Properties

Label 2366.2.a.k.1.1
Level $2366$
Weight $2$
Character 2366.1
Self dual yes
Analytic conductor $18.893$
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] = [2366,2,Mod(1,2366)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2366, 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("2366.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.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: \(18.8926051182\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2366.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{10} +6.00000 q^{11} -2.00000 q^{12} -1.00000 q^{14} -6.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +3.00000 q^{20} +2.00000 q^{21} +6.00000 q^{22} -6.00000 q^{23} -2.00000 q^{24} +4.00000 q^{25} +4.00000 q^{27} -1.00000 q^{28} +3.00000 q^{29} -6.00000 q^{30} +10.0000 q^{31} +1.00000 q^{32} -12.0000 q^{33} -3.00000 q^{34} -3.00000 q^{35} +1.00000 q^{36} +1.00000 q^{37} +4.00000 q^{38} +3.00000 q^{40} +3.00000 q^{41} +2.00000 q^{42} -10.0000 q^{43} +6.00000 q^{44} +3.00000 q^{45} -6.00000 q^{46} -2.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +6.00000 q^{51} -9.00000 q^{53} +4.00000 q^{54} +18.0000 q^{55} -1.00000 q^{56} -8.00000 q^{57} +3.00000 q^{58} +6.00000 q^{59} -6.00000 q^{60} -7.00000 q^{61} +10.0000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -12.0000 q^{66} -2.00000 q^{67} -3.00000 q^{68} +12.0000 q^{69} -3.00000 q^{70} +1.00000 q^{72} +7.00000 q^{73} +1.00000 q^{74} -8.00000 q^{75} +4.00000 q^{76} -6.00000 q^{77} +14.0000 q^{79} +3.00000 q^{80} -11.0000 q^{81} +3.00000 q^{82} +18.0000 q^{83} +2.00000 q^{84} -9.00000 q^{85} -10.0000 q^{86} -6.00000 q^{87} +6.00000 q^{88} +6.00000 q^{89} +3.00000 q^{90} -6.00000 q^{92} -20.0000 q^{93} +12.0000 q^{95} -2.00000 q^{96} -2.00000 q^{97} +1.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) −2.00000 −0.816497
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 3.00000 0.948683
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) −2.00000 −0.577350
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) −6.00000 −1.54919
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 3.00000 0.670820
\(21\) 2.00000 0.436436
\(22\) 6.00000 1.27920
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −2.00000 −0.408248
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) −1.00000 −0.188982
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −6.00000 −1.09545
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) −12.0000 −2.08893
\(34\) −3.00000 −0.514496
\(35\) −3.00000 −0.507093
\(36\) 1.00000 0.166667
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 2.00000 0.308607
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 6.00000 0.904534
\(45\) 3.00000 0.447214
\(46\) −6.00000 −0.884652
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 6.00000 0.840168
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 4.00000 0.544331
\(55\) 18.0000 2.42712
\(56\) −1.00000 −0.133631
\(57\) −8.00000 −1.05963
\(58\) 3.00000 0.393919
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) −6.00000 −0.774597
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 10.0000 1.27000
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −12.0000 −1.47710
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −3.00000 −0.363803
\(69\) 12.0000 1.44463
\(70\) −3.00000 −0.358569
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 1.00000 0.116248
\(75\) −8.00000 −0.923760
\(76\) 4.00000 0.458831
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 3.00000 0.335410
\(81\) −11.0000 −1.22222
\(82\) 3.00000 0.331295
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 2.00000 0.218218
\(85\) −9.00000 −0.976187
\(86\) −10.0000 −1.07833
\(87\) −6.00000 −0.643268
\(88\) 6.00000 0.639602
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) −20.0000 −2.07390
\(94\) 0 0
\(95\) 12.0000 1.23117
\(96\) −2.00000 −0.204124
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 1.00000 0.101015
\(99\) 6.00000 0.603023
\(100\) 4.00000 0.400000
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 6.00000 0.594089
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) 6.00000 0.585540
\(106\) −9.00000 −0.874157
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 4.00000 0.384900
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 18.0000 1.71623
\(111\) −2.00000 −0.189832
\(112\) −1.00000 −0.0944911
\(113\) 3.00000 0.282216 0.141108 0.989994i \(-0.454933\pi\)
0.141108 + 0.989994i \(0.454933\pi\)
\(114\) −8.00000 −0.749269
\(115\) −18.0000 −1.67851
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 3.00000 0.275010
\(120\) −6.00000 −0.547723
\(121\) 25.0000 2.27273
\(122\) −7.00000 −0.633750
\(123\) −6.00000 −0.541002
\(124\) 10.0000 0.898027
\(125\) −3.00000 −0.268328
\(126\) −1.00000 −0.0890871
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 1.00000 0.0883883
\(129\) 20.0000 1.76090
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −12.0000 −1.04447
\(133\) −4.00000 −0.346844
\(134\) −2.00000 −0.172774
\(135\) 12.0000 1.03280
\(136\) −3.00000 −0.257248
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) 12.0000 1.02151
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 9.00000 0.747409
\(146\) 7.00000 0.579324
\(147\) −2.00000 −0.164957
\(148\) 1.00000 0.0821995
\(149\) 21.0000 1.72039 0.860194 0.509968i \(-0.170343\pi\)
0.860194 + 0.509968i \(0.170343\pi\)
\(150\) −8.00000 −0.653197
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 4.00000 0.324443
\(153\) −3.00000 −0.242536
\(154\) −6.00000 −0.483494
\(155\) 30.0000 2.40966
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 14.0000 1.11378
\(159\) 18.0000 1.42749
\(160\) 3.00000 0.237171
\(161\) 6.00000 0.472866
\(162\) −11.0000 −0.864242
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 3.00000 0.234261
\(165\) −36.0000 −2.80260
\(166\) 18.0000 1.39707
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 2.00000 0.154303
\(169\) 0 0
\(170\) −9.00000 −0.690268
\(171\) 4.00000 0.305888
\(172\) −10.0000 −0.762493
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −6.00000 −0.454859
\(175\) −4.00000 −0.302372
\(176\) 6.00000 0.452267
\(177\) −12.0000 −0.901975
\(178\) 6.00000 0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 3.00000 0.223607
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) −6.00000 −0.442326
\(185\) 3.00000 0.220564
\(186\) −20.0000 −1.46647
\(187\) −18.0000 −1.31629
\(188\) 0 0
\(189\) −4.00000 −0.290957
\(190\) 12.0000 0.870572
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) −2.00000 −0.144338
\(193\) −23.0000 −1.65558 −0.827788 0.561041i \(-0.810401\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 6.00000 0.426401
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 4.00000 0.282843
\(201\) 4.00000 0.282138
\(202\) −3.00000 −0.211079
\(203\) −3.00000 −0.210559
\(204\) 6.00000 0.420084
\(205\) 9.00000 0.628587
\(206\) −4.00000 −0.278693
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 24.0000 1.66011
\(210\) 6.00000 0.414039
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) −9.00000 −0.618123
\(213\) 0 0
\(214\) 0 0
\(215\) −30.0000 −2.04598
\(216\) 4.00000 0.272166
\(217\) −10.0000 −0.678844
\(218\) −2.00000 −0.135457
\(219\) −14.0000 −0.946032
\(220\) 18.0000 1.21356
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) 28.0000 1.87502 0.937509 0.347960i \(-0.113126\pi\)
0.937509 + 0.347960i \(0.113126\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.00000 0.266667
\(226\) 3.00000 0.199557
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) −8.00000 −0.529813
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) −18.0000 −1.18688
\(231\) 12.0000 0.789542
\(232\) 3.00000 0.196960
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) −28.0000 −1.81880
\(238\) 3.00000 0.194461
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −6.00000 −0.387298
\(241\) −17.0000 −1.09507 −0.547533 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 25.0000 1.60706
\(243\) 10.0000 0.641500
\(244\) −7.00000 −0.448129
\(245\) 3.00000 0.191663
\(246\) −6.00000 −0.382546
\(247\) 0 0
\(248\) 10.0000 0.635001
\(249\) −36.0000 −2.28141
\(250\) −3.00000 −0.189737
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −36.0000 −2.26330
\(254\) 20.0000 1.25491
\(255\) 18.0000 1.12720
\(256\) 1.00000 0.0625000
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 20.0000 1.24515
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 0 0
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) −12.0000 −0.738549
\(265\) −27.0000 −1.65860
\(266\) −4.00000 −0.245256
\(267\) −12.0000 −0.734388
\(268\) −2.00000 −0.122169
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 12.0000 0.730297
\(271\) −2.00000 −0.121491 −0.0607457 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 24.0000 1.44725
\(276\) 12.0000 0.722315
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) 2.00000 0.119952
\(279\) 10.0000 0.598684
\(280\) −3.00000 −0.179284
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) 0 0
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 0 0
\(285\) −24.0000 −1.42164
\(286\) 0 0
\(287\) −3.00000 −0.177084
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 9.00000 0.528498
\(291\) 4.00000 0.234484
\(292\) 7.00000 0.409644
\(293\) 3.00000 0.175262 0.0876309 0.996153i \(-0.472070\pi\)
0.0876309 + 0.996153i \(0.472070\pi\)
\(294\) −2.00000 −0.116642
\(295\) 18.0000 1.04800
\(296\) 1.00000 0.0581238
\(297\) 24.0000 1.39262
\(298\) 21.0000 1.21650
\(299\) 0 0
\(300\) −8.00000 −0.461880
\(301\) 10.0000 0.576390
\(302\) −8.00000 −0.460348
\(303\) 6.00000 0.344691
\(304\) 4.00000 0.229416
\(305\) −21.0000 −1.20246
\(306\) −3.00000 −0.171499
\(307\) 22.0000 1.25561 0.627803 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) −6.00000 −0.341882
\(309\) 8.00000 0.455104
\(310\) 30.0000 1.70389
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −7.00000 −0.395033
\(315\) −3.00000 −0.169031
\(316\) 14.0000 0.787562
\(317\) 9.00000 0.505490 0.252745 0.967533i \(-0.418667\pi\)
0.252745 + 0.967533i \(0.418667\pi\)
\(318\) 18.0000 1.00939
\(319\) 18.0000 1.00781
\(320\) 3.00000 0.167705
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) −12.0000 −0.667698
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −2.00000 −0.110770
\(327\) 4.00000 0.221201
\(328\) 3.00000 0.165647
\(329\) 0 0
\(330\) −36.0000 −1.98173
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) 18.0000 0.987878
\(333\) 1.00000 0.0547997
\(334\) 6.00000 0.328305
\(335\) −6.00000 −0.327815
\(336\) 2.00000 0.109109
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) −9.00000 −0.488094
\(341\) 60.0000 3.24918
\(342\) 4.00000 0.216295
\(343\) −1.00000 −0.0539949
\(344\) −10.0000 −0.539164
\(345\) 36.0000 1.93817
\(346\) 6.00000 0.322562
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) −6.00000 −0.321634
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 6.00000 0.319801
\(353\) 3.00000 0.159674 0.0798369 0.996808i \(-0.474560\pi\)
0.0798369 + 0.996808i \(0.474560\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) −6.00000 −0.317554
\(358\) 0 0
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.00000 −0.157895
\(362\) 5.00000 0.262794
\(363\) −50.0000 −2.62432
\(364\) 0 0
\(365\) 21.0000 1.09919
\(366\) 14.0000 0.731792
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −6.00000 −0.312772
\(369\) 3.00000 0.156174
\(370\) 3.00000 0.155963
\(371\) 9.00000 0.467257
\(372\) −20.0000 −1.03695
\(373\) −13.0000 −0.673114 −0.336557 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −18.0000 −0.930758
\(375\) 6.00000 0.309839
\(376\) 0 0
\(377\) 0 0
\(378\) −4.00000 −0.205738
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 12.0000 0.615587
\(381\) −40.0000 −2.04926
\(382\) 18.0000 0.920960
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) −2.00000 −0.102062
\(385\) −18.0000 −0.917365
\(386\) −23.0000 −1.17067
\(387\) −10.0000 −0.508329
\(388\) −2.00000 −0.101535
\(389\) −33.0000 −1.67317 −0.836583 0.547840i \(-0.815450\pi\)
−0.836583 + 0.547840i \(0.815450\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 42.0000 2.11325
\(396\) 6.00000 0.301511
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) −4.00000 −0.200502
\(399\) 8.00000 0.400501
\(400\) 4.00000 0.200000
\(401\) −15.0000 −0.749064 −0.374532 0.927214i \(-0.622197\pi\)
−0.374532 + 0.927214i \(0.622197\pi\)
\(402\) 4.00000 0.199502
\(403\) 0 0
\(404\) −3.00000 −0.149256
\(405\) −33.0000 −1.63978
\(406\) −3.00000 −0.148888
\(407\) 6.00000 0.297409
\(408\) 6.00000 0.297044
\(409\) −5.00000 −0.247234 −0.123617 0.992330i \(-0.539449\pi\)
−0.123617 + 0.992330i \(0.539449\pi\)
\(410\) 9.00000 0.444478
\(411\) 6.00000 0.295958
\(412\) −4.00000 −0.197066
\(413\) −6.00000 −0.295241
\(414\) −6.00000 −0.294884
\(415\) 54.0000 2.65076
\(416\) 0 0
\(417\) −4.00000 −0.195881
\(418\) 24.0000 1.17388
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 6.00000 0.292770
\(421\) −35.0000 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(422\) −22.0000 −1.07094
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 7.00000 0.338754
\(428\) 0 0
\(429\) 0 0
\(430\) −30.0000 −1.44673
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 4.00000 0.192450
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) −10.0000 −0.480015
\(435\) −18.0000 −0.863034
\(436\) −2.00000 −0.0957826
\(437\) −24.0000 −1.14808
\(438\) −14.0000 −0.668946
\(439\) −22.0000 −1.05000 −0.525001 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 18.0000 0.858116
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 18.0000 0.853282
\(446\) 28.0000 1.32584
\(447\) −42.0000 −1.98653
\(448\) −1.00000 −0.0472456
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 4.00000 0.188562
\(451\) 18.0000 0.847587
\(452\) 3.00000 0.141108
\(453\) 16.0000 0.751746
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) 25.0000 1.16945 0.584725 0.811231i \(-0.301202\pi\)
0.584725 + 0.811231i \(0.301202\pi\)
\(458\) −14.0000 −0.654177
\(459\) −12.0000 −0.560112
\(460\) −18.0000 −0.839254
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 12.0000 0.558291
\(463\) 22.0000 1.02243 0.511213 0.859454i \(-0.329196\pi\)
0.511213 + 0.859454i \(0.329196\pi\)
\(464\) 3.00000 0.139272
\(465\) −60.0000 −2.78243
\(466\) −18.0000 −0.833834
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) 2.00000 0.0923514
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) 6.00000 0.276172
\(473\) −60.0000 −2.75880
\(474\) −28.0000 −1.28608
\(475\) 16.0000 0.734130
\(476\) 3.00000 0.137505
\(477\) −9.00000 −0.412082
\(478\) 6.00000 0.274434
\(479\) −42.0000 −1.91903 −0.959514 0.281659i \(-0.909115\pi\)
−0.959514 + 0.281659i \(0.909115\pi\)
\(480\) −6.00000 −0.273861
\(481\) 0 0
\(482\) −17.0000 −0.774329
\(483\) −12.0000 −0.546019
\(484\) 25.0000 1.13636
\(485\) −6.00000 −0.272446
\(486\) 10.0000 0.453609
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) −7.00000 −0.316875
\(489\) 4.00000 0.180886
\(490\) 3.00000 0.135526
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −6.00000 −0.270501
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) 18.0000 0.809040
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) −36.0000 −1.61320
\(499\) 22.0000 0.984855 0.492428 0.870353i \(-0.336110\pi\)
0.492428 + 0.870353i \(0.336110\pi\)
\(500\) −3.00000 −0.134164
\(501\) −12.0000 −0.536120
\(502\) −12.0000 −0.535586
\(503\) −18.0000 −0.802580 −0.401290 0.915951i \(-0.631438\pi\)
−0.401290 + 0.915951i \(0.631438\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −9.00000 −0.400495
\(506\) −36.0000 −1.60040
\(507\) 0 0
\(508\) 20.0000 0.887357
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 18.0000 0.797053
\(511\) −7.00000 −0.309662
\(512\) 1.00000 0.0441942
\(513\) 16.0000 0.706417
\(514\) 21.0000 0.926270
\(515\) −12.0000 −0.528783
\(516\) 20.0000 0.880451
\(517\) 0 0
\(518\) −1.00000 −0.0439375
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) −39.0000 −1.70862 −0.854311 0.519763i \(-0.826020\pi\)
−0.854311 + 0.519763i \(0.826020\pi\)
\(522\) 3.00000 0.131306
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 0 0
\(525\) 8.00000 0.349149
\(526\) −6.00000 −0.261612
\(527\) −30.0000 −1.30682
\(528\) −12.0000 −0.522233
\(529\) 13.0000 0.565217
\(530\) −27.0000 −1.17281
\(531\) 6.00000 0.260378
\(532\) −4.00000 −0.173422
\(533\) 0 0
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 6.00000 0.258438
\(540\) 12.0000 0.516398
\(541\) 25.0000 1.07483 0.537417 0.843317i \(-0.319400\pi\)
0.537417 + 0.843317i \(0.319400\pi\)
\(542\) −2.00000 −0.0859074
\(543\) −10.0000 −0.429141
\(544\) −3.00000 −0.128624
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) −3.00000 −0.128154
\(549\) −7.00000 −0.298753
\(550\) 24.0000 1.02336
\(551\) 12.0000 0.511217
\(552\) 12.0000 0.510754
\(553\) −14.0000 −0.595341
\(554\) −1.00000 −0.0424859
\(555\) −6.00000 −0.254686
\(556\) 2.00000 0.0848189
\(557\) 9.00000 0.381342 0.190671 0.981654i \(-0.438934\pi\)
0.190671 + 0.981654i \(0.438934\pi\)
\(558\) 10.0000 0.423334
\(559\) 0 0
\(560\) −3.00000 −0.126773
\(561\) 36.0000 1.51992
\(562\) −27.0000 −1.13893
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 0 0
\(565\) 9.00000 0.378633
\(566\) −22.0000 −0.924729
\(567\) 11.0000 0.461957
\(568\) 0 0
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) −24.0000 −1.00525
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 0 0
\(573\) −36.0000 −1.50392
\(574\) −3.00000 −0.125218
\(575\) −24.0000 −1.00087
\(576\) 1.00000 0.0416667
\(577\) 19.0000 0.790980 0.395490 0.918470i \(-0.370575\pi\)
0.395490 + 0.918470i \(0.370575\pi\)
\(578\) −8.00000 −0.332756
\(579\) 46.0000 1.91169
\(580\) 9.00000 0.373705
\(581\) −18.0000 −0.746766
\(582\) 4.00000 0.165805
\(583\) −54.0000 −2.23645
\(584\) 7.00000 0.289662
\(585\) 0 0
\(586\) 3.00000 0.123929
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 40.0000 1.64817
\(590\) 18.0000 0.741048
\(591\) 36.0000 1.48084
\(592\) 1.00000 0.0410997
\(593\) 15.0000 0.615976 0.307988 0.951390i \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) 24.0000 0.984732
\(595\) 9.00000 0.368964
\(596\) 21.0000 0.860194
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) 36.0000 1.47092 0.735460 0.677568i \(-0.236966\pi\)
0.735460 + 0.677568i \(0.236966\pi\)
\(600\) −8.00000 −0.326599
\(601\) −19.0000 −0.775026 −0.387513 0.921864i \(-0.626666\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(602\) 10.0000 0.407570
\(603\) −2.00000 −0.0814463
\(604\) −8.00000 −0.325515
\(605\) 75.0000 3.04918
\(606\) 6.00000 0.243733
\(607\) 44.0000 1.78590 0.892952 0.450151i \(-0.148630\pi\)
0.892952 + 0.450151i \(0.148630\pi\)
\(608\) 4.00000 0.162221
\(609\) 6.00000 0.243132
\(610\) −21.0000 −0.850265
\(611\) 0 0
\(612\) −3.00000 −0.121268
\(613\) 13.0000 0.525065 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(614\) 22.0000 0.887848
\(615\) −18.0000 −0.725830
\(616\) −6.00000 −0.241747
\(617\) 45.0000 1.81163 0.905816 0.423672i \(-0.139259\pi\)
0.905816 + 0.423672i \(0.139259\pi\)
\(618\) 8.00000 0.321807
\(619\) −26.0000 −1.04503 −0.522514 0.852631i \(-0.675006\pi\)
−0.522514 + 0.852631i \(0.675006\pi\)
\(620\) 30.0000 1.20483
\(621\) −24.0000 −0.963087
\(622\) −18.0000 −0.721734
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −10.0000 −0.399680
\(627\) −48.0000 −1.91694
\(628\) −7.00000 −0.279330
\(629\) −3.00000 −0.119618
\(630\) −3.00000 −0.119523
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 14.0000 0.556890
\(633\) 44.0000 1.74884
\(634\) 9.00000 0.357436
\(635\) 60.0000 2.38103
\(636\) 18.0000 0.713746
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) 0 0
\(643\) 40.0000 1.57745 0.788723 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 6.00000 0.236433
\(645\) 60.0000 2.36250
\(646\) −12.0000 −0.472134
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −11.0000 −0.432121
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 20.0000 0.783862
\(652\) −2.00000 −0.0783260
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) 7.00000 0.273096
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) −36.0000 −1.40130
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) 18.0000 0.698535
\(665\) −12.0000 −0.465340
\(666\) 1.00000 0.0387492
\(667\) −18.0000 −0.696963
\(668\) 6.00000 0.232147
\(669\) −56.0000 −2.16509
\(670\) −6.00000 −0.231800
\(671\) −42.0000 −1.62139
\(672\) 2.00000 0.0771517
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) −13.0000 −0.500741
\(675\) 16.0000 0.615840
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −6.00000 −0.230429
\(679\) 2.00000 0.0767530
\(680\) −9.00000 −0.345134
\(681\) −12.0000 −0.459841
\(682\) 60.0000 2.29752
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 4.00000 0.152944
\(685\) −9.00000 −0.343872
\(686\) −1.00000 −0.0381802
\(687\) 28.0000 1.06827
\(688\) −10.0000 −0.381246
\(689\) 0 0
\(690\) 36.0000 1.37050
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 6.00000 0.228086
\(693\) −6.00000 −0.227921
\(694\) −6.00000 −0.227757
\(695\) 6.00000 0.227593
\(696\) −6.00000 −0.227429
\(697\) −9.00000 −0.340899
\(698\) −2.00000 −0.0757011
\(699\) 36.0000 1.36165
\(700\) −4.00000 −0.151186
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 6.00000 0.226134
\(705\) 0 0
\(706\) 3.00000 0.112906
\(707\) 3.00000 0.112827
\(708\) −12.0000 −0.450988
\(709\) 1.00000 0.0375558 0.0187779 0.999824i \(-0.494022\pi\)
0.0187779 + 0.999824i \(0.494022\pi\)
\(710\) 0 0
\(711\) 14.0000 0.525041
\(712\) 6.00000 0.224860
\(713\) −60.0000 −2.24702
\(714\) −6.00000 −0.224544
\(715\) 0 0
\(716\) 0 0
\(717\) −12.0000 −0.448148
\(718\) −12.0000 −0.447836
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 3.00000 0.111803
\(721\) 4.00000 0.148968
\(722\) −3.00000 −0.111648
\(723\) 34.0000 1.26447
\(724\) 5.00000 0.185824
\(725\) 12.0000 0.445669
\(726\) −50.0000 −1.85567
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 21.0000 0.777245
\(731\) 30.0000 1.10959
\(732\) 14.0000 0.517455
\(733\) −17.0000 −0.627909 −0.313955 0.949438i \(-0.601654\pi\)
−0.313955 + 0.949438i \(0.601654\pi\)
\(734\) −10.0000 −0.369107
\(735\) −6.00000 −0.221313
\(736\) −6.00000 −0.221163
\(737\) −12.0000 −0.442026
\(738\) 3.00000 0.110432
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 3.00000 0.110282
\(741\) 0 0
\(742\) 9.00000 0.330400
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) −20.0000 −0.733236
\(745\) 63.0000 2.30814
\(746\) −13.0000 −0.475964
\(747\) 18.0000 0.658586
\(748\) −18.0000 −0.658145
\(749\) 0 0
\(750\) 6.00000 0.219089
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) 0 0
\(753\) 24.0000 0.874609
\(754\) 0 0
\(755\) −24.0000 −0.873449
\(756\) −4.00000 −0.145479
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −26.0000 −0.944363
\(759\) 72.0000 2.61343
\(760\) 12.0000 0.435286
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −40.0000 −1.44905
\(763\) 2.00000 0.0724049
\(764\) 18.0000 0.651217
\(765\) −9.00000 −0.325396
\(766\) 18.0000 0.650366
\(767\) 0 0
\(768\) −2.00000 −0.0721688
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) −18.0000 −0.648675
\(771\) −42.0000 −1.51259
\(772\) −23.0000 −0.827788
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −10.0000 −0.359443
\(775\) 40.0000 1.43684
\(776\) −2.00000 −0.0717958
\(777\) 2.00000 0.0717496
\(778\) −33.0000 −1.18311
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) 0 0
\(782\) 18.0000 0.643679
\(783\) 12.0000 0.428845
\(784\) 1.00000 0.0357143
\(785\) −21.0000 −0.749522
\(786\) 0 0
\(787\) 10.0000 0.356462 0.178231 0.983989i \(-0.442963\pi\)
0.178231 + 0.983989i \(0.442963\pi\)
\(788\) −18.0000 −0.641223
\(789\) 12.0000 0.427211
\(790\) 42.0000 1.49429
\(791\) −3.00000 −0.106668
\(792\) 6.00000 0.213201
\(793\) 0 0
\(794\) 34.0000 1.20661
\(795\) 54.0000 1.91518
\(796\) −4.00000 −0.141776
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 8.00000 0.283197
\(799\) 0 0
\(800\) 4.00000 0.141421
\(801\) 6.00000 0.212000
\(802\) −15.0000 −0.529668
\(803\) 42.0000 1.48215
\(804\) 4.00000 0.141069
\(805\) 18.0000 0.634417
\(806\) 0 0
\(807\) −36.0000 −1.26726
\(808\) −3.00000 −0.105540
\(809\) 51.0000 1.79306 0.896532 0.442978i \(-0.146078\pi\)
0.896532 + 0.442978i \(0.146078\pi\)
\(810\) −33.0000 −1.15950
\(811\) −26.0000 −0.912983 −0.456492 0.889728i \(-0.650894\pi\)
−0.456492 + 0.889728i \(0.650894\pi\)
\(812\) −3.00000 −0.105279
\(813\) 4.00000 0.140286
\(814\) 6.00000 0.210300
\(815\) −6.00000 −0.210171
\(816\) 6.00000 0.210042
\(817\) −40.0000 −1.39942
\(818\) −5.00000 −0.174821
\(819\) 0 0
\(820\) 9.00000 0.314294
\(821\) 42.0000 1.46581 0.732905 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 6.00000 0.209274
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) −4.00000 −0.139347
\(825\) −48.0000 −1.67115
\(826\) −6.00000 −0.208767
\(827\) −42.0000 −1.46048 −0.730242 0.683189i \(-0.760592\pi\)
−0.730242 + 0.683189i \(0.760592\pi\)
\(828\) −6.00000 −0.208514
\(829\) −7.00000 −0.243120 −0.121560 0.992584i \(-0.538790\pi\)
−0.121560 + 0.992584i \(0.538790\pi\)
\(830\) 54.0000 1.87437
\(831\) 2.00000 0.0693792
\(832\) 0 0
\(833\) −3.00000 −0.103944
\(834\) −4.00000 −0.138509
\(835\) 18.0000 0.622916
\(836\) 24.0000 0.830057
\(837\) 40.0000 1.38260
\(838\) 6.00000 0.207267
\(839\) −12.0000 −0.414286 −0.207143 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 6.00000 0.207020
\(841\) −20.0000 −0.689655
\(842\) −35.0000 −1.20618
\(843\) 54.0000 1.85986
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) −9.00000 −0.309061
\(849\) 44.0000 1.51008
\(850\) −12.0000 −0.411597
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) 19.0000 0.650548 0.325274 0.945620i \(-0.394544\pi\)
0.325274 + 0.945620i \(0.394544\pi\)
\(854\) 7.00000 0.239535
\(855\) 12.0000 0.410391
\(856\) 0 0
\(857\) 33.0000 1.12726 0.563629 0.826028i \(-0.309405\pi\)
0.563629 + 0.826028i \(0.309405\pi\)
\(858\) 0 0
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) −30.0000 −1.02299
\(861\) 6.00000 0.204479
\(862\) 12.0000 0.408722
\(863\) −54.0000 −1.83818 −0.919091 0.394046i \(-0.871075\pi\)
−0.919091 + 0.394046i \(0.871075\pi\)
\(864\) 4.00000 0.136083
\(865\) 18.0000 0.612018
\(866\) 5.00000 0.169907
\(867\) 16.0000 0.543388
\(868\) −10.0000 −0.339422
\(869\) 84.0000 2.84950
\(870\) −18.0000 −0.610257
\(871\) 0 0
\(872\) −2.00000 −0.0677285
\(873\) −2.00000 −0.0676897
\(874\) −24.0000 −0.811812
\(875\) 3.00000 0.101419
\(876\) −14.0000 −0.473016
\(877\) 49.0000 1.65461 0.827306 0.561751i \(-0.189872\pi\)
0.827306 + 0.561751i \(0.189872\pi\)
\(878\) −22.0000 −0.742464
\(879\) −6.00000 −0.202375
\(880\) 18.0000 0.606780
\(881\) 45.0000 1.51609 0.758044 0.652203i \(-0.226155\pi\)
0.758044 + 0.652203i \(0.226155\pi\)
\(882\) 1.00000 0.0336718
\(883\) 38.0000 1.27880 0.639401 0.768874i \(-0.279182\pi\)
0.639401 + 0.768874i \(0.279182\pi\)
\(884\) 0 0
\(885\) −36.0000 −1.21013
\(886\) −24.0000 −0.806296
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −20.0000 −0.670778
\(890\) 18.0000 0.603361
\(891\) −66.0000 −2.21108
\(892\) 28.0000 0.937509
\(893\) 0 0
\(894\) −42.0000 −1.40469
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −30.0000 −1.00111
\(899\) 30.0000 1.00056
\(900\) 4.00000 0.133333
\(901\) 27.0000 0.899500
\(902\) 18.0000 0.599334
\(903\) −20.0000 −0.665558
\(904\) 3.00000 0.0997785
\(905\) 15.0000 0.498617
\(906\) 16.0000 0.531564
\(907\) 14.0000 0.464862 0.232431 0.972613i \(-0.425332\pi\)
0.232431 + 0.972613i \(0.425332\pi\)
\(908\) 6.00000 0.199117
\(909\) −3.00000 −0.0995037
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −8.00000 −0.264906
\(913\) 108.000 3.57428
\(914\) 25.0000 0.826927
\(915\) 42.0000 1.38848
\(916\) −14.0000 −0.462573
\(917\) 0 0
\(918\) −12.0000 −0.396059
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) −18.0000 −0.593442
\(921\) −44.0000 −1.44985
\(922\) −33.0000 −1.08680
\(923\) 0 0
\(924\) 12.0000 0.394771
\(925\) 4.00000 0.131519
\(926\) 22.0000 0.722965
\(927\) −4.00000 −0.131377
\(928\) 3.00000 0.0984798
\(929\) −33.0000 −1.08269 −0.541347 0.840799i \(-0.682086\pi\)
−0.541347 + 0.840799i \(0.682086\pi\)
\(930\) −60.0000 −1.96748
\(931\) 4.00000 0.131095
\(932\) −18.0000 −0.589610
\(933\) 36.0000 1.17859
\(934\) −18.0000 −0.588978
\(935\) −54.0000 −1.76599
\(936\) 0 0
\(937\) −19.0000 −0.620703 −0.310351 0.950622i \(-0.600447\pi\)
−0.310351 + 0.950622i \(0.600447\pi\)
\(938\) 2.00000 0.0653023
\(939\) 20.0000 0.652675
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 14.0000 0.456145
\(943\) −18.0000 −0.586161
\(944\) 6.00000 0.195283
\(945\) −12.0000 −0.390360
\(946\) −60.0000 −1.95077
\(947\) 42.0000 1.36482 0.682408 0.730971i \(-0.260933\pi\)
0.682408 + 0.730971i \(0.260933\pi\)
\(948\) −28.0000 −0.909398
\(949\) 0 0
\(950\) 16.0000 0.519109
\(951\) −18.0000 −0.583690
\(952\) 3.00000 0.0972306
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −9.00000 −0.291386
\(955\) 54.0000 1.74740
\(956\) 6.00000 0.194054
\(957\) −36.0000 −1.16371
\(958\) −42.0000 −1.35696
\(959\) 3.00000 0.0968751
\(960\) −6.00000 −0.193649
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) 0 0
\(964\) −17.0000 −0.547533
\(965\) −69.0000 −2.22119
\(966\) −12.0000 −0.386094
\(967\) 34.0000 1.09337 0.546683 0.837340i \(-0.315890\pi\)
0.546683 + 0.837340i \(0.315890\pi\)
\(968\) 25.0000 0.803530
\(969\) 24.0000 0.770991
\(970\) −6.00000 −0.192648
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 10.0000 0.320750
\(973\) −2.00000 −0.0641171
\(974\) −32.0000 −1.02535
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) −51.0000 −1.63163 −0.815817 0.578310i \(-0.803713\pi\)
−0.815817 + 0.578310i \(0.803713\pi\)
\(978\) 4.00000 0.127906
\(979\) 36.0000 1.15056
\(980\) 3.00000 0.0958315
\(981\) −2.00000 −0.0638551
\(982\) 0 0
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) −6.00000 −0.191273
\(985\) −54.0000 −1.72058
\(986\) −9.00000 −0.286618
\(987\) 0 0
\(988\) 0 0
\(989\) 60.0000 1.90789
\(990\) 18.0000 0.572078
\(991\) −10.0000 −0.317660 −0.158830 0.987306i \(-0.550772\pi\)
−0.158830 + 0.987306i \(0.550772\pi\)
\(992\) 10.0000 0.317500
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) −12.0000 −0.380426
\(996\) −36.0000 −1.14070
\(997\) 53.0000 1.67853 0.839263 0.543725i \(-0.182987\pi\)
0.839263 + 0.543725i \(0.182987\pi\)
\(998\) 22.0000 0.696398
\(999\) 4.00000 0.126554
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 2366.2.a.k.1.1 1
13.4 even 6 182.2.g.c.29.1 2
13.5 odd 4 2366.2.d.a.337.1 2
13.8 odd 4 2366.2.d.a.337.2 2
13.10 even 6 182.2.g.c.113.1 yes 2
13.12 even 2 2366.2.a.a.1.1 1
39.17 odd 6 1638.2.r.m.757.1 2
39.23 odd 6 1638.2.r.m.1387.1 2
52.23 odd 6 1456.2.s.a.113.1 2
52.43 odd 6 1456.2.s.a.1121.1 2
91.4 even 6 1274.2.e.k.471.1 2
91.10 odd 6 1274.2.h.l.373.1 2
91.17 odd 6 1274.2.e.b.471.1 2
91.23 even 6 1274.2.e.k.165.1 2
91.30 even 6 1274.2.h.e.263.1 2
91.62 odd 6 1274.2.g.c.295.1 2
91.69 odd 6 1274.2.g.c.393.1 2
91.75 odd 6 1274.2.e.b.165.1 2
91.82 odd 6 1274.2.h.l.263.1 2
91.88 even 6 1274.2.h.e.373.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.g.c.29.1 2 13.4 even 6
182.2.g.c.113.1 yes 2 13.10 even 6
1274.2.e.b.165.1 2 91.75 odd 6
1274.2.e.b.471.1 2 91.17 odd 6
1274.2.e.k.165.1 2 91.23 even 6
1274.2.e.k.471.1 2 91.4 even 6
1274.2.g.c.295.1 2 91.62 odd 6
1274.2.g.c.393.1 2 91.69 odd 6
1274.2.h.e.263.1 2 91.30 even 6
1274.2.h.e.373.1 2 91.88 even 6
1274.2.h.l.263.1 2 91.82 odd 6
1274.2.h.l.373.1 2 91.10 odd 6
1456.2.s.a.113.1 2 52.23 odd 6
1456.2.s.a.1121.1 2 52.43 odd 6
1638.2.r.m.757.1 2 39.17 odd 6
1638.2.r.m.1387.1 2 39.23 odd 6
2366.2.a.a.1.1 1 13.12 even 2
2366.2.a.k.1.1 1 1.1 even 1 trivial
2366.2.d.a.337.1 2 13.5 odd 4
2366.2.d.a.337.2 2 13.8 odd 4