\pi\) |
0.510506 | + | 0.859874i | \(0.329458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2108.53 | −0.117610 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3513.39 | + | 6085.37i | 0.194690 | + | 0.337213i | ||||
\(689\) | 121.087 | − | 209.730i | 0.00669531 | − | 0.0115966i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3658.55 | + | 6336.80i | 0.201415 | + | 0.348861i | 0.948985 | − | 0.315322i | \(-0.102113\pi\) |
−0.747569 | + | 0.664184i | \(0.768779\pi\) | |||||||
\(692\) | 5462.77 | 0.300091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12766.4 | 0.698280 | ||||||||
\(695\) | −14084.4 | − | 24394.8i | −0.768706 | − | 1.33144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20628.8 | − | 35730.1i | 1.12105 | − | 1.94171i | ||||
\(698\) | 7040.52 | + | 12194.5i | 0.381787 | + | 0.661275i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7874.65 | −0.424282 | −0.212141 | − | 0.977239i | \(-0.568044\pi\) | ||||
−0.212141 | + | 0.977239i | \(0.568044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16526.4 | + | 28624.5i | −0.886634 | + | 1.53570i | ||||
\(704\) | 7819.36 | − | 13543.5i | 0.418612 | − | 0.725058i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11893.4 | 0.634017 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12618.4 | + | 21855.7i | 0.668398 | + | 1.15770i | 0.978352 | + | 0.206948i | \(0.0663531\pi\) |
−0.309954 | + | 0.950752i | \(0.600314\pi\) | |||||||
\(710\) | 6101.64 | − | 10568.4i | 0.322522 | − | 0.558624i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4153.30 | + | 7193.73i | 0.218612 | + | 0.378647i | ||||
\(713\) | 6943.76 | 0.364721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 417.580 | 0.0218414 | ||||||||
\(716\) | −8594.85 | − | 14886.7i | −0.448610 | − | 0.777015i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1708.71 | + | 2959.57i | −0.0888139 | + | 0.153830i | ||||
\(719\) | 9836.48 | + | 17037.3i | 0.510207 | + | 0.883704i | 0.999930 | + | 0.0118262i | \(0.00376448\pi\) |
−0.489723 | + | 0.871878i | \(0.662902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8578.62 | −0.442193 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7723.32 | − | 13377.2i | 0.396457 | − | 0.686684i | ||||
\(725\) | 1879.61 | − | 3255.58i | 0.0962856 | − | 0.166772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31921.7 | −1.62849 | −0.814243 | − | 0.580525i | \(-0.802848\pi\) | ||||
−0.814243 | + | 0.580525i | \(0.802848\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7339.69 | − | 12712.7i | −0.372129 | − | 0.644546i | ||||
\(731\) | −25701.6 | + | 44516.4i | −1.30042 | + | 2.25239i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6772.65 | − | 11730.6i | −0.341274 | − | 0.591103i | 0.643396 | − | 0.765534i | \(-0.277525\pi\) |
−0.984669 | + | 0.174430i | \(0.944192\pi\) | |||||||
\(734\) | 17638.9 | 0.887007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8932.74 | 0.447371 | ||||||||
\(737\) | 9219.04 | + | 15967.8i | 0.460770 | + | 0.798078i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12748.8 | + | 22081.6i | −0.634604 | + | 1.09917i | 0.351995 | + | 0.936002i | \(0.385503\pi\) |
−0.986599 | + | 0.163164i | \(0.947830\pi\) | |||||||
\(740\) | 7709.48 | + | 13353.2i | 0.382981 | + | 0.663343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11146.9 | 0.550390 | 0.275195 | − | 0.961388i | \(-0.411258\pi\) | ||||
0.275195 | + | 0.961388i | \(0.411258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8863.95 | − | 15352.8i | 0.435906 | − | 0.755011i | ||||
\(746\) | 5165.92 | − | 8947.64i | 0.253536 | − | 0.439137i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14879.3 | 0.727328 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10706.2 | − | 18543.8i | −0.520208 | − | 0.901027i | −0.999724 | − | 0.0234936i | \(-0.992521\pi\) |
0.479516 | − | 0.877533i | \(-0.340812\pi\) | |||||||
\(752\) | 1815.38 | − | 3144.32i | 0.0880318 | − | 0.152476i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 217.127 | + | 376.075i | 0.0104871 | + | 0.0181643i | ||||
\(755\) | 4880.24 | 0.235245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33963.9 | −1.63070 | −0.815350 | − | 0.578968i | \(-0.803456\pi\) | ||||
−0.815350 | + | 0.578968i | \(0.803456\pi\) | |||||||
\(758\) | 10269.6 | + | 17787.5i | 0.492096 | + | 0.852335i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15016.5 | + | 26009.4i | −0.716719 | + | 1.24139i | ||||
\(761\) | −9959.98 | − | 17251.2i | −0.474440 | − | 0.821754i | 0.525132 | − | 0.851021i | \(-0.324016\pi\) |
−0.999572 | + | 0.0292668i | \(0.990683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12761.3 | −0.604305 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1346.44 | + | 2332.11i | −0.0635105 | + | 0.110003i | ||||
\(767\) | 196.777 | − | 340.828i | 0.00926364 | − | 0.0160451i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10039.2 | 0.470769 | 0.235385 | − | 0.971902i | \(-0.424365\pi\) | ||||
0.235385 | + | 0.971902i | \(0.424365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4345.17 | + | 7526.05i | 0.202573 | + | 0.350866i | ||||
\(773\) | −10692.7 | + | 18520.2i | −0.497527 | + | 0.861742i | −0.999996 | − | 0.00285350i | \(-0.999092\pi\) |
0.502469 | + | 0.864595i | \(0.332425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1045.08 | + | 1810.13i | 0.0484392 | + | 0.0838992i | ||||
\(776\) | 3860.33 | 0.178579 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3720.32 | 0.171440 | ||||||||
\(779\) | 22255.9 | + | 38548.3i | 1.02362 | + | 1.77296i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9534.79 | − | 16514.7i | 0.436852 | − | 0.756650i | ||||
\(782\) | −5234.04 | − | 9065.62i | −0.239346 | − | 0.414560i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5391.96 | 0.245156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18710.7 | + | 32407.8i | −0.847475 | + | 1.46787i | 0.0359790 | + | 0.999353i | \(0.488545\pi\) |
−0.883454 | + | 0.468518i | \(0.844788\pi\) | |||||||
\(788\) | 7756.28 | − | 13434.3i | 0.350642 | − | 0.607330i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7446.10 | −0.335342 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 415.009 | + | 718.817i | 0.0185844 | + | 0.0321891i | ||||
\(794\) | 5460.44 | − | 9457.75i | 0.244060 | − | 0.422724i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4385.33 | + | 7595.62i | 0.195269 | + | 0.338216i | ||||
\(797\) | −30888.7 | −1.37281 | −0.686407 | − | 0.727217i | \(-0.740813\pi\) | ||||
−0.686407 | + | 0.727217i | \(0.740813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26560.1 | 1.17601 | ||||||||
\(800\) | 1344.44 | + | 2328.63i | 0.0594162 | + | 0.102912i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5601.63 | − | 9702.30i | 0.246634 | − | 0.427182i | ||||
\(803\) | −11469.4 | − | 19865.7i | −0.504045 | − | 0.873031i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −241.449 | −0.0105517 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2601.53 | − | 4505.97i | 0.113269 | − | 0.196188i | ||||
\(809\) | 3619.25 | − | 6268.73i | 0.157288 | − | 0.272431i | −0.776602 | − | 0.629992i | \(-0.783058\pi\) |
0.933890 | + | 0.357561i | \(0.116392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35466.4 | −1.53563 | −0.767814 | − | 0.640673i | \(-0.778656\pi\) | ||||
−0.767814 | + | 0.640673i | \(0.778656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11126.2 | − | 19271.2i | −0.479083 | − | 0.829796i | ||||
\(815\) | −4447.72 | + | 7703.68i | −0.191162 | + | 0.331102i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27728.8 | − | 48027.6i | −1.18740 | − | 2.05664i | ||||
\(818\) | 20281.6 | 0.866905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20764.6 | 0.884304 | ||||||||
\(821\) | −18973.6 | − | 32863.3i | −0.806558 | − | 1.39700i | −0.915234 | − | 0.402923i | \(-0.867994\pi\) |
0.108676 | − | 0.994077i | \(-0.465339\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13466.1 | + | 23324.0i | −0.570351 | + | 0.987876i | 0.426179 | + | 0.904639i | \(0.359859\pi\) |
−0.996530 | + | 0.0832376i | \(0.973474\pi\) | |||||||
\(824\) | −2753.42 | − | 4769.06i | −0.116408 | − | 0.201624i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1913.98 | 0.0804783 | 0.0402391 | − | 0.999190i | \(-0.487188\pi\) | ||||
0.0402391 | + | 0.999190i | \(0.487188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7640.96 | − | 13234.5i | 0.320122 | − | 0.554468i | −0.660391 | − | 0.750922i | \(-0.729609\pi\) |
0.980513 | + | 0.196454i | \(0.0629427\pi\) | |||||||
\(830\) | 15252.9 | − | 26418.9i | 0.637876 | − | 1.10483i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −414.246 | −0.0172613 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3081.02 | + | 5336.49i | 0.127692 | + | 0.221170i | ||||
\(836\) | −8026.46 | + | 13902.2i | −0.332058 | + | 0.575142i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3186.52 | − | 5519.21i | −0.131356 | − | 0.227515i | ||||
\(839\) | −25779.5 | −1.06079 | −0.530397 | − | 0.847749i | \(-0.677957\pi\) | ||||
−0.530397 | + | 0.847749i | \(0.677957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28384.4 | 1.16382 | ||||||||
\(842\) | 3634.18 | + | 6294.58i | 0.148743 | + | 0.257631i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3215.99 | + | 5570.26i | −0.131160 | + | 0.227176i | ||||
\(845\) | 13055.3 | + | 22612.4i | 0.531497 | + | 0.920579i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3372.26 | −0.136561 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1575.51 | − | 2728.87i | 0.0635761 | − | 0.110117i | ||||
\(851\) | 8475.66 | − | 14680.3i | 0.341412 | − | 0.591343i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6452.21 | −0.258991 | −0.129496 | − | 0.991580i | \(-0.541336\pi\) | ||||
−0.129496 | + | 0.991580i | \(0.541336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22222.8 | − | 38491.0i | −0.887335 | − | 1.53691i | ||||
\(857\) | 16030.9 | − | 27766.4i | 0.638980 | − | 1.10675i | −0.346677 | − | 0.937984i | \(-0.612690\pi\) |
0.985657 | − | 0.168761i | \(-0.0539766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1967.32 | + | 3407.50i | 0.0781421 | + | 0.135346i | 0.902448 | − | 0.430798i | \(-0.141768\pi\) |
−0.824306 | + | 0.566144i | \(0.808435\pi\) | |||||||
\(860\) | −25870.7 | −1.02579 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8130.91 | 0.321276 | ||||||||
\(863\) | −7021.57 | − | 12161.7i | −0.276961 | − | 0.479710i | 0.693667 | − | 0.720296i | \(-0.255994\pi\) |
−0.970628 | + | 0.240586i | \(0.922660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7808.44 | − | 13524.6i | 0.306931 | − | 0.531619i | ||||
\(866\) | −1945.78 | − | 3370.19i | −0.0763514 | − | 0.132244i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11635.7 | −0.454217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 244.198 | − | 422.964i | 0.00949982 | − | 0.0164542i | ||||
\(872\) | −7160.91 | + | 12403.1i | −0.278095 | + | 0.481675i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11293.7 | 0.437090 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1045.66 | − | 1811.13i | −0.0402614 | − | 0.0697348i | 0.845193 | − | 0.534462i | \(-0.179486\pi\) |
−0.885454 | + | 0.464727i | \(0.846152\pi\) | |||||||
\(878\) | 6775.62 | − | 11735.7i | 0.260440 | − | 0.451095i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2907.38 | − | 5035.72i | −0.111372 | − | 0.192903i | ||||
\(881\) | −11548.6 | −0.441639 | −0.220819 | − | 0.975315i | \(-0.570873\pi\) | ||||
−0.220819 | + | 0.975315i | \(0.570873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7531.24 | 0.287029 | 0.143514 | − | 0.989648i | \(-0.454160\pi\) | ||||
0.143514 | + | 0.989648i | \(0.454160\pi\) | |||||||
\(884\) | −197.065 | − | 341.327i | −0.00749776 | − | 0.0129865i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4152.40 | + | 7192.17i | −0.157452 | + | 0.272715i | ||||
\(887\) | −19251.3 | − | 33344.3i | −0.728745 | − | 1.26222i | −0.957414 | − | 0.288719i | \(-0.906771\pi\) |
0.228669 | − | 0.973504i | \(-0.426563\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8122.61 | 0.305922 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10107.2 | − | 17506.1i | 0.379387 | − | 0.657117i | ||||
\(893\) | −14327.5 | + | 24816.0i | −0.536900 | + | 0.929938i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49141.7 | −1.83534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2054.92 | + | 3559.23i | 0.0763627 | + | 0.132264i | ||||
\(899\) | −14671.2 | + | 25411.3i | −0.544286 | + | 0.942731i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12334.6 | − | 21364.1i | −0.456076 | − | 0.789947i | ||||
\(902\) | −29967.1 | −1.10620 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11327.5 | 0.416755 | ||||||||
\(905\) | −22079.3 | − | 38242.5i | −0.810985 | − | 1.40467i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15653.3 | − | 27112.4i | 0.573054 | − | 0.992559i | −0.423196 | − | 0.906038i | \(-0.639092\pi\) |
0.996250 | − | 0.0865211i | \(-0.0275750\pi\) | |||||||
\(908\) | −1457.61 | − | 2524.65i | −0.0532735 | − | 0.0922724i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34154.3 | −1.24213 | −0.621067 | − | 0.783758i | \(-0.713300\pi\) | ||||
−0.621067 | + | 0.783758i | \(0.713300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23835.2 | − | 41283.7i | 0.863996 | − | 1.49649i | ||||
\(914\) | −18301.4 | + | 31698.9i | −0.662314 | + | 1.14716i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15364.3 | 0.554204 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17994.4 | − | 31167.3i | −0.645899 | − | 1.11873i | −0.984093 | − | 0.177654i | \(-0.943149\pi\) |
0.338194 | − | 0.941077i | \(-0.390184\pi\) | |||||||
\(920\) | 7701.32 | − | 13339.1i | 0.275984 | − | 0.478018i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13600.9 | − | 23557.4i | −0.485815 | − | 0.841456i | ||||
\(923\) | −505.124 | −0.0180134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5102.57 | 0.181374 | ||||||||
\(926\) | 4684.91 | + | 8114.50i | 0.166259 | + | 0.287969i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18873.7 | + | 32690.2i | −0.667629 | + | 1.15637i | ||||
\(929\) | 6952.99 | + | 12042.9i | 0.245554 | + | 0.425313i | 0.962287 | − | 0.272035i | \(-0.0876966\pi\) |
−0.716733 | + | 0.697348i | \(0.754363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1432.03 | 0.0503302 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8208.03 | − | 14216.7i | 0.287554 | − | 0.498057i | ||||
\(935\) | 21268.4 | − | 36837.9i | 0.743905 | − | 1.28848i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40905.3 | −1.42617 | −0.713083 | − | 0.701079i | \(-0.752702\pi\) | ||||
−0.713083 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6683.72 | + | 11576.5i | 0.231914 | + | 0.401687i | ||||
\(941\) | −4033.75 | + | 6986.66i | −0.139741 | + | 0.242039i | −0.927399 | − | 0.374075i | \(-0.877960\pi\) |
0.787657 | + | 0.616113i | \(0.211294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11414.1 | − | 19769.8i | −0.394161 | − | 0.682706i | ||||
\(944\) | −5480.20 | −0.188946 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37336.2 | 1.28320 | ||||||||
\(947\) | 19890.6 | + | 34451.5i | 0.682531 | + | 1.18218i | 0.974206 | + | 0.225661i | \(0.0724542\pi\) |
−0.291675 | + | 0.956518i | \(0.594212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −303.808 | + | 526.211i | −0.0103920 | + | 0.0179995i | ||||
\(950\) | 1699.78 | + | 2944.11i | 0.0580507 | + | 0.100547i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32354.0 | −1.09974 | −0.549868 | − | 0.835252i | \(-0.685322\pi\) | ||||
−0.549868 | + | 0.835252i | \(0.685322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18241.0 | + | 31594.3i | −0.618077 | + | 1.07054i | ||||
\(956\) | −12776.9 | + | 22130.2i | −0.432252 | + | 0.748683i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33339.7 | 1.12438 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6738.16 | + | 11670.8i | 0.226181 | + | 0.391757i | ||||
\(962\) | −294.716 | + | 510.464i | −0.00987738 | + | 0.0171081i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11699.5 | − | 20264.1i | −0.390887 | − | 0.677035i | ||||
\(965\) | 24843.8 | 0.828757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17389.2 | 0.578282 | 0.289141 | − | 0.957287i | \(-0.406630\pi\) | ||||
0.289141 | + | 0.957287i | \(0.406630\pi\) | |||||||
\(968\) | 60.6722 | + | 105.087i | 0.00201454 | + | 0.00348929i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1887.41 | − | 3269.09i | 0.0624753 | − | 0.108210i | ||||
\(971\) | 26203.1 | + | 45385.1i | 0.866012 | + | 1.49998i | 0.866038 | + | 0.499977i | \(0.166658\pi\) |
−2.60137e−5 | 1.00000i | \(0.500008\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11793.7 | −0.387982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5778.95 | − | 10009.4i | 0.189528 | − | 0.328273i | ||||
\(977\) | 3423.35 | − | 5929.42i | 0.112101 | − | 0.194165i | −0.804516 | − | 0.593931i | \(-0.797575\pi\) |
0.916617 | + | 0.399766i | \(0.130909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12692.9 | 0.414368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12059.5 | + | 20887.7i | 0.391888 | + | 0.678770i | ||||
\(983\) | 18824.0 | − | 32604.1i | 0.610774 | − | 1.05789i | −0.380336 | − | 0.924848i | \(-0.624192\pi\) |
0.991110 | − | 0.133044i | \(-0.0424751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22173.6 | − | 38405.7i | −0.717267 | − | 1.24234i | ||||
\(986\) | 44235.3 | 1.42874 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 425.217 | 0.0136923 | ||||||||
\(989\) | 14220.9 | + | 24631.3i | 0.457227 | + | 0.791941i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1018.09 | + | 1763.38i | −0.0326343 | + | 0.0565242i | −0.881881 | − | 0.471472i | \(-0.843723\pi\) |
0.849247 | + | 0.527996i | \(0.177056\pi\) | |||||||
\(992\) | −10493.9 | − | 18176.0i | −0.335870 | − | 0.581744i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25073.5 | 0.798877 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6770.32 | − | 11726.5i | 0.215064 | − | 0.372501i | −0.738229 | − | 0.674550i | \(-0.764337\pi\) |
0.953292 | + | 0.302050i | \(0.0976708\pi\) | |||||||
\(998\) | 8393.96 | − | 14538.8i | 0.266239 | − | 0.461139i | ||||
\(999\) | 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 | 441.4.e.z.361.5 | 16 | ||
3.2 | odd | 2 | inner | 441.4.e.z.361.4 | 16 | ||
7.2 | even | 3 | inner | 441.4.e.z.226.5 | 16 | ||
7.3 | odd | 6 | 441.4.a.x.1.3 | ✓ | 8 | ||
7.4 | even | 3 | 441.4.a.x.1.4 | yes | 8 | ||
7.5 | odd | 6 | inner | 441.4.e.z.226.6 | 16 | ||
7.6 | odd | 2 | inner | 441.4.e.z.361.6 | 16 | ||
21.2 | odd | 6 | inner | 441.4.e.z.226.4 | 16 | ||
21.5 | even | 6 | inner | 441.4.e.z.226.3 | 16 | ||
21.11 | odd | 6 | 441.4.a.x.1.5 | yes | 8 | ||
21.17 | even | 6 | 441.4.a.x.1.6 | yes | 8 | ||
21.20 | even | 2 | inner | 441.4.e.z.361.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.a.x.1.3 | ✓ | 8 | 7.3 | odd | 6 | ||
441.4.a.x.1.4 | yes | 8 | 7.4 | even | 3 | ||
441.4.a.x.1.5 | yes | 8 | 21.11 | odd | 6 | ||
441.4.a.x.1.6 | yes | 8 | 21.17 | even | 6 | ||
441.4.e.z.226.3 | 16 | 21.5 | even | 6 | inner | ||
441.4.e.z.226.4 | 16 | 21.2 | odd | 6 | inner | ||
441.4.e.z.226.5 | 16 | 7.2 | even | 3 | inner | ||
441.4.e.z.226.6 | 16 | 7.5 | odd | 6 | inner | ||
441.4.e.z.361.3 | 16 | 21.20 | even | 2 | inner | ||
441.4.e.z.361.4 | 16 | 3.2 | odd | 2 | inner | ||
441.4.e.z.361.5 | 16 | 1.1 | even | 1 | trivial | ||
441.4.e.z.361.6 | 16 | 7.6 | odd | 2 | inner |