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Properties

Label 7350.2.a.cx.1.1
Level $7350$
Weight $2$
Character 7350.1
Self dual yes
Analytic conductor $58.690$
Analytic rank $0$
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] = [7350,2,Mod(1,7350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7350, 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("7350.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.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: \(58.6900454856\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7350.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{16} +1.00000 q^{18} -5.00000 q^{19} +3.00000 q^{22} +9.00000 q^{23} +1.00000 q^{24} +5.00000 q^{26} +1.00000 q^{27} +10.0000 q^{31} +1.00000 q^{32} +3.00000 q^{33} +1.00000 q^{36} +1.00000 q^{37} -5.00000 q^{38} +5.00000 q^{39} -9.00000 q^{41} -8.00000 q^{43} +3.00000 q^{44} +9.00000 q^{46} +3.00000 q^{47} +1.00000 q^{48} +5.00000 q^{52} +3.00000 q^{53} +1.00000 q^{54} -5.00000 q^{57} -12.0000 q^{59} -8.00000 q^{61} +10.0000 q^{62} +1.00000 q^{64} +3.00000 q^{66} -8.00000 q^{67} +9.00000 q^{69} -6.00000 q^{71} +1.00000 q^{72} +2.00000 q^{73} +1.00000 q^{74} -5.00000 q^{76} +5.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} -9.00000 q^{82} -8.00000 q^{86} +3.00000 q^{88} -6.00000 q^{89} +9.00000 q^{92} +10.0000 q^{93} +3.00000 q^{94} +1.00000 q^{96} +8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 − 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.00000 −1.14708 −0.573539 − 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 9.00000 1.87663 0.938315 − 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 5.00000 0.980581
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 − 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.00000 0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.00000 0.164399 0.0821995 − 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) −5.00000 −0.811107
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 − 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 9.00000 1.32698
\(47\) 3.00000 0.437595 0.218797 − 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 − 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 − 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 10.0000 1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) −8.00000 −0.977356 −0.488678 − 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 − 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000 0.117851
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −9.00000 −0.993884
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 9.00000 0.938315
\(93\) 10.0000 1.03695
\(94\) 3.00000 0.309426
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 8.00000 0.812277 0.406138 − 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −6.00000 −0.580042 −0.290021 − 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 1.00000 0.0962250
\(109\) 14.0000 1.34096 0.670478 − 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −5.00000 −0.468293
\(115\) 0 0
\(116\) 0 0
\(117\) 5.00000 0.462250
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −8.00000 −0.724286
\(123\) −9.00000 −0.811503
\(124\) 10.0000 0.898027
\(125\) 0 0
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 − 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) 9.00000 0.786334 0.393167 − 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 − 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 9.00000 0.766131
\(139\) −20.0000 −1.69638 −0.848189 − 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) −6.00000 −0.503509
\(143\) 15.0000 1.25436
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 1.00000 0.0821995
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −5.00000 −0.405554
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) 5.00000 0.399043 0.199522 − 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 8.00000 0.636446
\(159\) 3.00000 0.237915
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 16.0000 1.25322 0.626608 − 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 − 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −5.00000 −0.382360
\(172\) −8.00000 −0.609994
\(173\) 9.00000 0.684257 0.342129 − 0.939653i \(-0.388852\pi\)
0.342129 + 0.939653i \(0.388852\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) −12.0000 −0.901975
\(178\) −6.00000 −0.449719
\(179\) −15.0000 −1.12115 −0.560576 − 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 − 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 9.00000 0.663489
\(185\) 0 0
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 − 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 1.00000 0.0721688
\(193\) 10.0000 0.719816 0.359908 − 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) 0 0
\(197\) −15.0000 −1.06871 −0.534353 − 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 3.00000 0.213201
\(199\) 16.0000 1.13421 0.567105 − 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 9.00000 0.625543
\(208\) 5.00000 0.346688
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 − 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 3.00000 0.206041
\(213\) −6.00000 −0.411113
\(214\) −6.00000 −0.410152
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 0 0
\(222\) 1.00000 0.0671156
\(223\) −28.0000 −1.87502 −0.937509 − 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 18.0000 1.19734
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −5.00000 −0.331133
\(229\) −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
\(233\) 6.00000 0.393073 0.196537 − 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 5.00000 0.326860
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 30.0000 1.94054 0.970269 − 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157 0.0322078 − 0.999481i \(-0.489746\pi\)
0.0322078 + 0.999481i \(0.489746\pi\)
\(242\) −2.00000 −0.128565
\(243\) 1.00000 0.0641500
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) −25.0000 −1.59071
\(248\) 10.0000 0.635001
\(249\) 0 0
\(250\) 0 0
\(251\) −9.00000 −0.568075 −0.284037 − 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 13.0000 0.815693
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 9.00000 0.556022
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 3.00000 0.184637
\(265\) 0 0
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) −8.00000 −0.488678
\(269\) −12.0000 −0.731653 −0.365826 − 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 − 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 9.00000 0.541736
\(277\) −26.0000 −1.56219 −0.781094 − 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) −20.0000 −1.19952
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) −21.0000 −1.25275 −0.626377 − 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 3.00000 0.178647
\(283\) −22.0000 −1.30776 −0.653882 − 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 15.0000 0.886969
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 2.00000 0.117041
\(293\) −21.0000 −1.22683 −0.613417 − 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 3.00000 0.174078
\(298\) 0 0
\(299\) 45.0000 2.60242
\(300\) 0 0
\(301\) 0 0
\(302\) −10.0000 −0.575435
\(303\) 0 0
\(304\) −5.00000 −0.286770
\(305\) 0 0
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 − 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 − 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 5.00000 0.283069
\(313\) −4.00000 −0.226093 −0.113047 − 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) 5.00000 0.282166
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 18.0000 1.01098 0.505490 − 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 3.00000 0.168232
\(319\) 0 0
\(320\) 0 0
\(321\) −6.00000 −0.334887
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 16.0000 0.886158
\(327\) 14.0000 0.774202
\(328\) −9.00000 −0.496942
\(329\) 0 0
\(330\) 0 0
\(331\) 11.0000 0.604615 0.302307 − 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) 0 0
\(333\) 1.00000 0.0547997
\(334\) −3.00000 −0.164153
\(335\) 0 0
\(336\) 0 0
\(337\) −20.0000 −1.08947 −0.544735 − 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) 12.0000 0.652714
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 30.0000 1.62459
\(342\) −5.00000 −0.270369
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 9.00000 0.483843
\(347\) −30.0000 −1.61048 −0.805242 − 0.592946i \(-0.797965\pi\)
−0.805242 + 0.592946i \(0.797965\pi\)
\(348\) 0 0
\(349\) 28.0000 1.49881 0.749403 − 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 3.00000 0.159901
\(353\) 24.0000 1.27739 0.638696 − 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) 12.0000 0.633336 0.316668 − 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −8.00000 −0.420471
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 0 0
\(366\) −8.00000 −0.418167
\(367\) −19.0000 −0.991792 −0.495896 − 0.868382i \(-0.665160\pi\)
−0.495896 + 0.868382i \(0.665160\pi\)
\(368\) 9.00000 0.469157
\(369\) −9.00000 −0.468521
\(370\) 0 0
\(371\) 0 0
\(372\) 10.0000 0.518476
\(373\) 10.0000 0.517780 0.258890 − 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 0 0
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 − 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 0 0
\(381\) 13.0000 0.666010
\(382\) 18.0000 0.920960
\(383\) 27.0000 1.37964 0.689818 − 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −8.00000 −0.406663
\(388\) 8.00000 0.406138
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 9.00000 0.453990
\(394\) −15.0000 −0.755689
\(395\) 0 0
\(396\) 3.00000 0.150756
\(397\) 14.0000 0.702640 0.351320 − 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 0 0
\(401\) 15.0000 0.749064 0.374532 − 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) −8.00000 −0.399004
\(403\) 50.0000 2.49068
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) −2.00000 −0.0988936 −0.0494468 − 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 9.00000 0.442326
\(415\) 0 0
\(416\) 5.00000 0.245145
\(417\) −20.0000 −0.979404
\(418\) −15.0000 −0.733674
\(419\) 9.00000 0.439679 0.219839 − 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 14.0000 0.682318 0.341159 − 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 5.00000 0.243396
\(423\) 3.00000 0.145865
\(424\) 3.00000 0.145693
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) −6.00000 −0.290021
\(429\) 15.0000 0.724207
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) −45.0000 −2.15264
\(438\) 2.00000 0.0955637
\(439\) −8.00000 −0.381819 −0.190910 − 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 − 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 1.00000 0.0474579
\(445\) 0 0
\(446\) −28.0000 −1.32584
\(447\) 0 0
\(448\) 0 0
\(449\) −33.0000 −1.55737 −0.778683 − 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) −27.0000 −1.27138
\(452\) 18.0000 0.846649
\(453\) −10.0000 −0.469841
\(454\) 0 0
\(455\) 0 0
\(456\) −5.00000 −0.234146
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 − 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 − 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 5.00000 0.231125
\(469\) 0 0
\(470\) 0 0
\(471\) 5.00000 0.230388
\(472\) −12.0000 −0.552345
\(473\) −24.0000 −1.10352
\(474\) 8.00000 0.367452
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000 0.137361
\(478\) 30.0000 1.37217
\(479\) 18.0000 0.822441 0.411220 − 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 0 0
\(481\) 5.00000 0.227980
\(482\) 1.00000 0.0455488
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 40.0000 1.81257 0.906287 − 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) −8.00000 −0.362143
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −9.00000 −0.405751
\(493\) 0 0
\(494\) −25.0000 −1.12480
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) 0 0
\(499\) −16.0000 −0.716258 −0.358129 − 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) 0 0
\(501\) −3.00000 −0.134030
\(502\) −9.00000 −0.401690
\(503\) −12.0000 −0.535054 −0.267527 − 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 27.0000 1.20030
\(507\) 12.0000 0.532939
\(508\) 13.0000 0.576782
\(509\) −6.00000 −0.265945 −0.132973 − 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −5.00000 −0.220755
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 9.00000 0.395820
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) −27.0000 −1.18289 −0.591446 − 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 0 0
\(523\) −22.0000 −0.961993 −0.480996 − 0.876723i \(-0.659725\pi\)
−0.480996 + 0.876723i \(0.659725\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 3.00000 0.130558
\(529\) 58.0000 2.52174
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) −45.0000 −1.94917
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) −8.00000 −0.345547
\(537\) −15.0000 −0.647298
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 − 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 16.0000 0.687259
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 − 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 18.0000 0.768922
\(549\) −8.00000 −0.341432
\(550\) 0 0
\(551\) 0 0
\(552\) 9.00000 0.383065
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) −39.0000 −1.65248 −0.826242 − 0.563316i \(-0.809525\pi\)
−0.826242 + 0.563316i \(0.809525\pi\)
\(558\) 10.0000 0.423334
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −21.0000 −0.885832
\(563\) −6.00000 −0.252870 −0.126435 − 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 27.0000 1.13190 0.565949 − 0.824440i \(-0.308510\pi\)
0.565949 + 0.824440i \(0.308510\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 − 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 15.0000 0.627182
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −22.0000 −0.915872 −0.457936 − 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) −17.0000 −0.707107
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000 0.331611
\(583\) 9.00000 0.372742
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −21.0000 −0.867502
\(587\) −42.0000 −1.73353 −0.866763 − 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) −50.0000 −2.06021
\(590\) 0 0
\(591\) −15.0000 −0.617018
\(592\) 1.00000 0.0410997
\(593\) 24.0000 0.985562 0.492781 − 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 0 0
\(597\) 16.0000 0.654836
\(598\) 45.0000 1.84019
\(599\) 18.0000 0.735460 0.367730 − 0.929933i \(-0.380135\pi\)
0.367730 + 0.929933i \(0.380135\pi\)
\(600\) 0 0
\(601\) −38.0000 −1.55005 −0.775026 − 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −25.0000 −1.01472 −0.507359 − 0.861735i \(-0.669378\pi\)
−0.507359 + 0.861735i \(0.669378\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) 15.0000 0.606835
\(612\) 0 0
\(613\) −11.0000 −0.444286 −0.222143 − 0.975014i \(-0.571305\pi\)
−0.222143 + 0.975014i \(0.571305\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 − 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 8.00000 0.321807
\(619\) −29.0000 −1.16561 −0.582804 − 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) 0 0
\(621\) 9.00000 0.361158
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 5.00000 0.200160
\(625\) 0 0
\(626\) −4.00000 −0.159872
\(627\) −15.0000 −0.599042
\(628\) 5.00000 0.199522
\(629\) 0 0
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 − 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 8.00000 0.318223
\(633\) 5.00000 0.198732
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 3.00000 0.118958
\(637\) 0 0
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) 33.0000 1.30342 0.651711 − 0.758468i \(-0.274052\pi\)
0.651711 + 0.758468i \(0.274052\pi\)
\(642\) −6.00000 −0.236801
\(643\) −34.0000 −1.34083 −0.670415 − 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 −0.353827 −0.176913 − 0.984226i \(-0.556611\pi\)
−0.176913 + 0.984226i \(0.556611\pi\)
\(648\) 1.00000 0.0392837
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) −39.0000 −1.52619 −0.763094 − 0.646288i \(-0.776321\pi\)
−0.763094 + 0.646288i \(0.776321\pi\)
\(654\) 14.0000 0.547443
\(655\) 0 0
\(656\) −9.00000 −0.351391
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 − 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 40.0000 1.55582 0.777910 − 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) 11.0000 0.427527
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) −3.00000 −0.116073
\(669\) −28.0000 −1.08254
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −20.0000 −0.770943 −0.385472 − 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) −20.0000 −0.770371
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 3.00000 0.115299 0.0576497 − 0.998337i \(-0.481639\pi\)
0.0576497 + 0.998337i \(0.481639\pi\)
\(678\) 18.0000 0.691286
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 30.0000 1.14876
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −5.00000 −0.191180
\(685\) 0 0
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) −8.00000 −0.304997
\(689\) 15.0000 0.571454
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 − 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 9.00000 0.342129
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 28.0000 1.05982
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 − 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 5.00000 0.188713
\(703\) −5.00000 −0.188579
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −28.0000 −1.05156 −0.525781 − 0.850620i \(-0.676227\pi\)
−0.525781 + 0.850620i \(0.676227\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) −6.00000 −0.224860
\(713\) 90.0000 3.37053
\(714\) 0 0
\(715\) 0 0
\(716\) −15.0000 −0.560576
\(717\) 30.0000 1.12037
\(718\) 12.0000 0.447836
\(719\) −18.0000 −0.671287 −0.335643 − 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.00000 0.223297
\(723\) 1.00000 0.0371904
\(724\) −8.00000 −0.297318
\(725\) 0 0
\(726\) −2.00000 −0.0742270
\(727\) 23.0000 0.853023 0.426511 − 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −8.00000 −0.295689
\(733\) −1.00000 −0.0369358 −0.0184679 − 0.999829i \(-0.505879\pi\)
−0.0184679 + 0.999829i \(0.505879\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 9.00000 0.331744
\(737\) −24.0000 −0.884051
\(738\) −9.00000 −0.331295
\(739\) 5.00000 0.183928 0.0919640 − 0.995762i \(-0.470686\pi\)
0.0919640 + 0.995762i \(0.470686\pi\)
\(740\) 0 0
\(741\) −25.0000 −0.918398
\(742\) 0 0
\(743\) 39.0000 1.43077 0.715386 − 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(744\) 10.0000 0.366618
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 0.0729810 0.0364905 − 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) 3.00000 0.109399
\(753\) −9.00000 −0.327978
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 − 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −19.0000 −0.690111
\(759\) 27.0000 0.980038
\(760\) 0 0
\(761\) 33.0000 1.19625 0.598125 − 0.801403i \(-0.295913\pi\)
0.598125 + 0.801403i \(0.295913\pi\)
\(762\) 13.0000 0.470940
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 27.0000 0.975550
\(767\) −60.0000 −2.16647
\(768\) 1.00000 0.0360844
\(769\) −35.0000 −1.26213 −0.631066 − 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 10.0000 0.359908
\(773\) 33.0000 1.18693 0.593464 − 0.804861i \(-0.297760\pi\)
0.593464 + 0.804861i \(0.297760\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 45.0000 1.61229
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 9.00000 0.321019
\(787\) 14.0000 0.499046 0.249523 − 0.968369i \(-0.419726\pi\)
0.249523 + 0.968369i \(0.419726\pi\)
\(788\) −15.0000 −0.534353
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) 3.00000 0.106600
\(793\) −40.0000 −1.42044
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 30.0000 1.06265 0.531327 − 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −6.00000 −0.212000
\(802\) 15.0000 0.529668
\(803\) 6.00000 0.211735
\(804\) −8.00000 −0.282138
\(805\) 0 0
\(806\) 50.0000 1.76117
\(807\) −12.0000 −0.422420
\(808\) 0 0
\(809\) −27.0000 −0.949269 −0.474635 − 0.880183i \(-0.657420\pi\)
−0.474635 + 0.880183i \(0.657420\pi\)
\(810\) 0 0
\(811\) 7.00000 0.245803 0.122902 − 0.992419i \(-0.460780\pi\)
0.122902 + 0.992419i \(0.460780\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 3.00000 0.105150
\(815\) 0 0
\(816\) 0 0
\(817\) 40.0000 1.39942
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 − 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 18.0000 0.627822
\(823\) −32.0000 −1.11545 −0.557725 − 0.830026i \(-0.688326\pi\)
−0.557725 + 0.830026i \(0.688326\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) 0 0
\(827\) −6.00000 −0.208640 −0.104320 − 0.994544i \(-0.533267\pi\)
−0.104320 + 0.994544i \(0.533267\pi\)
\(828\) 9.00000 0.312772
\(829\) 40.0000 1.38926 0.694629 − 0.719368i \(-0.255569\pi\)
0.694629 + 0.719368i \(0.255569\pi\)
\(830\) 0 0
\(831\) −26.0000 −0.901930
\(832\) 5.00000 0.173344
\(833\) 0 0
\(834\) −20.0000 −0.692543
\(835\) 0 0
\(836\) −15.0000 −0.518786
\(837\) 10.0000 0.345651
\(838\) 9.00000 0.310900
\(839\) 24.0000 0.828572 0.414286 − 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 14.0000 0.482472
\(843\) −21.0000 −0.723278
\(844\) 5.00000 0.172107
\(845\) 0 0
\(846\) 3.00000 0.103142
\(847\) 0 0
\(848\) 3.00000 0.103020
\(849\) −22.0000 −0.755038
\(850\) 0 0
\(851\) 9.00000 0.308516
\(852\) −6.00000 −0.205557
\(853\) −37.0000 −1.26686 −0.633428 − 0.773802i \(-0.718353\pi\)
−0.633428 + 0.773802i \(0.718353\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −6.00000 −0.205076
\(857\) −6.00000 −0.204956 −0.102478 − 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 15.0000 0.512092
\(859\) 4.00000 0.136478 0.0682391 − 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 21.0000 0.714848 0.357424 − 0.933942i \(-0.383655\pi\)
0.357424 + 0.933942i \(0.383655\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −16.0000 −0.543702
\(867\) −17.0000 −0.577350
\(868\) 0 0
\(869\) 24.0000 0.814144
\(870\) 0 0
\(871\) −40.0000 −1.35535
\(872\) 14.0000 0.474100
\(873\) 8.00000 0.270759
\(874\) −45.0000 −1.52215
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −5.00000 −0.168838 −0.0844190 − 0.996430i \(-0.526903\pi\)
−0.0844190 + 0.996430i \(0.526903\pi\)
\(878\) −8.00000 −0.269987
\(879\) −21.0000 −0.708312
\(880\) 0 0
\(881\) 33.0000 1.11180 0.555899 − 0.831250i \(-0.312374\pi\)
0.555899 + 0.831250i \(0.312374\pi\)
\(882\) 0 0
\(883\) −14.0000 −0.471138 −0.235569 − 0.971858i \(-0.575695\pi\)
−0.235569 + 0.971858i \(0.575695\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 12.0000 0.402921 0.201460 − 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 1.00000 0.0335578
\(889\) 0 0
\(890\) 0 0
\(891\) 3.00000 0.100504
\(892\) −28.0000 −0.937509
\(893\) −15.0000 −0.501956
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 45.0000 1.50251
\(898\) −33.0000 −1.10122
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −27.0000 −0.899002
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) 0 0
\(906\) −10.0000 −0.332228
\(907\) 10.0000 0.332045 0.166022 − 0.986122i \(-0.446908\pi\)
0.166022 + 0.986122i \(0.446908\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 6.00000 0.198789 0.0993944 − 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(912\) −5.00000 −0.165567
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 0 0
\(918\) 0 0
\(919\) −28.0000 −0.923635 −0.461817 − 0.886975i \(-0.652802\pi\)
−0.461817 + 0.886975i \(0.652802\pi\)
\(920\) 0 0
\(921\) −28.0000 −0.922631
\(922\) −12.0000 −0.395199
\(923\) −30.0000 −0.987462
\(924\) 0 0
\(925\) 0 0
\(926\) 1.00000 0.0328620
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) −39.0000 −1.27955 −0.639774 − 0.768563i \(-0.720972\pi\)
−0.639774 + 0.768563i \(0.720972\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 6.00000 0.196537
\(933\) 12.0000 0.392862
\(934\) 0 0
\(935\) 0 0
\(936\) 5.00000 0.163430
\(937\) 44.0000 1.43742 0.718709 − 0.695311i \(-0.244734\pi\)
0.718709 + 0.695311i \(0.244734\pi\)
\(938\) 0 0
\(939\) −4.00000 −0.130535
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 5.00000 0.162909
\(943\) −81.0000 −2.63772
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) −24.0000 −0.780307
\(947\) 18.0000 0.584921 0.292461 − 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(948\) 8.00000 0.259828
\(949\) 10.0000 0.324614
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 − 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 3.00000 0.0971286
\(955\) 0 0
\(956\) 30.0000 0.970269
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) 0 0
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 5.00000 0.161206
\(963\) −6.00000 −0.193347
\(964\) 1.00000 0.0322078
\(965\) 0 0
\(966\) 0 0
\(967\) 28.0000 0.900419 0.450210 − 0.892923i \(-0.351349\pi\)
0.450210 + 0.892923i \(0.351349\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) −15.0000 −0.481373 −0.240686 − 0.970603i \(-0.577373\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 40.0000 1.28168
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) −6.00000 −0.191957 −0.0959785 − 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 16.0000 0.511624
\(979\) −18.0000 −0.575282
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) 12.0000 0.382935
\(983\) 9.00000 0.287055 0.143528 − 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(984\) −9.00000 −0.286910
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −25.0000 −0.795356
\(989\) −72.0000 −2.28947
\(990\) 0 0
\(991\) −58.0000 −1.84243 −0.921215 − 0.389053i \(-0.872802\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) 10.0000 0.317500
\(993\) 11.0000 0.349074
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 14.0000 0.443384 0.221692 − 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) −16.0000 −0.506471
\(999\) 1.00000 0.0316386
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 7350.2.a.cx.1.1 1
5.4 even 2 1470.2.a.e.1.1 1
7.3 odd 6 1050.2.i.i.751.1 2
7.5 odd 6 1050.2.i.i.151.1 2
7.6 odd 2 7350.2.a.cd.1.1 1
15.14 odd 2 4410.2.a.w.1.1 1
35.3 even 12 1050.2.o.c.499.2 4
35.4 even 6 1470.2.i.p.961.1 2
35.9 even 6 1470.2.i.p.361.1 2
35.12 even 12 1050.2.o.c.949.2 4
35.17 even 12 1050.2.o.c.499.1 4
35.19 odd 6 210.2.i.c.151.1 yes 2
35.24 odd 6 210.2.i.c.121.1 ✓ 2
35.33 even 12 1050.2.o.c.949.1 4
35.34 odd 2 1470.2.a.f.1.1 1
105.59 even 6 630.2.k.a.541.1 2
105.89 even 6 630.2.k.a.361.1 2
105.104 even 2 4410.2.a.bh.1.1 1
140.19 even 6 1680.2.bg.n.1201.1 2
140.59 even 6 1680.2.bg.n.961.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.i.c.121.1 ✓ 2 35.24 odd 6
210.2.i.c.151.1 yes 2 35.19 odd 6
630.2.k.a.361.1 2 105.89 even 6
630.2.k.a.541.1 2 105.59 even 6
1050.2.i.i.151.1 2 7.5 odd 6
1050.2.i.i.751.1 2 7.3 odd 6
1050.2.o.c.499.1 4 35.17 even 12
1050.2.o.c.499.2 4 35.3 even 12
1050.2.o.c.949.1 4 35.33 even 12
1050.2.o.c.949.2 4 35.12 even 12
1470.2.a.e.1.1 1 5.4 even 2
1470.2.a.f.1.1 1 35.34 odd 2
1470.2.i.p.361.1 2 35.9 even 6
1470.2.i.p.961.1 2 35.4 even 6
1680.2.bg.n.961.1 2 140.59 even 6
1680.2.bg.n.1201.1 2 140.19 even 6
4410.2.a.w.1.1 1 15.14 odd 2
4410.2.a.bh.1.1 1 105.104 even 2
7350.2.a.cd.1.1 1 7.6 odd 2
7350.2.a.cx.1.1 1 1.1 even 1 trivial