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Properties

Label 3950.2.a.g.1.1
Level $3950$
Weight $2$
Character 3950.1
Self dual yes
Analytic conductor $31.541$
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] = [3950,2,Mod(1,3950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3950, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3950.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3950 = 2 \cdot 5^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3950.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: \(31.5409087984\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 158)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3950.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{12} -5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{18} +2.00000 q^{19} -1.00000 q^{21} +6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -4.00000 q^{31} +1.00000 q^{32} -2.00000 q^{36} -2.00000 q^{37} +2.00000 q^{38} +5.00000 q^{39} -12.0000 q^{41} -1.00000 q^{42} -8.00000 q^{43} +6.00000 q^{46} +9.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} -5.00000 q^{52} -6.00000 q^{53} +5.00000 q^{54} +1.00000 q^{56} -2.00000 q^{57} -9.00000 q^{59} +8.00000 q^{61} -4.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{67} -6.00000 q^{69} -9.00000 q^{71} -2.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} +2.00000 q^{76} +5.00000 q^{78} +1.00000 q^{79} +1.00000 q^{81} -12.0000 q^{82} -18.0000 q^{83} -1.00000 q^{84} -8.00000 q^{86} +9.00000 q^{89} -5.00000 q^{91} +6.00000 q^{92} +4.00000 q^{93} +9.00000 q^{94} -1.00000 q^{96} -17.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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 −0.288675 − 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) −5.00000 −1.38675 −0.693375 − 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −2.00000 −0.471405
\(19\) 2.00000 0.458831 0.229416 − 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −5.00000 −0.980581
\(27\) 5.00000 0.962250
\(28\) 1.00000 0.188982
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 2.00000 0.324443
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 − 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) −1.00000 −0.154303
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 9.00000 1.31278 0.656392 − 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) −5.00000 −0.693375
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −9.00000 −1.17170 −0.585850 − 0.810419i \(-0.699239\pi\)
−0.585850 + 0.810419i \(0.699239\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 − 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −4.00000 −0.508001
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 − 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −2.00000 −0.235702
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) −18.0000 −1.97576 −0.987878 − 0.155230i \(-0.950388\pi\)
−0.987878 + 0.155230i \(0.950388\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) 9.00000 0.953998 0.476999 − 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.524142
\(92\) 6.00000 0.625543
\(93\) 4.00000 0.414781
\(94\) 9.00000 0.928279
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −17.0000 −1.72609 −0.863044 − 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 0 0
\(101\) −15.0000 −1.49256 −0.746278 − 0.665635i \(-0.768161\pi\)
−0.746278 + 0.665635i \(0.768161\pi\)
\(102\) 0 0
\(103\) 13.0000 1.28093 0.640464 − 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −3.00000 −0.290021 −0.145010 − 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 5.00000 0.481125
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 1.00000 0.0944911
\(113\) −18.0000 −1.69330 −0.846649 − 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) 0 0
\(117\) 10.0000 0.924500
\(118\) −9.00000 −0.828517
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 8.00000 0.724286
\(123\) 12.0000 1.08200
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) 7.00000 0.621150 0.310575 − 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) −6.00000 −0.510754
\(139\) 5.00000 0.424094 0.212047 − 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) −9.00000 −0.757937
\(142\) −9.00000 −0.755263
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 6.00000 0.494872
\(148\) −2.00000 −0.164399
\(149\) 12.0000 0.983078 0.491539 − 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 − 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) 4.00000 0.319235 0.159617 − 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 1.00000 0.0795557
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 1.00000 0.0785674
\(163\) −20.0000 −1.56652 −0.783260 − 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) −18.0000 −1.39707
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) −8.00000 −0.609994
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.00000 0.676481
\(178\) 9.00000 0.674579
\(179\) 18.0000 1.34538 0.672692 − 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 − 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −5.00000 −0.370625
\(183\) −8.00000 −0.591377
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) 4.00000 0.293294
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 − 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 22.0000 1.58359 0.791797 − 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −17.0000 −1.22053
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 − 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) −15.0000 −1.05540
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 13.0000 0.905753
\(207\) −12.0000 −0.834058
\(208\) −5.00000 −0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 − 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −6.00000 −0.412082
\(213\) 9.00000 0.616670
\(214\) −3.00000 −0.205076
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) −4.00000 −0.271538
\(218\) 2.00000 0.135457
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 0 0
\(222\) 2.00000 0.134231
\(223\) −26.0000 −1.74109 −0.870544 − 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −18.0000 −1.19734
\(227\) −12.0000 −0.796468 −0.398234 − 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) −2.00000 −0.132453
\(229\) −22.0000 −1.45380 −0.726900 − 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.0000 0.786146 0.393073 − 0.919507i \(-0.371412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(234\) 10.0000 0.653720
\(235\) 0 0
\(236\) −9.00000 −0.585850
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 − 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 − 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −11.0000 −0.707107
\(243\) −16.0000 −1.02640
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) −10.0000 −0.636285
\(248\) −4.00000 −0.254000
\(249\) 18.0000 1.14070
\(250\) 0 0
\(251\) −27.0000 −1.70422 −0.852112 − 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 7.00000 0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 8.00000 0.498058
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 18.0000 1.10993 0.554964 − 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.00000 0.122628
\(267\) −9.00000 −0.550791
\(268\) 4.00000 0.244339
\(269\) −21.0000 −1.28039 −0.640196 − 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 5.00000 0.302614
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) −17.0000 −1.02143 −0.510716 − 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 5.00000 0.299880
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 15.0000 0.894825 0.447412 − 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) −9.00000 −0.535942
\(283\) −14.0000 −0.832214 −0.416107 − 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) −9.00000 −0.534052
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) −2.00000 −0.117851
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) −2.00000 −0.117041
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 6.00000 0.349927
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) −30.0000 −1.73494
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 8.00000 0.460348
\(303\) 15.0000 0.861727
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 − 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 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
\(313\) 10.0000 0.565233 0.282617 − 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) 15.0000 0.842484 0.421242 − 0.906948i \(-0.361594\pi\)
0.421242 + 0.906948i \(0.361594\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) 3.00000 0.167444
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) −2.00000 −0.110600
\(328\) −12.0000 −0.662589
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −18.0000 −0.987878
\(333\) 4.00000 0.219199
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) 13.0000 0.708155 0.354078 − 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 12.0000 0.652714
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) −13.0000 −0.701934
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 6.00000 0.322097 0.161048 − 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 − 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) −25.0000 −1.33440
\(352\) 0 0
\(353\) −24.0000 −1.27739 −0.638696 − 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 9.00000 0.478345
\(355\) 0 0
\(356\) 9.00000 0.476999
\(357\) 0 0
\(358\) 18.0000 0.951330
\(359\) −15.0000 −0.791670 −0.395835 − 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 2.00000 0.105118
\(363\) 11.0000 0.577350
\(364\) −5.00000 −0.262071
\(365\) 0 0
\(366\) −8.00000 −0.418167
\(367\) 28.0000 1.46159 0.730794 − 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) 6.00000 0.312772
\(369\) 24.0000 1.24939
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 4.00000 0.207390
\(373\) 22.0000 1.13912 0.569558 − 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 9.00000 0.464140
\(377\) 0 0
\(378\) 5.00000 0.257172
\(379\) 11.0000 0.565032 0.282516 − 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) −7.00000 −0.358621
\(382\) −15.0000 −0.767467
\(383\) −6.00000 −0.306586 −0.153293 − 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) 16.0000 0.813326
\(388\) −17.0000 −0.863044
\(389\) 9.00000 0.456318 0.228159 − 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) −6.00000 −0.302660
\(394\) −6.00000 −0.302276
\(395\) 0 0
\(396\) 0 0
\(397\) 7.00000 0.351320 0.175660 − 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(398\) 11.0000 0.551380
\(399\) −2.00000 −0.100125
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 − 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) −4.00000 −0.199502
\(403\) 20.0000 0.996271
\(404\) −15.0000 −0.746278
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 13.0000 0.640464
\(413\) −9.00000 −0.442861
\(414\) −12.0000 −0.589768
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) −5.00000 −0.244851
\(418\) 0 0
\(419\) 27.0000 1.31904 0.659518 − 0.751689i \(-0.270760\pi\)
0.659518 + 0.751689i \(0.270760\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 − 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) −4.00000 −0.194717
\(423\) −18.0000 −0.875190
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 9.00000 0.436051
\(427\) 8.00000 0.387147
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 −0.289010 −0.144505 − 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) 5.00000 0.240563
\(433\) −29.0000 −1.39365 −0.696826 − 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 12.0000 0.574038
\(438\) 2.00000 0.0955637
\(439\) 26.0000 1.24091 0.620456 − 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 − 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) −12.0000 −0.567581
\(448\) 1.00000 0.0472456
\(449\) 12.0000 0.566315 0.283158 − 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −18.0000 −0.846649
\(453\) −8.00000 −0.375873
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 37.0000 1.73079 0.865393 − 0.501093i \(-0.167069\pi\)
0.865393 + 0.501093i \(0.167069\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) 0 0
\(461\) 42.0000 1.95614 0.978068 − 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 0 0
\(463\) −41.0000 −1.90543 −0.952716 − 0.303863i \(-0.901724\pi\)
−0.952716 + 0.303863i \(0.901724\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 12.0000 0.555889
\(467\) −6.00000 −0.277647 −0.138823 − 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 10.0000 0.462250
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) −4.00000 −0.184310
\(472\) −9.00000 −0.414259
\(473\) 0 0
\(474\) −1.00000 −0.0459315
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 18.0000 0.823301
\(479\) −18.0000 −0.822441 −0.411220 − 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 17.0000 0.774329
\(483\) −6.00000 −0.273009
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) −16.0000 −0.725775
\(487\) 16.0000 0.725029 0.362515 − 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 8.00000 0.362143
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 − 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 12.0000 0.541002
\(493\) 0 0
\(494\) −10.0000 −0.449921
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −9.00000 −0.403705
\(498\) 18.0000 0.806599
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) −27.0000 −1.20507
\(503\) 21.0000 0.936344 0.468172 − 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 7.00000 0.310575
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 10.0000 0.441511
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) −2.00000 −0.0878750
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 − 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) 0 0
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 2.00000 0.0867110
\(533\) 60.0000 2.59889
\(534\) −9.00000 −0.389468
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −18.0000 −0.776757
\(538\) −21.0000 −0.905374
\(539\) 0 0
\(540\) 0 0
\(541\) 29.0000 1.24681 0.623404 − 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −16.0000 −0.687259
\(543\) −2.00000 −0.0858282
\(544\) 0 0
\(545\) 0 0
\(546\) 5.00000 0.213980
\(547\) −26.0000 −1.11168 −0.555840 − 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) −12.0000 −0.512615
\(549\) −16.0000 −0.682863
\(550\) 0 0
\(551\) 0 0
\(552\) −6.00000 −0.255377
\(553\) 1.00000 0.0425243
\(554\) −17.0000 −0.722261
\(555\) 0 0
\(556\) 5.00000 0.212047
\(557\) −15.0000 −0.635570 −0.317785 − 0.948163i \(-0.602939\pi\)
−0.317785 + 0.948163i \(0.602939\pi\)
\(558\) 8.00000 0.338667
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 15.0000 0.632737
\(563\) 12.0000 0.505740 0.252870 − 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) −9.00000 −0.378968
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 1.00000 0.0419961
\(568\) −9.00000 −0.377632
\(569\) 6.00000 0.251533 0.125767 − 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 − 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 15.0000 0.626634
\(574\) −12.0000 −0.500870
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) 34.0000 1.41544 0.707719 − 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) −17.0000 −0.707107
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) 17.0000 0.704673
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 21.0000 0.866763 0.433381 − 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) 6.00000 0.247436
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) −2.00000 −0.0821995
\(593\) 21.0000 0.862367 0.431183 − 0.902264i \(-0.358096\pi\)
0.431183 + 0.902264i \(0.358096\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −11.0000 −0.450200
\(598\) −30.0000 −1.22679
\(599\) 6.00000 0.245153 0.122577 − 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 − 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) −8.00000 −0.326056
\(603\) −8.00000 −0.325785
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 15.0000 0.609333
\(607\) −5.00000 −0.202944 −0.101472 − 0.994838i \(-0.532355\pi\)
−0.101472 + 0.994838i \(0.532355\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −45.0000 −1.82051
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) 39.0000 1.57008 0.785040 − 0.619445i \(-0.212642\pi\)
0.785040 + 0.619445i \(0.212642\pi\)
\(618\) −13.0000 −0.522937
\(619\) −1.00000 −0.0401934 −0.0200967 − 0.999798i \(-0.506397\pi\)
−0.0200967 + 0.999798i \(0.506397\pi\)
\(620\) 0 0
\(621\) 30.0000 1.20386
\(622\) 12.0000 0.481156
\(623\) 9.00000 0.360577
\(624\) 5.00000 0.200160
\(625\) 0 0
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 0 0
\(630\) 0 0
\(631\) −43.0000 −1.71180 −0.855901 − 0.517139i \(-0.826997\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) 1.00000 0.0397779
\(633\) 4.00000 0.158986
\(634\) 15.0000 0.595726
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 30.0000 1.18864
\(638\) 0 0
\(639\) 18.0000 0.712069
\(640\) 0 0
\(641\) 27.0000 1.06644 0.533218 − 0.845978i \(-0.320983\pi\)
0.533218 + 0.845978i \(0.320983\pi\)
\(642\) 3.00000 0.118401
\(643\) −14.0000 −0.552106 −0.276053 − 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 6.00000 0.236433
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) −20.0000 −0.783260
\(653\) 21.0000 0.821794 0.410897 − 0.911682i \(-0.365216\pi\)
0.410897 + 0.911682i \(0.365216\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 0 0
\(656\) −12.0000 −0.468521
\(657\) 4.00000 0.156055
\(658\) 9.00000 0.350857
\(659\) 21.0000 0.818044 0.409022 − 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 − 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 8.00000 0.310929
\(663\) 0 0
\(664\) −18.0000 −0.698535
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 28.0000 1.07932 0.539660 − 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 13.0000 0.500741
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −15.0000 −0.576497 −0.288248 − 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 18.0000 0.691286
\(679\) −17.0000 −0.652400
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −30.0000 −1.14792 −0.573959 − 0.818884i \(-0.694593\pi\)
−0.573959 + 0.818884i \(0.694593\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) 22.0000 0.839352
\(688\) −8.00000 −0.304997
\(689\) 30.0000 1.14291
\(690\) 0 0
\(691\) 35.0000 1.33146 0.665731 − 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −28.0000 −1.05982
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −25.0000 −0.943564
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) −15.0000 −0.564133
\(708\) 9.00000 0.338241
\(709\) −10.0000 −0.375558 −0.187779 − 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) −2.00000 −0.0750059
\(712\) 9.00000 0.337289
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) 18.0000 0.672692
\(717\) −18.0000 −0.672222
\(718\) −15.0000 −0.559795
\(719\) −18.0000 −0.671287 −0.335643 − 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) 13.0000 0.484145
\(722\) −15.0000 −0.558242
\(723\) −17.0000 −0.632237
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 11.0000 0.408248
\(727\) 28.0000 1.03846 0.519231 − 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) −5.00000 −0.185312
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) −8.00000 −0.295689
\(733\) −50.0000 −1.84679 −0.923396 − 0.383849i \(-0.874598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 24.0000 0.883452
\(739\) −43.0000 −1.58178 −0.790890 − 0.611958i \(-0.790382\pi\)
−0.790890 + 0.611958i \(0.790382\pi\)
\(740\) 0 0
\(741\) 10.0000 0.367359
\(742\) −6.00000 −0.220267
\(743\) 6.00000 0.220119 0.110059 − 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 4.00000 0.146647
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 36.0000 1.31717
\(748\) 0 0
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) 50.0000 1.82453 0.912263 − 0.409605i \(-0.134333\pi\)
0.912263 + 0.409605i \(0.134333\pi\)
\(752\) 9.00000 0.328196
\(753\) 27.0000 0.983935
\(754\) 0 0
\(755\) 0 0
\(756\) 5.00000 0.181848
\(757\) −29.0000 −1.05402 −0.527011 − 0.849858i \(-0.676688\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 11.0000 0.399538
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000 1.08750 0.543750 − 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) −7.00000 −0.253583
\(763\) 2.00000 0.0724049
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 45.0000 1.62486
\(768\) −1.00000 −0.0360844
\(769\) 14.0000 0.504853 0.252426 − 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 22.0000 0.791797
\(773\) 18.0000 0.647415 0.323708 − 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 16.0000 0.575108
\(775\) 0 0
\(776\) −17.0000 −0.610264
\(777\) 2.00000 0.0717496
\(778\) 9.00000 0.322666
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) −6.00000 −0.214013
\(787\) 4.00000 0.142585 0.0712923 − 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) −6.00000 −0.213741
\(789\) −18.0000 −0.640817
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) −40.0000 −1.42044
\(794\) 7.00000 0.248421
\(795\) 0 0
\(796\) 11.0000 0.389885
\(797\) 42.0000 1.48772 0.743858 − 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 0 0
\(800\) 0 0
\(801\) −18.0000 −0.635999
\(802\) −6.00000 −0.211867
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 20.0000 0.704470
\(807\) 21.0000 0.739235
\(808\) −15.0000 −0.527698
\(809\) 15.0000 0.527372 0.263686 − 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) −22.0000 −0.769212
\(819\) 10.0000 0.349428
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 − 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 12.0000 0.418548
\(823\) 40.0000 1.39431 0.697156 − 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) 13.0000 0.452876
\(825\) 0 0
\(826\) −9.00000 −0.313150
\(827\) −21.0000 −0.730242 −0.365121 − 0.930960i \(-0.618972\pi\)
−0.365121 + 0.930960i \(0.618972\pi\)
\(828\) −12.0000 −0.417029
\(829\) −16.0000 −0.555703 −0.277851 − 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) 17.0000 0.589723
\(832\) −5.00000 −0.173344
\(833\) 0 0
\(834\) −5.00000 −0.173136
\(835\) 0 0
\(836\) 0 0
\(837\) −20.0000 −0.691301
\(838\) 27.0000 0.932700
\(839\) −48.0000 −1.65714 −0.828572 − 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 17.0000 0.585859
\(843\) −15.0000 −0.516627
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) −18.0000 −0.618853
\(847\) −11.0000 −0.377964
\(848\) −6.00000 −0.206041
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 9.00000 0.308335
\(853\) −26.0000 −0.890223 −0.445112 − 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 8.00000 0.273754
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) −21.0000 −0.717346 −0.358673 − 0.933463i \(-0.616771\pi\)
−0.358673 + 0.933463i \(0.616771\pi\)
\(858\) 0 0
\(859\) 23.0000 0.784750 0.392375 − 0.919805i \(-0.371654\pi\)
0.392375 + 0.919805i \(0.371654\pi\)
\(860\) 0 0
\(861\) 12.0000 0.408959
\(862\) −6.00000 −0.204361
\(863\) −24.0000 −0.816970 −0.408485 − 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 5.00000 0.170103
\(865\) 0 0
\(866\) −29.0000 −0.985460
\(867\) 17.0000 0.577350
\(868\) −4.00000 −0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) 2.00000 0.0677285
\(873\) 34.0000 1.15073
\(874\) 12.0000 0.405906
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −14.0000 −0.472746 −0.236373 − 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 26.0000 0.877457
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 − 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 12.0000 0.404061
\(883\) −29.0000 −0.975928 −0.487964 − 0.872864i \(-0.662260\pi\)
−0.487964 + 0.872864i \(0.662260\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 36.0000 1.20944
\(887\) 12.0000 0.402921 0.201460 − 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 2.00000 0.0671156
\(889\) 7.00000 0.234772
\(890\) 0 0
\(891\) 0 0
\(892\) −26.0000 −0.870544
\(893\) 18.0000 0.602347
\(894\) −12.0000 −0.401340
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 30.0000 1.00167
\(898\) 12.0000 0.400445
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 8.00000 0.266223
\(904\) −18.0000 −0.598671
\(905\) 0 0
\(906\) −8.00000 −0.265782
\(907\) 10.0000 0.332045 0.166022 − 0.986122i \(-0.446908\pi\)
0.166022 + 0.986122i \(0.446908\pi\)
\(908\) −12.0000 −0.398234
\(909\) 30.0000 0.995037
\(910\) 0 0
\(911\) 42.0000 1.39152 0.695761 − 0.718273i \(-0.255067\pi\)
0.695761 + 0.718273i \(0.255067\pi\)
\(912\) −2.00000 −0.0662266
\(913\) 0 0
\(914\) 37.0000 1.22385
\(915\) 0 0
\(916\) −22.0000 −0.726900
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) 42.0000 1.38320
\(923\) 45.0000 1.48119
\(924\) 0 0
\(925\) 0 0
\(926\) −41.0000 −1.34734
\(927\) −26.0000 −0.853952
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 − 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) −12.0000 −0.393284
\(932\) 12.0000 0.393073
\(933\) −12.0000 −0.392862
\(934\) −6.00000 −0.196326
\(935\) 0 0
\(936\) 10.0000 0.326860
\(937\) 52.0000 1.69877 0.849383 − 0.527777i \(-0.176974\pi\)
0.849383 + 0.527777i \(0.176974\pi\)
\(938\) 4.00000 0.130605
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 30.0000 0.977972 0.488986 − 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −4.00000 −0.130327
\(943\) −72.0000 −2.34464
\(944\) −9.00000 −0.292925
\(945\) 0 0
\(946\) 0 0
\(947\) 60.0000 1.94974 0.974869 − 0.222779i \(-0.0715128\pi\)
0.974869 + 0.222779i \(0.0715128\pi\)
\(948\) −1.00000 −0.0324785
\(949\) 10.0000 0.324614
\(950\) 0 0
\(951\) −15.0000 −0.486408
\(952\) 0 0
\(953\) 3.00000 0.0971795 0.0485898 − 0.998819i \(-0.484527\pi\)
0.0485898 + 0.998819i \(0.484527\pi\)
\(954\) 12.0000 0.388514
\(955\) 0 0
\(956\) 18.0000 0.582162
\(957\) 0 0
\(958\) −18.0000 −0.581554
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 10.0000 0.322413
\(963\) 6.00000 0.193347
\(964\) 17.0000 0.547533
\(965\) 0 0
\(966\) −6.00000 −0.193047
\(967\) 22.0000 0.707472 0.353736 − 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 − 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) −16.0000 −0.513200
\(973\) 5.00000 0.160293
\(974\) 16.0000 0.512673
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) −30.0000 −0.959785 −0.479893 − 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 20.0000 0.639529
\(979\) 0 0
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) 15.0000 0.478669
\(983\) −24.0000 −0.765481 −0.382741 − 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 12.0000 0.382546
\(985\) 0 0
\(986\) 0 0
\(987\) −9.00000 −0.286473
\(988\) −10.0000 −0.318142
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) −25.0000 −0.794151 −0.397076 − 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) −4.00000 −0.127000
\(993\) −8.00000 −0.253872
\(994\) −9.00000 −0.285463
\(995\) 0 0
\(996\) 18.0000 0.570352
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) −4.00000 −0.126618
\(999\) −10.0000 −0.316386
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 3950.2.a.g.1.1 1
5.4 even 2 158.2.a.b.1.1 ✓ 1
15.14 odd 2 1422.2.a.f.1.1 1
20.19 odd 2 1264.2.a.c.1.1 1
35.34 odd 2 7742.2.a.b.1.1 1
40.19 odd 2 5056.2.a.l.1.1 1
40.29 even 2 5056.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
158.2.a.b.1.1 ✓ 1 5.4 even 2
1264.2.a.c.1.1 1 20.19 odd 2
1422.2.a.f.1.1 1 15.14 odd 2
3950.2.a.g.1.1 1 1.1 even 1 trivial
5056.2.a.d.1.1 1 40.29 even 2
5056.2.a.l.1.1 1 40.19 odd 2
7742.2.a.b.1.1 1 35.34 odd 2