Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.a (trivial) |
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: | yes |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 25.0000 | 0.790569 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | −51.0000 | −1.22687 | ||||||||
\(13\) | 30.0000 | 0.640039 | 0.320019 | − | 0.947411i | \(-0.396311\pi\) | ||||
0.320019 | + | 0.947411i | \(0.396311\pi\) | |||||||
\(14\) | 35.0000 | 0.668153 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | −134.000 | −1.91175 | −0.955876 | − | 0.293771i | \(-0.905090\pi\) | ||||
−0.955876 | + | 0.293771i | \(0.905090\pi\) | |||||||
\(18\) | 45.0000 | 0.589256 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 85.0000 | 0.950329 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | 112.000 | 1.01537 | 0.507687 | − | 0.861541i | \(-0.330501\pi\) | ||||
0.507687 | + | 0.861541i | \(0.330501\pi\) | |||||||
\(24\) | −135.000 | −1.14820 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 150.000 | 1.13144 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 119.000 | 0.803175 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | −75.0000 | −0.456435 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 85.0000 | 0.469563 | ||||||||
\(33\) | −36.0000 | −0.189903 | ||||||||
\(34\) | −670.000 | −3.37953 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | −460.000 | −1.96373 | ||||||||
\(39\) | −90.0000 | −0.369527 | ||||||||
\(40\) | 225.000 | 0.889391 | ||||||||
\(41\) | 18.0000 | 0.0685641 | 0.0342820 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342820 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(42\) | −105.000 | −0.385758 | ||||||||
\(43\) | 340.000 | 1.20580 | 0.602901 | − | 0.797816i | \(-0.294011\pi\) | ||||
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(44\) | 204.000 | 0.698958 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 560.000 | 1.79495 | ||||||||
\(47\) | 208.000 | 0.645530 | 0.322765 | − | 0.946479i | \(-0.395388\pi\) | ||||
0.322765 | + | 0.946479i | \(0.395388\pi\) | |||||||
\(48\) | −267.000 | −0.802878 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 125.000 | 0.353553 | ||||||||
\(51\) | 402.000 | 1.10375 | ||||||||
\(52\) | 510.000 | 1.36008 | ||||||||
\(53\) | −754.000 | −1.95415 | −0.977074 | − | 0.212899i | \(-0.931709\pi\) | ||||
−0.977074 | + | 0.212899i | \(0.931709\pi\) | |||||||
\(54\) | −135.000 | −0.340207 | ||||||||
\(55\) | 60.0000 | 0.147098 | ||||||||
\(56\) | 315.000 | 0.751672 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | −290.000 | −0.656532 | ||||||||
\(59\) | 380.000 | 0.838505 | 0.419252 | − | 0.907870i | \(-0.362292\pi\) | ||||
0.419252 | + | 0.907870i | \(0.362292\pi\) | |||||||
\(60\) | −255.000 | −0.548673 | ||||||||
\(61\) | 718.000 | 1.50706 | 0.753529 | − | 0.657415i | \(-0.228350\pi\) | ||||
0.753529 | + | 0.657415i | \(0.228350\pi\) | |||||||
\(62\) | −1120.00 | −2.29420 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 150.000 | 0.286234 | ||||||||
\(66\) | −180.000 | −0.335704 | ||||||||
\(67\) | 412.000 | 0.751251 | 0.375625 | − | 0.926772i | \(-0.377428\pi\) | ||||
0.375625 | + | 0.926772i | \(0.377428\pi\) | |||||||
\(68\) | −2278.00 | −4.06247 | ||||||||
\(69\) | −336.000 | −0.586227 | ||||||||
\(70\) | 175.000 | 0.298807 | ||||||||
\(71\) | −960.000 | −1.60466 | −0.802331 | − | 0.596879i | \(-0.796407\pi\) | ||||
−0.802331 | + | 0.596879i | \(0.796407\pi\) | |||||||
\(72\) | 405.000 | 0.662913 | ||||||||
\(73\) | 1066.00 | 1.70912 | 0.854561 | − | 0.519352i | \(-0.173826\pi\) | ||||
0.854561 | + | 0.519352i | \(0.173826\pi\) | |||||||
\(74\) | −730.000 | −1.14677 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −1564.00 | −2.36057 | ||||||||
\(77\) | 84.0000 | 0.124321 | ||||||||
\(78\) | −450.000 | −0.653237 | ||||||||
\(79\) | 896.000 | 1.27605 | 0.638025 | − | 0.770016i | \(-0.279752\pi\) | ||||
0.638025 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(80\) | 445.000 | 0.621906 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 90.0000 | 0.121205 | ||||||||
\(83\) | 436.000 | 0.576593 | 0.288296 | − | 0.957541i | \(-0.406911\pi\) | ||||
0.288296 | + | 0.957541i | \(0.406911\pi\) | |||||||
\(84\) | −357.000 | −0.463713 | ||||||||
\(85\) | −670.000 | −0.854961 | ||||||||
\(86\) | 1700.00 | 2.13158 | ||||||||
\(87\) | 174.000 | 0.214423 | ||||||||
\(88\) | 540.000 | 0.654139 | ||||||||
\(89\) | −1038.00 | −1.23627 | −0.618134 | − | 0.786073i | \(-0.712111\pi\) | ||||
−0.618134 | + | 0.786073i | \(0.712111\pi\) | |||||||
\(90\) | 225.000 | 0.263523 | ||||||||
\(91\) | 210.000 | 0.241912 | ||||||||
\(92\) | 1904.00 | 2.15767 | ||||||||
\(93\) | 672.000 | 0.749281 | ||||||||
\(94\) | 1040.00 | 1.14115 | ||||||||
\(95\) | −460.000 | −0.496790 | ||||||||
\(96\) | −255.000 | −0.271102 | ||||||||
\(97\) | −702.000 | −0.734818 | −0.367409 | − | 0.930060i | \(-0.619755\pi\) | ||||
−0.367409 | + | 0.930060i | \(0.619755\pi\) | |||||||
\(98\) | 245.000 | 0.252538 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 425.000 | 0.425000 | ||||||||
\(101\) | 46.0000 | 0.0453185 | 0.0226593 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226593 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(102\) | 2010.00 | 1.95117 | ||||||||
\(103\) | 1880.00 | 1.79847 | 0.899233 | − | 0.437471i | \(-0.144126\pi\) | ||||
0.899233 | + | 0.437471i | \(0.144126\pi\) | |||||||
\(104\) | 1350.00 | 1.27287 | ||||||||
\(105\) | −105.000 | −0.0975900 | ||||||||
\(106\) | −3770.00 | −3.45448 | ||||||||
\(107\) | 732.000 | 0.661356 | 0.330678 | − | 0.943744i | \(-0.392723\pi\) | ||||
0.330678 | + | 0.943744i | \(0.392723\pi\) | |||||||
\(108\) | −459.000 | −0.408956 | ||||||||
\(109\) | −378.000 | −0.332164 | −0.166082 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166082 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(110\) | 300.000 | 0.260035 | ||||||||
\(111\) | 438.000 | 0.374533 | ||||||||
\(112\) | 623.000 | 0.525607 | ||||||||
\(113\) | 1458.00 | 1.21378 | 0.606890 | − | 0.794786i | \(-0.292417\pi\) | ||||
0.606890 | + | 0.794786i | \(0.292417\pi\) | |||||||
\(114\) | 1380.00 | 1.13376 | ||||||||
\(115\) | 560.000 | 0.454089 | ||||||||
\(116\) | −986.000 | −0.789205 | ||||||||
\(117\) | 270.000 | 0.213346 | ||||||||
\(118\) | 1900.00 | 1.48228 | ||||||||
\(119\) | −938.000 | −0.722574 | ||||||||
\(120\) | −675.000 | −0.513490 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 3590.00 | 2.66413 | ||||||||
\(123\) | −54.0000 | −0.0395855 | ||||||||
\(124\) | −3808.00 | −2.75781 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 315.000 | 0.222718 | ||||||||
\(127\) | 608.000 | 0.424813 | 0.212407 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212407 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(128\) | −2115.00 | −1.46048 | ||||||||
\(129\) | −1020.00 | −0.696170 | ||||||||
\(130\) | 750.000 | 0.505995 | ||||||||
\(131\) | −956.000 | −0.637604 | −0.318802 | − | 0.947821i | \(-0.603280\pi\) | ||||
−0.318802 | + | 0.947821i | \(0.603280\pi\) | |||||||
\(132\) | −612.000 | −0.403544 | ||||||||
\(133\) | −644.000 | −0.419864 | ||||||||
\(134\) | 2060.00 | 1.32804 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −6030.00 | −3.80197 | ||||||||
\(137\) | −374.000 | −0.233233 | −0.116617 | − | 0.993177i | \(-0.537205\pi\) | ||||
−0.116617 | + | 0.993177i | \(0.537205\pi\) | |||||||
\(138\) | −1680.00 | −1.03631 | ||||||||
\(139\) | 396.000 | 0.241642 | 0.120821 | − | 0.992674i | \(-0.461447\pi\) | ||||
0.120821 | + | 0.992674i | \(0.461447\pi\) | |||||||
\(140\) | 595.000 | 0.359191 | ||||||||
\(141\) | −624.000 | −0.372697 | ||||||||
\(142\) | −4800.00 | −2.83667 | ||||||||
\(143\) | 360.000 | 0.210522 | ||||||||
\(144\) | 801.000 | 0.463542 | ||||||||
\(145\) | −290.000 | −0.166091 | ||||||||
\(146\) | 5330.00 | 3.02133 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −2482.00 | −1.37851 | ||||||||
\(149\) | −1874.00 | −1.03036 | −0.515181 | − | 0.857081i | \(-0.672275\pi\) | ||||
−0.515181 | + | 0.857081i | \(0.672275\pi\) | |||||||
\(150\) | −375.000 | −0.204124 | ||||||||
\(151\) | −1096.00 | −0.590670 | −0.295335 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295335 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(152\) | −4140.00 | −2.20920 | ||||||||
\(153\) | −1206.00 | −0.637250 | ||||||||
\(154\) | 420.000 | 0.219770 | ||||||||
\(155\) | −1120.00 | −0.580391 | ||||||||
\(156\) | −1530.00 | −0.785244 | ||||||||
\(157\) | 1918.00 | 0.974988 | 0.487494 | − | 0.873126i | \(-0.337911\pi\) | ||||
0.487494 | + | 0.873126i | \(0.337911\pi\) | |||||||
\(158\) | 4480.00 | 2.25576 | ||||||||
\(159\) | 2262.00 | 1.12823 | ||||||||
\(160\) | 425.000 | 0.209995 | ||||||||
\(161\) | 784.000 | 0.383776 | ||||||||
\(162\) | 405.000 | 0.196419 | ||||||||
\(163\) | 2316.00 | 1.11290 | 0.556451 | − | 0.830880i | \(-0.312163\pi\) | ||||
0.556451 | + | 0.830880i | \(0.312163\pi\) | |||||||
\(164\) | 306.000 | 0.145699 | ||||||||
\(165\) | −180.000 | −0.0849272 | ||||||||
\(166\) | 2180.00 | 1.01928 | ||||||||
\(167\) | −1736.00 | −0.804405 | −0.402203 | − | 0.915551i | \(-0.631755\pi\) | ||||
−0.402203 | + | 0.915551i | \(0.631755\pi\) | |||||||
\(168\) | −945.000 | −0.433978 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | −3350.00 | −1.51137 | ||||||||
\(171\) | −828.000 | −0.370285 | ||||||||
\(172\) | 5780.00 | 2.56233 | ||||||||
\(173\) | −2442.00 | −1.07319 | −0.536595 | − | 0.843840i | \(-0.680290\pi\) | ||||
−0.536595 | + | 0.843840i | \(0.680290\pi\) | |||||||
\(174\) | 870.000 | 0.379049 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 1068.00 | 0.457406 | ||||||||
\(177\) | −1140.00 | −0.484111 | ||||||||
\(178\) | −5190.00 | −2.18543 | ||||||||
\(179\) | −4092.00 | −1.70866 | −0.854331 | − | 0.519730i | \(-0.826033\pi\) | ||||
−0.854331 | + | 0.519730i | \(0.826033\pi\) | |||||||
\(180\) | 765.000 | 0.316776 | ||||||||
\(181\) | 1270.00 | 0.521538 | 0.260769 | − | 0.965401i | \(-0.416024\pi\) | ||||
0.260769 | + | 0.965401i | \(0.416024\pi\) | |||||||
\(182\) | 1050.00 | 0.427644 | ||||||||
\(183\) | −2154.00 | −0.870100 | ||||||||
\(184\) | 5040.00 | 2.01931 | ||||||||
\(185\) | −730.000 | −0.290112 | ||||||||
\(186\) | 3360.00 | 1.32455 | ||||||||
\(187\) | −1608.00 | −0.628816 | ||||||||
\(188\) | 3536.00 | 1.37175 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −2300.00 | −0.878208 | ||||||||
\(191\) | 4904.00 | 1.85781 | 0.928903 | − | 0.370323i | \(-0.120753\pi\) | ||||
0.928903 | + | 0.370323i | \(0.120753\pi\) | |||||||
\(192\) | 861.000 | 0.323632 | ||||||||
\(193\) | 2178.00 | 0.812310 | 0.406155 | − | 0.913804i | \(-0.366869\pi\) | ||||
0.406155 | + | 0.913804i | \(0.366869\pi\) | |||||||
\(194\) | −3510.00 | −1.29899 | ||||||||
\(195\) | −450.000 | −0.165257 | ||||||||
\(196\) | 833.000 | 0.303571 | ||||||||
\(197\) | −2850.00 | −1.03073 | −0.515366 | − | 0.856970i | \(-0.672344\pi\) | ||||
−0.515366 | + | 0.856970i | \(0.672344\pi\) | |||||||
\(198\) | 540.000 | 0.193819 | ||||||||
\(199\) | −1144.00 | −0.407518 | −0.203759 | − | 0.979021i | \(-0.565316\pi\) | ||||
−0.203759 | + | 0.979021i | \(0.565316\pi\) | |||||||
\(200\) | 1125.00 | 0.397748 | ||||||||
\(201\) | −1236.00 | −0.433735 | ||||||||
\(202\) | 230.000 | 0.0801126 | ||||||||
\(203\) | −406.000 | −0.140372 | ||||||||
\(204\) | 6834.00 | 2.34547 | ||||||||
\(205\) | 90.0000 | 0.0306628 | ||||||||
\(206\) | 9400.00 | 3.17927 | ||||||||
\(207\) | 1008.00 | 0.338458 | ||||||||
\(208\) | 2670.00 | 0.890054 | ||||||||
\(209\) | −1104.00 | −0.365384 | ||||||||
\(210\) | −525.000 | −0.172516 | ||||||||
\(211\) | 412.000 | 0.134423 | 0.0672115 | − | 0.997739i | \(-0.478590\pi\) | ||||
0.0672115 | + | 0.997739i | \(0.478590\pi\) | |||||||
\(212\) | −12818.0 | −4.15257 | ||||||||
\(213\) | 2880.00 | 0.926452 | ||||||||
\(214\) | 3660.00 | 1.16912 | ||||||||
\(215\) | 1700.00 | 0.539251 | ||||||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | −1568.00 | −0.490520 | ||||||||
\(218\) | −1890.00 | −0.587188 | ||||||||
\(219\) | −3198.00 | −0.986762 | ||||||||
\(220\) | 1020.00 | 0.312584 | ||||||||
\(221\) | −4020.00 | −1.22359 | ||||||||
\(222\) | 2190.00 | 0.662086 | ||||||||
\(223\) | −1632.00 | −0.490075 | −0.245038 | − | 0.969514i | \(-0.578800\pi\) | ||||
−0.245038 | + | 0.969514i | \(0.578800\pi\) | |||||||
\(224\) | 595.000 | 0.177478 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 7290.00 | 2.14568 | ||||||||
\(227\) | 4084.00 | 1.19412 | 0.597059 | − | 0.802198i | \(-0.296336\pi\) | ||||
0.597059 | + | 0.802198i | \(0.296336\pi\) | |||||||
\(228\) | 4692.00 | 1.36287 | ||||||||
\(229\) | −3386.00 | −0.977088 | −0.488544 | − | 0.872539i | \(-0.662472\pi\) | ||||
−0.488544 | + | 0.872539i | \(0.662472\pi\) | |||||||
\(230\) | 2800.00 | 0.802724 | ||||||||
\(231\) | −252.000 | −0.0717765 | ||||||||
\(232\) | −2610.00 | −0.738599 | ||||||||
\(233\) | 5322.00 | 1.49638 | 0.748188 | − | 0.663486i | \(-0.230924\pi\) | ||||
0.748188 | + | 0.663486i | \(0.230924\pi\) | |||||||
\(234\) | 1350.00 | 0.377146 | ||||||||
\(235\) | 1040.00 | 0.288690 | ||||||||
\(236\) | 6460.00 | 1.78182 | ||||||||
\(237\) | −2688.00 | −0.736727 | ||||||||
\(238\) | −4690.00 | −1.27734 | ||||||||
\(239\) | 3736.00 | 1.01114 | 0.505569 | − | 0.862786i | \(-0.331283\pi\) | ||||
0.505569 | + | 0.862786i | \(0.331283\pi\) | |||||||
\(240\) | −1335.00 | −0.359058 | ||||||||
\(241\) | 210.000 | 0.0561298 | 0.0280649 | − | 0.999606i | \(-0.491065\pi\) | ||||
0.0280649 | + | 0.999606i | \(0.491065\pi\) | |||||||
\(242\) | −5935.00 | −1.57651 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 12206.0 | 3.20250 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | −270.000 | −0.0699779 | ||||||||
\(247\) | −2760.00 | −0.710990 | ||||||||
\(248\) | −10080.0 | −2.58097 | ||||||||
\(249\) | −1308.00 | −0.332896 | ||||||||
\(250\) | 625.000 | 0.158114 | ||||||||
\(251\) | −4212.00 | −1.05920 | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
−0.529600 | + | 0.848248i | \(0.677658\pi\) | |||||||
\(252\) | 1071.00 | 0.267725 | ||||||||
\(253\) | 1344.00 | 0.333978 | ||||||||
\(254\) | 3040.00 | 0.750971 | ||||||||
\(255\) | 2010.00 | 0.493612 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | 5130.00 | 1.24514 | 0.622569 | − | 0.782565i | \(-0.286089\pi\) | ||||
0.622569 | + | 0.782565i | \(0.286089\pi\) | |||||||
\(258\) | −5100.00 | −1.23067 | ||||||||
\(259\) | −1022.00 | −0.245189 | ||||||||
\(260\) | 2550.00 | 0.608247 | ||||||||
\(261\) | −522.000 | −0.123797 | ||||||||
\(262\) | −4780.00 | −1.12714 | ||||||||
\(263\) | 848.000 | 0.198821 | 0.0994105 | − | 0.995047i | \(-0.468304\pi\) | ||||
0.0994105 | + | 0.995047i | \(0.468304\pi\) | |||||||
\(264\) | −1620.00 | −0.377667 | ||||||||
\(265\) | −3770.00 | −0.873922 | ||||||||
\(266\) | −3220.00 | −0.742221 | ||||||||
\(267\) | 3114.00 | 0.713759 | ||||||||
\(268\) | 7004.00 | 1.59641 | ||||||||
\(269\) | −1274.00 | −0.288763 | −0.144381 | − | 0.989522i | \(-0.546119\pi\) | ||||
−0.144381 | + | 0.989522i | \(0.546119\pi\) | |||||||
\(270\) | −675.000 | −0.152145 | ||||||||
\(271\) | 864.000 | 0.193669 | 0.0968344 | − | 0.995301i | \(-0.469128\pi\) | ||||
0.0968344 | + | 0.995301i | \(0.469128\pi\) | |||||||
\(272\) | −11926.0 | −2.65853 | ||||||||
\(273\) | −630.000 | −0.139668 | ||||||||
\(274\) | −1870.00 | −0.412302 | ||||||||
\(275\) | 300.000 | 0.0657843 | ||||||||
\(276\) | −5712.00 | −1.24573 | ||||||||
\(277\) | −8530.00 | −1.85025 | −0.925123 | − | 0.379668i | \(-0.876038\pi\) | ||||
−0.925123 | + | 0.379668i | \(0.876038\pi\) | |||||||
\(278\) | 1980.00 | 0.427167 | ||||||||
\(279\) | −2016.00 | −0.432598 | ||||||||
\(280\) | 1575.00 | 0.336158 | ||||||||
\(281\) | −5382.00 | −1.14257 | −0.571287 | − | 0.820750i | \(-0.693556\pi\) | ||||
−0.571287 | + | 0.820750i | \(0.693556\pi\) | |||||||
\(282\) | −3120.00 | −0.658841 | ||||||||
\(283\) | 6236.00 | 1.30986 | 0.654932 | − | 0.755687i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755687i | \(0.272697\pi\) | |||||||
\(284\) | −16320.0 | −3.40991 | ||||||||
\(285\) | 1380.00 | 0.286822 | ||||||||
\(286\) | 1800.00 | 0.372155 | ||||||||
\(287\) | 126.000 | 0.0259148 | ||||||||
\(288\) | 765.000 | 0.156521 | ||||||||
\(289\) | 13043.0 | 2.65479 | ||||||||
\(290\) | −1450.00 | −0.293610 | ||||||||
\(291\) | 2106.00 | 0.424247 | ||||||||
\(292\) | 18122.0 | 3.63188 | ||||||||
\(293\) | −818.000 | −0.163099 | −0.0815496 | − | 0.996669i | \(-0.525987\pi\) | ||||
−0.0815496 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(294\) | −735.000 | −0.145803 | ||||||||
\(295\) | 1900.00 | 0.374991 | ||||||||
\(296\) | −6570.00 | −1.29011 | ||||||||
\(297\) | −324.000 | −0.0633010 | ||||||||
\(298\) | −9370.00 | −1.82144 | ||||||||
\(299\) | 3360.00 | 0.649879 | ||||||||
\(300\) | −1275.00 | −0.245374 | ||||||||
\(301\) | 2380.00 | 0.455751 | ||||||||
\(302\) | −5480.00 | −1.04417 | ||||||||
\(303\) | −138.000 | −0.0261647 | ||||||||
\(304\) | −8188.00 | −1.54478 | ||||||||
\(305\) | 3590.00 | 0.673976 | ||||||||
\(306\) | −6030.00 | −1.12651 | ||||||||
\(307\) | −2268.00 | −0.421634 | −0.210817 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210817 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(308\) | 1428.00 | 0.264181 | ||||||||
\(309\) | −5640.00 | −1.03834 | ||||||||
\(310\) | −5600.00 | −1.02600 | ||||||||
\(311\) | 6648.00 | 1.21213 | 0.606067 | − | 0.795414i | \(-0.292746\pi\) | ||||
0.606067 | + | 0.795414i | \(0.292746\pi\) | |||||||
\(312\) | −4050.00 | −0.734891 | ||||||||
\(313\) | 9818.00 | 1.77299 | 0.886495 | − | 0.462737i | \(-0.153133\pi\) | ||||
0.886495 | + | 0.462737i | \(0.153133\pi\) | |||||||
\(314\) | 9590.00 | 1.72355 | ||||||||
\(315\) | 315.000 | 0.0563436 | ||||||||
\(316\) | 15232.0 | 2.71160 | ||||||||
\(317\) | 934.000 | 0.165485 | 0.0827424 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827424 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(318\) | 11310.0 | 1.99444 | ||||||||
\(319\) | −696.000 | −0.122158 | ||||||||
\(320\) | −1435.00 | −0.250684 | ||||||||
\(321\) | −2196.00 | −0.381834 | ||||||||
\(322\) | 3920.00 | 0.678426 | ||||||||
\(323\) | 12328.0 | 2.12368 | ||||||||
\(324\) | 1377.00 | 0.236111 | ||||||||
\(325\) | 750.000 | 0.128008 | ||||||||
\(326\) | 11580.0 | 1.96735 | ||||||||
\(327\) | 1134.00 | 0.191775 | ||||||||
\(328\) | 810.000 | 0.136356 | ||||||||
\(329\) | 1456.00 | 0.243987 | ||||||||
\(330\) | −900.000 | −0.150131 | ||||||||
\(331\) | 2292.00 | 0.380603 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(332\) | 7412.00 | 1.22526 | ||||||||
\(333\) | −1314.00 | −0.216237 | ||||||||
\(334\) | −8680.00 | −1.42200 | ||||||||
\(335\) | 2060.00 | 0.335970 | ||||||||
\(336\) | −1869.00 | −0.303459 | ||||||||
\(337\) | −6062.00 | −0.979876 | −0.489938 | − | 0.871757i | \(-0.662981\pi\) | ||||
−0.489938 | + | 0.871757i | \(0.662981\pi\) | |||||||
\(338\) | −6485.00 | −1.04360 | ||||||||
\(339\) | −4374.00 | −0.700776 | ||||||||
\(340\) | −11390.0 | −1.81679 | ||||||||
\(341\) | −2688.00 | −0.426872 | ||||||||
\(342\) | −4140.00 | −0.654578 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 15300.0 | 2.39803 | ||||||||
\(345\) | −1680.00 | −0.262169 | ||||||||
\(346\) | −12210.0 | −1.89715 | ||||||||
\(347\) | 1484.00 | 0.229583 | 0.114791 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114791 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(348\) | 2958.00 | 0.455648 | ||||||||
\(349\) | 254.000 | 0.0389579 | 0.0194790 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194790 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(350\) | 875.000 | 0.133631 | ||||||||
\(351\) | −810.000 | −0.123176 | ||||||||
\(352\) | 1020.00 | 0.154449 | ||||||||
\(353\) | −10950.0 | −1.65102 | −0.825509 | − | 0.564388i | \(-0.809112\pi\) | ||||
−0.825509 | + | 0.564388i | \(0.809112\pi\) | |||||||
\(354\) | −5700.00 | −0.855795 | ||||||||
\(355\) | −4800.00 | −0.717627 | ||||||||
\(356\) | −17646.0 | −2.62707 | ||||||||
\(357\) | 2814.00 | 0.417178 | ||||||||
\(358\) | −20460.0 | −3.02052 | ||||||||
\(359\) | 11376.0 | 1.67243 | 0.836215 | − | 0.548402i | \(-0.184764\pi\) | ||||
0.836215 | + | 0.548402i | \(0.184764\pi\) | |||||||
\(360\) | 2025.00 | 0.296464 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 6350.00 | 0.921957 | ||||||||
\(363\) | 3561.00 | 0.514887 | ||||||||
\(364\) | 3570.00 | 0.514063 | ||||||||
\(365\) | 5330.00 | 0.764342 | ||||||||
\(366\) | −10770.0 | −1.53813 | ||||||||
\(367\) | −1136.00 | −0.161577 | −0.0807884 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807884 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(368\) | 9968.00 | 1.41201 | ||||||||
\(369\) | 162.000 | 0.0228547 | ||||||||
\(370\) | −3650.00 | −0.512850 | ||||||||
\(371\) | −5278.00 | −0.738599 | ||||||||
\(372\) | 11424.0 | 1.59222 | ||||||||
\(373\) | −8242.00 | −1.14411 | −0.572057 | − | 0.820214i | \(-0.693854\pi\) | ||||
−0.572057 | + | 0.820214i | \(0.693854\pi\) | |||||||
\(374\) | −8040.00 | −1.11160 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 9360.00 | 1.28379 | ||||||||
\(377\) | −1740.00 | −0.237704 | ||||||||
\(378\) | −945.000 | −0.128586 | ||||||||
\(379\) | 3620.00 | 0.490625 | 0.245313 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245313 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(380\) | −7820.00 | −1.05568 | ||||||||
\(381\) | −1824.00 | −0.245266 | ||||||||
\(382\) | 24520.0 | 3.28417 | ||||||||
\(383\) | −8464.00 | −1.12922 | −0.564609 | − | 0.825359i | \(-0.690973\pi\) | ||||
−0.564609 | + | 0.825359i | \(0.690973\pi\) | |||||||
\(384\) | 6345.00 | 0.843208 | ||||||||
\(385\) | 420.000 | 0.0555979 | ||||||||
\(386\) | 10890.0 | 1.43598 | ||||||||
\(387\) | 3060.00 | 0.401934 | ||||||||
\(388\) | −11934.0 | −1.56149 | ||||||||
\(389\) | 3678.00 | 0.479388 | 0.239694 | − | 0.970848i | \(-0.422953\pi\) | ||||
0.239694 | + | 0.970848i | \(0.422953\pi\) | |||||||
\(390\) | −2250.00 | −0.292136 | ||||||||
\(391\) | −15008.0 | −1.94114 | ||||||||
\(392\) | 2205.00 | 0.284105 | ||||||||
\(393\) | 2868.00 | 0.368121 | ||||||||
\(394\) | −14250.0 | −1.82209 | ||||||||
\(395\) | 4480.00 | 0.570666 | ||||||||
\(396\) | 1836.00 | 0.232986 | ||||||||
\(397\) | 12590.0 | 1.59162 | 0.795811 | − | 0.605545i | \(-0.207045\pi\) | ||||
0.795811 | + | 0.605545i | \(0.207045\pi\) | |||||||
\(398\) | −5720.00 | −0.720396 | ||||||||
\(399\) | 1932.00 | 0.242408 | ||||||||
\(400\) | 2225.00 | 0.278125 | ||||||||
\(401\) | 2850.00 | 0.354918 | 0.177459 | − | 0.984128i | \(-0.443212\pi\) | ||||
0.177459 | + | 0.984128i | \(0.443212\pi\) | |||||||
\(402\) | −6180.00 | −0.766742 | ||||||||
\(403\) | −6720.00 | −0.830638 | ||||||||
\(404\) | 782.000 | 0.0963019 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −2030.00 | −0.248146 | ||||||||
\(407\) | −1752.00 | −0.213374 | ||||||||
\(408\) | 18090.0 | 2.19507 | ||||||||
\(409\) | 1226.00 | 0.148220 | 0.0741098 | − | 0.997250i | \(-0.476388\pi\) | ||||
0.0741098 | + | 0.997250i | \(0.476388\pi\) | |||||||
\(410\) | 450.000 | 0.0542047 | ||||||||
\(411\) | 1122.00 | 0.134657 | ||||||||
\(412\) | 31960.0 | 3.82174 | ||||||||
\(413\) | 2660.00 | 0.316925 | ||||||||
\(414\) | 5040.00 | 0.598315 | ||||||||
\(415\) | 2180.00 | 0.257860 | ||||||||
\(416\) | 2550.00 | 0.300539 | ||||||||
\(417\) | −1188.00 | −0.139512 | ||||||||
\(418\) | −5520.00 | −0.645914 | ||||||||
\(419\) | 612.000 | 0.0713560 | 0.0356780 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356780 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(420\) | −1785.00 | −0.207379 | ||||||||
\(421\) | 5182.00 | 0.599894 | 0.299947 | − | 0.953956i | \(-0.403031\pi\) | ||||
0.299947 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(422\) | 2060.00 | 0.237629 | ||||||||
\(423\) | 1872.00 | 0.215177 | ||||||||
\(424\) | −33930.0 | −3.88629 | ||||||||
\(425\) | −3350.00 | −0.382350 | ||||||||
\(426\) | 14400.0 | 1.63775 | ||||||||
\(427\) | 5026.00 | 0.569614 | ||||||||
\(428\) | 12444.0 | 1.40538 | ||||||||
\(429\) | −1080.00 | −0.121545 | ||||||||
\(430\) | 8500.00 | 0.953271 | ||||||||
\(431\) | −4984.00 | −0.557009 | −0.278504 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278504 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(432\) | −2403.00 | −0.267626 | ||||||||
\(433\) | −1694.00 | −0.188010 | −0.0940051 | − | 0.995572i | \(-0.529967\pi\) | ||||
−0.0940051 | + | 0.995572i | \(0.529967\pi\) | |||||||
\(434\) | −7840.00 | −0.867125 | ||||||||
\(435\) | 870.000 | 0.0958927 | ||||||||
\(436\) | −6426.00 | −0.705848 | ||||||||
\(437\) | −10304.0 | −1.12793 | ||||||||
\(438\) | −15990.0 | −1.74436 | ||||||||
\(439\) | 13864.0 | 1.50727 | 0.753636 | − | 0.657292i | \(-0.228298\pi\) | ||||
0.753636 | + | 0.657292i | \(0.228298\pi\) | |||||||
\(440\) | 2700.00 | 0.292540 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −20100.0 | −2.16303 | ||||||||
\(443\) | −4644.00 | −0.498066 | −0.249033 | − | 0.968495i | \(-0.580113\pi\) | ||||
−0.249033 | + | 0.968495i | \(0.580113\pi\) | |||||||
\(444\) | 7446.00 | 0.795882 | ||||||||
\(445\) | −5190.00 | −0.552875 | ||||||||
\(446\) | −8160.00 | −0.866339 | ||||||||
\(447\) | 5622.00 | 0.594880 | ||||||||
\(448\) | −2009.00 | −0.211867 | ||||||||
\(449\) | −4926.00 | −0.517756 | −0.258878 | − | 0.965910i | \(-0.583353\pi\) | ||||
−0.258878 | + | 0.965910i | \(0.583353\pi\) | |||||||
\(450\) | 1125.00 | 0.117851 | ||||||||
\(451\) | 216.000 | 0.0225522 | ||||||||
\(452\) | 24786.0 | 2.57928 | ||||||||
\(453\) | 3288.00 | 0.341024 | ||||||||
\(454\) | 20420.0 | 2.11092 | ||||||||
\(455\) | 1050.00 | 0.108186 | ||||||||
\(456\) | 12420.0 | 1.27548 | ||||||||
\(457\) | −14694.0 | −1.50406 | −0.752031 | − | 0.659128i | \(-0.770926\pi\) | ||||
−0.752031 | + | 0.659128i | \(0.770926\pi\) | |||||||
\(458\) | −16930.0 | −1.72726 | ||||||||
\(459\) | 3618.00 | 0.367917 | ||||||||
\(460\) | 9520.00 | 0.964940 | ||||||||
\(461\) | 2006.00 | 0.202665 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(462\) | −1260.00 | −0.126884 | ||||||||
\(463\) | 4896.00 | 0.491439 | 0.245720 | − | 0.969341i | \(-0.420976\pi\) | ||||
0.245720 | + | 0.969341i | \(0.420976\pi\) | |||||||
\(464\) | −5162.00 | −0.516465 | ||||||||
\(465\) | 3360.00 | 0.335089 | ||||||||
\(466\) | 26610.0 | 2.64525 | ||||||||
\(467\) | 2660.00 | 0.263576 | 0.131788 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131788 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(468\) | 4590.00 | 0.453361 | ||||||||
\(469\) | 2884.00 | 0.283946 | ||||||||
\(470\) | 5200.00 | 0.510336 | ||||||||
\(471\) | −5754.00 | −0.562909 | ||||||||
\(472\) | 17100.0 | 1.66757 | ||||||||
\(473\) | 4080.00 | 0.396614 | ||||||||
\(474\) | −13440.0 | −1.30236 | ||||||||
\(475\) | −2300.00 | −0.222171 | ||||||||
\(476\) | −15946.0 | −1.53547 | ||||||||
\(477\) | −6786.00 | −0.651383 | ||||||||
\(478\) | 18680.0 | 1.78745 | ||||||||
\(479\) | −5600.00 | −0.534176 | −0.267088 | − | 0.963672i | \(-0.586062\pi\) | ||||
−0.267088 | + | 0.963672i | \(0.586062\pi\) | |||||||
\(480\) | −1275.00 | −0.121241 | ||||||||
\(481\) | −4380.00 | −0.415199 | ||||||||
\(482\) | 1050.00 | 0.0992245 | ||||||||
\(483\) | −2352.00 | −0.221573 | ||||||||
\(484\) | −20179.0 | −1.89510 | ||||||||
\(485\) | −3510.00 | −0.328620 | ||||||||
\(486\) | −1215.00 | −0.113402 | ||||||||
\(487\) | −6424.00 | −0.597740 | −0.298870 | − | 0.954294i | \(-0.596610\pi\) | ||||
−0.298870 | + | 0.954294i | \(0.596610\pi\) | |||||||
\(488\) | 32310.0 | 2.99714 | ||||||||
\(489\) | −6948.00 | −0.642535 | ||||||||
\(490\) | 1225.00 | 0.112938 | ||||||||
\(491\) | −18900.0 | −1.73716 | −0.868579 | − | 0.495550i | \(-0.834967\pi\) | ||||
−0.868579 | + | 0.495550i | \(0.834967\pi\) | |||||||
\(492\) | −918.000 | −0.0841192 | ||||||||
\(493\) | 7772.00 | 0.710007 | ||||||||
\(494\) | −13800.0 | −1.25687 | ||||||||
\(495\) | 540.000 | 0.0490327 | ||||||||
\(496\) | −19936.0 | −1.80474 | ||||||||
\(497\) | −6720.00 | −0.606505 | ||||||||
\(498\) | −6540.00 | −0.588483 | ||||||||
\(499\) | −15364.0 | −1.37833 | −0.689165 | − | 0.724604i | \(-0.742023\pi\) | ||||
−0.689165 | + | 0.724604i | \(0.742023\pi\) | |||||||
\(500\) | 2125.00 | 0.190066 | ||||||||
\(501\) | 5208.00 | 0.464424 | ||||||||
\(502\) | −21060.0 | −1.87242 | ||||||||
\(503\) | 2216.00 | 0.196435 | 0.0982173 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982173 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(504\) | 2835.00 | 0.250557 | ||||||||
\(505\) | 230.000 | 0.0202671 | ||||||||
\(506\) | 6720.00 | 0.590396 | ||||||||
\(507\) | 3891.00 | 0.340839 | ||||||||
\(508\) | 10336.0 | 0.902728 | ||||||||
\(509\) | −3754.00 | −0.326902 | −0.163451 | − | 0.986551i | \(-0.552263\pi\) | ||||
−0.163451 | + | 0.986551i | \(0.552263\pi\) | |||||||
\(510\) | 10050.0 | 0.872591 | ||||||||
\(511\) | 7462.00 | 0.645987 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 25650.0 | 2.20111 | ||||||||
\(515\) | 9400.00 | 0.804298 | ||||||||
\(516\) | −17340.0 | −1.47936 | ||||||||
\(517\) | 2496.00 | 0.212329 | ||||||||
\(518\) | −5110.00 | −0.433437 | ||||||||
\(519\) | 7326.00 | 0.619606 | ||||||||
\(520\) | 6750.00 | 0.569244 | ||||||||
\(521\) | −4702.00 | −0.395390 | −0.197695 | − | 0.980264i | \(-0.563346\pi\) | ||||
−0.197695 | + | 0.980264i | \(0.563346\pi\) | |||||||
\(522\) | −2610.00 | −0.218844 | ||||||||
\(523\) | −22660.0 | −1.89456 | −0.947278 | − | 0.320413i | \(-0.896178\pi\) | ||||
−0.947278 | + | 0.320413i | \(0.896178\pi\) | |||||||
\(524\) | −16252.0 | −1.35491 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 4240.00 | 0.351469 | ||||||||
\(527\) | 30016.0 | 2.48106 | ||||||||
\(528\) | −3204.00 | −0.264084 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | −18850.0 | −1.54489 | ||||||||
\(531\) | 3420.00 | 0.279502 | ||||||||
\(532\) | −10948.0 | −0.892211 | ||||||||
\(533\) | 540.000 | 0.0438837 | ||||||||
\(534\) | 15570.0 | 1.26176 | ||||||||
\(535\) | 3660.00 | 0.295767 | ||||||||
\(536\) | 18540.0 | 1.49404 | ||||||||
\(537\) | 12276.0 | 0.986496 | ||||||||
\(538\) | −6370.00 | −0.510465 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | −2295.00 | −0.182891 | ||||||||
\(541\) | −8634.00 | −0.686145 | −0.343073 | − | 0.939309i | \(-0.611468\pi\) | ||||
−0.343073 | + | 0.939309i | \(0.611468\pi\) | |||||||
\(542\) | 4320.00 | 0.342361 | ||||||||
\(543\) | −3810.00 | −0.301110 | ||||||||
\(544\) | −11390.0 | −0.897688 | ||||||||
\(545\) | −1890.00 | −0.148548 | ||||||||
\(546\) | −3150.00 | −0.246900 | ||||||||
\(547\) | −19284.0 | −1.50736 | −0.753679 | − | 0.657243i | \(-0.771722\pi\) | ||||
−0.753679 | + | 0.657243i | \(0.771722\pi\) | |||||||
\(548\) | −6358.00 | −0.495621 | ||||||||
\(549\) | 6462.00 | 0.502352 | ||||||||
\(550\) | 1500.00 | 0.116291 | ||||||||
\(551\) | 5336.00 | 0.412561 | ||||||||
\(552\) | −15120.0 | −1.16585 | ||||||||
\(553\) | 6272.00 | 0.482301 | ||||||||
\(554\) | −42650.0 | −3.27080 | ||||||||
\(555\) | 2190.00 | 0.167496 | ||||||||
\(556\) | 6732.00 | 0.513490 | ||||||||
\(557\) | −19658.0 | −1.49540 | −0.747699 | − | 0.664038i | \(-0.768841\pi\) | ||||
−0.747699 | + | 0.664038i | \(0.768841\pi\) | |||||||
\(558\) | −10080.0 | −0.764732 | ||||||||
\(559\) | 10200.0 | 0.771760 | ||||||||
\(560\) | 3115.00 | 0.235059 | ||||||||
\(561\) | 4824.00 | 0.363047 | ||||||||
\(562\) | −26910.0 | −2.01980 | ||||||||
\(563\) | −25612.0 | −1.91726 | −0.958630 | − | 0.284656i | \(-0.908121\pi\) | ||||
−0.958630 | + | 0.284656i | \(0.908121\pi\) | |||||||
\(564\) | −10608.0 | −0.791981 | ||||||||
\(565\) | 7290.00 | 0.542819 | ||||||||
\(566\) | 31180.0 | 2.31554 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −43200.0 | −3.19125 | ||||||||
\(569\) | 7002.00 | 0.515886 | 0.257943 | − | 0.966160i | \(-0.416955\pi\) | ||||
0.257943 | + | 0.966160i | \(0.416955\pi\) | |||||||
\(570\) | 6900.00 | 0.507034 | ||||||||
\(571\) | −4524.00 | −0.331565 | −0.165782 | − | 0.986162i | \(-0.553015\pi\) | ||||
−0.165782 | + | 0.986162i | \(0.553015\pi\) | |||||||
\(572\) | 6120.00 | 0.447360 | ||||||||
\(573\) | −14712.0 | −1.07260 | ||||||||
\(574\) | 630.000 | 0.0458113 | ||||||||
\(575\) | 2800.00 | 0.203075 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | −6014.00 | −0.433910 | −0.216955 | − | 0.976182i | \(-0.569612\pi\) | ||||
−0.216955 | + | 0.976182i | \(0.569612\pi\) | |||||||
\(578\) | 65215.0 | 4.69306 | ||||||||
\(579\) | −6534.00 | −0.468988 | ||||||||
\(580\) | −4930.00 | −0.352943 | ||||||||
\(581\) | 3052.00 | 0.217932 | ||||||||
\(582\) | 10530.0 | 0.749970 | ||||||||
\(583\) | −9048.00 | −0.642761 | ||||||||
\(584\) | 47970.0 | 3.39899 | ||||||||
\(585\) | 1350.00 | 0.0954113 | ||||||||
\(586\) | −4090.00 | −0.288321 | ||||||||
\(587\) | −11748.0 | −0.826051 | −0.413025 | − | 0.910719i | \(-0.635528\pi\) | ||||
−0.413025 | + | 0.910719i | \(0.635528\pi\) | |||||||
\(588\) | −2499.00 | −0.175267 | ||||||||
\(589\) | 20608.0 | 1.44166 | ||||||||
\(590\) | 9500.00 | 0.662896 | ||||||||
\(591\) | 8550.00 | 0.595093 | ||||||||
\(592\) | −12994.0 | −0.902112 | ||||||||
\(593\) | −9462.00 | −0.655241 | −0.327620 | − | 0.944809i | \(-0.606247\pi\) | ||||
−0.327620 | + | 0.944809i | \(0.606247\pi\) | |||||||
\(594\) | −1620.00 | −0.111901 | ||||||||
\(595\) | −4690.00 | −0.323145 | ||||||||
\(596\) | −31858.0 | −2.18952 | ||||||||
\(597\) | 3432.00 | 0.235280 | ||||||||
\(598\) | 16800.0 | 1.14883 | ||||||||
\(599\) | 2320.00 | 0.158251 | 0.0791257 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791257 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(600\) | −3375.00 | −0.229640 | ||||||||
\(601\) | 4650.00 | 0.315603 | 0.157802 | − | 0.987471i | \(-0.449559\pi\) | ||||
0.157802 | + | 0.987471i | \(0.449559\pi\) | |||||||
\(602\) | 11900.0 | 0.805661 | ||||||||
\(603\) | 3708.00 | 0.250417 | ||||||||
\(604\) | −18632.0 | −1.25517 | ||||||||
\(605\) | −5935.00 | −0.398830 | ||||||||
\(606\) | −690.000 | −0.0462530 | ||||||||
\(607\) | −14656.0 | −0.980014 | −0.490007 | − | 0.871718i | \(-0.663006\pi\) | ||||
−0.490007 | + | 0.871718i | \(0.663006\pi\) | |||||||
\(608\) | −7820.00 | −0.521617 | ||||||||
\(609\) | 1218.00 | 0.0810441 | ||||||||
\(610\) | 17950.0 | 1.19143 | ||||||||
\(611\) | 6240.00 | 0.413164 | ||||||||
\(612\) | −20502.0 | −1.35416 | ||||||||
\(613\) | 29166.0 | 1.92170 | 0.960851 | − | 0.277065i | \(-0.0893616\pi\) | ||||
0.960851 | + | 0.277065i | \(0.0893616\pi\) | |||||||
\(614\) | −11340.0 | −0.745350 | ||||||||
\(615\) | −270.000 | −0.0177032 | ||||||||
\(616\) | 3780.00 | 0.247241 | ||||||||
\(617\) | 28554.0 | 1.86311 | 0.931557 | − | 0.363597i | \(-0.118451\pi\) | ||||
0.931557 | + | 0.363597i | \(0.118451\pi\) | |||||||
\(618\) | −28200.0 | −1.83555 | ||||||||
\(619\) | −3876.00 | −0.251679 | −0.125840 | − | 0.992051i | \(-0.540163\pi\) | ||||
−0.125840 | + | 0.992051i | \(0.540163\pi\) | |||||||
\(620\) | −19040.0 | −1.23333 | ||||||||
\(621\) | −3024.00 | −0.195409 | ||||||||
\(622\) | 33240.0 | 2.14277 | ||||||||
\(623\) | −7266.00 | −0.467265 | ||||||||
\(624\) | −8010.00 | −0.513873 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 49090.0 | 3.13423 | ||||||||
\(627\) | 3312.00 | 0.210955 | ||||||||
\(628\) | 32606.0 | 2.07185 | ||||||||
\(629\) | 19564.0 | 1.24017 | ||||||||
\(630\) | 1575.00 | 0.0996024 | ||||||||
\(631\) | 2904.00 | 0.183211 | 0.0916057 | − | 0.995795i | \(-0.470800\pi\) | ||||
0.0916057 | + | 0.995795i | \(0.470800\pi\) | |||||||
\(632\) | 40320.0 | 2.53773 | ||||||||
\(633\) | −1236.00 | −0.0776091 | ||||||||
\(634\) | 4670.00 | 0.292538 | ||||||||
\(635\) | 3040.00 | 0.189982 | ||||||||
\(636\) | 38454.0 | 2.39748 | ||||||||
\(637\) | 1470.00 | 0.0914341 | ||||||||
\(638\) | −3480.00 | −0.215948 | ||||||||
\(639\) | −8640.00 | −0.534888 | ||||||||
\(640\) | −10575.0 | −0.653146 | ||||||||
\(641\) | 9330.00 | 0.574903 | 0.287452 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287452 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(642\) | −10980.0 | −0.674994 | ||||||||
\(643\) | −18332.0 | −1.12433 | −0.562164 | − | 0.827025i | \(-0.690031\pi\) | ||||
−0.562164 | + | 0.827025i | \(0.690031\pi\) | |||||||
\(644\) | 13328.0 | 0.815523 | ||||||||
\(645\) | −5100.00 | −0.311337 | ||||||||
\(646\) | 61640.0 | 3.75417 | ||||||||
\(647\) | −2088.00 | −0.126874 | −0.0634372 | − | 0.997986i | \(-0.520206\pi\) | ||||
−0.0634372 | + | 0.997986i | \(0.520206\pi\) | |||||||
\(648\) | 3645.00 | 0.220971 | ||||||||
\(649\) | 4560.00 | 0.275802 | ||||||||
\(650\) | 3750.00 | 0.226288 | ||||||||
\(651\) | 4704.00 | 0.283202 | ||||||||
\(652\) | 39372.0 | 2.36492 | ||||||||
\(653\) | 22.0000 | 0.00131842 | 0.000659209 | − | 1.00000i | \(-0.499790\pi\) | ||||
0.000659209 | 1.00000i | \(0.499790\pi\) | ||||||||
\(654\) | 5670.00 | 0.339013 | ||||||||
\(655\) | −4780.00 | −0.285145 | ||||||||
\(656\) | 1602.00 | 0.0953469 | ||||||||
\(657\) | 9594.00 | 0.569707 | ||||||||
\(658\) | 7280.00 | 0.431313 | ||||||||
\(659\) | 16260.0 | 0.961153 | 0.480576 | − | 0.876953i | \(-0.340427\pi\) | ||||
0.480576 | + | 0.876953i | \(0.340427\pi\) | |||||||
\(660\) | −3060.00 | −0.180470 | ||||||||
\(661\) | −23818.0 | −1.40153 | −0.700766 | − | 0.713391i | \(-0.747158\pi\) | ||||
−0.700766 | + | 0.713391i | \(0.747158\pi\) | |||||||
\(662\) | 11460.0 | 0.672818 | ||||||||
\(663\) | 12060.0 | 0.706443 | ||||||||
\(664\) | 19620.0 | 1.14669 | ||||||||
\(665\) | −3220.00 | −0.187769 | ||||||||
\(666\) | −6570.00 | −0.382256 | ||||||||
\(667\) | −6496.00 | −0.377101 | ||||||||
\(668\) | −29512.0 | −1.70936 | ||||||||
\(669\) | 4896.00 | 0.282945 | ||||||||
\(670\) | 10300.0 | 0.593916 | ||||||||
\(671\) | 8616.00 | 0.495703 | ||||||||
\(672\) | −1785.00 | −0.102467 | ||||||||
\(673\) | 31106.0 | 1.78165 | 0.890823 | − | 0.454350i | \(-0.150128\pi\) | ||||
0.890823 | + | 0.454350i | \(0.150128\pi\) | |||||||
\(674\) | −30310.0 | −1.73219 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −22049.0 | −1.25449 | ||||||||
\(677\) | −1090.00 | −0.0618790 | −0.0309395 | − | 0.999521i | \(-0.509850\pi\) | ||||
−0.0309395 | + | 0.999521i | \(0.509850\pi\) | |||||||
\(678\) | −21870.0 | −1.23881 | ||||||||
\(679\) | −4914.00 | −0.277735 | ||||||||
\(680\) | −30150.0 | −1.70029 | ||||||||
\(681\) | −12252.0 | −0.689424 | ||||||||
\(682\) | −13440.0 | −0.754610 | ||||||||
\(683\) | −12372.0 | −0.693121 | −0.346560 | − | 0.938028i | \(-0.612650\pi\) | ||||
−0.346560 | + | 0.938028i | \(0.612650\pi\) | |||||||
\(684\) | −14076.0 | −0.786856 | ||||||||
\(685\) | −1870.00 | −0.104305 | ||||||||
\(686\) | 1715.00 | 0.0954504 | ||||||||
\(687\) | 10158.0 | 0.564122 | ||||||||
\(688\) | 30260.0 | 1.67682 | ||||||||
\(689\) | −22620.0 | −1.25073 | ||||||||
\(690\) | −8400.00 | −0.463453 | ||||||||
\(691\) | 3252.00 | 0.179033 | 0.0895166 | − | 0.995985i | \(-0.471468\pi\) | ||||
0.0895166 | + | 0.995985i | \(0.471468\pi\) | |||||||
\(692\) | −41514.0 | −2.28053 | ||||||||
\(693\) | 756.000 | 0.0414402 | ||||||||
\(694\) | 7420.00 | 0.405849 | ||||||||
\(695\) | 1980.00 | 0.108066 | ||||||||
\(696\) | 7830.00 | 0.426430 | ||||||||
\(697\) | −2412.00 | −0.131077 | ||||||||
\(698\) | 1270.00 | 0.0688685 | ||||||||
\(699\) | −15966.0 | −0.863934 | ||||||||
\(700\) | 2975.00 | 0.160635 | ||||||||
\(701\) | −5434.00 | −0.292781 | −0.146390 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146390 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(702\) | −4050.00 | −0.217746 | ||||||||
\(703\) | 13432.0 | 0.720622 | ||||||||
\(704\) | −3444.00 | −0.184376 | ||||||||
\(705\) | −3120.00 | −0.166675 | ||||||||
\(706\) | −54750.0 | −2.91862 | ||||||||
\(707\) | 322.000 | 0.0171288 | ||||||||
\(708\) | −19380.0 | −1.02874 | ||||||||
\(709\) | −5330.00 | −0.282331 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(710\) | −24000.0 | −1.26860 | ||||||||
\(711\) | 8064.00 | 0.425350 | ||||||||
\(712\) | −46710.0 | −2.45861 | ||||||||
\(713\) | −25088.0 | −1.31775 | ||||||||
\(714\) | 14070.0 | 0.737474 | ||||||||
\(715\) | 1800.00 | 0.0941485 | ||||||||
\(716\) | −69564.0 | −3.63091 | ||||||||
\(717\) | −11208.0 | −0.583780 | ||||||||
\(718\) | 56880.0 | 2.95647 | ||||||||
\(719\) | −7520.00 | −0.390054 | −0.195027 | − | 0.980798i | \(-0.562479\pi\) | ||||
−0.195027 | + | 0.980798i | \(0.562479\pi\) | |||||||
\(720\) | 4005.00 | 0.207302 | ||||||||
\(721\) | 13160.0 | 0.679756 | ||||||||
\(722\) | 8025.00 | 0.413656 | ||||||||
\(723\) | −630.000 | −0.0324066 | ||||||||
\(724\) | 21590.0 | 1.10827 | ||||||||
\(725\) | −1450.00 | −0.0742781 | ||||||||
\(726\) | 17805.0 | 0.910200 | ||||||||
\(727\) | 19336.0 | 0.986427 | 0.493214 | − | 0.869908i | \(-0.335822\pi\) | ||||
0.493214 | + | 0.869908i | \(0.335822\pi\) | |||||||
\(728\) | 9450.00 | 0.481099 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 26650.0 | 1.35118 | ||||||||
\(731\) | −45560.0 | −2.30519 | ||||||||
\(732\) | −36618.0 | −1.84896 | ||||||||
\(733\) | −22498.0 | −1.13367 | −0.566837 | − | 0.823830i | \(-0.691833\pi\) | ||||
−0.566837 | + | 0.823830i | \(0.691833\pi\) | |||||||
\(734\) | −5680.00 | −0.285630 | ||||||||
\(735\) | −735.000 | −0.0368856 | ||||||||
\(736\) | 9520.00 | 0.476782 | ||||||||
\(737\) | 4944.00 | 0.247103 | ||||||||
\(738\) | 810.000 | 0.0404018 | ||||||||
\(739\) | −18292.0 | −0.910531 | −0.455265 | − | 0.890356i | \(-0.650456\pi\) | ||||
−0.455265 | + | 0.890356i | \(0.650456\pi\) | |||||||
\(740\) | −12410.0 | −0.616487 | ||||||||
\(741\) | 8280.00 | 0.410490 | ||||||||
\(742\) | −26390.0 | −1.30567 | ||||||||
\(743\) | 17904.0 | 0.884030 | 0.442015 | − | 0.897008i | \(-0.354264\pi\) | ||||
0.442015 | + | 0.897008i | \(0.354264\pi\) | |||||||
\(744\) | 30240.0 | 1.49012 | ||||||||
\(745\) | −9370.00 | −0.460792 | ||||||||
\(746\) | −41210.0 | −2.02253 | ||||||||
\(747\) | 3924.00 | 0.192198 | ||||||||
\(748\) | −27336.0 | −1.33623 | ||||||||
\(749\) | 5124.00 | 0.249969 | ||||||||
\(750\) | −1875.00 | −0.0912871 | ||||||||
\(751\) | 5408.00 | 0.262771 | 0.131385 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131385 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(752\) | 18512.0 | 0.897690 | ||||||||
\(753\) | 12636.0 | 0.611529 | ||||||||
\(754\) | −8700.00 | −0.420206 | ||||||||
\(755\) | −5480.00 | −0.264156 | ||||||||
\(756\) | −3213.00 | −0.154571 | ||||||||
\(757\) | 8318.00 | 0.399370 | 0.199685 | − | 0.979860i | \(-0.436008\pi\) | ||||
0.199685 | + | 0.979860i | \(0.436008\pi\) | |||||||
\(758\) | 18100.0 | 0.867311 | ||||||||
\(759\) | −4032.00 | −0.192823 | ||||||||
\(760\) | −20700.0 | −0.987984 | ||||||||
\(761\) | 6690.00 | 0.318676 | 0.159338 | − | 0.987224i | \(-0.449064\pi\) | ||||
0.159338 | + | 0.987224i | \(0.449064\pi\) | |||||||
\(762\) | −9120.00 | −0.433573 | ||||||||
\(763\) | −2646.00 | −0.125546 | ||||||||
\(764\) | 83368.0 | 3.94784 | ||||||||
\(765\) | −6030.00 | −0.284987 | ||||||||
\(766\) | −42320.0 | −1.99619 | ||||||||
\(767\) | 11400.0 | 0.536676 | ||||||||
\(768\) | 24837.0 | 1.16696 | ||||||||
\(769\) | 9266.00 | 0.434513 | 0.217257 | − | 0.976115i | \(-0.430289\pi\) | ||||
0.217257 | + | 0.976115i | \(0.430289\pi\) | |||||||
\(770\) | 2100.00 | 0.0982841 | ||||||||
\(771\) | −15390.0 | −0.718881 | ||||||||
\(772\) | 37026.0 | 1.72616 | ||||||||
\(773\) | 9678.00 | 0.450315 | 0.225157 | − | 0.974322i | \(-0.427710\pi\) | ||||
0.225157 | + | 0.974322i | \(0.427710\pi\) | |||||||
\(774\) | 15300.0 | 0.710526 | ||||||||
\(775\) | −5600.00 | −0.259559 | ||||||||
\(776\) | −31590.0 | −1.46136 | ||||||||
\(777\) | 3066.00 | 0.141560 | ||||||||
\(778\) | 18390.0 | 0.847447 | ||||||||
\(779\) | −1656.00 | −0.0761648 | ||||||||
\(780\) | −7650.00 | −0.351172 | ||||||||
\(781\) | −11520.0 | −0.527808 | ||||||||
\(782\) | −75040.0 | −3.43149 | ||||||||
\(783\) | 1566.00 | 0.0714742 | ||||||||
\(784\) | 4361.00 | 0.198661 | ||||||||
\(785\) | 9590.00 | 0.436028 | ||||||||
\(786\) | 14340.0 | 0.650752 | ||||||||
\(787\) | −6860.00 | −0.310715 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(788\) | −48450.0 | −2.19030 | ||||||||
\(789\) | −2544.00 | −0.114789 | ||||||||
\(790\) | 22400.0 | 1.00881 | ||||||||
\(791\) | 10206.0 | 0.458766 | ||||||||
\(792\) | 4860.00 | 0.218046 | ||||||||
\(793\) | 21540.0 | 0.964575 | ||||||||
\(794\) | 62950.0 | 2.81362 | ||||||||
\(795\) | 11310.0 | 0.504559 | ||||||||
\(796\) | −19448.0 | −0.865975 | ||||||||
\(797\) | 10950.0 | 0.486661 | 0.243331 | − | 0.969943i | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(798\) | 9660.00 | 0.428522 | ||||||||
\(799\) | −27872.0 | −1.23409 | ||||||||
\(800\) | 2125.00 | 0.0939126 | ||||||||
\(801\) | −9342.00 | −0.412089 | ||||||||
\(802\) | 14250.0 | 0.627413 | ||||||||
\(803\) | 12792.0 | 0.562167 | ||||||||
\(804\) | −21012.0 | −0.921687 | ||||||||
\(805\) | 3920.00 | 0.171630 | ||||||||
\(806\) | −33600.0 | −1.46837 | ||||||||
\(807\) | 3822.00 | 0.166717 | ||||||||
\(808\) | 2070.00 | 0.0901267 | ||||||||
\(809\) | 26010.0 | 1.13036 | 0.565181 | − | 0.824967i | \(-0.308806\pi\) | ||||
0.565181 | + | 0.824967i | \(0.308806\pi\) | |||||||
\(810\) | 2025.00 | 0.0878410 | ||||||||
\(811\) | −14628.0 | −0.633364 | −0.316682 | − | 0.948532i | \(-0.602569\pi\) | ||||
−0.316682 | + | 0.948532i | \(0.602569\pi\) | |||||||
\(812\) | −6902.00 | −0.298292 | ||||||||
\(813\) | −2592.00 | −0.111815 | ||||||||
\(814\) | −8760.00 | −0.377196 | ||||||||
\(815\) | 11580.0 | 0.497705 | ||||||||
\(816\) | 35778.0 | 1.53490 | ||||||||
\(817\) | −31280.0 | −1.33947 | ||||||||
\(818\) | 6130.00 | 0.262018 | ||||||||
\(819\) | 1890.00 | 0.0806373 | ||||||||
\(820\) | 1530.00 | 0.0651584 | ||||||||
\(821\) | 8718.00 | 0.370597 | 0.185299 | − | 0.982682i | \(-0.440675\pi\) | ||||
0.185299 | + | 0.982682i | \(0.440675\pi\) | |||||||
\(822\) | 5610.00 | 0.238043 | ||||||||
\(823\) | −7432.00 | −0.314779 | −0.157390 | − | 0.987537i | \(-0.550308\pi\) | ||||
−0.157390 | + | 0.987537i | \(0.550308\pi\) | |||||||
\(824\) | 84600.0 | 3.57668 | ||||||||
\(825\) | −900.000 | −0.0379806 | ||||||||
\(826\) | 13300.0 | 0.560250 | ||||||||
\(827\) | 17388.0 | 0.731125 | 0.365562 | − | 0.930787i | \(-0.380877\pi\) | ||||
0.365562 | + | 0.930787i | \(0.380877\pi\) | |||||||
\(828\) | 17136.0 | 0.719224 | ||||||||
\(829\) | 7902.00 | 0.331059 | 0.165529 | − | 0.986205i | \(-0.447067\pi\) | ||||
0.165529 | + | 0.986205i | \(0.447067\pi\) | |||||||
\(830\) | 10900.0 | 0.455837 | ||||||||
\(831\) | 25590.0 | 1.06824 | ||||||||
\(832\) | −8610.00 | −0.358772 | ||||||||
\(833\) | −6566.00 | −0.273107 | ||||||||
\(834\) | −5940.00 | −0.246625 | ||||||||
\(835\) | −8680.00 | −0.359741 | ||||||||
\(836\) | −18768.0 | −0.776441 | ||||||||
\(837\) | 6048.00 | 0.249760 | ||||||||
\(838\) | 3060.00 | 0.126141 | ||||||||
\(839\) | −31848.0 | −1.31051 | −0.655253 | − | 0.755409i | \(-0.727438\pi\) | ||||
−0.655253 | + | 0.755409i | \(0.727438\pi\) | |||||||
\(840\) | −4725.00 | −0.194081 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 25910.0 | 1.06047 | ||||||||
\(843\) | 16146.0 | 0.659665 | ||||||||
\(844\) | 7004.00 | 0.285649 | ||||||||
\(845\) | −6485.00 | −0.264013 | ||||||||
\(846\) | 9360.00 | 0.380382 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | −67106.0 | −2.71749 | ||||||||
\(849\) | −18708.0 | −0.756251 | ||||||||
\(850\) | −16750.0 | −0.675906 | ||||||||
\(851\) | −16352.0 | −0.658683 | ||||||||
\(852\) | 48960.0 | 1.96871 | ||||||||
\(853\) | 30150.0 | 1.21022 | 0.605109 | − | 0.796142i | \(-0.293129\pi\) | ||||
0.605109 | + | 0.796142i | \(0.293129\pi\) | |||||||
\(854\) | 25130.0 | 1.00694 | ||||||||
\(855\) | −4140.00 | −0.165597 | ||||||||
\(856\) | 32940.0 | 1.31526 | ||||||||
\(857\) | −4350.00 | −0.173388 | −0.0866938 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866938 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(858\) | −5400.00 | −0.214864 | ||||||||
\(859\) | −30676.0 | −1.21845 | −0.609227 | − | 0.792996i | \(-0.708520\pi\) | ||||
−0.609227 | + | 0.792996i | \(0.708520\pi\) | |||||||
\(860\) | 28900.0 | 1.14591 | ||||||||
\(861\) | −378.000 | −0.0149619 | ||||||||
\(862\) | −24920.0 | −0.984662 | ||||||||
\(863\) | −23688.0 | −0.934356 | −0.467178 | − | 0.884163i | \(-0.654729\pi\) | ||||
−0.467178 | + | 0.884163i | \(0.654729\pi\) | |||||||
\(864\) | −2295.00 | −0.0903675 | ||||||||
\(865\) | −12210.0 | −0.479945 | ||||||||
\(866\) | −8470.00 | −0.332358 | ||||||||
\(867\) | −39129.0 | −1.53275 | ||||||||
\(868\) | −26656.0 | −1.04235 | ||||||||
\(869\) | 10752.0 | 0.419720 | ||||||||
\(870\) | 4350.00 | 0.169516 | ||||||||
\(871\) | 12360.0 | 0.480830 | ||||||||
\(872\) | −17010.0 | −0.660586 | ||||||||
\(873\) | −6318.00 | −0.244939 | ||||||||
\(874\) | −51520.0 | −1.99392 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | −54366.0 | −2.09687 | ||||||||
\(877\) | 31910.0 | 1.22865 | 0.614324 | − | 0.789054i | \(-0.289429\pi\) | ||||
0.614324 | + | 0.789054i | \(0.289429\pi\) | |||||||
\(878\) | 69320.0 | 2.66451 | ||||||||
\(879\) | 2454.00 | 0.0941654 | ||||||||
\(880\) | 5340.00 | 0.204558 | ||||||||
\(881\) | 50250.0 | 1.92164 | 0.960820 | − | 0.277172i | \(-0.0893971\pi\) | ||||
0.960820 | + | 0.277172i | \(0.0893971\pi\) | |||||||
\(882\) | 2205.00 | 0.0841794 | ||||||||
\(883\) | 5980.00 | 0.227908 | 0.113954 | − | 0.993486i | \(-0.463648\pi\) | ||||
0.113954 | + | 0.993486i | \(0.463648\pi\) | |||||||
\(884\) | −68340.0 | −2.60014 | ||||||||
\(885\) | −5700.00 | −0.216501 | ||||||||
\(886\) | −23220.0 | −0.880464 | ||||||||
\(887\) | −24568.0 | −0.930003 | −0.465002 | − | 0.885310i | \(-0.653946\pi\) | ||||
−0.465002 | + | 0.885310i | \(0.653946\pi\) | |||||||
\(888\) | 19710.0 | 0.744847 | ||||||||
\(889\) | 4256.00 | 0.160564 | ||||||||
\(890\) | −25950.0 | −0.977355 | ||||||||
\(891\) | 972.000 | 0.0365468 | ||||||||
\(892\) | −27744.0 | −1.04141 | ||||||||
\(893\) | −19136.0 | −0.717091 | ||||||||
\(894\) | 28110.0 | 1.05161 | ||||||||
\(895\) | −20460.0 | −0.764137 | ||||||||
\(896\) | −14805.0 | −0.552009 | ||||||||
\(897\) | −10080.0 | −0.375208 | ||||||||
\(898\) | −24630.0 | −0.915271 | ||||||||
\(899\) | 12992.0 | 0.481988 | ||||||||
\(900\) | 3825.00 | 0.141667 | ||||||||
\(901\) | 101036. | 3.73585 | ||||||||
\(902\) | 1080.00 | 0.0398670 | ||||||||
\(903\) | −7140.00 | −0.263128 | ||||||||
\(904\) | 65610.0 | 2.41389 | ||||||||
\(905\) | 6350.00 | 0.233239 | ||||||||
\(906\) | 16440.0 | 0.602850 | ||||||||
\(907\) | 13252.0 | 0.485144 | 0.242572 | − | 0.970133i | \(-0.422009\pi\) | ||||
0.242572 | + | 0.970133i | \(0.422009\pi\) | |||||||
\(908\) | 69428.0 | 2.53750 | ||||||||
\(909\) | 414.000 | 0.0151062 | ||||||||
\(910\) | 5250.00 | 0.191248 | ||||||||
\(911\) | −6744.00 | −0.245267 | −0.122634 | − | 0.992452i | \(-0.539134\pi\) | ||||
−0.122634 | + | 0.992452i | \(0.539134\pi\) | |||||||
\(912\) | 24564.0 | 0.891881 | ||||||||
\(913\) | 5232.00 | 0.189654 | ||||||||
\(914\) | −73470.0 | −2.65883 | ||||||||
\(915\) | −10770.0 | −0.389120 | ||||||||
\(916\) | −57562.0 | −2.07631 | ||||||||
\(917\) | −6692.00 | −0.240992 | ||||||||
\(918\) | 18090.0 | 0.650391 | ||||||||
\(919\) | −45336.0 | −1.62731 | −0.813654 | − | 0.581349i | \(-0.802525\pi\) | ||||
−0.813654 | + | 0.581349i | \(0.802525\pi\) | |||||||
\(920\) | 25200.0 | 0.903065 | ||||||||
\(921\) | 6804.00 | 0.243430 | ||||||||
\(922\) | 10030.0 | 0.358265 | ||||||||
\(923\) | −28800.0 | −1.02705 | ||||||||
\(924\) | −4284.00 | −0.152525 | ||||||||
\(925\) | −3650.00 | −0.129742 | ||||||||
\(926\) | 24480.0 | 0.868750 | ||||||||
\(927\) | 16920.0 | 0.599488 | ||||||||
\(928\) | −4930.00 | −0.174391 | ||||||||
\(929\) | 30074.0 | 1.06211 | 0.531053 | − | 0.847339i | \(-0.321797\pi\) | ||||
0.531053 | + | 0.847339i | \(0.321797\pi\) | |||||||
\(930\) | 16800.0 | 0.592359 | ||||||||
\(931\) | −4508.00 | −0.158694 | ||||||||
\(932\) | 90474.0 | 3.17980 | ||||||||
\(933\) | −19944.0 | −0.699826 | ||||||||
\(934\) | 13300.0 | 0.465941 | ||||||||
\(935\) | −8040.00 | −0.281215 | ||||||||
\(936\) | 12150.0 | 0.424290 | ||||||||
\(937\) | 21754.0 | 0.758455 | 0.379227 | − | 0.925303i | \(-0.376190\pi\) | ||||
0.379227 | + | 0.925303i | \(0.376190\pi\) | |||||||
\(938\) | 14420.0 | 0.501951 | ||||||||
\(939\) | −29454.0 | −1.02364 | ||||||||
\(940\) | 17680.0 | 0.613466 | ||||||||
\(941\) | 14550.0 | 0.504056 | 0.252028 | − | 0.967720i | \(-0.418903\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418903\pi\) | |||||||
\(942\) | −28770.0 | −0.995093 | ||||||||
\(943\) | 2016.00 | 0.0696182 | ||||||||
\(944\) | 33820.0 | 1.16605 | ||||||||
\(945\) | −945.000 | −0.0325300 | ||||||||
\(946\) | 20400.0 | 0.701122 | ||||||||
\(947\) | 46660.0 | 1.60110 | 0.800552 | − | 0.599263i | \(-0.204540\pi\) | ||||
0.800552 | + | 0.599263i | \(0.204540\pi\) | |||||||
\(948\) | −45696.0 | −1.56555 | ||||||||
\(949\) | 31980.0 | 1.09390 | ||||||||
\(950\) | −11500.0 | −0.392747 | ||||||||
\(951\) | −2802.00 | −0.0955427 | ||||||||
\(952\) | −42210.0 | −1.43701 | ||||||||
\(953\) | 20810.0 | 0.707347 | 0.353674 | − | 0.935369i | \(-0.384932\pi\) | ||||
0.353674 | + | 0.935369i | \(0.384932\pi\) | |||||||
\(954\) | −33930.0 | −1.15149 | ||||||||
\(955\) | 24520.0 | 0.830836 | ||||||||
\(956\) | 63512.0 | 2.14867 | ||||||||
\(957\) | 2088.00 | 0.0705282 | ||||||||
\(958\) | −28000.0 | −0.944300 | ||||||||
\(959\) | −2618.00 | −0.0881539 | ||||||||
\(960\) | 4305.00 | 0.144733 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | −21900.0 | −0.733975 | ||||||||
\(963\) | 6588.00 | 0.220452 | ||||||||
\(964\) | 3570.00 | 0.119276 | ||||||||
\(965\) | 10890.0 | 0.363276 | ||||||||
\(966\) | −11760.0 | −0.391689 | ||||||||
\(967\) | 2776.00 | 0.0923166 | 0.0461583 | − | 0.998934i | \(-0.485302\pi\) | ||||
0.0461583 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(968\) | −53415.0 | −1.77358 | ||||||||
\(969\) | −36984.0 | −1.22611 | ||||||||
\(970\) | −17550.0 | −0.580924 | ||||||||
\(971\) | 27292.0 | 0.902000 | 0.451000 | − | 0.892524i | \(-0.351067\pi\) | ||||
0.451000 | + | 0.892524i | \(0.351067\pi\) | |||||||
\(972\) | −4131.00 | −0.136319 | ||||||||
\(973\) | 2772.00 | 0.0913322 | ||||||||
\(974\) | −32120.0 | −1.05666 | ||||||||
\(975\) | −2250.00 | −0.0739053 | ||||||||
\(976\) | 63902.0 | 2.09575 | ||||||||
\(977\) | −62.0000 | −0.00203025 | −0.00101513 | − | 0.999999i | \(-0.500323\pi\) | ||||
−0.00101513 | + | 0.999999i | \(0.500323\pi\) | |||||||
\(978\) | −34740.0 | −1.13585 | ||||||||
\(979\) | −12456.0 | −0.406635 | ||||||||
\(980\) | 4165.00 | 0.135761 | ||||||||
\(981\) | −3402.00 | −0.110721 | ||||||||
\(982\) | −94500.0 | −3.07089 | ||||||||
\(983\) | 37912.0 | 1.23012 | 0.615058 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615058 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(984\) | −2430.00 | −0.0787252 | ||||||||
\(985\) | −14250.0 | −0.460957 | ||||||||
\(986\) | 38860.0 | 1.25513 | ||||||||
\(987\) | −4368.00 | −0.140866 | ||||||||
\(988\) | −46920.0 | −1.51085 | ||||||||
\(989\) | 38080.0 | 1.22434 | ||||||||
\(990\) | 2700.00 | 0.0866784 | ||||||||
\(991\) | 10656.0 | 0.341573 | 0.170787 | − | 0.985308i | \(-0.445369\pi\) | ||||
0.170787 | + | 0.985308i | \(0.445369\pi\) | |||||||
\(992\) | −19040.0 | −0.609396 | ||||||||
\(993\) | −6876.00 | −0.219741 | ||||||||
\(994\) | −33600.0 | −1.07216 | ||||||||
\(995\) | −5720.00 | −0.182247 | ||||||||
\(996\) | −22236.0 | −0.707404 | ||||||||
\(997\) | −29434.0 | −0.934989 | −0.467495 | − | 0.883996i | \(-0.654843\pi\) | ||||
−0.467495 | + | 0.883996i | \(0.654843\pi\) | |||||||
\(998\) | −76820.0 | −2.43657 | ||||||||
\(999\) | 3942.00 | 0.124844 |
(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 | 105.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 315.4.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 1680.4.a.u.1.1 | 1 | |||
5.2 | odd | 4 | 525.4.d.a.274.2 | 2 | |||
5.3 | odd | 4 | 525.4.d.a.274.1 | 2 | |||
5.4 | even | 2 | 525.4.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 735.4.a.j.1.1 | 1 | |||
15.14 | odd | 2 | 1575.4.a.l.1.1 | 1 | |||
21.20 | even | 2 | 2205.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
315.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
525.4.a.a.1.1 | 1 | 5.4 | even | 2 | |||
525.4.d.a.274.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.a.274.2 | 2 | 5.2 | odd | 4 | |||
735.4.a.j.1.1 | 1 | 7.6 | odd | 2 | |||
1575.4.a.l.1.1 | 1 | 15.14 | odd | 2 | |||
1680.4.a.u.1.1 | 1 | 4.3 | odd | 2 | |||
2205.4.a.b.1.1 | 1 | 21.20 | even | 2 |