Properties

Label 3700.2.a.d.1.1
Level $3700$
Weight $2$
Character 3700.1
Self dual yes
Analytic conductor $29.545$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3700,2,Mod(1,3700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3700.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3700.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: \(29.5446487479\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 740)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3700.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} -3.00000 q^{11} +6.00000 q^{13} -1.00000 q^{21} -2.00000 q^{23} -5.00000 q^{27} -6.00000 q^{29} -3.00000 q^{33} +1.00000 q^{37} +6.00000 q^{39} -9.00000 q^{41} +10.0000 q^{43} -1.00000 q^{47} -6.00000 q^{49} -1.00000 q^{53} -12.0000 q^{61} +2.00000 q^{63} -2.00000 q^{69} -5.00000 q^{71} -3.00000 q^{73} +3.00000 q^{77} +16.0000 q^{79} +1.00000 q^{81} -11.0000 q^{83} -6.00000 q^{87} -6.00000 q^{91} -8.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −12.0000 −1.53644 −0.768221 0.640184i \(-0.778858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) −2.00000 −0.240772
\(70\) 0 0
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) −3.00000 −0.351123 −0.175562 0.984468i \(-0.556174\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.0000 −1.20741 −0.603703 0.797209i \(-0.706309\pi\)
−0.603703 + 0.797209i \(0.706309\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −1.00000 −0.0995037 −0.0497519 0.998762i \(-0.515843\pi\)
−0.0497519 + 0.998762i \(0.515843\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −20.0000 −1.93347 −0.966736 0.255774i \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −12.0000 −1.10940
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −9.00000 −0.811503
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.00000 0.0887357 0.0443678 0.999015i \(-0.485873\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) 0 0
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) 0 0
\(143\) −18.0000 −1.50524
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.00000 −0.494872
\(148\) 0 0
\(149\) −9.00000 −0.737309 −0.368654 0.929567i \(-0.620181\pi\)
−0.368654 + 0.929567i \(0.620181\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.0000 −1.19713 −0.598565 0.801074i \(-0.704262\pi\)
−0.598565 + 0.801074i \(0.704262\pi\)
\(158\) 0 0
\(159\) −1.00000 −0.0793052
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 15.0000 1.14043 0.570214 0.821496i \(-0.306860\pi\)
0.570214 + 0.821496i \(0.306860\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 0 0
\(183\) −12.0000 −0.887066
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) 22.0000 1.58359 0.791797 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.00000 0.278019
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −27.0000 −1.85876 −0.929378 0.369129i \(-0.879656\pi\)
−0.929378 + 0.369129i \(0.879656\pi\)
\(212\) 0 0
\(213\) −5.00000 −0.342594
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.00000 −0.202721
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −17.0000 −1.13840 −0.569202 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) 3.00000 0.198246 0.0991228 0.995075i \(-0.468396\pi\)
0.0991228 + 0.995075i \(0.468396\pi\)
\(230\) 0 0
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) 2.00000 0.131024 0.0655122 0.997852i \(-0.479132\pi\)
0.0655122 + 0.997852i \(0.479132\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) 30.0000 1.94054 0.970269 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0 0
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −11.0000 −0.697097
\(250\) 0 0
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −20.0000 −1.24757 −0.623783 0.781598i \(-0.714405\pi\)
−0.623783 + 0.781598i \(0.714405\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 12.0000 0.742781
\(262\) 0 0
\(263\) −5.00000 −0.308313 −0.154157 0.988046i \(-0.549266\pi\)
−0.154157 + 0.988046i \(0.549266\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 0 0
\(273\) −6.00000 −0.363137
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −8.00000 −0.468968
\(292\) 0 0
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 15.0000 0.870388
\(298\) 0 0
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) −10.0000 −0.576390
\(302\) 0 0
\(303\) −1.00000 −0.0574485
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 0 0
\(309\) 10.0000 0.568880
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) 18.0000 1.00781
\(320\) 0 0
\(321\) −20.0000 −1.11629
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −12.0000 −0.663602
\(328\) 0 0
\(329\) 1.00000 0.0551318
\(330\) 0 0
\(331\) 6.00000 0.329790 0.164895 0.986311i \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(332\) 0 0
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.00000 −0.163420 −0.0817102 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) 0 0
\(339\) −14.0000 −0.760376
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 34.0000 1.82522 0.912608 0.408836i \(-0.134065\pi\)
0.912608 + 0.408836i \(0.134065\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −30.0000 −1.60128
\(352\) 0 0
\(353\) −4.00000 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 19.0000 1.00278 0.501391 0.865221i \(-0.332822\pi\)
0.501391 + 0.865221i \(0.332822\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) 1.00000 0.0519174
\(372\) 0 0
\(373\) 11.0000 0.569558 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) 1.00000 0.0512316
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −20.0000 −1.01666
\(388\) 0 0
\(389\) −36.0000 −1.82527 −0.912636 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 21.0000 1.05396 0.526980 0.849878i \(-0.323324\pi\)
0.526980 + 0.849878i \(0.323324\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −12.0000 −0.593362 −0.296681 0.954977i \(-0.595880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 0 0
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) −32.0000 −1.55958 −0.779792 0.626038i \(-0.784675\pi\)
−0.779792 + 0.626038i \(0.784675\pi\)
\(422\) 0 0
\(423\) 2.00000 0.0972433
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.0000 0.580721
\(428\) 0 0
\(429\) −18.0000 −0.869048
\(430\) 0 0
\(431\) 26.0000 1.25238 0.626188 0.779672i \(-0.284614\pi\)
0.626188 + 0.779672i \(0.284614\pi\)
\(432\) 0 0
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 4.00000 0.190910 0.0954548 0.995434i \(-0.469569\pi\)
0.0954548 + 0.995434i \(0.469569\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 13.0000 0.617649 0.308824 0.951119i \(-0.400064\pi\)
0.308824 + 0.951119i \(0.400064\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −9.00000 −0.425685
\(448\) 0 0
\(449\) −16.0000 −0.755087 −0.377543 0.925992i \(-0.623231\pi\)
−0.377543 + 0.925992i \(0.623231\pi\)
\(450\) 0 0
\(451\) 27.0000 1.27138
\(452\) 0 0
\(453\) −8.00000 −0.375873
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 30.0000 1.40334 0.701670 0.712502i \(-0.252438\pi\)
0.701670 + 0.712502i \(0.252438\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) −6.00000 −0.278844 −0.139422 0.990233i \(-0.544524\pi\)
−0.139422 + 0.990233i \(0.544524\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.0000 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −15.0000 −0.691164
\(472\) 0 0
\(473\) −30.0000 −1.37940
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) −26.0000 −1.18797 −0.593985 0.804476i \(-0.702446\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 0 0
\(483\) 2.00000 0.0910032
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 0 0
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.00000 0.224281
\(498\) 0 0
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.0000 1.02147
\(508\) 0 0
\(509\) −27.0000 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(510\) 0 0
\(511\) 3.00000 0.132712
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3.00000 0.131940
\(518\) 0 0
\(519\) 15.0000 0.658427
\(520\) 0 0
\(521\) 7.00000 0.306676 0.153338 0.988174i \(-0.450998\pi\)
0.153338 + 0.988174i \(0.450998\pi\)
\(522\) 0 0
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −54.0000 −2.33900
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 18.0000 0.776757
\(538\) 0 0
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 0 0
\(543\) 17.0000 0.729540
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 40.0000 1.71028 0.855138 0.518400i \(-0.173472\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 0 0
\(549\) 24.0000 1.02430
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −26.0000 −1.10166 −0.550828 0.834619i \(-0.685688\pi\)
−0.550828 + 0.834619i \(0.685688\pi\)
\(558\) 0 0
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 38.0000 1.60151 0.800755 0.598993i \(-0.204432\pi\)
0.800755 + 0.598993i \(0.204432\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) 28.0000 1.17382 0.586911 0.809652i \(-0.300344\pi\)
0.586911 + 0.809652i \(0.300344\pi\)
\(570\) 0 0
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 24.0000 0.999133 0.499567 0.866276i \(-0.333493\pi\)
0.499567 + 0.866276i \(0.333493\pi\)
\(578\) 0 0
\(579\) 22.0000 0.914289
\(580\) 0 0
\(581\) 11.0000 0.456357
\(582\) 0 0
\(583\) 3.00000 0.124247
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −3.00000 −0.123404
\(592\) 0 0
\(593\) 33.0000 1.35515 0.677574 0.735455i \(-0.263031\pi\)
0.677574 + 0.735455i \(0.263031\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.0000 0.572982
\(598\) 0 0
\(599\) −21.0000 −0.858037 −0.429018 0.903296i \(-0.641140\pi\)
−0.429018 + 0.903296i \(0.641140\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) 0 0
\(609\) 6.00000 0.243132
\(610\) 0 0
\(611\) −6.00000 −0.242734
\(612\) 0 0
\(613\) −23.0000 −0.928961 −0.464481 0.885583i \(-0.653759\pi\)
−0.464481 + 0.885583i \(0.653759\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00000 0.120775 0.0603877 0.998175i \(-0.480766\pi\)
0.0603877 + 0.998175i \(0.480766\pi\)
\(618\) 0 0
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) 0 0
\(621\) 10.0000 0.401286
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) −27.0000 −1.07315
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −36.0000 −1.42637
\(638\) 0 0
\(639\) 10.0000 0.395594
\(640\) 0 0
\(641\) 15.0000 0.592464 0.296232 0.955116i \(-0.404270\pi\)
0.296232 + 0.955116i \(0.404270\pi\)
\(642\) 0 0
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) −17.0000 −0.657258
\(670\) 0 0
\(671\) 36.0000 1.38976
\(672\) 0 0
\(673\) −47.0000 −1.81172 −0.905858 0.423581i \(-0.860773\pi\)
−0.905858 + 0.423581i \(0.860773\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −37.0000 −1.42203 −0.711013 0.703179i \(-0.751763\pi\)
−0.711013 + 0.703179i \(0.751763\pi\)
\(678\) 0 0
\(679\) 8.00000 0.307012
\(680\) 0 0
\(681\) 8.00000 0.306561
\(682\) 0 0
\(683\) −26.0000 −0.994862 −0.497431 0.867503i \(-0.665723\pi\)
−0.497431 + 0.867503i \(0.665723\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3.00000 0.114457
\(688\) 0 0
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 0 0
\(693\) −6.00000 −0.227921
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 2.00000 0.0756469
\(700\) 0 0
\(701\) 20.0000 0.755390 0.377695 0.925930i \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.00000 0.0376089
\(708\) 0 0
\(709\) −40.0000 −1.50223 −0.751116 0.660171i \(-0.770484\pi\)
−0.751116 + 0.660171i \(0.770484\pi\)
\(710\) 0 0
\(711\) −32.0000 −1.20009
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 30.0000 1.12037
\(718\) 0 0
\(719\) −3.00000 −0.111881 −0.0559406 0.998434i \(-0.517816\pi\)
−0.0559406 + 0.998434i \(0.517816\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) −6.00000 −0.223142
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 17.0000 0.627909 0.313955 0.949438i \(-0.398346\pi\)
0.313955 + 0.949438i \(0.398346\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 33.0000 1.21392 0.606962 0.794731i \(-0.292388\pi\)
0.606962 + 0.794731i \(0.292388\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 45.0000 1.65089 0.825445 0.564483i \(-0.190924\pi\)
0.825445 + 0.564483i \(0.190924\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 22.0000 0.804938
\(748\) 0 0
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) 11.0000 0.401396 0.200698 0.979653i \(-0.435679\pi\)
0.200698 + 0.979653i \(0.435679\pi\)
\(752\) 0 0
\(753\) 6.00000 0.218652
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 6.00000 0.217786
\(760\) 0 0
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) 0 0
\(763\) 12.0000 0.434429
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) −20.0000 −0.720282
\(772\) 0 0
\(773\) −31.0000 −1.11499 −0.557496 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.00000 −0.0358748
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 15.0000 0.536742
\(782\) 0 0
\(783\) 30.0000 1.07211
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −17.0000 −0.605985 −0.302992 0.952993i \(-0.597986\pi\)
−0.302992 + 0.952993i \(0.597986\pi\)
\(788\) 0 0
\(789\) −5.00000 −0.178005
\(790\) 0 0
\(791\) 14.0000 0.497783
\(792\) 0 0
\(793\) −72.0000 −2.55679
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −28.0000 −0.991811 −0.495905 0.868377i \(-0.665164\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.00000 0.317603
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000 0.0704033
\(808\) 0 0
\(809\) −50.0000 −1.75791 −0.878953 0.476908i \(-0.841757\pi\)
−0.878953 + 0.476908i \(0.841757\pi\)
\(810\) 0 0
\(811\) 41.0000 1.43970 0.719852 0.694127i \(-0.244209\pi\)
0.719852 + 0.694127i \(0.244209\pi\)
\(812\) 0 0
\(813\) −13.0000 −0.455930
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 12.0000 0.419314
\(820\) 0 0
\(821\) −19.0000 −0.663105 −0.331552 0.943437i \(-0.607572\pi\)
−0.331552 + 0.943437i \(0.607572\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 0.0695468 0.0347734 0.999395i \(-0.488929\pi\)
0.0347734 + 0.999395i \(0.488929\pi\)
\(828\) 0 0
\(829\) −12.0000 −0.416777 −0.208389 0.978046i \(-0.566822\pi\)
−0.208389 + 0.978046i \(0.566822\pi\)
\(830\) 0 0
\(831\) 8.00000 0.277517
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −36.0000 −1.24286 −0.621429 0.783470i \(-0.713448\pi\)
−0.621429 + 0.783470i \(0.713448\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) −2.00000 −0.0685591
\(852\) 0 0
\(853\) 2.00000 0.0684787 0.0342393 0.999414i \(-0.489099\pi\)
0.0342393 + 0.999414i \(0.489099\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 12.0000 0.409912 0.204956 0.978771i \(-0.434295\pi\)
0.204956 + 0.978771i \(0.434295\pi\)
\(858\) 0 0
\(859\) 36.0000 1.22830 0.614152 0.789188i \(-0.289498\pi\)
0.614152 + 0.789188i \(0.289498\pi\)
\(860\) 0 0
\(861\) 9.00000 0.306719
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −17.0000 −0.577350
\(868\) 0 0
\(869\) −48.0000 −1.62829
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 16.0000 0.541518
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 46.0000 1.55331 0.776655 0.629926i \(-0.216915\pi\)
0.776655 + 0.629926i \(0.216915\pi\)
\(878\) 0 0
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 33.0000 1.10803 0.554016 0.832506i \(-0.313095\pi\)
0.554016 + 0.832506i \(0.313095\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −12.0000 −0.400668
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −10.0000 −0.332779
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 2.00000 0.0663358
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 0 0
\(913\) 33.0000 1.09214
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 14.0000 0.461817 0.230909 0.972975i \(-0.425830\pi\)
0.230909 + 0.972975i \(0.425830\pi\)
\(920\) 0 0
\(921\) 11.0000 0.362462
\(922\) 0 0
\(923\) −30.0000 −0.987462
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −20.0000 −0.656886
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 16.0000 0.523816
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.00000 −0.0326686 −0.0163343 0.999867i \(-0.505200\pi\)
−0.0163343 + 0.999867i \(0.505200\pi\)
\(938\) 0 0
\(939\) 10.0000 0.326338
\(940\) 0 0
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 0 0
\(943\) 18.0000 0.586161
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 0 0
\(949\) −18.0000 −0.584305
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 18.0000 0.581857
\(958\) 0 0
\(959\) 2.00000 0.0645834
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 40.0000 1.28898
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −6.00000 −0.192947 −0.0964735 0.995336i \(-0.530756\pi\)
−0.0964735 + 0.995336i \(0.530756\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) 0 0
\(973\) 12.0000 0.384702
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 52.0000 1.66363 0.831814 0.555055i \(-0.187303\pi\)
0.831814 + 0.555055i \(0.187303\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 24.0000 0.766261
\(982\) 0 0
\(983\) −39.0000 −1.24391 −0.621953 0.783054i \(-0.713661\pi\)
−0.621953 + 0.783054i \(0.713661\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.00000 0.0318304
\(988\) 0 0
\(989\) −20.0000 −0.635963
\(990\) 0 0
\(991\) −30.0000 −0.952981 −0.476491 0.879180i \(-0.658091\pi\)
−0.476491 + 0.879180i \(0.658091\pi\)
\(992\) 0 0
\(993\) 6.00000 0.190404
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −42.0000 −1.33015 −0.665077 0.746775i \(-0.731601\pi\)
−0.665077 + 0.746775i \(0.731601\pi\)
\(998\) 0 0
\(999\) −5.00000 −0.158193
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 3700.2.a.d.1.1 1
5.2 odd 4 3700.2.d.c.149.1 2
5.3 odd 4 3700.2.d.c.149.2 2
5.4 even 2 740.2.a.a.1.1 1
15.14 odd 2 6660.2.a.a.1.1 1
20.19 odd 2 2960.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
740.2.a.a.1.1 1 5.4 even 2
2960.2.a.h.1.1 1 20.19 odd 2
3700.2.a.d.1.1 1 1.1 even 1 trivial
3700.2.d.c.149.1 2 5.2 odd 4
3700.2.d.c.149.2 2 5.3 odd 4
6660.2.a.a.1.1 1 15.14 odd 2