Properties

Label 7245.2.a.h.1.1
Level $7245$
Weight $2$
Character 7245.1
Self dual yes
Analytic conductor $57.852$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(57.8516162644\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2415)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7245.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} +3.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} +3.00000 q^{8} -1.00000 q^{10} +4.00000 q^{11} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{16} -6.00000 q^{17} -4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} -1.00000 q^{23} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{28} -6.00000 q^{29} +8.00000 q^{31} -5.00000 q^{32} +6.00000 q^{34} +1.00000 q^{35} +6.00000 q^{37} +4.00000 q^{38} +3.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} -4.00000 q^{44} +1.00000 q^{46} +1.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} +10.0000 q^{53} +4.00000 q^{55} +3.00000 q^{56} +6.00000 q^{58} +10.0000 q^{61} -8.00000 q^{62} +7.00000 q^{64} +2.00000 q^{65} -12.0000 q^{67} +6.00000 q^{68} -1.00000 q^{70} +8.00000 q^{71} +14.0000 q^{73} -6.00000 q^{74} +4.00000 q^{76} +4.00000 q^{77} +4.00000 q^{79} -1.00000 q^{80} +6.00000 q^{82} -6.00000 q^{85} -4.00000 q^{86} +12.0000 q^{88} -6.00000 q^{89} +2.00000 q^{91} +1.00000 q^{92} -4.00000 q^{95} +2.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) −1.00000 −0.119523
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) −6.00000 −0.697486
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 12.0000 1.27920
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) −4.00000 −0.381385
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) −8.00000 −0.718421
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) −2.00000 −0.175412
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −18.0000 −1.54349
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) −14.0000 −1.15865
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −12.0000 −0.973329
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) −4.00000 −0.318223
\(159\) 0 0
\(160\) −5.00000 −0.395285
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −24.0000 −1.87983 −0.939913 0.341415i \(-0.889094\pi\)
−0.939913 + 0.341415i \(0.889094\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −2.00000 −0.148250
\(183\) 0 0
\(184\) −3.00000 −0.221163
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 18.0000 1.29567 0.647834 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) −26.0000 −1.85242 −0.926212 0.377004i \(-0.876954\pi\)
−0.926212 + 0.377004i \(0.876954\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) 2.00000 0.140720
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) −2.00000 −0.138675
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −10.0000 −0.686803
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) −6.00000 −0.406371
\(219\) 0 0
\(220\) −4.00000 −0.269680
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −5.00000 −0.334077
\(225\) 0 0
\(226\) 2.00000 0.133038
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 1.00000 0.0659380
\(231\) 0 0
\(232\) −18.0000 −1.18176
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 6.00000 0.388922
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) 24.0000 1.52400
\(249\) 0 0
\(250\) −1.00000 −0.0632456
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −8.00000 −0.494242
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 4.00000 0.245256
\(267\) 0 0
\(268\) 12.0000 0.733017
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) −12.0000 −0.719712
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 6.00000 0.352332
\(291\) 0 0
\(292\) −14.0000 −0.819288
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 18.0000 1.04623
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −4.00000 −0.227921
\(309\) 0 0
\(310\) −8.00000 −0.454369
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 22.0000 1.23564 0.617822 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) 7.00000 0.391312
\(321\) 0 0
\(322\) 1.00000 0.0557278
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 24.0000 1.32924
\(327\) 0 0
\(328\) −18.0000 −0.993884
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 32.0000 1.73290
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) −14.0000 −0.752645
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) −20.0000 −1.06600
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) −2.00000 −0.104828
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) 10.0000 0.519174
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 4.00000 0.205196
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0000 0.613171 0.306586 0.951843i \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) −18.0000 −0.916176
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) 26.0000 1.30986
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) 10.0000 0.501886 0.250943 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 0 0
\(403\) 16.0000 0.797017
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 6.00000 0.296319
\(411\) 0 0
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −10.0000 −0.490290
\(417\) 0 0
\(418\) 16.0000 0.782586
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 30.0000 1.45693
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) 10.0000 0.483934
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) −4.00000 −0.192897
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) −30.0000 −1.44171 −0.720854 0.693087i \(-0.756250\pi\)
−0.720854 + 0.693087i \(0.756250\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) 4.00000 0.191346
\(438\) 0 0
\(439\) 24.0000 1.14546 0.572729 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) 12.0000 0.572078
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) 7.00000 0.330719
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) 0 0
\(455\) 2.00000 0.0937614
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 6.00000 0.280362
\(459\) 0 0
\(460\) 1.00000 0.0466252
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) 12.0000 0.557687 0.278844 0.960337i \(-0.410049\pi\)
0.278844 + 0.960337i \(0.410049\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 16.0000 0.740392 0.370196 0.928954i \(-0.379291\pi\)
0.370196 + 0.928954i \(0.379291\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 8.00000 0.365911
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 28.0000 1.26880 0.634401 0.773004i \(-0.281247\pi\)
0.634401 + 0.773004i \(0.281247\pi\)
\(488\) 30.0000 1.35804
\(489\) 0 0
\(490\) −1.00000 −0.0451754
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 36.0000 1.62136
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) −20.0000 −0.892644
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) 4.00000 0.177822
\(507\) 0 0
\(508\) −12.0000 −0.532414
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) 0 0
\(518\) −6.00000 −0.263625
\(519\) 0 0
\(520\) 6.00000 0.263117
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −48.0000 −2.09091
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −10.0000 −0.434372
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 4.00000 0.172935
\(536\) −36.0000 −1.55496
\(537\) 0 0
\(538\) −30.0000 −1.29339
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) −24.0000 −1.03089
\(543\) 0 0
\(544\) 30.0000 1.28624
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 2.00000 0.0854358
\(549\) 0 0
\(550\) −4.00000 −0.170561
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) −2.00000 −0.0843649
\(563\) 16.0000 0.674320 0.337160 0.941447i \(-0.390534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(564\) 0 0
\(565\) −2.00000 −0.0841406
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 24.0000 1.00702
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) −8.00000 −0.334497
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) −19.0000 −0.790296
\(579\) 0 0
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) 0 0
\(583\) 40.0000 1.65663
\(584\) 42.0000 1.73797
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) −4.00000 −0.165098 −0.0825488 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) −6.00000 −0.246598
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 2.00000 0.0817861
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 5.00000 0.203279
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 20.0000 0.811107
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 0 0
\(612\) 0 0
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) 12.0000 0.483494
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −2.00000 −0.0799361
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −36.0000 −1.43541
\(630\) 0 0
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 12.0000 0.477334
\(633\) 0 0
\(634\) −22.0000 −0.873732
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 24.0000 0.950169
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) 12.0000 0.473234 0.236617 0.971603i \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(644\) 1.00000 0.0394055
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 40.0000 1.57256 0.786281 0.617869i \(-0.212004\pi\)
0.786281 + 0.617869i \(0.212004\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 24.0000 0.939913
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) −46.0000 −1.78919 −0.894596 0.446875i \(-0.852537\pi\)
−0.894596 + 0.446875i \(0.852537\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 −0.155113
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) 0 0
\(669\) 0 0
\(670\) 12.0000 0.463600
\(671\) 40.0000 1.54418
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) −18.0000 −0.693334
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 2.00000 0.0767530
\(680\) −18.0000 −0.690268
\(681\) 0 0
\(682\) −32.0000 −1.22534
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 12.0000 0.455186
\(696\) 0 0
\(697\) 36.0000 1.36360
\(698\) −30.0000 −1.13552
\(699\) 0 0
\(700\) −1.00000 −0.0377964
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 28.0000 1.05529
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) −2.00000 −0.0752177
\(708\) 0 0
\(709\) −2.00000 −0.0751116 −0.0375558 0.999295i \(-0.511957\pi\)
−0.0375558 + 0.999295i \(0.511957\pi\)
\(710\) −8.00000 −0.300235
\(711\) 0 0
\(712\) −18.0000 −0.674579
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 14.0000 0.520306
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 6.00000 0.222375
\(729\) 0 0
\(730\) −14.0000 −0.518163
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 5.00000 0.184302
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) −36.0000 −1.32428 −0.662141 0.749380i \(-0.730352\pi\)
−0.662141 + 0.749380i \(0.730352\pi\)
\(740\) −6.00000 −0.220564
\(741\) 0 0
\(742\) −10.0000 −0.367112
\(743\) 40.0000 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) 26.0000 0.951928
\(747\) 0 0
\(748\) 24.0000 0.877527
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) −8.00000 −0.290573
\(759\) 0 0
\(760\) −12.0000 −0.435286
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) 0 0
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) 0 0
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) −4.00000 −0.144150
\(771\) 0 0
\(772\) −18.0000 −0.647834
\(773\) 14.0000 0.503545 0.251773 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) −6.00000 −0.214560
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) 22.0000 0.785214
\(786\) 0 0
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 26.0000 0.926212
\(789\) 0 0
\(790\) −4.00000 −0.142314
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) 20.0000 0.710221
\(794\) −10.0000 −0.354887
\(795\) 0 0
\(796\) −24.0000 −0.850657
\(797\) 22.0000 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 0 0
\(802\) −10.0000 −0.353112
\(803\) 56.0000 1.97620
\(804\) 0 0
\(805\) −1.00000 −0.0352454
\(806\) −16.0000 −0.563576
\(807\) 0 0
\(808\) −6.00000 −0.211079
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 6.00000 0.210559
\(813\) 0 0
\(814\) −24.0000 −0.841200
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 0 0
\(823\) 20.0000 0.697156 0.348578 0.937280i \(-0.386665\pi\)
0.348578 + 0.937280i \(0.386665\pi\)
\(824\) −48.0000 −1.67216
\(825\) 0 0
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 14.0000 0.485363
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) 16.0000 0.553372
\(837\) 0 0
\(838\) 12.0000 0.414533
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −22.0000 −0.758170
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) −10.0000 −0.343401
\(849\) 0 0
\(850\) 6.00000 0.205798
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) 50.0000 1.71197 0.855984 0.517003i \(-0.172952\pi\)
0.855984 + 0.517003i \(0.172952\pi\)
\(854\) −10.0000 −0.342193
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −54.0000 −1.84460 −0.922302 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) −36.0000 −1.22830 −0.614152 0.789188i \(-0.710502\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(860\) −4.00000 −0.136399
\(861\) 0 0
\(862\) 16.0000 0.544962
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 14.0000 0.476014
\(866\) 30.0000 1.01944
\(867\) 0 0
\(868\) −8.00000 −0.271538
\(869\) 16.0000 0.542763
\(870\) 0 0
\(871\) −24.0000 −0.813209
\(872\) 18.0000 0.609557
\(873\) 0 0
\(874\) −4.00000 −0.135302
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −50.0000 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(878\) −24.0000 −0.809961
\(879\) 0 0
\(880\) −4.00000 −0.134840
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 0 0
\(883\) 32.0000 1.07689 0.538443 0.842662i \(-0.319013\pi\)
0.538443 + 0.842662i \(0.319013\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) 36.0000 1.20944
\(887\) 32.0000 1.07445 0.537227 0.843437i \(-0.319472\pi\)
0.537227 + 0.843437i \(0.319472\pi\)
\(888\) 0 0
\(889\) 12.0000 0.402467
\(890\) 6.00000 0.201120
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) 0 0
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) 3.00000 0.100223
\(897\) 0 0
\(898\) 2.00000 0.0667409
\(899\) −48.0000 −1.60089
\(900\) 0 0
\(901\) −60.0000 −1.99889
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) −14.0000 −0.465376
\(906\) 0 0
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −2.00000 −0.0662994
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 22.0000 0.727695
\(915\) 0 0
\(916\) 6.00000 0.198246
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) 4.00000 0.131948 0.0659739 0.997821i \(-0.478985\pi\)
0.0659739 + 0.997821i \(0.478985\pi\)
\(920\) −3.00000 −0.0989071
\(921\) 0 0
\(922\) 42.0000 1.38320
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) −12.0000 −0.394344
\(927\) 0 0
\(928\) 30.0000 0.984798
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) −4.00000 −0.131095
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) −16.0000 −0.523536
\(935\) −24.0000 −0.784884
\(936\) 0 0
\(937\) −14.0000 −0.457360 −0.228680 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) 12.0000 0.391814
\(939\) 0 0
\(940\) 0 0
\(941\) 14.0000 0.456387 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(942\) 0 0
\(943\) 6.00000 0.195387
\(944\) 0 0
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 0 0
\(949\) 28.0000 0.908918
\(950\) 4.00000 0.129777
\(951\) 0 0
\(952\) −18.0000 −0.583383
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 8.00000 0.258738
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) −2.00000 −0.0645834
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −12.0000 −0.386896
\(963\) 0 0
\(964\) 10.0000 0.322078
\(965\) 18.0000 0.579441
\(966\) 0 0
\(967\) 52.0000 1.67221 0.836104 0.548572i \(-0.184828\pi\)
0.836104 + 0.548572i \(0.184828\pi\)
\(968\) 15.0000 0.482118
\(969\) 0 0
\(970\) −2.00000 −0.0642161
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 0 0
\(973\) 12.0000 0.384702
\(974\) −28.0000 −0.897178
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 0 0
\(979\) −24.0000 −0.767043
\(980\) −1.00000 −0.0319438
\(981\) 0 0
\(982\) −12.0000 −0.382935
\(983\) 52.0000 1.65854 0.829271 0.558846i \(-0.188756\pi\)
0.829271 + 0.558846i \(0.188756\pi\)
\(984\) 0 0
\(985\) −26.0000 −0.828429
\(986\) −36.0000 −1.14647
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) −40.0000 −1.27000
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 24.0000 0.760851
\(996\) 0 0
\(997\) 42.0000 1.33015 0.665077 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) 28.0000 0.886325
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7245.2.a.h.1.1 1
3.2 odd 2 2415.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2415.2.a.h.1.1 1 3.2 odd 2
7245.2.a.h.1.1 1 1.1 even 1 trivial