Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.58579 | 1.16472 | 0.582358 | − | 0.812932i | \(-0.302130\pi\) | ||||
0.582358 | + | 0.812932i | \(0.302130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.82843 | −1.45370 | −0.726851 | − | 0.686795i | \(-0.759017\pi\) | ||||
−0.726851 | + | 0.686795i | \(0.759017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.343146 | −0.0597340 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65685 | −0.929981 | −0.464991 | − | 0.885316i | \(-0.653942\pi\) | ||||
−0.464991 | + | 0.885316i | \(0.653942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.828427 | 0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.82843 | 0.910247 | 0.455124 | − | 0.890428i | \(-0.349595\pi\) | ||||
0.455124 | + | 0.890428i | \(0.349595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.89949 | 1.05216 | 0.526082 | − | 0.850434i | \(-0.323661\pi\) | ||||
0.526082 | + | 0.850434i | \(0.323661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.6569 | −1.70033 | −0.850163 | − | 0.526519i | \(-0.823497\pi\) | ||||
−0.850163 | + | 0.526519i | \(0.823497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.17157 | −0.444109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.34315 | 0.310357 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.65685 | 0.852323 | 0.426161 | − | 0.904647i | \(-0.359866\pi\) | ||||
0.426161 | + | 0.904647i | \(0.359866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8995 | 1.57592 | 0.787962 | − | 0.615724i | \(-0.211136\pi\) | ||||
0.787962 | + | 0.615724i | \(0.211136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.31371 | −0.278538 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65685 | −0.428002 | −0.214001 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214001 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.75736 | 0.522188 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.24264 | 0.347648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.34315 | −0.566372 | −0.283186 | − | 0.959065i | \(-0.591391\pi\) | ||||
−0.283186 | + | 0.959065i | \(0.591391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.343146 | −0.0355826 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34315 | −0.235495 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4853 | −1.14283 | −0.571414 | − | 0.820662i | \(-0.693605\pi\) | ||||
−0.571414 | + | 0.820662i | \(0.693605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.58579 | −0.747450 | −0.373725 | − | 0.927540i | \(-0.621920\pi\) | ||||
−0.373725 | + | 0.927540i | \(0.621920\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.58579 | 0.539998 | 0.269999 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269999 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.3137 | 1.75414 | 0.877068 | − | 0.480367i | \(-0.159497\pi\) | ||||
0.877068 | + | 0.480367i | \(0.159497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.34315 | 0.222402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3137 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.41421 | −0.217682 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315 | 0.385392 | 0.192696 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.85786 | −0.251621 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6569 | 1.19320 | 0.596602 | − | 0.802537i | \(-0.296517\pi\) | ||||
0.596602 | + | 0.802537i | \(0.296517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.48528 | 0.210799 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.65685 | −0.138553 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.65685 | 0.381504 | 0.190752 | − | 0.981638i | \(-0.438907\pi\) | ||||
0.190752 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1716 | −0.909130 | −0.454565 | − | 0.890714i | \(-0.650205\pi\) | ||||
−0.454565 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.6569 | −1.75085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.31371 | −0.104845 | −0.0524227 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524227 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.34315 | −0.185824 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6569 | 1.22634 | 0.613170 | − | 0.789951i | \(-0.289894\pi\) | ||||
0.613170 | + | 0.789951i | \(0.289894\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07107 | −0.160264 | −0.0801320 | − | 0.996784i | \(-0.525534\pi\) | ||||
−0.0801320 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.0000 | 1.22355 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3431 | −0.786375 | −0.393187 | − | 0.919458i | \(-0.628628\pi\) | ||||
−0.393187 | + | 0.919458i | \(0.628628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.65685 | 0.124537 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48528 | −0.484733 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.17157 | −0.310071 | −0.155035 | − | 0.987909i | \(-0.549549\pi\) | ||||
−0.155035 | + | 0.987909i | \(0.549549\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.75736 | −0.203830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.34315 | 0.463857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.51472 | −0.399031 | −0.199516 | − | 0.979895i | \(-0.563937\pi\) | ||||
−0.199516 | + | 0.979895i | \(0.563937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.31371 | 0.382489 | 0.191245 | − | 0.981542i | \(-0.438748\pi\) | ||||
0.191245 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.343146 | −0.0244481 | −0.0122241 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122241 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3137 | −1.65266 | −0.826332 | − | 0.563183i | \(-0.809577\pi\) | ||||
−0.826332 | + | 0.563183i | \(0.809577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.34315 | −0.376876 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.7990 | −1.09811 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.68629 | −0.324158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.6274 | 1.83311 | 0.916553 | − | 0.399912i | \(-0.130959\pi\) | ||||
0.916553 | + | 0.399912i | \(0.130959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.97056 | 0.340577 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.51472 | 0.102355 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.3137 | −1.03011 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9706 | 1.00250 | 0.501252 | − | 0.865302i | \(-0.332873\pi\) | ||||
0.501252 | + | 0.865302i | \(0.332873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0000 | −0.929213 | −0.464606 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6569 | −0.763666 | −0.381833 | − | 0.924231i | \(-0.624707\pi\) | ||||
−0.381833 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.65685 | 0.107624 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.4853 | −1.97193 | −0.985964 | − | 0.166955i | \(-0.946606\pi\) | ||||
−0.985964 | + | 0.166955i | \(0.946606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3137 | 0.719874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.97056 | −0.124879 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4558 | −1.73300 | −0.866499 | − | 0.499179i | \(-0.833635\pi\) | ||||
−0.866499 | + | 0.499179i | \(0.833635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.62742 | 0.290923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.3137 | −0.955243 | −0.477621 | − | 0.878566i | \(-0.658501\pi\) | ||||
−0.477621 | + | 0.878566i | \(0.658501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.1421 | 1.37056 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.7279 | 0.969825 | 0.484913 | − | 0.874563i | \(-0.338851\pi\) | ||||
0.484913 | + | 0.874563i | \(0.338851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.21320 | 0.135446 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.65685 | −0.405876 | −0.202938 | − | 0.979192i | \(-0.565049\pi\) | ||||
−0.202938 | + | 0.979192i | \(0.565049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.31371 | −0.201293 | −0.100647 | − | 0.994922i | \(-0.532091\pi\) | ||||
−0.100647 | + | 0.994922i | \(0.532091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.6274 | −1.72005 | −0.860027 | − | 0.510248i | \(-0.829554\pi\) | ||||
−0.860027 | + | 0.510248i | \(0.829554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34315 | −0.140280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.68629 | 0.160251 | 0.0801254 | − | 0.996785i | \(-0.474468\pi\) | ||||
0.0801254 | + | 0.996785i | \(0.474468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | −1.06999 | −0.534994 | − | 0.844856i | \(-0.679686\pi\) | ||||
−0.534994 | + | 0.844856i | \(0.679686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.48528 | 0.145690 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9706 | −0.991431 | −0.495715 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495715 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1716 | −0.646069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.75736 | 0.273303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.75736 | −0.271517 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.14214 | 0.178750 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6569 | 1.22805 | 0.614024 | − | 0.789288i | \(-0.289550\pi\) | ||||
0.614024 | + | 0.789288i | \(0.289550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.9706 | −1.18533 | −0.592663 | − | 0.805450i | \(-0.701923\pi\) | ||||
−0.592663 | + | 0.805450i | \(0.701923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.0000 | 1.23564 | 0.617822 | − | 0.786318i | \(-0.288015\pi\) | ||||
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.48528 | −0.363106 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31371 | −0.129139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.3137 | −2.41004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.58579 | −0.419495 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.4853 | 1.45576 | 0.727881 | − | 0.685703i | \(-0.240505\pi\) | ||||
0.727881 | + | 0.685703i | \(0.240505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.0000 | 0.876795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.9706 | −1.36023 | −0.680117 | − | 0.733104i | \(-0.738071\pi\) | ||||
−0.680117 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.68629 | 0.254524 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.686292 | 0.0371648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.3848 | −0.611167 | −0.305583 | − | 0.952165i | \(-0.598851\pi\) | ||||
−0.305583 | + | 0.952165i | \(0.598851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.82843 | 0.526104 | 0.263052 | − | 0.964782i | \(-0.415271\pi\) | ||||
0.263052 | + | 0.964782i | \(0.415271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.6569 | −1.79137 | −0.895687 | − | 0.444685i | \(-0.853315\pi\) | ||||
−0.895687 | + | 0.444685i | \(0.853315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.48528 | −0.342280 | −0.171140 | − | 0.985247i | \(-0.554745\pi\) | ||||
−0.171140 | + | 0.985247i | \(0.554745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.27208 | 0.224226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5858 | −1.12677 | −0.563384 | − | 0.826195i | \(-0.690501\pi\) | ||||
−0.563384 | + | 0.826195i | \(0.690501\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4853 | −0.858189 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0000 | −0.621336 | −0.310668 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310668 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.6569 | 0.806369 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.68629 | 0.240719 | 0.120359 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120359 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.79899 | −0.0921650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.899495 | 0.0459620 | 0.0229810 | − | 0.999736i | \(-0.492684\pi\) | ||||
0.0229810 | + | 0.999736i | \(0.492684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.5147 | −0.991989 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.31371 | 0.269416 | 0.134708 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134708 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.7696 | 2.16295 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | −0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6274 | 1.23601 | 0.618007 | − | 0.786172i | \(-0.287940\pi\) | ||||
0.618007 | + | 0.786172i | \(0.287940\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.3137 | −1.61367 | −0.806835 | − | 0.590777i | \(-0.798821\pi\) | ||||
−0.806835 | + | 0.590777i | \(0.798821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65685 | −0.0825338 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.68629 | −0.232291 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.1421 | −1.24320 | −0.621599 | − | 0.783335i | \(-0.713517\pi\) | ||||
−0.621599 | + | 0.783335i | \(0.713517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.65685 | −0.0817266 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.02944 | −0.0504118 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3137 | −0.748124 | −0.374062 | − | 0.927404i | \(-0.622035\pi\) | ||||
−0.374062 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3431 | 1.33262 | 0.666312 | − | 0.745673i | \(-0.267872\pi\) | ||||
0.666312 | + | 0.745673i | \(0.267872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 32.9706 | 1.60308 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.686292 | 0.0331345 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.828427 | −0.0399039 | −0.0199520 | − | 0.999801i | \(-0.506351\pi\) | ||||
−0.0199520 | + | 0.999801i | \(0.506351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3137 | 0.928158 | 0.464079 | − | 0.885794i | \(-0.346385\pi\) | ||||
0.464079 | + | 0.885794i | \(0.346385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.5980 | −1.51154 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.3431 | −0.875471 | −0.437735 | − | 0.899104i | \(-0.644219\pi\) | ||||
−0.437735 | + | 0.899104i | \(0.644219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5858 | 0.740503 | 0.370252 | − | 0.928932i | \(-0.379271\pi\) | ||||
0.370252 | + | 0.928932i | \(0.379271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.92893 | −0.0912354 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.48528 | −0.353252 | −0.176626 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176626 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.82843 | 0.227362 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.62742 | 0.217415 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.9706 | −1.35519 | −0.677593 | − | 0.735437i | \(-0.736977\pi\) | ||||
−0.677593 | + | 0.735437i | \(0.736977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4853 | 0.862819 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.31371 | 0.0611855 | 0.0305928 | − | 0.999532i | \(-0.490261\pi\) | ||||
0.0305928 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8995 | −0.692438 | −0.346219 | − | 0.938154i | \(-0.612535\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.8701 | 1.75242 | 0.876209 | − | 0.481932i | \(-0.160065\pi\) | ||||
0.876209 | + | 0.481932i | \(0.160065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.544156 | 0.0250734 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.71573 | 0.262809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0000 | −0.732590 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.51472 | −0.0692093 | −0.0346046 | − | 0.999401i | \(-0.511017\pi\) | ||||
−0.0346046 | + | 0.999401i | \(0.511017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3137 | 0.515861 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.2843 | 1.73483 | 0.867413 | − | 0.497589i | \(-0.165781\pi\) | ||||
0.867413 | + | 0.497589i | \(0.165781\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.48528 | −0.293275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51472 | 0.0683583 | 0.0341791 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341791 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −59.9411 | −2.69961 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.1421 | 1.97607 | 0.988037 | − | 0.154219i | \(-0.0492861\pi\) | ||||
0.988037 | + | 0.154219i | \(0.0492861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.857864 | 0.0383266 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.92893 | 0.175182 | 0.0875912 | − | 0.996157i | \(-0.472083\pi\) | ||||
0.0875912 | + | 0.996157i | \(0.472083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.72792 | 0.165563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4853 | −1.48421 | −0.742105 | − | 0.670284i | \(-0.766172\pi\) | ||||
−0.742105 | + | 0.670284i | \(0.766172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.6569 | −0.602965 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.65685 | −0.424708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.28427 | 0.188059 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6274 | 1.60468 | 0.802338 | − | 0.596870i | \(-0.203589\pi\) | ||||
0.802338 | + | 0.596870i | \(0.203589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9411 | −1.22178 | −0.610890 | − | 0.791715i | \(-0.709188\pi\) | ||||
−0.610890 | + | 0.791715i | \(0.709188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.34315 | 0.276312 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.20101 | 0.356566 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | 0.490973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.6569 | −0.504914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.68629 | 0.115922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4853 | −1.00971 | −0.504856 | − | 0.863204i | \(-0.668454\pi\) | ||||
−0.504856 | + | 0.863204i | \(0.668454\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.72792 | 0.0741522 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.27208 | 0.0971470 | 0.0485735 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485735 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.8284 | −0.803578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.2843 | 1.88657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3137 | 0.733605 | 0.366803 | − | 0.930299i | \(-0.380452\pi\) | ||||
0.366803 | + | 0.930299i | \(0.380452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7990 | −0.583635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.62742 | −0.110930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.07107 | 0.171575 | 0.0857875 | − | 0.996313i | \(-0.472659\pi\) | ||||
0.0857875 | + | 0.996313i | \(0.472659\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.6274 | −1.53550 | −0.767751 | − | 0.640749i | \(-0.778624\pi\) | ||||
−0.767751 | + | 0.640749i | \(0.778624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.28427 | 0.0954268 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.2843 | 0.927706 | 0.463853 | − | 0.885912i | \(-0.346467\pi\) | ||||
0.463853 | + | 0.885912i | \(0.346467\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.20101 | −0.0914709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.68629 | 0.194086 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6863 | 0.936363 | 0.468182 | − | 0.883632i | \(-0.344909\pi\) | ||||
0.468182 | + | 0.883632i | \(0.344909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.68629 | −0.193095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.142136 | 0.00584668 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.9411 | −1.22953 | −0.614767 | − | 0.788709i | \(-0.710750\pi\) | ||||
−0.614767 | + | 0.788709i | \(0.710750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.65685 | 0.395229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.6274 | 1.74171 | 0.870855 | − | 0.491541i | \(-0.163566\pi\) | ||||
0.870855 | + | 0.491541i | \(0.163566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.4853 | −1.48580 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.2426 | −1.10574 | −0.552872 | − | 0.833266i | \(-0.686468\pi\) | ||||
−0.552872 | + | 0.833266i | \(0.686468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3137 | 0.943172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.9706 | −1.57401 | −0.787003 | − | 0.616949i | \(-0.788368\pi\) | ||||
−0.787003 | + | 0.616949i | \(0.788368\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6863 | 0.510731 | 0.255365 | − | 0.966845i | \(-0.417804\pi\) | ||||
0.255365 | + | 0.966845i | \(0.417804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4558 | 1.58586 | 0.792932 | − | 0.609310i | \(-0.208553\pi\) | ||||
0.792932 | + | 0.609310i | \(0.208553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.4853 | 0.541146 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.94113 | 0.0775211 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.3137 | −1.72703 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51472 | −0.0603000 | −0.0301500 | − | 0.999545i | \(-0.509598\pi\) | ||||
−0.0301500 | + | 0.999545i | \(0.509598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0294 | −0.438381 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.9411 | 1.34269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.1127 | 0.557418 | 0.278709 | − | 0.960376i | \(-0.410093\pi\) | ||||
0.278709 | + | 0.960376i | \(0.410093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7574 | 0.816056 | 0.408028 | − | 0.912969i | \(-0.366217\pi\) | ||||
0.408028 | + | 0.912969i | \(0.366217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.31371 | −0.130074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6569 | 0.612700 | 0.306350 | − | 0.951919i | \(-0.400892\pi\) | ||||
0.306350 | + | 0.951919i | \(0.400892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3431 | 0.403525 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.6863 | 0.494188 | 0.247094 | − | 0.968992i | \(-0.420524\pi\) | ||||
0.247094 | + | 0.968992i | \(0.420524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −50.3137 | −1.95698 | −0.978488 | − | 0.206303i | \(-0.933857\pi\) | ||||
−0.978488 | + | 0.206303i | \(0.933857\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.34315 | 0.246347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.7279 | −1.69315 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.20101 | −0.239745 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.51472 | 0.212893 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.65685 | 0.218056 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.9706 | −0.882830 | −0.441415 | − | 0.897303i | \(-0.645523\pi\) | ||||
−0.441415 | + | 0.897303i | \(0.645523\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.79899 | 0.222218 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.92893 | 0.0738085 | 0.0369043 | − | 0.999319i | \(-0.488250\pi\) | ||||
0.0369043 | + | 0.999319i | \(0.488250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.79899 | 0.221245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3137 | −0.431018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.7696 | −1.62703 | −0.813515 | − | 0.581544i | \(-0.802449\pi\) | ||||
−0.813515 | + | 0.581544i | \(0.802449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44.6274 | 1.69038 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.82843 | 0.182628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0000 | −0.415464 | −0.207732 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207732 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.0000 | 1.20690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4264 | −1.33047 | −0.665233 | − | 0.746636i | \(-0.731668\pi\) | ||||
−0.665233 | + | 0.746636i | \(0.731668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3137 | 0.424297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.62742 | 0.173298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.6274 | 0.471580 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7990 | −0.962140 | −0.481070 | − | 0.876682i | \(-0.659752\pi\) | ||||
−0.481070 | + | 0.876682i | \(0.659752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.14214 | 0.154048 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.0711 | −1.41198 | −0.705989 | − | 0.708223i | \(-0.749497\pi\) | ||||
−0.705989 | + | 0.708223i | \(0.749497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.8284 | 1.95393 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.65685 | −0.282812 | −0.141406 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141406 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.6863 | 0.393635 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8284 | 0.619044 | 0.309522 | − | 0.950892i | \(-0.399831\pi\) | ||||
0.309522 | + | 0.950892i | \(0.399831\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.68629 | −0.172155 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7574 | 0.394649 | 0.197325 | − | 0.980338i | \(-0.436775\pi\) | ||||
0.197325 | + | 0.980338i | \(0.436775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.4558 | −0.492324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3726 | 0.414440 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00000 | −0.218074 | −0.109037 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109037 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.91674 | −0.0695732 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.9411 | −1.59286 | −0.796432 | − | 0.604728i | \(-0.793282\pi\) | ||||
−0.796432 | + | 0.604728i | \(0.793282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.2548 | 1.55981 | 0.779905 | − | 0.625898i | \(-0.215268\pi\) | ||||
0.779905 | + | 0.625898i | \(0.215268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.34315 | 0.228443 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.3431 | −0.875562 | −0.437781 | − | 0.899082i | \(-0.644235\pi\) | ||||
−0.437781 | + | 0.899082i | \(0.644235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.9706 | −1.18129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.94113 | −0.355721 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.8995 | −0.675413 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.58579 | 0.0565272 | 0.0282636 | − | 0.999601i | \(-0.491002\pi\) | ||||
0.0282636 | + | 0.999601i | \(0.491002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.51472 | −0.231930 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.3137 | −0.472784 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3137 | 1.25088 | 0.625438 | − | 0.780274i | \(-0.284920\pi\) | ||||
0.625438 | + | 0.780274i | \(0.284920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −89.2548 | −3.15761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.1127 | 0.533981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.02944 | −0.106907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.75736 | 0.0970636 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.9706 | −1.26466 | −0.632329 | − | 0.774700i | \(-0.717901\pi\) | ||||
−0.632329 | + | 0.774700i | \(0.717901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.1421 | 1.83096 | 0.915479 | − | 0.402366i | \(-0.131812\pi\) | ||||
0.915479 | + | 0.402366i | \(0.131812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37258 | 0.0481386 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.0294 | −1.36547 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.6274 | −1.13870 | −0.569352 | − | 0.822094i | \(-0.692806\pi\) | ||||
−0.569352 | + | 0.822094i | \(0.692806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.0122 | −1.04616 | −0.523080 | − | 0.852284i | \(-0.675217\pi\) | ||||
−0.523080 | + | 0.852284i | \(0.675217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.5269 | −0.470377 | −0.235188 | − | 0.971950i | \(-0.575571\pi\) | ||||
−0.235188 | + | 0.971950i | \(0.575571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.31371 | 0.184553 | 0.0922764 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922764 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.8579 | 0.411345 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000 | 0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.1421 | 0.695384 | 0.347692 | − | 0.937609i | \(-0.386966\pi\) | ||||
0.347692 | + | 0.937609i | \(0.386966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.2843 | 1.11325 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.11270 | −0.0383234 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.45584 | 0.255884 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.5980 | −1.08316 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.6863 | −0.434370 | −0.217185 | − | 0.976130i | \(-0.569688\pi\) | ||||
−0.217185 | + | 0.976130i | \(0.569688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.9706 | 0.648022 | 0.324011 | − | 0.946053i | \(-0.394969\pi\) | ||||
0.324011 | + | 0.946053i | \(0.394969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.6274 | −1.04499 | −0.522497 | − | 0.852641i | \(-0.674999\pi\) | ||||
−0.522497 | + | 0.852641i | \(0.674999\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.0122 | 1.90668 | 0.953339 | − | 0.301903i | \(-0.0976219\pi\) | ||||
0.953339 | + | 0.301903i | \(0.0976219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.2426 | −0.585591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.31371 | −0.112410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.7990 | −0.874165 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.9706 | 0.574367 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.2843 | 0.955092 | 0.477546 | − | 0.878607i | \(-0.341526\pi\) | ||||
0.477546 | + | 0.878607i | \(0.341526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.02944 | 0.237097 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.4558 | −0.891320 | −0.445660 | − | 0.895202i | \(-0.647031\pi\) | ||||
−0.445660 | + | 0.895202i | \(0.647031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.68629 | −0.225012 | −0.112506 | − | 0.993651i | \(-0.535888\pi\) | ||||
−0.112506 | + | 0.993651i | \(0.535888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5858 | −0.590473 | −0.295236 | − | 0.955424i | \(-0.595398\pi\) | ||||
−0.295236 | + | 0.955424i | \(0.595398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.20101 | 0.207742 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.9411 | 2.20664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.62742 | 0.154505 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.48528 | −0.216296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.3137 | 1.44299 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.2132 | −1.53448 | −0.767242 | − | 0.641358i | \(-0.778372\pi\) | ||||
−0.767242 | + | 0.641358i | \(0.778372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4853 | 1.07747 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4853 | −0.612445 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.94113 | 0.130432 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.2548 | −1.09698 | −0.548488 | − | 0.836159i | \(-0.684796\pi\) | ||||
−0.548488 | + | 0.836159i | \(0.684796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.97056 | 0.0649323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.4558 | 0.704702 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.20101 | 0.301875 | 0.150938 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150938 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.97056 | −0.293683 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.6274 | −0.608531 | −0.304266 | − | 0.952587i | \(-0.598411\pi\) | ||||
−0.304266 | + | 0.952587i | \(0.598411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.68629 | 0.283466 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0000 | −0.325991 | −0.162995 | − | 0.986627i | \(-0.552116\pi\) | ||||
−0.162995 | + | 0.986627i | \(0.552116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.5563 | 1.06018 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.1005 | −0.360718 | −0.180359 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180359 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.31371 | 0.237413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.11270 | −0.295499 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.6274 | 1.76956 | 0.884778 | − | 0.466013i | \(-0.154310\pi\) | ||||
0.884778 | + | 0.466013i | \(0.154310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.68629 | 0.0868355 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7990 | −0.509115 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7574 | 0.796143 | 0.398072 | − | 0.917354i | \(-0.369680\pi\) | ||||
0.398072 | + | 0.917354i | \(0.369680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.9411 | 0.576352 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.00000 | 0.256732 | 0.128366 | − | 0.991727i | \(-0.459027\pi\) | ||||
0.128366 | + | 0.991727i | \(0.459027\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.2843 | −0.968880 | −0.484440 | − | 0.874825i | \(-0.660977\pi\) | ||||
−0.484440 | + | 0.874825i | \(0.660977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.42641 | −0.141469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.7990 | −1.65381 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3848 | 1.31997 | 0.659985 | − | 0.751279i | \(-0.270563\pi\) | ||||
0.659985 | + | 0.751279i | \(0.270563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.5391 | 1.22547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.82843 | 0.153380 | 0.0766900 | − | 0.997055i | \(-0.475565\pi\) | ||||
0.0766900 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9706 | −0.348140 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3431 | 0.454252 | 0.227126 | − | 0.973865i | \(-0.427067\pi\) | ||||
0.227126 | + | 0.973865i | \(0.427067\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.6569 | −0.432084 |
(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 | 9800.2.a.bz.1.1 | 2 | ||
5.4 | even | 2 | 1960.2.a.p.1.2 | 2 | |||
7.2 | even | 3 | 1400.2.q.h.1201.2 | 4 | |||
7.4 | even | 3 | 1400.2.q.h.401.2 | 4 | |||
7.6 | odd | 2 | 9800.2.a.br.1.2 | 2 | |||
20.19 | odd | 2 | 3920.2.a.bz.1.1 | 2 | |||
35.2 | odd | 12 | 1400.2.bh.g.249.2 | 8 | |||
35.4 | even | 6 | 280.2.q.d.121.1 | yes | 4 | ||
35.9 | even | 6 | 280.2.q.d.81.1 | ✓ | 4 | ||
35.18 | odd | 12 | 1400.2.bh.g.849.2 | 8 | |||
35.19 | odd | 6 | 1960.2.q.q.361.2 | 4 | |||
35.23 | odd | 12 | 1400.2.bh.g.249.3 | 8 | |||
35.24 | odd | 6 | 1960.2.q.q.961.2 | 4 | |||
35.32 | odd | 12 | 1400.2.bh.g.849.3 | 8 | |||
35.34 | odd | 2 | 1960.2.a.t.1.1 | 2 | |||
105.44 | odd | 6 | 2520.2.bi.k.361.2 | 4 | |||
105.74 | odd | 6 | 2520.2.bi.k.1801.2 | 4 | |||
140.39 | odd | 6 | 560.2.q.j.401.2 | 4 | |||
140.79 | odd | 6 | 560.2.q.j.81.2 | 4 | |||
140.139 | even | 2 | 3920.2.a.bp.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.d.81.1 | ✓ | 4 | 35.9 | even | 6 | ||
280.2.q.d.121.1 | yes | 4 | 35.4 | even | 6 | ||
560.2.q.j.81.2 | 4 | 140.79 | odd | 6 | |||
560.2.q.j.401.2 | 4 | 140.39 | odd | 6 | |||
1400.2.q.h.401.2 | 4 | 7.4 | even | 3 | |||
1400.2.q.h.1201.2 | 4 | 7.2 | even | 3 | |||
1400.2.bh.g.249.2 | 8 | 35.2 | odd | 12 | |||
1400.2.bh.g.249.3 | 8 | 35.23 | odd | 12 | |||
1400.2.bh.g.849.2 | 8 | 35.18 | odd | 12 | |||
1400.2.bh.g.849.3 | 8 | 35.32 | odd | 12 | |||
1960.2.a.p.1.2 | 2 | 5.4 | even | 2 | |||
1960.2.a.t.1.1 | 2 | 35.34 | odd | 2 | |||
1960.2.q.q.361.2 | 4 | 35.19 | odd | 6 | |||
1960.2.q.q.961.2 | 4 | 35.24 | odd | 6 | |||
2520.2.bi.k.361.2 | 4 | 105.44 | odd | 6 | |||
2520.2.bi.k.1801.2 | 4 | 105.74 | odd | 6 | |||
3920.2.a.bp.1.2 | 2 | 140.139 | even | 2 | |||
3920.2.a.bz.1.1 | 2 | 20.19 | odd | 2 | |||
9800.2.a.br.1.2 | 2 | 7.6 | odd | 2 | |||
9800.2.a.bz.1.1 | 2 | 1.1 | even | 1 | trivial |