Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(721,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.o (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: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.219615408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 22x^{4} - 39x^{3} + 112x^{2} - 93x + 39 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.1 | ||
Root | \(0.500000 + 2.79345i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.721 |
Dual form | 912.3.o.c.721.4 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.39180 | −1.47836 | −0.739180 | − | 0.673508i | \(-0.764787\pi\) | ||||
−0.739180 | + | 0.673508i | \(0.764787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.28502 | −0.469288 | −0.234644 | − | 0.972081i | \(-0.575392\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575392\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.714984 | 0.0649986 | 0.0324993 | − | 0.999472i | \(-0.489653\pi\) | ||||
0.0324993 | + | 0.999472i | \(0.489653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 25.4210i | − | 1.95546i | −0.209866 | − | 0.977730i | \(-0.567303\pi\) | ||
0.209866 | − | 0.977730i | \(-0.432697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.8030i | 0.853531i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −26.0686 | −1.53345 | −0.766724 | − | 0.641977i | \(-0.778114\pi\) | ||||
−0.766724 | + | 0.641977i | \(0.778114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.7836 | + | 10.5773i | 0.830715 | + | 0.556697i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.68981i | 0.270944i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.46325 | −0.367967 | −0.183984 | − | 0.982929i | \(-0.558899\pi\) | ||||
−0.183984 | + | 0.982929i | \(0.558899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.6386 | 1.18555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 23.1292i | − | 0.797557i | −0.917047 | − | 0.398778i | \(-0.869434\pi\) | ||
0.917047 | − | 0.398778i | \(-0.130566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.8627i | 0.608473i | 0.952596 | + | 0.304237i | \(0.0984014\pi\) | ||||
−0.952596 | + | 0.304237i | \(0.901599\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.23839i | − | 0.0375269i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.2822 | 0.693776 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 48.5501i | 1.31217i | 0.754689 | + | 0.656083i | \(0.227788\pi\) | ||||
−0.754689 | + | 0.656083i | \(0.772212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −44.0304 | −1.12899 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.3808i | 0.862946i | 0.902126 | + | 0.431473i | \(0.142006\pi\) | ||||
−0.902126 | + | 0.431473i | \(0.857994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.5014 | 0.569801 | 0.284900 | − | 0.958557i | \(-0.408040\pi\) | ||||
0.284900 | + | 0.958557i | \(0.408040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 22.1754 | 0.492786 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.0990 | 0.980831 | 0.490415 | − | 0.871489i | \(-0.336845\pi\) | ||||
0.490415 | + | 0.871489i | \(0.336845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.2087 | −0.779769 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 45.1522i | 0.885336i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 51.2119i | 0.966262i | 0.875548 | + | 0.483131i | \(0.160500\pi\) | ||||
−0.875548 | + | 0.483131i | \(0.839500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.28502 | −0.0960912 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.3203 | − | 27.3380i | 0.321409 | − | 0.479614i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.314i | 1.71719i | 0.512657 | + | 0.858594i | \(0.328661\pi\) | ||||
−0.512657 | + | 0.858594i | \(0.671339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.5721 | 0.632329 | 0.316165 | − | 0.948704i | \(-0.397605\pi\) | ||||
0.316165 | + | 0.948704i | \(0.397605\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.85505 | 0.156429 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 187.907i | 2.89087i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.2837i | 0.660950i | 0.943815 | + | 0.330475i | \(0.107209\pi\) | ||||
−0.943815 | + | 0.330475i | \(0.892791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.6588i | 0.212446i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 74.3410i | − | 1.04706i | −0.852008 | − | 0.523528i | \(-0.824615\pi\) | ||
0.852008 | − | 0.523528i | \(-0.175385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 112.200 | 1.53699 | 0.768494 | − | 0.639857i | \(-0.221006\pi\) | ||||
0.768494 | + | 0.639857i | \(0.221006\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 51.3356i | − | 0.684475i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.34873 | −0.0305030 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 125.500i | − | 1.58861i | −0.607519 | − | 0.794305i | \(-0.707835\pi\) | ||
0.607519 | − | 0.794305i | \(-0.292165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 95.5672 | 1.15141 | 0.575706 | − | 0.817657i | \(-0.304727\pi\) | ||||
0.575706 | + | 0.817657i | \(0.304727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 192.694 | 2.26699 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −40.0609 | −0.460470 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 28.0827i | 0.315536i | 0.987476 | + | 0.157768i | \(0.0504298\pi\) | ||||
−0.987476 | + | 0.157768i | \(0.949570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 83.5083i | 0.917674i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 32.6711 | 0.351302 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −116.669 | − | 78.1849i | −1.22810 | − | 0.822999i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 55.7955i | − | 0.575212i | −0.957749 | − | 0.287606i | \(-0.907141\pi\) | ||
0.957749 | − | 0.287606i | \(-0.0928593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.14495 | −0.0216662 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −131.018 | −1.29721 | −0.648603 | − | 0.761127i | \(-0.724646\pi\) | ||||
−0.648603 | + | 0.761127i | \(0.724646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 74.6582i | − | 0.724837i | −0.932015 | − | 0.362418i | \(-0.881951\pi\) | ||
0.932015 | − | 0.362418i | \(-0.118049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 42.0579i | − | 0.400552i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 171.811i | 1.60571i | 0.596173 | + | 0.802856i | \(0.296687\pi\) | ||||
−0.596173 | + | 0.802856i | \(0.703313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 34.9582i | − | 0.320717i | −0.987059 | − | 0.160359i | \(-0.948735\pi\) | ||
0.987059 | − | 0.160359i | \(-0.0512651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 84.0913 | 0.757579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 42.8041i | − | 0.378797i | −0.981900 | − | 0.189399i | \(-0.939346\pi\) | ||
0.981900 | − | 0.189399i | \(-0.0606538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 62.5586 | 0.543988 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 76.2629i | 0.651820i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 85.6358 | 0.719628 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.489 | −0.995775 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 61.2814 | 0.498222 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −34.2879 | −0.274303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 176.342i | 1.38852i | 0.719724 | + | 0.694260i | \(0.244268\pi\) | ||||
−0.719724 | + | 0.694260i | \(0.755732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 42.4377i | − | 0.328975i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −202.114 | −1.54285 | −0.771427 | − | 0.636317i | \(-0.780457\pi\) | ||||
−0.771427 | + | 0.636317i | \(0.780457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51.8493 | − | 34.7464i | −0.389845 | − | 0.261251i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 38.4089i | − | 0.284510i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.2891 | −0.0824021 | −0.0412011 | − | 0.999151i | \(-0.513118\pi\) | ||||
−0.0412011 | + | 0.999151i | \(0.513118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 56.6427 | 0.407502 | 0.203751 | − | 0.979023i | \(-0.434687\pi\) | ||||
0.203751 | + | 0.979023i | \(0.434687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 79.8459i | − | 0.566283i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 18.1756i | − | 0.127102i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 170.966i | 1.17908i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 66.1794i | 0.450200i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.96590 | −0.0400396 | −0.0200198 | − | 0.999800i | \(-0.506373\pi\) | ||||
−0.0200198 | + | 0.999800i | \(0.506373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 28.0300i | − | 0.185629i | −0.995683 | − | 0.0928146i | \(-0.970414\pi\) | ||
0.995683 | − | 0.0928146i | \(-0.0295864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 78.2058 | 0.511149 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 139.429i | − | 0.899542i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 141.317 | 0.900108 | 0.450054 | − | 0.893001i | \(-0.351405\pi\) | ||||
0.450054 | + | 0.893001i | \(0.351405\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 88.7015 | 0.557871 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.8019 | 0.172683 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 181.550 | 1.11380 | 0.556902 | − | 0.830578i | \(-0.311990\pi\) | ||||
0.556902 | + | 0.830578i | \(0.311990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.15392i | 0.0554783i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 301.737i | 1.80681i | 0.428791 | + | 0.903404i | \(0.358940\pi\) | ||||
−0.428791 | + | 0.903404i | \(0.641060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −477.226 | −2.82382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −47.3508 | − | 31.7318i | −0.276905 | − | 0.185566i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 195.469i | − | 1.12988i | −0.825132 | − | 0.564940i | \(-0.808899\pi\) | ||
0.825132 | − | 0.564940i | \(-0.191101\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −97.3634 | −0.556362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 175.481 | 0.991418 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 91.2818i | 0.509954i | 0.966947 | + | 0.254977i | \(0.0820679\pi\) | ||||
−0.966947 | + | 0.254977i | \(0.917932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7783i | 0.0871732i | 0.999050 | + | 0.0435866i | \(0.0138784\pi\) | ||||
−0.999050 | + | 0.0435866i | \(0.986122\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 66.8088i | − | 0.365075i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 358.873i | − | 1.93985i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.6386 | −0.0996719 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 17.0694i | − | 0.0903145i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −193.939 | −1.01539 | −0.507694 | − | 0.861538i | \(-0.669502\pi\) | ||||
−0.507694 | + | 0.861538i | \(0.669502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 150.941i | 0.782077i | 0.920374 | + | 0.391039i | \(0.127884\pi\) | ||||
−0.920374 | + | 0.391039i | \(0.872116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 325.464 | 1.66905 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 68.0052 | 0.345204 | 0.172602 | − | 0.984992i | \(-0.444783\pi\) | ||||
0.172602 | + | 0.984992i | \(0.444783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29.4815 | −0.148148 | −0.0740741 | − | 0.997253i | \(-0.523600\pi\) | ||||
−0.0740741 | + | 0.997253i | \(0.523600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 76.7015 | 0.381600 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 75.9796i | 0.374284i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 261.528i | − | 1.27574i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.3898 | 0.122656 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2850 | + | 7.56257i | 0.0539953 | + | 0.0361845i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.92686i | 0.0470467i | 0.999723 | + | 0.0235234i | \(0.00748841\pi\) | ||||
−0.999723 | + | 0.0235234i | \(0.992512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −128.762 | −0.604518 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −181.110 | −0.842370 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 61.9642i | − | 0.285549i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 194.336i | − | 0.887380i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 662.690i | 2.99860i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 177.702i | 0.796871i | 0.917196 | + | 0.398435i | \(0.130447\pi\) | ||||
−0.917196 | + | 0.398435i | \(0.869553\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −88.9159 | −0.395182 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 79.1694i | 0.348764i | 0.984678 | + | 0.174382i | \(0.0557927\pi\) | ||||
−0.984678 | + | 0.174382i | \(0.944207\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 161.424 | 0.704908 | 0.352454 | − | 0.935829i | \(-0.385347\pi\) | ||||
0.352454 | + | 0.935829i | \(0.385347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.06813i | 0.0176109i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −196.958 | −0.845315 | −0.422658 | − | 0.906289i | \(-0.638903\pi\) | ||||
−0.422658 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −340.755 | −1.45002 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −217.373 | −0.917184 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −179.160 | −0.749621 | −0.374811 | − | 0.927101i | \(-0.622292\pi\) | ||||
−0.374811 | + | 0.927101i | \(0.622292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 464.116i | 1.92579i | 0.269870 | + | 0.962897i | \(0.413019\pi\) | ||||
−0.269870 | + | 0.962897i | \(0.586981\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 282.431 | 1.15278 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 268.884 | − | 401.234i | 1.08860 | − | 1.62443i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 165.527i | − | 0.664768i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −140.760 | −0.560798 | −0.280399 | − | 0.959883i | \(-0.590467\pi\) | ||||
−0.280399 | + | 0.959883i | \(0.590467\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.05109 | −0.0239174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 333.755i | − | 1.30884i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 184.717i | 0.718743i | 0.933195 | + | 0.359371i | \(0.117009\pi\) | ||||
−0.933195 | + | 0.359371i | \(0.882991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 159.488i | − | 0.615784i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 69.3875i | 0.265852i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −254.011 | −0.965822 | −0.482911 | − | 0.875669i | \(-0.660421\pi\) | ||||
−0.482911 | + | 0.875669i | \(0.660421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 378.548i | − | 1.42848i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 48.6407 | 0.182175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 54.2105i | 0.201526i | 0.994910 | + | 0.100763i | \(0.0321284\pi\) | ||||
−0.994910 | + | 0.100763i | \(0.967872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −397.966 | −1.46851 | −0.734254 | − | 0.678875i | \(-0.762468\pi\) | ||||
−0.734254 | + | 0.678875i | \(0.762468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 144.641 | 0.529819 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.1912 | 0.0770587 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −310.820 | −1.12209 | −0.561046 | − | 0.827784i | \(-0.689601\pi\) | ||||
−0.561046 | + | 0.827784i | \(0.689601\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 56.5880i | − | 0.202824i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 189.796i | − | 0.675429i | −0.941249 | − | 0.337715i | \(-0.890346\pi\) | ||
0.941249 | − | 0.337715i | \(-0.109654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 352.032 | 1.24393 | 0.621965 | − | 0.783045i | \(-0.286335\pi\) | ||||
0.621965 | + | 0.783045i | \(0.286335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −135.420 | + | 202.077i | −0.475159 | + | 0.709041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 116.227i | − | 0.404970i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 390.572 | 1.35146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −96.6407 | −0.332099 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 238.729i | − | 0.814774i | −0.913256 | − | 0.407387i | \(-0.866440\pi\) | ||
0.913256 | − | 0.407387i | \(-0.133560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 748.893i | − | 2.53862i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.71517i | 0.0125090i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 215.144i | 0.719546i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80.4876 | −0.267401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 226.929i | 0.748942i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −285.117 | −0.934809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 78.3760i | 0.255296i | 0.991820 | + | 0.127648i | \(0.0407428\pi\) | ||||
−0.991820 | + | 0.127648i | \(0.959257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −129.312 | −0.418485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 257.012 | 0.826404 | 0.413202 | − | 0.910639i | \(-0.364410\pi\) | ||||
0.413202 | + | 0.910639i | \(0.364410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 152.676 | 0.487784 | 0.243892 | − | 0.969802i | \(-0.421576\pi\) | ||||
0.243892 | + | 0.969802i | \(0.421576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −72.8465 | −0.231259 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 293.190i | − | 0.924889i | −0.886648 | − | 0.462444i | \(-0.846972\pi\) | ||
0.886648 | − | 0.462444i | \(-0.153028\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 16.5370i | − | 0.0518400i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 297.586 | 0.927058 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −411.456 | − | 275.734i | −1.27386 | − | 0.853666i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 753.443i | − | 2.31829i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −60.5494 | −0.185166 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −151.436 | −0.460292 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 515.401i | − | 1.55710i | −0.627580 | − | 0.778552i | \(-0.715954\pi\) | ||
0.627580 | − | 0.778552i | \(-0.284046\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 145.650i | − | 0.437389i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 327.336i | − | 0.977122i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 452.163i | − | 1.34173i | −0.741580 | − | 0.670865i | \(-0.765923\pi\) | ||
0.741580 | − | 0.670865i | \(-0.234077\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −74.1388 | −0.218699 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4865i | 0.0395499i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 286.482 | 0.835224 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 108.355i | − | 0.314072i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −378.380 | −1.09043 | −0.545217 | − | 0.838295i | \(-0.683553\pi\) | ||||
−0.545217 | + | 0.838295i | \(0.683553\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −95.1859 | −0.272739 | −0.136369 | − | 0.990658i | \(-0.543543\pi\) | ||||
−0.136369 | + | 0.990658i | \(0.543543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 132.091 | 0.376328 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 457.473 | 1.29596 | 0.647979 | − | 0.761659i | \(-0.275615\pi\) | ||||
0.647979 | + | 0.761659i | \(0.275615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 549.514i | 1.54793i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 148.326i | − | 0.415478i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −308.486 | −0.859294 | −0.429647 | − | 0.902997i | \(-0.641362\pi\) | ||||
−0.429647 | + | 0.902997i | \(0.641362\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 137.243 | + | 333.894i | 0.380176 | + | 0.924914i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 208.693i | 0.574911i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −829.360 | −2.27222 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 432.928 | 1.17964 | 0.589820 | − | 0.807535i | \(-0.299199\pi\) | ||||
0.589820 | + | 0.807535i | \(0.299199\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 106.142i | − | 0.287649i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 168.232i | − | 0.453455i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 649.540i | 1.74139i | 0.491820 | + | 0.870697i | \(0.336332\pi\) | ||||
−0.491820 | + | 0.870697i | \(0.663668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 59.3883i | 0.158369i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −587.966 | −1.55959 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 103.303i | 0.272567i | 0.990670 | + | 0.136283i | \(0.0435158\pi\) | ||||
−0.990670 | + | 0.136283i | \(0.956484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 305.434 | 0.801663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 526.913i | − | 1.37575i | −0.725828 | − | 0.687876i | \(-0.758543\pi\) | ||
0.725828 | − | 0.687876i | \(-0.241457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.3614 | 0.0450944 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −73.5043 | −0.189934 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 93.9846 | 0.241606 | 0.120803 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120803 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 220.625 | 0.564259 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 350.072i | 0.890768i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 927.672i | 2.34854i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 218.605 | 0.550643 | 0.275321 | − | 0.961352i | \(-0.411216\pi\) | ||||
0.275321 | + | 0.961352i | \(0.411216\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −60.1826 | + | 89.8057i | −0.150834 | + | 0.225077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.984510i | 0.00245514i | 0.999999 | + | 0.00122757i | \(0.000390747\pi\) | ||||
−0.999999 | + | 0.00122757i | \(0.999609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 479.508 | 1.18985 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −66.5262 | −0.164262 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.7126i | 0.0852889i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 711.378i | − | 1.73931i | −0.493659 | − | 0.869655i | \(-0.664341\pi\) | ||
0.493659 | − | 0.869655i | \(-0.335659\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5533i | 0.0475749i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 332.818i | − | 0.805855i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −706.413 | −1.70220 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 98.1081i | − | 0.235271i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 692.753 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 205.304i | 0.487658i | 0.969818 | + | 0.243829i | \(0.0784035\pi\) | ||||
−0.969818 | + | 0.243829i | \(0.921596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −138.297 | −0.326944 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −772.638 | −1.81797 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −126.710 | −0.296744 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.4811 | −0.0733824 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 534.388i | 1.23988i | 0.784649 | + | 0.619940i | \(0.212843\pi\) | ||||
−0.784649 | + | 0.619940i | \(0.787157\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 561.059i | − | 1.29575i | −0.761747 | − | 0.647874i | \(-0.775658\pi\) | ||
0.761747 | − | 0.647874i | \(-0.224342\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 296.122 | 0.680740 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −133.581 | − | 89.5180i | −0.305676 | − | 0.204847i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 422.164i | 0.961649i | 0.876817 | + | 0.480825i | \(0.159663\pi\) | ||||
−0.876817 | + | 0.480825i | \(0.840337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 114.626 | 0.259923 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 780.825 | 1.76259 | 0.881293 | − | 0.472571i | \(-0.156674\pi\) | ||||
0.881293 | + | 0.472571i | \(0.156674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 207.582i | − | 0.466476i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3332i | 0.0231169i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 671.171i | 1.49481i | 0.664367 | + | 0.747406i | \(0.268701\pi\) | ||||
−0.664367 | + | 0.747406i | \(0.731299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.2967i | 0.0560903i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −48.5494 | −0.107173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 617.277i | − | 1.35665i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −371.441 | −0.812781 | −0.406390 | − | 0.913700i | \(-0.633213\pi\) | ||||
−0.406390 | + | 0.913700i | \(0.633213\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 135.456i | − | 0.295112i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 301.718 | 0.654487 | 0.327243 | − | 0.944940i | \(-0.393880\pi\) | ||||
0.327243 | + | 0.944940i | \(0.393880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −665.736 | −1.43788 | −0.718938 | − | 0.695074i | \(-0.755371\pi\) | ||||
−0.718938 | + | 0.695074i | \(0.755371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −241.498 | −0.519351 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 95.4717 | 0.204436 | 0.102218 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102218 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 145.473i | − | 0.310176i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 244.768i | − | 0.519678i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.5181 | 0.0370362 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 467.804 | + | 313.495i | 0.984851 | + | 0.659990i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 153.636i | − | 0.322087i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.3541 | 0.0821590 | 0.0410795 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410795 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1234.19 | 2.56589 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 48.1543i | − | 0.0996984i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 412.429i | 0.850369i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 344.218i | 0.706813i | 0.935470 | + | 0.353407i | \(0.114977\pi\) | ||||
−0.935470 | + | 0.353407i | \(0.885023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 314.454i | − | 0.643055i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 582.955 | 1.18728 | 0.593641 | − | 0.804730i | \(-0.297690\pi\) | ||||
0.593641 | + | 0.804730i | \(0.297690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 602.945i | 1.22301i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.8550 | 0.0320304 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 244.211i | 0.491371i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 166.892 | 0.334453 | 0.167226 | − | 0.985919i | \(-0.446519\pi\) | ||||
0.167226 | + | 0.985919i | \(0.446519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 522.624 | 1.04316 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −559.547 | −1.11242 | −0.556210 | − | 0.831042i | \(-0.687745\pi\) | ||||
−0.556210 | + | 0.831042i | \(0.687745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 968.457 | 1.91774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 826.580i | 1.63034i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 371.176i | 0.729226i | 0.931159 | + | 0.364613i | \(0.118799\pi\) | ||||
−0.931159 | + | 0.364613i | \(0.881201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −368.579 | −0.721290 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −54.9610 | + | 82.0139i | −0.107136 | + | 0.159871i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 551.858i | 1.07157i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.9601 | 0.0637526 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −338.563 | −0.652337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 967.227i | 1.85648i | 0.371981 | + | 0.928240i | \(0.378679\pi\) | ||||
−0.371981 | + | 0.928240i | \(0.621321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 316.578i | 0.605311i | 0.953100 | + | 0.302656i | \(0.0978732\pi\) | ||||
−0.953100 | + | 0.302656i | \(0.902127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 168.638i | 0.321216i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 491.724i | − | 0.933062i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −457.373 | −0.864600 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 303.942i | − | 0.572396i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 899.415 | 1.68746 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1269.99i | − | 2.37382i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 158.105 | 0.294422 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.3186 | −0.0506838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −700.118 | −1.29412 | −0.647059 | − | 0.762440i | \(-0.724001\pi\) | ||||
−0.647059 | + | 0.762440i | \(0.724001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.3289 | 0.0503294 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 258.404i | 0.474135i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 782.925i | 1.43131i | 0.698456 | + | 0.715653i | \(0.253871\pi\) | ||||
−0.698456 | + | 0.715653i | \(0.746129\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −115.716 | −0.210776 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 244.643 | − | 365.061i | 0.443998 | − | 0.662543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 412.270i | 0.745515i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −621.586 | −1.11997 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −358.027 | −0.642777 | −0.321388 | − | 0.946947i | \(-0.604150\pi\) | ||||
−0.321388 | + | 0.946947i | \(0.604150\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 622.850i | − | 1.11422i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.2831i | 0.0575456i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 982.338i | 1.74483i | 0.488769 | + | 0.872413i | \(0.337446\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 316.399i | 0.559998i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.5651 | −0.0521431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.6426i | − | 0.0468236i | −0.999726 | − | 0.0234118i | \(-0.992547\pi\) | ||
0.999726 | − | 0.0234118i | \(-0.00745289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −309.230 | −0.541559 | −0.270779 | − | 0.962641i | \(-0.587281\pi\) | ||||
−0.270779 | + | 0.962641i | \(0.587281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 335.912i | 0.586234i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −250.839 | −0.436242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 163.804 | 0.283889 | 0.141945 | − | 0.989875i | \(-0.454665\pi\) | ||||
0.141945 | + | 0.989875i | \(0.454665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 261.437 | 0.451532 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −313.940 | −0.540344 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.6157i | 0.0628056i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 563.720i | − | 0.963624i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 216.974 | 0.369632 | 0.184816 | − | 0.982773i | \(-0.440831\pi\) | ||||
0.184816 | + | 0.982773i | \(0.440831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −199.515 | + | 297.721i | −0.338736 | + | 0.505468i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 117.788i | − | 0.199304i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −893.250 | −1.50632 | −0.753162 | − | 0.657835i | \(-0.771472\pi\) | ||||
−0.753162 | + | 0.657835i | \(0.771472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −633.002 | −1.06387 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 51.0634i | 0.0855333i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1086.97i | 1.81464i | 0.420446 | + | 0.907318i | \(0.361874\pi\) | ||||
−0.420446 | + | 0.907318i | \(0.638126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 60.8027i | 0.101169i | 0.998720 | + | 0.0505846i | \(0.0161085\pi\) | ||||
−0.998720 | + | 0.0505846i | \(0.983892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 132.851i | − | 0.220317i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 890.629 | 1.47211 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 394.292i | 0.649575i | 0.945787 | + | 0.324788i | \(0.105293\pi\) | ||||
−0.945787 | + | 0.324788i | \(0.894707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 131.601 | 0.216093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1171.88i | − | 1.91798i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −899.074 | −1.46668 | −0.733340 | − | 0.679862i | \(-0.762039\pi\) | ||||
−0.733340 | + | 0.679862i | \(0.762039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −452.979 | −0.736552 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 593.943 | 0.962630 | 0.481315 | − | 0.876548i | \(-0.340159\pi\) | ||||
0.481315 | + | 0.876548i | \(0.340159\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 459.655 | 0.742576 | 0.371288 | − | 0.928518i | \(-0.378916\pi\) | ||||
0.371288 | + | 0.928518i | \(0.378916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 43.9763i | − | 0.0708154i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 92.2521i | − | 0.148077i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −487.517 | −0.780027 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0988 | − | 19.5462i | 0.0208911 | − | 0.0311742i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1265.63i | − | 2.01214i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −856.677 | −1.35765 | −0.678825 | − | 0.734300i | \(-0.737510\pi\) | ||||
−0.678825 | + | 0.734300i | \(0.737510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.1938 | 0.0271624 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1303.48i | − | 2.05273i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 971.302i | 1.52481i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 223.023i | 0.349019i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 264.843i | − | 0.413171i | −0.978429 | − | 0.206585i | \(-0.933765\pi\) | ||
0.978429 | − | 0.206585i | \(-0.0662352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −355.596 | −0.553026 | −0.276513 | − | 0.961010i | \(-0.589179\pi\) | ||||
−0.276513 | + | 0.961010i | \(0.589179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 313.691i | 0.486342i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 589.871 | 0.911701 | 0.455851 | − | 0.890056i | \(-0.349335\pi\) | ||||
0.455851 | + | 0.890056i | \(0.349335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72.4379i | 0.111615i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −107.325 | −0.164862 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 891.917 | 1.36588 | 0.682938 | − | 0.730477i | \(-0.260702\pi\) | ||||
0.682938 | + | 0.730477i | \(0.260702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1493.99 | 2.28089 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −336.600 | −0.512329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 828.284i | − | 1.25688i | −0.777858 | − | 0.628440i | \(-0.783694\pi\) | ||
0.777858 | − | 0.628440i | \(-0.216306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 769.980i | 1.16487i | 0.812877 | + | 0.582436i | \(0.197900\pi\) | ||||
−0.812877 | + | 0.582436i | \(0.802100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1147.81 | 1.73124 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 383.260 | + | 256.839i | 0.576330 | + | 0.386223i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 195.748i | 0.293475i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 307.789 | 0.460073 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.5784 | 0.0411005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 372.195i | 0.553038i | 0.961008 | + | 0.276519i | \(0.0891809\pi\) | ||||
−0.961008 | + | 0.276519i | \(0.910819\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 154.007i | 0.228158i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 484.617i | − | 0.715830i | −0.933754 | − | 0.357915i | \(-0.883488\pi\) | ||
0.933754 | − | 0.357915i | \(-0.116512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 183.289i | 0.269940i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 137.125 | 0.201359 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 779.041i | 1.14062i | 0.821431 | + | 0.570308i | \(0.193176\pi\) | ||||
−0.821431 | + | 0.570308i | \(0.806824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 83.4467 | 0.121820 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 279.594i | − | 0.406979i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1301.86 | 1.88949 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 76.9998 | 0.111432 | 0.0557162 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557162 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.04620 | 0.0101677 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −418.691 | −0.602434 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 922.328i | − | 1.32328i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 341.142i | 0.488043i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 754.168 | 1.07585 | 0.537923 | − | 0.842994i | \(-0.319209\pi\) | ||||
0.537923 | + | 0.842994i | \(0.319209\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −513.527 | + | 766.295i | −0.730479 | + | 1.09004i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 590.204i | 0.837169i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 430.396 | 0.608763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.7186 | 0.0687146 | 0.0343573 | − | 0.999410i | \(-0.489062\pi\) | ||||
0.0343573 | + | 0.999410i | \(0.489062\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 376.500i | 0.529537i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 159.640i | − | 0.223898i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 134.350i | 0.187903i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 310.313i | 0.432794i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 583.791 | 0.811949 | 0.405974 | − | 0.913884i | \(-0.366932\pi\) | ||||
0.405974 | + | 0.913884i | \(0.366932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 245.253i | 0.340157i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 803.873 | 1.11186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 685.517i | − | 0.945540i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1005.23 | 1.38271 | 0.691357 | − | 0.722513i | \(-0.257013\pi\) | ||||
0.691357 | + | 0.722513i | \(0.257013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −638.718 | −0.873759 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 850.053 | 1.15969 | 0.579845 | − | 0.814727i | \(-0.303113\pi\) | ||||
0.579845 | + | 0.814727i | \(0.303113\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 489.184i | − | 0.665557i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.6621i | 0.0429608i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1215.10 | −1.64425 | −0.822127 | − | 0.569305i | \(-0.807212\pi\) | ||||
−0.822127 | + | 0.569305i | \(0.807212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −694.958 | − | 465.721i | −0.937866 | − | 0.628503i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 661.859i | 0.890792i | 0.895334 | + | 0.445396i | \(0.146937\pi\) | ||||
−0.895334 | + | 0.445396i | \(0.853063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.0987 | 0.0591929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −286.702 | −0.383804 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 564.402i | − | 0.753541i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1354.03i | 1.80297i | 0.432812 | + | 0.901484i | \(0.357521\pi\) | ||||
−0.432812 | + | 0.901484i | \(0.642479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 243.804i | 0.323777i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 207.192i | 0.274426i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −972.577 | −1.28478 | −0.642389 | − | 0.766379i | \(-0.722057\pi\) | ||||
−0.642389 | + | 0.766379i | \(0.722057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.4808i | 0.0138087i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −644.913 | −0.847454 | −0.423727 | − | 0.905790i | \(-0.639278\pi\) | ||||
−0.423727 | + | 0.905790i | \(0.639278\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 114.838i | 0.150509i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −578.081 | −0.755662 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2575.50 | 3.35789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −665.867 | −0.865887 | −0.432943 | − | 0.901421i | \(-0.642525\pi\) | ||||
−0.432943 | + | 0.901421i | \(0.642525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 319.939 | 0.414966 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 127.536i | − | 0.164988i | −0.996592 | − | 0.0824942i | \(-0.973711\pi\) | ||
0.996592 | − | 0.0824942i | \(-0.0262886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 559.064i | 0.721373i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −276.241 | −0.355523 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −374.232 | + | 558.436i | −0.480400 | + | 0.716863i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 53.1526i | − | 0.0680572i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 120.183 | 0.153490 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1044.59 | −1.33068 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 627.730i | 0.797625i | 0.917033 | + | 0.398812i | \(0.130577\pi\) | ||||
−0.917033 | + | 0.398812i | \(0.869423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 439.960i | 0.557618i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 140.612i | 0.177765i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 980.540i | − | 1.23649i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −655.664 | −0.824734 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1418.77i | − | 1.78014i | −0.455827 | − | 0.890069i | \(-0.650656\pi\) | ||
0.455827 | − | 0.890069i | \(-0.349344\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1201.74 | −1.50405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 84.2481i | − | 0.105179i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 80.2213 | 0.0999020 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −205.506 | −0.255287 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 93.8954 | 0.116351 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −753.612 | −0.931535 | −0.465768 | − | 0.884907i | \(-0.654222\pi\) | ||||
−0.465768 | + | 0.884907i | \(0.654222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 225.670i | − | 0.278261i | −0.990274 | − | 0.139131i | \(-0.955569\pi\) | ||
0.990274 | − | 0.139131i | \(-0.0444308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 689.297i | 0.847844i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1341.98 | −1.64660 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 386.720 | + | 259.158i | 0.473342 | + | 0.317207i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 250.525i | − | 0.305891i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 515.673 | 0.628104 | 0.314052 | − | 0.949406i | \(-0.398313\pi\) | ||||
0.314052 | + | 0.949406i | \(0.398313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1436.24 | 1.74513 | 0.872564 | − | 0.488500i | \(-0.162456\pi\) | ||||
0.872564 | + | 0.488500i | \(0.162456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 36.7042i | − | 0.0444899i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 134.792i | − | 0.162989i | −0.996674 | − | 0.0814944i | \(-0.974031\pi\) | ||
0.996674 | − | 0.0814944i | \(-0.0259693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 376.958i | 0.454714i | 0.973811 | + | 0.227357i | \(0.0730084\pi\) | ||||
−0.973811 | + | 0.227357i | \(0.926992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 538.355i | 0.647840i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 996.047 | 1.19573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2230.38i | − | 2.67111i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −98.0133 | −0.117101 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 572.973i | 0.682924i | 0.939896 | + | 0.341462i | \(0.110922\pi\) | ||||
−0.939896 | + | 0.341462i | \(0.889078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 306.042 | 0.363903 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −328.736 | −0.389959 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3527.56 | 4.17463 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 395.808 | 0.467305 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 609.737i | − | 0.718183i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 410.892i | − | 0.482834i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1076.65 | −1.26219 | −0.631096 | − | 0.775705i | \(-0.717395\pi\) | ||||
−0.631096 | + | 0.775705i | \(0.717395\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 350.007 | + | 234.555i | 0.409365 | + | 0.274333i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1506.83i | 1.75826i | 0.476578 | + | 0.879132i | \(0.341877\pi\) | ||||
−0.476578 | + | 0.879132i | \(0.658123\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 929.147 | 1.08166 | 0.540831 | − | 0.841131i | \(-0.318110\pi\) | ||||
0.540831 | + | 0.841131i | \(0.318110\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −201.310 | −0.233810 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 211.241i | 0.244775i | 0.992482 | + | 0.122388i | \(0.0390551\pi\) | ||||
−0.992482 | + | 0.122388i | \(0.960945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1444.87i | 1.67037i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 676.491i | − | 0.780266i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 89.7306i | − | 0.103257i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1125.73 | 1.29246 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 167.387i | 0.191737i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 112.636 | 0.128727 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 229.052i | 0.261176i | 0.991437 | + | 0.130588i | \(0.0416865\pi\) | ||||
−0.991437 | + | 0.130588i | \(0.958313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −413.491 | −0.470410 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1354.01 | −1.53690 | −0.768449 | − | 0.639911i | \(-0.778971\pi\) | ||||
−0.768449 | + | 0.639911i | \(0.778971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 391.523 | 0.443401 | 0.221701 | − | 0.975115i | \(-0.428839\pi\) | ||||
0.221701 | + | 0.975115i | \(0.428839\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1297.12 | −1.46567 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 697.322i | 0.786158i | 0.919505 | + | 0.393079i | \(0.128590\pi\) | ||||
−0.919505 | + | 0.393079i | \(0.871410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 579.287i | − | 0.651616i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.43486 | 0.00722206 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 727.608 | + | 487.601i | 0.814791 | + | 0.546026i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 674.736i | − | 0.753895i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 372.641 | 0.415430 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 436.278 | 0.485292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1335.02i | − | 1.48171i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 139.409i | 0.154384i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 116.630i | − | 0.128873i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 626.344i | − | 0.690567i | −0.938498 | − | 0.345283i | \(-0.887783\pi\) | ||
0.938498 | − | 0.345283i | \(-0.112217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 393.053 | 0.432402 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 517.549i | − | 0.568111i | −0.958808 | − | 0.284056i | \(-0.908320\pi\) | ||
0.958808 | − | 0.284056i | \(-0.0916800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.3290 | 0.0748401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 493.837i | 0.539712i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 663.948 | 0.724043 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −900.211 | −0.979555 | −0.489777 | − | 0.871848i | \(-0.662922\pi\) | ||||
−0.489777 | + | 0.871848i | \(0.662922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 135.751 | 0.147395 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1889.82 | −2.04748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1438.96i | 1.55563i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 223.975i | 0.241612i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −734.220 | −0.790333 | −0.395167 | − | 0.918609i | \(-0.629313\pi\) | ||||
−0.395167 | + | 0.918609i | \(0.629313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −603.070 | − | 404.143i | −0.647766 | − | 0.434095i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 445.157i | − | 0.477125i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 137.773 | 0.147351 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 832.710 | 0.888698 | 0.444349 | − | 0.895854i | \(-0.353435\pi\) | ||||
0.444349 | + | 0.895854i | \(0.353435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 264.443i | − | 0.281622i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1383.55i | 1.47030i | 0.677905 | + | 0.735149i | \(0.262888\pi\) | ||||
−0.677905 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 299.437i | − | 0.317536i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 126.174i | 0.133517i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −322.935 | −0.341008 | −0.170504 | − | 0.985357i | \(-0.554540\pi\) | ||||
−0.170504 | + | 0.985357i | \(0.554540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2852.24i | − | 3.00552i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −507.820 | −0.533985 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1815.82i | − | 1.90537i | −0.303962 | − | 0.952684i | \(-0.598309\pi\) | ||
0.303962 | − | 0.952684i | \(-0.401691\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1433.56 | 1.50111 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.6429 | −0.0299299 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.0848 | 0.0386703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 605.200 | 0.629760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 515.434i | − | 0.535237i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1115.72i | − | 1.15619i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −738.252 | −0.763446 | −0.381723 | − | 0.924277i | \(-0.624669\pi\) | ||||
−0.381723 | + | 0.924277i | \(0.624669\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −477.586 | + | 712.663i | −0.492864 | + | 0.735462i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1140.17i | − | 1.17422i | −0.809507 | − | 0.587111i | \(-0.800265\pi\) | ||
0.809507 | − | 0.587111i | \(-0.199735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −186.072 | −0.191236 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1305.00 | −1.33846 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1559.45i | − | 1.59616i | −0.602550 | − | 0.798081i | \(-0.705849\pi\) | ||
0.602550 | − | 0.798081i | \(-0.294151\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0787i | 0.0205094i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 104.875i | 0.106906i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 635.108i | − | 0.646091i | −0.946383 | − | 0.323046i | \(-0.895293\pi\) | ||
0.946383 | − | 0.323046i | \(-0.104707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −502.680 | −0.510335 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 262.295i | 0.265750i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −207.362 | −0.209668 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 700.746i | 0.707110i | 0.935414 | + | 0.353555i | \(0.115027\pi\) | ||||
−0.935414 | + | 0.353555i | \(0.884973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −892.702 | −0.898995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 217.921 | 0.219016 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1462.90 | −1.46730 | −0.733649 | − | 0.679529i | \(-0.762184\pi\) | ||||
−0.733649 | + | 0.679529i | \(0.762184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −252.274 | −0.252526 |
(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 | 912.3.o.c.721.1 | 6 | ||
3.2 | odd | 2 | 2736.3.o.m.721.5 | 6 | |||
4.3 | odd | 2 | 228.3.h.a.37.4 | yes | 6 | ||
12.11 | even | 2 | 684.3.h.e.37.5 | 6 | |||
19.18 | odd | 2 | inner | 912.3.o.c.721.4 | 6 | ||
57.56 | even | 2 | 2736.3.o.m.721.6 | 6 | |||
76.75 | even | 2 | 228.3.h.a.37.1 | ✓ | 6 | ||
228.227 | odd | 2 | 684.3.h.e.37.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.h.a.37.1 | ✓ | 6 | 76.75 | even | 2 | ||
228.3.h.a.37.4 | yes | 6 | 4.3 | odd | 2 | ||
684.3.h.e.37.5 | 6 | 12.11 | even | 2 | |||
684.3.h.e.37.6 | 6 | 228.227 | odd | 2 | |||
912.3.o.c.721.1 | 6 | 1.1 | even | 1 | trivial | ||
912.3.o.c.721.4 | 6 | 19.18 | odd | 2 | inner | ||
2736.3.o.m.721.5 | 6 | 3.2 | odd | 2 | |||
2736.3.o.m.721.6 | 6 | 57.56 | even | 2 |