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Properties

Label 930.2.a.i.1.1
Level $930$
Weight $2$
Character 930.1
Self dual yes
Analytic conductor $7.426$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(1,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, 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("930.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 930.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +5.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} +3.00000 q^{22} +9.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} -1.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} -5.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} +1.00000 q^{42} +11.0000 q^{43} -3.00000 q^{44} +1.00000 q^{45} -9.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} -9.00000 q^{53} -1.00000 q^{54} -3.00000 q^{55} +1.00000 q^{56} +5.00000 q^{57} +6.00000 q^{59} +1.00000 q^{60} -10.0000 q^{61} -1.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +3.00000 q^{66} +14.0000 q^{67} +9.00000 q^{69} +1.00000 q^{70} +9.00000 q^{71} -1.00000 q^{72} -1.00000 q^{73} -8.00000 q^{74} +1.00000 q^{75} +5.00000 q^{76} +3.00000 q^{77} -2.00000 q^{78} -1.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{83} -1.00000 q^{84} -11.0000 q^{86} +3.00000 q^{88} -9.00000 q^{89} -1.00000 q^{90} -2.00000 q^{91} +9.00000 q^{92} +1.00000 q^{93} +6.00000 q^{94} +5.00000 q^{95} -1.00000 q^{96} +14.0000 q^{97} +6.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)

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
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964 −0.188982 − 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.00000 0.267261
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.00000 1.14708 0.573539 − 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.00000 −0.218218
\(22\) 3.00000 0.639602
\(23\) 9.00000 1.87663 0.938315 − 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −1.00000 −0.182574
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −5.00000 −0.811107
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 1.00000 0.154303
\(43\) 11.0000 1.67748 0.838742 − 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) −3.00000 −0.452267
\(45\) 1.00000 0.149071
\(46\) −9.00000 −1.32698
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −1.00000 −0.136083
\(55\) −3.00000 −0.404520
\(56\) 1.00000 0.133631
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 − 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 1.00000 0.129099
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −1.00000 −0.127000
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 3.00000 0.369274
\(67\) 14.0000 1.71037 0.855186 − 0.518321i \(-0.173443\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 1.00000 0.119523
\(71\) 9.00000 1.06810 0.534052 − 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −1.00000 −0.117851
\(73\) −1.00000 −0.117041 −0.0585206 − 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −8.00000 −0.929981
\(75\) 1.00000 0.115470
\(76\) 5.00000 0.573539
\(77\) 3.00000 0.341882
\(78\) −2.00000 −0.226455
\(79\) −1.00000 −0.112509 −0.0562544 − 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −11.0000 −1.18616
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) −9.00000 −0.953998 −0.476999 − 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.00000 −0.209657
\(92\) 9.00000 0.938315
\(93\) 1.00000 0.103695
\(94\) 6.00000 0.618853
\(95\) 5.00000 0.512989
\(96\) −1.00000 −0.102062
\(97\) 14.0000 1.42148 0.710742 − 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 6.00000 0.606092
\(99\) −3.00000 −0.301511
\(100\) 1.00000 0.100000
\(101\) −15.0000 −1.49256 −0.746278 − 0.665635i \(-0.768161\pi\)
−0.746278 + 0.665635i \(0.768161\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −2.00000 −0.196116
\(105\) −1.00000 −0.0975900
\(106\) 9.00000 0.874157
\(107\) −3.00000 −0.290021 −0.145010 − 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 1.00000 0.0962250
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 3.00000 0.286039
\(111\) 8.00000 0.759326
\(112\) −1.00000 −0.0944911
\(113\) −3.00000 −0.282216 −0.141108 − 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) −5.00000 −0.468293
\(115\) 9.00000 0.839254
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −2.00000 −0.181818
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 1.00000 0.0898027
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) 8.00000 0.709885 0.354943 − 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.0000 0.968496
\(130\) −2.00000 −0.175412
\(131\) −6.00000 −0.524222 −0.262111 − 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) −3.00000 −0.261116
\(133\) −5.00000 −0.433555
\(134\) −14.0000 −1.20942
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 − 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −9.00000 −0.766131
\(139\) 14.0000 1.18746 0.593732 − 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −6.00000 −0.505291
\(142\) −9.00000 −0.755263
\(143\) −6.00000 −0.501745
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 1.00000 0.0827606
\(147\) −6.00000 −0.494872
\(148\) 8.00000 0.657596
\(149\) 3.00000 0.245770 0.122885 − 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −5.00000 −0.405554
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) 1.00000 0.0803219
\(156\) 2.00000 0.160128
\(157\) −7.00000 −0.558661 −0.279330 − 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 1.00000 0.0795557
\(159\) −9.00000 −0.713746
\(160\) −1.00000 −0.0790569
\(161\) −9.00000 −0.709299
\(162\) −1.00000 −0.0785674
\(163\) −22.0000 −1.72317 −0.861586 − 0.507611i \(-0.830529\pi\)
−0.861586 + 0.507611i \(0.830529\pi\)
\(164\) 0 0
\(165\) −3.00000 −0.233550
\(166\) 12.0000 0.931381
\(167\) 9.00000 0.696441 0.348220 − 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 1.00000 0.0771517
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 5.00000 0.382360
\(172\) 11.0000 0.838742
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) −3.00000 −0.226134
\(177\) 6.00000 0.450988
\(178\) 9.00000 0.674579
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 0.0745356
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 2.00000 0.148250
\(183\) −10.0000 −0.739221
\(184\) −9.00000 −0.663489
\(185\) 8.00000 0.588172
\(186\) −1.00000 −0.0733236
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −1.00000 −0.0727393
\(190\) −5.00000 −0.362738
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) −10.0000 −0.719816 −0.359908 − 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −14.0000 −1.00514
\(195\) 2.00000 0.143223
\(196\) −6.00000 −0.428571
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 3.00000 0.213201
\(199\) −25.0000 −1.77220 −0.886102 − 0.463491i \(-0.846597\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 14.0000 0.987484
\(202\) 15.0000 1.05540
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) 9.00000 0.625543
\(208\) 2.00000 0.138675
\(209\) −15.0000 −1.03757
\(210\) 1.00000 0.0690066
\(211\) −19.0000 −1.30801 −0.654007 − 0.756489i \(-0.726913\pi\)
−0.654007 + 0.756489i \(0.726913\pi\)
\(212\) −9.00000 −0.618123
\(213\) 9.00000 0.616670
\(214\) 3.00000 0.205076
\(215\) 11.0000 0.750194
\(216\) −1.00000 −0.0680414
\(217\) −1.00000 −0.0678844
\(218\) −8.00000 −0.541828
\(219\) −1.00000 −0.0675737
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) −8.00000 −0.536925
\(223\) −10.0000 −0.669650 −0.334825 − 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.00000 0.0666667
\(226\) 3.00000 0.199557
\(227\) −15.0000 −0.995585 −0.497792 − 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) 5.00000 0.331133
\(229\) 5.00000 0.330409 0.165205 − 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) −9.00000 −0.593442
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) 3.00000 0.196537 0.0982683 − 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −2.00000 −0.130744
\(235\) −6.00000 −0.391397
\(236\) 6.00000 0.390567
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 − 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 1.00000 0.0645497
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 2.00000 0.128565
\(243\) 1.00000 0.0641500
\(244\) −10.0000 −0.640184
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) −1.00000 −0.0635001
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −27.0000 −1.69748
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −27.0000 −1.68421 −0.842107 − 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) −11.0000 −0.684830
\(259\) −8.00000 −0.497096
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 3.00000 0.184637
\(265\) −9.00000 −0.552866
\(266\) 5.00000 0.306570
\(267\) −9.00000 −0.550791
\(268\) 14.0000 0.855186
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 5.00000 0.303728 0.151864 − 0.988401i \(-0.451472\pi\)
0.151864 + 0.988401i \(0.451472\pi\)
\(272\) 0 0
\(273\) −2.00000 −0.121046
\(274\) −18.0000 −1.08742
\(275\) −3.00000 −0.180907
\(276\) 9.00000 0.541736
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −14.0000 −0.839664
\(279\) 1.00000 0.0598684
\(280\) 1.00000 0.0597614
\(281\) −24.0000 −1.43172 −0.715860 − 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 6.00000 0.357295
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 9.00000 0.534052
\(285\) 5.00000 0.296174
\(286\) 6.00000 0.354787
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) −1.00000 −0.0585206
\(293\) 18.0000 1.05157 0.525786 − 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 6.00000 0.349927
\(295\) 6.00000 0.349334
\(296\) −8.00000 −0.464991
\(297\) −3.00000 −0.174078
\(298\) −3.00000 −0.173785
\(299\) 18.0000 1.04097
\(300\) 1.00000 0.0577350
\(301\) −11.0000 −0.634029
\(302\) 16.0000 0.920697
\(303\) −15.0000 −0.861727
\(304\) 5.00000 0.286770
\(305\) −10.0000 −0.572598
\(306\) 0 0
\(307\) 32.0000 1.82634 0.913168 − 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) 3.00000 0.170941
\(309\) 8.00000 0.455104
\(310\) −1.00000 −0.0567962
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −2.00000 −0.113228
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 7.00000 0.395033
\(315\) −1.00000 −0.0563436
\(316\) −1.00000 −0.0562544
\(317\) 24.0000 1.34797 0.673987 − 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 9.00000 0.504695
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −3.00000 −0.167444
\(322\) 9.00000 0.501550
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) 22.0000 1.21847
\(327\) 8.00000 0.442401
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 3.00000 0.165145
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −12.0000 −0.658586
\(333\) 8.00000 0.438397
\(334\) −9.00000 −0.492458
\(335\) 14.0000 0.764902
\(336\) −1.00000 −0.0545545
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 9.00000 0.489535
\(339\) −3.00000 −0.162938
\(340\) 0 0
\(341\) −3.00000 −0.162459
\(342\) −5.00000 −0.270369
\(343\) 13.0000 0.701934
\(344\) −11.0000 −0.593080
\(345\) 9.00000 0.484544
\(346\) −6.00000 −0.322562
\(347\) −36.0000 −1.93258 −0.966291 − 0.257454i \(-0.917117\pi\)
−0.966291 + 0.257454i \(0.917117\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 − 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 1.00000 0.0534522
\(351\) 2.00000 0.106752
\(352\) 3.00000 0.159901
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) −6.00000 −0.318896
\(355\) 9.00000 0.477670
\(356\) −9.00000 −0.476999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 9.00000 0.475002 0.237501 − 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 6.00000 0.315789
\(362\) −5.00000 −0.262794
\(363\) −2.00000 −0.104973
\(364\) −2.00000 −0.104828
\(365\) −1.00000 −0.0523424
\(366\) 10.0000 0.522708
\(367\) 26.0000 1.35719 0.678594 − 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 9.00000 0.469157
\(369\) 0 0
\(370\) −8.00000 −0.415900
\(371\) 9.00000 0.467257
\(372\) 1.00000 0.0518476
\(373\) −19.0000 −0.983783 −0.491891 − 0.870657i \(-0.663694\pi\)
−0.491891 + 0.870657i \(0.663694\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −1.00000 −0.0513665 −0.0256833 − 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 5.00000 0.256495
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) 36.0000 1.83951 0.919757 − 0.392488i \(-0.128386\pi\)
0.919757 + 0.392488i \(0.128386\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 3.00000 0.152894
\(386\) 10.0000 0.508987
\(387\) 11.0000 0.559161
\(388\) 14.0000 0.710742
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −2.00000 −0.101274
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) −6.00000 −0.302660
\(394\) 6.00000 0.302276
\(395\) −1.00000 −0.0503155
\(396\) −3.00000 −0.150756
\(397\) −7.00000 −0.351320 −0.175660 − 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) 25.0000 1.25314
\(399\) −5.00000 −0.250313
\(400\) 1.00000 0.0500000
\(401\) 15.0000 0.749064 0.374532 − 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) −14.0000 −0.698257
\(403\) 2.00000 0.0996271
\(404\) −15.0000 −0.746278
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −28.0000 −1.38451 −0.692255 − 0.721653i \(-0.743383\pi\)
−0.692255 + 0.721653i \(0.743383\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 8.00000 0.394132
\(413\) −6.00000 −0.295241
\(414\) −9.00000 −0.442326
\(415\) −12.0000 −0.589057
\(416\) −2.00000 −0.0980581
\(417\) 14.0000 0.685583
\(418\) 15.0000 0.733674
\(419\) −24.0000 −1.17248 −0.586238 − 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −10.0000 −0.487370 −0.243685 − 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 19.0000 0.924906
\(423\) −6.00000 −0.291730
\(424\) 9.00000 0.437079
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) 10.0000 0.483934
\(428\) −3.00000 −0.145010
\(429\) −6.00000 −0.289683
\(430\) −11.0000 −0.530467
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000 0.0481125
\(433\) 5.00000 0.240285 0.120142 − 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 1.00000 0.0480015
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) 45.0000 2.15264
\(438\) 1.00000 0.0477818
\(439\) 14.0000 0.668184 0.334092 − 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 3.00000 0.143019
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 27.0000 1.28281 0.641404 − 0.767203i \(-0.278352\pi\)
0.641404 + 0.767203i \(0.278352\pi\)
\(444\) 8.00000 0.379663
\(445\) −9.00000 −0.426641
\(446\) 10.0000 0.473514
\(447\) 3.00000 0.141895
\(448\) −1.00000 −0.0472456
\(449\) 6.00000 0.283158 0.141579 − 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) −3.00000 −0.141108
\(453\) −16.0000 −0.751746
\(454\) 15.0000 0.703985
\(455\) −2.00000 −0.0937614
\(456\) −5.00000 −0.234146
\(457\) 38.0000 1.77757 0.888783 − 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) −5.00000 −0.233635
\(459\) 0 0
\(460\) 9.00000 0.419627
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) −3.00000 −0.139573
\(463\) 32.0000 1.48717 0.743583 − 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 0 0
\(465\) 1.00000 0.0463739
\(466\) −3.00000 −0.138972
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 2.00000 0.0924500
\(469\) −14.0000 −0.646460
\(470\) 6.00000 0.276759
\(471\) −7.00000 −0.322543
\(472\) −6.00000 −0.276172
\(473\) −33.0000 −1.51734
\(474\) 1.00000 0.0459315
\(475\) 5.00000 0.229416
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) −12.0000 −0.548867
\(479\) 21.0000 0.959514 0.479757 − 0.877401i \(-0.340725\pi\)
0.479757 + 0.877401i \(0.340725\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 16.0000 0.729537
\(482\) 22.0000 1.00207
\(483\) −9.00000 −0.409514
\(484\) −2.00000 −0.0909091
\(485\) 14.0000 0.635707
\(486\) −1.00000 −0.0453609
\(487\) −40.0000 −1.81257 −0.906287 − 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 10.0000 0.452679
\(489\) −22.0000 −0.994874
\(490\) 6.00000 0.271052
\(491\) 21.0000 0.947717 0.473858 − 0.880601i \(-0.342861\pi\)
0.473858 + 0.880601i \(0.342861\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −10.0000 −0.449921
\(495\) −3.00000 −0.134840
\(496\) 1.00000 0.0449013
\(497\) −9.00000 −0.403705
\(498\) 12.0000 0.537733
\(499\) 32.0000 1.43252 0.716258 − 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 1.00000 0.0447214
\(501\) 9.00000 0.402090
\(502\) −12.0000 −0.535586
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 1.00000 0.0445435
\(505\) −15.0000 −0.667491
\(506\) 27.0000 1.20030
\(507\) −9.00000 −0.399704
\(508\) 8.00000 0.354943
\(509\) 36.0000 1.59567 0.797836 − 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 1.00000 0.0442374
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 0.220755
\(514\) 27.0000 1.19092
\(515\) 8.00000 0.352522
\(516\) 11.0000 0.484248
\(517\) 18.0000 0.791639
\(518\) 8.00000 0.351500
\(519\) 6.00000 0.263371
\(520\) −2.00000 −0.0877058
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −25.0000 −1.09317 −0.546587 − 0.837402i \(-0.684073\pi\)
−0.546587 + 0.837402i \(0.684073\pi\)
\(524\) −6.00000 −0.262111
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 0 0
\(528\) −3.00000 −0.130558
\(529\) 58.0000 2.52174
\(530\) 9.00000 0.390935
\(531\) 6.00000 0.260378
\(532\) −5.00000 −0.216777
\(533\) 0 0
\(534\) 9.00000 0.389468
\(535\) −3.00000 −0.129701
\(536\) −14.0000 −0.604708
\(537\) −12.0000 −0.517838
\(538\) −6.00000 −0.258678
\(539\) 18.0000 0.775315
\(540\) 1.00000 0.0430331
\(541\) −34.0000 −1.46177 −0.730887 − 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) −5.00000 −0.214768
\(543\) 5.00000 0.214571
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 2.00000 0.0855921
\(547\) −34.0000 −1.45374 −0.726868 − 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 18.0000 0.768922
\(549\) −10.0000 −0.426790
\(550\) 3.00000 0.127920
\(551\) 0 0
\(552\) −9.00000 −0.383065
\(553\) 1.00000 0.0425243
\(554\) −8.00000 −0.339887
\(555\) 8.00000 0.339581
\(556\) 14.0000 0.593732
\(557\) 3.00000 0.127114 0.0635570 − 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) −1.00000 −0.0423334
\(559\) 22.0000 0.930501
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) −6.00000 −0.252646
\(565\) −3.00000 −0.126211
\(566\) 4.00000 0.168133
\(567\) −1.00000 −0.0419961
\(568\) −9.00000 −0.377632
\(569\) 15.0000 0.628833 0.314416 − 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) −5.00000 −0.209427
\(571\) 14.0000 0.585882 0.292941 − 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) −6.00000 −0.250873
\(573\) 0 0
\(574\) 0 0
\(575\) 9.00000 0.375326
\(576\) 1.00000 0.0416667
\(577\) −16.0000 −0.666089 −0.333044 − 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 17.0000 0.707107
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) −14.0000 −0.580319
\(583\) 27.0000 1.11823
\(584\) 1.00000 0.0413803
\(585\) 2.00000 0.0826898
\(586\) −18.0000 −0.743573
\(587\) −24.0000 −0.990586 −0.495293 − 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) −6.00000 −0.247436
\(589\) 5.00000 0.206021
\(590\) −6.00000 −0.247016
\(591\) −6.00000 −0.246807
\(592\) 8.00000 0.328798
\(593\) 6.00000 0.246390 0.123195 − 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) −25.0000 −1.02318
\(598\) −18.0000 −0.736075
\(599\) 27.0000 1.10319 0.551595 − 0.834112i \(-0.314019\pi\)
0.551595 + 0.834112i \(0.314019\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 11.0000 0.448327
\(603\) 14.0000 0.570124
\(604\) −16.0000 −0.651031
\(605\) −2.00000 −0.0813116
\(606\) 15.0000 0.609333
\(607\) −1.00000 −0.0405887 −0.0202944 − 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 10.0000 0.404888
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) −22.0000 −0.888572 −0.444286 − 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) −32.0000 −1.29141
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) −15.0000 −0.603877 −0.301939 − 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) −8.00000 −0.321807
\(619\) 14.0000 0.562708 0.281354 − 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) 1.00000 0.0401610
\(621\) 9.00000 0.361158
\(622\) 0 0
\(623\) 9.00000 0.360577
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) 22.0000 0.879297
\(627\) −15.0000 −0.599042
\(628\) −7.00000 −0.279330
\(629\) 0 0
\(630\) 1.00000 0.0398410
\(631\) −7.00000 −0.278666 −0.139333 − 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 1.00000 0.0397779
\(633\) −19.0000 −0.755182
\(634\) −24.0000 −0.953162
\(635\) 8.00000 0.317470
\(636\) −9.00000 −0.356873
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 9.00000 0.356034
\(640\) −1.00000 −0.0395285
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 3.00000 0.118401
\(643\) −31.0000 −1.22252 −0.611260 − 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) −9.00000 −0.354650
\(645\) 11.0000 0.433125
\(646\) 0 0
\(647\) −33.0000 −1.29736 −0.648682 − 0.761060i \(-0.724679\pi\)
−0.648682 + 0.761060i \(0.724679\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −18.0000 −0.706562
\(650\) −2.00000 −0.0784465
\(651\) −1.00000 −0.0391931
\(652\) −22.0000 −0.861586
\(653\) 30.0000 1.17399 0.586995 − 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) −8.00000 −0.312825
\(655\) −6.00000 −0.234439
\(656\) 0 0
\(657\) −1.00000 −0.0390137
\(658\) −6.00000 −0.233904
\(659\) −48.0000 −1.86981 −0.934907 − 0.354892i \(-0.884518\pi\)
−0.934907 + 0.354892i \(0.884518\pi\)
\(660\) −3.00000 −0.116775
\(661\) −46.0000 −1.78919 −0.894596 − 0.446875i \(-0.852537\pi\)
−0.894596 + 0.446875i \(0.852537\pi\)
\(662\) −8.00000 −0.310929
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) −5.00000 −0.193892
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) 9.00000 0.348220
\(669\) −10.0000 −0.386622
\(670\) −14.0000 −0.540867
\(671\) 30.0000 1.15814
\(672\) 1.00000 0.0385758
\(673\) −10.0000 −0.385472 −0.192736 − 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 22.0000 0.847408
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −33.0000 −1.26829 −0.634147 − 0.773213i \(-0.718648\pi\)
−0.634147 + 0.773213i \(0.718648\pi\)
\(678\) 3.00000 0.115214
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) 3.00000 0.114876
\(683\) −15.0000 −0.573959 −0.286980 − 0.957937i \(-0.592651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(684\) 5.00000 0.191180
\(685\) 18.0000 0.687745
\(686\) −13.0000 −0.496342
\(687\) 5.00000 0.190762
\(688\) 11.0000 0.419371
\(689\) −18.0000 −0.685745
\(690\) −9.00000 −0.342624
\(691\) 17.0000 0.646710 0.323355 − 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) 6.00000 0.228086
\(693\) 3.00000 0.113961
\(694\) 36.0000 1.36654
\(695\) 14.0000 0.531050
\(696\) 0 0
\(697\) 0 0
\(698\) 4.00000 0.151402
\(699\) 3.00000 0.113470
\(700\) −1.00000 −0.0377964
\(701\) −3.00000 −0.113308 −0.0566542 − 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 40.0000 1.50863
\(704\) −3.00000 −0.113067
\(705\) −6.00000 −0.225973
\(706\) −6.00000 −0.225813
\(707\) 15.0000 0.564133
\(708\) 6.00000 0.225494
\(709\) 23.0000 0.863783 0.431892 − 0.901926i \(-0.357846\pi\)
0.431892 + 0.901926i \(0.357846\pi\)
\(710\) −9.00000 −0.337764
\(711\) −1.00000 −0.0375029
\(712\) 9.00000 0.337289
\(713\) 9.00000 0.337053
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) −12.0000 −0.448461
\(717\) 12.0000 0.448148
\(718\) −9.00000 −0.335877
\(719\) 18.0000 0.671287 0.335643 − 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 1.00000 0.0372678
\(721\) −8.00000 −0.297936
\(722\) −6.00000 −0.223297
\(723\) −22.0000 −0.818189
\(724\) 5.00000 0.185824
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) 23.0000 0.853023 0.426511 − 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 2.00000 0.0741249
\(729\) 1.00000 0.0370370
\(730\) 1.00000 0.0370117
\(731\) 0 0
\(732\) −10.0000 −0.369611
\(733\) 26.0000 0.960332 0.480166 − 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) −26.0000 −0.959678
\(735\) −6.00000 −0.221313
\(736\) −9.00000 −0.331744
\(737\) −42.0000 −1.54709
\(738\) 0 0
\(739\) 32.0000 1.17714 0.588570 − 0.808447i \(-0.299691\pi\)
0.588570 + 0.808447i \(0.299691\pi\)
\(740\) 8.00000 0.294086
\(741\) 10.0000 0.367359
\(742\) −9.00000 −0.330400
\(743\) −9.00000 −0.330178 −0.165089 − 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 3.00000 0.109911
\(746\) 19.0000 0.695639
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 3.00000 0.109618
\(750\) −1.00000 −0.0365148
\(751\) 26.0000 0.948753 0.474377 − 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(752\) −6.00000 −0.218797
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) −1.00000 −0.0363696
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 1.00000 0.0363216
\(759\) −27.0000 −0.980038
\(760\) −5.00000 −0.181369
\(761\) −21.0000 −0.761249 −0.380625 − 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) −8.00000 −0.289809
\(763\) −8.00000 −0.289619
\(764\) 0 0
\(765\) 0 0
\(766\) −36.0000 −1.30073
\(767\) 12.0000 0.433295
\(768\) 1.00000 0.0360844
\(769\) −31.0000 −1.11789 −0.558944 − 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) −3.00000 −0.108112
\(771\) −27.0000 −0.972381
\(772\) −10.0000 −0.359908
\(773\) −27.0000 −0.971123 −0.485561 − 0.874203i \(-0.661385\pi\)
−0.485561 + 0.874203i \(0.661385\pi\)
\(774\) −11.0000 −0.395387
\(775\) 1.00000 0.0359211
\(776\) −14.0000 −0.502571
\(777\) −8.00000 −0.286998
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) 2.00000 0.0716115
\(781\) −27.0000 −0.966136
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) −7.00000 −0.249841
\(786\) 6.00000 0.214013
\(787\) −25.0000 −0.891154 −0.445577 − 0.895244i \(-0.647001\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) 1.00000 0.0355784
\(791\) 3.00000 0.106668
\(792\) 3.00000 0.106600
\(793\) −20.0000 −0.710221
\(794\) 7.00000 0.248421
\(795\) −9.00000 −0.319197
\(796\) −25.0000 −0.886102
\(797\) 18.0000 0.637593 0.318796 − 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 5.00000 0.176998
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) −9.00000 −0.317999
\(802\) −15.0000 −0.529668
\(803\) 3.00000 0.105868
\(804\) 14.0000 0.493742
\(805\) −9.00000 −0.317208
\(806\) −2.00000 −0.0704470
\(807\) 6.00000 0.211210
\(808\) 15.0000 0.527698
\(809\) 39.0000 1.37117 0.685583 − 0.727994i \(-0.259547\pi\)
0.685583 + 0.727994i \(0.259547\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −43.0000 −1.50993 −0.754967 − 0.655763i \(-0.772347\pi\)
−0.754967 + 0.655763i \(0.772347\pi\)
\(812\) 0 0
\(813\) 5.00000 0.175358
\(814\) 24.0000 0.841200
\(815\) −22.0000 −0.770626
\(816\) 0 0
\(817\) 55.0000 1.92421
\(818\) 28.0000 0.978997
\(819\) −2.00000 −0.0698857
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 − 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) −18.0000 −0.627822
\(823\) −22.0000 −0.766872 −0.383436 − 0.923567i \(-0.625259\pi\)
−0.383436 + 0.923567i \(0.625259\pi\)
\(824\) −8.00000 −0.278693
\(825\) −3.00000 −0.104447
\(826\) 6.00000 0.208767
\(827\) −36.0000 −1.25184 −0.625921 − 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 9.00000 0.312772
\(829\) 29.0000 1.00721 0.503606 − 0.863934i \(-0.332006\pi\)
0.503606 + 0.863934i \(0.332006\pi\)
\(830\) 12.0000 0.416526
\(831\) 8.00000 0.277517
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) −14.0000 −0.484780
\(835\) 9.00000 0.311458
\(836\) −15.0000 −0.518786
\(837\) 1.00000 0.0345651
\(838\) 24.0000 0.829066
\(839\) 21.0000 0.725001 0.362500 − 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(840\) 1.00000 0.0345033
\(841\) −29.0000 −1.00000
\(842\) 10.0000 0.344623
\(843\) −24.0000 −0.826604
\(844\) −19.0000 −0.654007
\(845\) −9.00000 −0.309609
\(846\) 6.00000 0.206284
\(847\) 2.00000 0.0687208
\(848\) −9.00000 −0.309061
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) 72.0000 2.46813
\(852\) 9.00000 0.308335
\(853\) −19.0000 −0.650548 −0.325274 − 0.945620i \(-0.605456\pi\)
−0.325274 + 0.945620i \(0.605456\pi\)
\(854\) −10.0000 −0.342193
\(855\) 5.00000 0.170996
\(856\) 3.00000 0.102538
\(857\) −6.00000 −0.204956 −0.102478 − 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 6.00000 0.204837
\(859\) 8.00000 0.272956 0.136478 − 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) 11.0000 0.375097
\(861\) 0 0
\(862\) 0 0
\(863\) 15.0000 0.510606 0.255303 − 0.966861i \(-0.417825\pi\)
0.255303 + 0.966861i \(0.417825\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 6.00000 0.204006
\(866\) −5.00000 −0.169907
\(867\) −17.0000 −0.577350
\(868\) −1.00000 −0.0339422
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) 28.0000 0.948744
\(872\) −8.00000 −0.270914
\(873\) 14.0000 0.473828
\(874\) −45.0000 −1.52215
\(875\) −1.00000 −0.0338062
\(876\) −1.00000 −0.0337869
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −14.0000 −0.472477
\(879\) 18.0000 0.607125
\(880\) −3.00000 −0.101130
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 6.00000 0.202031
\(883\) −31.0000 −1.04323 −0.521617 − 0.853180i \(-0.674671\pi\)
−0.521617 + 0.853180i \(0.674671\pi\)
\(884\) 0 0
\(885\) 6.00000 0.201688
\(886\) −27.0000 −0.907083
\(887\) −18.0000 −0.604381 −0.302190 − 0.953248i \(-0.597718\pi\)
−0.302190 + 0.953248i \(0.597718\pi\)
\(888\) −8.00000 −0.268462
\(889\) −8.00000 −0.268311
\(890\) 9.00000 0.301681
\(891\) −3.00000 −0.100504
\(892\) −10.0000 −0.334825
\(893\) −30.0000 −1.00391
\(894\) −3.00000 −0.100335
\(895\) −12.0000 −0.401116
\(896\) 1.00000 0.0334077
\(897\) 18.0000 0.601003
\(898\) −6.00000 −0.200223
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 0 0
\(903\) −11.0000 −0.366057
\(904\) 3.00000 0.0997785
\(905\) 5.00000 0.166206
\(906\) 16.0000 0.531564
\(907\) 8.00000 0.265636 0.132818 − 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) −15.0000 −0.497792
\(909\) −15.0000 −0.497519
\(910\) 2.00000 0.0662994
\(911\) 12.0000 0.397578 0.198789 − 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 5.00000 0.165567
\(913\) 36.0000 1.19143
\(914\) −38.0000 −1.25693
\(915\) −10.0000 −0.330590
\(916\) 5.00000 0.165205
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) 26.0000 0.857661 0.428830 − 0.903385i \(-0.358926\pi\)
0.428830 + 0.903385i \(0.358926\pi\)
\(920\) −9.00000 −0.296721
\(921\) 32.0000 1.05444
\(922\) 0 0
\(923\) 18.0000 0.592477
\(924\) 3.00000 0.0986928
\(925\) 8.00000 0.263038
\(926\) −32.0000 −1.05159
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) −15.0000 −0.492134 −0.246067 − 0.969253i \(-0.579138\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(930\) −1.00000 −0.0327913
\(931\) −30.0000 −0.983210
\(932\) 3.00000 0.0982683
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 20.0000 0.653372 0.326686 − 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(938\) 14.0000 0.457116
\(939\) −22.0000 −0.717943
\(940\) −6.00000 −0.195698
\(941\) −12.0000 −0.391189 −0.195594 − 0.980685i \(-0.562664\pi\)
−0.195594 + 0.980685i \(0.562664\pi\)
\(942\) 7.00000 0.228072
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) −1.00000 −0.0325300
\(946\) 33.0000 1.07292
\(947\) 54.0000 1.75476 0.877382 − 0.479792i \(-0.159288\pi\)
0.877382 + 0.479792i \(0.159288\pi\)
\(948\) −1.00000 −0.0324785
\(949\) −2.00000 −0.0649227
\(950\) −5.00000 −0.162221
\(951\) 24.0000 0.778253
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 − 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 9.00000 0.291386
\(955\) 0 0
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) −21.0000 −0.678479
\(959\) −18.0000 −0.581250
\(960\) 1.00000 0.0322749
\(961\) 1.00000 0.0322581
\(962\) −16.0000 −0.515861
\(963\) −3.00000 −0.0966736
\(964\) −22.0000 −0.708572
\(965\) −10.0000 −0.321911
\(966\) 9.00000 0.289570
\(967\) −4.00000 −0.128631 −0.0643157 − 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) −14.0000 −0.449513
\(971\) −42.0000 −1.34784 −0.673922 − 0.738802i \(-0.735392\pi\)
−0.673922 + 0.738802i \(0.735392\pi\)
\(972\) 1.00000 0.0320750
\(973\) −14.0000 −0.448819
\(974\) 40.0000 1.28168
\(975\) 2.00000 0.0640513
\(976\) −10.0000 −0.320092
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 22.0000 0.703482
\(979\) 27.0000 0.862924
\(980\) −6.00000 −0.191663
\(981\) 8.00000 0.255420
\(982\) −21.0000 −0.670137
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) 0 0
\(987\) 6.00000 0.190982
\(988\) 10.0000 0.318142
\(989\) 99.0000 3.14802
\(990\) 3.00000 0.0953463
\(991\) 23.0000 0.730619 0.365310 − 0.930886i \(-0.380963\pi\)
0.365310 + 0.930886i \(0.380963\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 8.00000 0.253872
\(994\) 9.00000 0.285463
\(995\) −25.0000 −0.792553
\(996\) −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
\(999\) 8.00000 0.253109
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 930.2.a.i.1.1 ✓ 1
3.2 odd 2 2790.2.a.r.1.1 1
4.3 odd 2 7440.2.a.k.1.1 1
5.2 odd 4 4650.2.d.d.3349.1 2
5.3 odd 4 4650.2.d.d.3349.2 2
5.4 even 2 4650.2.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.i.1.1 ✓ 1 1.1 even 1 trivial
2790.2.a.r.1.1 1 3.2 odd 2
4650.2.a.bd.1.1 1 5.4 even 2
4650.2.d.d.3349.1 2 5.2 odd 4
4650.2.d.d.3349.2 2 5.3 odd 4
7440.2.a.k.1.1 1 4.3 odd 2