Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 16x^{3} + 33x^{2} - 4x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.70452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 2.70452 | 1.56145 | 0.780727 | − | 0.624872i | \(-0.214849\pi\) | ||||
0.780727 | + | 0.624872i | \(0.214849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.77934 | 1.42846 | 0.714228 | − | 0.699914i | \(-0.246778\pi\) | ||||
0.714228 | + | 0.699914i | \(0.246778\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.31442 | 1.43814 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.71724 | 1.42230 | 0.711150 | − | 0.703040i | \(-0.248175\pi\) | ||||
0.711150 | + | 0.703040i | \(0.248175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.44195 | −1.50933 | −0.754663 | − | 0.656113i | \(-0.772200\pi\) | ||||
−0.754663 | + | 0.656113i | \(0.772200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.40944 | −0.584375 | −0.292187 | − | 0.956361i | \(-0.594383\pi\) | ||||
−0.292187 | + | 0.956361i | \(0.594383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.2213 | 2.23047 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.38924 | 0.915220 | 0.457610 | − | 0.889153i | \(-0.348706\pi\) | ||||
0.457610 | + | 0.889153i | \(0.348706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.55488 | 0.684137 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.05146 | 1.68081 | 0.840407 | − | 0.541956i | \(-0.182316\pi\) | ||||
0.840407 | + | 0.541956i | \(0.182316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.92581 | −1.78273 | −0.891364 | − | 0.453288i | \(-0.850251\pi\) | ||||
−0.891364 | + | 0.453288i | \(0.850251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.7579 | 2.22086 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0429 | 1.65105 | 0.825524 | − | 0.564367i | \(-0.190880\pi\) | ||||
0.825524 | + | 0.564367i | \(0.190880\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.7179 | −2.35674 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11712 | 0.174465 | 0.0872326 | − | 0.996188i | \(-0.472198\pi\) | ||||
0.0872326 | + | 0.996188i | \(0.472198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1169 | −1.84781 | −0.923904 | − | 0.382625i | \(-0.875020\pi\) | ||||
−0.923904 | + | 0.382625i | \(0.875020\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.72432 | 0.980842 | 0.490421 | − | 0.871486i | \(-0.336843\pi\) | ||||
0.490421 | + | 0.871486i | \(0.336843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.28339 | 1.04048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.51637 | −0.912474 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.34694 | 0.597098 | 0.298549 | − | 0.954394i | \(-0.403497\pi\) | ||||
0.298549 | + | 0.954394i | \(0.403497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.70452 | 0.358222 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.03914 | −0.525851 | −0.262926 | − | 0.964816i | \(-0.584687\pi\) | ||||
−0.262926 | + | 0.964816i | \(0.584687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.14562 | −1.17098 | −0.585488 | − | 0.810681i | \(-0.699097\pi\) | ||||
−0.585488 | + | 0.810681i | \(0.699097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.3057 | 2.05432 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.39672 | 0.537145 | 0.268572 | − | 0.963259i | \(-0.413448\pi\) | ||||
0.268572 | + | 0.963259i | \(0.413448\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.8708 | 1.42907 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.90222 | 0.937821 | 0.468910 | − | 0.883246i | \(-0.344647\pi\) | ||||
0.468910 | + | 0.883246i | \(0.344647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.07165 | 0.359510 | 0.179755 | − | 0.983711i | \(-0.442470\pi\) | ||||
0.179755 | + | 0.983711i | \(0.442470\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.8280 | 2.03169 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3996 | 1.28256 | 0.641280 | − | 0.767307i | \(-0.278404\pi\) | ||||
0.641280 | + | 0.767307i | \(0.278404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.32902 | −0.369891 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.37652 | −0.480386 | −0.240193 | − | 0.970725i | \(-0.577211\pi\) | ||||
−0.240193 | + | 0.970725i | \(0.577211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.4798 | 2.62451 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.53933 | 0.269169 | 0.134584 | − | 0.990902i | \(-0.457030\pi\) | ||||
0.134584 | + | 0.990902i | \(0.457030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.5670 | −2.15600 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.8445 | −2.78365 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.302105 | −0.0306741 | −0.0153371 | − | 0.999882i | \(-0.504882\pi\) | ||||
−0.0153371 | + | 0.999882i | \(0.504882\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.3522 | 2.04547 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.77080 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9014 | −1.76388 | −0.881939 | − | 0.471364i | \(-0.843762\pi\) | ||||
−0.881939 | + | 0.471364i | \(0.843762\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.1673 | −1.27293 | −0.636465 | − | 0.771305i | \(-0.719604\pi\) | ||||
−0.636465 | + | 0.771305i | \(0.719604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.756212 | 0.0724320 | 0.0362160 | − | 0.999344i | \(-0.488470\pi\) | ||||
0.0362160 | + | 0.999344i | \(0.488470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.1613 | 2.57804 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.6082 | −1.93866 | −0.969329 | − | 0.245766i | \(-0.920960\pi\) | ||||
−0.969329 | + | 0.245766i | \(0.920960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23.4789 | −2.17062 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.10608 | −0.834753 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2523 | 1.02294 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.02128 | 0.272419 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3178 | 1.71418 | 0.857089 | − | 0.515168i | \(-0.172270\pi\) | ||||
0.857089 | + | 0.515168i | \(0.172270\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −32.7703 | −2.88527 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29192 | −0.374986 | −0.187493 | − | 0.982266i | \(-0.560036\pi\) | ||||
−0.187493 | + | 0.982266i | \(0.560036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.77934 | 0.327710 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.2413 | −1.81476 | −0.907382 | − | 0.420306i | \(-0.861923\pi\) | ||||
−0.907382 | + | 0.420306i | \(0.861923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.94814 | 0.165239 | 0.0826197 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826197 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.1860 | 1.53154 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.6710 | −2.14671 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.6981 | 1.62467 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.56655 | −0.374107 | −0.187053 | − | 0.982350i | \(-0.559894\pi\) | ||||
−0.187053 | + | 0.982350i | \(0.559894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.84246 | −0.719590 | −0.359795 | − | 0.933031i | \(-0.617153\pi\) | ||||
−0.359795 | + | 0.933031i | \(0.617153\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.3953 | −0.840413 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.63494 | 0.449717 | 0.224859 | − | 0.974391i | \(-0.427808\pi\) | ||||
0.224859 | + | 0.974391i | \(0.427808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.7564 | 0.932341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5884 | 1.30735 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.71114 | 0.290679 | 0.145340 | − | 0.989382i | \(-0.453573\pi\) | ||||
0.145340 | + | 0.989382i | \(0.453573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.403668 | 0.0312368 | 0.0156184 | − | 0.999878i | \(-0.495028\pi\) | ||||
0.0156184 | + | 0.999878i | \(0.495028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.6148 | 1.27806 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.31442 | 0.329932 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9048 | 1.05716 | 0.528580 | − | 0.848884i | \(-0.322725\pi\) | ||||
0.528580 | + | 0.848884i | \(0.322725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.9239 | −0.821093 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.27673 | 0.244914 | 0.122457 | − | 0.992474i | \(-0.460923\pi\) | ||||
0.122457 | + | 0.992474i | \(0.460923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0254 | 0.968173 | 0.484086 | − | 0.875020i | \(-0.339152\pi\) | ||||
0.484086 | + | 0.875020i | \(0.339152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.7345 | −1.82843 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3659 | −0.831156 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.4351 | 0.977260 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6403 | −1.27641 | −0.638203 | − | 0.769868i | \(-0.720322\pi\) | ||||
−0.638203 | + | 0.769868i | \(0.720322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.8445 | 1.21250 | 0.606248 | − | 0.795276i | \(-0.292674\pi\) | ||||
0.606248 | + | 0.795276i | \(0.292674\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8742 | −1.41598 | −0.707988 | − | 0.706224i | \(-0.750397\pi\) | ||||
−0.707988 | + | 0.706224i | \(0.750397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.54003 | −0.605386 | −0.302693 | − | 0.953088i | \(-0.597886\pi\) | ||||
−0.302693 | + | 0.953088i | \(0.597886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.8910 | 0.838727 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.2085 | 2.40097 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9370 | 1.31622 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.71724 | 0.326298 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0127177 | −0.000875525 0 | −0.000437762 | − | 1.00000i | \(-0.500139\pi\) | ||||
−0.000437762 | 1.00000i | \(0.500139\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.3717 | 1.46437 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.5130 | −2.54655 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.30734 | 0.561358 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1120 | 0.882012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6403 | −1.24825 | −0.624124 | − | 0.781326i | \(-0.714544\pi\) | ||||
−0.624124 | + | 0.781326i | \(0.714544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.75187 | 0.514510 | 0.257255 | − | 0.966344i | \(-0.417182\pi\) | ||||
0.257255 | + | 0.966344i | \(0.417182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3735 | −1.28023 | −0.640117 | − | 0.768277i | \(-0.721114\pi\) | ||||
−0.640117 | + | 0.768277i | \(0.721114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 48.2162 | 3.17240 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.63389 | −0.565625 | −0.282813 | − | 0.959175i | \(-0.591267\pi\) | ||||
−0.282813 | + | 0.959175i | \(0.591267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.8306 | 2.00266 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.47644 | 0.612980 | 0.306490 | − | 0.951874i | \(-0.400845\pi\) | ||||
0.306490 | + | 0.951874i | \(0.400845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.3641 | 1.89151 | 0.945755 | − | 0.324880i | \(-0.105324\pi\) | ||||
0.945755 | + | 0.324880i | \(0.105324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.6681 | −1.26171 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.44195 | −0.346263 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.8364 | −0.750101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.57377 | −0.478052 | −0.239026 | − | 0.971013i | \(-0.576828\pi\) | ||||
−0.239026 | + | 0.971013i | \(0.576828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7051 | 1.30172 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7573 | −0.733400 | −0.366700 | − | 0.930339i | \(-0.619512\pi\) | ||||
−0.366700 | + | 0.930339i | \(0.619512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.9556 | 2.35845 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 39.0518 | 2.41725 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.20334 | 0.135864 | 0.0679319 | − | 0.997690i | \(-0.478360\pi\) | ||||
0.0679319 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.86767 | 0.420295 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.14642 | 0.374754 | 0.187377 | − | 0.982288i | \(-0.440001\pi\) | ||||
0.187377 | + | 0.982288i | \(0.440001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6620 | 1.55886 | 0.779428 | − | 0.626491i | \(-0.215510\pi\) | ||||
0.779428 | + | 0.626491i | \(0.215510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55.6238 | −3.36650 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.64202 | −0.278912 | −0.139456 | − | 0.990228i | \(-0.544535\pi\) | ||||
−0.139456 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −42.8241 | −2.56381 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.369967 | −0.0220704 | −0.0110352 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110352 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.21325 | −0.0721203 | −0.0360602 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360602 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.22198 | 0.249216 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1946 | −0.658506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.817050 | −0.0478963 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.66265 | 0.506077 | 0.253039 | − | 0.967456i | \(-0.418570\pi\) | ||||
0.253039 | + | 0.967456i | \(0.418570\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.7692 | 0.973049 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8860 | −1.38137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.7938 | −2.63951 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9027 | 0.741242 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.26123 | 0.471493 | 0.235747 | − | 0.971815i | \(-0.424246\pi\) | ||||
0.235747 | + | 0.971815i | \(0.424246\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.4147 | −2.75421 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.54408 | 0.427786 | 0.213893 | − | 0.976857i | \(-0.431386\pi\) | ||||
0.213893 | + | 0.976857i | \(0.431386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.43152 | −0.193961 | −0.0969804 | − | 0.995286i | \(-0.530918\pi\) | ||||
−0.0969804 | + | 0.995286i | \(0.530918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.50784 | 0.140854 | 0.0704270 | − | 0.997517i | \(-0.477564\pi\) | ||||
0.0704270 | + | 0.997517i | \(0.477564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.6979 | 2.39062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.6112 | −1.98762 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.40944 | −0.134065 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.04519 | 0.113099 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.4135 | 1.40109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1167 | 1.60040 | 0.800200 | − | 0.599734i | \(-0.204727\pi\) | ||||
0.800200 | + | 0.599734i | \(0.204727\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 43.3295 | 2.37444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4033 | 1.11144 | 0.555720 | − | 0.831370i | \(-0.312443\pi\) | ||||
0.555720 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −55.7353 | −3.02713 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −46.8224 | −2.53557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.07103 | 0.0578300 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.9967 | −1.39557 | −0.697787 | − | 0.716305i | \(-0.745832\pi\) | ||||
−0.697787 | + | 0.716305i | \(0.745832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.32628 | 0.178052 | 0.0890258 | − | 0.996029i | \(-0.471625\pi\) | ||||
0.0890258 | + | 0.996029i | \(0.471625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.3455 | −1.03259 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0904 | −0.803179 | −0.401590 | − | 0.915820i | \(-0.631542\pi\) | ||||
−0.401590 | + | 0.915820i | \(0.631542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.6276 | −1.30343 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.8292 | −0.677102 | −0.338551 | − | 0.940948i | \(-0.609937\pi\) | ||||
−0.338551 | + | 0.940948i | \(0.609937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.4321 | 1.59727 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.11198 | 0.214644 | 0.107322 | − | 0.994224i | \(-0.465772\pi\) | ||||
0.107322 | + | 0.994224i | \(0.465772\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.81974 | 0.250905 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4285 | 0.852927 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5930 | −0.859153 | −0.429576 | − | 0.903031i | \(-0.641337\pi\) | ||||
−0.429576 | + | 0.903031i | \(0.641337\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.2576 | −2.53690 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6822 | 1.57604 | 0.788021 | − | 0.615649i | \(-0.211106\pi\) | ||||
0.788021 | + | 0.615649i | \(0.211106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.2454 | 2.67661 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.4909 | −1.55801 | −0.779006 | − | 0.627017i | \(-0.784276\pi\) | ||||
−0.779006 | + | 0.627017i | \(0.784276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −52.2774 | −2.65741 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3448 | 0.828714 | 0.414357 | − | 0.910114i | \(-0.364006\pi\) | ||||
0.414357 | + | 0.910114i | \(0.364006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5756 | −0.534831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.6076 | −0.585524 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5946 | −0.782670 | −0.391335 | − | 0.920248i | \(-0.627987\pi\) | ||||
−0.391335 | + | 0.920248i | \(0.627987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2213 | 0.511705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.3465 | −1.01606 | −0.508029 | − | 0.861340i | \(-0.669626\pi\) | ||||
−0.508029 | + | 0.861340i | \(0.669626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 54.0158 | 2.69072 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.3749 | 2.34829 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.65655 | −0.279699 | −0.139849 | − | 0.990173i | \(-0.544662\pi\) | ||||
−0.139849 | + | 0.990173i | \(0.544662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.4474 | −2.83367 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.2653 | −0.751155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.26879 | 0.258014 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1490 | −0.886635 | −0.443318 | − | 0.896365i | \(-0.646199\pi\) | ||||
−0.443318 | + | 0.896365i | \(0.646199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.94874 | 0.289924 | 0.144962 | − | 0.989437i | \(-0.453694\pi\) | ||||
0.144962 | + | 0.989437i | \(0.453694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0115 | 1.41059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.5644 | −1.67269 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −69.4276 | −3.35200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.93242 | 0.0930816 | 0.0465408 | − | 0.998916i | \(-0.485180\pi\) | ||||
0.0465408 | + | 0.998916i | \(0.485180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7014 | −0.706505 | −0.353253 | − | 0.935528i | \(-0.614924\pi\) | ||||
−0.353253 | + | 0.935528i | \(0.614924\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.38924 | 0.209966 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5922 | 0.505540 | 0.252770 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252770 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.4236 | 1.49636 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.7357 | −1.84039 | −0.920195 | − | 0.391459i | \(-0.871970\pi\) | ||||
−0.920195 | + | 0.391459i | \(0.871970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.3503 | −0.584151 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.2298 | −1.37944 | −0.689719 | − | 0.724078i | \(-0.742266\pi\) | ||||
−0.689719 | + | 0.724078i | \(0.742266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.26973 | 0.248142 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.9146 | −1.12361 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.18004 | 0.195534 | 0.0977671 | − | 0.995209i | \(-0.468830\pi\) | ||||
0.0977671 | + | 0.995209i | \(0.468830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.56527 | −0.399793 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.9590 | 1.67478 | 0.837389 | − | 0.546607i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546607i | \(0.184081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.5866 | −1.51443 | −0.757214 | − | 0.653167i | \(-0.773440\pi\) | ||||
−0.757214 | + | 0.653167i | \(0.773440\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.66769 | 0.262269 | 0.131135 | − | 0.991365i | \(-0.458138\pi\) | ||||
0.131135 | + | 0.991365i | \(0.458138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.6167 | 0.767287 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.2398 | 0.702213 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.1582 | −2.62814 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.7545 | 0.858711 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.2096 | −0.740635 | −0.370318 | − | 0.928905i | \(-0.620751\pi\) | ||||
−0.370318 | + | 0.928905i | \(0.620751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −54.6531 | −2.49197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 44.8637 | 2.04137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0329 | 0.862461 | 0.431231 | − | 0.902242i | \(-0.358080\pi\) | ||||
0.431231 | + | 0.902242i | \(0.358080\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0369 | 0.453882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5658 | −0.747602 | −0.373801 | − | 0.927509i | \(-0.621946\pi\) | ||||
−0.373801 | + | 0.927509i | \(0.621946\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8089 | −0.982224 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.8652 | 1.33964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.36691 | 0.285022 | 0.142511 | − | 0.989793i | \(-0.454482\pi\) | ||||
0.142511 | + | 0.989793i | \(0.454482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.09173 | 0.0487748 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.79766 | 0.258505 | 0.129252 | − | 0.991612i | \(-0.458742\pi\) | ||||
0.129252 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 44.9352 | 1.99564 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.0521 | 1.02177 | 0.510883 | − | 0.859650i | \(-0.329319\pi\) | ||||
0.510883 | + | 0.859650i | \(0.329319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6088 | 0.513544 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.55488 | 0.156952 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.7202 | 1.39505 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.6057 | 1.65071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7470 | 0.514645 | 0.257323 | − | 0.966326i | \(-0.417160\pi\) | ||||
0.257323 | + | 0.966326i | \(0.417160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0715 | −1.05257 | −0.526286 | − | 0.850308i | \(-0.676416\pi\) | ||||
−0.526286 | + | 0.850308i | \(0.676416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.9156 | 1.04178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.73456 | −0.162372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.4266 | −0.756248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.07932 | −0.263325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.86198 | 0.382423 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.3575 | 1.47988 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.93335 | −0.169108 | −0.0845540 | − | 0.996419i | \(-0.526947\pi\) | ||||
−0.0845540 | + | 0.996419i | \(0.526947\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.2275 | 1.51176 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2622 | −0.909105 | −0.454553 | − | 0.890720i | \(-0.650201\pi\) | ||||
−0.454553 | + | 0.890720i | \(0.650201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.4581 | −1.68403 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.05146 | 0.385605 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.0831 | 1.83208 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.2899 | −0.435996 | −0.217998 | − | 0.975949i | \(-0.569953\pi\) | ||||
−0.217998 | + | 0.975949i | \(0.569953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.9395 | 2.78894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.7393 | −1.29781 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.8745 | 0.921901 | 0.460950 | − | 0.887426i | \(-0.347509\pi\) | ||||
0.460950 | + | 0.887426i | \(0.347509\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.5815 | −0.528373 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8560 | 0.958172 | 0.479086 | − | 0.877768i | \(-0.340968\pi\) | ||||
0.479086 | + | 0.877768i | \(0.340968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.58019 | −0.233524 | −0.116762 | − | 0.993160i | \(-0.537251\pi\) | ||||
−0.116762 | + | 0.993160i | \(0.537251\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −47.7085 | −1.99305 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.48419 | −0.353201 | −0.176601 | − | 0.984283i | \(-0.556510\pi\) | ||||
−0.176601 | + | 0.984283i | \(0.556510\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 45.5564 | 1.89326 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.5404 | −0.686210 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.5055 | 0.849252 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.8166 | 1.06557 | 0.532783 | − | 0.846252i | \(-0.321146\pi\) | ||||
0.532783 | + | 0.846252i | \(0.321146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.92581 | −0.408986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −53.7501 | −2.21098 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.3984 | 1.08405 | 0.542025 | − | 0.840362i | \(-0.317658\pi\) | ||||
0.542025 | + | 0.840362i | \(0.317658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.0967 | −0.945284 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.1825 | 1.47838 | 0.739188 | − | 0.673499i | \(-0.235210\pi\) | ||||
0.739188 | + | 0.673499i | \(0.235210\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.20839 | 0.130873 | 0.0654364 | − | 0.997857i | \(-0.479156\pi\) | ||||
0.0654364 | + | 0.997857i | \(0.479156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.9693 | 0.772490 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3390 | −0.825534 | −0.412767 | − | 0.910837i | \(-0.635438\pi\) | ||||
−0.412767 | + | 0.910837i | \(0.635438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 92.5176 | 3.74900 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.5934 | −1.48041 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9062 | 0.763616 | 0.381808 | − | 0.924242i | \(-0.375302\pi\) | ||||
0.381808 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.0702 | 1.41187 | 0.705936 | − | 0.708275i | \(-0.250527\pi\) | ||||
0.705936 | + | 0.708275i | \(0.250527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.1329 | −1.81404 | −0.907021 | − | 0.421085i | \(-0.861650\pi\) | ||||
−0.907021 | + | 0.421085i | \(0.861650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.6032 | 0.626136 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.59699 | 0.384495 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.7579 | 0.509500 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.1978 | −0.964830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0467 | 1.39519 | 0.697593 | − | 0.716494i | \(-0.254254\pi\) | ||||
0.697593 | + | 0.716494i | \(0.254254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0343954 | −0.00136709 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.6359 | −1.57043 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.0935 | 1.34872 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8470 | −0.428431 | −0.214215 | − | 0.976786i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976786i | \(0.568719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.6665 | 1.48542 | 0.742712 | − | 0.669611i | \(-0.233539\pi\) | ||||
0.742712 | + | 0.669611i | \(0.233539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.2893 | −1.46599 | −0.732997 | − | 0.680231i | \(-0.761879\pi\) | ||||
−0.732997 | + | 0.680231i | \(0.761879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0536 | −0.747918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −101.455 | −3.97632 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.10026 | −0.199588 | −0.0997942 | − | 0.995008i | \(-0.531818\pi\) | ||||
−0.0997942 | + | 0.995008i | \(0.531818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.2524 | 0.517026 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.1180 | 1.40696 | 0.703479 | − | 0.710716i | \(-0.251629\pi\) | ||||
0.703479 | + | 0.710716i | \(0.251629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5014 | −0.602934 | −0.301467 | − | 0.953477i | \(-0.597476\pi\) | ||||
−0.301467 | + | 0.953477i | \(0.597476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.4618 | 1.37722 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.7290 | 1.53831 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −50.4131 | −1.94908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −43.1420 | −1.66548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8897 | 0.805240 | 0.402620 | − | 0.915367i | \(-0.368100\pi\) | ||||
0.402620 | + | 0.915367i | \(0.368100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.3686 | −1.51306 | −0.756529 | − | 0.653960i | \(-0.773106\pi\) | ||||
−0.756529 | + | 0.653960i | \(0.773106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.14176 | −0.0438166 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.9651 | 0.803383 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.6596 | −1.59406 | −0.797030 | − | 0.603940i | \(-0.793597\pi\) | ||||
−0.797030 | + | 0.603940i | \(0.793597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −52.3959 | −1.99903 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.6558 | −0.901215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.90123 | 0.148410 | 0.0742050 | − | 0.997243i | \(-0.476358\pi\) | ||||
0.0742050 | + | 0.997243i | \(0.476358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 76.9177 | 2.92186 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.69164 | −0.101953 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.3505 | −0.883198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.6495 | −0.931000 | −0.465500 | − | 0.885048i | \(-0.654125\pi\) | ||||
−0.465500 | + | 0.885048i | \(0.654125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0429 | 0.378776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0305 | 0.678106 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.56624 | 0.359268 | 0.179634 | − | 0.983734i | \(-0.442509\pi\) | ||||
0.179634 | + | 0.983734i | \(0.442509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49.1829 | 1.84450 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.5668 | −1.63159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.6292 | 0.957141 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.6273 | −0.993030 | −0.496515 | − | 0.868028i | \(-0.665387\pi\) | ||||
−0.496515 | + | 0.868028i | \(0.665387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.6554 | −2.51962 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 79.4159 | 2.95351 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.3779 | −0.904127 | −0.452063 | − | 0.891986i | \(-0.649312\pi\) | ||||
−0.452063 | + | 0.891986i | \(0.649312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.2056 | −1.60021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.1949 | 1.07981 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.53865 | −0.241511 | −0.120755 | − | 0.992682i | \(-0.538532\pi\) | ||||
−0.120755 | + | 0.992682i | \(0.538532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.7404 | 0.763981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7605 | 0.432617 | 0.216308 | − | 0.976325i | \(-0.430598\pi\) | ||||
0.216308 | + | 0.976325i | \(0.430598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.7179 | −0.540674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.7714 | −1.49576 | −0.747879 | − | 0.663835i | \(-0.768928\pi\) | ||||
−0.747879 | + | 0.663835i | \(0.768928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.8822 | −0.690863 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.7636 | −1.81832 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.578858 | −0.0211228 | −0.0105614 | − | 0.999944i | \(-0.503362\pi\) | ||||
−0.0105614 | + | 0.999944i | \(0.503362\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.4834 | −0.746457 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.3710 | −0.522325 | −0.261162 | − | 0.965295i | \(-0.584106\pi\) | ||||
−0.261162 | + | 0.965295i | \(0.584106\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55.9973 | 2.03257 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4753 | −0.597230 | −0.298615 | − | 0.954374i | \(-0.596525\pi\) | ||||
−0.298615 | + | 0.954374i | \(0.596525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.85798 | 0.103466 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.9808 | 0.793681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8410 | −0.679425 | −0.339712 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339712 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.7978 | −1.14517 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.5917 | 1.35208 | 0.676039 | − | 0.736866i | \(-0.263695\pi\) | ||||
0.676039 | + | 0.736866i | \(0.263695\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 102.652 | 3.68261 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.11712 | 0.0400251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.2766 | 1.33386 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.1769 | 1.14991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.5235 | −1.58709 | −0.793545 | − | 0.608511i | \(-0.791767\pi\) | ||||
−0.793545 | + | 0.608511i | \(0.791767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.95897 | 0.212145 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −77.8854 | −2.76929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7700 | 1.76738 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.84212 | −0.136095 | −0.0680475 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680475 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.2018 | −0.573179 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.9558 | 0.387103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.4897 | 0.511331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.6231 | 0.585161 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.51537 | −0.0532774 | −0.0266387 | − | 0.999645i | \(-0.508480\pi\) | ||||
−0.0266387 | + | 0.999645i | \(0.508480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.1768 | −0.708502 | −0.354251 | − | 0.935150i | \(-0.615264\pi\) | ||||
−0.354251 | + | 0.935150i | \(0.615264\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69.4034 | 2.43408 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.1169 | −0.423916 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −88.7346 | −3.10064 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.0855 | −1.15469 | −0.577347 | − | 0.816499i | \(-0.695912\pi\) | ||||
−0.577347 | + | 0.816499i | \(0.695912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9779 | −0.800958 | −0.400479 | − | 0.916306i | \(-0.631156\pi\) | ||||
−0.400479 | + | 0.916306i | \(0.631156\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.9730 | 1.91160 | 0.955798 | − | 0.294023i | \(-0.0949942\pi\) | ||||
0.955798 | + | 0.294023i | \(0.0949942\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.6692 | 1.27357 | 0.636787 | − | 0.771039i | \(-0.280263\pi\) | ||||
0.636787 | + | 0.771039i | \(0.280263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.5544 | −0.435508 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.5489 | −0.608033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.2851 | −1.21963 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.4619 | −1.08619 | −0.543093 | − | 0.839672i | \(-0.682747\pi\) | ||||
−0.543093 | + | 0.839672i | \(0.682747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.9289 | 1.82513 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.00058 | −0.0344619 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.5263 | 1.46122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.28126 | −0.112613 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.0808 | 1.51107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.45230 | 0.323641 | 0.161820 | − | 0.986820i | \(-0.448263\pi\) | ||||
0.161820 | + | 0.986820i | \(0.448263\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.9551 | 0.613335 | 0.306668 | − | 0.951817i | \(-0.400786\pi\) | ||||
0.306668 | + | 0.951817i | \(0.400786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.3628 | −0.831249 | −0.415624 | − | 0.909536i | \(-0.636437\pi\) | ||||
−0.415624 | + | 0.909536i | \(0.636437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4184 | 0.389139 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.1946 | 1.53844 | 0.769222 | − | 0.638982i | \(-0.220644\pi\) | ||||
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.2760 | −1.02823 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.7748 | 1.82419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9267 | −0.810727 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.30341 | −0.0441138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.55736 | 0.255194 | 0.127597 | − | 0.991826i | \(-0.459274\pi\) | ||||
0.127597 | + | 0.991826i | \(0.459274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.4283 | 0.790217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.5760 | −1.70395 | −0.851974 | − | 0.523584i | \(-0.824595\pi\) | ||||
−0.851974 | + | 0.523584i | \(0.824595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.40946 | 0.215696 | 0.107848 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107848 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.14684 | 0.0720838 | 0.0360419 | − | 0.999350i | \(-0.488525\pi\) | ||||
0.0360419 | + | 0.999350i | \(0.488525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 73.0085 | 2.44863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.7038 | −0.526097 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.72432 | 0.225021 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −64.6003 | −2.15694 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −89.8430 | −2.99643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.4737 | −0.348929 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −123.850 | −4.12148 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.3186 | −1.37196 | −0.685980 | − | 0.727620i | \(-0.740626\pi\) | ||||
−0.685980 | + | 0.727620i | \(0.740626\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.5833 | 0.682704 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.7328 | 1.97903 | 0.989517 | − | 0.144415i | \(-0.0461300\pi\) | ||||
0.989517 | + | 0.144415i | \(0.0461300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6451 | −0.683253 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.2206 | −0.535651 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.3526 | −1.13319 | −0.566594 | − | 0.823997i | \(-0.691739\pi\) | ||||
−0.566594 | + | 0.823997i | \(0.691739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.3426 | 0.736215 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.0035 | −1.41548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −77.2342 | −2.53670 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.0752 | −1.57729 | −0.788647 | − | 0.614846i | \(-0.789218\pi\) | ||||
−0.788647 | + | 0.614846i | \(0.789218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.28339 | 0.238703 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.4031 | 0.667968 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.9537 | −1.40324 | −0.701619 | − | 0.712552i | \(-0.747539\pi\) | ||||
−0.701619 | + | 0.712552i | \(0.747539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.28060 | −0.302861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.8745 | −1.39767 | −0.698835 | − | 0.715283i | \(-0.746298\pi\) | ||||
−0.698835 | + | 0.715283i | \(0.746298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.90332 | 0.159674 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.1350 | 0.914264 | 0.457132 | − | 0.889399i | \(-0.348877\pi\) | ||||
0.457132 | + | 0.889399i | \(0.348877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.7158 | −0.542617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.78249 | 0.219937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.7612 | −0.542949 | −0.271474 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271474 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 115.477 | 3.73285 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −80.2780 | −2.59231 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.5217 | 2.17812 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.8093 | −1.83065 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.3277 | −1.13606 | −0.568030 | − | 0.823008i | \(-0.692294\pi\) | ||||
−0.568030 | + | 0.823008i | \(0.692294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.51637 | −0.209336 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.3917 | 1.74551 | 0.872756 | − | 0.488156i | \(-0.162330\pi\) | ||||
0.872756 | + | 0.488156i | \(0.162330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.36269 | 0.236037 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.4481 | −1.51800 | −0.759000 | − | 0.651091i | \(-0.774312\pi\) | ||||
−0.759000 | + | 0.651091i | \(0.774312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9786 | 0.382839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.26262 | 0.104167 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.8550 | 1.36686 | 0.683432 | − | 0.730014i | \(-0.260487\pi\) | ||||
0.683432 | + | 0.730014i | \(0.260487\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 68.7312 | 2.18774 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.1839 | −1.69115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4118 | 0.743700 | 0.371850 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371850 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 78.7467 | 2.49895 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.9905 | 0.411412 | 0.205706 | − | 0.978614i | \(-0.434051\pi\) | ||||
0.205706 | + | 0.978614i | \(0.434051\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.7014 | 1.12954 |
(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 | 3800.2.a.bd.1.5 | yes | 6 | |
4.3 | odd | 2 | 7600.2.a.ci.1.2 | 6 | |||
5.2 | odd | 4 | 3800.2.d.p.3649.3 | 12 | |||
5.3 | odd | 4 | 3800.2.d.p.3649.10 | 12 | |||
5.4 | even | 2 | 3800.2.a.bb.1.2 | ✓ | 6 | ||
20.19 | odd | 2 | 7600.2.a.cm.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3800.2.a.bb.1.2 | ✓ | 6 | 5.4 | even | 2 | ||
3800.2.a.bd.1.5 | yes | 6 | 1.1 | even | 1 | trivial | |
3800.2.d.p.3649.3 | 12 | 5.2 | odd | 4 | |||
3800.2.d.p.3649.10 | 12 | 5.3 | odd | 4 | |||
7600.2.a.ci.1.2 | 6 | 4.3 | odd | 2 | |||
7600.2.a.cm.1.5 | 6 | 20.19 | odd | 2 |