Properties

Label 6034.2.a.c.1.1
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{10} -4.00000 q^{11} -2.00000 q^{12} -6.00000 q^{13} +1.00000 q^{14} +8.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} -4.00000 q^{20} +2.00000 q^{21} +4.00000 q^{22} +2.00000 q^{24} +11.0000 q^{25} +6.00000 q^{26} +4.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} -8.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} +8.00000 q^{33} +2.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} +2.00000 q^{38} +12.0000 q^{39} +4.00000 q^{40} -10.0000 q^{41} -2.00000 q^{42} -6.00000 q^{43} -4.00000 q^{44} -4.00000 q^{45} -2.00000 q^{48} +1.00000 q^{49} -11.0000 q^{50} +4.00000 q^{51} -6.00000 q^{52} +6.00000 q^{53} -4.00000 q^{54} +16.0000 q^{55} +1.00000 q^{56} +4.00000 q^{57} -6.00000 q^{58} +6.00000 q^{59} +8.00000 q^{60} +8.00000 q^{61} +8.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +24.0000 q^{65} -8.00000 q^{66} +10.0000 q^{67} -2.00000 q^{68} -4.00000 q^{70} -1.00000 q^{72} -2.00000 q^{73} -8.00000 q^{74} -22.0000 q^{75} -2.00000 q^{76} +4.00000 q^{77} -12.0000 q^{78} -4.00000 q^{80} -11.0000 q^{81} +10.0000 q^{82} +4.00000 q^{83} +2.00000 q^{84} +8.00000 q^{85} +6.00000 q^{86} -12.0000 q^{87} +4.00000 q^{88} -18.0000 q^{89} +4.00000 q^{90} +6.00000 q^{91} +16.0000 q^{93} +8.00000 q^{95} +2.00000 q^{96} +6.00000 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 2.00000 0.816497
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 4.00000 1.26491
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −2.00000 −0.577350
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 1.00000 0.267261
\(15\) 8.00000 2.06559
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −4.00000 −0.894427
\(21\) 2.00000 0.436436
\(22\) 4.00000 0.852803
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.00000 0.408248
\(25\) 11.0000 2.20000
\(26\) 6.00000 1.17670
\(27\) 4.00000 0.769800
\(28\) −1.00000 −0.188982
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −8.00000 −1.46059
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.00000 1.39262
\(34\) 2.00000 0.342997
\(35\) 4.00000 0.676123
\(36\) 1.00000 0.166667
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 2.00000 0.324443
\(39\) 12.0000 1.92154
\(40\) 4.00000 0.632456
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) −2.00000 −0.308607
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −4.00000 −0.603023
\(45\) −4.00000 −0.596285
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 0.142857
\(50\) −11.0000 −1.55563
\(51\) 4.00000 0.560112
\(52\) −6.00000 −0.832050
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −4.00000 −0.544331
\(55\) 16.0000 2.15744
\(56\) 1.00000 0.133631
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 8.00000 1.03280
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 8.00000 1.01600
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 24.0000 2.97683
\(66\) −8.00000 −0.984732
\(67\) 10.0000 1.22169 0.610847 0.791748i \(-0.290829\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) −4.00000 −0.478091
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −8.00000 −0.929981
\(75\) −22.0000 −2.54034
\(76\) −2.00000 −0.229416
\(77\) 4.00000 0.455842
\(78\) −12.0000 −1.35873
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −4.00000 −0.447214
\(81\) −11.0000 −1.22222
\(82\) 10.0000 1.10432
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 2.00000 0.218218
\(85\) 8.00000 0.867722
\(86\) 6.00000 0.646997
\(87\) −12.0000 −1.28654
\(88\) 4.00000 0.426401
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 4.00000 0.421637
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 16.0000 1.65912
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 2.00000 0.204124
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −1.00000 −0.101015
\(99\) −4.00000 −0.402015
\(100\) 11.0000 1.10000
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) −4.00000 −0.396059
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 6.00000 0.588348
\(105\) −8.00000 −0.780720
\(106\) −6.00000 −0.582772
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 4.00000 0.384900
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −16.0000 −1.52554
\(111\) −16.0000 −1.51865
\(112\) −1.00000 −0.0944911
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −6.00000 −0.554700
\(118\) −6.00000 −0.552345
\(119\) 2.00000 0.183340
\(120\) −8.00000 −0.730297
\(121\) 5.00000 0.454545
\(122\) −8.00000 −0.724286
\(123\) 20.0000 1.80334
\(124\) −8.00000 −0.718421
\(125\) −24.0000 −2.14663
\(126\) 1.00000 0.0890871
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0000 1.05654
\(130\) −24.0000 −2.10494
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 8.00000 0.696311
\(133\) 2.00000 0.173422
\(134\) −10.0000 −0.863868
\(135\) −16.0000 −1.37706
\(136\) 2.00000 0.171499
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) 0 0
\(143\) 24.0000 2.00698
\(144\) 1.00000 0.0833333
\(145\) −24.0000 −1.99309
\(146\) 2.00000 0.165521
\(147\) −2.00000 −0.164957
\(148\) 8.00000 0.657596
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 22.0000 1.79629
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000 0.162221
\(153\) −2.00000 −0.161690
\(154\) −4.00000 −0.322329
\(155\) 32.0000 2.57030
\(156\) 12.0000 0.960769
\(157\) 20.0000 1.59617 0.798087 0.602542i \(-0.205846\pi\)
0.798087 + 0.602542i \(0.205846\pi\)
\(158\) 0 0
\(159\) −12.0000 −0.951662
\(160\) 4.00000 0.316228
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −10.0000 −0.780869
\(165\) −32.0000 −2.49120
\(166\) −4.00000 −0.310460
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) −2.00000 −0.154303
\(169\) 23.0000 1.76923
\(170\) −8.00000 −0.613572
\(171\) −2.00000 −0.152944
\(172\) −6.00000 −0.457496
\(173\) −24.0000 −1.82469 −0.912343 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) 12.0000 0.909718
\(175\) −11.0000 −0.831522
\(176\) −4.00000 −0.301511
\(177\) −12.0000 −0.901975
\(178\) 18.0000 1.34916
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) −4.00000 −0.298142
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) −6.00000 −0.444750
\(183\) −16.0000 −1.18275
\(184\) 0 0
\(185\) −32.0000 −2.35269
\(186\) −16.0000 −1.17318
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) −4.00000 −0.290957
\(190\) −8.00000 −0.580381
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) −2.00000 −0.144338
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −6.00000 −0.430775
\(195\) −48.0000 −3.43735
\(196\) 1.00000 0.0714286
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 4.00000 0.284268
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) −11.0000 −0.777817
\(201\) −20.0000 −1.41069
\(202\) −18.0000 −1.26648
\(203\) −6.00000 −0.421117
\(204\) 4.00000 0.280056
\(205\) 40.0000 2.79372
\(206\) 0 0
\(207\) 0 0
\(208\) −6.00000 −0.416025
\(209\) 8.00000 0.553372
\(210\) 8.00000 0.552052
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 6.00000 0.410152
\(215\) 24.0000 1.63679
\(216\) −4.00000 −0.272166
\(217\) 8.00000 0.543075
\(218\) −2.00000 −0.135457
\(219\) 4.00000 0.270295
\(220\) 16.0000 1.07872
\(221\) 12.0000 0.807207
\(222\) 16.0000 1.07385
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 1.00000 0.0668153
\(225\) 11.0000 0.733333
\(226\) 14.0000 0.931266
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 4.00000 0.264906
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 0 0
\(231\) −8.00000 −0.526361
\(232\) −6.00000 −0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 6.00000 0.392232
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) 0 0
\(238\) −2.00000 −0.129641
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 8.00000 0.516398
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −5.00000 −0.321412
\(243\) 10.0000 0.641500
\(244\) 8.00000 0.512148
\(245\) −4.00000 −0.255551
\(246\) −20.0000 −1.27515
\(247\) 12.0000 0.763542
\(248\) 8.00000 0.508001
\(249\) −8.00000 −0.506979
\(250\) 24.0000 1.51789
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 0 0
\(254\) 0 0
\(255\) −16.0000 −1.00196
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) −12.0000 −0.747087
\(259\) −8.00000 −0.497096
\(260\) 24.0000 1.48842
\(261\) 6.00000 0.371391
\(262\) 12.0000 0.741362
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) −8.00000 −0.492366
\(265\) −24.0000 −1.47431
\(266\) −2.00000 −0.122628
\(267\) 36.0000 2.20316
\(268\) 10.0000 0.610847
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 16.0000 0.973729
\(271\) −24.0000 −1.45790 −0.728948 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) −2.00000 −0.121268
\(273\) −12.0000 −0.726273
\(274\) 2.00000 0.120824
\(275\) −44.0000 −2.65330
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −10.0000 −0.599760
\(279\) −8.00000 −0.478947
\(280\) −4.00000 −0.239046
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 0 0
\(285\) −16.0000 −0.947758
\(286\) −24.0000 −1.41915
\(287\) 10.0000 0.590281
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 24.0000 1.40933
\(291\) −12.0000 −0.703452
\(292\) −2.00000 −0.117041
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 2.00000 0.116642
\(295\) −24.0000 −1.39733
\(296\) −8.00000 −0.464991
\(297\) −16.0000 −0.928414
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) −22.0000 −1.27017
\(301\) 6.00000 0.345834
\(302\) −8.00000 −0.460348
\(303\) −36.0000 −2.06815
\(304\) −2.00000 −0.114708
\(305\) −32.0000 −1.83231
\(306\) 2.00000 0.114332
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 4.00000 0.227921
\(309\) 0 0
\(310\) −32.0000 −1.81748
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −12.0000 −0.679366
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −20.0000 −1.12867
\(315\) 4.00000 0.225374
\(316\) 0 0
\(317\) 20.0000 1.12331 0.561656 0.827371i \(-0.310164\pi\)
0.561656 + 0.827371i \(0.310164\pi\)
\(318\) 12.0000 0.672927
\(319\) −24.0000 −1.34374
\(320\) −4.00000 −0.223607
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) −11.0000 −0.611111
\(325\) −66.0000 −3.66102
\(326\) 4.00000 0.221540
\(327\) −4.00000 −0.221201
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 32.0000 1.76154
\(331\) 14.0000 0.769510 0.384755 0.923019i \(-0.374286\pi\)
0.384755 + 0.923019i \(0.374286\pi\)
\(332\) 4.00000 0.219529
\(333\) 8.00000 0.438397
\(334\) −16.0000 −0.875481
\(335\) −40.0000 −2.18543
\(336\) 2.00000 0.109109
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −23.0000 −1.25104
\(339\) 28.0000 1.52075
\(340\) 8.00000 0.433861
\(341\) 32.0000 1.73290
\(342\) 2.00000 0.108148
\(343\) −1.00000 −0.0539949
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) 24.0000 1.29025
\(347\) 24.0000 1.28839 0.644194 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) −12.0000 −0.643268
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 11.0000 0.587975
\(351\) −24.0000 −1.28103
\(352\) 4.00000 0.213201
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 12.0000 0.637793
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) −4.00000 −0.211702
\(358\) −24.0000 −1.26844
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 4.00000 0.210819
\(361\) −15.0000 −0.789474
\(362\) −18.0000 −0.946059
\(363\) −10.0000 −0.524864
\(364\) 6.00000 0.314485
\(365\) 8.00000 0.418739
\(366\) 16.0000 0.836333
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 0 0
\(369\) −10.0000 −0.520579
\(370\) 32.0000 1.66360
\(371\) −6.00000 −0.311504
\(372\) 16.0000 0.829561
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) −8.00000 −0.413670
\(375\) 48.0000 2.47871
\(376\) 0 0
\(377\) −36.0000 −1.85409
\(378\) 4.00000 0.205738
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 8.00000 0.410391
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 2.00000 0.102062
\(385\) −16.0000 −0.815436
\(386\) −14.0000 −0.712581
\(387\) −6.00000 −0.304997
\(388\) 6.00000 0.304604
\(389\) −2.00000 −0.101404 −0.0507020 0.998714i \(-0.516146\pi\)
−0.0507020 + 0.998714i \(0.516146\pi\)
\(390\) 48.0000 2.43057
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) 24.0000 1.21064
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) −24.0000 −1.20301
\(399\) −4.00000 −0.200250
\(400\) 11.0000 0.550000
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 20.0000 0.997509
\(403\) 48.0000 2.39105
\(404\) 18.0000 0.895533
\(405\) 44.0000 2.18638
\(406\) 6.00000 0.297775
\(407\) −32.0000 −1.58618
\(408\) −4.00000 −0.198030
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) −40.0000 −1.97546
\(411\) 4.00000 0.197305
\(412\) 0 0
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) −16.0000 −0.785409
\(416\) 6.00000 0.294174
\(417\) −20.0000 −0.979404
\(418\) −8.00000 −0.391293
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) −8.00000 −0.390360
\(421\) −32.0000 −1.55958 −0.779792 0.626038i \(-0.784675\pi\)
−0.779792 + 0.626038i \(0.784675\pi\)
\(422\) −2.00000 −0.0973585
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) −22.0000 −1.06716
\(426\) 0 0
\(427\) −8.00000 −0.387147
\(428\) −6.00000 −0.290021
\(429\) −48.0000 −2.31746
\(430\) −24.0000 −1.15738
\(431\) −1.00000 −0.0481683
\(432\) 4.00000 0.192450
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) −8.00000 −0.384012
\(435\) 48.0000 2.30142
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) −12.0000 −0.572729 −0.286364 0.958121i \(-0.592447\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(440\) −16.0000 −0.762770
\(441\) 1.00000 0.0476190
\(442\) −12.0000 −0.570782
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −16.0000 −0.759326
\(445\) 72.0000 3.41313
\(446\) 0 0
\(447\) 36.0000 1.70274
\(448\) −1.00000 −0.0472456
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −11.0000 −0.518545
\(451\) 40.0000 1.88353
\(452\) −14.0000 −0.658505
\(453\) −16.0000 −0.751746
\(454\) −6.00000 −0.281594
\(455\) −24.0000 −1.12514
\(456\) −4.00000 −0.187317
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 12.0000 0.560723
\(459\) −8.00000 −0.373408
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 8.00000 0.372194
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 6.00000 0.278543
\(465\) −64.0000 −2.96793
\(466\) 6.00000 0.277945
\(467\) 10.0000 0.462745 0.231372 0.972865i \(-0.425678\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(468\) −6.00000 −0.277350
\(469\) −10.0000 −0.461757
\(470\) 0 0
\(471\) −40.0000 −1.84310
\(472\) −6.00000 −0.276172
\(473\) 24.0000 1.10352
\(474\) 0 0
\(475\) −22.0000 −1.00943
\(476\) 2.00000 0.0916698
\(477\) 6.00000 0.274721
\(478\) −12.0000 −0.548867
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) −8.00000 −0.365148
\(481\) −48.0000 −2.18861
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −24.0000 −1.08978
\(486\) −10.0000 −0.453609
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) −8.00000 −0.362143
\(489\) 8.00000 0.361773
\(490\) 4.00000 0.180702
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 20.0000 0.901670
\(493\) −12.0000 −0.540453
\(494\) −12.0000 −0.539906
\(495\) 16.0000 0.719147
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 8.00000 0.358489
\(499\) −26.0000 −1.16392 −0.581960 0.813217i \(-0.697714\pi\)
−0.581960 + 0.813217i \(0.697714\pi\)
\(500\) −24.0000 −1.07331
\(501\) −32.0000 −1.42965
\(502\) 24.0000 1.07117
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 1.00000 0.0445435
\(505\) −72.0000 −3.20396
\(506\) 0 0
\(507\) −46.0000 −2.04293
\(508\) 0 0
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 16.0000 0.708492
\(511\) 2.00000 0.0884748
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 −0.353209
\(514\) −18.0000 −0.793946
\(515\) 0 0
\(516\) 12.0000 0.528271
\(517\) 0 0
\(518\) 8.00000 0.351500
\(519\) 48.0000 2.10697
\(520\) −24.0000 −1.05247
\(521\) −34.0000 −1.48957 −0.744784 0.667306i \(-0.767447\pi\)
−0.744784 + 0.667306i \(0.767447\pi\)
\(522\) −6.00000 −0.262613
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) −12.0000 −0.524222
\(525\) 22.0000 0.960159
\(526\) 16.0000 0.697633
\(527\) 16.0000 0.696971
\(528\) 8.00000 0.348155
\(529\) −23.0000 −1.00000
\(530\) 24.0000 1.04249
\(531\) 6.00000 0.260378
\(532\) 2.00000 0.0867110
\(533\) 60.0000 2.59889
\(534\) −36.0000 −1.55787
\(535\) 24.0000 1.03761
\(536\) −10.0000 −0.431934
\(537\) −48.0000 −2.07135
\(538\) 14.0000 0.603583
\(539\) −4.00000 −0.172292
\(540\) −16.0000 −0.688530
\(541\) −26.0000 −1.11783 −0.558914 0.829226i \(-0.688782\pi\)
−0.558914 + 0.829226i \(0.688782\pi\)
\(542\) 24.0000 1.03089
\(543\) −36.0000 −1.54491
\(544\) 2.00000 0.0857493
\(545\) −8.00000 −0.342682
\(546\) 12.0000 0.513553
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 8.00000 0.341432
\(550\) 44.0000 1.87617
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 64.0000 2.71665
\(556\) 10.0000 0.424094
\(557\) 16.0000 0.677942 0.338971 0.940797i \(-0.389921\pi\)
0.338971 + 0.940797i \(0.389921\pi\)
\(558\) 8.00000 0.338667
\(559\) 36.0000 1.52264
\(560\) 4.00000 0.169031
\(561\) −16.0000 −0.675521
\(562\) 22.0000 0.928014
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 0 0
\(565\) 56.0000 2.35594
\(566\) 22.0000 0.924729
\(567\) 11.0000 0.461957
\(568\) 0 0
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 16.0000 0.670166
\(571\) 2.00000 0.0836974 0.0418487 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) 24.0000 1.00349
\(573\) 24.0000 1.00261
\(574\) −10.0000 −0.417392
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 13.0000 0.540729
\(579\) −28.0000 −1.16364
\(580\) −24.0000 −0.996546
\(581\) −4.00000 −0.165948
\(582\) 12.0000 0.497416
\(583\) −24.0000 −0.993978
\(584\) 2.00000 0.0827606
\(585\) 24.0000 0.992278
\(586\) 26.0000 1.07405
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 16.0000 0.659269
\(590\) 24.0000 0.988064
\(591\) −36.0000 −1.48084
\(592\) 8.00000 0.328798
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 16.0000 0.656488
\(595\) −8.00000 −0.327968
\(596\) −18.0000 −0.737309
\(597\) −48.0000 −1.96451
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 22.0000 0.898146
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) −6.00000 −0.244542
\(603\) 10.0000 0.407231
\(604\) 8.00000 0.325515
\(605\) −20.0000 −0.813116
\(606\) 36.0000 1.46240
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 2.00000 0.0811107
\(609\) 12.0000 0.486265
\(610\) 32.0000 1.29564
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 2.00000 0.0807134
\(615\) −80.0000 −3.22591
\(616\) −4.00000 −0.161165
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 32.0000 1.28515
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 18.0000 0.721155
\(624\) 12.0000 0.480384
\(625\) 41.0000 1.64000
\(626\) −22.0000 −0.879297
\(627\) −16.0000 −0.638978
\(628\) 20.0000 0.798087
\(629\) −16.0000 −0.637962
\(630\) −4.00000 −0.159364
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) −20.0000 −0.794301
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) −6.00000 −0.237729
\(638\) 24.0000 0.950169
\(639\) 0 0
\(640\) 4.00000 0.158114
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) −12.0000 −0.473602
\(643\) 50.0000 1.97181 0.985904 0.167313i \(-0.0535092\pi\)
0.985904 + 0.167313i \(0.0535092\pi\)
\(644\) 0 0
\(645\) −48.0000 −1.89000
\(646\) −4.00000 −0.157378
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 11.0000 0.432121
\(649\) −24.0000 −0.942082
\(650\) 66.0000 2.58873
\(651\) −16.0000 −0.627089
\(652\) −4.00000 −0.156652
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 4.00000 0.156412
\(655\) 48.0000 1.87552
\(656\) −10.0000 −0.390434
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) −32.0000 −1.24560
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) −14.0000 −0.544125
\(663\) −24.0000 −0.932083
\(664\) −4.00000 −0.155230
\(665\) −8.00000 −0.310227
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) 40.0000 1.54533
\(671\) −32.0000 −1.23535
\(672\) −2.00000 −0.0771517
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) −18.0000 −0.693334
\(675\) 44.0000 1.69356
\(676\) 23.0000 0.884615
\(677\) −4.00000 −0.153732 −0.0768662 0.997041i \(-0.524491\pi\)
−0.0768662 + 0.997041i \(0.524491\pi\)
\(678\) −28.0000 −1.07533
\(679\) −6.00000 −0.230259
\(680\) −8.00000 −0.306786
\(681\) −12.0000 −0.459841
\(682\) −32.0000 −1.22534
\(683\) 46.0000 1.76014 0.880071 0.474843i \(-0.157495\pi\)
0.880071 + 0.474843i \(0.157495\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 8.00000 0.305664
\(686\) 1.00000 0.0381802
\(687\) 24.0000 0.915657
\(688\) −6.00000 −0.228748
\(689\) −36.0000 −1.37149
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −24.0000 −0.912343
\(693\) 4.00000 0.151947
\(694\) −24.0000 −0.911028
\(695\) −40.0000 −1.51729
\(696\) 12.0000 0.454859
\(697\) 20.0000 0.757554
\(698\) −18.0000 −0.681310
\(699\) 12.0000 0.453882
\(700\) −11.0000 −0.415761
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 24.0000 0.905822
\(703\) −16.0000 −0.603451
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) −18.0000 −0.676960
\(708\) −12.0000 −0.450988
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 18.0000 0.674579
\(713\) 0 0
\(714\) 4.00000 0.149696
\(715\) −96.0000 −3.59020
\(716\) 24.0000 0.896922
\(717\) −24.0000 −0.896296
\(718\) 24.0000 0.895672
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) −4.00000 −0.149071
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) −4.00000 −0.148762
\(724\) 18.0000 0.668965
\(725\) 66.0000 2.45118
\(726\) 10.0000 0.371135
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) −6.00000 −0.222375
\(729\) 13.0000 0.481481
\(730\) −8.00000 −0.296093
\(731\) 12.0000 0.443836
\(732\) −16.0000 −0.591377
\(733\) −12.0000 −0.443230 −0.221615 0.975134i \(-0.571133\pi\)
−0.221615 + 0.975134i \(0.571133\pi\)
\(734\) −32.0000 −1.18114
\(735\) 8.00000 0.295084
\(736\) 0 0
\(737\) −40.0000 −1.47342
\(738\) 10.0000 0.368105
\(739\) 26.0000 0.956425 0.478213 0.878244i \(-0.341285\pi\)
0.478213 + 0.878244i \(0.341285\pi\)
\(740\) −32.0000 −1.17634
\(741\) −24.0000 −0.881662
\(742\) 6.00000 0.220267
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −16.0000 −0.586588
\(745\) 72.0000 2.63788
\(746\) −4.00000 −0.146450
\(747\) 4.00000 0.146352
\(748\) 8.00000 0.292509
\(749\) 6.00000 0.219235
\(750\) −48.0000 −1.75271
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 0 0
\(753\) 48.0000 1.74922
\(754\) 36.0000 1.31104
\(755\) −32.0000 −1.16460
\(756\) −4.00000 −0.145479
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) −8.00000 −0.290191
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 0 0
\(763\) −2.00000 −0.0724049
\(764\) −12.0000 −0.434145
\(765\) 8.00000 0.289241
\(766\) 24.0000 0.867155
\(767\) −36.0000 −1.29988
\(768\) −2.00000 −0.0721688
\(769\) 38.0000 1.37032 0.685158 0.728395i \(-0.259733\pi\)
0.685158 + 0.728395i \(0.259733\pi\)
\(770\) 16.0000 0.576600
\(771\) −36.0000 −1.29651
\(772\) 14.0000 0.503871
\(773\) −4.00000 −0.143870 −0.0719350 0.997409i \(-0.522917\pi\)
−0.0719350 + 0.997409i \(0.522917\pi\)
\(774\) 6.00000 0.215666
\(775\) −88.0000 −3.16105
\(776\) −6.00000 −0.215387
\(777\) 16.0000 0.573997
\(778\) 2.00000 0.0717035
\(779\) 20.0000 0.716574
\(780\) −48.0000 −1.71868
\(781\) 0 0
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) 1.00000 0.0357143
\(785\) −80.0000 −2.85532
\(786\) −24.0000 −0.856052
\(787\) 24.0000 0.855508 0.427754 0.903895i \(-0.359305\pi\)
0.427754 + 0.903895i \(0.359305\pi\)
\(788\) 18.0000 0.641223
\(789\) 32.0000 1.13923
\(790\) 0 0
\(791\) 14.0000 0.497783
\(792\) 4.00000 0.142134
\(793\) −48.0000 −1.70453
\(794\) 0 0
\(795\) 48.0000 1.70238
\(796\) 24.0000 0.850657
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 4.00000 0.141598
\(799\) 0 0
\(800\) −11.0000 −0.388909
\(801\) −18.0000 −0.635999
\(802\) 10.0000 0.353112
\(803\) 8.00000 0.282314
\(804\) −20.0000 −0.705346
\(805\) 0 0
\(806\) −48.0000 −1.69073
\(807\) 28.0000 0.985647
\(808\) −18.0000 −0.633238
\(809\) −10.0000 −0.351581 −0.175791 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) −44.0000 −1.54600
\(811\) 10.0000 0.351147 0.175574 0.984466i \(-0.443822\pi\)
0.175574 + 0.984466i \(0.443822\pi\)
\(812\) −6.00000 −0.210559
\(813\) 48.0000 1.68343
\(814\) 32.0000 1.12160
\(815\) 16.0000 0.560456
\(816\) 4.00000 0.140028
\(817\) 12.0000 0.419827
\(818\) −6.00000 −0.209785
\(819\) 6.00000 0.209657
\(820\) 40.0000 1.39686
\(821\) 52.0000 1.81481 0.907406 0.420255i \(-0.138059\pi\)
0.907406 + 0.420255i \(0.138059\pi\)
\(822\) −4.00000 −0.139516
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 0 0
\(825\) 88.0000 3.06377
\(826\) 6.00000 0.208767
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 16.0000 0.555368
\(831\) −4.00000 −0.138758
\(832\) −6.00000 −0.208013
\(833\) −2.00000 −0.0692959
\(834\) 20.0000 0.692543
\(835\) −64.0000 −2.21481
\(836\) 8.00000 0.276686
\(837\) −32.0000 −1.10608
\(838\) −12.0000 −0.414533
\(839\) −16.0000 −0.552381 −0.276191 0.961103i \(-0.589072\pi\)
−0.276191 + 0.961103i \(0.589072\pi\)
\(840\) 8.00000 0.276026
\(841\) 7.00000 0.241379
\(842\) 32.0000 1.10279
\(843\) 44.0000 1.51544
\(844\) 2.00000 0.0688428
\(845\) −92.0000 −3.16490
\(846\) 0 0
\(847\) −5.00000 −0.171802
\(848\) 6.00000 0.206041
\(849\) 44.0000 1.51008
\(850\) 22.0000 0.754594
\(851\) 0 0
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 8.00000 0.273754
\(855\) 8.00000 0.273594
\(856\) 6.00000 0.205076
\(857\) 54.0000 1.84460 0.922302 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) 48.0000 1.63869
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 24.0000 0.818393
\(861\) −20.0000 −0.681598
\(862\) 1.00000 0.0340601
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) −4.00000 −0.136083
\(865\) 96.0000 3.26410
\(866\) −6.00000 −0.203888
\(867\) 26.0000 0.883006
\(868\) 8.00000 0.271538
\(869\) 0 0
\(870\) −48.0000 −1.62735
\(871\) −60.0000 −2.03302
\(872\) −2.00000 −0.0677285
\(873\) 6.00000 0.203069
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) 4.00000 0.135147
\(877\) −58.0000 −1.95852 −0.979260 0.202606i \(-0.935059\pi\)
−0.979260 + 0.202606i \(0.935059\pi\)
\(878\) 12.0000 0.404980
\(879\) 52.0000 1.75392
\(880\) 16.0000 0.539360
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −34.0000 −1.14419 −0.572096 0.820187i \(-0.693869\pi\)
−0.572096 + 0.820187i \(0.693869\pi\)
\(884\) 12.0000 0.403604
\(885\) 48.0000 1.61350
\(886\) 24.0000 0.806296
\(887\) 16.0000 0.537227 0.268614 0.963248i \(-0.413434\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(888\) 16.0000 0.536925
\(889\) 0 0
\(890\) −72.0000 −2.41345
\(891\) 44.0000 1.47406
\(892\) 0 0
\(893\) 0 0
\(894\) −36.0000 −1.20402
\(895\) −96.0000 −3.20893
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −2.00000 −0.0667409
\(899\) −48.0000 −1.60089
\(900\) 11.0000 0.366667
\(901\) −12.0000 −0.399778
\(902\) −40.0000 −1.33185
\(903\) −12.0000 −0.399335
\(904\) 14.0000 0.465633
\(905\) −72.0000 −2.39336
\(906\) 16.0000 0.531564
\(907\) 4.00000 0.132818 0.0664089 0.997792i \(-0.478846\pi\)
0.0664089 + 0.997792i \(0.478846\pi\)
\(908\) 6.00000 0.199117
\(909\) 18.0000 0.597022
\(910\) 24.0000 0.795592
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 4.00000 0.132453
\(913\) −16.0000 −0.529523
\(914\) −38.0000 −1.25693
\(915\) 64.0000 2.11577
\(916\) −12.0000 −0.396491
\(917\) 12.0000 0.396275
\(918\) 8.00000 0.264039
\(919\) 16.0000 0.527791 0.263896 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 0 0
\(921\) 4.00000 0.131804
\(922\) −12.0000 −0.395199
\(923\) 0 0
\(924\) −8.00000 −0.263181
\(925\) 88.0000 2.89342
\(926\) 32.0000 1.05159
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) −14.0000 −0.459325 −0.229663 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 64.0000 2.09864
\(931\) −2.00000 −0.0655474
\(932\) −6.00000 −0.196537
\(933\) 16.0000 0.523816
\(934\) −10.0000 −0.327210
\(935\) −32.0000 −1.04651
\(936\) 6.00000 0.196116
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 10.0000 0.326512
\(939\) −44.0000 −1.43589
\(940\) 0 0
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 40.0000 1.30327
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) 16.0000 0.520480
\(946\) −24.0000 −0.780307
\(947\) −46.0000 −1.49480 −0.747400 0.664375i \(-0.768698\pi\)
−0.747400 + 0.664375i \(0.768698\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 22.0000 0.713774
\(951\) −40.0000 −1.29709
\(952\) −2.00000 −0.0648204
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) −6.00000 −0.194257
\(955\) 48.0000 1.55324
\(956\) 12.0000 0.388108
\(957\) 48.0000 1.55162
\(958\) 12.0000 0.387702
\(959\) 2.00000 0.0645834
\(960\) 8.00000 0.258199
\(961\) 33.0000 1.06452
\(962\) 48.0000 1.54758
\(963\) −6.00000 −0.193347
\(964\) 2.00000 0.0644157
\(965\) −56.0000 −1.80270
\(966\) 0 0
\(967\) 44.0000 1.41494 0.707472 0.706741i \(-0.249835\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(968\) −5.00000 −0.160706
\(969\) −8.00000 −0.256997
\(970\) 24.0000 0.770594
\(971\) 6.00000 0.192549 0.0962746 0.995355i \(-0.469307\pi\)
0.0962746 + 0.995355i \(0.469307\pi\)
\(972\) 10.0000 0.320750
\(973\) −10.0000 −0.320585
\(974\) 8.00000 0.256337
\(975\) 132.000 4.22738
\(976\) 8.00000 0.256074
\(977\) 46.0000 1.47167 0.735835 0.677161i \(-0.236790\pi\)
0.735835 + 0.677161i \(0.236790\pi\)
\(978\) −8.00000 −0.255812
\(979\) 72.0000 2.30113
\(980\) −4.00000 −0.127775
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) −20.0000 −0.637577
\(985\) −72.0000 −2.29411
\(986\) 12.0000 0.382158
\(987\) 0 0
\(988\) 12.0000 0.381771
\(989\) 0 0
\(990\) −16.0000 −0.508513
\(991\) −24.0000 −0.762385 −0.381193 0.924496i \(-0.624487\pi\)
−0.381193 + 0.924496i \(0.624487\pi\)
\(992\) 8.00000 0.254000
\(993\) −28.0000 −0.888553
\(994\) 0 0
\(995\) −96.0000 −3.04340
\(996\) −8.00000 −0.253490
\(997\) −12.0000 −0.380044 −0.190022 0.981780i \(-0.560856\pi\)
−0.190022 + 0.981780i \(0.560856\pi\)
\(998\) 26.0000 0.823016
\(999\) 32.0000 1.01244
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 6034.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.c.1.1 1 1.1 even 1 trivial