Properties

Label 666.2.a.d.1.1
Level $666$
Weight $2$
Character 666.1
Self dual yes
Analytic conductor $5.318$
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] = [666,2,Mod(1,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, 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("666.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.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: \(5.31803677462\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 222)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 666.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} -4.00000 q^{10} +1.00000 q^{11} -3.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -5.00000 q^{19} -4.00000 q^{20} +1.00000 q^{22} -5.00000 q^{23} +11.0000 q^{25} -3.00000 q^{26} -1.00000 q^{28} -4.00000 q^{29} -10.0000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +4.00000 q^{35} -1.00000 q^{37} -5.00000 q^{38} -4.00000 q^{40} +6.00000 q^{41} +4.00000 q^{43} +1.00000 q^{44} -5.00000 q^{46} -2.00000 q^{47} -6.00000 q^{49} +11.0000 q^{50} -3.00000 q^{52} +11.0000 q^{53} -4.00000 q^{55} -1.00000 q^{56} -4.00000 q^{58} +12.0000 q^{59} +10.0000 q^{61} -10.0000 q^{62} +1.00000 q^{64} +12.0000 q^{65} +14.0000 q^{67} -3.00000 q^{68} +4.00000 q^{70} -11.0000 q^{73} -1.00000 q^{74} -5.00000 q^{76} -1.00000 q^{77} -10.0000 q^{79} -4.00000 q^{80} +6.00000 q^{82} +9.00000 q^{83} +12.0000 q^{85} +4.00000 q^{86} +1.00000 q^{88} -11.0000 q^{89} +3.00000 q^{91} -5.00000 q^{92} -2.00000 q^{94} +20.0000 q^{95} +10.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −4.00000 −1.26491
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) −1.00000 −0.164399
\(38\) −5.00000 −0.811107
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −5.00000 −0.737210
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 11.0000 1.55563
\(51\) 0 0
\(52\) −3.00000 −0.416025
\(53\) 11.0000 1.51097 0.755483 0.655168i \(-0.227402\pi\)
0.755483 + 0.655168i \(0.227402\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −10.0000 −1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) 14.0000 1.71037 0.855186 0.518321i \(-0.173443\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 1.00000 0.106600
\(89\) −11.0000 −1.16600 −0.582999 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) −5.00000 −0.521286
\(93\) 0 0
\(94\) −2.00000 −0.206284
\(95\) 20.0000 2.05196
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 11.0000 1.10000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −2.00000 −0.197066 −0.0985329 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) −3.00000 −0.294174
\(105\) 0 0
\(106\) 11.0000 1.06841
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) −4.00000 −0.381385
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 20.0000 1.86501
\(116\) −4.00000 −0.371391
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −10.0000 −0.898027
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 12.0000 1.05247
\(131\) −22.0000 −1.92215 −0.961074 0.276289i \(-0.910895\pi\)
−0.961074 + 0.276289i \(0.910895\pi\)
\(132\) 0 0
\(133\) 5.00000 0.433555
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) −20.0000 −1.70872 −0.854358 0.519685i \(-0.826049\pi\)
−0.854358 + 0.519685i \(0.826049\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) 0 0
\(143\) −3.00000 −0.250873
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 5.00000 0.406894 0.203447 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) −5.00000 −0.405554
\(153\) 0 0
\(154\) −1.00000 −0.0805823
\(155\) 40.0000 3.21288
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) −10.0000 −0.795557
\(159\) 0 0
\(160\) −4.00000 −0.316228
\(161\) 5.00000 0.394055
\(162\) 0 0
\(163\) 9.00000 0.704934 0.352467 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) 17.0000 1.31550 0.657750 0.753237i \(-0.271508\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 12.0000 0.920358
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 13.0000 0.988372 0.494186 0.869356i \(-0.335466\pi\)
0.494186 + 0.869356i \(0.335466\pi\)
\(174\) 0 0
\(175\) −11.0000 −0.831522
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −11.0000 −0.824485
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 3.00000 0.222375
\(183\) 0 0
\(184\) −5.00000 −0.368605
\(185\) 4.00000 0.294086
\(186\) 0 0
\(187\) −3.00000 −0.219382
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 20.0000 1.45095
\(191\) −9.00000 −0.651217 −0.325609 0.945505i \(-0.605569\pi\)
−0.325609 + 0.945505i \(0.605569\pi\)
\(192\) 0 0
\(193\) 18.0000 1.29567 0.647834 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −7.00000 −0.498729 −0.249365 0.968410i \(-0.580222\pi\)
−0.249365 + 0.968410i \(0.580222\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 11.0000 0.777817
\(201\) 0 0
\(202\) −6.00000 −0.422159
\(203\) 4.00000 0.280745
\(204\) 0 0
\(205\) −24.0000 −1.67623
\(206\) −2.00000 −0.139347
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 11.0000 0.755483
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) −16.0000 −1.09119
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) −9.00000 −0.609557
\(219\) 0 0
\(220\) −4.00000 −0.269680
\(221\) 9.00000 0.605406
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) −16.0000 −1.06196 −0.530979 0.847385i \(-0.678176\pi\)
−0.530979 + 0.847385i \(0.678176\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 20.0000 1.31876
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 12.0000 0.781133
\(237\) 0 0
\(238\) 3.00000 0.194461
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 28.0000 1.80364 0.901819 0.432113i \(-0.142232\pi\)
0.901819 + 0.432113i \(0.142232\pi\)
\(242\) −10.0000 −0.642824
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) 24.0000 1.53330
\(246\) 0 0
\(247\) 15.0000 0.954427
\(248\) −10.0000 −0.635001
\(249\) 0 0
\(250\) −24.0000 −1.51789
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) −3.00000 −0.188237
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −27.0000 −1.68421 −0.842107 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −22.0000 −1.35916
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) −44.0000 −2.70290
\(266\) 5.00000 0.306570
\(267\) 0 0
\(268\) 14.0000 0.855186
\(269\) −27.0000 −1.64622 −0.823110 0.567883i \(-0.807763\pi\)
−0.823110 + 0.567883i \(0.807763\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −20.0000 −1.20824
\(275\) 11.0000 0.663325
\(276\) 0 0
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) −14.0000 −0.839664
\(279\) 0 0
\(280\) 4.00000 0.239046
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 21.0000 1.24832 0.624160 0.781296i \(-0.285441\pi\)
0.624160 + 0.781296i \(0.285441\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 16.0000 0.939552
\(291\) 0 0
\(292\) −11.0000 −0.643726
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) −48.0000 −2.79467
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) 15.0000 0.867472
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 5.00000 0.287718
\(303\) 0 0
\(304\) −5.00000 −0.286770
\(305\) −40.0000 −2.29039
\(306\) 0 0
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 0 0
\(310\) 40.0000 2.27185
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) −4.00000 −0.223957
\(320\) −4.00000 −0.223607
\(321\) 0 0
\(322\) 5.00000 0.278639
\(323\) 15.0000 0.834622
\(324\) 0 0
\(325\) −33.0000 −1.83051
\(326\) 9.00000 0.498464
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 9.00000 0.493939
\(333\) 0 0
\(334\) 17.0000 0.930199
\(335\) −56.0000 −3.05961
\(336\) 0 0
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −4.00000 −0.217571
\(339\) 0 0
\(340\) 12.0000 0.650791
\(341\) −10.0000 −0.541530
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 13.0000 0.698884
\(347\) −18.0000 −0.966291 −0.483145 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) −11.0000 −0.587975
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −11.0000 −0.582999
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −16.0000 −0.840941
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) 44.0000 2.30307
\(366\) 0 0
\(367\) 15.0000 0.782994 0.391497 0.920179i \(-0.371957\pi\)
0.391497 + 0.920179i \(0.371957\pi\)
\(368\) −5.00000 −0.260643
\(369\) 0 0
\(370\) 4.00000 0.207950
\(371\) −11.0000 −0.571092
\(372\) 0 0
\(373\) −28.0000 −1.44979 −0.724893 0.688862i \(-0.758111\pi\)
−0.724893 + 0.688862i \(0.758111\pi\)
\(374\) −3.00000 −0.155126
\(375\) 0 0
\(376\) −2.00000 −0.103142
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 20.0000 1.02598
\(381\) 0 0
\(382\) −9.00000 −0.460480
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 18.0000 0.916176
\(387\) 0 0
\(388\) 10.0000 0.507673
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 15.0000 0.758583
\(392\) −6.00000 −0.303046
\(393\) 0 0
\(394\) −7.00000 −0.352655
\(395\) 40.0000 2.01262
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) −19.0000 −0.948815 −0.474407 0.880305i \(-0.657338\pi\)
−0.474407 + 0.880305i \(0.657338\pi\)
\(402\) 0 0
\(403\) 30.0000 1.49441
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 4.00000 0.198517
\(407\) −1.00000 −0.0495682
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −24.0000 −1.18528
\(411\) 0 0
\(412\) −2.00000 −0.0985329
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) −36.0000 −1.76717
\(416\) −3.00000 −0.147087
\(417\) 0 0
\(418\) −5.00000 −0.244558
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 11.0000 0.534207
\(425\) −33.0000 −1.60074
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) −16.0000 −0.771589
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) −9.00000 −0.431022
\(437\) 25.0000 1.19591
\(438\) 0 0
\(439\) −14.0000 −0.668184 −0.334092 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) −4.00000 −0.190693
\(441\) 0 0
\(442\) 9.00000 0.428086
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) 44.0000 2.08580
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 6.00000 0.282529
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) −16.0000 −0.750917
\(455\) −12.0000 −0.562569
\(456\) 0 0
\(457\) 28.0000 1.30978 0.654892 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) −8.00000 −0.373815
\(459\) 0 0
\(460\) 20.0000 0.932505
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −4.00000 −0.185695
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) 34.0000 1.57333 0.786666 0.617379i \(-0.211805\pi\)
0.786666 + 0.617379i \(0.211805\pi\)
\(468\) 0 0
\(469\) −14.0000 −0.646460
\(470\) 8.00000 0.369012
\(471\) 0 0
\(472\) 12.0000 0.552345
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) −55.0000 −2.52357
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) 0 0
\(479\) −15.0000 −0.685367 −0.342684 0.939451i \(-0.611336\pi\)
−0.342684 + 0.939451i \(0.611336\pi\)
\(480\) 0 0
\(481\) 3.00000 0.136788
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) −40.0000 −1.81631
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 10.0000 0.452679
\(489\) 0 0
\(490\) 24.0000 1.08421
\(491\) 29.0000 1.30875 0.654376 0.756169i \(-0.272931\pi\)
0.654376 + 0.756169i \(0.272931\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 15.0000 0.674882
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) 0 0
\(498\) 0 0
\(499\) −15.0000 −0.671492 −0.335746 0.941953i \(-0.608988\pi\)
−0.335746 + 0.941953i \(0.608988\pi\)
\(500\) −24.0000 −1.07331
\(501\) 0 0
\(502\) 6.00000 0.267793
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) −5.00000 −0.222277
\(507\) 0 0
\(508\) −3.00000 −0.133103
\(509\) 15.0000 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) 0 0
\(511\) 11.0000 0.486611
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −27.0000 −1.19092
\(515\) 8.00000 0.352522
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) 1.00000 0.0439375
\(519\) 0 0
\(520\) 12.0000 0.526235
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −22.0000 −0.961074
\(525\) 0 0
\(526\) −18.0000 −0.784837
\(527\) 30.0000 1.30682
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) −44.0000 −1.91124
\(531\) 0 0
\(532\) 5.00000 0.216777
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 14.0000 0.604708
\(537\) 0 0
\(538\) −27.0000 −1.16405
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 1.00000 0.0429934 0.0214967 0.999769i \(-0.493157\pi\)
0.0214967 + 0.999769i \(0.493157\pi\)
\(542\) 8.00000 0.343629
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 36.0000 1.54207
\(546\) 0 0
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) −20.0000 −0.854358
\(549\) 0 0
\(550\) 11.0000 0.469042
\(551\) 20.0000 0.852029
\(552\) 0 0
\(553\) 10.0000 0.425243
\(554\) −5.00000 −0.212430
\(555\) 0 0
\(556\) −14.0000 −0.593732
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) 9.00000 0.379642
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 56.0000 2.35594
\(566\) 21.0000 0.882696
\(567\) 0 0
\(568\) 0 0
\(569\) 3.00000 0.125767 0.0628833 0.998021i \(-0.479970\pi\)
0.0628833 + 0.998021i \(0.479970\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) −6.00000 −0.250435
\(575\) −55.0000 −2.29366
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 16.0000 0.664364
\(581\) −9.00000 −0.373383
\(582\) 0 0
\(583\) 11.0000 0.455573
\(584\) −11.0000 −0.455183
\(585\) 0 0
\(586\) −21.0000 −0.867502
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 50.0000 2.06021
\(590\) −48.0000 −1.97613
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) −28.0000 −1.14982 −0.574911 0.818216i \(-0.694963\pi\)
−0.574911 + 0.818216i \(0.694963\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 15.0000 0.613396
\(599\) −42.0000 −1.71607 −0.858037 0.513588i \(-0.828316\pi\)
−0.858037 + 0.513588i \(0.828316\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 5.00000 0.203447
\(605\) 40.0000 1.62623
\(606\) 0 0
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) −40.0000 −1.61955
\(611\) 6.00000 0.242734
\(612\) 0 0
\(613\) −10.0000 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 32.0000 1.29141
\(615\) 0 0
\(616\) −1.00000 −0.0402911
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 0 0
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 40.0000 1.60644
\(621\) 0 0
\(622\) 16.0000 0.641542
\(623\) 11.0000 0.440706
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 0 0
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 44.0000 1.75161 0.875806 0.482663i \(-0.160330\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) −10.0000 −0.397779
\(633\) 0 0
\(634\) 18.0000 0.714871
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) 18.0000 0.713186
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) −4.00000 −0.158114
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 0 0
\(643\) −41.0000 −1.61688 −0.808441 0.588577i \(-0.799688\pi\)
−0.808441 + 0.588577i \(0.799688\pi\)
\(644\) 5.00000 0.197028
\(645\) 0 0
\(646\) 15.0000 0.590167
\(647\) 11.0000 0.432455 0.216227 0.976343i \(-0.430625\pi\)
0.216227 + 0.976343i \(0.430625\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) −33.0000 −1.29437
\(651\) 0 0
\(652\) 9.00000 0.352467
\(653\) 20.0000 0.782660 0.391330 0.920250i \(-0.372015\pi\)
0.391330 + 0.920250i \(0.372015\pi\)
\(654\) 0 0
\(655\) 88.0000 3.43844
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 2.00000 0.0779681
\(659\) −16.0000 −0.623272 −0.311636 0.950202i \(-0.600877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(660\) 0 0
\(661\) 5.00000 0.194477 0.0972387 0.995261i \(-0.468999\pi\)
0.0972387 + 0.995261i \(0.468999\pi\)
\(662\) 28.0000 1.08825
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) −20.0000 −0.775567
\(666\) 0 0
\(667\) 20.0000 0.774403
\(668\) 17.0000 0.657750
\(669\) 0 0
\(670\) −56.0000 −2.16347
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 37.0000 1.42625 0.713123 0.701039i \(-0.247280\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 5.00000 0.192593
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −15.0000 −0.576497 −0.288248 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 0 0
\(679\) −10.0000 −0.383765
\(680\) 12.0000 0.460179
\(681\) 0 0
\(682\) −10.0000 −0.382920
\(683\) 22.0000 0.841807 0.420903 0.907106i \(-0.361713\pi\)
0.420903 + 0.907106i \(0.361713\pi\)
\(684\) 0 0
\(685\) 80.0000 3.05664
\(686\) 13.0000 0.496342
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −33.0000 −1.25720
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 13.0000 0.494186
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) 56.0000 2.12420
\(696\) 0 0
\(697\) −18.0000 −0.681799
\(698\) −30.0000 −1.13552
\(699\) 0 0
\(700\) −11.0000 −0.415761
\(701\) 40.0000 1.51078 0.755390 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) 0 0
\(703\) 5.00000 0.188579
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 26.0000 0.978523
\(707\) 6.00000 0.225653
\(708\) 0 0
\(709\) −19.0000 −0.713560 −0.356780 0.934188i \(-0.616125\pi\)
−0.356780 + 0.934188i \(0.616125\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −11.0000 −0.412242
\(713\) 50.0000 1.87251
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) −4.00000 −0.149487
\(717\) 0 0
\(718\) −6.00000 −0.223918
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 2.00000 0.0744839
\(722\) 6.00000 0.223297
\(723\) 0 0
\(724\) −16.0000 −0.594635
\(725\) −44.0000 −1.63412
\(726\) 0 0
\(727\) 20.0000 0.741759 0.370879 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) 3.00000 0.111187
\(729\) 0 0
\(730\) 44.0000 1.62851
\(731\) −12.0000 −0.443836
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 15.0000 0.553660
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 14.0000 0.515697
\(738\) 0 0
\(739\) −38.0000 −1.39785 −0.698926 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) 4.00000 0.147043
\(741\) 0 0
\(742\) −11.0000 −0.403823
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) −28.0000 −1.02515
\(747\) 0 0
\(748\) −3.00000 −0.109691
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −2.00000 −0.0729325
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) 15.0000 0.545184 0.272592 0.962130i \(-0.412119\pi\)
0.272592 + 0.962130i \(0.412119\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 20.0000 0.725476
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 9.00000 0.325822
\(764\) −9.00000 −0.325609
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) −36.0000 −1.29988
\(768\) 0 0
\(769\) −4.00000 −0.144244 −0.0721218 0.997396i \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 4.00000 0.144150
\(771\) 0 0
\(772\) 18.0000 0.647834
\(773\) 33.0000 1.18693 0.593464 0.804861i \(-0.297760\pi\)
0.593464 + 0.804861i \(0.297760\pi\)
\(774\) 0 0
\(775\) −110.000 −3.95132
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) 0 0
\(782\) 15.0000 0.536399
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) 0 0
\(787\) 38.0000 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) −7.00000 −0.249365
\(789\) 0 0
\(790\) 40.0000 1.42314
\(791\) 14.0000 0.497783
\(792\) 0 0
\(793\) −30.0000 −1.06533
\(794\) −32.0000 −1.13564
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) −4.00000 −0.141687 −0.0708436 0.997487i \(-0.522569\pi\)
−0.0708436 + 0.997487i \(0.522569\pi\)
\(798\) 0 0
\(799\) 6.00000 0.212265
\(800\) 11.0000 0.388909
\(801\) 0 0
\(802\) −19.0000 −0.670913
\(803\) −11.0000 −0.388182
\(804\) 0 0
\(805\) −20.0000 −0.704907
\(806\) 30.0000 1.05670
\(807\) 0 0
\(808\) −6.00000 −0.211079
\(809\) −19.0000 −0.668004 −0.334002 0.942572i \(-0.608399\pi\)
−0.334002 + 0.942572i \(0.608399\pi\)
\(810\) 0 0
\(811\) −32.0000 −1.12367 −0.561836 0.827249i \(-0.689905\pi\)
−0.561836 + 0.827249i \(0.689905\pi\)
\(812\) 4.00000 0.140372
\(813\) 0 0
\(814\) −1.00000 −0.0350500
\(815\) −36.0000 −1.26102
\(816\) 0 0
\(817\) −20.0000 −0.699711
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) −24.0000 −0.838116
\(821\) −33.0000 −1.15171 −0.575854 0.817553i \(-0.695330\pi\)
−0.575854 + 0.817553i \(0.695330\pi\)
\(822\) 0 0
\(823\) 9.00000 0.313720 0.156860 0.987621i \(-0.449863\pi\)
0.156860 + 0.987621i \(0.449863\pi\)
\(824\) −2.00000 −0.0696733
\(825\) 0 0
\(826\) −12.0000 −0.417533
\(827\) 14.0000 0.486828 0.243414 0.969923i \(-0.421733\pi\)
0.243414 + 0.969923i \(0.421733\pi\)
\(828\) 0 0
\(829\) 19.0000 0.659897 0.329949 0.943999i \(-0.392969\pi\)
0.329949 + 0.943999i \(0.392969\pi\)
\(830\) −36.0000 −1.24958
\(831\) 0 0
\(832\) −3.00000 −0.104006
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) −68.0000 −2.35324
\(836\) −5.00000 −0.172929
\(837\) 0 0
\(838\) −5.00000 −0.172722
\(839\) 4.00000 0.138095 0.0690477 0.997613i \(-0.478004\pi\)
0.0690477 + 0.997613i \(0.478004\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) −6.00000 −0.206774
\(843\) 0 0
\(844\) 0 0
\(845\) 16.0000 0.550417
\(846\) 0 0
\(847\) 10.0000 0.343604
\(848\) 11.0000 0.377742
\(849\) 0 0
\(850\) −33.0000 −1.13189
\(851\) 5.00000 0.171398
\(852\) 0 0
\(853\) −55.0000 −1.88316 −0.941582 0.336784i \(-0.890661\pi\)
−0.941582 + 0.336784i \(0.890661\pi\)
\(854\) −10.0000 −0.342193
\(855\) 0 0
\(856\) 3.00000 0.102538
\(857\) 3.00000 0.102478 0.0512390 0.998686i \(-0.483683\pi\)
0.0512390 + 0.998686i \(0.483683\pi\)
\(858\) 0 0
\(859\) −23.0000 −0.784750 −0.392375 0.919805i \(-0.628346\pi\)
−0.392375 + 0.919805i \(0.628346\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −15.0000 −0.510902
\(863\) 22.0000 0.748889 0.374444 0.927249i \(-0.377833\pi\)
0.374444 + 0.927249i \(0.377833\pi\)
\(864\) 0 0
\(865\) −52.0000 −1.76805
\(866\) −25.0000 −0.849535
\(867\) 0 0
\(868\) 10.0000 0.339422
\(869\) −10.0000 −0.339227
\(870\) 0 0
\(871\) −42.0000 −1.42312
\(872\) −9.00000 −0.304778
\(873\) 0 0
\(874\) 25.0000 0.845638
\(875\) 24.0000 0.811348
\(876\) 0 0
\(877\) −14.0000 −0.472746 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) −14.0000 −0.472477
\(879\) 0 0
\(880\) −4.00000 −0.134840
\(881\) 36.0000 1.21287 0.606435 0.795133i \(-0.292599\pi\)
0.606435 + 0.795133i \(0.292599\pi\)
\(882\) 0 0
\(883\) −11.0000 −0.370179 −0.185090 0.982722i \(-0.559258\pi\)
−0.185090 + 0.982722i \(0.559258\pi\)
\(884\) 9.00000 0.302703
\(885\) 0 0
\(886\) −36.0000 −1.20944
\(887\) −6.00000 −0.201460 −0.100730 0.994914i \(-0.532118\pi\)
−0.100730 + 0.994914i \(0.532118\pi\)
\(888\) 0 0
\(889\) 3.00000 0.100617
\(890\) 44.0000 1.47488
\(891\) 0 0
\(892\) 0 0
\(893\) 10.0000 0.334637
\(894\) 0 0
\(895\) 16.0000 0.534821
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −2.00000 −0.0667409
\(899\) 40.0000 1.33407
\(900\) 0 0
\(901\) −33.0000 −1.09939
\(902\) 6.00000 0.199778
\(903\) 0 0
\(904\) −14.0000 −0.465633
\(905\) 64.0000 2.12743
\(906\) 0 0
\(907\) −11.0000 −0.365249 −0.182625 0.983183i \(-0.558459\pi\)
−0.182625 + 0.983183i \(0.558459\pi\)
\(908\) −16.0000 −0.530979
\(909\) 0 0
\(910\) −12.0000 −0.397796
\(911\) −40.0000 −1.32526 −0.662630 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 28.0000 0.926158
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 22.0000 0.726504
\(918\) 0 0
\(919\) 46.0000 1.51740 0.758700 0.651440i \(-0.225835\pi\)
0.758700 + 0.651440i \(0.225835\pi\)
\(920\) 20.0000 0.659380
\(921\) 0 0
\(922\) 14.0000 0.461065
\(923\) 0 0
\(924\) 0 0
\(925\) −11.0000 −0.361678
\(926\) −22.0000 −0.722965
\(927\) 0 0
\(928\) −4.00000 −0.131306
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 30.0000 0.983210
\(932\) −10.0000 −0.327561
\(933\) 0 0
\(934\) 34.0000 1.11251
\(935\) 12.0000 0.392442
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) −14.0000 −0.457116
\(939\) 0 0
\(940\) 8.00000 0.260931
\(941\) −50.0000 −1.62995 −0.814977 0.579494i \(-0.803250\pi\)
−0.814977 + 0.579494i \(0.803250\pi\)
\(942\) 0 0
\(943\) −30.0000 −0.976934
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 26.0000 0.844886 0.422443 0.906389i \(-0.361173\pi\)
0.422443 + 0.906389i \(0.361173\pi\)
\(948\) 0 0
\(949\) 33.0000 1.07123
\(950\) −55.0000 −1.78444
\(951\) 0 0
\(952\) 3.00000 0.0972306
\(953\) −8.00000 −0.259145 −0.129573 0.991570i \(-0.541361\pi\)
−0.129573 + 0.991570i \(0.541361\pi\)
\(954\) 0 0
\(955\) 36.0000 1.16493
\(956\) 0 0
\(957\) 0 0
\(958\) −15.0000 −0.484628
\(959\) 20.0000 0.645834
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 3.00000 0.0967239
\(963\) 0 0
\(964\) 28.0000 0.901819
\(965\) −72.0000 −2.31776
\(966\) 0 0
\(967\) −12.0000 −0.385894 −0.192947 0.981209i \(-0.561805\pi\)
−0.192947 + 0.981209i \(0.561805\pi\)
\(968\) −10.0000 −0.321412
\(969\) 0 0
\(970\) −40.0000 −1.28432
\(971\) 60.0000 1.92549 0.962746 0.270408i \(-0.0871586\pi\)
0.962746 + 0.270408i \(0.0871586\pi\)
\(972\) 0 0
\(973\) 14.0000 0.448819
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) −27.0000 −0.863807 −0.431903 0.901920i \(-0.642158\pi\)
−0.431903 + 0.901920i \(0.642158\pi\)
\(978\) 0 0
\(979\) −11.0000 −0.351562
\(980\) 24.0000 0.766652
\(981\) 0 0
\(982\) 29.0000 0.925427
\(983\) 14.0000 0.446531 0.223265 0.974758i \(-0.428328\pi\)
0.223265 + 0.974758i \(0.428328\pi\)
\(984\) 0 0
\(985\) 28.0000 0.892154
\(986\) 12.0000 0.382158
\(987\) 0 0
\(988\) 15.0000 0.477214
\(989\) −20.0000 −0.635963
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) −10.0000 −0.317500
\(993\) 0 0
\(994\) 0 0
\(995\) −64.0000 −2.02894
\(996\) 0 0
\(997\) −9.00000 −0.285033 −0.142516 0.989792i \(-0.545519\pi\)
−0.142516 + 0.989792i \(0.545519\pi\)
\(998\) −15.0000 −0.474817
\(999\) 0 0
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 666.2.a.d.1.1 1
3.2 odd 2 222.2.a.c.1.1 1
4.3 odd 2 5328.2.a.b.1.1 1
12.11 even 2 1776.2.a.e.1.1 1
15.14 odd 2 5550.2.a.z.1.1 1
24.5 odd 2 7104.2.a.a.1.1 1
24.11 even 2 7104.2.a.p.1.1 1
111.110 odd 2 8214.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
222.2.a.c.1.1 1 3.2 odd 2
666.2.a.d.1.1 1 1.1 even 1 trivial
1776.2.a.e.1.1 1 12.11 even 2
5328.2.a.b.1.1 1 4.3 odd 2
5550.2.a.z.1.1 1 15.14 odd 2
7104.2.a.a.1.1 1 24.5 odd 2
7104.2.a.p.1.1 1 24.11 even 2
8214.2.a.j.1.1 1 111.110 odd 2