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Properties

Label 1290.2.a.c.1.1
Level $1290$
Weight $2$
Character 1290.1
Self dual yes
Analytic conductor $10.301$
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] = [1290,2,Mod(1,1290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1290, 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("1290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1290.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: \(10.3007018607\)
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 \(\chi\) \(=\) 1290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.00000 q^{11} +1.00000 q^{12} -6.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +1.00000 q^{27} +10.0000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +4.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} +8.00000 q^{38} -6.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{43} +4.00000 q^{44} -1.00000 q^{45} +4.00000 q^{46} +12.0000 q^{47} +1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} -6.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} -8.00000 q^{57} -10.0000 q^{58} -4.00000 q^{59} -1.00000 q^{60} -6.00000 q^{61} +1.00000 q^{64} +6.00000 q^{65} -4.00000 q^{66} +4.00000 q^{67} -6.00000 q^{68} -4.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -8.00000 q^{76} +6.00000 q^{78} -8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} +6.00000 q^{85} -1.00000 q^{86} +10.0000 q^{87} -4.00000 q^{88} +2.00000 q^{89} +1.00000 q^{90} -4.00000 q^{92} -12.0000 q^{94} +8.00000 q^{95} -1.00000 q^{96} +10.0000 q^{97} +7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 1.00000 0.288675
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 − 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −1.00000 −0.235702
\(19\) −8.00000 −1.83533 −0.917663 − 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 − 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.00000 0.696311
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 8.00000 1.29777
\(39\) −6.00000 −0.960769
\(40\) 1.00000 0.158114
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499
\(44\) 4.00000 0.603023
\(45\) −1.00000 −0.149071
\(46\) 4.00000 0.589768
\(47\) 12.0000 1.75038 0.875190 − 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) −6.00000 −0.840168
\(52\) −6.00000 −0.832050
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) −10.0000 −1.31306
\(59\) −4.00000 −0.520756 −0.260378 − 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) −1.00000 −0.129099
\(61\) −6.00000 −0.768221 −0.384111 − 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −4.00000 −0.492366
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −6.00000 −0.727607
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) −10.0000 −1.17041 −0.585206 − 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 6.00000 0.697486
\(75\) 1.00000 0.115470
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) 6.00000 0.679366
\(79\) −8.00000 −0.900070 −0.450035 − 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 6.00000 0.650791
\(86\) −1.00000 −0.107833
\(87\) 10.0000 1.07211
\(88\) −4.00000 −0.426401
\(89\) 2.00000 0.212000 0.106000 − 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) −12.0000 −1.23771
\(95\) 8.00000 0.820783
\(96\) −1.00000 −0.102062
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 7.00000 0.707107
\(99\) 4.00000 0.402015
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 − 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 6.00000 0.594089
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 20.0000 1.93347 0.966736 − 0.255774i \(-0.0823304\pi\)
0.966736 + 0.255774i \(0.0823304\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 − 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 4.00000 0.381385
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 − 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 8.00000 0.749269
\(115\) 4.00000 0.373002
\(116\) 10.0000 0.928477
\(117\) −6.00000 −0.554700
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 5.00000 0.454545
\(122\) 6.00000 0.543214
\(123\) −6.00000 −0.541002
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 − 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) −6.00000 −0.526235
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) −1.00000 −0.0860663
\(136\) 6.00000 0.514496
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 4.00000 0.340503
\(139\) −20.0000 −1.69638 −0.848189 − 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) −8.00000 −0.671345
\(143\) −24.0000 −2.00698
\(144\) 1.00000 0.0833333
\(145\) −10.0000 −0.830455
\(146\) 10.0000 0.827606
\(147\) −7.00000 −0.577350
\(148\) −6.00000 −0.493197
\(149\) 2.00000 0.163846 0.0819232 − 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 8.00000 0.648886
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 8.00000 0.636446
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −6.00000 −0.468521
\(165\) −4.00000 −0.311400
\(166\) 12.0000 0.931381
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) −6.00000 −0.460179
\(171\) −8.00000 −0.611775
\(172\) 1.00000 0.0762493
\(173\) 18.0000 1.36851 0.684257 − 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −10.0000 −0.758098
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) −4.00000 −0.300658
\(178\) −2.00000 −0.149906
\(179\) −16.0000 −1.19590 −0.597948 − 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 4.00000 0.294884
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −8.00000 −0.580381
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 1.00000 0.0721688
\(193\) 10.0000 0.719816 0.359908 − 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) −10.0000 −0.717958
\(195\) 6.00000 0.429669
\(196\) −7.00000 −0.500000
\(197\) 2.00000 0.142494 0.0712470 − 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −4.00000 −0.284268
\(199\) 8.00000 0.567105 0.283552 − 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 4.00000 0.282138
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 6.00000 0.419058
\(206\) −4.00000 −0.278693
\(207\) −4.00000 −0.278019
\(208\) −6.00000 −0.416025
\(209\) −32.0000 −2.21349
\(210\) 0 0
\(211\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) −6.00000 −0.412082
\(213\) 8.00000 0.548151
\(214\) −20.0000 −1.36717
\(215\) −1.00000 −0.0681994
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −10.0000 −0.675737
\(220\) −4.00000 −0.269680
\(221\) 36.0000 2.42162
\(222\) 6.00000 0.402694
\(223\) −8.00000 −0.535720 −0.267860 − 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 18.0000 1.19734
\(227\) −20.0000 −1.32745 −0.663723 − 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) −8.00000 −0.529813
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) 22.0000 1.44127 0.720634 − 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 6.00000 0.392232
\(235\) −12.0000 −0.782794
\(236\) −4.00000 −0.260378
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 − 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 18.0000 1.15948 0.579741 − 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000 0.0641500
\(244\) −6.00000 −0.384111
\(245\) 7.00000 0.447214
\(246\) 6.00000 0.382546
\(247\) 48.0000 3.05417
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) 1.00000 0.0632456
\(251\) 4.00000 0.252478 0.126239 − 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) 20.0000 1.25491
\(255\) 6.00000 0.375735
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 − 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 10.0000 0.618984
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) −4.00000 −0.246183
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 4.00000 0.244339
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 1.00000 0.0608581
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 4.00000 0.241209
\(276\) −4.00000 −0.240772
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 20.0000 1.19952
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −12.0000 −0.714590
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 8.00000 0.474713
\(285\) 8.00000 0.473879
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 10.0000 0.587220
\(291\) 10.0000 0.586210
\(292\) −10.0000 −0.585206
\(293\) −14.0000 −0.817889 −0.408944 − 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 7.00000 0.408248
\(295\) 4.00000 0.232889
\(296\) 6.00000 0.348743
\(297\) 4.00000 0.232104
\(298\) −2.00000 −0.115857
\(299\) 24.0000 1.38796
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −2.00000 −0.114897
\(304\) −8.00000 −0.458831
\(305\) 6.00000 0.343559
\(306\) 6.00000 0.342997
\(307\) −20.0000 −1.14146 −0.570730 − 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 − 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 6.00000 0.339683
\(313\) −10.0000 −0.565233 −0.282617 − 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 34.0000 1.90963 0.954815 − 0.297200i \(-0.0960529\pi\)
0.954815 + 0.297200i \(0.0960529\pi\)
\(318\) 6.00000 0.336463
\(319\) 40.0000 2.23957
\(320\) −1.00000 −0.0559017
\(321\) 20.0000 1.11629
\(322\) 0 0
\(323\) 48.0000 2.67079
\(324\) 1.00000 0.0555556
\(325\) −6.00000 −0.332820
\(326\) 4.00000 0.221540
\(327\) −2.00000 −0.110600
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 4.00000 0.220193
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −12.0000 −0.658586
\(333\) −6.00000 −0.328798
\(334\) −12.0000 −0.656611
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) −23.0000 −1.25104
\(339\) −18.0000 −0.977626
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) 8.00000 0.432590
\(343\) 0 0
\(344\) −1.00000 −0.0539164
\(345\) 4.00000 0.215353
\(346\) −18.0000 −0.967686
\(347\) −12.0000 −0.644194 −0.322097 − 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 10.0000 0.536056
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) −4.00000 −0.213201
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 4.00000 0.212598
\(355\) −8.00000 −0.424596
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) 32.0000 1.68890 0.844448 − 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 1.00000 0.0527046
\(361\) 45.0000 2.36842
\(362\) −14.0000 −0.735824
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 6.00000 0.313625
\(367\) −4.00000 −0.208798 −0.104399 − 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −4.00000 −0.208514
\(369\) −6.00000 −0.312348
\(370\) −6.00000 −0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) −6.00000 −0.310668 −0.155334 − 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 24.0000 1.24101
\(375\) −1.00000 −0.0516398
\(376\) −12.0000 −0.618853
\(377\) −60.0000 −3.09016
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 − 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 8.00000 0.410391
\(381\) −20.0000 −1.02463
\(382\) 8.00000 0.409316
\(383\) −32.0000 −1.63512 −0.817562 − 0.575841i \(-0.804675\pi\)
−0.817562 + 0.575841i \(0.804675\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 1.00000 0.0508329
\(388\) 10.0000 0.507673
\(389\) 18.0000 0.912636 0.456318 − 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) −6.00000 −0.303822
\(391\) 24.0000 1.21373
\(392\) 7.00000 0.353553
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) 8.00000 0.402524
\(396\) 4.00000 0.201008
\(397\) 34.0000 1.70641 0.853206 − 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 6.00000 0.297044
\(409\) −30.0000 −1.48340 −0.741702 − 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) −6.00000 −0.296319
\(411\) −18.0000 −0.887875
\(412\) 4.00000 0.197066
\(413\) 0 0
\(414\) 4.00000 0.196589
\(415\) 12.0000 0.589057
\(416\) 6.00000 0.294174
\(417\) −20.0000 −0.979404
\(418\) 32.0000 1.56517
\(419\) −8.00000 −0.390826 −0.195413 − 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 − 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 12.0000 0.583460
\(424\) 6.00000 0.291386
\(425\) −6.00000 −0.291043
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) 20.0000 0.966736
\(429\) −24.0000 −1.15873
\(430\) 1.00000 0.0482243
\(431\) 16.0000 0.770693 0.385346 − 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 1.00000 0.0481125
\(433\) 22.0000 1.05725 0.528626 − 0.848855i \(-0.322707\pi\)
0.528626 + 0.848855i \(0.322707\pi\)
\(434\) 0 0
\(435\) −10.0000 −0.479463
\(436\) −2.00000 −0.0957826
\(437\) 32.0000 1.53077
\(438\) 10.0000 0.477818
\(439\) 16.0000 0.763638 0.381819 − 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 4.00000 0.190693
\(441\) −7.00000 −0.333333
\(442\) −36.0000 −1.71235
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −6.00000 −0.284747
\(445\) −2.00000 −0.0948091
\(446\) 8.00000 0.378811
\(447\) 2.00000 0.0945968
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 − 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −24.0000 −1.13012
\(452\) −18.0000 −0.846649
\(453\) 16.0000 0.751746
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 8.00000 0.374634
\(457\) 38.0000 1.77757 0.888783 − 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) −22.0000 −1.02799
\(459\) −6.00000 −0.280056
\(460\) 4.00000 0.186501
\(461\) −18.0000 −0.838344 −0.419172 − 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 − 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) −22.0000 −1.01913
\(467\) 28.0000 1.29569 0.647843 − 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 12.0000 0.553519
\(471\) 2.00000 0.0921551
\(472\) 4.00000 0.184115
\(473\) 4.00000 0.183920
\(474\) 8.00000 0.367452
\(475\) −8.00000 −0.367065
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) −16.0000 −0.731823
\(479\) −24.0000 −1.09659 −0.548294 − 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 1.00000 0.0456435
\(481\) 36.0000 1.64146
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −10.0000 −0.454077
\(486\) −1.00000 −0.0453609
\(487\) 20.0000 0.906287 0.453143 − 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 6.00000 0.271607
\(489\) −4.00000 −0.180886
\(490\) −7.00000 −0.316228
\(491\) 8.00000 0.361035 0.180517 − 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) −6.00000 −0.270501
\(493\) −60.0000 −2.70226
\(494\) −48.0000 −2.15962
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −32.0000 −1.43252 −0.716258 − 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 12.0000 0.536120
\(502\) −4.00000 −0.178529
\(503\) −32.0000 −1.42681 −0.713405 − 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 16.0000 0.711287
\(507\) 23.0000 1.02147
\(508\) −20.0000 −0.887357
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) −6.00000 −0.265684
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 −0.353209
\(514\) −14.0000 −0.617514
\(515\) −4.00000 −0.176261
\(516\) 1.00000 0.0440225
\(517\) 48.0000 2.11104
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) −6.00000 −0.263117
\(521\) −30.0000 −1.31432 −0.657162 − 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) −10.0000 −0.437688
\(523\) 4.00000 0.174908 0.0874539 − 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) −7.00000 −0.304348
\(530\) −6.00000 −0.260623
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 36.0000 1.55933
\(534\) −2.00000 −0.0865485
\(535\) −20.0000 −0.864675
\(536\) −4.00000 −0.172774
\(537\) −16.0000 −0.690451
\(538\) 10.0000 0.431131
\(539\) −28.0000 −1.20605
\(540\) −1.00000 −0.0430331
\(541\) 38.0000 1.63375 0.816874 − 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 16.0000 0.687259
\(543\) 14.0000 0.600798
\(544\) 6.00000 0.257248
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 − 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) −18.0000 −0.768922
\(549\) −6.00000 −0.256074
\(550\) −4.00000 −0.170561
\(551\) −80.0000 −3.40811
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) 6.00000 0.254686
\(556\) −20.0000 −0.848189
\(557\) −6.00000 −0.254228 −0.127114 − 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 6.00000 0.253095
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 12.0000 0.505291
\(565\) 18.0000 0.757266
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −8.00000 −0.335083
\(571\) 16.0000 0.669579 0.334790 − 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) −24.0000 −1.00349
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) −10.0000 −0.416305 −0.208153 − 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −19.0000 −0.790296
\(579\) 10.0000 0.415586
\(580\) −10.0000 −0.415227
\(581\) 0 0
\(582\) −10.0000 −0.414513
\(583\) −24.0000 −0.993978
\(584\) 10.0000 0.413803
\(585\) 6.00000 0.248069
\(586\) 14.0000 0.578335
\(587\) −36.0000 −1.48588 −0.742940 − 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) −7.00000 −0.288675
\(589\) 0 0
\(590\) −4.00000 −0.164677
\(591\) 2.00000 0.0822690
\(592\) −6.00000 −0.246598
\(593\) 46.0000 1.88899 0.944497 − 0.328521i \(-0.106550\pi\)
0.944497 + 0.328521i \(0.106550\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 2.00000 0.0819232
\(597\) 8.00000 0.327418
\(598\) −24.0000 −0.981433
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 2.00000 0.0815817 0.0407909 − 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 16.0000 0.651031
\(605\) −5.00000 −0.203279
\(606\) 2.00000 0.0812444
\(607\) −32.0000 −1.29884 −0.649420 − 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) −6.00000 −0.242933
\(611\) −72.0000 −2.91281
\(612\) −6.00000 −0.242536
\(613\) −38.0000 −1.53481 −0.767403 − 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 20.0000 0.807134
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 − 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −4.00000 −0.160904
\(619\) −28.0000 −1.12542 −0.562708 − 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) −16.0000 −0.641542
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 1.00000 0.0400000
\(626\) 10.0000 0.399680
\(627\) −32.0000 −1.27796
\(628\) 2.00000 0.0798087
\(629\) 36.0000 1.43541
\(630\) 0 0
\(631\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 8.00000 0.318223
\(633\) 0 0
\(634\) −34.0000 −1.35031
\(635\) 20.0000 0.793676
\(636\) −6.00000 −0.237915
\(637\) 42.0000 1.66410
\(638\) −40.0000 −1.58362
\(639\) 8.00000 0.316475
\(640\) 1.00000 0.0395285
\(641\) −14.0000 −0.552967 −0.276483 − 0.961019i \(-0.589169\pi\)
−0.276483 + 0.961019i \(0.589169\pi\)
\(642\) −20.0000 −0.789337
\(643\) −12.0000 −0.473234 −0.236617 − 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) −1.00000 −0.0393750
\(646\) −48.0000 −1.88853
\(647\) −24.0000 −0.943537 −0.471769 − 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −16.0000 −0.628055
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −30.0000 −1.17399 −0.586995 − 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 − 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) −4.00000 −0.155700
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −8.00000 −0.310929
\(663\) 36.0000 1.39812
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −40.0000 −1.54881
\(668\) 12.0000 0.464294
\(669\) −8.00000 −0.309298
\(670\) 4.00000 0.154533
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 − 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 6.00000 0.231111
\(675\) 1.00000 0.0384900
\(676\) 23.0000 0.884615
\(677\) −38.0000 −1.46046 −0.730229 − 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(678\) 18.0000 0.691286
\(679\) 0 0
\(680\) −6.00000 −0.230089
\(681\) −20.0000 −0.766402
\(682\) 0 0
\(683\) 44.0000 1.68361 0.841807 − 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) −8.00000 −0.305888
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) 1.00000 0.0381246
\(689\) 36.0000 1.37149
\(690\) −4.00000 −0.152277
\(691\) 24.0000 0.913003 0.456502 − 0.889723i \(-0.349102\pi\)
0.456502 + 0.889723i \(0.349102\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 20.0000 0.758643
\(696\) −10.0000 −0.379049
\(697\) 36.0000 1.36360
\(698\) 14.0000 0.529908
\(699\) 22.0000 0.832116
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 − 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 6.00000 0.226455
\(703\) 48.0000 1.81035
\(704\) 4.00000 0.150756
\(705\) −12.0000 −0.451946
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −34.0000 −1.27690 −0.638448 − 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 8.00000 0.300235
\(711\) −8.00000 −0.300023
\(712\) −2.00000 −0.0749532
\(713\) 0 0
\(714\) 0 0
\(715\) 24.0000 0.897549
\(716\) −16.0000 −0.597948
\(717\) 16.0000 0.597531
\(718\) −32.0000 −1.19423
\(719\) 32.0000 1.19340 0.596699 − 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −45.0000 −1.67473
\(723\) 18.0000 0.669427
\(724\) 14.0000 0.520306
\(725\) 10.0000 0.371391
\(726\) −5.00000 −0.185567
\(727\) −8.00000 −0.296704 −0.148352 − 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −10.0000 −0.370117
\(731\) −6.00000 −0.221918
\(732\) −6.00000 −0.221766
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 4.00000 0.147643
\(735\) 7.00000 0.258199
\(736\) 4.00000 0.147442
\(737\) 16.0000 0.589368
\(738\) 6.00000 0.220863
\(739\) 8.00000 0.294285 0.147142 − 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) 6.00000 0.220564
\(741\) 48.0000 1.76332
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 − 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −2.00000 −0.0732743
\(746\) 6.00000 0.219676
\(747\) −12.0000 −0.439057
\(748\) −24.0000 −0.877527
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −48.0000 −1.75154 −0.875772 − 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 12.0000 0.437595
\(753\) 4.00000 0.145768
\(754\) 60.0000 2.18507
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −54.0000 −1.96266 −0.981332 − 0.192323i \(-0.938398\pi\)
−0.981332 + 0.192323i \(0.938398\pi\)
\(758\) 20.0000 0.726433
\(759\) −16.0000 −0.580763
\(760\) −8.00000 −0.290191
\(761\) −14.0000 −0.507500 −0.253750 − 0.967270i \(-0.581664\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(762\) 20.0000 0.724524
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 6.00000 0.216930
\(766\) 32.0000 1.15621
\(767\) 24.0000 0.866590
\(768\) 1.00000 0.0360844
\(769\) 34.0000 1.22607 0.613036 − 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 10.0000 0.359908
\(773\) −6.00000 −0.215805 −0.107903 − 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 48.0000 1.71978
\(780\) 6.00000 0.214834
\(781\) 32.0000 1.14505
\(782\) −24.0000 −0.858238
\(783\) 10.0000 0.357371
\(784\) −7.00000 −0.250000
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −52.0000 −1.85360 −0.926800 − 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 36.0000 1.27840
\(794\) −34.0000 −1.20661
\(795\) 6.00000 0.212798
\(796\) 8.00000 0.283552
\(797\) 34.0000 1.20434 0.602171 − 0.798367i \(-0.294303\pi\)
0.602171 + 0.798367i \(0.294303\pi\)
\(798\) 0 0
\(799\) −72.0000 −2.54718
\(800\) −1.00000 −0.0353553
\(801\) 2.00000 0.0706665
\(802\) −2.00000 −0.0706225
\(803\) −40.0000 −1.41157
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 0 0
\(807\) −10.0000 −0.352017
\(808\) 2.00000 0.0703598
\(809\) −38.0000 −1.33601 −0.668004 − 0.744157i \(-0.732851\pi\)
−0.668004 + 0.744157i \(0.732851\pi\)
\(810\) 1.00000 0.0351364
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 24.0000 0.841200
\(815\) 4.00000 0.140114
\(816\) −6.00000 −0.210042
\(817\) −8.00000 −0.279885
\(818\) 30.0000 1.04893
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 14.0000 0.488603 0.244302 − 0.969699i \(-0.421441\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(822\) 18.0000 0.627822
\(823\) −12.0000 −0.418294 −0.209147 − 0.977884i \(-0.567069\pi\)
−0.209147 + 0.977884i \(0.567069\pi\)
\(824\) −4.00000 −0.139347
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 − 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) −4.00000 −0.139010
\(829\) 18.0000 0.625166 0.312583 − 0.949890i \(-0.398806\pi\)
0.312583 + 0.949890i \(0.398806\pi\)
\(830\) −12.0000 −0.416526
\(831\) −22.0000 −0.763172
\(832\) −6.00000 −0.208013
\(833\) 42.0000 1.45521
\(834\) 20.0000 0.692543
\(835\) −12.0000 −0.415277
\(836\) −32.0000 −1.10674
\(837\) 0 0
\(838\) 8.00000 0.276355
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −10.0000 −0.344623
\(843\) −6.00000 −0.206651
\(844\) 0 0
\(845\) −23.0000 −0.791224
\(846\) −12.0000 −0.412568
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −4.00000 −0.137280
\(850\) 6.00000 0.205798
\(851\) 24.0000 0.822709
\(852\) 8.00000 0.274075
\(853\) 42.0000 1.43805 0.719026 − 0.694983i \(-0.244588\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(854\) 0 0
\(855\) 8.00000 0.273594
\(856\) −20.0000 −0.683586
\(857\) 42.0000 1.43469 0.717346 − 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 24.0000 0.819346
\(859\) −8.00000 −0.272956 −0.136478 − 0.990643i \(-0.543578\pi\)
−0.136478 + 0.990643i \(0.543578\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 0 0
\(862\) −16.0000 −0.544962
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −18.0000 −0.612018
\(866\) −22.0000 −0.747590
\(867\) 19.0000 0.645274
\(868\) 0 0
\(869\) −32.0000 −1.08553
\(870\) 10.0000 0.339032
\(871\) −24.0000 −0.813209
\(872\) 2.00000 0.0677285
\(873\) 10.0000 0.338449
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −16.0000 −0.539974
\(879\) −14.0000 −0.472208
\(880\) −4.00000 −0.134840
\(881\) −46.0000 −1.54978 −0.774890 − 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 7.00000 0.235702
\(883\) −36.0000 −1.21150 −0.605748 − 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 36.0000 1.21081
\(885\) 4.00000 0.134459
\(886\) −12.0000 −0.403148
\(887\) 8.00000 0.268614 0.134307 − 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 6.00000 0.201347
\(889\) 0 0
\(890\) 2.00000 0.0670402
\(891\) 4.00000 0.134005
\(892\) −8.00000 −0.267860
\(893\) −96.0000 −3.21252
\(894\) −2.00000 −0.0668900
\(895\) 16.0000 0.534821
\(896\) 0 0
\(897\) 24.0000 0.801337
\(898\) 22.0000 0.734150
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 36.0000 1.19933
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) −14.0000 −0.465376
\(906\) −16.0000 −0.531564
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) −20.0000 −0.663723
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 − 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) −8.00000 −0.264906
\(913\) −48.0000 −1.58857
\(914\) −38.0000 −1.25693
\(915\) 6.00000 0.198354
\(916\) 22.0000 0.726900
\(917\) 0 0
\(918\) 6.00000 0.198030
\(919\) −32.0000 −1.05558 −0.527791 − 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) −4.00000 −0.131876
\(921\) −20.0000 −0.659022
\(922\) 18.0000 0.592798
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) −24.0000 −0.788689
\(927\) 4.00000 0.131377
\(928\) −10.0000 −0.328266
\(929\) −6.00000 −0.196854 −0.0984268 − 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) 56.0000 1.83533
\(932\) 22.0000 0.720634
\(933\) 16.0000 0.523816
\(934\) −28.0000 −0.916188
\(935\) 24.0000 0.784884
\(936\) 6.00000 0.196116
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) −10.0000 −0.326338
\(940\) −12.0000 −0.391397
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 24.0000 0.781548
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) −8.00000 −0.259828
\(949\) 60.0000 1.94768
\(950\) 8.00000 0.259554
\(951\) 34.0000 1.10253
\(952\) 0 0
\(953\) 54.0000 1.74923 0.874616 − 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 6.00000 0.194257
\(955\) 8.00000 0.258874
\(956\) 16.0000 0.517477
\(957\) 40.0000 1.29302
\(958\) 24.0000 0.775405
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) −36.0000 −1.16069
\(963\) 20.0000 0.644491
\(964\) 18.0000 0.579741
\(965\) −10.0000 −0.321911
\(966\) 0 0
\(967\) 12.0000 0.385894 0.192947 − 0.981209i \(-0.438195\pi\)
0.192947 + 0.981209i \(0.438195\pi\)
\(968\) −5.00000 −0.160706
\(969\) 48.0000 1.54198
\(970\) 10.0000 0.321081
\(971\) 36.0000 1.15529 0.577647 − 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −20.0000 −0.640841
\(975\) −6.00000 −0.192154
\(976\) −6.00000 −0.192055
\(977\) −30.0000 −0.959785 −0.479893 − 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 4.00000 0.127906
\(979\) 8.00000 0.255681
\(980\) 7.00000 0.223607
\(981\) −2.00000 −0.0638551
\(982\) −8.00000 −0.255290
\(983\) 8.00000 0.255160 0.127580 − 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(984\) 6.00000 0.191273
\(985\) −2.00000 −0.0637253
\(986\) 60.0000 1.91079
\(987\) 0 0
\(988\) 48.0000 1.52708
\(989\) −4.00000 −0.127193
\(990\) 4.00000 0.127128
\(991\) −32.0000 −1.01651 −0.508257 − 0.861206i \(-0.669710\pi\)
−0.508257 + 0.861206i \(0.669710\pi\)
\(992\) 0 0
\(993\) 8.00000 0.253872
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) −12.0000 −0.380235
\(997\) 26.0000 0.823428 0.411714 − 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) 32.0000 1.01294
\(999\) −6.00000 −0.189832
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 1290.2.a.c.1.1 ✓ 1
3.2 odd 2 3870.2.a.w.1.1 1
5.4 even 2 6450.2.a.y.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1290.2.a.c.1.1 ✓ 1 1.1 even 1 trivial
3870.2.a.w.1.1 1 3.2 odd 2
6450.2.a.y.1.1 1 5.4 even 2