Properties

Label 2156.4.a.c.1.1
Level $2156$
Weight $4$
Character 2156.1
Self dual yes
Analytic conductor $127.208$
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] = [2156,4,Mod(1,2156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2156, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("2156.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2156.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: \(127.208117972\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 308)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2156.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.00000 q^{3} +1.00000 q^{5} +22.0000 q^{9} +11.0000 q^{11} -12.0000 q^{13} +7.00000 q^{15} -2.00000 q^{17} -82.0000 q^{19} +7.00000 q^{23} -124.000 q^{25} -35.0000 q^{27} -102.000 q^{29} +171.000 q^{31} +77.0000 q^{33} -357.000 q^{37} -84.0000 q^{39} +114.000 q^{41} -344.000 q^{43} +22.0000 q^{45} -96.0000 q^{47} -14.0000 q^{51} -430.000 q^{53} +11.0000 q^{55} -574.000 q^{57} +201.000 q^{59} +2.00000 q^{61} -12.0000 q^{65} +313.000 q^{67} +49.0000 q^{69} -579.000 q^{71} +438.000 q^{73} -868.000 q^{75} +494.000 q^{79} -839.000 q^{81} -748.000 q^{83} -2.00000 q^{85} -714.000 q^{87} -457.000 q^{89} +1197.00 q^{93} -82.0000 q^{95} +1037.00 q^{97} +242.000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 7.00000 1.34715 0.673575 0.739119i \(-0.264758\pi\)
0.673575 + 0.739119i \(0.264758\pi\)
\(4\) 0 0
\(5\) 1.00000 0.0894427 0.0447214 0.998999i \(-0.485760\pi\)
0.0447214 + 0.998999i \(0.485760\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −12.0000 −0.256015 −0.128008 0.991773i \(-0.540858\pi\)
−0.128008 + 0.991773i \(0.540858\pi\)
\(14\) 0 0
\(15\) 7.00000 0.120493
\(16\) 0 0
\(17\) −2.00000 −0.0285336 −0.0142668 0.999898i \(-0.504541\pi\)
−0.0142668 + 0.999898i \(0.504541\pi\)
\(18\) 0 0
\(19\) −82.0000 −0.990110 −0.495055 0.868862i \(-0.664852\pi\)
−0.495055 + 0.868862i \(0.664852\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.00000 0.0634609 0.0317305 0.999496i \(-0.489898\pi\)
0.0317305 + 0.999496i \(0.489898\pi\)
\(24\) 0 0
\(25\) −124.000 −0.992000
\(26\) 0 0
\(27\) −35.0000 −0.249472
\(28\) 0 0
\(29\) −102.000 −0.653135 −0.326568 0.945174i \(-0.605892\pi\)
−0.326568 + 0.945174i \(0.605892\pi\)
\(30\) 0 0
\(31\) 171.000 0.990726 0.495363 0.868686i \(-0.335035\pi\)
0.495363 + 0.868686i \(0.335035\pi\)
\(32\) 0 0
\(33\) 77.0000 0.406181
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −357.000 −1.58623 −0.793114 0.609073i \(-0.791542\pi\)
−0.793114 + 0.609073i \(0.791542\pi\)
\(38\) 0 0
\(39\) −84.0000 −0.344891
\(40\) 0 0
\(41\) 114.000 0.434239 0.217120 0.976145i \(-0.430334\pi\)
0.217120 + 0.976145i \(0.430334\pi\)
\(42\) 0 0
\(43\) −344.000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 22.0000 0.0728793
\(46\) 0 0
\(47\) −96.0000 −0.297937 −0.148969 0.988842i \(-0.547595\pi\)
−0.148969 + 0.988842i \(0.547595\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −14.0000 −0.0384391
\(52\) 0 0
\(53\) −430.000 −1.11443 −0.557217 0.830367i \(-0.688131\pi\)
−0.557217 + 0.830367i \(0.688131\pi\)
\(54\) 0 0
\(55\) 11.0000 0.0269680
\(56\) 0 0
\(57\) −574.000 −1.33383
\(58\) 0 0
\(59\) 201.000 0.443525 0.221762 0.975101i \(-0.428819\pi\)
0.221762 + 0.975101i \(0.428819\pi\)
\(60\) 0 0
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.0000 −0.0228987
\(66\) 0 0
\(67\) 313.000 0.570732 0.285366 0.958419i \(-0.407885\pi\)
0.285366 + 0.958419i \(0.407885\pi\)
\(68\) 0 0
\(69\) 49.0000 0.0854914
\(70\) 0 0
\(71\) −579.000 −0.967812 −0.483906 0.875120i \(-0.660782\pi\)
−0.483906 + 0.875120i \(0.660782\pi\)
\(72\) 0 0
\(73\) 438.000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0 0
\(75\) −868.000 −1.33637
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 494.000 0.703536 0.351768 0.936087i \(-0.385581\pi\)
0.351768 + 0.936087i \(0.385581\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 0 0
\(83\) −748.000 −0.989201 −0.494600 0.869121i \(-0.664686\pi\)
−0.494600 + 0.869121i \(0.664686\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.00255212
\(86\) 0 0
\(87\) −714.000 −0.879872
\(88\) 0 0
\(89\) −457.000 −0.544291 −0.272146 0.962256i \(-0.587733\pi\)
−0.272146 + 0.962256i \(0.587733\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1197.00 1.33466
\(94\) 0 0
\(95\) −82.0000 −0.0885581
\(96\) 0 0
\(97\) 1037.00 1.08548 0.542739 0.839901i \(-0.317387\pi\)
0.542739 + 0.839901i \(0.317387\pi\)
\(98\) 0 0
\(99\) 242.000 0.245676
\(100\) 0 0
\(101\) −68.0000 −0.0669926 −0.0334963 0.999439i \(-0.510664\pi\)
−0.0334963 + 0.999439i \(0.510664\pi\)
\(102\) 0 0
\(103\) 468.000 0.447703 0.223852 0.974623i \(-0.428137\pi\)
0.223852 + 0.974623i \(0.428137\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1582.00 1.42932 0.714662 0.699470i \(-0.246580\pi\)
0.714662 + 0.699470i \(0.246580\pi\)
\(108\) 0 0
\(109\) 516.000 0.453430 0.226715 0.973961i \(-0.427201\pi\)
0.226715 + 0.973961i \(0.427201\pi\)
\(110\) 0 0
\(111\) −2499.00 −2.13689
\(112\) 0 0
\(113\) −1627.00 −1.35447 −0.677236 0.735766i \(-0.736822\pi\)
−0.677236 + 0.735766i \(0.736822\pi\)
\(114\) 0 0
\(115\) 7.00000 0.00567612
\(116\) 0 0
\(117\) −264.000 −0.208605
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 798.000 0.584986
\(124\) 0 0
\(125\) −249.000 −0.178170
\(126\) 0 0
\(127\) −2790.00 −1.94939 −0.974695 0.223540i \(-0.928239\pi\)
−0.974695 + 0.223540i \(0.928239\pi\)
\(128\) 0 0
\(129\) −2408.00 −1.64351
\(130\) 0 0
\(131\) −730.000 −0.486873 −0.243437 0.969917i \(-0.578275\pi\)
−0.243437 + 0.969917i \(0.578275\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −35.0000 −0.0223135
\(136\) 0 0
\(137\) −1819.00 −1.13436 −0.567181 0.823593i \(-0.691966\pi\)
−0.567181 + 0.823593i \(0.691966\pi\)
\(138\) 0 0
\(139\) 802.000 0.489387 0.244693 0.969601i \(-0.421313\pi\)
0.244693 + 0.969601i \(0.421313\pi\)
\(140\) 0 0
\(141\) −672.000 −0.401366
\(142\) 0 0
\(143\) −132.000 −0.0771916
\(144\) 0 0
\(145\) −102.000 −0.0584182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 314.000 0.172644 0.0863218 0.996267i \(-0.472489\pi\)
0.0863218 + 0.996267i \(0.472489\pi\)
\(150\) 0 0
\(151\) 766.000 0.412822 0.206411 0.978465i \(-0.433822\pi\)
0.206411 + 0.978465i \(0.433822\pi\)
\(152\) 0 0
\(153\) −44.0000 −0.0232496
\(154\) 0 0
\(155\) 171.000 0.0886132
\(156\) 0 0
\(157\) 1681.00 0.854512 0.427256 0.904131i \(-0.359480\pi\)
0.427256 + 0.904131i \(0.359480\pi\)
\(158\) 0 0
\(159\) −3010.00 −1.50131
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 724.000 0.347902 0.173951 0.984754i \(-0.444347\pi\)
0.173951 + 0.984754i \(0.444347\pi\)
\(164\) 0 0
\(165\) 77.0000 0.0363300
\(166\) 0 0
\(167\) 1242.00 0.575502 0.287751 0.957705i \(-0.407092\pi\)
0.287751 + 0.957705i \(0.407092\pi\)
\(168\) 0 0
\(169\) −2053.00 −0.934456
\(170\) 0 0
\(171\) −1804.00 −0.806756
\(172\) 0 0
\(173\) −2432.00 −1.06880 −0.534398 0.845233i \(-0.679461\pi\)
−0.534398 + 0.845233i \(0.679461\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1407.00 0.597495
\(178\) 0 0
\(179\) −2035.00 −0.849738 −0.424869 0.905255i \(-0.639680\pi\)
−0.424869 + 0.905255i \(0.639680\pi\)
\(180\) 0 0
\(181\) −1405.00 −0.576977 −0.288488 0.957483i \(-0.593153\pi\)
−0.288488 + 0.957483i \(0.593153\pi\)
\(182\) 0 0
\(183\) 14.0000 0.00565524
\(184\) 0 0
\(185\) −357.000 −0.141877
\(186\) 0 0
\(187\) −22.0000 −0.00860320
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1671.00 −0.633033 −0.316517 0.948587i \(-0.602513\pi\)
−0.316517 + 0.948587i \(0.602513\pi\)
\(192\) 0 0
\(193\) −2066.00 −0.770539 −0.385269 0.922804i \(-0.625891\pi\)
−0.385269 + 0.922804i \(0.625891\pi\)
\(194\) 0 0
\(195\) −84.0000 −0.0308480
\(196\) 0 0
\(197\) 3442.00 1.24483 0.622417 0.782686i \(-0.286151\pi\)
0.622417 + 0.782686i \(0.286151\pi\)
\(198\) 0 0
\(199\) −3008.00 −1.07151 −0.535757 0.844372i \(-0.679974\pi\)
−0.535757 + 0.844372i \(0.679974\pi\)
\(200\) 0 0
\(201\) 2191.00 0.768862
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 114.000 0.0388395
\(206\) 0 0
\(207\) 154.000 0.0517089
\(208\) 0 0
\(209\) −902.000 −0.298529
\(210\) 0 0
\(211\) −778.000 −0.253838 −0.126919 0.991913i \(-0.540509\pi\)
−0.126919 + 0.991913i \(0.540509\pi\)
\(212\) 0 0
\(213\) −4053.00 −1.30379
\(214\) 0 0
\(215\) −344.000 −0.109119
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 3066.00 0.946032
\(220\) 0 0
\(221\) 24.0000 0.00730504
\(222\) 0 0
\(223\) 2739.00 0.822498 0.411249 0.911523i \(-0.365093\pi\)
0.411249 + 0.911523i \(0.365093\pi\)
\(224\) 0 0
\(225\) −2728.00 −0.808296
\(226\) 0 0
\(227\) 732.000 0.214029 0.107014 0.994257i \(-0.465871\pi\)
0.107014 + 0.994257i \(0.465871\pi\)
\(228\) 0 0
\(229\) 823.000 0.237491 0.118745 0.992925i \(-0.462113\pi\)
0.118745 + 0.992925i \(0.462113\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1462.00 0.411068 0.205534 0.978650i \(-0.434107\pi\)
0.205534 + 0.978650i \(0.434107\pi\)
\(234\) 0 0
\(235\) −96.0000 −0.0266483
\(236\) 0 0
\(237\) 3458.00 0.947769
\(238\) 0 0
\(239\) 1700.00 0.460100 0.230050 0.973179i \(-0.426111\pi\)
0.230050 + 0.973179i \(0.426111\pi\)
\(240\) 0 0
\(241\) −3460.00 −0.924806 −0.462403 0.886670i \(-0.653013\pi\)
−0.462403 + 0.886670i \(0.653013\pi\)
\(242\) 0 0
\(243\) −4928.00 −1.30095
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 984.000 0.253483
\(248\) 0 0
\(249\) −5236.00 −1.33260
\(250\) 0 0
\(251\) 265.000 0.0666400 0.0333200 0.999445i \(-0.489392\pi\)
0.0333200 + 0.999445i \(0.489392\pi\)
\(252\) 0 0
\(253\) 77.0000 0.0191342
\(254\) 0 0
\(255\) −14.0000 −0.00343809
\(256\) 0 0
\(257\) 6502.00 1.57815 0.789073 0.614299i \(-0.210561\pi\)
0.789073 + 0.614299i \(0.210561\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2244.00 −0.532184
\(262\) 0 0
\(263\) −1398.00 −0.327773 −0.163887 0.986479i \(-0.552403\pi\)
−0.163887 + 0.986479i \(0.552403\pi\)
\(264\) 0 0
\(265\) −430.000 −0.0996781
\(266\) 0 0
\(267\) −3199.00 −0.733242
\(268\) 0 0
\(269\) −3686.00 −0.835462 −0.417731 0.908571i \(-0.637175\pi\)
−0.417731 + 0.908571i \(0.637175\pi\)
\(270\) 0 0
\(271\) 3808.00 0.853578 0.426789 0.904351i \(-0.359645\pi\)
0.426789 + 0.904351i \(0.359645\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1364.00 −0.299099
\(276\) 0 0
\(277\) −8872.00 −1.92443 −0.962214 0.272293i \(-0.912218\pi\)
−0.962214 + 0.272293i \(0.912218\pi\)
\(278\) 0 0
\(279\) 3762.00 0.807258
\(280\) 0 0
\(281\) −2788.00 −0.591879 −0.295940 0.955207i \(-0.595633\pi\)
−0.295940 + 0.955207i \(0.595633\pi\)
\(282\) 0 0
\(283\) −160.000 −0.0336078 −0.0168039 0.999859i \(-0.505349\pi\)
−0.0168039 + 0.999859i \(0.505349\pi\)
\(284\) 0 0
\(285\) −574.000 −0.119301
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4909.00 −0.999186
\(290\) 0 0
\(291\) 7259.00 1.46230
\(292\) 0 0
\(293\) 1142.00 0.227701 0.113850 0.993498i \(-0.463682\pi\)
0.113850 + 0.993498i \(0.463682\pi\)
\(294\) 0 0
\(295\) 201.000 0.0396701
\(296\) 0 0
\(297\) −385.000 −0.0752187
\(298\) 0 0
\(299\) −84.0000 −0.0162470
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −476.000 −0.0902491
\(304\) 0 0
\(305\) 2.00000 0.000375474 0
\(306\) 0 0
\(307\) 10220.0 1.89996 0.949978 0.312318i \(-0.101106\pi\)
0.949978 + 0.312318i \(0.101106\pi\)
\(308\) 0 0
\(309\) 3276.00 0.603123
\(310\) 0 0
\(311\) −4864.00 −0.886856 −0.443428 0.896310i \(-0.646238\pi\)
−0.443428 + 0.896310i \(0.646238\pi\)
\(312\) 0 0
\(313\) 3703.00 0.668709 0.334355 0.942447i \(-0.391482\pi\)
0.334355 + 0.942447i \(0.391482\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 81.0000 0.0143515 0.00717573 0.999974i \(-0.497716\pi\)
0.00717573 + 0.999974i \(0.497716\pi\)
\(318\) 0 0
\(319\) −1122.00 −0.196928
\(320\) 0 0
\(321\) 11074.0 1.92552
\(322\) 0 0
\(323\) 164.000 0.0282514
\(324\) 0 0
\(325\) 1488.00 0.253967
\(326\) 0 0
\(327\) 3612.00 0.610838
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2675.00 0.444203 0.222102 0.975024i \(-0.428708\pi\)
0.222102 + 0.975024i \(0.428708\pi\)
\(332\) 0 0
\(333\) −7854.00 −1.29248
\(334\) 0 0
\(335\) 313.000 0.0510478
\(336\) 0 0
\(337\) 1422.00 0.229855 0.114928 0.993374i \(-0.463336\pi\)
0.114928 + 0.993374i \(0.463336\pi\)
\(338\) 0 0
\(339\) −11389.0 −1.82468
\(340\) 0 0
\(341\) 1881.00 0.298715
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 49.0000 0.00764658
\(346\) 0 0
\(347\) 9110.00 1.40937 0.704684 0.709522i \(-0.251089\pi\)
0.704684 + 0.709522i \(0.251089\pi\)
\(348\) 0 0
\(349\) 114.000 0.0174850 0.00874252 0.999962i \(-0.497217\pi\)
0.00874252 + 0.999962i \(0.497217\pi\)
\(350\) 0 0
\(351\) 420.000 0.0638688
\(352\) 0 0
\(353\) −12465.0 −1.87945 −0.939724 0.341934i \(-0.888918\pi\)
−0.939724 + 0.341934i \(0.888918\pi\)
\(354\) 0 0
\(355\) −579.000 −0.0865637
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7944.00 1.16788 0.583939 0.811797i \(-0.301511\pi\)
0.583939 + 0.811797i \(0.301511\pi\)
\(360\) 0 0
\(361\) −135.000 −0.0196822
\(362\) 0 0
\(363\) 847.000 0.122468
\(364\) 0 0
\(365\) 438.000 0.0628109
\(366\) 0 0
\(367\) 1591.00 0.226293 0.113146 0.993578i \(-0.463907\pi\)
0.113146 + 0.993578i \(0.463907\pi\)
\(368\) 0 0
\(369\) 2508.00 0.353825
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 6892.00 0.956714 0.478357 0.878166i \(-0.341233\pi\)
0.478357 + 0.878166i \(0.341233\pi\)
\(374\) 0 0
\(375\) −1743.00 −0.240022
\(376\) 0 0
\(377\) 1224.00 0.167213
\(378\) 0 0
\(379\) 3935.00 0.533318 0.266659 0.963791i \(-0.414080\pi\)
0.266659 + 0.963791i \(0.414080\pi\)
\(380\) 0 0
\(381\) −19530.0 −2.62612
\(382\) 0 0
\(383\) −7325.00 −0.977259 −0.488629 0.872492i \(-0.662503\pi\)
−0.488629 + 0.872492i \(0.662503\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7568.00 −0.994065
\(388\) 0 0
\(389\) 8937.00 1.16484 0.582421 0.812887i \(-0.302105\pi\)
0.582421 + 0.812887i \(0.302105\pi\)
\(390\) 0 0
\(391\) −14.0000 −0.00181077
\(392\) 0 0
\(393\) −5110.00 −0.655892
\(394\) 0 0
\(395\) 494.000 0.0629262
\(396\) 0 0
\(397\) 7526.00 0.951434 0.475717 0.879599i \(-0.342189\pi\)
0.475717 + 0.879599i \(0.342189\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6202.00 0.772352 0.386176 0.922425i \(-0.373796\pi\)
0.386176 + 0.922425i \(0.373796\pi\)
\(402\) 0 0
\(403\) −2052.00 −0.253641
\(404\) 0 0
\(405\) −839.000 −0.102939
\(406\) 0 0
\(407\) −3927.00 −0.478266
\(408\) 0 0
\(409\) −1366.00 −0.165145 −0.0825726 0.996585i \(-0.526314\pi\)
−0.0825726 + 0.996585i \(0.526314\pi\)
\(410\) 0 0
\(411\) −12733.0 −1.52816
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −748.000 −0.0884768
\(416\) 0 0
\(417\) 5614.00 0.659278
\(418\) 0 0
\(419\) −6384.00 −0.744341 −0.372170 0.928164i \(-0.621386\pi\)
−0.372170 + 0.928164i \(0.621386\pi\)
\(420\) 0 0
\(421\) 5534.00 0.640643 0.320321 0.947309i \(-0.396209\pi\)
0.320321 + 0.947309i \(0.396209\pi\)
\(422\) 0 0
\(423\) −2112.00 −0.242763
\(424\) 0 0
\(425\) 248.000 0.0283053
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −924.000 −0.103989
\(430\) 0 0
\(431\) −10740.0 −1.20030 −0.600148 0.799889i \(-0.704892\pi\)
−0.600148 + 0.799889i \(0.704892\pi\)
\(432\) 0 0
\(433\) −16151.0 −1.79253 −0.896267 0.443514i \(-0.853732\pi\)
−0.896267 + 0.443514i \(0.853732\pi\)
\(434\) 0 0
\(435\) −714.000 −0.0786981
\(436\) 0 0
\(437\) −574.000 −0.0628333
\(438\) 0 0
\(439\) −5914.00 −0.642961 −0.321480 0.946916i \(-0.604180\pi\)
−0.321480 + 0.946916i \(0.604180\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7237.00 0.776163 0.388082 0.921625i \(-0.373138\pi\)
0.388082 + 0.921625i \(0.373138\pi\)
\(444\) 0 0
\(445\) −457.000 −0.0486829
\(446\) 0 0
\(447\) 2198.00 0.232577
\(448\) 0 0
\(449\) 9839.00 1.03415 0.517073 0.855942i \(-0.327022\pi\)
0.517073 + 0.855942i \(0.327022\pi\)
\(450\) 0 0
\(451\) 1254.00 0.130928
\(452\) 0 0
\(453\) 5362.00 0.556134
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6824.00 −0.698497 −0.349249 0.937030i \(-0.613563\pi\)
−0.349249 + 0.937030i \(0.613563\pi\)
\(458\) 0 0
\(459\) 70.0000 0.00711834
\(460\) 0 0
\(461\) −13922.0 −1.40653 −0.703267 0.710926i \(-0.748276\pi\)
−0.703267 + 0.710926i \(0.748276\pi\)
\(462\) 0 0
\(463\) −1551.00 −0.155683 −0.0778413 0.996966i \(-0.524803\pi\)
−0.0778413 + 0.996966i \(0.524803\pi\)
\(464\) 0 0
\(465\) 1197.00 0.119375
\(466\) 0 0
\(467\) −10719.0 −1.06213 −0.531067 0.847330i \(-0.678209\pi\)
−0.531067 + 0.847330i \(0.678209\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 11767.0 1.15116
\(472\) 0 0
\(473\) −3784.00 −0.367840
\(474\) 0 0
\(475\) 10168.0 0.982189
\(476\) 0 0
\(477\) −9460.00 −0.908058
\(478\) 0 0
\(479\) 12252.0 1.16870 0.584351 0.811501i \(-0.301349\pi\)
0.584351 + 0.811501i \(0.301349\pi\)
\(480\) 0 0
\(481\) 4284.00 0.406099
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1037.00 0.0970881
\(486\) 0 0
\(487\) −8521.00 −0.792861 −0.396431 0.918065i \(-0.629751\pi\)
−0.396431 + 0.918065i \(0.629751\pi\)
\(488\) 0 0
\(489\) 5068.00 0.468677
\(490\) 0 0
\(491\) 7946.00 0.730342 0.365171 0.930940i \(-0.381011\pi\)
0.365171 + 0.930940i \(0.381011\pi\)
\(492\) 0 0
\(493\) 204.000 0.0186363
\(494\) 0 0
\(495\) 242.000 0.0219739
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4660.00 −0.418057 −0.209028 0.977910i \(-0.567030\pi\)
−0.209028 + 0.977910i \(0.567030\pi\)
\(500\) 0 0
\(501\) 8694.00 0.775288
\(502\) 0 0
\(503\) 18880.0 1.67359 0.836797 0.547514i \(-0.184426\pi\)
0.836797 + 0.547514i \(0.184426\pi\)
\(504\) 0 0
\(505\) −68.0000 −0.00599200
\(506\) 0 0
\(507\) −14371.0 −1.25885
\(508\) 0 0
\(509\) 1999.00 0.174075 0.0870374 0.996205i \(-0.472260\pi\)
0.0870374 + 0.996205i \(0.472260\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2870.00 0.247005
\(514\) 0 0
\(515\) 468.000 0.0400438
\(516\) 0 0
\(517\) −1056.00 −0.0898314
\(518\) 0 0
\(519\) −17024.0 −1.43983
\(520\) 0 0
\(521\) −18063.0 −1.51891 −0.759457 0.650557i \(-0.774535\pi\)
−0.759457 + 0.650557i \(0.774535\pi\)
\(522\) 0 0
\(523\) −7712.00 −0.644784 −0.322392 0.946606i \(-0.604487\pi\)
−0.322392 + 0.946606i \(0.604487\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −342.000 −0.0282690
\(528\) 0 0
\(529\) −12118.0 −0.995973
\(530\) 0 0
\(531\) 4422.00 0.361391
\(532\) 0 0
\(533\) −1368.00 −0.111172
\(534\) 0 0
\(535\) 1582.00 0.127843
\(536\) 0 0
\(537\) −14245.0 −1.14472
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −704.000 −0.0559470 −0.0279735 0.999609i \(-0.508905\pi\)
−0.0279735 + 0.999609i \(0.508905\pi\)
\(542\) 0 0
\(543\) −9835.00 −0.777275
\(544\) 0 0
\(545\) 516.000 0.0405560
\(546\) 0 0
\(547\) −20680.0 −1.61648 −0.808239 0.588855i \(-0.799579\pi\)
−0.808239 + 0.588855i \(0.799579\pi\)
\(548\) 0 0
\(549\) 44.0000 0.00342054
\(550\) 0 0
\(551\) 8364.00 0.646676
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2499.00 −0.191129
\(556\) 0 0
\(557\) −19266.0 −1.46558 −0.732789 0.680456i \(-0.761782\pi\)
−0.732789 + 0.680456i \(0.761782\pi\)
\(558\) 0 0
\(559\) 4128.00 0.312336
\(560\) 0 0
\(561\) −154.000 −0.0115898
\(562\) 0 0
\(563\) 18956.0 1.41901 0.709503 0.704703i \(-0.248920\pi\)
0.709503 + 0.704703i \(0.248920\pi\)
\(564\) 0 0
\(565\) −1627.00 −0.121148
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13726.0 1.01129 0.505645 0.862742i \(-0.331255\pi\)
0.505645 + 0.862742i \(0.331255\pi\)
\(570\) 0 0
\(571\) 8620.00 0.631761 0.315881 0.948799i \(-0.397700\pi\)
0.315881 + 0.948799i \(0.397700\pi\)
\(572\) 0 0
\(573\) −11697.0 −0.852791
\(574\) 0 0
\(575\) −868.000 −0.0629532
\(576\) 0 0
\(577\) 5761.00 0.415656 0.207828 0.978165i \(-0.433361\pi\)
0.207828 + 0.978165i \(0.433361\pi\)
\(578\) 0 0
\(579\) −14462.0 −1.03803
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4730.00 −0.336015
\(584\) 0 0
\(585\) −264.000 −0.0186582
\(586\) 0 0
\(587\) −13188.0 −0.927303 −0.463652 0.886018i \(-0.653461\pi\)
−0.463652 + 0.886018i \(0.653461\pi\)
\(588\) 0 0
\(589\) −14022.0 −0.980928
\(590\) 0 0
\(591\) 24094.0 1.67698
\(592\) 0 0
\(593\) −26766.0 −1.85354 −0.926769 0.375632i \(-0.877426\pi\)
−0.926769 + 0.375632i \(0.877426\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −21056.0 −1.44349
\(598\) 0 0
\(599\) 20664.0 1.40953 0.704765 0.709441i \(-0.251053\pi\)
0.704765 + 0.709441i \(0.251053\pi\)
\(600\) 0 0
\(601\) −23656.0 −1.60557 −0.802786 0.596268i \(-0.796650\pi\)
−0.802786 + 0.596268i \(0.796650\pi\)
\(602\) 0 0
\(603\) 6886.00 0.465041
\(604\) 0 0
\(605\) 121.000 0.00813116
\(606\) 0 0
\(607\) 18674.0 1.24869 0.624345 0.781149i \(-0.285366\pi\)
0.624345 + 0.781149i \(0.285366\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1152.00 0.0762765
\(612\) 0 0
\(613\) 7248.00 0.477559 0.238780 0.971074i \(-0.423253\pi\)
0.238780 + 0.971074i \(0.423253\pi\)
\(614\) 0 0
\(615\) 798.000 0.0523227
\(616\) 0 0
\(617\) 2066.00 0.134804 0.0674020 0.997726i \(-0.478529\pi\)
0.0674020 + 0.997726i \(0.478529\pi\)
\(618\) 0 0
\(619\) −1997.00 −0.129671 −0.0648354 0.997896i \(-0.520652\pi\)
−0.0648354 + 0.997896i \(0.520652\pi\)
\(620\) 0 0
\(621\) −245.000 −0.0158317
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15251.0 0.976064
\(626\) 0 0
\(627\) −6314.00 −0.402164
\(628\) 0 0
\(629\) 714.000 0.0452608
\(630\) 0 0
\(631\) −5129.00 −0.323585 −0.161793 0.986825i \(-0.551728\pi\)
−0.161793 + 0.986825i \(0.551728\pi\)
\(632\) 0 0
\(633\) −5446.00 −0.341957
\(634\) 0 0
\(635\) −2790.00 −0.174359
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −12738.0 −0.788588
\(640\) 0 0
\(641\) −15129.0 −0.932230 −0.466115 0.884724i \(-0.654347\pi\)
−0.466115 + 0.884724i \(0.654347\pi\)
\(642\) 0 0
\(643\) −2807.00 −0.172158 −0.0860788 0.996288i \(-0.527434\pi\)
−0.0860788 + 0.996288i \(0.527434\pi\)
\(644\) 0 0
\(645\) −2408.00 −0.147000
\(646\) 0 0
\(647\) 20137.0 1.22360 0.611798 0.791014i \(-0.290446\pi\)
0.611798 + 0.791014i \(0.290446\pi\)
\(648\) 0 0
\(649\) 2211.00 0.133728
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26247.0 1.57293 0.786466 0.617634i \(-0.211909\pi\)
0.786466 + 0.617634i \(0.211909\pi\)
\(654\) 0 0
\(655\) −730.000 −0.0435473
\(656\) 0 0
\(657\) 9636.00 0.572201
\(658\) 0 0
\(659\) −28074.0 −1.65950 −0.829748 0.558138i \(-0.811516\pi\)
−0.829748 + 0.558138i \(0.811516\pi\)
\(660\) 0 0
\(661\) −2355.00 −0.138576 −0.0692881 0.997597i \(-0.522073\pi\)
−0.0692881 + 0.997597i \(0.522073\pi\)
\(662\) 0 0
\(663\) 168.000 0.00984099
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −714.000 −0.0414486
\(668\) 0 0
\(669\) 19173.0 1.10803
\(670\) 0 0
\(671\) 22.0000 0.00126572
\(672\) 0 0
\(673\) −19180.0 −1.09857 −0.549283 0.835637i \(-0.685099\pi\)
−0.549283 + 0.835637i \(0.685099\pi\)
\(674\) 0 0
\(675\) 4340.00 0.247477
\(676\) 0 0
\(677\) 27482.0 1.56015 0.780073 0.625688i \(-0.215182\pi\)
0.780073 + 0.625688i \(0.215182\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 5124.00 0.288329
\(682\) 0 0
\(683\) −24468.0 −1.37078 −0.685389 0.728177i \(-0.740368\pi\)
−0.685389 + 0.728177i \(0.740368\pi\)
\(684\) 0 0
\(685\) −1819.00 −0.101460
\(686\) 0 0
\(687\) 5761.00 0.319936
\(688\) 0 0
\(689\) 5160.00 0.285313
\(690\) 0 0
\(691\) −147.000 −0.00809283 −0.00404641 0.999992i \(-0.501288\pi\)
−0.00404641 + 0.999992i \(0.501288\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 802.000 0.0437721
\(696\) 0 0
\(697\) −228.000 −0.0123904
\(698\) 0 0
\(699\) 10234.0 0.553770
\(700\) 0 0
\(701\) 5760.00 0.310346 0.155173 0.987887i \(-0.450407\pi\)
0.155173 + 0.987887i \(0.450407\pi\)
\(702\) 0 0
\(703\) 29274.0 1.57054
\(704\) 0 0
\(705\) −672.000 −0.0358993
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 11775.0 0.623723 0.311861 0.950128i \(-0.399048\pi\)
0.311861 + 0.950128i \(0.399048\pi\)
\(710\) 0 0
\(711\) 10868.0 0.573252
\(712\) 0 0
\(713\) 1197.00 0.0628724
\(714\) 0 0
\(715\) −132.000 −0.00690422
\(716\) 0 0
\(717\) 11900.0 0.619824
\(718\) 0 0
\(719\) 21687.0 1.12488 0.562440 0.826838i \(-0.309863\pi\)
0.562440 + 0.826838i \(0.309863\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −24220.0 −1.24585
\(724\) 0 0
\(725\) 12648.0 0.647910
\(726\) 0 0
\(727\) −33585.0 −1.71334 −0.856670 0.515864i \(-0.827471\pi\)
−0.856670 + 0.515864i \(0.827471\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) 688.000 0.0348107
\(732\) 0 0
\(733\) 32404.0 1.63284 0.816418 0.577461i \(-0.195956\pi\)
0.816418 + 0.577461i \(0.195956\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3443.00 0.172082
\(738\) 0 0
\(739\) 6038.00 0.300557 0.150278 0.988644i \(-0.451983\pi\)
0.150278 + 0.988644i \(0.451983\pi\)
\(740\) 0 0
\(741\) 6888.00 0.341480
\(742\) 0 0
\(743\) −3656.00 −0.180519 −0.0902595 0.995918i \(-0.528770\pi\)
−0.0902595 + 0.995918i \(0.528770\pi\)
\(744\) 0 0
\(745\) 314.000 0.0154417
\(746\) 0 0
\(747\) −16456.0 −0.806015
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4915.00 −0.238816 −0.119408 0.992845i \(-0.538100\pi\)
−0.119408 + 0.992845i \(0.538100\pi\)
\(752\) 0 0
\(753\) 1855.00 0.0897742
\(754\) 0 0
\(755\) 766.000 0.0369240
\(756\) 0 0
\(757\) −19186.0 −0.921172 −0.460586 0.887615i \(-0.652361\pi\)
−0.460586 + 0.887615i \(0.652361\pi\)
\(758\) 0 0
\(759\) 539.000 0.0257766
\(760\) 0 0
\(761\) −2448.00 −0.116610 −0.0583048 0.998299i \(-0.518570\pi\)
−0.0583048 + 0.998299i \(0.518570\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −44.0000 −0.00207951
\(766\) 0 0
\(767\) −2412.00 −0.113549
\(768\) 0 0
\(769\) 8312.00 0.389777 0.194888 0.980825i \(-0.437566\pi\)
0.194888 + 0.980825i \(0.437566\pi\)
\(770\) 0 0
\(771\) 45514.0 2.12600
\(772\) 0 0
\(773\) 17598.0 0.818831 0.409415 0.912348i \(-0.365733\pi\)
0.409415 + 0.912348i \(0.365733\pi\)
\(774\) 0 0
\(775\) −21204.0 −0.982800
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9348.00 −0.429945
\(780\) 0 0
\(781\) −6369.00 −0.291806
\(782\) 0 0
\(783\) 3570.00 0.162939
\(784\) 0 0
\(785\) 1681.00 0.0764299
\(786\) 0 0
\(787\) 7982.00 0.361534 0.180767 0.983526i \(-0.442142\pi\)
0.180767 + 0.983526i \(0.442142\pi\)
\(788\) 0 0
\(789\) −9786.00 −0.441560
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −24.0000 −0.00107474
\(794\) 0 0
\(795\) −3010.00 −0.134281
\(796\) 0 0
\(797\) 12489.0 0.555060 0.277530 0.960717i \(-0.410484\pi\)
0.277530 + 0.960717i \(0.410484\pi\)
\(798\) 0 0
\(799\) 192.000 0.00850122
\(800\) 0 0
\(801\) −10054.0 −0.443496
\(802\) 0 0
\(803\) 4818.00 0.211735
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −25802.0 −1.12549
\(808\) 0 0
\(809\) 31966.0 1.38920 0.694601 0.719395i \(-0.255581\pi\)
0.694601 + 0.719395i \(0.255581\pi\)
\(810\) 0 0
\(811\) −20786.0 −0.899994 −0.449997 0.893030i \(-0.648575\pi\)
−0.449997 + 0.893030i \(0.648575\pi\)
\(812\) 0 0
\(813\) 26656.0 1.14990
\(814\) 0 0
\(815\) 724.000 0.0311173
\(816\) 0 0
\(817\) 28208.0 1.20792
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33038.0 −1.40443 −0.702213 0.711967i \(-0.747805\pi\)
−0.702213 + 0.711967i \(0.747805\pi\)
\(822\) 0 0
\(823\) −6877.00 −0.291272 −0.145636 0.989338i \(-0.546523\pi\)
−0.145636 + 0.989338i \(0.546523\pi\)
\(824\) 0 0
\(825\) −9548.00 −0.402932
\(826\) 0 0
\(827\) 28964.0 1.21787 0.608934 0.793221i \(-0.291597\pi\)
0.608934 + 0.793221i \(0.291597\pi\)
\(828\) 0 0
\(829\) 30365.0 1.27216 0.636080 0.771623i \(-0.280555\pi\)
0.636080 + 0.771623i \(0.280555\pi\)
\(830\) 0 0
\(831\) −62104.0 −2.59250
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1242.00 0.0514745
\(836\) 0 0
\(837\) −5985.00 −0.247159
\(838\) 0 0
\(839\) −27393.0 −1.12719 −0.563594 0.826052i \(-0.690582\pi\)
−0.563594 + 0.826052i \(0.690582\pi\)
\(840\) 0 0
\(841\) −13985.0 −0.573414
\(842\) 0 0
\(843\) −19516.0 −0.797351
\(844\) 0 0
\(845\) −2053.00 −0.0835803
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1120.00 −0.0452748
\(850\) 0 0
\(851\) −2499.00 −0.100663
\(852\) 0 0
\(853\) 38994.0 1.56522 0.782608 0.622515i \(-0.213889\pi\)
0.782608 + 0.622515i \(0.213889\pi\)
\(854\) 0 0
\(855\) −1804.00 −0.0721585
\(856\) 0 0
\(857\) −2564.00 −0.102199 −0.0510995 0.998694i \(-0.516273\pi\)
−0.0510995 + 0.998694i \(0.516273\pi\)
\(858\) 0 0
\(859\) −21643.0 −0.859662 −0.429831 0.902909i \(-0.641427\pi\)
−0.429831 + 0.902909i \(0.641427\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10988.0 0.433414 0.216707 0.976237i \(-0.430468\pi\)
0.216707 + 0.976237i \(0.430468\pi\)
\(864\) 0 0
\(865\) −2432.00 −0.0955959
\(866\) 0 0
\(867\) −34363.0 −1.34605
\(868\) 0 0
\(869\) 5434.00 0.212124
\(870\) 0 0
\(871\) −3756.00 −0.146116
\(872\) 0 0
\(873\) 22814.0 0.884464
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 23082.0 0.888739 0.444369 0.895844i \(-0.353428\pi\)
0.444369 + 0.895844i \(0.353428\pi\)
\(878\) 0 0
\(879\) 7994.00 0.306747
\(880\) 0 0
\(881\) −29107.0 −1.11310 −0.556549 0.830815i \(-0.687875\pi\)
−0.556549 + 0.830815i \(0.687875\pi\)
\(882\) 0 0
\(883\) 40852.0 1.55694 0.778471 0.627681i \(-0.215996\pi\)
0.778471 + 0.627681i \(0.215996\pi\)
\(884\) 0 0
\(885\) 1407.00 0.0534416
\(886\) 0 0
\(887\) 35034.0 1.32619 0.663093 0.748537i \(-0.269243\pi\)
0.663093 + 0.748537i \(0.269243\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −9229.00 −0.347007
\(892\) 0 0
\(893\) 7872.00 0.294990
\(894\) 0 0
\(895\) −2035.00 −0.0760028
\(896\) 0 0
\(897\) −588.000 −0.0218871
\(898\) 0 0
\(899\) −17442.0 −0.647078
\(900\) 0 0
\(901\) 860.000 0.0317988
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1405.00 −0.0516064
\(906\) 0 0
\(907\) 50728.0 1.85711 0.928553 0.371199i \(-0.121053\pi\)
0.928553 + 0.371199i \(0.121053\pi\)
\(908\) 0 0
\(909\) −1496.00 −0.0545866
\(910\) 0 0
\(911\) 20088.0 0.730565 0.365283 0.930897i \(-0.380972\pi\)
0.365283 + 0.930897i \(0.380972\pi\)
\(912\) 0 0
\(913\) −8228.00 −0.298255
\(914\) 0 0
\(915\) 14.0000 0.000505820 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 11504.0 0.412929 0.206465 0.978454i \(-0.433804\pi\)
0.206465 + 0.978454i \(0.433804\pi\)
\(920\) 0 0
\(921\) 71540.0 2.55953
\(922\) 0 0
\(923\) 6948.00 0.247775
\(924\) 0 0
\(925\) 44268.0 1.57354
\(926\) 0 0
\(927\) 10296.0 0.364795
\(928\) 0 0
\(929\) 7134.00 0.251947 0.125974 0.992034i \(-0.459795\pi\)
0.125974 + 0.992034i \(0.459795\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −34048.0 −1.19473
\(934\) 0 0
\(935\) −22.0000 −0.000769494 0
\(936\) 0 0
\(937\) −10036.0 −0.349906 −0.174953 0.984577i \(-0.555977\pi\)
−0.174953 + 0.984577i \(0.555977\pi\)
\(938\) 0 0
\(939\) 25921.0 0.900852
\(940\) 0 0
\(941\) 54438.0 1.88590 0.942948 0.332940i \(-0.108041\pi\)
0.942948 + 0.332940i \(0.108041\pi\)
\(942\) 0 0
\(943\) 798.000 0.0275572
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15975.0 −0.548171 −0.274085 0.961705i \(-0.588375\pi\)
−0.274085 + 0.961705i \(0.588375\pi\)
\(948\) 0 0
\(949\) −5256.00 −0.179786
\(950\) 0 0
\(951\) 567.000 0.0193336
\(952\) 0 0
\(953\) 33996.0 1.15555 0.577775 0.816196i \(-0.303921\pi\)
0.577775 + 0.816196i \(0.303921\pi\)
\(954\) 0 0
\(955\) −1671.00 −0.0566202
\(956\) 0 0
\(957\) −7854.00 −0.265291
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −550.000 −0.0184620
\(962\) 0 0
\(963\) 34804.0 1.16463
\(964\) 0 0
\(965\) −2066.00 −0.0689191
\(966\) 0 0
\(967\) 40966.0 1.36233 0.681167 0.732128i \(-0.261473\pi\)
0.681167 + 0.732128i \(0.261473\pi\)
\(968\) 0 0
\(969\) 1148.00 0.0380589
\(970\) 0 0
\(971\) −23793.0 −0.786358 −0.393179 0.919462i \(-0.628625\pi\)
−0.393179 + 0.919462i \(0.628625\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 10416.0 0.342132
\(976\) 0 0
\(977\) −439.000 −0.0143755 −0.00718775 0.999974i \(-0.502288\pi\)
−0.00718775 + 0.999974i \(0.502288\pi\)
\(978\) 0 0
\(979\) −5027.00 −0.164110
\(980\) 0 0
\(981\) 11352.0 0.369461
\(982\) 0 0
\(983\) 7863.00 0.255128 0.127564 0.991830i \(-0.459284\pi\)
0.127564 + 0.991830i \(0.459284\pi\)
\(984\) 0 0
\(985\) 3442.00 0.111341
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2408.00 −0.0774216
\(990\) 0 0
\(991\) −46360.0 −1.48605 −0.743024 0.669265i \(-0.766609\pi\)
−0.743024 + 0.669265i \(0.766609\pi\)
\(992\) 0 0
\(993\) 18725.0 0.598409
\(994\) 0 0
\(995\) −3008.00 −0.0958392
\(996\) 0 0
\(997\) −5860.00 −0.186147 −0.0930733 0.995659i \(-0.529669\pi\)
−0.0930733 + 0.995659i \(0.529669\pi\)
\(998\) 0 0
\(999\) 12495.0 0.395720
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 2156.4.a.c.1.1 1
7.6 odd 2 308.4.a.a.1.1 1
28.27 even 2 1232.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
308.4.a.a.1.1 1 7.6 odd 2
1232.4.a.h.1.1 1 28.27 even 2
2156.4.a.c.1.1 1 1.1 even 1 trivial