Properties

Label 7200.2.h.l.1151.10
Level $7200$
Weight $2$
Character 7200.1151
Analytic conductor $57.492$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7200,2,Mod(1151,7200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7200.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.h (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(57.4922894553\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.426337261060096.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 1440)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1151.10
Root \(1.41127 + 0.0912546i\) of defining polynomial
Character \(\chi\) \(=\) 7200.1151
Dual form 7200.2.h.l.1151.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.64002i q^{7} +O(q^{10})\) \(q+2.64002i q^{7} +3.00504 q^{11} +0.640023 q^{13} +0.685698i q^{17} +5.28005i q^{19} -2.27653 q^{23} -8.15281i q^{29} -2.96972i q^{31} +1.60975 q^{37} +7.42430i q^{41} +11.2195i q^{43} +4.19982 q^{47} +0.0302761 q^{49} +9.60984i q^{53} -7.20487 q^{59} +10.4995 q^{61} -8.49954i q^{67} +13.1240 q^{71} -14.2498 q^{73} +7.93338i q^{77} +11.4693i q^{79} +13.1240 q^{83} -10.2527i q^{89} +1.68968i q^{91} -8.31032 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 24 q^{13} - 16 q^{37} + 4 q^{49} - 8 q^{61} - 104 q^{73} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7200\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(6401\) \(6751\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.64002i 0.997835i 0.866649 + 0.498918i \(0.166269\pi\)
−0.866649 + 0.498918i \(0.833731\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00504 0.906054 0.453027 0.891497i \(-0.350344\pi\)
0.453027 + 0.891497i \(0.350344\pi\)
\(12\) 0 0
\(13\) 0.640023 0.177511 0.0887553 0.996053i \(-0.471711\pi\)
0.0887553 + 0.996053i \(0.471711\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.685698i 0.166306i 0.996537 + 0.0831531i \(0.0264991\pi\)
−0.996537 + 0.0831531i \(0.973501\pi\)
\(18\) 0 0
\(19\) 5.28005i 1.21133i 0.795721 + 0.605663i \(0.207092\pi\)
−0.795721 + 0.605663i \(0.792908\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.27653 −0.474689 −0.237344 0.971426i \(-0.576277\pi\)
−0.237344 + 0.971426i \(0.576277\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 8.15281i − 1.51394i −0.653450 0.756970i \(-0.726679\pi\)
0.653450 0.756970i \(-0.273321\pi\)
\(30\) 0 0
\(31\) − 2.96972i − 0.533378i −0.963783 0.266689i \(-0.914070\pi\)
0.963783 0.266689i \(-0.0859297\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.60975 0.264641 0.132320 0.991207i \(-0.457757\pi\)
0.132320 + 0.991207i \(0.457757\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.42430i 1.15948i 0.814801 + 0.579740i \(0.196846\pi\)
−0.814801 + 0.579740i \(0.803154\pi\)
\(42\) 0 0
\(43\) 11.2195i 1.71096i 0.517838 + 0.855478i \(0.326737\pi\)
−0.517838 + 0.855478i \(0.673263\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.19982 0.612607 0.306304 0.951934i \(-0.400908\pi\)
0.306304 + 0.951934i \(0.400908\pi\)
\(48\) 0 0
\(49\) 0.0302761 0.00432516
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.60984i 1.32001i 0.751260 + 0.660007i \(0.229447\pi\)
−0.751260 + 0.660007i \(0.770553\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.20487 −0.937994 −0.468997 0.883200i \(-0.655384\pi\)
−0.468997 + 0.883200i \(0.655384\pi\)
\(60\) 0 0
\(61\) 10.4995 1.34433 0.672164 0.740402i \(-0.265365\pi\)
0.672164 + 0.740402i \(0.265365\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 8.49954i − 1.03838i −0.854658 0.519192i \(-0.826233\pi\)
0.854658 0.519192i \(-0.173767\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.1240 1.55753 0.778764 0.627317i \(-0.215847\pi\)
0.778764 + 0.627317i \(0.215847\pi\)
\(72\) 0 0
\(73\) −14.2498 −1.66781 −0.833905 0.551908i \(-0.813900\pi\)
−0.833905 + 0.551908i \(0.813900\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.93338i 0.904093i
\(78\) 0 0
\(79\) 11.4693i 1.29039i 0.764017 + 0.645197i \(0.223225\pi\)
−0.764017 + 0.645197i \(0.776775\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.1240 1.44054 0.720271 0.693692i \(-0.244017\pi\)
0.720271 + 0.693692i \(0.244017\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 10.2527i − 1.08679i −0.839478 0.543393i \(-0.817139\pi\)
0.839478 0.543393i \(-0.182861\pi\)
\(90\) 0 0
\(91\) 1.68968i 0.177126i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.31032 −0.843785 −0.421893 0.906646i \(-0.638634\pi\)
−0.421893 + 0.906646i \(0.638634\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.51413i 0.349669i 0.984598 + 0.174834i \(0.0559390\pi\)
−0.984598 + 0.174834i \(0.944061\pi\)
\(102\) 0 0
\(103\) − 3.13957i − 0.309351i −0.987965 0.154675i \(-0.950567\pi\)
0.987965 0.154675i \(-0.0494331\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.46711 −0.721873 −0.360937 0.932590i \(-0.617543\pi\)
−0.360937 + 0.932590i \(0.617543\pi\)
\(108\) 0 0
\(109\) −2.96972 −0.284448 −0.142224 0.989835i \(-0.545425\pi\)
−0.142224 + 0.989835i \(0.545425\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 5.67761i − 0.534105i −0.963682 0.267053i \(-0.913950\pi\)
0.963682 0.267053i \(-0.0860497\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.81026 −0.165946
\(120\) 0 0
\(121\) −1.96972 −0.179066
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.1396i 1.69836i 0.528102 + 0.849181i \(0.322904\pi\)
−0.528102 + 0.849181i \(0.677096\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.5760 −1.01140 −0.505698 0.862711i \(-0.668765\pi\)
−0.505698 + 0.862711i \(0.668765\pi\)
\(132\) 0 0
\(133\) −13.9394 −1.20870
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 2.49596i − 0.213244i −0.994300 0.106622i \(-0.965997\pi\)
0.994300 0.106622i \(-0.0340035\pi\)
\(138\) 0 0
\(139\) − 7.46927i − 0.633535i −0.948503 0.316767i \(-0.897403\pi\)
0.948503 0.316767i \(-0.102597\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.92330 0.160834
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.60984i 0.787269i 0.919267 + 0.393634i \(0.128782\pi\)
−0.919267 + 0.393634i \(0.871218\pi\)
\(150\) 0 0
\(151\) − 19.4693i − 1.58439i −0.610270 0.792193i \(-0.708939\pi\)
0.610270 0.792193i \(-0.291061\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.8292 −1.02388 −0.511942 0.859020i \(-0.671074\pi\)
−0.511942 + 0.859020i \(0.671074\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 6.01008i − 0.473661i
\(162\) 0 0
\(163\) 21.2800i 1.66678i 0.552684 + 0.833391i \(0.313604\pi\)
−0.552684 + 0.833391i \(0.686396\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.8676 1.76955 0.884774 0.466020i \(-0.154312\pi\)
0.884774 + 0.466020i \(0.154312\pi\)
\(168\) 0 0
\(169\) −12.5904 −0.968490
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.98932i 0.455360i 0.973736 + 0.227680i \(0.0731140\pi\)
−0.973736 + 0.227680i \(0.926886\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.65181 −0.198206 −0.0991029 0.995077i \(-0.531597\pi\)
−0.0991029 + 0.995077i \(0.531597\pi\)
\(180\) 0 0
\(181\) −11.4693 −0.852504 −0.426252 0.904605i \(-0.640166\pi\)
−0.426252 + 0.904605i \(0.640166\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.06055i 0.150682i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.30362 0.383757 0.191878 0.981419i \(-0.438542\pi\)
0.191878 + 0.981419i \(0.438542\pi\)
\(192\) 0 0
\(193\) −10.0606 −0.724174 −0.362087 0.932144i \(-0.617936\pi\)
−0.362087 + 0.932144i \(0.617936\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 5.79065i − 0.412567i −0.978492 0.206283i \(-0.933863\pi\)
0.978492 0.206283i \(-0.0661369\pi\)
\(198\) 0 0
\(199\) − 24.0899i − 1.70769i −0.520529 0.853844i \(-0.674265\pi\)
0.520529 0.853844i \(-0.325735\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 21.5236 1.51066
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 15.8668i 1.09753i
\(210\) 0 0
\(211\) 23.4693i 1.61569i 0.589394 + 0.807845i \(0.299366\pi\)
−0.589394 + 0.807845i \(0.700634\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 7.84014 0.532223
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.438863i 0.0295211i
\(222\) 0 0
\(223\) 13.3600i 0.894650i 0.894371 + 0.447325i \(0.147623\pi\)
−0.894371 + 0.447325i \(0.852377\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.57092 0.568872 0.284436 0.958695i \(-0.408194\pi\)
0.284436 + 0.958695i \(0.408194\pi\)
\(228\) 0 0
\(229\) 8.90917 0.588735 0.294367 0.955692i \(-0.404891\pi\)
0.294367 + 0.955692i \(0.404891\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0196i 1.57357i 0.617224 + 0.786787i \(0.288257\pi\)
−0.617224 + 0.786787i \(0.711743\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.4097 0.932088 0.466044 0.884762i \(-0.345679\pi\)
0.466044 + 0.884762i \(0.345679\pi\)
\(240\) 0 0
\(241\) 3.87890 0.249862 0.124931 0.992165i \(-0.460129\pi\)
0.124931 + 0.992165i \(0.460129\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.37935i 0.215023i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −24.1754 −1.52594 −0.762970 0.646434i \(-0.776259\pi\)
−0.762970 + 0.646434i \(0.776259\pi\)
\(252\) 0 0
\(253\) −6.84106 −0.430094
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.4383i 0.775878i 0.921685 + 0.387939i \(0.126813\pi\)
−0.921685 + 0.387939i \(0.873187\pi\)
\(258\) 0 0
\(259\) 4.24977i 0.264068i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.2471 1.18683 0.593413 0.804898i \(-0.297780\pi\)
0.593413 + 0.804898i \(0.297780\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.8875i 0.968679i 0.874880 + 0.484340i \(0.160940\pi\)
−0.874880 + 0.484340i \(0.839060\pi\)
\(270\) 0 0
\(271\) 6.02936i 0.366258i 0.983089 + 0.183129i \(0.0586225\pi\)
−0.983089 + 0.183129i \(0.941377\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.3591 0.742584 0.371292 0.928516i \(-0.378915\pi\)
0.371292 + 0.928516i \(0.378915\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 17.7198i − 1.05708i −0.848909 0.528538i \(-0.822740\pi\)
0.848909 0.528538i \(-0.177260\pi\)
\(282\) 0 0
\(283\) 20.6206i 1.22577i 0.790172 + 0.612885i \(0.209991\pi\)
−0.790172 + 0.612885i \(0.790009\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −19.6003 −1.15697
\(288\) 0 0
\(289\) 16.5298 0.972342
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.6574i 1.26524i 0.774463 + 0.632620i \(0.218020\pi\)
−0.774463 + 0.632620i \(0.781980\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.45703 −0.0842622
\(300\) 0 0
\(301\) −29.6197 −1.70725
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3.87890i 0.221380i 0.993855 + 0.110690i \(0.0353061\pi\)
−0.993855 + 0.110690i \(0.964694\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.71654 −0.380860 −0.190430 0.981701i \(-0.560988\pi\)
−0.190430 + 0.981701i \(0.560988\pi\)
\(312\) 0 0
\(313\) −21.9394 −1.24009 −0.620045 0.784566i \(-0.712886\pi\)
−0.620045 + 0.784566i \(0.712886\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.3616i 0.806626i 0.915062 + 0.403313i \(0.132141\pi\)
−0.915062 + 0.403313i \(0.867859\pi\)
\(318\) 0 0
\(319\) − 24.4995i − 1.37171i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.62052 −0.201451
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.0876i 0.611281i
\(330\) 0 0
\(331\) 4.78051i 0.262760i 0.991332 + 0.131380i \(0.0419409\pi\)
−0.991332 + 0.131380i \(0.958059\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −33.1883 −1.80788 −0.903941 0.427657i \(-0.859339\pi\)
−0.903941 + 0.427657i \(0.859339\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 8.92414i − 0.483270i
\(342\) 0 0
\(343\) 18.5601i 1.00215i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.8304 −0.742456 −0.371228 0.928542i \(-0.621063\pi\)
−0.371228 + 0.928542i \(0.621063\pi\)
\(348\) 0 0
\(349\) −20.4390 −1.09407 −0.547037 0.837108i \(-0.684244\pi\)
−0.547037 + 0.837108i \(0.684244\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 20.8379i 1.10909i 0.832154 + 0.554545i \(0.187108\pi\)
−0.832154 + 0.554545i \(0.812892\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 22.0481 1.16365 0.581827 0.813312i \(-0.302338\pi\)
0.581827 + 0.813312i \(0.302338\pi\)
\(360\) 0 0
\(361\) −8.87890 −0.467310
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.70058i 0.245368i 0.992446 + 0.122684i \(0.0391502\pi\)
−0.992446 + 0.122684i \(0.960850\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −25.3702 −1.31716
\(372\) 0 0
\(373\) −35.5104 −1.83866 −0.919330 0.393486i \(-0.871269\pi\)
−0.919330 + 0.393486i \(0.871269\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 5.21799i − 0.268740i
\(378\) 0 0
\(379\) − 1.52982i − 0.0785815i −0.999228 0.0392907i \(-0.987490\pi\)
0.999228 0.0392907i \(-0.0125098\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.16349 −0.110549 −0.0552746 0.998471i \(-0.517603\pi\)
−0.0552746 + 0.998471i \(0.517603\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 0.0207603i − 0.00105259i −1.00000 0.000526294i \(-0.999832\pi\)
1.00000 0.000526294i \(-0.000167524\pi\)
\(390\) 0 0
\(391\) − 1.56101i − 0.0789437i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −36.6694 −1.84038 −0.920192 0.391468i \(-0.871967\pi\)
−0.920192 + 0.391468i \(0.871967\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.59556i 0.379304i 0.981851 + 0.189652i \(0.0607360\pi\)
−0.981851 + 0.189652i \(0.939264\pi\)
\(402\) 0 0
\(403\) − 1.90069i − 0.0946803i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.83736 0.239779
\(408\) 0 0
\(409\) 26.5289 1.31177 0.655885 0.754861i \(-0.272296\pi\)
0.655885 + 0.754861i \(0.272296\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 19.0210i − 0.935963i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.841553 −0.0411125 −0.0205563 0.999789i \(-0.506544\pi\)
−0.0205563 + 0.999789i \(0.506544\pi\)
\(420\) 0 0
\(421\) 26.1505 1.27450 0.637248 0.770659i \(-0.280073\pi\)
0.637248 + 0.770659i \(0.280073\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 27.7190i 1.34142i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 38.8474 1.87121 0.935607 0.353044i \(-0.114853\pi\)
0.935607 + 0.353044i \(0.114853\pi\)
\(432\) 0 0
\(433\) 30.7787 1.47913 0.739564 0.673086i \(-0.235032\pi\)
0.739564 + 0.673086i \(0.235032\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 12.0202i − 0.575003i
\(438\) 0 0
\(439\) 26.1505i 1.24809i 0.781387 + 0.624047i \(0.214513\pi\)
−0.781387 + 0.624047i \(0.785487\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.8304 −0.657103 −0.328552 0.944486i \(-0.606561\pi\)
−0.328552 + 0.944486i \(0.606561\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.07915i 0.0981212i 0.998796 + 0.0490606i \(0.0156228\pi\)
−0.998796 + 0.0490606i \(0.984377\pi\)
\(450\) 0 0
\(451\) 22.3103i 1.05055i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.6282 0.871391 0.435695 0.900094i \(-0.356502\pi\)
0.435695 + 0.900094i \(0.356502\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 23.0014i − 1.07128i −0.844446 0.535641i \(-0.820070\pi\)
0.844446 0.535641i \(-0.179930\pi\)
\(462\) 0 0
\(463\) 25.9806i 1.20742i 0.797203 + 0.603711i \(0.206312\pi\)
−0.797203 + 0.603711i \(0.793688\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 33.3177 1.54176 0.770880 0.636981i \(-0.219817\pi\)
0.770880 + 0.636981i \(0.219817\pi\)
\(468\) 0 0
\(469\) 22.4390 1.03614
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 33.7151i 1.55022i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 16.0380 0.732796 0.366398 0.930458i \(-0.380591\pi\)
0.366398 + 0.930458i \(0.380591\pi\)
\(480\) 0 0
\(481\) 1.03028 0.0469765
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 19.1396i − 0.867296i −0.901082 0.433648i \(-0.857226\pi\)
0.901082 0.433648i \(-0.142774\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −36.3669 −1.64121 −0.820607 0.571493i \(-0.806364\pi\)
−0.820607 + 0.571493i \(0.806364\pi\)
\(492\) 0 0
\(493\) 5.59037 0.251778
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 34.6476i 1.55416i
\(498\) 0 0
\(499\) 8.65940i 0.387648i 0.981036 + 0.193824i \(0.0620891\pi\)
−0.981036 + 0.193824i \(0.937911\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1542 1.38910 0.694549 0.719445i \(-0.255604\pi\)
0.694549 + 0.719445i \(0.255604\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 28.3907i − 1.25839i −0.777246 0.629197i \(-0.783384\pi\)
0.777246 0.629197i \(-0.216616\pi\)
\(510\) 0 0
\(511\) − 37.6197i − 1.66420i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 12.6206 0.555055
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 16.4341i − 0.719990i −0.932954 0.359995i \(-0.882778\pi\)
0.932954 0.359995i \(-0.117222\pi\)
\(522\) 0 0
\(523\) − 14.2791i − 0.624383i −0.950019 0.312191i \(-0.898937\pi\)
0.950019 0.312191i \(-0.101063\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.03633 0.0887041
\(528\) 0 0
\(529\) −17.8174 −0.774671
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.75172i 0.205820i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.0909809 0.00391883
\(540\) 0 0
\(541\) 1.40871 0.0605653 0.0302827 0.999541i \(-0.490359\pi\)
0.0302827 + 0.999541i \(0.490359\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.3406i 0.655917i 0.944692 + 0.327958i \(0.106361\pi\)
−0.944692 + 0.327958i \(0.893639\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 43.0472 1.83387
\(552\) 0 0
\(553\) −30.2791 −1.28760
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 7.53199i − 0.319141i −0.987187 0.159570i \(-0.948989\pi\)
0.987187 0.159570i \(-0.0510109\pi\)
\(558\) 0 0
\(559\) 7.18074i 0.303713i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 40.0784 1.68910 0.844551 0.535475i \(-0.179868\pi\)
0.844551 + 0.535475i \(0.179868\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 28.6803i − 1.20234i −0.799121 0.601171i \(-0.794701\pi\)
0.799121 0.601171i \(-0.205299\pi\)
\(570\) 0 0
\(571\) 33.9007i 1.41870i 0.704857 + 0.709350i \(0.251011\pi\)
−0.704857 + 0.709350i \(0.748989\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 18.4002 0.766012 0.383006 0.923746i \(-0.374889\pi\)
0.383006 + 0.923746i \(0.374889\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 34.6476i 1.43742i
\(582\) 0 0
\(583\) 28.8780i 1.19600i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 27.8869 1.15102 0.575508 0.817796i \(-0.304804\pi\)
0.575508 + 0.817796i \(0.304804\pi\)
\(588\) 0 0
\(589\) 15.6803 0.646095
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 34.2295i − 1.40564i −0.711370 0.702818i \(-0.751925\pi\)
0.711370 0.702818i \(-0.248075\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22.7546 −0.929727 −0.464863 0.885382i \(-0.653897\pi\)
−0.464863 + 0.885382i \(0.653897\pi\)
\(600\) 0 0
\(601\) 11.5298 0.470311 0.235156 0.971958i \(-0.424440\pi\)
0.235156 + 0.971958i \(0.424440\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 17.0790i − 0.693216i −0.938010 0.346608i \(-0.887333\pi\)
0.938010 0.346608i \(-0.112667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.68799 0.108744
\(612\) 0 0
\(613\) −43.1084 −1.74113 −0.870565 0.492053i \(-0.836247\pi\)
−0.870565 + 0.492053i \(0.836247\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 23.7935i − 0.957890i −0.877845 0.478945i \(-0.841019\pi\)
0.877845 0.478945i \(-0.158981\pi\)
\(618\) 0 0
\(619\) 32.4683i 1.30501i 0.757783 + 0.652507i \(0.226283\pi\)
−0.757783 + 0.652507i \(0.773717\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 27.0674 1.08443
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.10380i 0.0440114i
\(630\) 0 0
\(631\) − 13.0303i − 0.518727i −0.965780 0.259364i \(-0.916487\pi\)
0.965780 0.259364i \(-0.0835128\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.0193774 0.000767761 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.1397i 1.50643i 0.657777 + 0.753213i \(0.271497\pi\)
−0.657777 + 0.753213i \(0.728503\pi\)
\(642\) 0 0
\(643\) − 17.1589i − 0.676683i −0.941023 0.338341i \(-0.890134\pi\)
0.941023 0.338341i \(-0.109866\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.4478 −1.19702 −0.598512 0.801113i \(-0.704241\pi\)
−0.598512 + 0.801113i \(0.704241\pi\)
\(648\) 0 0
\(649\) −21.6509 −0.849873
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 11.7151i − 0.458447i −0.973374 0.229224i \(-0.926381\pi\)
0.973374 0.229224i \(-0.0736187\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.1189 −0.394177 −0.197089 0.980386i \(-0.563149\pi\)
−0.197089 + 0.980386i \(0.563149\pi\)
\(660\) 0 0
\(661\) 11.1202 0.432525 0.216263 0.976335i \(-0.430613\pi\)
0.216263 + 0.976335i \(0.430613\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 18.5601i 0.718650i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 31.5516 1.21803
\(672\) 0 0
\(673\) −15.0984 −0.582000 −0.291000 0.956723i \(-0.593988\pi\)
−0.291000 + 0.956723i \(0.593988\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.82699i 0.300816i 0.988624 + 0.150408i \(0.0480587\pi\)
−0.988624 + 0.150408i \(0.951941\pi\)
\(678\) 0 0
\(679\) − 21.9394i − 0.841959i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −34.4763 −1.31920 −0.659600 0.751617i \(-0.729274\pi\)
−0.659600 + 0.751617i \(0.729274\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.15052i 0.234316i
\(690\) 0 0
\(691\) − 36.7181i − 1.39682i −0.715696 0.698412i \(-0.753891\pi\)
0.715696 0.698412i \(-0.246109\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −5.09083 −0.192829
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.47779i 0.0558154i 0.999611 + 0.0279077i \(0.00888445\pi\)
−0.999611 + 0.0279077i \(0.991116\pi\)
\(702\) 0 0
\(703\) 8.49954i 0.320566i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.27737 −0.348912
\(708\) 0 0
\(709\) −6.02936 −0.226437 −0.113219 0.993570i \(-0.536116\pi\)
−0.113219 + 0.993570i \(0.536116\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.76066i 0.253189i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13.3059 −0.496227 −0.248114 0.968731i \(-0.579811\pi\)
−0.248114 + 0.968731i \(0.579811\pi\)
\(720\) 0 0
\(721\) 8.28853 0.308681
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 17.7384i − 0.657881i −0.944351 0.328941i \(-0.893308\pi\)
0.944351 0.328941i \(-0.106692\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7.69319 −0.284543
\(732\) 0 0
\(733\) 29.6391 1.09475 0.547373 0.836889i \(-0.315628\pi\)
0.547373 + 0.836889i \(0.315628\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 25.5415i − 0.940832i
\(738\) 0 0
\(739\) 19.2195i 0.707001i 0.935434 + 0.353500i \(0.115009\pi\)
−0.935434 + 0.353500i \(0.884991\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21.8768 −0.802584 −0.401292 0.915950i \(-0.631439\pi\)
−0.401292 + 0.915950i \(0.631439\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 19.7134i − 0.720310i
\(750\) 0 0
\(751\) − 14.5913i − 0.532444i −0.963912 0.266222i \(-0.914225\pi\)
0.963912 0.266222i \(-0.0857754\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.26067 −0.191202 −0.0956011 0.995420i \(-0.530477\pi\)
−0.0956011 + 0.995420i \(0.530477\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.6261i 0.820196i 0.912041 + 0.410098i \(0.134506\pi\)
−0.912041 + 0.410098i \(0.865494\pi\)
\(762\) 0 0
\(763\) − 7.84014i − 0.283832i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.61128 −0.166504
\(768\) 0 0
\(769\) −0.150464 −0.00542586 −0.00271293 0.999996i \(-0.500864\pi\)
−0.00271293 + 0.999996i \(0.500864\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 1.23760i − 0.0445133i −0.999752 0.0222567i \(-0.992915\pi\)
0.999752 0.0222567i \(-0.00708510\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −39.2006 −1.40451
\(780\) 0 0
\(781\) 39.4381 1.41121
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 6.84106i − 0.243857i −0.992539 0.121929i \(-0.961092\pi\)
0.992539 0.121929i \(-0.0389079\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.9890 0.532949
\(792\) 0 0
\(793\) 6.71995 0.238633
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 32.9437i 1.16693i 0.812140 + 0.583463i \(0.198303\pi\)
−0.812140 + 0.583463i \(0.801697\pi\)
\(798\) 0 0
\(799\) 2.87981i 0.101880i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −42.8212 −1.51113
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 53.6532i − 1.88635i −0.332303 0.943173i \(-0.607826\pi\)
0.332303 0.943173i \(-0.392174\pi\)
\(810\) 0 0
\(811\) 19.5904i 0.687911i 0.938986 + 0.343955i \(0.111767\pi\)
−0.938986 + 0.343955i \(0.888233\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −59.2395 −2.07253
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.49596i 0.0871095i 0.999051 + 0.0435548i \(0.0138683\pi\)
−0.999051 + 0.0435548i \(0.986132\pi\)
\(822\) 0 0
\(823\) − 4.04117i − 0.140866i −0.997516 0.0704332i \(-0.977562\pi\)
0.997516 0.0704332i \(-0.0224382\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −6.76066 −0.235091 −0.117546 0.993067i \(-0.537503\pi\)
−0.117546 + 0.993067i \(0.537503\pi\)
\(828\) 0 0
\(829\) −29.5298 −1.02561 −0.512806 0.858504i \(-0.671394\pi\)
−0.512806 + 0.858504i \(0.671394\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.0207603i 0 0.000719301i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.7344 0.370593 0.185296 0.982683i \(-0.440675\pi\)
0.185296 + 0.982683i \(0.440675\pi\)
\(840\) 0 0
\(841\) −37.4683 −1.29201
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 5.20012i − 0.178678i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.66463 −0.125622
\(852\) 0 0
\(853\) 19.0109 0.650921 0.325460 0.945556i \(-0.394481\pi\)
0.325460 + 0.945556i \(0.394481\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.4584i 0.835484i 0.908566 + 0.417742i \(0.137178\pi\)
−0.908566 + 0.417742i \(0.862822\pi\)
\(858\) 0 0
\(859\) 23.4693i 0.800761i 0.916349 + 0.400381i \(0.131122\pi\)
−0.916349 + 0.400381i \(0.868878\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11.5539 0.393299 0.196650 0.980474i \(-0.436994\pi\)
0.196650 + 0.980474i \(0.436994\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 34.4656i 1.16917i
\(870\) 0 0
\(871\) − 5.43991i − 0.184324i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 7.38934 0.249520 0.124760 0.992187i \(-0.460184\pi\)
0.124760 + 0.992187i \(0.460184\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 3.05321i − 0.102865i −0.998676 0.0514326i \(-0.983621\pi\)
0.998676 0.0514326i \(-0.0163787\pi\)
\(882\) 0 0
\(883\) − 21.2800i − 0.716131i −0.933697 0.358065i \(-0.883437\pi\)
0.933697 0.358065i \(-0.116563\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 31.9737 1.07357 0.536786 0.843718i \(-0.319638\pi\)
0.536786 + 0.843718i \(0.319638\pi\)
\(888\) 0 0
\(889\) −50.5289 −1.69468
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 22.1753i 0.742067i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −24.2116 −0.807502
\(900\) 0 0
\(901\) −6.58945 −0.219527
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 16.6594i − 0.553166i −0.960990 0.276583i \(-0.910798\pi\)
0.960990 0.276583i \(-0.0892021\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 23.3339 0.773086 0.386543 0.922271i \(-0.373669\pi\)
0.386543 + 0.922271i \(0.373669\pi\)
\(912\) 0 0
\(913\) 39.4381 1.30521
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 30.5608i − 1.00921i
\(918\) 0 0
\(919\) − 21.0303i − 0.693725i −0.937916 0.346862i \(-0.887247\pi\)
0.937916 0.346862i \(-0.112753\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 8.39965 0.276478
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 39.8536i 1.30755i 0.756687 + 0.653777i \(0.226816\pi\)
−0.756687 + 0.653777i \(0.773184\pi\)
\(930\) 0 0
\(931\) 0.159859i 0.00523917i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 42.5601 1.39038 0.695189 0.718827i \(-0.255321\pi\)
0.695189 + 0.718827i \(0.255321\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 2.05710i − 0.0670594i −0.999438 0.0335297i \(-0.989325\pi\)
0.999438 0.0335297i \(-0.0106748\pi\)
\(942\) 0 0
\(943\) − 16.9016i − 0.550392i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26.4740 0.860290 0.430145 0.902760i \(-0.358462\pi\)
0.430145 + 0.902760i \(0.358462\pi\)
\(948\) 0 0
\(949\) −9.12019 −0.296054
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 42.9717i − 1.39199i −0.718047 0.695994i \(-0.754964\pi\)
0.718047 0.695994i \(-0.245036\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.58939 0.212782
\(960\) 0 0
\(961\) 22.1807 0.715508
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 11.7990i 0.379429i 0.981839 + 0.189715i \(0.0607563\pi\)
−0.981839 + 0.189715i \(0.939244\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.23112 −0.103691 −0.0518457 0.998655i \(-0.516510\pi\)
−0.0518457 + 0.998655i \(0.516510\pi\)
\(972\) 0 0
\(973\) 19.7190 0.632163
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 47.6210i 1.52353i 0.647852 + 0.761766i \(0.275667\pi\)
−0.647852 + 0.761766i \(0.724333\pi\)
\(978\) 0 0
\(979\) − 30.8099i − 0.984688i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −13.4772 −0.429856 −0.214928 0.976630i \(-0.568952\pi\)
−0.214928 + 0.976630i \(0.568952\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 25.5415i − 0.812172i
\(990\) 0 0
\(991\) − 47.0284i − 1.49391i −0.664876 0.746954i \(-0.731516\pi\)
0.664876 0.746954i \(-0.268484\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 31.2295 0.989047 0.494524 0.869164i \(-0.335343\pi\)
0.494524 + 0.869164i \(0.335343\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 7200.2.h.l.1151.10 12
3.2 odd 2 inner 7200.2.h.l.1151.9 12
4.3 odd 2 inner 7200.2.h.l.1151.3 12
5.2 odd 4 1440.2.o.b.1439.2 yes 12
5.3 odd 4 1440.2.o.a.1439.12 yes 12
5.4 even 2 7200.2.h.m.1151.4 12
12.11 even 2 inner 7200.2.h.l.1151.4 12
15.2 even 4 1440.2.o.b.1439.11 yes 12
15.8 even 4 1440.2.o.a.1439.1 12
15.14 odd 2 7200.2.h.m.1151.3 12
20.3 even 4 1440.2.o.b.1439.12 yes 12
20.7 even 4 1440.2.o.a.1439.2 yes 12
20.19 odd 2 7200.2.h.m.1151.9 12
40.3 even 4 2880.2.o.e.2879.1 12
40.13 odd 4 2880.2.o.f.2879.1 12
40.27 even 4 2880.2.o.f.2879.11 12
40.37 odd 4 2880.2.o.e.2879.11 12
60.23 odd 4 1440.2.o.b.1439.1 yes 12
60.47 odd 4 1440.2.o.a.1439.11 yes 12
60.59 even 2 7200.2.h.m.1151.10 12
120.53 even 4 2880.2.o.f.2879.12 12
120.77 even 4 2880.2.o.e.2879.2 12
120.83 odd 4 2880.2.o.e.2879.12 12
120.107 odd 4 2880.2.o.f.2879.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1440.2.o.a.1439.1 12 15.8 even 4
1440.2.o.a.1439.2 yes 12 20.7 even 4
1440.2.o.a.1439.11 yes 12 60.47 odd 4
1440.2.o.a.1439.12 yes 12 5.3 odd 4
1440.2.o.b.1439.1 yes 12 60.23 odd 4
1440.2.o.b.1439.2 yes 12 5.2 odd 4
1440.2.o.b.1439.11 yes 12 15.2 even 4
1440.2.o.b.1439.12 yes 12 20.3 even 4
2880.2.o.e.2879.1 12 40.3 even 4
2880.2.o.e.2879.2 12 120.77 even 4
2880.2.o.e.2879.11 12 40.37 odd 4
2880.2.o.e.2879.12 12 120.83 odd 4
2880.2.o.f.2879.1 12 40.13 odd 4
2880.2.o.f.2879.2 12 120.107 odd 4
2880.2.o.f.2879.11 12 40.27 even 4
2880.2.o.f.2879.12 12 120.53 even 4
7200.2.h.l.1151.3 12 4.3 odd 2 inner
7200.2.h.l.1151.4 12 12.11 even 2 inner
7200.2.h.l.1151.9 12 3.2 odd 2 inner
7200.2.h.l.1151.10 12 1.1 even 1 trivial
7200.2.h.m.1151.3 12 15.14 odd 2
7200.2.h.m.1151.4 12 5.4 even 2
7200.2.h.m.1151.9 12 20.19 odd 2
7200.2.h.m.1151.10 12 60.59 even 2