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Properties

Label 1800.4.a.g.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
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] = [1800,4,Mod(1,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.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: \(106.203438010\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-19.0000 q^{7} -22.0000 q^{11} +1.00000 q^{13} +58.0000 q^{17} -53.0000 q^{19} -58.0000 q^{23} -22.0000 q^{29} -35.0000 q^{31} -270.000 q^{37} +468.000 q^{41} -431.000 q^{43} +230.000 q^{47} +18.0000 q^{49} -446.000 q^{59} +127.000 q^{61} -811.000 q^{67} -36.0000 q^{71} +522.000 q^{73} +418.000 q^{77} +1368.00 q^{79} +1138.00 q^{83} -144.000 q^{89} -19.0000 q^{91} -1079.00 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −19.0000 −1.02590 −0.512952 − 0.858417i \(-0.671448\pi\)
−0.512952 + 0.858417i \(0.671448\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −22.0000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.00000 0.0213346 0.0106673 − 0.999943i \(-0.496604\pi\)
0.0106673 + 0.999943i \(0.496604\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 58.0000 0.827474 0.413737 − 0.910396i \(-0.364223\pi\)
0.413737 + 0.910396i \(0.364223\pi\)
\(18\) 0 0
\(19\) −53.0000 −0.639949 −0.319975 − 0.947426i \(-0.603674\pi\)
−0.319975 + 0.947426i \(0.603674\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −58.0000 −0.525819 −0.262909 − 0.964821i \(-0.584682\pi\)
−0.262909 + 0.964821i \(0.584682\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −22.0000 −0.140872 −0.0704362 − 0.997516i \(-0.522439\pi\)
−0.0704362 + 0.997516i \(0.522439\pi\)
\(30\) 0 0
\(31\) −35.0000 −0.202780 −0.101390 − 0.994847i \(-0.532329\pi\)
−0.101390 + 0.994847i \(0.532329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −270.000 −1.19967 −0.599834 − 0.800124i \(-0.704767\pi\)
−0.599834 + 0.800124i \(0.704767\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 468.000 1.78267 0.891333 − 0.453349i \(-0.149771\pi\)
0.891333 + 0.453349i \(0.149771\pi\)
\(42\) 0 0
\(43\) −431.000 −1.52853 −0.764266 − 0.644901i \(-0.776899\pi\)
−0.764266 + 0.644901i \(0.776899\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 230.000 0.713807 0.356904 − 0.934141i \(-0.383832\pi\)
0.356904 + 0.934141i \(0.383832\pi\)
\(48\) 0 0
\(49\) 18.0000 0.0524781
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −446.000 −0.984140 −0.492070 − 0.870556i \(-0.663760\pi\)
−0.492070 + 0.870556i \(0.663760\pi\)
\(60\) 0 0
\(61\) 127.000 0.266569 0.133284 − 0.991078i \(-0.457448\pi\)
0.133284 + 0.991078i \(0.457448\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −811.000 −1.47880 −0.739399 − 0.673268i \(-0.764890\pi\)
−0.739399 + 0.673268i \(0.764890\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −36.0000 −0.0601748 −0.0300874 − 0.999547i \(-0.509579\pi\)
−0.0300874 + 0.999547i \(0.509579\pi\)
\(72\) 0 0
\(73\) 522.000 0.836924 0.418462 − 0.908234i \(-0.362569\pi\)
0.418462 + 0.908234i \(0.362569\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 418.000 0.618643
\(78\) 0 0
\(79\) 1368.00 1.94825 0.974127 − 0.226002i \(-0.0725657\pi\)
0.974127 + 0.226002i \(0.0725657\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1138.00 1.50496 0.752480 − 0.658615i \(-0.228857\pi\)
0.752480 + 0.658615i \(0.228857\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −144.000 −0.171505 −0.0857526 − 0.996316i \(-0.527329\pi\)
−0.0857526 + 0.996316i \(0.527329\pi\)
\(90\) 0 0
\(91\) −19.0000 −0.0218873
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1079.00 −1.12944 −0.564721 − 0.825282i \(-0.691016\pi\)
−0.564721 + 0.825282i \(0.691016\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1440.00 1.41867 0.709333 − 0.704873i \(-0.248996\pi\)
0.709333 + 0.704873i \(0.248996\pi\)
\(102\) 0 0
\(103\) 124.000 0.118622 0.0593111 − 0.998240i \(-0.481110\pi\)
0.0593111 + 0.998240i \(0.481110\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 432.000 0.390309 0.195154 − 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(108\) 0 0
\(109\) 701.000 0.615997 0.307998 − 0.951387i \(-0.400341\pi\)
0.307998 + 0.951387i \(0.400341\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1044.00 0.869126 0.434563 − 0.900641i \(-0.356903\pi\)
0.434563 + 0.900641i \(0.356903\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1102.00 −0.848909
\(120\) 0 0
\(121\) −847.000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 504.000 0.352148 0.176074 − 0.984377i \(-0.443660\pi\)
0.176074 + 0.984377i \(0.443660\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −72.0000 −0.0480204 −0.0240102 − 0.999712i \(-0.507643\pi\)
−0.0240102 + 0.999712i \(0.507643\pi\)
\(132\) 0 0
\(133\) 1007.00 0.656526
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1850.00 1.15369 0.576847 − 0.816852i \(-0.304283\pi\)
0.576847 + 0.816852i \(0.304283\pi\)
\(138\) 0 0
\(139\) 1836.00 1.12034 0.560171 − 0.828377i \(-0.310735\pi\)
0.560171 + 0.828377i \(0.310735\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −22.0000 −0.0128653
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2398.00 1.31847 0.659234 − 0.751938i \(-0.270881\pi\)
0.659234 + 0.751938i \(0.270881\pi\)
\(150\) 0 0
\(151\) 1871.00 1.00834 0.504172 − 0.863604i \(-0.331798\pi\)
0.504172 + 0.863604i \(0.331798\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3293.00 −1.67395 −0.836975 − 0.547242i \(-0.815678\pi\)
−0.836975 + 0.547242i \(0.815678\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1102.00 0.539440
\(162\) 0 0
\(163\) 883.000 0.424306 0.212153 − 0.977236i \(-0.431952\pi\)
0.212153 + 0.977236i \(0.431952\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4104.00 −1.90166 −0.950830 − 0.309715i \(-0.899766\pi\)
−0.950830 + 0.309715i \(0.899766\pi\)
\(168\) 0 0
\(169\) −2196.00 −0.999545
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1706.00 −0.749739 −0.374869 − 0.927078i \(-0.622312\pi\)
−0.374869 + 0.927078i \(0.622312\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −662.000 −0.276426 −0.138213 − 0.990403i \(-0.544136\pi\)
−0.138213 + 0.990403i \(0.544136\pi\)
\(180\) 0 0
\(181\) 4121.00 1.69233 0.846164 − 0.532922i \(-0.178906\pi\)
0.846164 + 0.532922i \(0.178906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1276.00 −0.498986
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 958.000 0.362924 0.181462 − 0.983398i \(-0.441917\pi\)
0.181462 + 0.983398i \(0.441917\pi\)
\(192\) 0 0
\(193\) 3187.00 1.18863 0.594314 − 0.804233i \(-0.297424\pi\)
0.594314 + 0.804233i \(0.297424\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2282.00 0.825308 0.412654 − 0.910888i \(-0.364602\pi\)
0.412654 + 0.910888i \(0.364602\pi\)
\(198\) 0 0
\(199\) 1043.00 0.371539 0.185770 − 0.982593i \(-0.440522\pi\)
0.185770 + 0.982593i \(0.440522\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 418.000 0.144521
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1166.00 0.385904
\(210\) 0 0
\(211\) 4139.00 1.35043 0.675214 − 0.737621i \(-0.264051\pi\)
0.675214 + 0.737621i \(0.264051\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 665.000 0.208033
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 58.0000 0.0176539
\(222\) 0 0
\(223\) 413.000 0.124020 0.0620101 − 0.998076i \(-0.480249\pi\)
0.0620101 + 0.998076i \(0.480249\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5652.00 −1.65258 −0.826292 − 0.563242i \(-0.809554\pi\)
−0.826292 + 0.563242i \(0.809554\pi\)
\(228\) 0 0
\(229\) −4391.00 −1.26710 −0.633549 − 0.773703i \(-0.718403\pi\)
−0.633549 + 0.773703i \(0.718403\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2052.00 0.576957 0.288479 − 0.957486i \(-0.406851\pi\)
0.288479 + 0.957486i \(0.406851\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4320.00 1.16919 0.584597 − 0.811324i \(-0.301252\pi\)
0.584597 + 0.811324i \(0.301252\pi\)
\(240\) 0 0
\(241\) 4265.00 1.13997 0.569985 − 0.821655i \(-0.306949\pi\)
0.569985 + 0.821655i \(0.306949\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −53.0000 −0.0136531
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2412.00 0.606550 0.303275 − 0.952903i \(-0.401920\pi\)
0.303275 + 0.952903i \(0.401920\pi\)
\(252\) 0 0
\(253\) 1276.00 0.317081
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6948.00 −1.68640 −0.843199 − 0.537601i \(-0.819331\pi\)
−0.843199 + 0.537601i \(0.819331\pi\)
\(258\) 0 0
\(259\) 5130.00 1.23074
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3564.00 0.835611 0.417805 − 0.908537i \(-0.362799\pi\)
0.417805 + 0.908537i \(0.362799\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1534.00 0.347694 0.173847 − 0.984773i \(-0.444380\pi\)
0.173847 + 0.984773i \(0.444380\pi\)
\(270\) 0 0
\(271\) 7704.00 1.72688 0.863440 − 0.504451i \(-0.168305\pi\)
0.863440 + 0.504451i \(0.168305\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4877.00 1.05787 0.528936 − 0.848662i \(-0.322591\pi\)
0.528936 + 0.848662i \(0.322591\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3758.00 0.797806 0.398903 − 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(282\) 0 0
\(283\) 935.000 0.196396 0.0981978 − 0.995167i \(-0.468692\pi\)
0.0981978 + 0.995167i \(0.468692\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8892.00 −1.82884
\(288\) 0 0
\(289\) −1549.00 −0.315286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6214.00 −1.23900 −0.619498 − 0.784998i \(-0.712664\pi\)
−0.619498 + 0.784998i \(0.712664\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −58.0000 −0.0112181
\(300\) 0 0
\(301\) 8189.00 1.56813
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −3905.00 −0.725961 −0.362981 − 0.931797i \(-0.618241\pi\)
−0.362981 + 0.931797i \(0.618241\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9662.00 −1.76168 −0.880839 − 0.473416i \(-0.843021\pi\)
−0.880839 + 0.473416i \(0.843021\pi\)
\(312\) 0 0
\(313\) 5147.00 0.929475 0.464737 − 0.885449i \(-0.346149\pi\)
0.464737 + 0.885449i \(0.346149\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9216.00 1.63288 0.816439 − 0.577432i \(-0.195945\pi\)
0.816439 + 0.577432i \(0.195945\pi\)
\(318\) 0 0
\(319\) 484.000 0.0849492
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3074.00 −0.529542
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4370.00 −0.732298
\(330\) 0 0
\(331\) 2196.00 0.364662 0.182331 − 0.983237i \(-0.441636\pi\)
0.182331 + 0.983237i \(0.441636\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2521.00 0.407500 0.203750 − 0.979023i \(-0.434687\pi\)
0.203750 + 0.979023i \(0.434687\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 770.000 0.122281
\(342\) 0 0
\(343\) 6175.00 0.972066
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7034.00 −1.08820 −0.544099 − 0.839021i \(-0.683129\pi\)
−0.544099 + 0.839021i \(0.683129\pi\)
\(348\) 0 0
\(349\) 7362.00 1.12917 0.564583 − 0.825376i \(-0.309037\pi\)
0.564583 + 0.825376i \(0.309037\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9382.00 1.41460 0.707300 − 0.706914i \(-0.249913\pi\)
0.707300 + 0.706914i \(0.249913\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10116.0 1.48719 0.743596 − 0.668629i \(-0.233119\pi\)
0.743596 + 0.668629i \(0.233119\pi\)
\(360\) 0 0
\(361\) −4050.00 −0.590465
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3277.00 −0.466098 −0.233049 − 0.972465i \(-0.574870\pi\)
−0.233049 + 0.972465i \(0.574870\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10891.0 1.51184 0.755918 − 0.654667i \(-0.227191\pi\)
0.755918 + 0.654667i \(0.227191\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.0000 −0.00300546
\(378\) 0 0
\(379\) −2591.00 −0.351163 −0.175581 − 0.984465i \(-0.556181\pi\)
−0.175581 + 0.984465i \(0.556181\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 612.000 0.0816494 0.0408247 − 0.999166i \(-0.487001\pi\)
0.0408247 + 0.999166i \(0.487001\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3708.00 −0.483298 −0.241649 − 0.970364i \(-0.577688\pi\)
−0.241649 + 0.970364i \(0.577688\pi\)
\(390\) 0 0
\(391\) −3364.00 −0.435102
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −3833.00 −0.484566 −0.242283 − 0.970206i \(-0.577896\pi\)
−0.242283 + 0.970206i \(0.577896\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9288.00 1.15666 0.578330 − 0.815803i \(-0.303705\pi\)
0.578330 + 0.815803i \(0.303705\pi\)
\(402\) 0 0
\(403\) −35.0000 −0.00432624
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5940.00 0.723427
\(408\) 0 0
\(409\) −755.000 −0.0912771 −0.0456386 − 0.998958i \(-0.514532\pi\)
−0.0456386 + 0.998958i \(0.514532\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8474.00 1.00963
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9576.00 1.11651 0.558256 − 0.829669i \(-0.311471\pi\)
0.558256 + 0.829669i \(0.311471\pi\)
\(420\) 0 0
\(421\) 9414.00 1.08981 0.544905 − 0.838498i \(-0.316566\pi\)
0.544905 + 0.838498i \(0.316566\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2413.00 −0.273474
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2254.00 0.251906 0.125953 − 0.992036i \(-0.459801\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(432\) 0 0
\(433\) −6301.00 −0.699323 −0.349661 − 0.936876i \(-0.613703\pi\)
−0.349661 + 0.936876i \(0.613703\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3074.00 0.336497
\(438\) 0 0
\(439\) −3779.00 −0.410847 −0.205423 − 0.978673i \(-0.565857\pi\)
−0.205423 + 0.978673i \(0.565857\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7632.00 −0.818527 −0.409263 − 0.912416i \(-0.634214\pi\)
−0.409263 + 0.912416i \(0.634214\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2988.00 −0.314059 −0.157029 − 0.987594i \(-0.550192\pi\)
−0.157029 + 0.987594i \(0.550192\pi\)
\(450\) 0 0
\(451\) −10296.0 −1.07499
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1370.00 −0.140232 −0.0701159 − 0.997539i \(-0.522337\pi\)
−0.0701159 + 0.997539i \(0.522337\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7992.00 0.807429 0.403714 − 0.914885i \(-0.367719\pi\)
0.403714 + 0.914885i \(0.367719\pi\)
\(462\) 0 0
\(463\) −3096.00 −0.310763 −0.155382 − 0.987855i \(-0.549661\pi\)
−0.155382 + 0.987855i \(0.549661\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8338.00 0.826203 0.413101 − 0.910685i \(-0.364446\pi\)
0.413101 + 0.910685i \(0.364446\pi\)
\(468\) 0 0
\(469\) 15409.0 1.51710
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9482.00 0.921740
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4918.00 −0.469121 −0.234561 − 0.972101i \(-0.575365\pi\)
−0.234561 + 0.972101i \(0.575365\pi\)
\(480\) 0 0
\(481\) −270.000 −0.0255945
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −19637.0 −1.82718 −0.913591 − 0.406635i \(-0.866702\pi\)
−0.913591 + 0.406635i \(0.866702\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3096.00 −0.284563 −0.142282 − 0.989826i \(-0.545444\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(492\) 0 0
\(493\) −1276.00 −0.116568
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 684.000 0.0617336
\(498\) 0 0
\(499\) 6875.00 0.616768 0.308384 − 0.951262i \(-0.400212\pi\)
0.308384 + 0.951262i \(0.400212\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11268.0 −0.998838 −0.499419 − 0.866361i \(-0.666453\pi\)
−0.499419 + 0.866361i \(0.666453\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16078.0 −1.40009 −0.700044 − 0.714100i \(-0.746836\pi\)
−0.700044 + 0.714100i \(0.746836\pi\)
\(510\) 0 0
\(511\) −9918.00 −0.858604
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5060.00 −0.430442
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17366.0 1.46030 0.730152 − 0.683285i \(-0.239449\pi\)
0.730152 + 0.683285i \(0.239449\pi\)
\(522\) 0 0
\(523\) −4913.00 −0.410766 −0.205383 − 0.978682i \(-0.565844\pi\)
−0.205383 + 0.978682i \(0.565844\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2030.00 −0.167795
\(528\) 0 0
\(529\) −8803.00 −0.723514
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 468.000 0.0380325
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −396.000 −0.0316455
\(540\) 0 0
\(541\) 17605.0 1.39907 0.699536 − 0.714597i \(-0.253390\pi\)
0.699536 + 0.714597i \(0.253390\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −14560.0 −1.13810 −0.569050 − 0.822303i \(-0.692689\pi\)
−0.569050 + 0.822303i \(0.692689\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1166.00 0.0901511
\(552\) 0 0
\(553\) −25992.0 −1.99872
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 20614.0 1.56812 0.784060 − 0.620685i \(-0.213145\pi\)
0.784060 + 0.620685i \(0.213145\pi\)
\(558\) 0 0
\(559\) −431.000 −0.0326107
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3442.00 −0.257661 −0.128830 − 0.991667i \(-0.541122\pi\)
−0.128830 + 0.991667i \(0.541122\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22082.0 −1.62693 −0.813467 − 0.581611i \(-0.802423\pi\)
−0.813467 + 0.581611i \(0.802423\pi\)
\(570\) 0 0
\(571\) 451.000 0.0330539 0.0165269 − 0.999863i \(-0.494739\pi\)
0.0165269 + 0.999863i \(0.494739\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 20987.0 1.51421 0.757106 − 0.653292i \(-0.226613\pi\)
0.757106 + 0.653292i \(0.226613\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −21622.0 −1.54394
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3888.00 −0.273381 −0.136691 − 0.990614i \(-0.543647\pi\)
−0.136691 + 0.990614i \(0.543647\pi\)
\(588\) 0 0
\(589\) 1855.00 0.129769
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11268.0 0.780306 0.390153 − 0.920750i \(-0.372422\pi\)
0.390153 + 0.920750i \(0.372422\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3996.00 0.272575 0.136287 − 0.990669i \(-0.456483\pi\)
0.136287 + 0.990669i \(0.456483\pi\)
\(600\) 0 0
\(601\) −24965.0 −1.69442 −0.847208 − 0.531262i \(-0.821718\pi\)
−0.847208 + 0.531262i \(0.821718\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 4176.00 0.279240 0.139620 − 0.990205i \(-0.455412\pi\)
0.139620 + 0.990205i \(0.455412\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 230.000 0.0152288
\(612\) 0 0
\(613\) −9558.00 −0.629762 −0.314881 − 0.949131i \(-0.601965\pi\)
−0.314881 + 0.949131i \(0.601965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9000.00 0.587239 0.293619 − 0.955922i \(-0.405140\pi\)
0.293619 + 0.955922i \(0.405140\pi\)
\(618\) 0 0
\(619\) −15625.0 −1.01457 −0.507287 − 0.861777i \(-0.669352\pi\)
−0.507287 + 0.861777i \(0.669352\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2736.00 0.175948
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −15660.0 −0.992695
\(630\) 0 0
\(631\) −31175.0 −1.96681 −0.983405 − 0.181424i \(-0.941929\pi\)
−0.983405 + 0.181424i \(0.941929\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 18.0000 0.00111960
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6732.00 0.414817 0.207409 − 0.978254i \(-0.433497\pi\)
0.207409 + 0.978254i \(0.433497\pi\)
\(642\) 0 0
\(643\) −6228.00 −0.381973 −0.190986 − 0.981593i \(-0.561169\pi\)
−0.190986 + 0.981593i \(0.561169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 396.000 0.0240624 0.0120312 − 0.999928i \(-0.496170\pi\)
0.0120312 + 0.999928i \(0.496170\pi\)
\(648\) 0 0
\(649\) 9812.00 0.593459
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4702.00 0.281782 0.140891 − 0.990025i \(-0.455003\pi\)
0.140891 + 0.990025i \(0.455003\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22140.0 1.30873 0.654364 − 0.756180i \(-0.272936\pi\)
0.654364 + 0.756180i \(0.272936\pi\)
\(660\) 0 0
\(661\) −13518.0 −0.795445 −0.397723 − 0.917506i \(-0.630199\pi\)
−0.397723 + 0.917506i \(0.630199\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1276.00 0.0740733
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2794.00 −0.160747
\(672\) 0 0
\(673\) −11250.0 −0.644362 −0.322181 − 0.946678i \(-0.604416\pi\)
−0.322181 + 0.946678i \(0.604416\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15170.0 0.861197 0.430599 − 0.902544i \(-0.358302\pi\)
0.430599 + 0.902544i \(0.358302\pi\)
\(678\) 0 0
\(679\) 20501.0 1.15870
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −22680.0 −1.27061 −0.635305 − 0.772262i \(-0.719125\pi\)
−0.635305 + 0.772262i \(0.719125\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 128.000 0.00704682 0.00352341 − 0.999994i \(-0.498878\pi\)
0.00352341 + 0.999994i \(0.498878\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 27144.0 1.47511
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −25682.0 −1.38373 −0.691866 − 0.722026i \(-0.743211\pi\)
−0.691866 + 0.722026i \(0.743211\pi\)
\(702\) 0 0
\(703\) 14310.0 0.767727
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27360.0 −1.45542
\(708\) 0 0
\(709\) −4951.00 −0.262255 −0.131127 − 0.991366i \(-0.541860\pi\)
−0.131127 + 0.991366i \(0.541860\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2030.00 0.106626
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22190.0 1.15097 0.575485 − 0.817812i \(-0.304813\pi\)
0.575485 + 0.817812i \(0.304813\pi\)
\(720\) 0 0
\(721\) −2356.00 −0.121695
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 7685.00 0.392051 0.196025 − 0.980599i \(-0.437197\pi\)
0.196025 + 0.980599i \(0.437197\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24998.0 −1.26482
\(732\) 0 0
\(733\) 29574.0 1.49023 0.745116 − 0.666934i \(-0.232394\pi\)
0.745116 + 0.666934i \(0.232394\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 17842.0 0.891748
\(738\) 0 0
\(739\) −32580.0 −1.62175 −0.810876 − 0.585218i \(-0.801009\pi\)
−0.810876 + 0.585218i \(0.801009\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3060.00 0.151091 0.0755454 − 0.997142i \(-0.475930\pi\)
0.0755454 + 0.997142i \(0.475930\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8208.00 −0.400419
\(750\) 0 0
\(751\) −7992.00 −0.388325 −0.194163 − 0.980969i \(-0.562199\pi\)
−0.194163 + 0.980969i \(0.562199\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22841.0 1.09666 0.548329 − 0.836263i \(-0.315264\pi\)
0.548329 + 0.836263i \(0.315264\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17172.0 0.817982 0.408991 − 0.912538i \(-0.365881\pi\)
0.408991 + 0.912538i \(0.365881\pi\)
\(762\) 0 0
\(763\) −13319.0 −0.631953
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −446.000 −0.0209963
\(768\) 0 0
\(769\) −30869.0 −1.44755 −0.723774 − 0.690037i \(-0.757594\pi\)
−0.723774 + 0.690037i \(0.757594\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −34884.0 −1.62314 −0.811572 − 0.584252i \(-0.801388\pi\)
−0.811572 + 0.584252i \(0.801388\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24804.0 −1.14082
\(780\) 0 0
\(781\) 792.000 0.0362868
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 5039.00 0.228235 0.114118 − 0.993467i \(-0.463596\pi\)
0.114118 + 0.993467i \(0.463596\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −19836.0 −0.891640
\(792\) 0 0
\(793\) 127.000 0.00568714
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −540.000 −0.0239997 −0.0119999 − 0.999928i \(-0.503820\pi\)
−0.0119999 + 0.999928i \(0.503820\pi\)
\(798\) 0 0
\(799\) 13340.0 0.590657
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11484.0 −0.504684
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 41328.0 1.79606 0.898032 − 0.439931i \(-0.144997\pi\)
0.898032 + 0.439931i \(0.144997\pi\)
\(810\) 0 0
\(811\) −12853.0 −0.556510 −0.278255 − 0.960507i \(-0.589756\pi\)
−0.278255 + 0.960507i \(0.589756\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 22843.0 0.978183
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29470.0 −1.25275 −0.626376 − 0.779521i \(-0.715463\pi\)
−0.626376 + 0.779521i \(0.715463\pi\)
\(822\) 0 0
\(823\) −24407.0 −1.03375 −0.516874 − 0.856062i \(-0.672904\pi\)
−0.516874 + 0.856062i \(0.672904\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15048.0 −0.632733 −0.316367 − 0.948637i \(-0.602463\pi\)
−0.316367 + 0.948637i \(0.602463\pi\)
\(828\) 0 0
\(829\) −28406.0 −1.19009 −0.595043 − 0.803694i \(-0.702865\pi\)
−0.595043 + 0.803694i \(0.702865\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1044.00 0.0434243
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26914.0 1.10748 0.553739 − 0.832690i \(-0.313200\pi\)
0.553739 + 0.832690i \(0.313200\pi\)
\(840\) 0 0
\(841\) −23905.0 −0.980155
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 16093.0 0.652848
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 15660.0 0.630808
\(852\) 0 0
\(853\) 21275.0 0.853977 0.426988 − 0.904257i \(-0.359575\pi\)
0.426988 + 0.904257i \(0.359575\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −39132.0 −1.55977 −0.779885 − 0.625922i \(-0.784723\pi\)
−0.779885 + 0.625922i \(0.784723\pi\)
\(858\) 0 0
\(859\) −448.000 −0.0177946 −0.00889730 − 0.999960i \(-0.502832\pi\)
−0.00889730 + 0.999960i \(0.502832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26856.0 1.05932 0.529658 − 0.848212i \(-0.322320\pi\)
0.529658 + 0.848212i \(0.322320\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −30096.0 −1.17484
\(870\) 0 0
\(871\) −811.000 −0.0315496
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −3653.00 −0.140653 −0.0703267 − 0.997524i \(-0.522404\pi\)
−0.0703267 + 0.997524i \(0.522404\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6552.00 0.250559 0.125280 − 0.992121i \(-0.460017\pi\)
0.125280 + 0.992121i \(0.460017\pi\)
\(882\) 0 0
\(883\) 4481.00 0.170779 0.0853894 − 0.996348i \(-0.472787\pi\)
0.0853894 + 0.996348i \(0.472787\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14666.0 0.555170 0.277585 − 0.960701i \(-0.410466\pi\)
0.277585 + 0.960701i \(0.410466\pi\)
\(888\) 0 0
\(889\) −9576.00 −0.361270
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12190.0 −0.456800
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 770.000 0.0285661
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 51804.0 1.89650 0.948249 − 0.317528i \(-0.102853\pi\)
0.948249 + 0.317528i \(0.102853\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −31198.0 −1.13462 −0.567308 − 0.823505i \(-0.692015\pi\)
−0.567308 + 0.823505i \(0.692015\pi\)
\(912\) 0 0
\(913\) −25036.0 −0.907525
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1368.00 0.0492643
\(918\) 0 0
\(919\) −27001.0 −0.969185 −0.484592 − 0.874740i \(-0.661032\pi\)
−0.484592 + 0.874740i \(0.661032\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −36.0000 −0.00128381
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 22694.0 0.801470 0.400735 − 0.916194i \(-0.368755\pi\)
0.400735 + 0.916194i \(0.368755\pi\)
\(930\) 0 0
\(931\) −954.000 −0.0335833
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 29503.0 1.02862 0.514312 − 0.857603i \(-0.328047\pi\)
0.514312 + 0.857603i \(0.328047\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14566.0 −0.504610 −0.252305 − 0.967648i \(-0.581189\pi\)
−0.252305 + 0.967648i \(0.581189\pi\)
\(942\) 0 0
\(943\) −27144.0 −0.937360
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42322.0 −1.45225 −0.726125 − 0.687563i \(-0.758681\pi\)
−0.726125 + 0.687563i \(0.758681\pi\)
\(948\) 0 0
\(949\) 522.000 0.0178555
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −43416.0 −1.47574 −0.737871 − 0.674942i \(-0.764169\pi\)
−0.737871 + 0.674942i \(0.764169\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −35150.0 −1.18358
\(960\) 0 0
\(961\) −28566.0 −0.958880
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 21528.0 0.715919 0.357960 − 0.933737i \(-0.383473\pi\)
0.357960 + 0.933737i \(0.383473\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27050.0 −0.894002 −0.447001 − 0.894533i \(-0.647508\pi\)
−0.447001 + 0.894533i \(0.647508\pi\)
\(972\) 0 0
\(973\) −34884.0 −1.14936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 24934.0 0.816489 0.408244 − 0.912873i \(-0.366141\pi\)
0.408244 + 0.912873i \(0.366141\pi\)
\(978\) 0 0
\(979\) 3168.00 0.103422
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8388.00 −0.272162 −0.136081 − 0.990698i \(-0.543451\pi\)
−0.136081 + 0.990698i \(0.543451\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 24998.0 0.803731
\(990\) 0 0
\(991\) 29033.0 0.930639 0.465320 − 0.885143i \(-0.345939\pi\)
0.465320 + 0.885143i \(0.345939\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −25326.0 −0.804496 −0.402248 − 0.915531i \(-0.631771\pi\)
−0.402248 + 0.915531i \(0.631771\pi\)
\(998\) 0 0
\(999\) 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 1800.4.a.g.1.1 1
3.2 odd 2 600.4.a.j.1.1 yes 1
5.2 odd 4 1800.4.f.g.649.1 2
5.3 odd 4 1800.4.f.g.649.2 2
5.4 even 2 1800.4.a.bf.1.1 1
12.11 even 2 1200.4.a.n.1.1 1
15.2 even 4 600.4.f.h.49.1 2
15.8 even 4 600.4.f.h.49.2 2
15.14 odd 2 600.4.a.g.1.1 ✓ 1
60.23 odd 4 1200.4.f.f.49.1 2
60.47 odd 4 1200.4.f.f.49.2 2
60.59 even 2 1200.4.a.x.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.4.a.g.1.1 ✓ 1 15.14 odd 2
600.4.a.j.1.1 yes 1 3.2 odd 2
600.4.f.h.49.1 2 15.2 even 4
600.4.f.h.49.2 2 15.8 even 4
1200.4.a.n.1.1 1 12.11 even 2
1200.4.a.x.1.1 1 60.59 even 2
1200.4.f.f.49.1 2 60.23 odd 4
1200.4.f.f.49.2 2 60.47 odd 4
1800.4.a.g.1.1 1 1.1 even 1 trivial
1800.4.a.bf.1.1 1 5.4 even 2
1800.4.f.g.649.1 2 5.2 odd 4
1800.4.f.g.649.2 2 5.3 odd 4