Properties

Label 3822.2.a.g.1.1
Level $3822$
Weight $2$
Character 3822.1
Self dual yes
Analytic conductor $30.519$
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] = [3822,2,Mod(1,3822)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3822, 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("3822.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.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: \(30.5188236525\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3822.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +5.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} -5.00000 q^{19} +1.00000 q^{20} -5.00000 q^{22} +9.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.00000 q^{29} +1.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} -5.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} +3.00000 q^{37} +5.00000 q^{38} +1.00000 q^{39} -1.00000 q^{40} +12.0000 q^{41} +7.00000 q^{43} +5.00000 q^{44} +1.00000 q^{45} -9.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +4.00000 q^{50} +3.00000 q^{51} -1.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} +5.00000 q^{55} +5.00000 q^{57} +1.00000 q^{58} -14.0000 q^{59} -1.00000 q^{60} +11.0000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} +5.00000 q^{66} +4.00000 q^{67} -3.00000 q^{68} -9.00000 q^{69} -10.0000 q^{71} -1.00000 q^{72} +11.0000 q^{73} -3.00000 q^{74} +4.00000 q^{75} -5.00000 q^{76} -1.00000 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} -6.00000 q^{83} -3.00000 q^{85} -7.00000 q^{86} +1.00000 q^{87} -5.00000 q^{88} -16.0000 q^{89} -1.00000 q^{90} +9.00000 q^{92} -2.00000 q^{93} -4.00000 q^{94} -5.00000 q^{95} +1.00000 q^{96} +14.0000 q^{97} +5.00000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −5.00000 −1.06600
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.00000 −0.870388
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 5.00000 0.811107
\(39\) 1.00000 0.160128
\(40\) −1.00000 −0.158114
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 5.00000 0.753778
\(45\) 1.00000 0.149071
\(46\) −9.00000 −1.32698
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 4.00000 0.565685
\(51\) 3.00000 0.420084
\(52\) −1.00000 −0.138675
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 5.00000 0.662266
\(58\) 1.00000 0.131306
\(59\) −14.0000 −1.82264 −0.911322 0.411693i \(-0.864937\pi\)
−0.911322 + 0.411693i \(0.864937\pi\)
\(60\) −1.00000 −0.129099
\(61\) 11.0000 1.40841 0.704203 0.709999i \(-0.251305\pi\)
0.704203 + 0.709999i \(0.251305\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 5.00000 0.615457
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −3.00000 −0.363803
\(69\) −9.00000 −1.08347
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) −1.00000 −0.117851
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) −3.00000 −0.348743
\(75\) 4.00000 0.461880
\(76\) −5.00000 −0.573539
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) −7.00000 −0.754829
\(87\) 1.00000 0.107211
\(88\) −5.00000 −0.533002
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 9.00000 0.938315
\(93\) −2.00000 −0.207390
\(94\) −4.00000 −0.412568
\(95\) −5.00000 −0.512989
\(96\) 1.00000 0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) −4.00000 −0.400000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) −3.00000 −0.297044
\(103\) 7.00000 0.689730 0.344865 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 16.0000 1.54678 0.773389 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −11.0000 −1.05361 −0.526804 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) −5.00000 −0.476731
\(111\) −3.00000 −0.284747
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) −5.00000 −0.468293
\(115\) 9.00000 0.839254
\(116\) −1.00000 −0.0928477
\(117\) −1.00000 −0.0924500
\(118\) 14.0000 1.28880
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 14.0000 1.27273
\(122\) −11.0000 −0.995893
\(123\) −12.0000 −1.08200
\(124\) 2.00000 0.179605
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.00000 −0.616316
\(130\) 1.00000 0.0877058
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) −5.00000 −0.435194
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) −1.00000 −0.0860663
\(136\) 3.00000 0.257248
\(137\) −1.00000 −0.0854358 −0.0427179 0.999087i \(-0.513602\pi\)
−0.0427179 + 0.999087i \(0.513602\pi\)
\(138\) 9.00000 0.766131
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 10.0000 0.839181
\(143\) −5.00000 −0.418121
\(144\) 1.00000 0.0833333
\(145\) −1.00000 −0.0830455
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) 3.00000 0.246598
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) −4.00000 −0.326599
\(151\) 7.00000 0.569652 0.284826 0.958579i \(-0.408064\pi\)
0.284826 + 0.958579i \(0.408064\pi\)
\(152\) 5.00000 0.405554
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 1.00000 0.0800641
\(157\) 7.00000 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) −4.00000 −0.318223
\(159\) 10.0000 0.793052
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 6.00000 0.469956 0.234978 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(164\) 12.0000 0.937043
\(165\) −5.00000 −0.389249
\(166\) 6.00000 0.465690
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 3.00000 0.230089
\(171\) −5.00000 −0.382360
\(172\) 7.00000 0.533745
\(173\) −4.00000 −0.304114 −0.152057 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) 14.0000 1.05230
\(178\) 16.0000 1.19925
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 1.00000 0.0745356
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −11.0000 −0.813143
\(184\) −9.00000 −0.663489
\(185\) 3.00000 0.220564
\(186\) 2.00000 0.146647
\(187\) −15.0000 −1.09691
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 5.00000 0.362738
\(191\) 21.0000 1.51951 0.759753 0.650211i \(-0.225320\pi\)
0.759753 + 0.650211i \(0.225320\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −14.0000 −1.00514
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −5.00000 −0.355335
\(199\) −19.0000 −1.34687 −0.673437 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 4.00000 0.282843
\(201\) −4.00000 −0.282138
\(202\) 14.0000 0.985037
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 12.0000 0.838116
\(206\) −7.00000 −0.487713
\(207\) 9.00000 0.625543
\(208\) −1.00000 −0.0693375
\(209\) −25.0000 −1.72929
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −10.0000 −0.686803
\(213\) 10.0000 0.685189
\(214\) −16.0000 −1.09374
\(215\) 7.00000 0.477396
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 11.0000 0.745014
\(219\) −11.0000 −0.743311
\(220\) 5.00000 0.337100
\(221\) 3.00000 0.201802
\(222\) 3.00000 0.201347
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) −16.0000 −1.06430
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 5.00000 0.331133
\(229\) 28.0000 1.85029 0.925146 0.379611i \(-0.123942\pi\)
0.925146 + 0.379611i \(0.123942\pi\)
\(230\) −9.00000 −0.593442
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 1.00000 0.0653720
\(235\) 4.00000 0.260931
\(236\) −14.0000 −0.911322
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) −14.0000 −0.899954
\(243\) −1.00000 −0.0641500
\(244\) 11.0000 0.704203
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 5.00000 0.318142
\(248\) −2.00000 −0.127000
\(249\) 6.00000 0.380235
\(250\) 9.00000 0.569210
\(251\) 1.00000 0.0631194 0.0315597 0.999502i \(-0.489953\pi\)
0.0315597 + 0.999502i \(0.489953\pi\)
\(252\) 0 0
\(253\) 45.0000 2.82913
\(254\) 4.00000 0.250982
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 7.00000 0.435801
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) −1.00000 −0.0618984
\(262\) 3.00000 0.185341
\(263\) 20.0000 1.23325 0.616626 0.787256i \(-0.288499\pi\)
0.616626 + 0.787256i \(0.288499\pi\)
\(264\) 5.00000 0.307729
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) 16.0000 0.979184
\(268\) 4.00000 0.244339
\(269\) 16.0000 0.975537 0.487769 0.872973i \(-0.337811\pi\)
0.487769 + 0.872973i \(0.337811\pi\)
\(270\) 1.00000 0.0608581
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) 1.00000 0.0604122
\(275\) −20.0000 −1.20605
\(276\) −9.00000 −0.541736
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 12.0000 0.719712
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 4.00000 0.238197
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) −10.0000 −0.593391
\(285\) 5.00000 0.296174
\(286\) 5.00000 0.295656
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −8.00000 −0.470588
\(290\) 1.00000 0.0587220
\(291\) −14.0000 −0.820695
\(292\) 11.0000 0.643726
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) −14.0000 −0.815112
\(296\) −3.00000 −0.174371
\(297\) −5.00000 −0.290129
\(298\) −20.0000 −1.15857
\(299\) −9.00000 −0.520483
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) −7.00000 −0.402805
\(303\) 14.0000 0.804279
\(304\) −5.00000 −0.286770
\(305\) 11.0000 0.629858
\(306\) 3.00000 0.171499
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) −2.00000 −0.113592
\(311\) 2.00000 0.113410 0.0567048 0.998391i \(-0.481941\pi\)
0.0567048 + 0.998391i \(0.481941\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −10.0000 −0.560772
\(319\) −5.00000 −0.279946
\(320\) 1.00000 0.0559017
\(321\) −16.0000 −0.893033
\(322\) 0 0
\(323\) 15.0000 0.834622
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) −6.00000 −0.332309
\(327\) 11.0000 0.608301
\(328\) −12.0000 −0.662589
\(329\) 0 0
\(330\) 5.00000 0.275241
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −6.00000 −0.329293
\(333\) 3.00000 0.164399
\(334\) −5.00000 −0.273588
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −16.0000 −0.869001
\(340\) −3.00000 −0.162698
\(341\) 10.0000 0.541530
\(342\) 5.00000 0.270369
\(343\) 0 0
\(344\) −7.00000 −0.377415
\(345\) −9.00000 −0.484544
\(346\) 4.00000 0.215041
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 1.00000 0.0536056
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) −5.00000 −0.266501
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) −14.0000 −0.744092
\(355\) −10.0000 −0.530745
\(356\) −16.0000 −0.847998
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 6.00000 0.315789
\(362\) −2.00000 −0.105118
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 11.0000 0.575766
\(366\) 11.0000 0.574979
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 9.00000 0.469157
\(369\) 12.0000 0.624695
\(370\) −3.00000 −0.155963
\(371\) 0 0
\(372\) −2.00000 −0.103695
\(373\) −2.00000 −0.103556 −0.0517780 0.998659i \(-0.516489\pi\)
−0.0517780 + 0.998659i \(0.516489\pi\)
\(374\) 15.0000 0.775632
\(375\) 9.00000 0.464758
\(376\) −4.00000 −0.206284
\(377\) 1.00000 0.0515026
\(378\) 0 0
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) −5.00000 −0.256495
\(381\) 4.00000 0.204926
\(382\) −21.0000 −1.07445
\(383\) −15.0000 −0.766464 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 7.00000 0.355830
\(388\) 14.0000 0.710742
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −1.00000 −0.0506370
\(391\) −27.0000 −1.36545
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) −18.0000 −0.906827
\(395\) 4.00000 0.201262
\(396\) 5.00000 0.251259
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 19.0000 0.952384
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 4.00000 0.199502
\(403\) −2.00000 −0.0996271
\(404\) −14.0000 −0.696526
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 15.0000 0.743522
\(408\) −3.00000 −0.148522
\(409\) 33.0000 1.63174 0.815872 0.578232i \(-0.196257\pi\)
0.815872 + 0.578232i \(0.196257\pi\)
\(410\) −12.0000 −0.592638
\(411\) 1.00000 0.0493264
\(412\) 7.00000 0.344865
\(413\) 0 0
\(414\) −9.00000 −0.442326
\(415\) −6.00000 −0.294528
\(416\) 1.00000 0.0490290
\(417\) 12.0000 0.587643
\(418\) 25.0000 1.22279
\(419\) 31.0000 1.51445 0.757225 0.653155i \(-0.226555\pi\)
0.757225 + 0.653155i \(0.226555\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) −5.00000 −0.243396
\(423\) 4.00000 0.194487
\(424\) 10.0000 0.485643
\(425\) 12.0000 0.582086
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) 16.0000 0.773389
\(429\) 5.00000 0.241402
\(430\) −7.00000 −0.337570
\(431\) 10.0000 0.481683 0.240842 0.970564i \(-0.422577\pi\)
0.240842 + 0.970564i \(0.422577\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 1.00000 0.0479463
\(436\) −11.0000 −0.526804
\(437\) −45.0000 −2.15264
\(438\) 11.0000 0.525600
\(439\) −21.0000 −1.00228 −0.501138 0.865368i \(-0.667085\pi\)
−0.501138 + 0.865368i \(0.667085\pi\)
\(440\) −5.00000 −0.238366
\(441\) 0 0
\(442\) −3.00000 −0.142695
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) −3.00000 −0.142374
\(445\) −16.0000 −0.758473
\(446\) −2.00000 −0.0947027
\(447\) −20.0000 −0.945968
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 4.00000 0.188562
\(451\) 60.0000 2.82529
\(452\) 16.0000 0.752577
\(453\) −7.00000 −0.328889
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) −5.00000 −0.234146
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −28.0000 −1.30835
\(459\) 3.00000 0.140028
\(460\) 9.00000 0.419627
\(461\) 3.00000 0.139724 0.0698620 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) 0 0
\(463\) 11.0000 0.511213 0.255607 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −2.00000 −0.0927478
\(466\) 16.0000 0.741186
\(467\) 5.00000 0.231372 0.115686 0.993286i \(-0.463093\pi\)
0.115686 + 0.993286i \(0.463093\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 0 0
\(470\) −4.00000 −0.184506
\(471\) −7.00000 −0.322543
\(472\) 14.0000 0.644402
\(473\) 35.0000 1.60930
\(474\) 4.00000 0.183726
\(475\) 20.0000 0.917663
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 18.0000 0.823301
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) 1.00000 0.0456435
\(481\) −3.00000 −0.136788
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 14.0000 0.635707
\(486\) 1.00000 0.0453609
\(487\) 40.0000 1.81257 0.906287 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) −11.0000 −0.497947
\(489\) −6.00000 −0.271329
\(490\) 0 0
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) −12.0000 −0.541002
\(493\) 3.00000 0.135113
\(494\) −5.00000 −0.224961
\(495\) 5.00000 0.224733
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) −9.00000 −0.402492
\(501\) −5.00000 −0.223384
\(502\) −1.00000 −0.0446322
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) −14.0000 −0.622992
\(506\) −45.0000 −2.00049
\(507\) −1.00000 −0.0444116
\(508\) −4.00000 −0.177471
\(509\) 11.0000 0.487566 0.243783 0.969830i \(-0.421611\pi\)
0.243783 + 0.969830i \(0.421611\pi\)
\(510\) −3.00000 −0.132842
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 0.220755
\(514\) −14.0000 −0.617514
\(515\) 7.00000 0.308457
\(516\) −7.00000 −0.308158
\(517\) 20.0000 0.879599
\(518\) 0 0
\(519\) 4.00000 0.175581
\(520\) 1.00000 0.0438529
\(521\) −25.0000 −1.09527 −0.547635 0.836717i \(-0.684472\pi\)
−0.547635 + 0.836717i \(0.684472\pi\)
\(522\) 1.00000 0.0437688
\(523\) −38.0000 −1.66162 −0.830812 0.556553i \(-0.812124\pi\)
−0.830812 + 0.556553i \(0.812124\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) −6.00000 −0.261364
\(528\) −5.00000 −0.217597
\(529\) 58.0000 2.52174
\(530\) 10.0000 0.434372
\(531\) −14.0000 −0.607548
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) −16.0000 −0.692388
\(535\) 16.0000 0.691740
\(536\) −4.00000 −0.172774
\(537\) 6.00000 0.258919
\(538\) −16.0000 −0.689809
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 25.0000 1.07483 0.537417 0.843317i \(-0.319400\pi\)
0.537417 + 0.843317i \(0.319400\pi\)
\(542\) 8.00000 0.343629
\(543\) −2.00000 −0.0858282
\(544\) 3.00000 0.128624
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −1.00000 −0.0427179
\(549\) 11.0000 0.469469
\(550\) 20.0000 0.852803
\(551\) 5.00000 0.213007
\(552\) 9.00000 0.383065
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) −3.00000 −0.127343
\(556\) −12.0000 −0.508913
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) −2.00000 −0.0846668
\(559\) −7.00000 −0.296068
\(560\) 0 0
\(561\) 15.0000 0.633300
\(562\) 6.00000 0.253095
\(563\) −31.0000 −1.30649 −0.653247 0.757145i \(-0.726594\pi\)
−0.653247 + 0.757145i \(0.726594\pi\)
\(564\) −4.00000 −0.168430
\(565\) 16.0000 0.673125
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 10.0000 0.419591
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −5.00000 −0.209427
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) −5.00000 −0.209061
\(573\) −21.0000 −0.877288
\(574\) 0 0
\(575\) −36.0000 −1.50130
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 8.00000 0.332756
\(579\) 10.0000 0.415586
\(580\) −1.00000 −0.0415227
\(581\) 0 0
\(582\) 14.0000 0.580319
\(583\) −50.0000 −2.07079
\(584\) −11.0000 −0.455183
\(585\) −1.00000 −0.0413449
\(586\) −18.0000 −0.743573
\(587\) −38.0000 −1.56843 −0.784214 0.620491i \(-0.786934\pi\)
−0.784214 + 0.620491i \(0.786934\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 14.0000 0.576371
\(591\) −18.0000 −0.740421
\(592\) 3.00000 0.123299
\(593\) 24.0000 0.985562 0.492781 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 20.0000 0.819232
\(597\) 19.0000 0.777618
\(598\) 9.00000 0.368037
\(599\) −9.00000 −0.367730 −0.183865 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) −4.00000 −0.163299
\(601\) −20.0000 −0.815817 −0.407909 0.913023i \(-0.633742\pi\)
−0.407909 + 0.913023i \(0.633742\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 7.00000 0.284826
\(605\) 14.0000 0.569181
\(606\) −14.0000 −0.568711
\(607\) −21.0000 −0.852364 −0.426182 0.904638i \(-0.640142\pi\)
−0.426182 + 0.904638i \(0.640142\pi\)
\(608\) 5.00000 0.202777
\(609\) 0 0
\(610\) −11.0000 −0.445377
\(611\) −4.00000 −0.161823
\(612\) −3.00000 −0.121268
\(613\) 5.00000 0.201948 0.100974 0.994889i \(-0.467804\pi\)
0.100974 + 0.994889i \(0.467804\pi\)
\(614\) −20.0000 −0.807134
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −23.0000 −0.925945 −0.462973 0.886373i \(-0.653217\pi\)
−0.462973 + 0.886373i \(0.653217\pi\)
\(618\) 7.00000 0.281581
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 2.00000 0.0803219
\(621\) −9.00000 −0.361158
\(622\) −2.00000 −0.0801927
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 11.0000 0.440000
\(626\) 6.00000 0.239808
\(627\) 25.0000 0.998404
\(628\) 7.00000 0.279330
\(629\) −9.00000 −0.358854
\(630\) 0 0
\(631\) −33.0000 −1.31371 −0.656855 0.754017i \(-0.728113\pi\)
−0.656855 + 0.754017i \(0.728113\pi\)
\(632\) −4.00000 −0.159111
\(633\) −5.00000 −0.198732
\(634\) −6.00000 −0.238290
\(635\) −4.00000 −0.158735
\(636\) 10.0000 0.396526
\(637\) 0 0
\(638\) 5.00000 0.197952
\(639\) −10.0000 −0.395594
\(640\) −1.00000 −0.0395285
\(641\) −32.0000 −1.26392 −0.631962 0.774999i \(-0.717750\pi\)
−0.631962 + 0.774999i \(0.717750\pi\)
\(642\) 16.0000 0.631470
\(643\) 9.00000 0.354925 0.177463 0.984128i \(-0.443211\pi\)
0.177463 + 0.984128i \(0.443211\pi\)
\(644\) 0 0
\(645\) −7.00000 −0.275625
\(646\) −15.0000 −0.590167
\(647\) −36.0000 −1.41531 −0.707653 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −70.0000 −2.74774
\(650\) −4.00000 −0.156893
\(651\) 0 0
\(652\) 6.00000 0.234978
\(653\) 5.00000 0.195665 0.0978326 0.995203i \(-0.468809\pi\)
0.0978326 + 0.995203i \(0.468809\pi\)
\(654\) −11.0000 −0.430134
\(655\) −3.00000 −0.117220
\(656\) 12.0000 0.468521
\(657\) 11.0000 0.429151
\(658\) 0 0
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) −5.00000 −0.194625
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −8.00000 −0.310929
\(663\) −3.00000 −0.116510
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) −9.00000 −0.348481
\(668\) 5.00000 0.193456
\(669\) −2.00000 −0.0773245
\(670\) −4.00000 −0.154533
\(671\) 55.0000 2.12325
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) −23.0000 −0.885927
\(675\) 4.00000 0.153960
\(676\) 1.00000 0.0384615
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 16.0000 0.614476
\(679\) 0 0
\(680\) 3.00000 0.115045
\(681\) 4.00000 0.153280
\(682\) −10.0000 −0.382920
\(683\) 7.00000 0.267848 0.133924 0.990992i \(-0.457242\pi\)
0.133924 + 0.990992i \(0.457242\pi\)
\(684\) −5.00000 −0.191180
\(685\) −1.00000 −0.0382080
\(686\) 0 0
\(687\) −28.0000 −1.06827
\(688\) 7.00000 0.266872
\(689\) 10.0000 0.380970
\(690\) 9.00000 0.342624
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) −4.00000 −0.152057
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) −12.0000 −0.455186
\(696\) −1.00000 −0.0379049
\(697\) −36.0000 −1.36360
\(698\) −24.0000 −0.908413
\(699\) 16.0000 0.605176
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −15.0000 −0.565736
\(704\) 5.00000 0.188445
\(705\) −4.00000 −0.150649
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) 14.0000 0.526152
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 10.0000 0.375293
\(711\) 4.00000 0.150012
\(712\) 16.0000 0.599625
\(713\) 18.0000 0.674105
\(714\) 0 0
\(715\) −5.00000 −0.186989
\(716\) −6.00000 −0.224231
\(717\) 18.0000 0.672222
\(718\) 20.0000 0.746393
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −6.00000 −0.223297
\(723\) −26.0000 −0.966950
\(724\) 2.00000 0.0743294
\(725\) 4.00000 0.148556
\(726\) 14.0000 0.519589
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −11.0000 −0.407128
\(731\) −21.0000 −0.776713
\(732\) −11.0000 −0.406572
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −9.00000 −0.331744
\(737\) 20.0000 0.736709
\(738\) −12.0000 −0.441726
\(739\) −26.0000 −0.956425 −0.478213 0.878244i \(-0.658715\pi\)
−0.478213 + 0.878244i \(0.658715\pi\)
\(740\) 3.00000 0.110282
\(741\) −5.00000 −0.183680
\(742\) 0 0
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 2.00000 0.0733236
\(745\) 20.0000 0.732743
\(746\) 2.00000 0.0732252
\(747\) −6.00000 −0.219529
\(748\) −15.0000 −0.548454
\(749\) 0 0
\(750\) −9.00000 −0.328634
\(751\) −54.0000 −1.97049 −0.985244 0.171156i \(-0.945250\pi\)
−0.985244 + 0.171156i \(0.945250\pi\)
\(752\) 4.00000 0.145865
\(753\) −1.00000 −0.0364420
\(754\) −1.00000 −0.0364179
\(755\) 7.00000 0.254756
\(756\) 0 0
\(757\) −32.0000 −1.16306 −0.581530 0.813525i \(-0.697546\pi\)
−0.581530 + 0.813525i \(0.697546\pi\)
\(758\) 30.0000 1.08965
\(759\) −45.0000 −1.63340
\(760\) 5.00000 0.181369
\(761\) 40.0000 1.45000 0.724999 0.688749i \(-0.241840\pi\)
0.724999 + 0.688749i \(0.241840\pi\)
\(762\) −4.00000 −0.144905
\(763\) 0 0
\(764\) 21.0000 0.759753
\(765\) −3.00000 −0.108465
\(766\) 15.0000 0.541972
\(767\) 14.0000 0.505511
\(768\) −1.00000 −0.0360844
\(769\) 25.0000 0.901523 0.450762 0.892644i \(-0.351152\pi\)
0.450762 + 0.892644i \(0.351152\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) −10.0000 −0.359908
\(773\) 51.0000 1.83434 0.917171 0.398493i \(-0.130467\pi\)
0.917171 + 0.398493i \(0.130467\pi\)
\(774\) −7.00000 −0.251610
\(775\) −8.00000 −0.287368
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −60.0000 −2.14972
\(780\) 1.00000 0.0358057
\(781\) −50.0000 −1.78914
\(782\) 27.0000 0.965518
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) 7.00000 0.249841
\(786\) −3.00000 −0.107006
\(787\) 23.0000 0.819861 0.409931 0.912117i \(-0.365553\pi\)
0.409931 + 0.912117i \(0.365553\pi\)
\(788\) 18.0000 0.641223
\(789\) −20.0000 −0.712019
\(790\) −4.00000 −0.142314
\(791\) 0 0
\(792\) −5.00000 −0.177667
\(793\) −11.0000 −0.390621
\(794\) 14.0000 0.496841
\(795\) 10.0000 0.354663
\(796\) −19.0000 −0.673437
\(797\) −54.0000 −1.91278 −0.956389 0.292096i \(-0.905647\pi\)
−0.956389 + 0.292096i \(0.905647\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 4.00000 0.141421
\(801\) −16.0000 −0.565332
\(802\) −30.0000 −1.05934
\(803\) 55.0000 1.94091
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 2.00000 0.0704470
\(807\) −16.0000 −0.563227
\(808\) 14.0000 0.492518
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −17.0000 −0.596951 −0.298475 0.954417i \(-0.596478\pi\)
−0.298475 + 0.954417i \(0.596478\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) −15.0000 −0.525750
\(815\) 6.00000 0.210171
\(816\) 3.00000 0.105021
\(817\) −35.0000 −1.22449
\(818\) −33.0000 −1.15382
\(819\) 0 0
\(820\) 12.0000 0.419058
\(821\) −40.0000 −1.39601 −0.698005 0.716093i \(-0.745929\pi\)
−0.698005 + 0.716093i \(0.745929\pi\)
\(822\) −1.00000 −0.0348790
\(823\) 46.0000 1.60346 0.801730 0.597687i \(-0.203913\pi\)
0.801730 + 0.597687i \(0.203913\pi\)
\(824\) −7.00000 −0.243857
\(825\) 20.0000 0.696311
\(826\) 0 0
\(827\) −39.0000 −1.35616 −0.678081 0.734987i \(-0.737188\pi\)
−0.678081 + 0.734987i \(0.737188\pi\)
\(828\) 9.00000 0.312772
\(829\) −13.0000 −0.451509 −0.225754 0.974184i \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(830\) 6.00000 0.208263
\(831\) −28.0000 −0.971309
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) −12.0000 −0.415526
\(835\) 5.00000 0.173032
\(836\) −25.0000 −0.864643
\(837\) −2.00000 −0.0691301
\(838\) −31.0000 −1.07088
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 6.00000 0.206774
\(843\) 6.00000 0.206651
\(844\) 5.00000 0.172107
\(845\) 1.00000 0.0344010
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) 16.0000 0.549119
\(850\) −12.0000 −0.411597
\(851\) 27.0000 0.925548
\(852\) 10.0000 0.342594
\(853\) 40.0000 1.36957 0.684787 0.728743i \(-0.259895\pi\)
0.684787 + 0.728743i \(0.259895\pi\)
\(854\) 0 0
\(855\) −5.00000 −0.170996
\(856\) −16.0000 −0.546869
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) −5.00000 −0.170697
\(859\) 24.0000 0.818869 0.409435 0.912339i \(-0.365726\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(860\) 7.00000 0.238698
\(861\) 0 0
\(862\) −10.0000 −0.340601
\(863\) −42.0000 −1.42970 −0.714848 0.699280i \(-0.753504\pi\)
−0.714848 + 0.699280i \(0.753504\pi\)
\(864\) 1.00000 0.0340207
\(865\) −4.00000 −0.136004
\(866\) −16.0000 −0.543702
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 20.0000 0.678454
\(870\) −1.00000 −0.0339032
\(871\) −4.00000 −0.135535
\(872\) 11.0000 0.372507
\(873\) 14.0000 0.473828
\(874\) 45.0000 1.52215
\(875\) 0 0
\(876\) −11.0000 −0.371656
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 21.0000 0.708716
\(879\) −18.0000 −0.607125
\(880\) 5.00000 0.168550
\(881\) 37.0000 1.24656 0.623281 0.781998i \(-0.285799\pi\)
0.623281 + 0.781998i \(0.285799\pi\)
\(882\) 0 0
\(883\) 19.0000 0.639401 0.319700 0.947519i \(-0.396418\pi\)
0.319700 + 0.947519i \(0.396418\pi\)
\(884\) 3.00000 0.100901
\(885\) 14.0000 0.470605
\(886\) −6.00000 −0.201574
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 3.00000 0.100673
\(889\) 0 0
\(890\) 16.0000 0.536321
\(891\) 5.00000 0.167506
\(892\) 2.00000 0.0669650
\(893\) −20.0000 −0.669274
\(894\) 20.0000 0.668900
\(895\) −6.00000 −0.200558
\(896\) 0 0
\(897\) 9.00000 0.300501
\(898\) 9.00000 0.300334
\(899\) −2.00000 −0.0667037
\(900\) −4.00000 −0.133333
\(901\) 30.0000 0.999445
\(902\) −60.0000 −1.99778
\(903\) 0 0
\(904\) −16.0000 −0.532152
\(905\) 2.00000 0.0664822
\(906\) 7.00000 0.232559
\(907\) 4.00000 0.132818 0.0664089 0.997792i \(-0.478846\pi\)
0.0664089 + 0.997792i \(0.478846\pi\)
\(908\) −4.00000 −0.132745
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) −41.0000 −1.35839 −0.679195 0.733958i \(-0.737671\pi\)
−0.679195 + 0.733958i \(0.737671\pi\)
\(912\) 5.00000 0.165567
\(913\) −30.0000 −0.992855
\(914\) −26.0000 −0.860004
\(915\) −11.0000 −0.363649
\(916\) 28.0000 0.925146
\(917\) 0 0
\(918\) −3.00000 −0.0990148
\(919\) 18.0000 0.593765 0.296883 0.954914i \(-0.404053\pi\)
0.296883 + 0.954914i \(0.404053\pi\)
\(920\) −9.00000 −0.296721
\(921\) −20.0000 −0.659022
\(922\) −3.00000 −0.0987997
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) −12.0000 −0.394558
\(926\) −11.0000 −0.361482
\(927\) 7.00000 0.229910
\(928\) 1.00000 0.0328266
\(929\) 24.0000 0.787414 0.393707 0.919236i \(-0.371192\pi\)
0.393707 + 0.919236i \(0.371192\pi\)
\(930\) 2.00000 0.0655826
\(931\) 0 0
\(932\) −16.0000 −0.524097
\(933\) −2.00000 −0.0654771
\(934\) −5.00000 −0.163605
\(935\) −15.0000 −0.490552
\(936\) 1.00000 0.0326860
\(937\) 12.0000 0.392023 0.196011 0.980602i \(-0.437201\pi\)
0.196011 + 0.980602i \(0.437201\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) 4.00000 0.130466
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 7.00000 0.228072
\(943\) 108.000 3.51696
\(944\) −14.0000 −0.455661
\(945\) 0 0
\(946\) −35.0000 −1.13795
\(947\) 29.0000 0.942373 0.471187 0.882034i \(-0.343826\pi\)
0.471187 + 0.882034i \(0.343826\pi\)
\(948\) −4.00000 −0.129914
\(949\) −11.0000 −0.357075
\(950\) −20.0000 −0.648886
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) −24.0000 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(954\) 10.0000 0.323762
\(955\) 21.0000 0.679544
\(956\) −18.0000 −0.582162
\(957\) 5.00000 0.161627
\(958\) −3.00000 −0.0969256
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) 3.00000 0.0967239
\(963\) 16.0000 0.515593
\(964\) 26.0000 0.837404
\(965\) −10.0000 −0.321911
\(966\) 0 0
\(967\) 1.00000 0.0321578 0.0160789 0.999871i \(-0.494882\pi\)
0.0160789 + 0.999871i \(0.494882\pi\)
\(968\) −14.0000 −0.449977
\(969\) −15.0000 −0.481869
\(970\) −14.0000 −0.449513
\(971\) −44.0000 −1.41203 −0.706014 0.708198i \(-0.749508\pi\)
−0.706014 + 0.708198i \(0.749508\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −40.0000 −1.28168
\(975\) −4.00000 −0.128103
\(976\) 11.0000 0.352101
\(977\) 29.0000 0.927792 0.463896 0.885890i \(-0.346451\pi\)
0.463896 + 0.885890i \(0.346451\pi\)
\(978\) 6.00000 0.191859
\(979\) −80.0000 −2.55681
\(980\) 0 0
\(981\) −11.0000 −0.351203
\(982\) −18.0000 −0.574403
\(983\) 7.00000 0.223265 0.111633 0.993750i \(-0.464392\pi\)
0.111633 + 0.993750i \(0.464392\pi\)
\(984\) 12.0000 0.382546
\(985\) 18.0000 0.573528
\(986\) −3.00000 −0.0955395
\(987\) 0 0
\(988\) 5.00000 0.159071
\(989\) 63.0000 2.00328
\(990\) −5.00000 −0.158910
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −8.00000 −0.253872
\(994\) 0 0
\(995\) −19.0000 −0.602340
\(996\) 6.00000 0.190117
\(997\) −26.0000 −0.823428 −0.411714 0.911313i \(-0.635070\pi\)
−0.411714 + 0.911313i \(0.635070\pi\)
\(998\) −18.0000 −0.569780
\(999\) −3.00000 −0.0949158
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 3822.2.a.g.1.1 1
7.6 odd 2 3822.2.a.m.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3822.2.a.g.1.1 1 1.1 even 1 trivial
3822.2.a.m.1.1 yes 1 7.6 odd 2