Properties

Label 930.2.a.h.1.1
Level $930$
Weight $2$
Character 930.1
Self dual yes
Analytic conductor $7.426$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.42608738798\)
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 \(\chi\) \(=\) 930.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +4.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} +4.00000 q^{29} -1.00000 q^{30} -1.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -2.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -12.0000 q^{37} +8.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} +2.00000 q^{42} +8.00000 q^{43} -4.00000 q^{44} +1.00000 q^{45} +8.00000 q^{46} -4.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +2.00000 q^{56} -8.00000 q^{57} -4.00000 q^{58} +2.00000 q^{59} +1.00000 q^{60} +10.0000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +4.00000 q^{66} -6.00000 q^{67} +2.00000 q^{68} -8.00000 q^{69} +2.00000 q^{70} +6.00000 q^{71} -1.00000 q^{72} -4.00000 q^{73} +12.0000 q^{74} +1.00000 q^{75} -8.00000 q^{76} +8.00000 q^{77} +4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} -2.00000 q^{84} +2.00000 q^{85} -8.00000 q^{86} +4.00000 q^{87} +4.00000 q^{88} -1.00000 q^{90} +8.00000 q^{91} -8.00000 q^{92} -1.00000 q^{93} +4.00000 q^{94} -8.00000 q^{95} -1.00000 q^{96} -18.0000 q^{97} +3.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.00000 0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) 4.00000 0.852803
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) −2.00000 −0.377964
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) −1.00000 −0.182574
\(31\) −1.00000 −0.179605
\(32\) −1.00000 −0.176777
\(33\) −4.00000 −0.696311
\(34\) −2.00000 −0.342997
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) −12.0000 −1.97279 −0.986394 0.164399i \(-0.947432\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 8.00000 1.29777
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 2.00000 0.308607
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −4.00000 −0.603023
\(45\) 1.00000 0.149071
\(46\) 8.00000 1.17954
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 2.00000 0.280056
\(52\) −4.00000 −0.554700
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.00000 −0.539360
\(56\) 2.00000 0.267261
\(57\) −8.00000 −1.05963
\(58\) −4.00000 −0.525226
\(59\) 2.00000 0.260378 0.130189 0.991489i \(-0.458442\pi\)
0.130189 + 0.991489i \(0.458442\pi\)
\(60\) 1.00000 0.129099
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 1.00000 0.127000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 4.00000 0.492366
\(67\) −6.00000 −0.733017 −0.366508 0.930415i \(-0.619447\pi\)
−0.366508 + 0.930415i \(0.619447\pi\)
\(68\) 2.00000 0.242536
\(69\) −8.00000 −0.963087
\(70\) 2.00000 0.239046
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −1.00000 −0.117851
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 12.0000 1.39497
\(75\) 1.00000 0.115470
\(76\) −8.00000 −0.917663
\(77\) 8.00000 0.911685
\(78\) 4.00000 0.452911
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −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
\(85\) 2.00000 0.216930
\(86\) −8.00000 −0.862662
\(87\) 4.00000 0.428845
\(88\) 4.00000 0.426401
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −1.00000 −0.105409
\(91\) 8.00000 0.838628
\(92\) −8.00000 −0.834058
\(93\) −1.00000 −0.103695
\(94\) 4.00000 0.412568
\(95\) −8.00000 −0.820783
\(96\) −1.00000 −0.102062
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 3.00000 0.303046
\(99\) −4.00000 −0.402015
\(100\) 1.00000 0.100000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) −2.00000 −0.198030
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 4.00000 0.392232
\(105\) −2.00000 −0.195180
\(106\) −6.00000 −0.582772
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 1.00000 0.0962250
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 4.00000 0.381385
\(111\) −12.0000 −1.13899
\(112\) −2.00000 −0.188982
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 8.00000 0.749269
\(115\) −8.00000 −0.746004
\(116\) 4.00000 0.371391
\(117\) −4.00000 −0.369800
\(118\) −2.00000 −0.184115
\(119\) −4.00000 −0.366679
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 0.454545
\(122\) −10.0000 −0.905357
\(123\) 10.0000 0.901670
\(124\) −1.00000 −0.0898027
\(125\) 1.00000 0.0894427
\(126\) 2.00000 0.178174
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) 4.00000 0.350823
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) −4.00000 −0.348155
\(133\) 16.0000 1.38738
\(134\) 6.00000 0.518321
\(135\) 1.00000 0.0860663
\(136\) −2.00000 −0.171499
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 8.00000 0.681005
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) −2.00000 −0.169031
\(141\) −4.00000 −0.336861
\(142\) −6.00000 −0.503509
\(143\) 16.0000 1.33799
\(144\) 1.00000 0.0833333
\(145\) 4.00000 0.332182
\(146\) 4.00000 0.331042
\(147\) −3.00000 −0.247436
\(148\) −12.0000 −0.986394
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 8.00000 0.648886
\(153\) 2.00000 0.161690
\(154\) −8.00000 −0.644658
\(155\) −1.00000 −0.0803219
\(156\) −4.00000 −0.320256
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 8.00000 0.636446
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 16.0000 1.26098
\(162\) −1.00000 −0.0785674
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) 10.0000 0.780869
\(165\) −4.00000 −0.311400
\(166\) −4.00000 −0.310460
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 2.00000 0.154303
\(169\) 3.00000 0.230769
\(170\) −2.00000 −0.153393
\(171\) −8.00000 −0.611775
\(172\) 8.00000 0.609994
\(173\) 22.0000 1.67263 0.836315 0.548250i \(-0.184706\pi\)
0.836315 + 0.548250i \(0.184706\pi\)
\(174\) −4.00000 −0.303239
\(175\) −2.00000 −0.151186
\(176\) −4.00000 −0.301511
\(177\) 2.00000 0.150329
\(178\) 0 0
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 1.00000 0.0745356
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) −8.00000 −0.592999
\(183\) 10.0000 0.739221
\(184\) 8.00000 0.589768
\(185\) −12.0000 −0.882258
\(186\) 1.00000 0.0733236
\(187\) −8.00000 −0.585018
\(188\) −4.00000 −0.291730
\(189\) −2.00000 −0.145479
\(190\) 8.00000 0.580381
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 1.00000 0.0721688
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 18.0000 1.29232
\(195\) −4.00000 −0.286446
\(196\) −3.00000 −0.214286
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 4.00000 0.284268
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −6.00000 −0.423207
\(202\) 18.0000 1.26648
\(203\) −8.00000 −0.561490
\(204\) 2.00000 0.140028
\(205\) 10.0000 0.698430
\(206\) 14.0000 0.975426
\(207\) −8.00000 −0.556038
\(208\) −4.00000 −0.277350
\(209\) 32.0000 2.21349
\(210\) 2.00000 0.138013
\(211\) 24.0000 1.65223 0.826114 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(212\) 6.00000 0.412082
\(213\) 6.00000 0.411113
\(214\) −8.00000 −0.546869
\(215\) 8.00000 0.545595
\(216\) −1.00000 −0.0680414
\(217\) 2.00000 0.135769
\(218\) −18.0000 −1.21911
\(219\) −4.00000 −0.270295
\(220\) −4.00000 −0.269680
\(221\) −8.00000 −0.538138
\(222\) 12.0000 0.805387
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 2.00000 0.133631
\(225\) 1.00000 0.0666667
\(226\) 6.00000 0.399114
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) −8.00000 −0.529813
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 8.00000 0.527504
\(231\) 8.00000 0.526361
\(232\) −4.00000 −0.262613
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 4.00000 0.261488
\(235\) −4.00000 −0.260931
\(236\) 2.00000 0.130189
\(237\) −8.00000 −0.519656
\(238\) 4.00000 0.259281
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 1.00000 0.0645497
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000 0.0641500
\(244\) 10.0000 0.640184
\(245\) −3.00000 −0.191663
\(246\) −10.0000 −0.637577
\(247\) 32.0000 2.03611
\(248\) 1.00000 0.0635001
\(249\) 4.00000 0.253490
\(250\) −1.00000 −0.0632456
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) −2.00000 −0.125988
\(253\) 32.0000 2.01182
\(254\) −4.00000 −0.250982
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) −8.00000 −0.498058
\(259\) 24.0000 1.49129
\(260\) −4.00000 −0.248069
\(261\) 4.00000 0.247594
\(262\) −10.0000 −0.617802
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 4.00000 0.246183
\(265\) 6.00000 0.368577
\(266\) −16.0000 −0.981023
\(267\) 0 0
\(268\) −6.00000 −0.366508
\(269\) −12.0000 −0.731653 −0.365826 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 2.00000 0.121268
\(273\) 8.00000 0.484182
\(274\) −6.00000 −0.362473
\(275\) −4.00000 −0.241209
\(276\) −8.00000 −0.481543
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −4.00000 −0.239904
\(279\) −1.00000 −0.0598684
\(280\) 2.00000 0.119523
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 4.00000 0.238197
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 6.00000 0.356034
\(285\) −8.00000 −0.473879
\(286\) −16.0000 −0.946100
\(287\) −20.0000 −1.18056
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) −4.00000 −0.234888
\(291\) −18.0000 −1.05518
\(292\) −4.00000 −0.234082
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 3.00000 0.174964
\(295\) 2.00000 0.116445
\(296\) 12.0000 0.697486
\(297\) −4.00000 −0.232104
\(298\) 18.0000 1.04271
\(299\) 32.0000 1.85061
\(300\) 1.00000 0.0577350
\(301\) −16.0000 −0.922225
\(302\) 16.0000 0.920697
\(303\) −18.0000 −1.03407
\(304\) −8.00000 −0.458831
\(305\) 10.0000 0.572598
\(306\) −2.00000 −0.114332
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 8.00000 0.455842
\(309\) −14.0000 −0.796432
\(310\) 1.00000 0.0567962
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 4.00000 0.226455
\(313\) 20.0000 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(314\) 22.0000 1.24153
\(315\) −2.00000 −0.112687
\(316\) −8.00000 −0.450035
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) −6.00000 −0.336463
\(319\) −16.0000 −0.895828
\(320\) 1.00000 0.0559017
\(321\) 8.00000 0.446516
\(322\) −16.0000 −0.891645
\(323\) −16.0000 −0.890264
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 6.00000 0.332309
\(327\) 18.0000 0.995402
\(328\) −10.0000 −0.552158
\(329\) 8.00000 0.441054
\(330\) 4.00000 0.220193
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 4.00000 0.219529
\(333\) −12.0000 −0.657596
\(334\) 8.00000 0.437741
\(335\) −6.00000 −0.327815
\(336\) −2.00000 −0.109109
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −3.00000 −0.163178
\(339\) −6.00000 −0.325875
\(340\) 2.00000 0.108465
\(341\) 4.00000 0.216612
\(342\) 8.00000 0.432590
\(343\) 20.0000 1.07990
\(344\) −8.00000 −0.431331
\(345\) −8.00000 −0.430706
\(346\) −22.0000 −1.18273
\(347\) −4.00000 −0.214731 −0.107366 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 4.00000 0.214423
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 2.00000 0.106904
\(351\) −4.00000 −0.213504
\(352\) 4.00000 0.213201
\(353\) 34.0000 1.80964 0.904819 0.425797i \(-0.140006\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) −2.00000 −0.106299
\(355\) 6.00000 0.318447
\(356\) 0 0
\(357\) −4.00000 −0.211702
\(358\) 20.0000 1.05703
\(359\) 10.0000 0.527780 0.263890 0.964553i \(-0.414994\pi\)
0.263890 + 0.964553i \(0.414994\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 45.0000 2.36842
\(362\) −18.0000 −0.946059
\(363\) 5.00000 0.262432
\(364\) 8.00000 0.419314
\(365\) −4.00000 −0.209370
\(366\) −10.0000 −0.522708
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −8.00000 −0.417029
\(369\) 10.0000 0.520579
\(370\) 12.0000 0.623850
\(371\) −12.0000 −0.623009
\(372\) −1.00000 −0.0518476
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) 8.00000 0.413670
\(375\) 1.00000 0.0516398
\(376\) 4.00000 0.206284
\(377\) −16.0000 −0.824042
\(378\) 2.00000 0.102869
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −8.00000 −0.410391
\(381\) 4.00000 0.204926
\(382\) −18.0000 −0.920960
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 8.00000 0.407718
\(386\) 2.00000 0.101797
\(387\) 8.00000 0.406663
\(388\) −18.0000 −0.913812
\(389\) −28.0000 −1.41966 −0.709828 0.704375i \(-0.751227\pi\)
−0.709828 + 0.704375i \(0.751227\pi\)
\(390\) 4.00000 0.202548
\(391\) −16.0000 −0.809155
\(392\) 3.00000 0.151523
\(393\) 10.0000 0.504433
\(394\) −10.0000 −0.503793
\(395\) −8.00000 −0.402524
\(396\) −4.00000 −0.201008
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −16.0000 −0.802008
\(399\) 16.0000 0.801002
\(400\) 1.00000 0.0500000
\(401\) 4.00000 0.199750 0.0998752 0.995000i \(-0.468156\pi\)
0.0998752 + 0.995000i \(0.468156\pi\)
\(402\) 6.00000 0.299253
\(403\) 4.00000 0.199254
\(404\) −18.0000 −0.895533
\(405\) 1.00000 0.0496904
\(406\) 8.00000 0.397033
\(407\) 48.0000 2.37927
\(408\) −2.00000 −0.0990148
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) −10.0000 −0.493865
\(411\) 6.00000 0.295958
\(412\) −14.0000 −0.689730
\(413\) −4.00000 −0.196827
\(414\) 8.00000 0.393179
\(415\) 4.00000 0.196352
\(416\) 4.00000 0.196116
\(417\) 4.00000 0.195881
\(418\) −32.0000 −1.56517
\(419\) −10.0000 −0.488532 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) −2.00000 −0.0975900
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −24.0000 −1.16830
\(423\) −4.00000 −0.194487
\(424\) −6.00000 −0.291386
\(425\) 2.00000 0.0970143
\(426\) −6.00000 −0.290701
\(427\) −20.0000 −0.967868
\(428\) 8.00000 0.386695
\(429\) 16.0000 0.772487
\(430\) −8.00000 −0.385794
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 1.00000 0.0481125
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 4.00000 0.191785
\(436\) 18.0000 0.862044
\(437\) 64.0000 3.06154
\(438\) 4.00000 0.191127
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 4.00000 0.190693
\(441\) −3.00000 −0.142857
\(442\) 8.00000 0.380521
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) −12.0000 −0.569495
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) −18.0000 −0.851371
\(448\) −2.00000 −0.0944911
\(449\) 28.0000 1.32140 0.660701 0.750649i \(-0.270259\pi\)
0.660701 + 0.750649i \(0.270259\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −40.0000 −1.88353
\(452\) −6.00000 −0.282216
\(453\) −16.0000 −0.751746
\(454\) −4.00000 −0.187729
\(455\) 8.00000 0.375046
\(456\) 8.00000 0.374634
\(457\) 36.0000 1.68401 0.842004 0.539471i \(-0.181376\pi\)
0.842004 + 0.539471i \(0.181376\pi\)
\(458\) −22.0000 −1.02799
\(459\) 2.00000 0.0933520
\(460\) −8.00000 −0.373002
\(461\) −40.0000 −1.86299 −0.931493 0.363760i \(-0.881493\pi\)
−0.931493 + 0.363760i \(0.881493\pi\)
\(462\) −8.00000 −0.372194
\(463\) −36.0000 −1.67306 −0.836531 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) 4.00000 0.185695
\(465\) −1.00000 −0.0463739
\(466\) 10.0000 0.463241
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) −4.00000 −0.184900
\(469\) 12.0000 0.554109
\(470\) 4.00000 0.184506
\(471\) −22.0000 −1.01371
\(472\) −2.00000 −0.0920575
\(473\) −32.0000 −1.47136
\(474\) 8.00000 0.367452
\(475\) −8.00000 −0.367065
\(476\) −4.00000 −0.183340
\(477\) 6.00000 0.274721
\(478\) 4.00000 0.182956
\(479\) −10.0000 −0.456912 −0.228456 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 48.0000 2.18861
\(482\) −10.0000 −0.455488
\(483\) 16.0000 0.728025
\(484\) 5.00000 0.227273
\(485\) −18.0000 −0.817338
\(486\) −1.00000 −0.0453609
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −10.0000 −0.452679
\(489\) −6.00000 −0.271329
\(490\) 3.00000 0.135526
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 10.0000 0.450835
\(493\) 8.00000 0.360302
\(494\) −32.0000 −1.43975
\(495\) −4.00000 −0.179787
\(496\) −1.00000 −0.0449013
\(497\) −12.0000 −0.538274
\(498\) −4.00000 −0.179244
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) −20.0000 −0.892644
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 2.00000 0.0890871
\(505\) −18.0000 −0.800989
\(506\) −32.0000 −1.42257
\(507\) 3.00000 0.133235
\(508\) 4.00000 0.177471
\(509\) 16.0000 0.709188 0.354594 0.935020i \(-0.384619\pi\)
0.354594 + 0.935020i \(0.384619\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 8.00000 0.353899
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 −0.353209
\(514\) 18.0000 0.793946
\(515\) −14.0000 −0.616914
\(516\) 8.00000 0.352180
\(517\) 16.0000 0.703679
\(518\) −24.0000 −1.05450
\(519\) 22.0000 0.965693
\(520\) 4.00000 0.175412
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −4.00000 −0.175075
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 10.0000 0.436852
\(525\) −2.00000 −0.0872872
\(526\) 0 0
\(527\) −2.00000 −0.0871214
\(528\) −4.00000 −0.174078
\(529\) 41.0000 1.78261
\(530\) −6.00000 −0.260623
\(531\) 2.00000 0.0867926
\(532\) 16.0000 0.693688
\(533\) −40.0000 −1.73259
\(534\) 0 0
\(535\) 8.00000 0.345870
\(536\) 6.00000 0.259161
\(537\) −20.0000 −0.863064
\(538\) 12.0000 0.517357
\(539\) 12.0000 0.516877
\(540\) 1.00000 0.0430331
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −8.00000 −0.343629
\(543\) 18.0000 0.772454
\(544\) −2.00000 −0.0857493
\(545\) 18.0000 0.771035
\(546\) −8.00000 −0.342368
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 6.00000 0.256307
\(549\) 10.0000 0.426790
\(550\) 4.00000 0.170561
\(551\) −32.0000 −1.36325
\(552\) 8.00000 0.340503
\(553\) 16.0000 0.680389
\(554\) −8.00000 −0.339887
\(555\) −12.0000 −0.509372
\(556\) 4.00000 0.169638
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 1.00000 0.0423334
\(559\) −32.0000 −1.35346
\(560\) −2.00000 −0.0845154
\(561\) −8.00000 −0.337760
\(562\) −6.00000 −0.253095
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) −4.00000 −0.168430
\(565\) −6.00000 −0.252422
\(566\) −2.00000 −0.0840663
\(567\) −2.00000 −0.0839921
\(568\) −6.00000 −0.251754
\(569\) −28.0000 −1.17382 −0.586911 0.809652i \(-0.699656\pi\)
−0.586911 + 0.809652i \(0.699656\pi\)
\(570\) 8.00000 0.335083
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 16.0000 0.668994
\(573\) 18.0000 0.751961
\(574\) 20.0000 0.834784
\(575\) −8.00000 −0.333623
\(576\) 1.00000 0.0416667
\(577\) −6.00000 −0.249783 −0.124892 0.992170i \(-0.539858\pi\)
−0.124892 + 0.992170i \(0.539858\pi\)
\(578\) 13.0000 0.540729
\(579\) −2.00000 −0.0831172
\(580\) 4.00000 0.166091
\(581\) −8.00000 −0.331896
\(582\) 18.0000 0.746124
\(583\) −24.0000 −0.993978
\(584\) 4.00000 0.165521
\(585\) −4.00000 −0.165380
\(586\) 6.00000 0.247858
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) −3.00000 −0.123718
\(589\) 8.00000 0.329634
\(590\) −2.00000 −0.0823387
\(591\) 10.0000 0.411345
\(592\) −12.0000 −0.493197
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 4.00000 0.164122
\(595\) −4.00000 −0.163984
\(596\) −18.0000 −0.737309
\(597\) 16.0000 0.654836
\(598\) −32.0000 −1.30858
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 16.0000 0.652111
\(603\) −6.00000 −0.244339
\(604\) −16.0000 −0.651031
\(605\) 5.00000 0.203279
\(606\) 18.0000 0.731200
\(607\) −14.0000 −0.568242 −0.284121 0.958788i \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) 8.00000 0.324443
\(609\) −8.00000 −0.324176
\(610\) −10.0000 −0.404888
\(611\) 16.0000 0.647291
\(612\) 2.00000 0.0808452
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) 2.00000 0.0807134
\(615\) 10.0000 0.403239
\(616\) −8.00000 −0.322329
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 14.0000 0.563163
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −1.00000 −0.0401610
\(621\) −8.00000 −0.321029
\(622\) 30.0000 1.20289
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) −20.0000 −0.799361
\(627\) 32.0000 1.27796
\(628\) −22.0000 −0.877896
\(629\) −24.0000 −0.956943
\(630\) 2.00000 0.0796819
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 8.00000 0.318223
\(633\) 24.0000 0.953914
\(634\) 22.0000 0.873732
\(635\) 4.00000 0.158735
\(636\) 6.00000 0.237915
\(637\) 12.0000 0.475457
\(638\) 16.0000 0.633446
\(639\) 6.00000 0.237356
\(640\) −1.00000 −0.0395285
\(641\) −4.00000 −0.157991 −0.0789953 0.996875i \(-0.525171\pi\)
−0.0789953 + 0.996875i \(0.525171\pi\)
\(642\) −8.00000 −0.315735
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 16.0000 0.630488
\(645\) 8.00000 0.315000
\(646\) 16.0000 0.629512
\(647\) 8.00000 0.314512 0.157256 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −8.00000 −0.314027
\(650\) 4.00000 0.156893
\(651\) 2.00000 0.0783862
\(652\) −6.00000 −0.234978
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −18.0000 −0.703856
\(655\) 10.0000 0.390732
\(656\) 10.0000 0.390434
\(657\) −4.00000 −0.156055
\(658\) −8.00000 −0.311872
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) −4.00000 −0.155700
\(661\) 46.0000 1.78919 0.894596 0.446875i \(-0.147463\pi\)
0.894596 + 0.446875i \(0.147463\pi\)
\(662\) 12.0000 0.466393
\(663\) −8.00000 −0.310694
\(664\) −4.00000 −0.155230
\(665\) 16.0000 0.620453
\(666\) 12.0000 0.464991
\(667\) −32.0000 −1.23904
\(668\) −8.00000 −0.309529
\(669\) −8.00000 −0.309298
\(670\) 6.00000 0.231800
\(671\) −40.0000 −1.54418
\(672\) 2.00000 0.0771517
\(673\) 8.00000 0.308377 0.154189 0.988041i \(-0.450724\pi\)
0.154189 + 0.988041i \(0.450724\pi\)
\(674\) 32.0000 1.23259
\(675\) 1.00000 0.0384900
\(676\) 3.00000 0.115385
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 6.00000 0.230429
\(679\) 36.0000 1.38155
\(680\) −2.00000 −0.0766965
\(681\) 4.00000 0.153280
\(682\) −4.00000 −0.153168
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) −8.00000 −0.305888
\(685\) 6.00000 0.229248
\(686\) −20.0000 −0.763604
\(687\) 22.0000 0.839352
\(688\) 8.00000 0.304997
\(689\) −24.0000 −0.914327
\(690\) 8.00000 0.304555
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 22.0000 0.836315
\(693\) 8.00000 0.303895
\(694\) 4.00000 0.151838
\(695\) 4.00000 0.151729
\(696\) −4.00000 −0.151620
\(697\) 20.0000 0.757554
\(698\) 30.0000 1.13552
\(699\) −10.0000 −0.378235
\(700\) −2.00000 −0.0755929
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 4.00000 0.150970
\(703\) 96.0000 3.62071
\(704\) −4.00000 −0.150756
\(705\) −4.00000 −0.150649
\(706\) −34.0000 −1.27961
\(707\) 36.0000 1.35392
\(708\) 2.00000 0.0751646
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) −6.00000 −0.225176
\(711\) −8.00000 −0.300023
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 4.00000 0.149696
\(715\) 16.0000 0.598366
\(716\) −20.0000 −0.747435
\(717\) −4.00000 −0.149383
\(718\) −10.0000 −0.373197
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 1.00000 0.0372678
\(721\) 28.0000 1.04277
\(722\) −45.0000 −1.67473
\(723\) 10.0000 0.371904
\(724\) 18.0000 0.668965
\(725\) 4.00000 0.148556
\(726\) −5.00000 −0.185567
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) 4.00000 0.148047
\(731\) 16.0000 0.591781
\(732\) 10.0000 0.369611
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) 8.00000 0.295285
\(735\) −3.00000 −0.110657
\(736\) 8.00000 0.294884
\(737\) 24.0000 0.884051
\(738\) −10.0000 −0.368105
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −12.0000 −0.441129
\(741\) 32.0000 1.17555
\(742\) 12.0000 0.440534
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 1.00000 0.0366618
\(745\) −18.0000 −0.659469
\(746\) −34.0000 −1.24483
\(747\) 4.00000 0.146352
\(748\) −8.00000 −0.292509
\(749\) −16.0000 −0.584627
\(750\) −1.00000 −0.0365148
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) −4.00000 −0.145865
\(753\) 20.0000 0.728841
\(754\) 16.0000 0.582686
\(755\) −16.0000 −0.582300
\(756\) −2.00000 −0.0727393
\(757\) 36.0000 1.30844 0.654221 0.756303i \(-0.272997\pi\)
0.654221 + 0.756303i \(0.272997\pi\)
\(758\) −16.0000 −0.581146
\(759\) 32.0000 1.16153
\(760\) 8.00000 0.290191
\(761\) −20.0000 −0.724999 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(762\) −4.00000 −0.144905
\(763\) −36.0000 −1.30329
\(764\) 18.0000 0.651217
\(765\) 2.00000 0.0723102
\(766\) 16.0000 0.578103
\(767\) −8.00000 −0.288863
\(768\) 1.00000 0.0360844
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) −8.00000 −0.288300
\(771\) −18.0000 −0.648254
\(772\) −2.00000 −0.0719816
\(773\) 14.0000 0.503545 0.251773 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) −8.00000 −0.287554
\(775\) −1.00000 −0.0359211
\(776\) 18.0000 0.646162
\(777\) 24.0000 0.860995
\(778\) 28.0000 1.00385
\(779\) −80.0000 −2.86630
\(780\) −4.00000 −0.143223
\(781\) −24.0000 −0.858788
\(782\) 16.0000 0.572159
\(783\) 4.00000 0.142948
\(784\) −3.00000 −0.107143
\(785\) −22.0000 −0.785214
\(786\) −10.0000 −0.356688
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 10.0000 0.356235
\(789\) 0 0
\(790\) 8.00000 0.284627
\(791\) 12.0000 0.426671
\(792\) 4.00000 0.142134
\(793\) −40.0000 −1.42044
\(794\) 34.0000 1.20661
\(795\) 6.00000 0.212798
\(796\) 16.0000 0.567105
\(797\) −30.0000 −1.06265 −0.531327 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) −16.0000 −0.566394
\(799\) −8.00000 −0.283020
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −4.00000 −0.141245
\(803\) 16.0000 0.564628
\(804\) −6.00000 −0.211604
\(805\) 16.0000 0.563926
\(806\) −4.00000 −0.140894
\(807\) −12.0000 −0.422420
\(808\) 18.0000 0.633238
\(809\) 28.0000 0.984428 0.492214 0.870474i \(-0.336188\pi\)
0.492214 + 0.870474i \(0.336188\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −8.00000 −0.280745
\(813\) 8.00000 0.280572
\(814\) −48.0000 −1.68240
\(815\) −6.00000 −0.210171
\(816\) 2.00000 0.0700140
\(817\) −64.0000 −2.23908
\(818\) −6.00000 −0.209785
\(819\) 8.00000 0.279543
\(820\) 10.0000 0.349215
\(821\) −4.00000 −0.139601 −0.0698005 0.997561i \(-0.522236\pi\)
−0.0698005 + 0.997561i \(0.522236\pi\)
\(822\) −6.00000 −0.209274
\(823\) 28.0000 0.976019 0.488009 0.872838i \(-0.337723\pi\)
0.488009 + 0.872838i \(0.337723\pi\)
\(824\) 14.0000 0.487713
\(825\) −4.00000 −0.139262
\(826\) 4.00000 0.139178
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) −8.00000 −0.278019
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) −4.00000 −0.138842
\(831\) 8.00000 0.277517
\(832\) −4.00000 −0.138675
\(833\) −6.00000 −0.207888
\(834\) −4.00000 −0.138509
\(835\) −8.00000 −0.276851
\(836\) 32.0000 1.10674
\(837\) −1.00000 −0.0345651
\(838\) 10.0000 0.345444
\(839\) 42.0000 1.45000 0.725001 0.688748i \(-0.241839\pi\)
0.725001 + 0.688748i \(0.241839\pi\)
\(840\) 2.00000 0.0690066
\(841\) −13.0000 −0.448276
\(842\) −2.00000 −0.0689246
\(843\) 6.00000 0.206651
\(844\) 24.0000 0.826114
\(845\) 3.00000 0.103203
\(846\) 4.00000 0.137523
\(847\) −10.0000 −0.343604
\(848\) 6.00000 0.206041
\(849\) 2.00000 0.0686398
\(850\) −2.00000 −0.0685994
\(851\) 96.0000 3.29084
\(852\) 6.00000 0.205557
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) 20.0000 0.684386
\(855\) −8.00000 −0.273594
\(856\) −8.00000 −0.273434
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) −16.0000 −0.546231
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 8.00000 0.272798
\(861\) −20.0000 −0.681598
\(862\) 30.0000 1.02180
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 22.0000 0.748022
\(866\) −4.00000 −0.135926
\(867\) −13.0000 −0.441503
\(868\) 2.00000 0.0678844
\(869\) 32.0000 1.08553
\(870\) −4.00000 −0.135613
\(871\) 24.0000 0.813209
\(872\) −18.0000 −0.609557
\(873\) −18.0000 −0.609208
\(874\) −64.0000 −2.16483
\(875\) −2.00000 −0.0676123
\(876\) −4.00000 −0.135147
\(877\) −2.00000 −0.0675352 −0.0337676 0.999430i \(-0.510751\pi\)
−0.0337676 + 0.999430i \(0.510751\pi\)
\(878\) 40.0000 1.34993
\(879\) −6.00000 −0.202375
\(880\) −4.00000 −0.134840
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 3.00000 0.101015
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −8.00000 −0.269069
\(885\) 2.00000 0.0672293
\(886\) −4.00000 −0.134383
\(887\) −56.0000 −1.88030 −0.940148 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 12.0000 0.402694
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) −8.00000 −0.267860
\(893\) 32.0000 1.07084
\(894\) 18.0000 0.602010
\(895\) −20.0000 −0.668526
\(896\) 2.00000 0.0668153
\(897\) 32.0000 1.06845
\(898\) −28.0000 −0.934372
\(899\) −4.00000 −0.133407
\(900\) 1.00000 0.0333333
\(901\) 12.0000 0.399778
\(902\) 40.0000 1.33185
\(903\) −16.0000 −0.532447
\(904\) 6.00000 0.199557
\(905\) 18.0000 0.598340
\(906\) 16.0000 0.531564
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 4.00000 0.132745
\(909\) −18.0000 −0.597022
\(910\) −8.00000 −0.265197
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) −8.00000 −0.264906
\(913\) −16.0000 −0.529523
\(914\) −36.0000 −1.19077
\(915\) 10.0000 0.330590
\(916\) 22.0000 0.726900
\(917\) −20.0000 −0.660458
\(918\) −2.00000 −0.0660098
\(919\) 4.00000 0.131948 0.0659739 0.997821i \(-0.478985\pi\)
0.0659739 + 0.997821i \(0.478985\pi\)
\(920\) 8.00000 0.263752
\(921\) −2.00000 −0.0659022
\(922\) 40.0000 1.31733
\(923\) −24.0000 −0.789970
\(924\) 8.00000 0.263181
\(925\) −12.0000 −0.394558
\(926\) 36.0000 1.18303
\(927\) −14.0000 −0.459820
\(928\) −4.00000 −0.131306
\(929\) 32.0000 1.04989 0.524943 0.851137i \(-0.324087\pi\)
0.524943 + 0.851137i \(0.324087\pi\)
\(930\) 1.00000 0.0327913
\(931\) 24.0000 0.786568
\(932\) −10.0000 −0.327561
\(933\) −30.0000 −0.982156
\(934\) 0 0
\(935\) −8.00000 −0.261628
\(936\) 4.00000 0.130744
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) −12.0000 −0.391814
\(939\) 20.0000 0.652675
\(940\) −4.00000 −0.130466
\(941\) 12.0000 0.391189 0.195594 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(942\) 22.0000 0.716799
\(943\) −80.0000 −2.60516
\(944\) 2.00000 0.0650945
\(945\) −2.00000 −0.0650600
\(946\) 32.0000 1.04041
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) −8.00000 −0.259828
\(949\) 16.0000 0.519382
\(950\) 8.00000 0.259554
\(951\) −22.0000 −0.713399
\(952\) 4.00000 0.129641
\(953\) 22.0000 0.712650 0.356325 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) −6.00000 −0.194257
\(955\) 18.0000 0.582466
\(956\) −4.00000 −0.129369
\(957\) −16.0000 −0.517207
\(958\) 10.0000 0.323085
\(959\) −12.0000 −0.387500
\(960\) 1.00000 0.0322749
\(961\) 1.00000 0.0322581
\(962\) −48.0000 −1.54758
\(963\) 8.00000 0.257796
\(964\) 10.0000 0.322078
\(965\) −2.00000 −0.0643823
\(966\) −16.0000 −0.514792
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −5.00000 −0.160706
\(969\) −16.0000 −0.513994
\(970\) 18.0000 0.577945
\(971\) −2.00000 −0.0641831 −0.0320915 0.999485i \(-0.510217\pi\)
−0.0320915 + 0.999485i \(0.510217\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.00000 −0.256468
\(974\) 12.0000 0.384505
\(975\) −4.00000 −0.128103
\(976\) 10.0000 0.320092
\(977\) −46.0000 −1.47167 −0.735835 0.677161i \(-0.763210\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(978\) 6.00000 0.191859
\(979\) 0 0
\(980\) −3.00000 −0.0958315
\(981\) 18.0000 0.574696
\(982\) 8.00000 0.255290
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −10.0000 −0.318788
\(985\) 10.0000 0.318626
\(986\) −8.00000 −0.254772
\(987\) 8.00000 0.254643
\(988\) 32.0000 1.01806
\(989\) −64.0000 −2.03508
\(990\) 4.00000 0.127128
\(991\) −56.0000 −1.77890 −0.889449 0.457034i \(-0.848912\pi\)
−0.889449 + 0.457034i \(0.848912\pi\)
\(992\) 1.00000 0.0317500
\(993\) −12.0000 −0.380808
\(994\) 12.0000 0.380617
\(995\) 16.0000 0.507234
\(996\) 4.00000 0.126745
\(997\) 18.0000 0.570066 0.285033 0.958518i \(-0.407995\pi\)
0.285033 + 0.958518i \(0.407995\pi\)
\(998\) 36.0000 1.13956
\(999\) −12.0000 −0.379663
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 930.2.a.h.1.1 1
3.2 odd 2 2790.2.a.p.1.1 1
4.3 odd 2 7440.2.a.m.1.1 1
5.2 odd 4 4650.2.d.b.3349.1 2
5.3 odd 4 4650.2.d.b.3349.2 2
5.4 even 2 4650.2.a.bg.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.h.1.1 1 1.1 even 1 trivial
2790.2.a.p.1.1 1 3.2 odd 2
4650.2.a.bg.1.1 1 5.4 even 2
4650.2.d.b.3349.1 2 5.2 odd 4
4650.2.d.b.3349.2 2 5.3 odd 4
7440.2.a.m.1.1 1 4.3 odd 2