Properties

Label 9555.2.a.v.1.1
Level $9555$
Weight $2$
Character 9555.1
Self dual yes
Analytic conductor $76.297$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9555.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(76.2970591313\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9555.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} -4.00000 q^{16} +1.00000 q^{17} +2.00000 q^{18} +2.00000 q^{19} -2.00000 q^{20} -2.00000 q^{22} -3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -2.00000 q^{29} -2.00000 q^{30} +6.00000 q^{31} -8.00000 q^{32} -1.00000 q^{33} +2.00000 q^{34} +2.00000 q^{36} +11.0000 q^{37} +4.00000 q^{38} +1.00000 q^{39} +5.00000 q^{41} +4.00000 q^{43} -2.00000 q^{44} -1.00000 q^{45} -6.00000 q^{46} +10.0000 q^{47} -4.00000 q^{48} +2.00000 q^{50} +1.00000 q^{51} +2.00000 q^{52} +11.0000 q^{53} +2.00000 q^{54} +1.00000 q^{55} +2.00000 q^{57} -4.00000 q^{58} -8.00000 q^{59} -2.00000 q^{60} -13.0000 q^{61} +12.0000 q^{62} -8.00000 q^{64} -1.00000 q^{65} -2.00000 q^{66} +12.0000 q^{67} +2.00000 q^{68} -3.00000 q^{69} -5.00000 q^{71} -10.0000 q^{73} +22.0000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +2.00000 q^{78} -3.00000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +12.0000 q^{83} -1.00000 q^{85} +8.00000 q^{86} -2.00000 q^{87} +15.0000 q^{89} -2.00000 q^{90} -6.00000 q^{92} +6.00000 q^{93} +20.0000 q^{94} -2.00000 q^{95} -8.00000 q^{96} -17.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.00000 1.00000
\(5\) −1.00000 −0.447214
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 2.00000 0.577350
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −4.00000 −1.00000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 2.00000 0.471405
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −2.00000 −0.365148
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −8.00000 −1.41421
\(33\) −1.00000 −0.174078
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 11.0000 1.80839 0.904194 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 4.00000 0.648886
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −2.00000 −0.301511
\(45\) −1.00000 −0.149071
\(46\) −6.00000 −0.884652
\(47\) 10.0000 1.45865 0.729325 0.684167i \(-0.239834\pi\)
0.729325 + 0.684167i \(0.239834\pi\)
\(48\) −4.00000 −0.577350
\(49\) 0 0
\(50\) 2.00000 0.282843
\(51\) 1.00000 0.140028
\(52\) 2.00000 0.277350
\(53\) 11.0000 1.51097 0.755483 0.655168i \(-0.227402\pi\)
0.755483 + 0.655168i \(0.227402\pi\)
\(54\) 2.00000 0.272166
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) −4.00000 −0.525226
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) −2.00000 −0.258199
\(61\) −13.0000 −1.66448 −0.832240 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 12.0000 1.52400
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −1.00000 −0.124035
\(66\) −2.00000 −0.246183
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 2.00000 0.242536
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 22.0000 2.55745
\(75\) 1.00000 0.115470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 8.00000 0.862662
\(87\) −2.00000 −0.214423
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) 6.00000 0.622171
\(94\) 20.0000 2.06284
\(95\) −2.00000 −0.205196
\(96\) −8.00000 −0.816497
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 2.00000 0.200000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 2.00000 0.198030
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 22.0000 2.13683
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) 2.00000 0.192450
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 2.00000 0.190693
\(111\) 11.0000 1.04407
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 4.00000 0.374634
\(115\) 3.00000 0.279751
\(116\) −4.00000 −0.371391
\(117\) 1.00000 0.0924500
\(118\) −16.0000 −1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −26.0000 −2.35393
\(123\) 5.00000 0.450835
\(124\) 12.0000 1.07763
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 10.0000 0.887357 0.443678 0.896186i \(-0.353673\pi\)
0.443678 + 0.896186i \(0.353673\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) −2.00000 −0.175412
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) −2.00000 −0.174078
\(133\) 0 0
\(134\) 24.0000 2.07328
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −6.00000 −0.510754
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 10.0000 0.842152
\(142\) −10.0000 −0.839181
\(143\) −1.00000 −0.0836242
\(144\) −4.00000 −0.333333
\(145\) 2.00000 0.166091
\(146\) −20.0000 −1.65521
\(147\) 0 0
\(148\) 22.0000 1.80839
\(149\) 13.0000 1.06500 0.532501 0.846430i \(-0.321252\pi\)
0.532501 + 0.846430i \(0.321252\pi\)
\(150\) 2.00000 0.163299
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 2.00000 0.160128
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −6.00000 −0.477334
\(159\) 11.0000 0.872357
\(160\) 8.00000 0.632456
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) −13.0000 −1.01824 −0.509119 0.860696i \(-0.670029\pi\)
−0.509119 + 0.860696i \(0.670029\pi\)
\(164\) 10.0000 0.780869
\(165\) 1.00000 0.0778499
\(166\) 24.0000 1.86276
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −2.00000 −0.153393
\(171\) 2.00000 0.152944
\(172\) 8.00000 0.609994
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) −8.00000 −0.601317
\(178\) 30.0000 2.24860
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) −2.00000 −0.149071
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) −13.0000 −0.960988
\(184\) 0 0
\(185\) −11.0000 −0.808736
\(186\) 12.0000 0.879883
\(187\) −1.00000 −0.0731272
\(188\) 20.0000 1.45865
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −8.00000 −0.577350
\(193\) −13.0000 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) −34.0000 −2.44106
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −2.00000 −0.142134
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 0 0
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −5.00000 −0.349215
\(206\) 32.0000 2.22955
\(207\) −3.00000 −0.208514
\(208\) −4.00000 −0.277350
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 22.0000 1.51097
\(213\) −5.00000 −0.342594
\(214\) 18.0000 1.23045
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) 0 0
\(218\) −32.0000 −2.16731
\(219\) −10.0000 −0.675737
\(220\) 2.00000 0.134840
\(221\) 1.00000 0.0672673
\(222\) 22.0000 1.47654
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 28.0000 1.86253
\(227\) −22.0000 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(228\) 4.00000 0.264906
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 0 0
\(233\) −27.0000 −1.76883 −0.884414 0.466702i \(-0.845442\pi\)
−0.884414 + 0.466702i \(0.845442\pi\)
\(234\) 2.00000 0.130744
\(235\) −10.0000 −0.652328
\(236\) −16.0000 −1.04151
\(237\) −3.00000 −0.194871
\(238\) 0 0
\(239\) −13.0000 −0.840900 −0.420450 0.907316i \(-0.638128\pi\)
−0.420450 + 0.907316i \(0.638128\pi\)
\(240\) 4.00000 0.258199
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −20.0000 −1.28565
\(243\) 1.00000 0.0641500
\(244\) −26.0000 −1.66448
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 12.0000 0.760469
\(250\) −2.00000 −0.126491
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 20.0000 1.25491
\(255\) −1.00000 −0.0626224
\(256\) 16.0000 1.00000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 8.00000 0.498058
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) −2.00000 −0.123797
\(262\) 12.0000 0.741362
\(263\) −8.00000 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 0 0
\(265\) −11.0000 −0.675725
\(266\) 0 0
\(267\) 15.0000 0.917985
\(268\) 24.0000 1.46603
\(269\) 4.00000 0.243884 0.121942 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(270\) −2.00000 −0.121716
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 36.0000 2.17484
\(275\) −1.00000 −0.0603023
\(276\) −6.00000 −0.361158
\(277\) −18.0000 −1.08152 −0.540758 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 2.00000 0.119952
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 20.0000 1.19098
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) −10.0000 −0.593391
\(285\) −2.00000 −0.118470
\(286\) −2.00000 −0.118262
\(287\) 0 0
\(288\) −8.00000 −0.471405
\(289\) −16.0000 −0.941176
\(290\) 4.00000 0.234888
\(291\) −17.0000 −0.996558
\(292\) −20.0000 −1.17041
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) −1.00000 −0.0580259
\(298\) 26.0000 1.50614
\(299\) −3.00000 −0.173494
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) 32.0000 1.84139
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) 13.0000 0.744378
\(306\) 2.00000 0.114332
\(307\) 5.00000 0.285365 0.142683 0.989769i \(-0.454427\pi\)
0.142683 + 0.989769i \(0.454427\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −12.0000 −0.681554
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 20.0000 1.12867
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) 28.0000 1.57264 0.786318 0.617822i \(-0.211985\pi\)
0.786318 + 0.617822i \(0.211985\pi\)
\(318\) 22.0000 1.23370
\(319\) 2.00000 0.111979
\(320\) 8.00000 0.447214
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 2.00000 0.111111
\(325\) 1.00000 0.0554700
\(326\) −26.0000 −1.44001
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) 0 0
\(330\) 2.00000 0.110096
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 24.0000 1.31717
\(333\) 11.0000 0.602796
\(334\) 24.0000 1.31322
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 2.00000 0.108786
\(339\) 14.0000 0.760376
\(340\) −2.00000 −0.108465
\(341\) −6.00000 −0.324918
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 0 0
\(345\) 3.00000 0.161515
\(346\) 12.0000 0.645124
\(347\) −19.0000 −1.01997 −0.509987 0.860182i \(-0.670350\pi\)
−0.509987 + 0.860182i \(0.670350\pi\)
\(348\) −4.00000 −0.214423
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 8.00000 0.426401
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −16.0000 −0.850390
\(355\) 5.00000 0.265372
\(356\) 30.0000 1.59000
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 14.0000 0.735824
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) −26.0000 −1.35904
\(367\) −36.0000 −1.87918 −0.939592 0.342296i \(-0.888796\pi\)
−0.939592 + 0.342296i \(0.888796\pi\)
\(368\) 12.0000 0.625543
\(369\) 5.00000 0.260290
\(370\) −22.0000 −1.14373
\(371\) 0 0
\(372\) 12.0000 0.622171
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) −2.00000 −0.103418
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) −4.00000 −0.205196
\(381\) 10.0000 0.512316
\(382\) −16.0000 −0.818631
\(383\) 30.0000 1.53293 0.766464 0.642287i \(-0.222014\pi\)
0.766464 + 0.642287i \(0.222014\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) 4.00000 0.203331
\(388\) −34.0000 −1.72609
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) −2.00000 −0.101274
\(391\) −3.00000 −0.151717
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 0 0
\(395\) 3.00000 0.150946
\(396\) −2.00000 −0.100504
\(397\) 29.0000 1.45547 0.727734 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 24.0000 1.19701
\(403\) 6.00000 0.298881
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −11.0000 −0.545250
\(408\) 0 0
\(409\) −2.00000 −0.0988936 −0.0494468 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) −10.0000 −0.493865
\(411\) 18.0000 0.887875
\(412\) 32.0000 1.57653
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) −12.0000 −0.589057
\(416\) −8.00000 −0.392232
\(417\) 1.00000 0.0489702
\(418\) −4.00000 −0.195646
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) −8.00000 −0.389434
\(423\) 10.0000 0.486217
\(424\) 0 0
\(425\) 1.00000 0.0485071
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) 18.0000 0.870063
\(429\) −1.00000 −0.0482805
\(430\) −8.00000 −0.385794
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) −4.00000 −0.192450
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 2.00000 0.0958927
\(436\) −32.0000 −1.53252
\(437\) −6.00000 −0.287019
\(438\) −20.0000 −0.955637
\(439\) 17.0000 0.811366 0.405683 0.914014i \(-0.367034\pi\)
0.405683 + 0.914014i \(0.367034\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 22.0000 1.04407
\(445\) −15.0000 −0.711068
\(446\) −16.0000 −0.757622
\(447\) 13.0000 0.614879
\(448\) 0 0
\(449\) −13.0000 −0.613508 −0.306754 0.951789i \(-0.599243\pi\)
−0.306754 + 0.951789i \(0.599243\pi\)
\(450\) 2.00000 0.0942809
\(451\) −5.00000 −0.235441
\(452\) 28.0000 1.31701
\(453\) 16.0000 0.751746
\(454\) −44.0000 −2.06502
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) −36.0000 −1.68217
\(459\) 1.00000 0.0466760
\(460\) 6.00000 0.279751
\(461\) −15.0000 −0.698620 −0.349310 0.937007i \(-0.613584\pi\)
−0.349310 + 0.937007i \(0.613584\pi\)
\(462\) 0 0
\(463\) 27.0000 1.25480 0.627398 0.778699i \(-0.284120\pi\)
0.627398 + 0.778699i \(0.284120\pi\)
\(464\) 8.00000 0.371391
\(465\) −6.00000 −0.278243
\(466\) −54.0000 −2.50150
\(467\) 23.0000 1.06431 0.532157 0.846646i \(-0.321382\pi\)
0.532157 + 0.846646i \(0.321382\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) −20.0000 −0.922531
\(471\) 10.0000 0.460776
\(472\) 0 0
\(473\) −4.00000 −0.183920
\(474\) −6.00000 −0.275589
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 11.0000 0.503655
\(478\) −26.0000 −1.18921
\(479\) −9.00000 −0.411220 −0.205610 0.978634i \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 8.00000 0.365148
\(481\) 11.0000 0.501557
\(482\) 4.00000 0.182195
\(483\) 0 0
\(484\) −20.0000 −0.909091
\(485\) 17.0000 0.771930
\(486\) 2.00000 0.0907218
\(487\) −7.00000 −0.317200 −0.158600 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(488\) 0 0
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 10.0000 0.450835
\(493\) −2.00000 −0.0900755
\(494\) 4.00000 0.179969
\(495\) 1.00000 0.0449467
\(496\) −24.0000 −1.07763
\(497\) 0 0
\(498\) 24.0000 1.07547
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) −2.00000 −0.0894427
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 6.00000 0.266733
\(507\) 1.00000 0.0444116
\(508\) 20.0000 0.887357
\(509\) 7.00000 0.310270 0.155135 0.987893i \(-0.450419\pi\)
0.155135 + 0.987893i \(0.450419\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) 2.00000 0.0883022
\(514\) 36.0000 1.58789
\(515\) −16.0000 −0.705044
\(516\) 8.00000 0.352180
\(517\) −10.0000 −0.439799
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) −4.00000 −0.175075
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 6.00000 0.261364
\(528\) 4.00000 0.174078
\(529\) −14.0000 −0.608696
\(530\) −22.0000 −0.955619
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 5.00000 0.216574
\(534\) 30.0000 1.29823
\(535\) −9.00000 −0.389104
\(536\) 0 0
\(537\) 2.00000 0.0863064
\(538\) 8.00000 0.344904
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) −44.0000 −1.88996
\(543\) 7.00000 0.300399
\(544\) −8.00000 −0.342997
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) 36.0000 1.53784
\(549\) −13.0000 −0.554826
\(550\) −2.00000 −0.0852803
\(551\) −4.00000 −0.170406
\(552\) 0 0
\(553\) 0 0
\(554\) −36.0000 −1.52949
\(555\) −11.0000 −0.466924
\(556\) 2.00000 0.0848189
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 12.0000 0.508001
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) 60.0000 2.53095
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 20.0000 0.842152
\(565\) −14.0000 −0.588984
\(566\) 24.0000 1.00880
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) −4.00000 −0.167542
\(571\) −31.0000 −1.29731 −0.648655 0.761083i \(-0.724668\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) −2.00000 −0.0836242
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) −3.00000 −0.125109
\(576\) −8.00000 −0.333333
\(577\) 19.0000 0.790980 0.395490 0.918470i \(-0.370575\pi\)
0.395490 + 0.918470i \(0.370575\pi\)
\(578\) −32.0000 −1.33102
\(579\) −13.0000 −0.540262
\(580\) 4.00000 0.166091
\(581\) 0 0
\(582\) −34.0000 −1.40935
\(583\) −11.0000 −0.455573
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) −48.0000 −1.98286
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 16.0000 0.658710
\(591\) 0 0
\(592\) −44.0000 −1.80839
\(593\) −4.00000 −0.164260 −0.0821302 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 26.0000 1.06500
\(597\) −4.00000 −0.163709
\(598\) −6.00000 −0.245358
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 37.0000 1.50926 0.754631 0.656150i \(-0.227816\pi\)
0.754631 + 0.656150i \(0.227816\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 32.0000 1.30206
\(605\) 10.0000 0.406558
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −16.0000 −0.648886
\(609\) 0 0
\(610\) 26.0000 1.05271
\(611\) 10.0000 0.404557
\(612\) 2.00000 0.0808452
\(613\) 13.0000 0.525065 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(614\) 10.0000 0.403567
\(615\) −5.00000 −0.201619
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 32.0000 1.28723
\(619\) 34.0000 1.36658 0.683288 0.730149i \(-0.260549\pi\)
0.683288 + 0.730149i \(0.260549\pi\)
\(620\) −12.0000 −0.481932
\(621\) −3.00000 −0.120386
\(622\) −48.0000 −1.92462
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) 20.0000 0.799361
\(627\) −2.00000 −0.0798723
\(628\) 20.0000 0.798087
\(629\) 11.0000 0.438599
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 56.0000 2.22404
\(635\) −10.0000 −0.396838
\(636\) 22.0000 0.872357
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) −5.00000 −0.197797
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 18.0000 0.710403
\(643\) −15.0000 −0.591542 −0.295771 0.955259i \(-0.595577\pi\)
−0.295771 + 0.955259i \(0.595577\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 4.00000 0.157378
\(647\) −47.0000 −1.84776 −0.923880 0.382682i \(-0.875001\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) −26.0000 −1.01824
\(653\) 22.0000 0.860927 0.430463 0.902608i \(-0.358350\pi\)
0.430463 + 0.902608i \(0.358350\pi\)
\(654\) −32.0000 −1.25130
\(655\) −6.00000 −0.234439
\(656\) −20.0000 −0.780869
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 2.00000 0.0778499
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 0 0
\(663\) 1.00000 0.0388368
\(664\) 0 0
\(665\) 0 0
\(666\) 22.0000 0.852483
\(667\) 6.00000 0.232321
\(668\) 24.0000 0.928588
\(669\) −8.00000 −0.309298
\(670\) −24.0000 −0.927201
\(671\) 13.0000 0.501859
\(672\) 0 0
\(673\) −6.00000 −0.231283 −0.115642 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 8.00000 0.308148
\(675\) 1.00000 0.0384900
\(676\) 2.00000 0.0769231
\(677\) −3.00000 −0.115299 −0.0576497 0.998337i \(-0.518361\pi\)
−0.0576497 + 0.998337i \(0.518361\pi\)
\(678\) 28.0000 1.07533
\(679\) 0 0
\(680\) 0 0
\(681\) −22.0000 −0.843042
\(682\) −12.0000 −0.459504
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 4.00000 0.152944
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) −18.0000 −0.686743
\(688\) −16.0000 −0.609994
\(689\) 11.0000 0.419067
\(690\) 6.00000 0.228416
\(691\) −22.0000 −0.836919 −0.418460 0.908235i \(-0.637430\pi\)
−0.418460 + 0.908235i \(0.637430\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −38.0000 −1.44246
\(695\) −1.00000 −0.0379322
\(696\) 0 0
\(697\) 5.00000 0.189389
\(698\) 16.0000 0.605609
\(699\) −27.0000 −1.02123
\(700\) 0 0
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 2.00000 0.0754851
\(703\) 22.0000 0.829746
\(704\) 8.00000 0.301511
\(705\) −10.0000 −0.376622
\(706\) −12.0000 −0.451626
\(707\) 0 0
\(708\) −16.0000 −0.601317
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 10.0000 0.375293
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −18.0000 −0.674105
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 4.00000 0.149487
\(717\) −13.0000 −0.485494
\(718\) 48.0000 1.79134
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 4.00000 0.149071
\(721\) 0 0
\(722\) −30.0000 −1.11648
\(723\) 2.00000 0.0743808
\(724\) 14.0000 0.520306
\(725\) −2.00000 −0.0742781
\(726\) −20.0000 −0.742270
\(727\) −38.0000 −1.40934 −0.704671 0.709534i \(-0.748905\pi\)
−0.704671 + 0.709534i \(0.748905\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 20.0000 0.740233
\(731\) 4.00000 0.147945
\(732\) −26.0000 −0.960988
\(733\) 49.0000 1.80986 0.904928 0.425564i \(-0.139924\pi\)
0.904928 + 0.425564i \(0.139924\pi\)
\(734\) −72.0000 −2.65757
\(735\) 0 0
\(736\) 24.0000 0.884652
\(737\) −12.0000 −0.442026
\(738\) 10.0000 0.368105
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) −22.0000 −0.808736
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 0 0
\(745\) −13.0000 −0.476283
\(746\) 8.00000 0.292901
\(747\) 12.0000 0.439057
\(748\) −2.00000 −0.0731272
\(749\) 0 0
\(750\) −2.00000 −0.0730297
\(751\) −5.00000 −0.182453 −0.0912263 0.995830i \(-0.529079\pi\)
−0.0912263 + 0.995830i \(0.529079\pi\)
\(752\) −40.0000 −1.45865
\(753\) 0 0
\(754\) −4.00000 −0.145671
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −8.00000 −0.290765 −0.145382 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) −28.0000 −1.01701
\(759\) 3.00000 0.108893
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 20.0000 0.724524
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −1.00000 −0.0361551
\(766\) 60.0000 2.16789
\(767\) −8.00000 −0.288863
\(768\) 16.0000 0.577350
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −26.0000 −0.935760
\(773\) −36.0000 −1.29483 −0.647415 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) 8.00000 0.287554
\(775\) 6.00000 0.215526
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.0000 0.358287
\(780\) −2.00000 −0.0716115
\(781\) 5.00000 0.178914
\(782\) −6.00000 −0.214560
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) −10.0000 −0.356915
\(786\) 12.0000 0.428026
\(787\) −52.0000 −1.85360 −0.926800 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) 0 0
\(789\) −8.00000 −0.284808
\(790\) 6.00000 0.213470
\(791\) 0 0
\(792\) 0 0
\(793\) −13.0000 −0.461644
\(794\) 58.0000 2.05834
\(795\) −11.0000 −0.390130
\(796\) −8.00000 −0.283552
\(797\) 47.0000 1.66483 0.832413 0.554156i \(-0.186959\pi\)
0.832413 + 0.554156i \(0.186959\pi\)
\(798\) 0 0
\(799\) 10.0000 0.353775
\(800\) −8.00000 −0.282843
\(801\) 15.0000 0.529999
\(802\) 60.0000 2.11867
\(803\) 10.0000 0.352892
\(804\) 24.0000 0.846415
\(805\) 0 0
\(806\) 12.0000 0.422682
\(807\) 4.00000 0.140807
\(808\) 0 0
\(809\) −26.0000 −0.914111 −0.457056 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) −2.00000 −0.0702728
\(811\) −36.0000 −1.26413 −0.632065 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 0 0
\(813\) −22.0000 −0.771574
\(814\) −22.0000 −0.771100
\(815\) 13.0000 0.455370
\(816\) −4.00000 −0.140028
\(817\) 8.00000 0.279885
\(818\) −4.00000 −0.139857
\(819\) 0 0
\(820\) −10.0000 −0.349215
\(821\) 27.0000 0.942306 0.471153 0.882051i \(-0.343838\pi\)
0.471153 + 0.882051i \(0.343838\pi\)
\(822\) 36.0000 1.25564
\(823\) 20.0000 0.697156 0.348578 0.937280i \(-0.386665\pi\)
0.348578 + 0.937280i \(0.386665\pi\)
\(824\) 0 0
\(825\) −1.00000 −0.0348155
\(826\) 0 0
\(827\) 26.0000 0.904109 0.452054 0.891990i \(-0.350691\pi\)
0.452054 + 0.891990i \(0.350691\pi\)
\(828\) −6.00000 −0.208514
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) −24.0000 −0.833052
\(831\) −18.0000 −0.624413
\(832\) −8.00000 −0.277350
\(833\) 0 0
\(834\) 2.00000 0.0692543
\(835\) −12.0000 −0.415277
\(836\) −4.00000 −0.138343
\(837\) 6.00000 0.207390
\(838\) 52.0000 1.79631
\(839\) 5.00000 0.172619 0.0863096 0.996268i \(-0.472493\pi\)
0.0863096 + 0.996268i \(0.472493\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 8.00000 0.275698
\(843\) 30.0000 1.03325
\(844\) −8.00000 −0.275371
\(845\) −1.00000 −0.0344010
\(846\) 20.0000 0.687614
\(847\) 0 0
\(848\) −44.0000 −1.51097
\(849\) 12.0000 0.411839
\(850\) 2.00000 0.0685994
\(851\) −33.0000 −1.13123
\(852\) −10.0000 −0.342594
\(853\) −45.0000 −1.54077 −0.770385 0.637579i \(-0.779936\pi\)
−0.770385 + 0.637579i \(0.779936\pi\)
\(854\) 0 0
\(855\) −2.00000 −0.0683986
\(856\) 0 0
\(857\) −29.0000 −0.990621 −0.495311 0.868716i \(-0.664946\pi\)
−0.495311 + 0.868716i \(0.664946\pi\)
\(858\) −2.00000 −0.0682789
\(859\) 29.0000 0.989467 0.494734 0.869045i \(-0.335266\pi\)
0.494734 + 0.869045i \(0.335266\pi\)
\(860\) −8.00000 −0.272798
\(861\) 0 0
\(862\) −48.0000 −1.63489
\(863\) 34.0000 1.15737 0.578687 0.815550i \(-0.303565\pi\)
0.578687 + 0.815550i \(0.303565\pi\)
\(864\) −8.00000 −0.272166
\(865\) −6.00000 −0.204006
\(866\) −8.00000 −0.271851
\(867\) −16.0000 −0.543388
\(868\) 0 0
\(869\) 3.00000 0.101768
\(870\) 4.00000 0.135613
\(871\) 12.0000 0.406604
\(872\) 0 0
\(873\) −17.0000 −0.575363
\(874\) −12.0000 −0.405906
\(875\) 0 0
\(876\) −20.0000 −0.675737
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 34.0000 1.14744
\(879\) −24.0000 −0.809500
\(880\) −4.00000 −0.134840
\(881\) −2.00000 −0.0673817 −0.0336909 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) 2.00000 0.0672673
\(885\) 8.00000 0.268917
\(886\) 18.0000 0.604722
\(887\) 21.0000 0.705111 0.352555 0.935791i \(-0.385313\pi\)
0.352555 + 0.935791i \(0.385313\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −30.0000 −1.00560
\(891\) −1.00000 −0.0335013
\(892\) −16.0000 −0.535720
\(893\) 20.0000 0.669274
\(894\) 26.0000 0.869570
\(895\) −2.00000 −0.0668526
\(896\) 0 0
\(897\) −3.00000 −0.100167
\(898\) −26.0000 −0.867631
\(899\) −12.0000 −0.400222
\(900\) 2.00000 0.0666667
\(901\) 11.0000 0.366463
\(902\) −10.0000 −0.332964
\(903\) 0 0
\(904\) 0 0
\(905\) −7.00000 −0.232688
\(906\) 32.0000 1.06313
\(907\) 6.00000 0.199227 0.0996134 0.995026i \(-0.468239\pi\)
0.0996134 + 0.995026i \(0.468239\pi\)
\(908\) −44.0000 −1.46019
\(909\) 0 0
\(910\) 0 0
\(911\) 44.0000 1.45779 0.728893 0.684628i \(-0.240035\pi\)
0.728893 + 0.684628i \(0.240035\pi\)
\(912\) −8.00000 −0.264906
\(913\) −12.0000 −0.397142
\(914\) −22.0000 −0.727695
\(915\) 13.0000 0.429767
\(916\) −36.0000 −1.18947
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) 37.0000 1.22052 0.610259 0.792202i \(-0.291065\pi\)
0.610259 + 0.792202i \(0.291065\pi\)
\(920\) 0 0
\(921\) 5.00000 0.164756
\(922\) −30.0000 −0.987997
\(923\) −5.00000 −0.164577
\(924\) 0 0
\(925\) 11.0000 0.361678
\(926\) 54.0000 1.77455
\(927\) 16.0000 0.525509
\(928\) 16.0000 0.525226
\(929\) −1.00000 −0.0328089 −0.0164045 0.999865i \(-0.505222\pi\)
−0.0164045 + 0.999865i \(0.505222\pi\)
\(930\) −12.0000 −0.393496
\(931\) 0 0
\(932\) −54.0000 −1.76883
\(933\) −24.0000 −0.785725
\(934\) 46.0000 1.50517
\(935\) 1.00000 0.0327035
\(936\) 0 0
\(937\) −30.0000 −0.980057 −0.490029 0.871706i \(-0.663014\pi\)
−0.490029 + 0.871706i \(0.663014\pi\)
\(938\) 0 0
\(939\) 10.0000 0.326338
\(940\) −20.0000 −0.652328
\(941\) −37.0000 −1.20617 −0.603083 0.797679i \(-0.706061\pi\)
−0.603083 + 0.797679i \(0.706061\pi\)
\(942\) 20.0000 0.651635
\(943\) −15.0000 −0.488467
\(944\) 32.0000 1.04151
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) −24.0000 −0.779895 −0.389948 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) −6.00000 −0.194871
\(949\) −10.0000 −0.324614
\(950\) 4.00000 0.129777
\(951\) 28.0000 0.907962
\(952\) 0 0
\(953\) −1.00000 −0.0323932 −0.0161966 0.999869i \(-0.505156\pi\)
−0.0161966 + 0.999869i \(0.505156\pi\)
\(954\) 22.0000 0.712276
\(955\) 8.00000 0.258874
\(956\) −26.0000 −0.840900
\(957\) 2.00000 0.0646508
\(958\) −18.0000 −0.581554
\(959\) 0 0
\(960\) 8.00000 0.258199
\(961\) 5.00000 0.161290
\(962\) 22.0000 0.709308
\(963\) 9.00000 0.290021
\(964\) 4.00000 0.128831
\(965\) 13.0000 0.418485
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 0 0
\(969\) 2.00000 0.0642493
\(970\) 34.0000 1.09167
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 2.00000 0.0641500
\(973\) 0 0
\(974\) −14.0000 −0.448589
\(975\) 1.00000 0.0320256
\(976\) 52.0000 1.66448
\(977\) 32.0000 1.02377 0.511885 0.859054i \(-0.328947\pi\)
0.511885 + 0.859054i \(0.328947\pi\)
\(978\) −26.0000 −0.831388
\(979\) −15.0000 −0.479402
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 56.0000 1.78703
\(983\) 12.0000 0.382741 0.191370 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −4.00000 −0.127386
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) −12.0000 −0.381578
\(990\) 2.00000 0.0635642
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) −48.0000 −1.52400
\(993\) 0 0
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) 24.0000 0.760469
\(997\) 36.0000 1.14013 0.570066 0.821599i \(-0.306918\pi\)
0.570066 + 0.821599i \(0.306918\pi\)
\(998\) −28.0000 −0.886325
\(999\) 11.0000 0.348025
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 9555.2.a.v.1.1 1
7.6 odd 2 195.2.a.b.1.1 1
21.20 even 2 585.2.a.b.1.1 1
28.27 even 2 3120.2.a.u.1.1 1
35.13 even 4 975.2.c.a.274.1 2
35.27 even 4 975.2.c.a.274.2 2
35.34 odd 2 975.2.a.c.1.1 1
84.83 odd 2 9360.2.a.d.1.1 1
91.90 odd 2 2535.2.a.a.1.1 1
105.62 odd 4 2925.2.c.c.2224.1 2
105.83 odd 4 2925.2.c.c.2224.2 2
105.104 even 2 2925.2.a.q.1.1 1
273.272 even 2 7605.2.a.u.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.b.1.1 1 7.6 odd 2
585.2.a.b.1.1 1 21.20 even 2
975.2.a.c.1.1 1 35.34 odd 2
975.2.c.a.274.1 2 35.13 even 4
975.2.c.a.274.2 2 35.27 even 4
2535.2.a.a.1.1 1 91.90 odd 2
2925.2.a.q.1.1 1 105.104 even 2
2925.2.c.c.2224.1 2 105.62 odd 4
2925.2.c.c.2224.2 2 105.83 odd 4
3120.2.a.u.1.1 1 28.27 even 2
7605.2.a.u.1.1 1 273.272 even 2
9360.2.a.d.1.1 1 84.83 odd 2
9555.2.a.v.1.1 1 1.1 even 1 trivial