Properties

Label 9450.2.a.dk.1.1
Level $9450$
Weight $2$
Character 9450.1
Self dual yes
Analytic conductor $75.459$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9450,2,Mod(1,9450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, 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("9450.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9450.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: \(75.4586299101\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1890)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{11} +3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -7.00000 q^{17} -6.00000 q^{19} -1.00000 q^{22} +3.00000 q^{23} +3.00000 q^{26} +1.00000 q^{28} +3.00000 q^{29} -7.00000 q^{31} +1.00000 q^{32} -7.00000 q^{34} -2.00000 q^{37} -6.00000 q^{38} -8.00000 q^{41} +5.00000 q^{43} -1.00000 q^{44} +3.00000 q^{46} -1.00000 q^{47} +1.00000 q^{49} +3.00000 q^{52} -2.00000 q^{53} +1.00000 q^{56} +3.00000 q^{58} -4.00000 q^{59} -8.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +12.0000 q^{67} -7.00000 q^{68} -8.00000 q^{71} -8.00000 q^{73} -2.00000 q^{74} -6.00000 q^{76} -1.00000 q^{77} +1.00000 q^{79} -8.00000 q^{82} -16.0000 q^{83} +5.00000 q^{86} -1.00000 q^{88} -4.00000 q^{89} +3.00000 q^{91} +3.00000 q^{92} -1.00000 q^{94} +16.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −7.00000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 3.00000 0.416025
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 3.00000 0.393919
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) −7.00000 −0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −7.00000 −0.848875
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 1.00000 0.112509 0.0562544 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −8.00000 −0.883452
\(83\) −16.0000 −1.75623 −0.878114 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 0.539164
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 3.00000 0.312772
\(93\) 0 0
\(94\) −1.00000 −0.103142
\(95\) 0 0
\(96\) 0 0
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) −7.00000 −0.628619
\(125\) 0 0
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −17.0000 −1.48530 −0.742648 0.669681i \(-0.766431\pi\)
−0.742648 + 0.669681i \(0.766431\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) −3.00000 −0.250873
\(144\) 0 0
\(145\) 0 0
\(146\) −8.00000 −0.662085
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) −6.00000 −0.486664
\(153\) 0 0
\(154\) −1.00000 −0.0805823
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 1.00000 0.0795557
\(159\) 0 0
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −23.0000 −1.80150 −0.900750 0.434339i \(-0.856982\pi\)
−0.900750 + 0.434339i \(0.856982\pi\)
\(164\) −8.00000 −0.624695
\(165\) 0 0
\(166\) −16.0000 −1.24184
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 5.00000 0.381246
\(173\) 26.0000 1.97674 0.988372 0.152057i \(-0.0485898\pi\)
0.988372 + 0.152057i \(0.0485898\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −4.00000 −0.299813
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 3.00000 0.222375
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) 0 0
\(186\) 0 0
\(187\) 7.00000 0.511891
\(188\) −1.00000 −0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 16.0000 1.14873
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.00000 0.211079
\(203\) 3.00000 0.210559
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) 3.00000 0.208013
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) −6.00000 −0.406371
\(219\) 0 0
\(220\) 0 0
\(221\) −21.0000 −1.41261
\(222\) 0 0
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −1.00000 −0.0665190
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) −7.00000 −0.453743
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −29.0000 −1.86805 −0.934027 0.357202i \(-0.883731\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(242\) −10.0000 −0.642824
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) −18.0000 −1.14531
\(248\) −7.00000 −0.444500
\(249\) 0 0
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 14.0000 0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −19.0000 −1.18519 −0.592594 0.805502i \(-0.701896\pi\)
−0.592594 + 0.805502i \(0.701896\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) −17.0000 −1.05026
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −6.00000 −0.367884
\(267\) 0 0
\(268\) 12.0000 0.733017
\(269\) 27.0000 1.64622 0.823110 0.567883i \(-0.192237\pi\)
0.823110 + 0.567883i \(0.192237\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) −6.00000 −0.360505 −0.180253 0.983620i \(-0.557691\pi\)
−0.180253 + 0.983620i \(0.557691\pi\)
\(278\) 10.0000 0.599760
\(279\) 0 0
\(280\) 0 0
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 0 0
\(292\) −8.00000 −0.468165
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 3.00000 0.173785
\(299\) 9.00000 0.520483
\(300\) 0 0
\(301\) 5.00000 0.288195
\(302\) −7.00000 −0.402805
\(303\) 0 0
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 0 0
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) −32.0000 −1.80875 −0.904373 0.426742i \(-0.859661\pi\)
−0.904373 + 0.426742i \(0.859661\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) −20.0000 −1.12331 −0.561656 0.827371i \(-0.689836\pi\)
−0.561656 + 0.827371i \(0.689836\pi\)
\(318\) 0 0
\(319\) −3.00000 −0.167968
\(320\) 0 0
\(321\) 0 0
\(322\) 3.00000 0.167183
\(323\) 42.0000 2.33694
\(324\) 0 0
\(325\) 0 0
\(326\) −23.0000 −1.27385
\(327\) 0 0
\(328\) −8.00000 −0.441726
\(329\) −1.00000 −0.0551318
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −16.0000 −0.878114
\(333\) 0 0
\(334\) 24.0000 1.31322
\(335\) 0 0
\(336\) 0 0
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) −4.00000 −0.217571
\(339\) 0 0
\(340\) 0 0
\(341\) 7.00000 0.379071
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 5.00000 0.269582
\(345\) 0 0
\(346\) 26.0000 1.39777
\(347\) −26.0000 −1.39575 −0.697877 0.716218i \(-0.745872\pi\)
−0.697877 + 0.716218i \(0.745872\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −4.00000 −0.212000
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −2.00000 −0.105556 −0.0527780 0.998606i \(-0.516808\pi\)
−0.0527780 + 0.998606i \(0.516808\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −8.00000 −0.420471
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) 0 0
\(366\) 0 0
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) −5.00000 −0.258890 −0.129445 0.991587i \(-0.541320\pi\)
−0.129445 + 0.991587i \(0.541320\pi\)
\(374\) 7.00000 0.361961
\(375\) 0 0
\(376\) −1.00000 −0.0515711
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.00000 0.459879 0.229939 0.973205i \(-0.426147\pi\)
0.229939 + 0.973205i \(0.426147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 0 0
\(388\) 16.0000 0.812277
\(389\) 19.0000 0.963338 0.481669 0.876353i \(-0.340031\pi\)
0.481669 + 0.876353i \(0.340031\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) 0 0
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 0 0
\(403\) −21.0000 −1.04608
\(404\) 3.00000 0.149256
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 21.0000 1.03838 0.519192 0.854658i \(-0.326233\pi\)
0.519192 + 0.854658i \(0.326233\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) −4.00000 −0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) 3.00000 0.147087
\(417\) 0 0
\(418\) 6.00000 0.293470
\(419\) 15.0000 0.732798 0.366399 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 22.0000 1.07094
\(423\) 0 0
\(424\) −2.00000 −0.0971286
\(425\) 0 0
\(426\) 0 0
\(427\) −8.00000 −0.387147
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) −7.00000 −0.336011
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) −18.0000 −0.861057
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −21.0000 −0.998868
\(443\) −32.0000 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 20.0000 0.947027
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) −1.00000 −0.0470360
\(453\) 0 0
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 4.00000 0.186908
\(459\) 0 0
\(460\) 0 0
\(461\) −34.0000 −1.58354 −0.791769 0.610821i \(-0.790840\pi\)
−0.791769 + 0.610821i \(0.790840\pi\)
\(462\) 0 0
\(463\) −38.0000 −1.76601 −0.883005 0.469364i \(-0.844483\pi\)
−0.883005 + 0.469364i \(0.844483\pi\)
\(464\) 3.00000 0.139272
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) −4.00000 −0.184115
\(473\) −5.00000 −0.229900
\(474\) 0 0
\(475\) 0 0
\(476\) −7.00000 −0.320844
\(477\) 0 0
\(478\) −16.0000 −0.731823
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) −29.0000 −1.32091
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 0 0
\(487\) −14.0000 −0.634401 −0.317200 0.948359i \(-0.602743\pi\)
−0.317200 + 0.948359i \(0.602743\pi\)
\(488\) −8.00000 −0.362143
\(489\) 0 0
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) −21.0000 −0.945792
\(494\) −18.0000 −0.809858
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) −8.00000 −0.358849
\(498\) 0 0
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −15.0000 −0.669483
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.00000 −0.133366
\(507\) 0 0
\(508\) 14.0000 0.621150
\(509\) −7.00000 −0.310270 −0.155135 0.987893i \(-0.549581\pi\)
−0.155135 + 0.987893i \(0.549581\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −19.0000 −0.838054
\(515\) 0 0
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) −2.00000 −0.0878750
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) −19.0000 −0.830812 −0.415406 0.909636i \(-0.636360\pi\)
−0.415406 + 0.909636i \(0.636360\pi\)
\(524\) −17.0000 −0.742648
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 49.0000 2.13447
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 −0.260133
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) 0 0
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 27.0000 1.16405
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −36.0000 −1.54776 −0.773880 0.633332i \(-0.781687\pi\)
−0.773880 + 0.633332i \(0.781687\pi\)
\(542\) 24.0000 1.03089
\(543\) 0 0
\(544\) −7.00000 −0.300123
\(545\) 0 0
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 1.00000 0.0425243
\(554\) −6.00000 −0.254916
\(555\) 0 0
\(556\) 10.0000 0.424094
\(557\) −32.0000 −1.35588 −0.677942 0.735116i \(-0.737128\pi\)
−0.677942 + 0.735116i \(0.737128\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0 0
\(561\) 0 0
\(562\) −8.00000 −0.337460
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 0 0
\(571\) −24.0000 −1.00437 −0.502184 0.864761i \(-0.667470\pi\)
−0.502184 + 0.864761i \(0.667470\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) −8.00000 −0.333914
\(575\) 0 0
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) 32.0000 1.33102
\(579\) 0 0
\(580\) 0 0
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) 2.00000 0.0828315
\(584\) −8.00000 −0.331042
\(585\) 0 0
\(586\) −8.00000 −0.330477
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) 0 0
\(592\) −2.00000 −0.0821995
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) 0 0
\(598\) 9.00000 0.368037
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) −33.0000 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(602\) 5.00000 0.203785
\(603\) 0 0
\(604\) −7.00000 −0.284826
\(605\) 0 0
\(606\) 0 0
\(607\) 2.00000 0.0811775 0.0405887 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) −3.00000 −0.121367
\(612\) 0 0
\(613\) 21.0000 0.848182 0.424091 0.905620i \(-0.360594\pi\)
0.424091 + 0.905620i \(0.360594\pi\)
\(614\) 23.0000 0.928204
\(615\) 0 0
\(616\) −1.00000 −0.0402911
\(617\) −19.0000 −0.764911 −0.382456 0.923974i \(-0.624922\pi\)
−0.382456 + 0.923974i \(0.624922\pi\)
\(618\) 0 0
\(619\) −34.0000 −1.36658 −0.683288 0.730149i \(-0.739451\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 0 0
\(626\) −32.0000 −1.27898
\(627\) 0 0
\(628\) −7.00000 −0.279330
\(629\) 14.0000 0.558217
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 1.00000 0.0397779
\(633\) 0 0
\(634\) −20.0000 −0.794301
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) −3.00000 −0.118771
\(639\) 0 0
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 0 0
\(643\) 35.0000 1.38027 0.690133 0.723683i \(-0.257552\pi\)
0.690133 + 0.723683i \(0.257552\pi\)
\(644\) 3.00000 0.118217
\(645\) 0 0
\(646\) 42.0000 1.65247
\(647\) −20.0000 −0.786281 −0.393141 0.919478i \(-0.628611\pi\)
−0.393141 + 0.919478i \(0.628611\pi\)
\(648\) 0 0
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −23.0000 −0.900750
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −8.00000 −0.312348
\(657\) 0 0
\(658\) −1.00000 −0.0389841
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 34.0000 1.32245 0.661223 0.750189i \(-0.270038\pi\)
0.661223 + 0.750189i \(0.270038\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) −16.0000 −0.620920
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 0.348481
\(668\) 24.0000 0.928588
\(669\) 0 0
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) 8.00000 0.308377 0.154189 0.988041i \(-0.450724\pi\)
0.154189 + 0.988041i \(0.450724\pi\)
\(674\) 20.0000 0.770371
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 16.0000 0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) 7.00000 0.268044
\(683\) 26.0000 0.994862 0.497431 0.867503i \(-0.334277\pi\)
0.497431 + 0.867503i \(0.334277\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 5.00000 0.190623
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) 26.0000 0.988372
\(693\) 0 0
\(694\) −26.0000 −0.986947
\(695\) 0 0
\(696\) 0 0
\(697\) 56.0000 2.12115
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) 0 0
\(701\) −25.0000 −0.944237 −0.472118 0.881535i \(-0.656511\pi\)
−0.472118 + 0.881535i \(0.656511\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −21.0000 −0.790345
\(707\) 3.00000 0.112827
\(708\) 0 0
\(709\) 40.0000 1.50223 0.751116 0.660171i \(-0.229516\pi\)
0.751116 + 0.660171i \(0.229516\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −4.00000 −0.149906
\(713\) −21.0000 −0.786456
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) −2.00000 −0.0746393
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) −8.00000 −0.297318
\(725\) 0 0
\(726\) 0 0
\(727\) −30.0000 −1.11264 −0.556319 0.830969i \(-0.687787\pi\)
−0.556319 + 0.830969i \(0.687787\pi\)
\(728\) 3.00000 0.111187
\(729\) 0 0
\(730\) 0 0
\(731\) −35.0000 −1.29452
\(732\) 0 0
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) 26.0000 0.959678
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) −14.0000 −0.514998 −0.257499 0.966279i \(-0.582898\pi\)
−0.257499 + 0.966279i \(0.582898\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −5.00000 −0.183063
\(747\) 0 0
\(748\) 7.00000 0.255945
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) 41.0000 1.49611 0.748056 0.663636i \(-0.230988\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 0 0
\(754\) 9.00000 0.327761
\(755\) 0 0
\(756\) 0 0
\(757\) −1.00000 −0.0363456 −0.0181728 0.999835i \(-0.505785\pi\)
−0.0181728 + 0.999835i \(0.505785\pi\)
\(758\) 6.00000 0.217930
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 0 0
\(763\) −6.00000 −0.217215
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 0.325183
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 13.0000 0.468792 0.234396 0.972141i \(-0.424689\pi\)
0.234396 + 0.972141i \(0.424689\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.00000 0.143963
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 16.0000 0.574367
\(777\) 0 0
\(778\) 19.0000 0.681183
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) −21.0000 −0.750958
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 11.0000 0.392108 0.196054 0.980593i \(-0.437187\pi\)
0.196054 + 0.980593i \(0.437187\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) 0 0
\(791\) −1.00000 −0.0355559
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) −13.0000 −0.461353
\(795\) 0 0
\(796\) 5.00000 0.177220
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) 7.00000 0.247642
\(800\) 0 0
\(801\) 0 0
\(802\) −10.0000 −0.353112
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) −21.0000 −0.739693
\(807\) 0 0
\(808\) 3.00000 0.105540
\(809\) 24.0000 0.843795 0.421898 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 3.00000 0.105279
\(813\) 0 0
\(814\) 2.00000 0.0701000
\(815\) 0 0
\(816\) 0 0
\(817\) −30.0000 −1.04957
\(818\) 21.0000 0.734248
\(819\) 0 0
\(820\) 0 0
\(821\) 42.0000 1.46581 0.732905 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 0 0
\(823\) 50.0000 1.74289 0.871445 0.490493i \(-0.163183\pi\)
0.871445 + 0.490493i \(0.163183\pi\)
\(824\) −4.00000 −0.139347
\(825\) 0 0
\(826\) −4.00000 −0.139178
\(827\) 2.00000 0.0695468 0.0347734 0.999395i \(-0.488929\pi\)
0.0347734 + 0.999395i \(0.488929\pi\)
\(828\) 0 0
\(829\) −28.0000 −0.972480 −0.486240 0.873825i \(-0.661632\pi\)
−0.486240 + 0.873825i \(0.661632\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 3.00000 0.104006
\(833\) −7.00000 −0.242536
\(834\) 0 0
\(835\) 0 0
\(836\) 6.00000 0.207514
\(837\) 0 0
\(838\) 15.0000 0.518166
\(839\) 28.0000 0.966667 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 32.0000 1.10279
\(843\) 0 0
\(844\) 22.0000 0.757271
\(845\) 0 0
\(846\) 0 0
\(847\) −10.0000 −0.343604
\(848\) −2.00000 −0.0686803
\(849\) 0 0
\(850\) 0 0
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) 19.0000 0.650548 0.325274 0.945620i \(-0.394544\pi\)
0.325274 + 0.945620i \(0.394544\pi\)
\(854\) −8.00000 −0.273754
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) 30.0000 1.02359 0.511793 0.859109i \(-0.328981\pi\)
0.511793 + 0.859109i \(0.328981\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 30.0000 1.02180
\(863\) 37.0000 1.25949 0.629747 0.776800i \(-0.283158\pi\)
0.629747 + 0.776800i \(0.283158\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −14.0000 −0.475739
\(867\) 0 0
\(868\) −7.00000 −0.237595
\(869\) −1.00000 −0.0339227
\(870\) 0 0
\(871\) 36.0000 1.21981
\(872\) −6.00000 −0.203186
\(873\) 0 0
\(874\) −18.0000 −0.608859
\(875\) 0 0
\(876\) 0 0
\(877\) 43.0000 1.45201 0.726003 0.687691i \(-0.241376\pi\)
0.726003 + 0.687691i \(0.241376\pi\)
\(878\) 16.0000 0.539974
\(879\) 0 0
\(880\) 0 0
\(881\) 52.0000 1.75192 0.875962 0.482380i \(-0.160227\pi\)
0.875962 + 0.482380i \(0.160227\pi\)
\(882\) 0 0
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −21.0000 −0.706306
\(885\) 0 0
\(886\) −32.0000 −1.07506
\(887\) 35.0000 1.17518 0.587592 0.809157i \(-0.300076\pi\)
0.587592 + 0.809157i \(0.300076\pi\)
\(888\) 0 0
\(889\) 14.0000 0.469545
\(890\) 0 0
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) 6.00000 0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 12.0000 0.400445
\(899\) −21.0000 −0.700389
\(900\) 0 0
\(901\) 14.0000 0.466408
\(902\) 8.00000 0.266371
\(903\) 0 0
\(904\) −1.00000 −0.0332595
\(905\) 0 0
\(906\) 0 0
\(907\) −23.0000 −0.763702 −0.381851 0.924224i \(-0.624713\pi\)
−0.381851 + 0.924224i \(0.624713\pi\)
\(908\) −4.00000 −0.132745
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 16.0000 0.529523
\(914\) −10.0000 −0.330771
\(915\) 0 0
\(916\) 4.00000 0.132164
\(917\) −17.0000 −0.561389
\(918\) 0 0
\(919\) −31.0000 −1.02260 −0.511298 0.859404i \(-0.670835\pi\)
−0.511298 + 0.859404i \(0.670835\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −34.0000 −1.11973
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 0 0
\(926\) −38.0000 −1.24876
\(927\) 0 0
\(928\) 3.00000 0.0984798
\(929\) −58.0000 −1.90292 −0.951459 0.307775i \(-0.900416\pi\)
−0.951459 + 0.307775i \(0.900416\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) −28.0000 −0.916188
\(935\) 0 0
\(936\) 0 0
\(937\) 28.0000 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(938\) 12.0000 0.391814
\(939\) 0 0
\(940\) 0 0
\(941\) 37.0000 1.20617 0.603083 0.797679i \(-0.293939\pi\)
0.603083 + 0.797679i \(0.293939\pi\)
\(942\) 0 0
\(943\) −24.0000 −0.781548
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −5.00000 −0.162564
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 0 0
\(949\) −24.0000 −0.779073
\(950\) 0 0
\(951\) 0 0
\(952\) −7.00000 −0.226871
\(953\) −39.0000 −1.26333 −0.631667 0.775240i \(-0.717629\pi\)
−0.631667 + 0.775240i \(0.717629\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 0 0
\(959\) 6.00000 0.193750
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) −6.00000 −0.193448
\(963\) 0 0
\(964\) −29.0000 −0.934027
\(965\) 0 0
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) −10.0000 −0.321412
\(969\) 0 0
\(970\) 0 0
\(971\) −15.0000 −0.481373 −0.240686 0.970603i \(-0.577373\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(972\) 0 0
\(973\) 10.0000 0.320585
\(974\) −14.0000 −0.448589
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) −33.0000 −1.05576 −0.527882 0.849318i \(-0.677014\pi\)
−0.527882 + 0.849318i \(0.677014\pi\)
\(978\) 0 0
\(979\) 4.00000 0.127841
\(980\) 0 0
\(981\) 0 0
\(982\) −36.0000 −1.14881
\(983\) −7.00000 −0.223265 −0.111633 0.993750i \(-0.535608\pi\)
−0.111633 + 0.993750i \(0.535608\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −21.0000 −0.668776
\(987\) 0 0
\(988\) −18.0000 −0.572656
\(989\) 15.0000 0.476972
\(990\) 0 0
\(991\) 7.00000 0.222362 0.111181 0.993800i \(-0.464537\pi\)
0.111181 + 0.993800i \(0.464537\pi\)
\(992\) −7.00000 −0.222250
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 0 0
\(996\) 0 0
\(997\) 37.0000 1.17180 0.585901 0.810383i \(-0.300741\pi\)
0.585901 + 0.810383i \(0.300741\pi\)
\(998\) 6.00000 0.189927
\(999\) 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 9450.2.a.dk.1.1 1
3.2 odd 2 9450.2.a.br.1.1 1
5.4 even 2 1890.2.a.e.1.1 1
15.14 odd 2 1890.2.a.o.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1890.2.a.e.1.1 1 5.4 even 2
1890.2.a.o.1.1 yes 1 15.14 odd 2
9450.2.a.br.1.1 1 3.2 odd 2
9450.2.a.dk.1.1 1 1.1 even 1 trivial