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Properties

Label 4650.2.a.b.1.1
Level $4650$
Weight $2$
Character 4650.1
Self dual yes
Analytic conductor $37.130$
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] = [4650,2,Mod(1,4650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, 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("4650.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.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: \(37.1304369399\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4650.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} +3.00000 q^{21} +3.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} -3.00000 q^{28} +10.0000 q^{29} +1.00000 q^{31} -1.00000 q^{32} +3.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -3.00000 q^{37} -1.00000 q^{39} +7.00000 q^{41} -3.00000 q^{42} +1.00000 q^{43} -3.00000 q^{44} +4.00000 q^{46} +7.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -2.00000 q^{51} +1.00000 q^{52} -9.00000 q^{53} +1.00000 q^{54} +3.00000 q^{56} -10.0000 q^{58} +7.00000 q^{61} -1.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} +2.00000 q^{67} +2.00000 q^{68} +4.00000 q^{69} +7.00000 q^{71} -1.00000 q^{72} -4.00000 q^{73} +3.00000 q^{74} +9.00000 q^{77} +1.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} -7.00000 q^{82} -9.00000 q^{83} +3.00000 q^{84} -1.00000 q^{86} -10.0000 q^{87} +3.00000 q^{88} +10.0000 q^{89} -3.00000 q^{91} -4.00000 q^{92} -1.00000 q^{93} -7.00000 q^{94} +1.00000 q^{96} +2.00000 q^{97} -2.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)

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
\(7\) −3.00000 −1.13389 −0.566947 − 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350 0.138675 − 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 3.00000 0.639602
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −3.00000 −0.566947
\(29\) 10.0000 1.85695 0.928477 − 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) 3.00000 0.522233
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.00000 −0.493197 −0.246598 − 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 7.00000 1.09322 0.546608 − 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) −3.00000 −0.462910
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 7.00000 1.02105 0.510527 − 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 1.00000 0.138675
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 − 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) −1.00000 −0.127000
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) 2.00000 0.244339 0.122169 − 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 2.00000 0.242536
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 − 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) −1.00000 −0.117851
\(73\) −4.00000 −0.468165 −0.234082 − 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 3.00000 0.348743
\(75\) 0 0
\(76\) 0 0
\(77\) 9.00000 1.02565
\(78\) 1.00000 0.113228
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −7.00000 −0.773021
\(83\) −9.00000 −0.987878 −0.493939 − 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 3.00000 0.327327
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) −10.0000 −1.07211
\(88\) 3.00000 0.319801
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) −4.00000 −0.417029
\(93\) −1.00000 −0.103695
\(94\) −7.00000 −0.721995
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −2.00000 −0.202031
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 2.00000 0.199007 0.0995037 − 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 2.00000 0.198030
\(103\) 1.00000 0.0985329 0.0492665 − 0.998786i \(-0.484312\pi\)
0.0492665 + 0.998786i \(0.484312\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) −18.0000 −1.74013 −0.870063 − 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) −3.00000 −0.283473
\(113\) 6.00000 0.564433 0.282216 − 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −7.00000 −0.633750
\(123\) −7.00000 −0.631169
\(124\) 1.00000 0.0898027
\(125\) 0 0
\(126\) 3.00000 0.267261
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 2.00000 0.170872 0.0854358 − 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) −4.00000 −0.340503
\(139\) −5.00000 −0.424094 −0.212047 − 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(140\) 0 0
\(141\) −7.00000 −0.589506
\(142\) −7.00000 −0.587427
\(143\) −3.00000 −0.250873
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) −2.00000 −0.164957
\(148\) −3.00000 −0.246598
\(149\) −20.0000 −1.63846 −0.819232 − 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) −18.0000 −1.46482 −0.732410 − 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) −9.00000 −0.725241
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 22.0000 1.75579 0.877896 − 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 10.0000 0.795557
\(159\) 9.00000 0.713746
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 7.00000 0.546608
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) 2.00000 0.154765 0.0773823 − 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) −3.00000 −0.231455
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) −4.00000 −0.304114 −0.152057 − 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 10.0000 0.758098
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) −5.00000 −0.373718 −0.186859 − 0.982387i \(-0.559831\pi\)
−0.186859 + 0.982387i \(0.559831\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 − 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 3.00000 0.222375
\(183\) −7.00000 −0.517455
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 1.00000 0.0733236
\(187\) −6.00000 −0.438763
\(188\) 7.00000 0.510527
\(189\) 3.00000 0.218218
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −9.00000 −0.647834 −0.323917 − 0.946085i \(-0.605000\pi\)
−0.323917 + 0.946085i \(0.605000\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 27.0000 1.92367 0.961835 − 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 3.00000 0.213201
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 0 0
\(201\) −2.00000 −0.141069
\(202\) −2.00000 −0.140720
\(203\) −30.0000 −2.10559
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) −1.00000 −0.0696733
\(207\) −4.00000 −0.278019
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 − 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) −9.00000 −0.618123
\(213\) −7.00000 −0.479632
\(214\) 18.0000 1.23045
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −3.00000 −0.203653
\(218\) 10.0000 0.677285
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) −3.00000 −0.201347
\(223\) 6.00000 0.401790 0.200895 − 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 3.00000 0.200446
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 − 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −9.00000 −0.592157
\(232\) −10.0000 −0.656532
\(233\) −9.00000 −0.589610 −0.294805 − 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 0 0
\(236\) 0 0
\(237\) 10.0000 0.649570
\(238\) 6.00000 0.388922
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 12.0000 0.772988 0.386494 − 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(242\) 2.00000 0.128565
\(243\) −1.00000 −0.0641500
\(244\) 7.00000 0.448129
\(245\) 0 0
\(246\) 7.00000 0.446304
\(247\) 0 0
\(248\) −1.00000 −0.0635001
\(249\) 9.00000 0.570352
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 − 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −3.00000 −0.188982
\(253\) 12.0000 0.754434
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 7.00000 0.436648 0.218324 − 0.975876i \(-0.429941\pi\)
0.218324 + 0.975876i \(0.429941\pi\)
\(258\) 1.00000 0.0622573
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) −12.0000 −0.741362
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) −3.00000 −0.184637
\(265\) 0 0
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) 2.00000 0.122169
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 − 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000 0.121268
\(273\) 3.00000 0.181568
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 4.00000 0.240772
\(277\) −18.0000 −1.08152 −0.540758 − 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 5.00000 0.299880
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 7.00000 0.417585 0.208792 − 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) 7.00000 0.416844
\(283\) −24.0000 −1.42665 −0.713326 − 0.700832i \(-0.752812\pi\)
−0.713326 + 0.700832i \(0.752812\pi\)
\(284\) 7.00000 0.415374
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) −21.0000 −1.23959
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −2.00000 −0.117242
\(292\) −4.00000 −0.234082
\(293\) −24.0000 −1.40209 −0.701047 − 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 2.00000 0.116642
\(295\) 0 0
\(296\) 3.00000 0.174371
\(297\) 3.00000 0.174078
\(298\) 20.0000 1.15857
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 18.0000 1.03578
\(303\) −2.00000 −0.114897
\(304\) 0 0
\(305\) 0 0
\(306\) −2.00000 −0.114332
\(307\) 22.0000 1.25561 0.627803 − 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) 9.00000 0.512823
\(309\) −1.00000 −0.0568880
\(310\) 0 0
\(311\) 27.0000 1.53103 0.765515 − 0.643418i \(-0.222484\pi\)
0.765515 + 0.643418i \(0.222484\pi\)
\(312\) 1.00000 0.0566139
\(313\) −24.0000 −1.35656 −0.678280 − 0.734803i \(-0.737274\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 22.0000 1.23564 0.617822 − 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) −9.00000 −0.504695
\(319\) −30.0000 −1.67968
\(320\) 0 0
\(321\) 18.0000 1.00466
\(322\) −12.0000 −0.668734
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 10.0000 0.553001
\(328\) −7.00000 −0.386510
\(329\) −21.0000 −1.15777
\(330\) 0 0
\(331\) −3.00000 −0.164895 −0.0824475 − 0.996595i \(-0.526274\pi\)
−0.0824475 + 0.996595i \(0.526274\pi\)
\(332\) −9.00000 −0.493939
\(333\) −3.00000 −0.164399
\(334\) −2.00000 −0.109435
\(335\) 0 0
\(336\) 3.00000 0.163663
\(337\) −8.00000 −0.435788 −0.217894 − 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) 12.0000 0.652714
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −3.00000 −0.162459
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) 4.00000 0.215041
\(347\) 7.00000 0.375780 0.187890 − 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) −10.0000 −0.536056
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 3.00000 0.159901
\(353\) −24.0000 −1.27739 −0.638696 − 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 6.00000 0.317554
\(358\) 5.00000 0.264258
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 13.0000 0.683265
\(363\) 2.00000 0.104973
\(364\) −3.00000 −0.157243
\(365\) 0 0
\(366\) 7.00000 0.365896
\(367\) −28.0000 −1.46159 −0.730794 − 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −4.00000 −0.208514
\(369\) 7.00000 0.364405
\(370\) 0 0
\(371\) 27.0000 1.40177
\(372\) −1.00000 −0.0518476
\(373\) −24.0000 −1.24267 −0.621336 − 0.783544i \(-0.713410\pi\)
−0.621336 + 0.783544i \(0.713410\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) −7.00000 −0.360997
\(377\) 10.0000 0.515026
\(378\) −3.00000 −0.154303
\(379\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −2.00000 −0.102463
\(382\) 8.00000 0.409316
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 9.00000 0.458088
\(387\) 1.00000 0.0508329
\(388\) 2.00000 0.101535
\(389\) 10.0000 0.507020 0.253510 − 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) −2.00000 −0.101015
\(393\) −12.0000 −0.605320
\(394\) −27.0000 −1.36024
\(395\) 0 0
\(396\) −3.00000 −0.150756
\(397\) −28.0000 −1.40528 −0.702640 − 0.711546i \(-0.747995\pi\)
−0.702640 + 0.711546i \(0.747995\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 0 0
\(401\) −8.00000 −0.399501 −0.199750 − 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 2.00000 0.0997509
\(403\) 1.00000 0.0498135
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) 30.0000 1.48888
\(407\) 9.00000 0.446113
\(408\) 2.00000 0.0990148
\(409\) −10.0000 −0.494468 −0.247234 − 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 1.00000 0.0492665
\(413\) 0 0
\(414\) 4.00000 0.196589
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 − 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 − 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −2.00000 −0.0973585
\(423\) 7.00000 0.340352
\(424\) 9.00000 0.437079
\(425\) 0 0
\(426\) 7.00000 0.339151
\(427\) −21.0000 −1.01626
\(428\) −18.0000 −0.870063
\(429\) 3.00000 0.144841
\(430\) 0 0
\(431\) 7.00000 0.337178 0.168589 − 0.985686i \(-0.446079\pi\)
0.168589 + 0.985686i \(0.446079\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −4.00000 −0.192228 −0.0961139 − 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 3.00000 0.144005
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −2.00000 −0.0951303
\(443\) 36.0000 1.71041 0.855206 − 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 3.00000 0.142374
\(445\) 0 0
\(446\) −6.00000 −0.284108
\(447\) 20.0000 0.945968
\(448\) −3.00000 −0.141737
\(449\) 20.0000 0.943858 0.471929 − 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 0 0
\(451\) −21.0000 −0.988851
\(452\) 6.00000 0.282216
\(453\) 18.0000 0.845714
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) −8.00000 −0.374224 −0.187112 − 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) −10.0000 −0.467269
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) −3.00000 −0.139724 −0.0698620 − 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) 9.00000 0.418718
\(463\) −14.0000 −0.650635 −0.325318 − 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 9.00000 0.416917
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 1.00000 0.0462250
\(469\) −6.00000 −0.277054
\(470\) 0 0
\(471\) −22.0000 −1.01371
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) −10.0000 −0.459315
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) −9.00000 −0.412082
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −3.00000 −0.136788
\(482\) −12.0000 −0.546585
\(483\) −12.0000 −0.546019
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −28.0000 −1.26880 −0.634401 − 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) −7.00000 −0.316875
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 − 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) −7.00000 −0.315584
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) −21.0000 −0.941979
\(498\) −9.00000 −0.403300
\(499\) −20.0000 −0.895323 −0.447661 − 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) −2.00000 −0.0893534
\(502\) 3.00000 0.133897
\(503\) 11.0000 0.490466 0.245233 − 0.969464i \(-0.421136\pi\)
0.245233 + 0.969464i \(0.421136\pi\)
\(504\) 3.00000 0.133631
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) 12.0000 0.532939
\(508\) 2.00000 0.0887357
\(509\) −15.0000 −0.664863 −0.332432 − 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −7.00000 −0.308757
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) −21.0000 −0.923579
\(518\) −9.00000 −0.395437
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) −33.0000 −1.44576 −0.722878 − 0.690976i \(-0.757181\pi\)
−0.722878 + 0.690976i \(0.757181\pi\)
\(522\) −10.0000 −0.437688
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) 2.00000 0.0871214
\(528\) 3.00000 0.130558
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7.00000 0.303204
\(534\) 10.0000 0.432742
\(535\) 0 0
\(536\) −2.00000 −0.0863868
\(537\) 5.00000 0.215766
\(538\) 10.0000 0.431131
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 − 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 8.00000 0.343629
\(543\) 13.0000 0.557883
\(544\) −2.00000 −0.0857493
\(545\) 0 0
\(546\) −3.00000 −0.128388
\(547\) 22.0000 0.940652 0.470326 − 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) 2.00000 0.0854358
\(549\) 7.00000 0.298753
\(550\) 0 0
\(551\) 0 0
\(552\) −4.00000 −0.170251
\(553\) 30.0000 1.27573
\(554\) 18.0000 0.764747
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) 2.00000 0.0847427 0.0423714 − 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) −1.00000 −0.0423334
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) −7.00000 −0.295277
\(563\) −34.0000 −1.43293 −0.716465 − 0.697623i \(-0.754241\pi\)
−0.716465 + 0.697623i \(0.754241\pi\)
\(564\) −7.00000 −0.294753
\(565\) 0 0
\(566\) 24.0000 1.00880
\(567\) −3.00000 −0.125988
\(568\) −7.00000 −0.293713
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −23.0000 −0.962520 −0.481260 − 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) −3.00000 −0.125436
\(573\) 8.00000 0.334205
\(574\) 21.0000 0.876523
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 22.0000 0.915872 0.457936 − 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 13.0000 0.540729
\(579\) 9.00000 0.374027
\(580\) 0 0
\(581\) 27.0000 1.12015
\(582\) 2.00000 0.0829027
\(583\) 27.0000 1.11823
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 24.0000 0.991431
\(587\) 17.0000 0.701665 0.350833 − 0.936438i \(-0.385899\pi\)
0.350833 + 0.936438i \(0.385899\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) 0 0
\(591\) −27.0000 −1.11063
\(592\) −3.00000 −0.123299
\(593\) 1.00000 0.0410651 0.0205325 − 0.999789i \(-0.493464\pi\)
0.0205325 + 0.999789i \(0.493464\pi\)
\(594\) −3.00000 −0.123091
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 20.0000 0.818546
\(598\) 4.00000 0.163572
\(599\) −15.0000 −0.612883 −0.306442 − 0.951889i \(-0.599138\pi\)
−0.306442 + 0.951889i \(0.599138\pi\)
\(600\) 0 0
\(601\) 12.0000 0.489490 0.244745 − 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 3.00000 0.122271
\(603\) 2.00000 0.0814463
\(604\) −18.0000 −0.732410
\(605\) 0 0
\(606\) 2.00000 0.0812444
\(607\) −43.0000 −1.74532 −0.872658 − 0.488332i \(-0.837606\pi\)
−0.872658 + 0.488332i \(0.837606\pi\)
\(608\) 0 0
\(609\) 30.0000 1.21566
\(610\) 0 0
\(611\) 7.00000 0.283190
\(612\) 2.00000 0.0808452
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) −22.0000 −0.887848
\(615\) 0 0
\(616\) −9.00000 −0.362620
\(617\) −3.00000 −0.120775 −0.0603877 − 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 1.00000 0.0402259
\(619\) −5.00000 −0.200967 −0.100483 − 0.994939i \(-0.532039\pi\)
−0.100483 + 0.994939i \(0.532039\pi\)
\(620\) 0 0
\(621\) 4.00000 0.160514
\(622\) −27.0000 −1.08260
\(623\) −30.0000 −1.20192
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) 24.0000 0.959233
\(627\) 0 0
\(628\) 22.0000 0.877896
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 − 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 10.0000 0.397779
\(633\) −2.00000 −0.0794929
\(634\) −22.0000 −0.873732
\(635\) 0 0
\(636\) 9.00000 0.356873
\(637\) 2.00000 0.0792429
\(638\) 30.0000 1.18771
\(639\) 7.00000 0.276916
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 − 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) −18.0000 −0.710403
\(643\) 31.0000 1.22252 0.611260 − 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 12.0000 0.472866
\(645\) 0 0
\(646\) 0 0
\(647\) 42.0000 1.65119 0.825595 − 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 3.00000 0.117579
\(652\) −4.00000 −0.156652
\(653\) 16.0000 0.626128 0.313064 − 0.949732i \(-0.398644\pi\)
0.313064 + 0.949732i \(0.398644\pi\)
\(654\) −10.0000 −0.391031
\(655\) 0 0
\(656\) 7.00000 0.273304
\(657\) −4.00000 −0.156055
\(658\) 21.0000 0.818665
\(659\) −40.0000 −1.55818 −0.779089 − 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) −38.0000 −1.47803 −0.739014 − 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 3.00000 0.116598
\(663\) −2.00000 −0.0776736
\(664\) 9.00000 0.349268
\(665\) 0 0
\(666\) 3.00000 0.116248
\(667\) −40.0000 −1.54881
\(668\) 2.00000 0.0773823
\(669\) −6.00000 −0.231973
\(670\) 0 0
\(671\) −21.0000 −0.810696
\(672\) −3.00000 −0.115728
\(673\) 26.0000 1.00223 0.501113 − 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 27.0000 1.03769 0.518847 − 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(678\) 6.00000 0.230429
\(679\) −6.00000 −0.230259
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 3.00000 0.114876
\(683\) 26.0000 0.994862 0.497431 − 0.867503i \(-0.334277\pi\)
0.497431 + 0.867503i \(0.334277\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −15.0000 −0.572703
\(687\) −10.0000 −0.381524
\(688\) 1.00000 0.0381246
\(689\) −9.00000 −0.342873
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −4.00000 −0.152057
\(693\) 9.00000 0.341882
\(694\) −7.00000 −0.265716
\(695\) 0 0
\(696\) 10.0000 0.379049
\(697\) 14.0000 0.530288
\(698\) 0 0
\(699\) 9.00000 0.340411
\(700\) 0 0
\(701\) −48.0000 −1.81293 −0.906467 − 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 1.00000 0.0377426
\(703\) 0 0
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) 50.0000 1.87779 0.938895 − 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) −10.0000 −0.374766
\(713\) −4.00000 −0.149801
\(714\) −6.00000 −0.224544
\(715\) 0 0
\(716\) −5.00000 −0.186859
\(717\) 0 0
\(718\) 0 0
\(719\) 50.0000 1.86469 0.932343 − 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) 19.0000 0.707107
\(723\) −12.0000 −0.446285
\(724\) −13.0000 −0.483141
\(725\) 0 0
\(726\) −2.00000 −0.0742270
\(727\) 27.0000 1.00137 0.500687 − 0.865628i \(-0.333081\pi\)
0.500687 + 0.865628i \(0.333081\pi\)
\(728\) 3.00000 0.111187
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.00000 0.0739727
\(732\) −7.00000 −0.258727
\(733\) 36.0000 1.32969 0.664845 − 0.746981i \(-0.268498\pi\)
0.664845 + 0.746981i \(0.268498\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −6.00000 −0.221013
\(738\) −7.00000 −0.257674
\(739\) −20.0000 −0.735712 −0.367856 − 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −27.0000 −0.991201
\(743\) −4.00000 −0.146746 −0.0733729 − 0.997305i \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) 1.00000 0.0366618
\(745\) 0 0
\(746\) 24.0000 0.878702
\(747\) −9.00000 −0.329293
\(748\) −6.00000 −0.219382
\(749\) 54.0000 1.97312
\(750\) 0 0
\(751\) 7.00000 0.255434 0.127717 − 0.991811i \(-0.459235\pi\)
0.127717 + 0.991811i \(0.459235\pi\)
\(752\) 7.00000 0.255264
\(753\) 3.00000 0.109326
\(754\) −10.0000 −0.364179
\(755\) 0 0
\(756\) 3.00000 0.109109
\(757\) −13.0000 −0.472493 −0.236247 − 0.971693i \(-0.575917\pi\)
−0.236247 + 0.971693i \(0.575917\pi\)
\(758\) 0 0
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) 12.0000 0.435000 0.217500 − 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 2.00000 0.0724524
\(763\) 30.0000 1.08607
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −45.0000 −1.62274 −0.811371 − 0.584532i \(-0.801278\pi\)
−0.811371 + 0.584532i \(0.801278\pi\)
\(770\) 0 0
\(771\) −7.00000 −0.252099
\(772\) −9.00000 −0.323917
\(773\) −34.0000 −1.22290 −0.611448 − 0.791285i \(-0.709412\pi\)
−0.611448 + 0.791285i \(0.709412\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) −9.00000 −0.322873
\(778\) −10.0000 −0.358517
\(779\) 0 0
\(780\) 0 0
\(781\) −21.0000 −0.751439
\(782\) 8.00000 0.286079
\(783\) −10.0000 −0.357371
\(784\) 2.00000 0.0714286
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) 7.00000 0.249523 0.124762 − 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(788\) 27.0000 0.961835
\(789\) −6.00000 −0.213606
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) 3.00000 0.106600
\(793\) 7.00000 0.248577
\(794\) 28.0000 0.993683
\(795\) 0 0
\(796\) −20.0000 −0.708881
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 14.0000 0.495284
\(800\) 0 0
\(801\) 10.0000 0.353333
\(802\) 8.00000 0.282490
\(803\) 12.0000 0.423471
\(804\) −2.00000 −0.0705346
\(805\) 0 0
\(806\) −1.00000 −0.0352235
\(807\) 10.0000 0.352017
\(808\) −2.00000 −0.0703598
\(809\) −10.0000 −0.351581 −0.175791 − 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 − 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) −30.0000 −1.05279
\(813\) 8.00000 0.280572
\(814\) −9.00000 −0.315450
\(815\) 0 0
\(816\) −2.00000 −0.0700140
\(817\) 0 0
\(818\) 10.0000 0.349642
\(819\) −3.00000 −0.104828
\(820\) 0 0
\(821\) −53.0000 −1.84971 −0.924856 − 0.380317i \(-0.875815\pi\)
−0.924856 + 0.380317i \(0.875815\pi\)
\(822\) 2.00000 0.0697580
\(823\) −24.0000 −0.836587 −0.418294 − 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 0 0
\(826\) 0 0
\(827\) −28.0000 −0.973655 −0.486828 − 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) −4.00000 −0.139010
\(829\) 55.0000 1.91023 0.955114 − 0.296237i \(-0.0957318\pi\)
0.955114 + 0.296237i \(0.0957318\pi\)
\(830\) 0 0
\(831\) 18.0000 0.624413
\(832\) 1.00000 0.0346688
\(833\) 4.00000 0.138592
\(834\) −5.00000 −0.173136
\(835\) 0 0
\(836\) 0 0
\(837\) −1.00000 −0.0345651
\(838\) 30.0000 1.03633
\(839\) 15.0000 0.517858 0.258929 − 0.965896i \(-0.416631\pi\)
0.258929 + 0.965896i \(0.416631\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 28.0000 0.964944
\(843\) −7.00000 −0.241093
\(844\) 2.00000 0.0688428
\(845\) 0 0
\(846\) −7.00000 −0.240665
\(847\) 6.00000 0.206162
\(848\) −9.00000 −0.309061
\(849\) 24.0000 0.823678
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) −7.00000 −0.239816
\(853\) 16.0000 0.547830 0.273915 − 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 21.0000 0.718605
\(855\) 0 0
\(856\) 18.0000 0.615227
\(857\) −3.00000 −0.102478 −0.0512390 − 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) −3.00000 −0.102418
\(859\) −25.0000 −0.852989 −0.426494 − 0.904490i \(-0.640252\pi\)
−0.426494 + 0.904490i \(0.640252\pi\)
\(860\) 0 0
\(861\) 21.0000 0.715678
\(862\) −7.00000 −0.238421
\(863\) 46.0000 1.56586 0.782929 − 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 4.00000 0.135926
\(867\) 13.0000 0.441503
\(868\) −3.00000 −0.101827
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) 2.00000 0.0677674
\(872\) 10.0000 0.338643
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) −8.00000 −0.270141 −0.135070 − 0.990836i \(-0.543126\pi\)
−0.135070 + 0.990836i \(0.543126\pi\)
\(878\) 0 0
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) 32.0000 1.07811 0.539054 − 0.842271i \(-0.318782\pi\)
0.539054 + 0.842271i \(0.318782\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 11.0000 0.370179 0.185090 − 0.982722i \(-0.440742\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(884\) 2.00000 0.0672673
\(885\) 0 0
\(886\) −36.0000 −1.20944
\(887\) −13.0000 −0.436497 −0.218249 − 0.975893i \(-0.570034\pi\)
−0.218249 + 0.975893i \(0.570034\pi\)
\(888\) −3.00000 −0.100673
\(889\) −6.00000 −0.201234
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 6.00000 0.200895
\(893\) 0 0
\(894\) −20.0000 −0.668900
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) 4.00000 0.133556
\(898\) −20.0000 −0.667409
\(899\) 10.0000 0.333519
\(900\) 0 0
\(901\) −18.0000 −0.599667
\(902\) 21.0000 0.699224
\(903\) 3.00000 0.0998337
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) −18.0000 −0.598010
\(907\) 32.0000 1.06254 0.531271 − 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 12.0000 0.398234
\(909\) 2.00000 0.0663358
\(910\) 0 0
\(911\) 32.0000 1.06021 0.530104 − 0.847933i \(-0.322153\pi\)
0.530104 + 0.847933i \(0.322153\pi\)
\(912\) 0 0
\(913\) 27.0000 0.893570
\(914\) 8.00000 0.264616
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) −36.0000 −1.18882
\(918\) 2.00000 0.0660098
\(919\) 25.0000 0.824674 0.412337 − 0.911031i \(-0.364713\pi\)
0.412337 + 0.911031i \(0.364713\pi\)
\(920\) 0 0
\(921\) −22.0000 −0.724925
\(922\) 3.00000 0.0987997
\(923\) 7.00000 0.230408
\(924\) −9.00000 −0.296078
\(925\) 0 0
\(926\) 14.0000 0.460069
\(927\) 1.00000 0.0328443
\(928\) −10.0000 −0.328266
\(929\) 40.0000 1.31236 0.656179 − 0.754606i \(-0.272172\pi\)
0.656179 + 0.754606i \(0.272172\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −9.00000 −0.294805
\(933\) −27.0000 −0.883940
\(934\) 18.0000 0.588978
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) 2.00000 0.0653372 0.0326686 − 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 6.00000 0.195907
\(939\) 24.0000 0.783210
\(940\) 0 0
\(941\) −38.0000 −1.23876 −0.619382 − 0.785090i \(-0.712617\pi\)
−0.619382 + 0.785090i \(0.712617\pi\)
\(942\) 22.0000 0.716799
\(943\) −28.0000 −0.911805
\(944\) 0 0
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) −3.00000 −0.0974869 −0.0487435 − 0.998811i \(-0.515522\pi\)
−0.0487435 + 0.998811i \(0.515522\pi\)
\(948\) 10.0000 0.324785
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) −22.0000 −0.713399
\(952\) 6.00000 0.194461
\(953\) −34.0000 −1.10137 −0.550684 − 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) 9.00000 0.291386
\(955\) 0 0
\(956\) 0 0
\(957\) 30.0000 0.969762
\(958\) 0 0
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 3.00000 0.0967239
\(963\) −18.0000 −0.580042
\(964\) 12.0000 0.386494
\(965\) 0 0
\(966\) 12.0000 0.386094
\(967\) −18.0000 −0.578841 −0.289420 − 0.957202i \(-0.593463\pi\)
−0.289420 + 0.957202i \(0.593463\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 − 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 15.0000 0.480878
\(974\) 28.0000 0.897178
\(975\) 0 0
\(976\) 7.00000 0.224065
\(977\) −13.0000 −0.415907 −0.207953 − 0.978139i \(-0.566680\pi\)
−0.207953 + 0.978139i \(0.566680\pi\)
\(978\) −4.00000 −0.127906
\(979\) −30.0000 −0.958804
\(980\) 0 0
\(981\) −10.0000 −0.319275
\(982\) 28.0000 0.893516
\(983\) 16.0000 0.510321 0.255160 − 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) 7.00000 0.223152
\(985\) 0 0
\(986\) −20.0000 −0.636930
\(987\) 21.0000 0.668437
\(988\) 0 0
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 − 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 3.00000 0.0952021
\(994\) 21.0000 0.666080
\(995\) 0 0
\(996\) 9.00000 0.285176
\(997\) 42.0000 1.33015 0.665077 − 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) 20.0000 0.633089
\(999\) 3.00000 0.0949158
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 4650.2.a.b.1.1 ✓ 1
5.2 odd 4 4650.2.d.q.3349.1 2
5.3 odd 4 4650.2.d.q.3349.2 2
5.4 even 2 4650.2.a.bu.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4650.2.a.b.1.1 ✓ 1 1.1 even 1 trivial
4650.2.a.bu.1.1 yes 1 5.4 even 2
4650.2.d.q.3349.1 2 5.2 odd 4
4650.2.d.q.3349.2 2 5.3 odd 4