Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.2094 | −0.875224 | −0.437612 | − | 0.899164i | \(-0.644176\pi\) | ||||
−0.437612 | + | 0.899164i | \(0.644176\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.2094 | 1.10214 | 0.551072 | − | 0.834458i | \(-0.314219\pi\) | ||||
0.551072 | + | 0.834458i | \(0.314219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.7906 | −0.422226 | −0.211113 | − | 0.977462i | \(-0.567709\pi\) | ||||
−0.211113 | + | 0.977462i | \(0.567709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −83.0156 | −1.18437 | −0.592184 | − | 0.805803i | \(-0.701734\pi\) | ||||
−0.592184 | + | 0.805803i | \(0.701734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.8375 | 0.589689 | 0.294844 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294844 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −48.6281 | −0.505311 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.61250 | 0.0146186 | 0.00730932 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00730932 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −24.5344 | −0.157101 | −0.0785504 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785504 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.4187 | 0.0719507 | 0.0359754 | − | 0.999353i | \(-0.488546\pi\) | ||||
0.0359754 | + | 0.999353i | \(0.488546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 120.628 | 0.636323 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −325.884 | −1.44797 | −0.723987 | − | 0.689813i | \(-0.757693\pi\) | ||||
−0.723987 | + | 0.689813i | \(0.757693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −59.3719 | −0.243772 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −242.419 | −0.923401 | −0.461701 | − | 0.887036i | \(-0.652761\pi\) | ||||
−0.461701 | + | 0.887036i | \(0.652761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 367.350 | 1.30280 | 0.651399 | − | 0.758735i | \(-0.274182\pi\) | ||||
0.651399 | + | 0.758735i | \(0.274182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −204.544 | −0.634804 | −0.317402 | − | 0.948291i | \(-0.602810\pi\) | ||||
−0.317402 | + | 0.948291i | \(0.602810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −80.2562 | −0.233983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −249.047 | −0.683795 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 61.5281 | 0.159463 | 0.0797314 | − | 0.996816i | \(-0.474594\pi\) | ||||
0.0797314 | + | 0.996816i | \(0.474594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 146.512 | 0.340457 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 112.209 | 0.247600 | 0.123800 | − | 0.992307i | \(-0.460492\pi\) | ||||
0.123800 | + | 0.992307i | \(0.460492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 477.350 | 1.00194 | 0.500970 | − | 0.865464i | \(-0.332977\pi\) | ||||
0.500970 | + | 0.865464i | \(0.332977\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −145.884 | −0.291741 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 558.094 | 1.01764 | 0.508821 | − | 0.860872i | \(-0.330082\pi\) | ||||
0.508821 | + | 0.860872i | \(0.330082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.83749 | 0.00844008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −558.281 | −0.933180 | −0.466590 | − | 0.884474i | \(-0.654518\pi\) | ||||
−0.466590 | + | 0.884474i | \(0.654518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1011.77 | −1.62217 | −0.811086 | − | 0.584927i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584927i | \(0.801123\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −651.769 | −0.964623 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1150.47 | −1.63845 | −0.819227 | − | 0.573470i | \(-0.805597\pi\) | ||||
−0.819227 | + | 0.573470i | \(0.805597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1157.92 | −1.53131 | −0.765655 | − | 0.643251i | \(-0.777585\pi\) | ||||
−0.765655 | + | 0.643251i | \(0.777585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −73.6032 | −0.0907022 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 96.9751 | 0.115498 | 0.0577491 | − | 0.998331i | \(-0.481608\pi\) | ||||
0.0577491 | + | 0.998331i | \(0.481608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 320.794 | 0.369542 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.2562 | 0.0415408 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1152.37 | 1.20625 | 0.603123 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603123 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 361.884 | 0.367381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1156.49 | −1.13936 | −0.569679 | − | 0.821867i | \(-0.692932\pi\) | ||||
−0.569679 | + | 0.821867i | \(0.692932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1333.70 | −1.27585 | −0.637927 | − | 0.770096i | \(-0.720208\pi\) | ||||
−0.637927 | + | 0.770096i | \(0.720208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −798.263 | −0.721224 | −0.360612 | − | 0.932716i | \(-0.617432\pi\) | ||||
−0.360612 | + | 0.932716i | \(0.617432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −985.119 | −0.865663 | −0.432831 | − | 0.901475i | \(-0.642485\pi\) | ||||
−0.432831 | + | 0.901475i | \(0.642485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −977.653 | −0.835988 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1888.25 | −1.57196 | −0.785979 | − | 0.618253i | \(-0.787841\pi\) | ||||
−0.785979 | + | 0.618253i | \(0.787841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −178.116 | −0.140742 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1345.63 | 1.03659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 285.794 | 0.214721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −727.256 | −0.533126 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −620.859 | −0.433798 | −0.216899 | − | 0.976194i | \(-0.569594\pi\) | ||||
−0.216899 | + | 0.976194i | \(0.569594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1102.05 | 0.752171 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2588.35 | 1.72630 | 0.863151 | − | 0.504947i | \(-0.168488\pi\) | ||||
0.863151 | + | 0.504947i | \(0.168488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −791.625 | −0.516110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1656.29 | 1.03289 | 0.516447 | − | 0.856319i | \(-0.327254\pi\) | ||||
0.516447 | + | 0.856319i | \(0.327254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 153.256 | 0.0935182 | 0.0467591 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467591 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −613.631 | −0.366504 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −795.769 | −0.465353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −240.769 | −0.135090 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1483.38 | 0.815591 | 0.407795 | − | 0.913073i | \(-0.366298\pi\) | ||||
0.407795 | + | 0.913073i | \(0.366298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 394.281 | 0.212491 | 0.106246 | − | 0.994340i | \(-0.466117\pi\) | ||||
0.106246 | + | 0.994340i | \(0.466117\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −747.141 | −0.394789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1727.05 | −0.877922 | −0.438961 | − | 0.898506i | \(-0.644653\pi\) | ||||
−0.438961 | + | 0.898506i | \(0.644653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 184.584 | 0.0920659 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.1376 | −0.0127946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2034.28 | −0.977529 | −0.488764 | − | 0.872416i | \(-0.662552\pi\) | ||||
−0.488764 | + | 0.872416i | \(0.662552\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 192.900 | 0.0893835 | 0.0446918 | − | 0.999001i | \(-0.485769\pi\) | ||||
0.0446918 | + | 0.999001i | \(0.485769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1805.33 | −0.821726 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 439.537 | 0.196563 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1239.91 | 0.544905 | 0.272452 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272452 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 336.628 | 0.142952 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2636.86 | 1.10105 | 0.550525 | − | 0.834818i | \(-0.314427\pi\) | ||||
0.550525 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3317.58 | 1.36240 | 0.681199 | − | 0.732099i | \(-0.261459\pi\) | ||||
0.681199 | + | 0.732099i | \(0.261459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1432.05 | 0.578471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3338.01 | −1.30534 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −437.653 | −0.168437 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 624.506 | 0.236585 | 0.118292 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118292 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 436.144 | 0.162665 | 0.0813324 | − | 0.996687i | \(-0.474082\pi\) | ||||
0.0813324 | + | 0.996687i | \(0.474082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3355.81 | −1.21366 | −0.606831 | − | 0.794831i | \(-0.707560\pi\) | ||||
−0.606831 | + | 0.794831i | \(0.707560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3799.77 | −1.35356 | −0.676780 | − | 0.736185i | \(-0.736625\pi\) | ||||
−0.676780 | + | 0.736185i | \(0.736625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1674.28 | 0.587536 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 397.687 | 0.137498 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.5125 | 0.00487288 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1963.72 | 0.649922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2365.27 | −0.771715 | −0.385857 | − | 0.922558i | \(-0.626094\pi\) | ||||
−0.385857 | + | 0.922558i | \(0.626094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1674.84 | −0.538772 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −201.300 | −0.0629730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3035.31 | −0.936562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1642.93 | 0.500070 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3328.58 | −0.999545 | −0.499772 | − | 0.866157i | \(-0.666583\pi\) | ||||
−0.499772 | + | 0.866157i | \(0.666583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −527.100 | −0.154118 | −0.0770592 | − | 0.997027i | \(-0.524553\pi\) | ||||
−0.0770592 | + | 0.997027i | \(0.524553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2566.06 | 0.740479 | 0.370240 | − | 0.928936i | \(-0.379276\pi\) | ||||
0.370240 | + | 0.928936i | \(0.379276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1955.31 | −0.556925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5534.99 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783832\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3451.41 | −0.945962 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1010.01 | −0.273355 | −0.136678 | − | 0.990616i | \(-0.543642\pi\) | ||||
−0.136678 | + | 0.990616i | \(0.543642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4074.29 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −966.525 | −0.248982 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3473.77 | −0.884103 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1773.98 | −0.446107 | −0.223054 | − | 0.974806i | \(-0.571602\pi\) | ||||
−0.223054 | + | 0.974806i | \(0.571602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 64.8375 | 0.0161119 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −662.784 | −0.160869 | −0.0804345 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804345 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5282.38 | 1.26730 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −220.810 | −0.0523669 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 712.312 | 0.167008 | 0.0835039 | − | 0.996507i | \(-0.473389\pi\) | ||||
0.0835039 | + | 0.996507i | \(0.473389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 290.925 | 0.0666829 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3136.41 | −0.710894 | −0.355447 | − | 0.934696i | \(-0.615671\pi\) | ||||
−0.355447 | + | 0.934696i | \(0.615671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2275.69 | 0.510105 | 0.255053 | − | 0.966927i | \(-0.417907\pi\) | ||||
0.255053 | + | 0.966927i | \(0.417907\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 962.381 | 0.213355 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5171.00 | −1.12164 | −0.560821 | − | 0.827937i | \(-0.689515\pi\) | ||||
−0.560821 | + | 0.827937i | \(0.689515\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 111.769 | 0.0239836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2240.14 | 0.475571 | 0.237785 | − | 0.971318i | \(-0.423578\pi\) | ||||
0.237785 | + | 0.971318i | \(0.423578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 225.244 | 0.0473123 | 0.0236561 | − | 0.999720i | \(-0.492469\pi\) | ||||
0.0236561 | + | 0.999720i | \(0.492469\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3929.46 | 0.808183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1978.59 | 0.402726 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3457.12 | 0.696427 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1139.86 | −0.227274 | −0.113637 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113637 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1085.65 | 0.212108 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.9123 | −0.00617237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5954.51 | −1.14024 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3469.47 | −0.657808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5244.86 | 0.975049 | 0.487525 | − | 0.873109i | \(-0.337900\pi\) | ||||
0.487525 | + | 0.873109i | \(0.337900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4001.09 | −0.736615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5188.26 | 0.945977 | 0.472989 | − | 0.881068i | \(-0.343175\pi\) | ||||
0.472989 | + | 0.881068i | \(0.343175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −486.656 | −0.0878832 | −0.0439416 | − | 0.999034i | \(-0.513992\pi\) | ||||
−0.0439416 | + | 0.999034i | \(0.513992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4218.87 | 0.747493 | 0.373747 | − | 0.927531i | \(-0.378073\pi\) | ||||
0.373747 | + | 0.927531i | \(0.378073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −986.512 | −0.173148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2394.79 | −0.416399 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4054.27 | −0.698408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2955.36 | −0.499791 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3315.53 | 0.555595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7439.94 | −1.23546 | −0.617728 | − | 0.786392i | \(-0.711947\pi\) | ||||
−0.617728 | + | 0.786392i | \(0.711947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2932.96 | −0.482658 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6555.39 | 1.05963 | 0.529815 | − | 0.848113i | \(-0.322261\pi\) | ||||
0.529815 | + | 0.848113i | \(0.322261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5664.74 | −0.907571 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 499.350 | 0.0793000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6860.72 | 1.08001 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1950.56 | 0.301763 | 0.150881 | − | 0.988552i | \(-0.451789\pi\) | ||||
0.150881 | + | 0.988552i | \(0.451789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1426.74 | −0.218830 | −0.109415 | − | 0.993996i | \(-0.534898\pi\) | ||||
−0.109415 | + | 0.993996i | \(0.534898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −534.347 | −0.0812573 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7078.96 | 1.06735 | 0.533676 | − | 0.845689i | \(-0.320810\pi\) | ||||
0.533676 | + | 0.845689i | \(0.320810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4036.89 | 0.598474 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5409.79 | 0.795314 | 0.397657 | − | 0.917534i | \(-0.369823\pi\) | ||||
0.397657 | + | 0.917534i | \(0.369823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4473.90 | −0.652267 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 857.381 | 0.123969 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4940.09 | 0.702645 | 0.351322 | − | 0.936255i | \(-0.385732\pi\) | ||||
0.351322 | + | 0.936255i | \(0.385732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2181.77 | −0.307800 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −997.332 | −0.139566 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12891.9 | −1.78959 | −0.894797 | − | 0.446473i | \(-0.852680\pi\) | ||||
−0.894797 | + | 0.446473i | \(0.852680\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 485.551 | 0.0663320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9475.15 | 1.28418 | 0.642092 | − | 0.766627i | \(-0.278067\pi\) | ||||
0.642092 | + | 0.766627i | \(0.278067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1862.58 | −0.250453 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5800.97 | −0.773931 | −0.386966 | − | 0.922094i | \(-0.626477\pi\) | ||||
−0.386966 | + | 0.922094i | \(0.626477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3306.15 | 0.434266 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13779.7 | 1.79603 | 0.898016 | − | 0.439962i | \(-0.145008\pi\) | ||||
0.898016 | + | 0.439962i | \(0.145008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −133.862 | −0.0173138 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7765.06 | 0.996680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2816.46 | 0.356056 | 0.178028 | − | 0.984025i | \(-0.443028\pi\) | ||||
0.178028 | + | 0.984025i | \(0.443028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2374.88 | −0.297976 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11986.4 | 1.49270 | 0.746352 | − | 0.665551i | \(-0.231804\pi\) | ||||
0.746352 | + | 0.665551i | \(0.231804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −245.775 | −0.0303794 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13103.6 | −1.59588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3339.07 | −0.403683 | −0.201841 | − | 0.979418i | \(-0.564693\pi\) | ||||
−0.201841 | + | 0.979418i | \(0.564693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4968.87 | 0.596342 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1818.84 | −0.216706 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 459.769 | 0.0539927 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1688.52 | −0.196873 | −0.0984363 | − | 0.995143i | \(-0.531384\pi\) | ||||
−0.0984363 | + | 0.995143i | \(0.531384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2664.27 | −0.308429 | −0.154214 | − | 0.988037i | \(-0.549285\pi\) | ||||
−0.154214 | + | 0.988037i | \(0.549285\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1840.89 | −0.211601 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7737.54 | −0.876923 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2387.31 | −0.268672 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12266.0 | −1.37084 | −0.685420 | − | 0.728148i | \(-0.740381\pi\) | ||||
−0.685420 | + | 0.728148i | \(0.740381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15647.3 | 1.73664 | 0.868318 | − | 0.496008i | \(-0.165201\pi\) | ||||
0.868318 | + | 0.496008i | \(0.165201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 78.7503 | 0.00862045 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16131.0 | −1.75373 | −0.876867 | − | 0.480733i | \(-0.840371\pi\) | ||||
−0.876867 | + | 0.480733i | \(0.840371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −722.306 | −0.0779944 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10053.7 | 1.07825 | 0.539127 | − | 0.842225i | \(-0.318754\pi\) | ||||
0.539127 | + | 0.842225i | \(0.318754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4450.13 | 0.470882 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7477.71 | 0.785957 | 0.392979 | − | 0.919548i | \(-0.371445\pi\) | ||||
0.392979 | + | 0.919548i | \(0.371445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9747.51 | −1.01772 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1182.84 | 0.122682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1363.46 | −0.139562 | −0.0697812 | − | 0.997562i | \(-0.522230\pi\) | ||||
−0.0697812 | + | 0.997562i | \(0.522230\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2241.42 | −0.227932 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5276.77 | 0.533109 | 0.266555 | − | 0.963820i | \(-0.414115\pi\) | ||||
0.266555 | + | 0.963820i | \(0.414115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5740.02 | 0.576159 | 0.288079 | − | 0.957607i | \(-0.406983\pi\) | ||||
0.288079 | + | 0.957607i | \(0.406983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6233.36 | 0.617657 | 0.308828 | − | 0.951118i | \(-0.400063\pi\) | ||||
0.308828 | + | 0.951118i | \(0.400063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9046.35 | −0.890664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5181.16 | −0.506869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14770.9 | 1.43587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 553.753 | 0.0531543 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19688.2 | 1.87803 | 0.939013 | − | 0.343881i | \(-0.111742\pi\) | ||||
0.939013 | + | 0.343881i | \(0.111742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6449.46 | 0.611372 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −78.4127 | −0.00738696 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3955.08 | −0.368012 | −0.184006 | − | 0.982925i | \(-0.558907\pi\) | ||||
−0.184006 | + | 0.982925i | \(0.558907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6102.84 | −0.564377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13893.5 | 1.27699 | 0.638497 | − | 0.769624i | \(-0.279557\pi\) | ||||
0.638497 | + | 0.769624i | \(0.279557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2036.74 | 0.186065 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9049.39 | 0.816741 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13523.7 | −1.21324 | −0.606618 | − | 0.794993i | \(-0.707474\pi\) | ||||
−0.606618 | + | 0.794993i | \(0.707474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 578.700 | 0.0516056 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13135.4 | 1.16437 | 0.582184 | − | 0.813057i | \(-0.302198\pi\) | ||||
0.582184 | + | 0.813057i | \(0.302198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5415.99 | −0.474423 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2222.71 | −0.193556 | −0.0967778 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967778 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16400.1 | 1.41976 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1318.61 | 0.113486 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8224.57 | −0.699645 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3719.73 | 0.314601 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4916.42 | −0.413421 | −0.206710 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206710 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17743.4 | 1.48349 | 0.741746 | − | 0.670681i | \(-0.233998\pi\) | ||||
0.741746 | + | 0.670681i | \(0.233998\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1030.95 | −0.0852161 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12164.4 | −0.999786 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1009.88 | 0.0825334 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4797.62 | 0.389884 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7910.58 | 0.635692 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3227.05 | −0.257883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12671.3 | −1.00699 | −0.503495 | − | 0.863998i | \(-0.667953\pi\) | ||||
−0.503495 | + | 0.863998i | \(0.667953\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9952.74 | 0.786580 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5250.90 | 0.410443 | 0.205221 | − | 0.978716i | \(-0.434209\pi\) | ||||
0.205221 | + | 0.978716i | \(0.434209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4296.15 | 0.333980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1198.20 | −0.0926406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18648.4 | 1.43401 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25830.2 | −1.96492 | −0.982462 | − | 0.186465i | \(-0.940297\pi\) | ||||
−0.982462 | + | 0.186465i | \(0.940297\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7270.09 | −0.550075 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10014.0 | −0.753640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2021.14 | 0.151298 | 0.0756490 | − | 0.997135i | \(-0.475897\pi\) | ||||
0.0756490 | + | 0.997135i | \(0.475897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1312.96 | −0.0972471 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8706.51 | 0.641469 | 0.320734 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320734 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12194.5 | 0.893740 | 0.446870 | − | 0.894599i | \(-0.352539\pi\) | ||||
0.446870 | + | 0.894599i | \(0.352539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1873.52 | 0.136592 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15264.0 | 1.10130 | 0.550649 | − | 0.834737i | \(-0.314380\pi\) | ||||
0.550649 | + | 0.834737i | \(0.314380\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1308.43 | 0.0939146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18769.2 | 1.34024 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2474.01 | 0.175751 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8456.89 | −0.594639 | −0.297319 | − | 0.954778i | \(-0.596093\pi\) | ||||
−0.297319 | + | 0.954778i | \(0.596093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 606.500 | 0.0424285 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10067.4 | −0.700708 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1225.23 | 0.0848467 | 0.0424234 | − | 0.999100i | \(-0.486492\pi\) | ||||
0.0424234 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11399.3 | −0.781478 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16060.0 | 1.09548 | 0.547741 | − | 0.836648i | \(-0.315488\pi\) | ||||
0.547741 | + | 0.836648i | \(0.315488\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9699.93 | 0.658350 | 0.329175 | − | 0.944269i | \(-0.393229\pi\) | ||||
0.329175 | + | 0.944269i | \(0.393229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5022.84 | 0.339214 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23661.2 | 1.58217 | 0.791087 | − | 0.611703i | \(-0.209515\pi\) | ||||
0.791087 | + | 0.611703i | \(0.209515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1193.06 | 0.0793847 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4048.05 | 0.268030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8085.63 | 0.532749 | 0.266375 | − | 0.963870i | \(-0.414174\pi\) | ||||
0.266375 | + | 0.963870i | \(0.414174\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11035.1 | 0.720029 | 0.360014 | − | 0.932947i | \(-0.382772\pi\) | ||||
0.360014 | + | 0.932947i | \(0.382772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16826.3 | 1.09258 | 0.546290 | − | 0.837596i | \(-0.316040\pi\) | ||||
0.546290 | + | 0.837596i | \(0.316040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.5374 | 0.00281336 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1571.90 | −0.101087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5891.17 | 0.375233 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27053.5 | 1.71493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3705.91 | 0.233803 | 0.116902 | − | 0.993144i | \(-0.462704\pi\) | ||||
0.116902 | + | 0.993144i | \(0.462704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7095.81 | −0.445550 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1588.32 | 0.0987937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5024.53 | −0.311060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24597.4 | −1.51566 | −0.757829 | − | 0.652453i | \(-0.773740\pi\) | ||||
−0.757829 | + | 0.652453i | \(0.773740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21479.5 | −1.31737 | −0.658685 | − | 0.752419i | \(-0.728887\pi\) | ||||
−0.658685 | + | 0.752419i | \(0.728887\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27119.7 | 1.64789 | 0.823946 | − | 0.566668i | \(-0.191768\pi\) | ||||
0.823946 | + | 0.566668i | \(0.191768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4511.87 | 0.272891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −603.900 | −0.0363575 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18476.4 | −1.10725 | −0.553627 | − | 0.832765i | \(-0.686757\pi\) | ||||
−0.553627 | + | 0.832765i | \(0.686757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9105.92 | −0.540724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19273.5 | 1.13928 | 0.569641 | − | 0.821894i | \(-0.307082\pi\) | ||||
0.569641 | + | 0.821894i | \(0.307082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25605.3 | 1.50670 | 0.753352 | − | 0.657618i | \(-0.228436\pi\) | ||||
0.753352 | + | 0.657618i | \(0.228436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4928.79 | 0.288716 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.5616 | −0.00229660 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9985.75 | −0.577087 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19193.9 | 1.10428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7855.52 | −0.449938 | −0.224969 | − | 0.974366i | \(-0.572228\pi\) | ||||
−0.224969 | + | 0.974366i | \(0.572228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6763.09 | 0.383939 | 0.191970 | − | 0.981401i | \(-0.438512\pi\) | ||||
0.191970 | + | 0.981401i | \(0.438512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18679.3 | −1.05574 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1581.30 | −0.0889803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15608.6 | 0.874447 | 0.437224 | − | 0.899353i | \(-0.355962\pi\) | ||||
0.437224 | + | 0.899353i | \(0.355962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7698.17 | 0.427516 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1217.68 | −0.0673293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6203.15 | −0.341504 | −0.170752 | − | 0.985314i | \(-0.554620\pi\) | ||||
−0.170752 | + | 0.985314i | \(0.554620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5865.92 | −0.321541 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20124.5 | 1.09365 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16605.0 | −0.898509 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16507.9 | −0.889435 | −0.444718 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444718 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15915.4 | −0.853854 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18746.0 | 0.997193 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25539.6 | −1.35283 | −0.676416 | − | 0.736520i | \(-0.736468\pi\) | ||||
−0.676416 | + | 0.736520i | \(0.736468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10354.2 | −0.546151 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.0252 | 0.00105182 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3030.02 | −0.157822 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7353.45 | 0.381415 | 0.190708 | − | 0.981647i | \(-0.438922\pi\) | ||||
0.190708 | + | 0.981647i | \(0.438922\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21618.4 | 1.11666 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12222.9 | −0.628732 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21696.5 | −1.10685 | −0.553424 | − | 0.832900i | \(-0.686679\pi\) | ||||
−0.553424 | + | 0.832900i | \(0.686679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30495.8 | −1.54299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −90.2714 | −0.00454877 | −0.00227439 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227439 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22440.6 | 1.12159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14273.1 | −0.710479 | −0.355239 | − | 0.934775i | \(-0.615601\pi\) | ||||
−0.355239 | + | 0.934775i | \(0.615601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2899.57 | −0.143750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15866.6 | 0.783429 | 0.391715 | − | 0.920087i | \(-0.371882\pi\) | ||||
0.391715 | + | 0.920087i | \(0.371882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10421.3 | −0.510437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12939.3 | 0.631232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26776.9 | −1.30107 | −0.650534 | − | 0.759477i | \(-0.725455\pi\) | ||||
−0.650534 | + | 0.759477i | \(0.725455\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5321.95 | −0.257560 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30478.0 | −1.46333 | −0.731666 | − | 0.681663i | \(-0.761257\pi\) | ||||
−0.731666 | + | 0.681663i | \(0.761257\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 194.512 | 0.00930218 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29104.7 | 1.38639 | 0.693195 | − | 0.720750i | \(-0.256202\pi\) | ||||
0.693195 | + | 0.720750i | \(0.256202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15968.2 | 0.757649 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2220.69 | −0.104543 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4170.65 | 0.195575 | 0.0977876 | − | 0.995207i | \(-0.468823\pi\) | ||||
0.0977876 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1988.35 | −0.0928778 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17738.5 | 0.825367 | 0.412684 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412684 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15847.1 | 0.731677 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11839.1 | −0.544519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22448.1 | −1.02850 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −662.429 | −0.0302341 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3807.92 | −0.172475 | −0.0862374 | − | 0.996275i | \(-0.527484\pi\) | ||||
−0.0862374 | + | 0.996275i | \(0.527484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2136.94 | 0.0964220 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30607.3 | 1.37582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9447.06 | −0.423045 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23840.3 | −1.05956 | −0.529779 | − | 0.848136i | \(-0.677725\pi\) | ||||
−0.529779 | + | 0.848136i | \(0.677725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16980.3 | 0.751841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 872.775 | 0.0384994 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40682.6 | −1.78787 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9409.24 | −0.410435 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1984.22 | −0.0862316 | −0.0431158 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431158 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9713.78 | 0.420588 | 0.210294 | − | 0.977638i | \(-0.432558\pi\) | ||||
0.210294 | + | 0.977638i | \(0.432558\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6827.08 | 0.294509 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17940.5 | 0.768246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2887.14 | 0.123181 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19235.4 | −0.817686 | −0.408843 | − | 0.912605i | \(-0.634068\pi\) | ||||
−0.408843 | + | 0.912605i | \(0.634068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12717.6 | −0.538650 | −0.269325 | − | 0.963049i | \(-0.586801\pi\) | ||||
−0.269325 | + | 0.963049i | \(0.586801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6744.75 | −0.283601 | −0.141800 | − | 0.989895i | \(-0.545289\pi\) | ||||
−0.141800 | + | 0.989895i | \(0.545289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3404.22 | 0.142622 | 0.0713108 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713108 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15513.0 | −0.647581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6662.52 | 0.277122 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 335.306 | 0.0138469 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21361.9 | 0.879015 | 0.439508 | − | 0.898239i | \(-0.355153\pi\) | ||||
0.439508 | + | 0.898239i | \(0.355153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23787.1 | −0.975319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6720.41 | 0.274571 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4632.54 | −0.187929 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 675.732 | 0.0273158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −525.488 | −0.0211674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10728.9 | 0.430657 | 0.215328 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215328 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42895.2 | 1.70977 | 0.854885 | − | 0.518817i | \(-0.173627\pi\) | ||||
0.854885 | + | 0.518817i | \(0.173627\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35530.5 | −1.41127 | −0.705637 | − | 0.708574i | \(-0.749339\pi\) | ||||
−0.705637 | + | 0.708574i | \(0.749339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11788.4 | 0.466605 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5704.35 | 0.225004 | 0.112502 | − | 0.993652i | \(-0.464114\pi\) | ||||
0.112502 | + | 0.993652i | \(0.464114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5935.78 | 0.232514 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46259.6 | −1.80581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11045.0 | −0.429674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10371.4 | 0.402082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50249.0 | −1.93476 | −0.967382 | − | 0.253324i | \(-0.918476\pi\) | ||||
−0.967382 | + | 0.253324i | \(0.918476\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3419.58 | −0.131217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26864.5 | −1.02734 | −0.513672 | − | 0.857987i | \(-0.671715\pi\) | ||||
−0.513672 | + | 0.857987i | \(0.671715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18942.1 | 0.721918 | 0.360959 | − | 0.932582i | \(-0.382449\pi\) | ||||
0.360959 | + | 0.932582i | \(0.382449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25344.8 | −0.959409 | −0.479705 | − | 0.877430i | \(-0.659256\pi\) | ||||
−0.479705 | + | 0.877430i | \(0.659256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10063.7 | 0.379670 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3256.96 | 0.122460 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9989.40 | −0.374337 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −95.7370 | −0.00356362 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −304.686 | −0.0113035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5107.79 | −0.188863 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17863.5 | −0.658318 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4800.11 | 0.175728 | 0.0878639 | − | 0.996132i | \(-0.471996\pi\) | ||||
0.0878639 | + | 0.996132i | \(0.471996\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10408.4 | −0.379786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25731.7 | 0.935819 | 0.467909 | − | 0.883776i | \(-0.345007\pi\) | ||||
0.467909 | + | 0.883776i | \(0.345007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46559.4 | −1.68772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41955.6 | −1.51090 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12751.9 | 0.457722 | 0.228861 | − | 0.973459i | \(-0.426500\pi\) | ||||
0.228861 | + | 0.973459i | \(0.426500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15734.6 | 0.562945 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11048.7 | 0.394012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12003.3 | −0.425285 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15557.8 | 0.549444 | 0.274722 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274722 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3919.51 | −0.137977 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15564.8 | 0.546160 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23858.0 | 0.831811 | 0.415905 | − | 0.909408i | \(-0.363465\pi\) | ||||
0.415905 | + | 0.909408i | \(0.363465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1459.97 | −0.0507394 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9748.00 | 0.337700 | 0.168850 | − | 0.985642i | \(-0.445995\pi\) | ||||
0.168850 | + | 0.985642i | \(0.445995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −390.899 | −0.0134989 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51537.0 | −1.76845 | −0.884227 | − | 0.467057i | \(-0.845314\pi\) | ||||
−0.884227 | + | 0.467057i | \(0.845314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20023.5 | 0.684923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12656.6 | 0.431566 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5631.36 | 0.191414 | 0.0957071 | − | 0.995410i | \(-0.469489\pi\) | ||||
0.0957071 | + | 0.995410i | \(0.469489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2959.54 | −0.0999668 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26847.4 | −0.904013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29636.8 | −0.994823 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7184.36 | −0.240408 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43360.9 | −1.44198 | −0.720989 | − | 0.692946i | \(-0.756312\pi\) | ||||
−0.720989 | + | 0.692946i | \(0.756312\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12162.8 | −0.403226 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12920.0 | −0.427007 | −0.213503 | − | 0.976942i | \(-0.568487\pi\) | ||||
−0.213503 | + | 0.976942i | \(0.568487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2484.19 | −0.0818493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10650.4 | 0.348759 | 0.174379 | − | 0.984679i | \(-0.444208\pi\) | ||||
0.174379 | + | 0.984679i | \(0.444208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3899.31 | 0.127296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8866.07 | −0.288554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49450.3 | −1.60450 | −0.802248 | − | 0.596991i | \(-0.796363\pi\) | ||||
−0.802248 | + | 0.596991i | \(0.796363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9946.58 | 0.320773 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 592.351 | 0.0190452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9410.47 | −0.301648 | −0.150824 | − | 0.988561i | \(-0.548193\pi\) | ||||
−0.150824 | + | 0.988561i | \(0.548193\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22319.8 | −0.713291 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −532.117 | −0.0169030 | −0.00845151 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00845151 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8798.88 | −0.278663 |
(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 | 1200.4.a.bt.1.1 | 2 | ||
4.3 | odd | 2 | 75.4.a.c.1.1 | 2 | |||
5.2 | odd | 4 | 240.4.f.f.49.2 | 4 | |||
5.3 | odd | 4 | 240.4.f.f.49.4 | 4 | |||
5.4 | even | 2 | 1200.4.a.bn.1.2 | 2 | |||
12.11 | even | 2 | 225.4.a.o.1.2 | 2 | |||
15.2 | even | 4 | 720.4.f.j.289.2 | 4 | |||
15.8 | even | 4 | 720.4.f.j.289.1 | 4 | |||
20.3 | even | 4 | 15.4.b.a.4.4 | yes | 4 | ||
20.7 | even | 4 | 15.4.b.a.4.1 | ✓ | 4 | ||
20.19 | odd | 2 | 75.4.a.f.1.2 | 2 | |||
40.3 | even | 4 | 960.4.f.q.769.3 | 4 | |||
40.13 | odd | 4 | 960.4.f.p.769.1 | 4 | |||
40.27 | even | 4 | 960.4.f.q.769.1 | 4 | |||
40.37 | odd | 4 | 960.4.f.p.769.3 | 4 | |||
60.23 | odd | 4 | 45.4.b.b.19.1 | 4 | |||
60.47 | odd | 4 | 45.4.b.b.19.4 | 4 | |||
60.59 | even | 2 | 225.4.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.1 | ✓ | 4 | 20.7 | even | 4 | ||
15.4.b.a.4.4 | yes | 4 | 20.3 | even | 4 | ||
45.4.b.b.19.1 | 4 | 60.23 | odd | 4 | |||
45.4.b.b.19.4 | 4 | 60.47 | odd | 4 | |||
75.4.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
75.4.a.f.1.2 | 2 | 20.19 | odd | 2 | |||
225.4.a.i.1.1 | 2 | 60.59 | even | 2 | |||
225.4.a.o.1.2 | 2 | 12.11 | even | 2 | |||
240.4.f.f.49.2 | 4 | 5.2 | odd | 4 | |||
240.4.f.f.49.4 | 4 | 5.3 | odd | 4 | |||
720.4.f.j.289.1 | 4 | 15.8 | even | 4 | |||
720.4.f.j.289.2 | 4 | 15.2 | even | 4 | |||
960.4.f.p.769.1 | 4 | 40.13 | odd | 4 | |||
960.4.f.p.769.3 | 4 | 40.37 | odd | 4 | |||
960.4.f.q.769.1 | 4 | 40.27 | even | 4 | |||
960.4.f.q.769.3 | 4 | 40.3 | even | 4 | |||
1200.4.a.bn.1.2 | 2 | 5.4 | even | 2 | |||
1200.4.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial |