Properties

Label 585.2.a.a.1.1
Level $585$
Weight $2$
Character 585.1
Self dual yes
Analytic conductor $4.671$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.67124851824\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 585.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} -3.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} -3.00000 q^{7} +2.00000 q^{10} +5.00000 q^{11} +1.00000 q^{13} +6.00000 q^{14} -4.00000 q^{16} -5.00000 q^{17} +2.00000 q^{19} -2.00000 q^{20} -10.0000 q^{22} +1.00000 q^{23} +1.00000 q^{25} -2.00000 q^{26} -6.00000 q^{28} -10.0000 q^{29} -2.00000 q^{31} +8.00000 q^{32} +10.0000 q^{34} +3.00000 q^{35} -3.00000 q^{37} -4.00000 q^{38} +9.00000 q^{41} -4.00000 q^{43} +10.0000 q^{44} -2.00000 q^{46} -10.0000 q^{47} +2.00000 q^{49} -2.00000 q^{50} +2.00000 q^{52} -9.00000 q^{53} -5.00000 q^{55} +20.0000 q^{58} -11.0000 q^{61} +4.00000 q^{62} -8.00000 q^{64} -1.00000 q^{65} -4.00000 q^{67} -10.0000 q^{68} -6.00000 q^{70} -15.0000 q^{71} +6.00000 q^{73} +6.00000 q^{74} +4.00000 q^{76} -15.0000 q^{77} -11.0000 q^{79} +4.00000 q^{80} -18.0000 q^{82} -8.00000 q^{83} +5.00000 q^{85} +8.00000 q^{86} +11.0000 q^{89} -3.00000 q^{91} +2.00000 q^{92} +20.0000 q^{94} -2.00000 q^{95} -9.00000 q^{97} -4.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 0 0
\(4\) 2.00000 1.00000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 6.00000 1.60357
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) 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
\(22\) −10.0000 −2.13201
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) −6.00000 −1.13389
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 8.00000 1.41421
\(33\) 0 0
\(34\) 10.0000 1.71499
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) −3.00000 −0.493197 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) −4.00000 −0.648886
\(39\) 0 0
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 10.0000 1.50756
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) −2.00000 −0.282843
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 20.0000 2.62613
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −11.0000 −1.40841 −0.704203 0.709999i \(-0.748695\pi\)
−0.704203 + 0.709999i \(0.748695\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −10.0000 −1.21268
\(69\) 0 0
\(70\) −6.00000 −0.717137
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) −15.0000 −1.70941
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 4.00000 0.447214
\(81\) 0 0
\(82\) −18.0000 −1.98777
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 5.00000 0.542326
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) 20.0000 2.06284
\(95\) −2.00000 −0.205196
\(96\) 0 0
\(97\) −9.00000 −0.913812 −0.456906 0.889515i \(-0.651042\pi\)
−0.456906 + 0.889515i \(0.651042\pi\)
\(98\) −4.00000 −0.404061
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000 1.74831
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 10.0000 0.953463
\(111\) 0 0
\(112\) 12.0000 1.13389
\(113\) −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
\(116\) −20.0000 −1.85695
\(117\) 0 0
\(118\) 0 0
\(119\) 15.0000 1.37505
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 22.0000 1.99179
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 2.00000 0.175412
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −17.0000 −1.44192 −0.720961 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) 6.00000 0.507093
\(141\) 0 0
\(142\) 30.0000 2.51754
\(143\) 5.00000 0.418121
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 7.00000 0.573462 0.286731 0.958011i \(-0.407431\pi\)
0.286731 + 0.958011i \(0.407431\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 30.0000 2.41747
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 22.0000 1.75023
\(159\) 0 0
\(160\) −8.00000 −0.632456
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 18.0000 1.40556
\(165\) 0 0
\(166\) 16.0000 1.24184
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −10.0000 −0.766965
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) −3.00000 −0.226779
\(176\) −20.0000 −1.50756
\(177\) 0 0
\(178\) −22.0000 −1.64897
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) −23.0000 −1.70958 −0.854788 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) 6.00000 0.444750
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) −25.0000 −1.82818
\(188\) −20.0000 −1.45865
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 20.0000 1.44715 0.723575 0.690246i \(-0.242498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(192\) 0 0
\(193\) 13.0000 0.935760 0.467880 0.883792i \(-0.345018\pi\)
0.467880 + 0.883792i \(0.345018\pi\)
\(194\) 18.0000 1.29232
\(195\) 0 0
\(196\) 4.00000 0.285714
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −24.0000 −1.68863
\(203\) 30.0000 2.10559
\(204\) 0 0
\(205\) −9.00000 −0.628587
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −18.0000 −1.23625
\(213\) 0 0
\(214\) 6.00000 0.410152
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) −32.0000 −2.16731
\(219\) 0 0
\(220\) −10.0000 −0.674200
\(221\) −5.00000 −0.336336
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −24.0000 −1.60357
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) 0 0
\(233\) 25.0000 1.63780 0.818902 0.573933i \(-0.194583\pi\)
0.818902 + 0.573933i \(0.194583\pi\)
\(234\) 0 0
\(235\) 10.0000 0.652328
\(236\) 0 0
\(237\) 0 0
\(238\) −30.0000 −1.94461
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −28.0000 −1.79991
\(243\) 0 0
\(244\) −22.0000 −1.40841
\(245\) −2.00000 −0.127775
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 2.00000 0.126491
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) −28.0000 −1.75688
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 0 0
\(259\) 9.00000 0.559233
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 12.0000 0.735767
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) −32.0000 −1.95107 −0.975537 0.219834i \(-0.929448\pi\)
−0.975537 + 0.219834i \(0.929448\pi\)
\(270\) 0 0
\(271\) −2.00000 −0.121491 −0.0607457 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) 20.0000 1.21268
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 5.00000 0.301511
\(276\) 0 0
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 34.0000 2.03918
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) −30.0000 −1.78017
\(285\) 0 0
\(286\) −10.0000 −0.591312
\(287\) −27.0000 −1.59376
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) −20.0000 −1.17444
\(291\) 0 0
\(292\) 12.0000 0.702247
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) 1.00000 0.0578315
\(300\) 0 0
\(301\) 12.0000 0.691669
\(302\) 24.0000 1.38104
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) 11.0000 0.629858
\(306\) 0 0
\(307\) −19.0000 −1.08439 −0.542194 0.840254i \(-0.682406\pi\)
−0.542194 + 0.840254i \(0.682406\pi\)
\(308\) −30.0000 −1.70941
\(309\) 0 0
\(310\) −4.00000 −0.227185
\(311\) −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 \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −44.0000 −2.48306
\(315\) 0 0
\(316\) −22.0000 −1.23760
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) −50.0000 −2.79946
\(320\) 8.00000 0.447214
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) −10.0000 −0.556415
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 22.0000 1.21847
\(327\) 0 0
\(328\) 0 0
\(329\) 30.0000 1.65395
\(330\) 0 0
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) −16.0000 −0.878114
\(333\) 0 0
\(334\) −16.0000 −0.875481
\(335\) 4.00000 0.218543
\(336\) 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
\(339\) 0 0
\(340\) 10.0000 0.542326
\(341\) −10.0000 −0.541530
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) −4.00000 −0.215041
\(347\) 1.00000 0.0536828 0.0268414 0.999640i \(-0.491455\pi\)
0.0268414 + 0.999640i \(0.491455\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 6.00000 0.320713
\(351\) 0 0
\(352\) 40.0000 2.13201
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 15.0000 0.796117
\(356\) 22.0000 1.16600
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 46.0000 2.41771
\(363\) 0 0
\(364\) −6.00000 −0.314485
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) 27.0000 1.40177
\(372\) 0 0
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 50.0000 2.58544
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 −0.515026
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) −4.00000 −0.205196
\(381\) 0 0
\(382\) −40.0000 −2.04658
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) −26.0000 −1.32337
\(387\) 0 0
\(388\) −18.0000 −0.913812
\(389\) 24.0000 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) 0 0
\(394\) −24.0000 −1.20910
\(395\) 11.0000 0.553470
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 24.0000 1.19404
\(405\) 0 0
\(406\) −60.0000 −2.97775
\(407\) −15.0000 −0.743522
\(408\) 0 0
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 18.0000 0.888957
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 8.00000 0.392232
\(417\) 0 0
\(418\) −20.0000 −0.978232
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 8.00000 0.389434
\(423\) 0 0
\(424\) 0 0
\(425\) −5.00000 −0.242536
\(426\) 0 0
\(427\) 33.0000 1.59698
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) −12.0000 −0.576018
\(435\) 0 0
\(436\) 32.0000 1.53252
\(437\) 2.00000 0.0956730
\(438\) 0 0
\(439\) −33.0000 −1.57500 −0.787502 0.616312i \(-0.788626\pi\)
−0.787502 + 0.616312i \(0.788626\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.0000 0.475651
\(443\) −35.0000 −1.66290 −0.831450 0.555599i \(-0.812489\pi\)
−0.831450 + 0.555599i \(0.812489\pi\)
\(444\) 0 0
\(445\) −11.0000 −0.521450
\(446\) 0 0
\(447\) 0 0
\(448\) 24.0000 1.13389
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 0 0
\(451\) 45.0000 2.11897
\(452\) −4.00000 −0.188144
\(453\) 0 0
\(454\) −36.0000 −1.68956
\(455\) 3.00000 0.140642
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 28.0000 1.30835
\(459\) 0 0
\(460\) −2.00000 −0.0932505
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 40.0000 1.85695
\(465\) 0 0
\(466\) −50.0000 −2.31621
\(467\) 29.0000 1.34196 0.670980 0.741475i \(-0.265874\pi\)
0.670980 + 0.741475i \(0.265874\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) −20.0000 −0.922531
\(471\) 0 0
\(472\) 0 0
\(473\) −20.0000 −0.919601
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 30.0000 1.37505
\(477\) 0 0
\(478\) 30.0000 1.37217
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) 0 0
\(481\) −3.00000 −0.136788
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) 9.00000 0.408669
\(486\) 0 0
\(487\) 7.00000 0.317200 0.158600 0.987343i \(-0.449302\pi\)
0.158600 + 0.987343i \(0.449302\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 4.00000 0.180702
\(491\) −16.0000 −0.722070 −0.361035 0.932552i \(-0.617576\pi\)
−0.361035 + 0.932552i \(0.617576\pi\)
\(492\) 0 0
\(493\) 50.0000 2.25189
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 45.0000 2.01853
\(498\) 0 0
\(499\) 34.0000 1.52205 0.761025 0.648723i \(-0.224697\pi\)
0.761025 + 0.648723i \(0.224697\pi\)
\(500\) −2.00000 −0.0894427
\(501\) 0 0
\(502\) 40.0000 1.78529
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) −10.0000 −0.444554
\(507\) 0 0
\(508\) 28.0000 1.24230
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 0 0
\(511\) −18.0000 −0.796273
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 36.0000 1.58789
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) −50.0000 −2.19900
\(518\) −18.0000 −0.790875
\(519\) 0 0
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0000 0.435607
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) −18.0000 −0.781870
\(531\) 0 0
\(532\) −12.0000 −0.520266
\(533\) 9.00000 0.389833
\(534\) 0 0
\(535\) 3.00000 0.129701
\(536\) 0 0
\(537\) 0 0
\(538\) 64.0000 2.75924
\(539\) 10.0000 0.430730
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 4.00000 0.171815
\(543\) 0 0
\(544\) −40.0000 −1.71499
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −12.0000 −0.512615
\(549\) 0 0
\(550\) −10.0000 −0.426401
\(551\) −20.0000 −0.852029
\(552\) 0 0
\(553\) 33.0000 1.40330
\(554\) −52.0000 −2.20927
\(555\) 0 0
\(556\) −34.0000 −1.44192
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) −12.0000 −0.507093
\(561\) 0 0
\(562\) −20.0000 −0.843649
\(563\) 41.0000 1.72794 0.863972 0.503540i \(-0.167969\pi\)
0.863972 + 0.503540i \(0.167969\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 0 0
\(569\) −16.0000 −0.670755 −0.335377 0.942084i \(-0.608864\pi\)
−0.335377 + 0.942084i \(0.608864\pi\)
\(570\) 0 0
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) 10.0000 0.418121
\(573\) 0 0
\(574\) 54.0000 2.25392
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −21.0000 −0.874241 −0.437121 0.899403i \(-0.644002\pi\)
−0.437121 + 0.899403i \(0.644002\pi\)
\(578\) −16.0000 −0.665512
\(579\) 0 0
\(580\) 20.0000 0.830455
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) −45.0000 −1.86371
\(584\) 0 0
\(585\) 0 0
\(586\) 48.0000 1.98286
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 12.0000 0.493197
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) −15.0000 −0.614940
\(596\) 14.0000 0.573462
\(597\) 0 0
\(598\) −2.00000 −0.0817861
\(599\) −4.00000 −0.163436 −0.0817178 0.996656i \(-0.526041\pi\)
−0.0817178 + 0.996656i \(0.526041\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) −24.0000 −0.978167
\(603\) 0 0
\(604\) −24.0000 −0.976546
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) −40.0000 −1.62355 −0.811775 0.583970i \(-0.801498\pi\)
−0.811775 + 0.583970i \(0.801498\pi\)
\(608\) 16.0000 0.648886
\(609\) 0 0
\(610\) −22.0000 −0.890754
\(611\) −10.0000 −0.404557
\(612\) 0 0
\(613\) 3.00000 0.121169 0.0605844 0.998163i \(-0.480704\pi\)
0.0605844 + 0.998163i \(0.480704\pi\)
\(614\) 38.0000 1.53356
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) −2.00000 −0.0803868 −0.0401934 0.999192i \(-0.512797\pi\)
−0.0401934 + 0.999192i \(0.512797\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 48.0000 1.92462
\(623\) −33.0000 −1.32212
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 20.0000 0.799361
\(627\) 0 0
\(628\) 44.0000 1.75579
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 24.0000 0.953162
\(635\) −14.0000 −0.555573
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 100.000 3.95904
\(639\) 0 0
\(640\) 0 0
\(641\) 36.0000 1.42191 0.710957 0.703235i \(-0.248262\pi\)
0.710957 + 0.703235i \(0.248262\pi\)
\(642\) 0 0
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) −6.00000 −0.236433
\(645\) 0 0
\(646\) 20.0000 0.786889
\(647\) −21.0000 −0.825595 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −22.0000 −0.861586
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 0 0
\(655\) 6.00000 0.234439
\(656\) −36.0000 −1.40556
\(657\) 0 0
\(658\) −60.0000 −2.33904
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) −64.0000 −2.48743
\(663\) 0 0
\(664\) 0 0
\(665\) 6.00000 0.232670
\(666\) 0 0
\(667\) −10.0000 −0.387202
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) −8.00000 −0.309067
\(671\) −55.0000 −2.12325
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) 2.00000 0.0769231
\(677\) 7.00000 0.269032 0.134516 0.990911i \(-0.457052\pi\)
0.134516 + 0.990911i \(0.457052\pi\)
\(678\) 0 0
\(679\) 27.0000 1.03616
\(680\) 0 0
\(681\) 0 0
\(682\) 20.0000 0.765840
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) −30.0000 −1.14541
\(687\) 0 0
\(688\) 16.0000 0.609994
\(689\) −9.00000 −0.342873
\(690\) 0 0
\(691\) 6.00000 0.228251 0.114125 0.993466i \(-0.463593\pi\)
0.114125 + 0.993466i \(0.463593\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) −2.00000 −0.0759190
\(695\) 17.0000 0.644847
\(696\) 0 0
\(697\) −45.0000 −1.70450
\(698\) −40.0000 −1.51402
\(699\) 0 0
\(700\) −6.00000 −0.226779
\(701\) 4.00000 0.151078 0.0755390 0.997143i \(-0.475932\pi\)
0.0755390 + 0.997143i \(0.475932\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −40.0000 −1.50756
\(705\) 0 0
\(706\) −28.0000 −1.05379
\(707\) −36.0000 −1.35392
\(708\) 0 0
\(709\) 20.0000 0.751116 0.375558 0.926799i \(-0.377451\pi\)
0.375558 + 0.926799i \(0.377451\pi\)
\(710\) −30.0000 −1.12588
\(711\) 0 0
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) −5.00000 −0.186989
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) 32.0000 1.19423
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 30.0000 1.11648
\(723\) 0 0
\(724\) −46.0000 −1.70958
\(725\) −10.0000 −0.371391
\(726\) 0 0
\(727\) 6.00000 0.222528 0.111264 0.993791i \(-0.464510\pi\)
0.111264 + 0.993791i \(0.464510\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) 20.0000 0.739727
\(732\) 0 0
\(733\) −15.0000 −0.554038 −0.277019 0.960864i \(-0.589346\pi\)
−0.277019 + 0.960864i \(0.589346\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) 38.0000 1.39785 0.698926 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) −54.0000 −1.98240
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) −7.00000 −0.256460
\(746\) −32.0000 −1.17160
\(747\) 0 0
\(748\) −50.0000 −1.82818
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) −45.0000 −1.64207 −0.821037 0.570875i \(-0.806604\pi\)
−0.821037 + 0.570875i \(0.806604\pi\)
\(752\) 40.0000 1.45865
\(753\) 0 0
\(754\) 20.0000 0.728357
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 36.0000 1.30844 0.654221 0.756303i \(-0.272997\pi\)
0.654221 + 0.756303i \(0.272997\pi\)
\(758\) −12.0000 −0.435860
\(759\) 0 0
\(760\) 0 0
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) 0 0
\(763\) −48.0000 −1.73772
\(764\) 40.0000 1.44715
\(765\) 0 0
\(766\) −36.0000 −1.30073
\(767\) 0 0
\(768\) 0 0
\(769\) −12.0000 −0.432731 −0.216366 0.976312i \(-0.569420\pi\)
−0.216366 + 0.976312i \(0.569420\pi\)
\(770\) −30.0000 −1.08112
\(771\) 0 0
\(772\) 26.0000 0.935760
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) −48.0000 −1.72088
\(779\) 18.0000 0.644917
\(780\) 0 0
\(781\) −75.0000 −2.68371
\(782\) 10.0000 0.357599
\(783\) 0 0
\(784\) −8.00000 −0.285714
\(785\) −22.0000 −0.785214
\(786\) 0 0
\(787\) 44.0000 1.56843 0.784215 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) 24.0000 0.854965
\(789\) 0 0
\(790\) −22.0000 −0.782725
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) −11.0000 −0.390621
\(794\) 38.0000 1.34857
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) 5.00000 0.177109 0.0885545 0.996071i \(-0.471775\pi\)
0.0885545 + 0.996071i \(0.471775\pi\)
\(798\) 0 0
\(799\) 50.0000 1.76887
\(800\) 8.00000 0.282843
\(801\) 0 0
\(802\) −36.0000 −1.27120
\(803\) 30.0000 1.05868
\(804\) 0 0
\(805\) 3.00000 0.105736
\(806\) 4.00000 0.140894
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 60.0000 2.10559
\(813\) 0 0
\(814\) 30.0000 1.05150
\(815\) 11.0000 0.385313
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 52.0000 1.81814
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) 41.0000 1.43091 0.715455 0.698659i \(-0.246219\pi\)
0.715455 + 0.698659i \(0.246219\pi\)
\(822\) 0 0
\(823\) −48.0000 −1.67317 −0.836587 0.547833i \(-0.815453\pi\)
−0.836587 + 0.547833i \(0.815453\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 0 0
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −16.0000 −0.555368
\(831\) 0 0
\(832\) −8.00000 −0.277350
\(833\) −10.0000 −0.346479
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 20.0000 0.691714
\(837\) 0 0
\(838\) 52.0000 1.79631
\(839\) −7.00000 −0.241667 −0.120833 0.992673i \(-0.538557\pi\)
−0.120833 + 0.992673i \(0.538557\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −64.0000 −2.20559
\(843\) 0 0
\(844\) −8.00000 −0.275371
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −42.0000 −1.44314
\(848\) 36.0000 1.23625
\(849\) 0 0
\(850\) 10.0000 0.342997
\(851\) −3.00000 −0.102839
\(852\) 0 0
\(853\) 51.0000 1.74621 0.873103 0.487535i \(-0.162104\pi\)
0.873103 + 0.487535i \(0.162104\pi\)
\(854\) −66.0000 −2.25847
\(855\) 0 0
\(856\) 0 0
\(857\) 17.0000 0.580709 0.290354 0.956919i \(-0.406227\pi\)
0.290354 + 0.956919i \(0.406227\pi\)
\(858\) 0 0
\(859\) 35.0000 1.19418 0.597092 0.802173i \(-0.296323\pi\)
0.597092 + 0.802173i \(0.296323\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −32.0000 −1.08992
\(863\) 22.0000 0.748889 0.374444 0.927249i \(-0.377833\pi\)
0.374444 + 0.927249i \(0.377833\pi\)
\(864\) 0 0
\(865\) −2.00000 −0.0680020
\(866\) −48.0000 −1.63111
\(867\) 0 0
\(868\) 12.0000 0.407307
\(869\) −55.0000 −1.86575
\(870\) 0 0
\(871\) −4.00000 −0.135535
\(872\) 0 0
\(873\) 0 0
\(874\) −4.00000 −0.135302
\(875\) 3.00000 0.101419
\(876\) 0 0
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 66.0000 2.22739
\(879\) 0 0
\(880\) 20.0000 0.674200
\(881\) 14.0000 0.471672 0.235836 0.971793i \(-0.424217\pi\)
0.235836 + 0.971793i \(0.424217\pi\)
\(882\) 0 0
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) −10.0000 −0.336336
\(885\) 0 0
\(886\) 70.0000 2.35170
\(887\) 15.0000 0.503651 0.251825 0.967773i \(-0.418969\pi\)
0.251825 + 0.967773i \(0.418969\pi\)
\(888\) 0 0
\(889\) −42.0000 −1.40863
\(890\) 22.0000 0.737442
\(891\) 0 0
\(892\) 0 0
\(893\) −20.0000 −0.669274
\(894\) 0 0
\(895\) −6.00000 −0.200558
\(896\) 0 0
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) 20.0000 0.667037
\(900\) 0 0
\(901\) 45.0000 1.49917
\(902\) −90.0000 −2.99667
\(903\) 0 0
\(904\) 0 0
\(905\) 23.0000 0.764546
\(906\) 0 0
\(907\) 2.00000 0.0664089 0.0332045 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) 36.0000 1.19470
\(909\) 0 0
\(910\) −6.00000 −0.198898
\(911\) −8.00000 −0.265052 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) 0 0
\(913\) −40.0000 −1.32381
\(914\) 26.0000 0.860004
\(915\) 0 0
\(916\) −28.0000 −0.925146
\(917\) 18.0000 0.594412
\(918\) 0 0
\(919\) 29.0000 0.956622 0.478311 0.878191i \(-0.341249\pi\)
0.478311 + 0.878191i \(0.341249\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 6.00000 0.197599
\(923\) −15.0000 −0.493731
\(924\) 0 0
\(925\) −3.00000 −0.0986394
\(926\) −10.0000 −0.328620
\(927\) 0 0
\(928\) −80.0000 −2.62613
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) 0 0
\(931\) 4.00000 0.131095
\(932\) 50.0000 1.63780
\(933\) 0 0
\(934\) −58.0000 −1.89782
\(935\) 25.0000 0.817587
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −24.0000 −0.783628
\(939\) 0 0
\(940\) 20.0000 0.652328
\(941\) 23.0000 0.749779 0.374889 0.927070i \(-0.377681\pi\)
0.374889 + 0.927070i \(0.377681\pi\)
\(942\) 0 0
\(943\) 9.00000 0.293080
\(944\) 0 0
\(945\) 0 0
\(946\) 40.0000 1.30051
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) −4.00000 −0.129777
\(951\) 0 0
\(952\) 0 0
\(953\) 11.0000 0.356325 0.178162 0.984001i \(-0.442985\pi\)
0.178162 + 0.984001i \(0.442985\pi\)
\(954\) 0 0
\(955\) −20.0000 −0.647185
\(956\) −30.0000 −0.970269
\(957\) 0 0
\(958\) 10.0000 0.323085
\(959\) 18.0000 0.581250
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 6.00000 0.193448
\(963\) 0 0
\(964\) −28.0000 −0.901819
\(965\) −13.0000 −0.418485
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −18.0000 −0.577945
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 51.0000 1.63498
\(974\) −14.0000 −0.448589
\(975\) 0 0
\(976\) 44.0000 1.40841
\(977\) −12.0000 −0.383914 −0.191957 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) 0 0
\(979\) 55.0000 1.75781
\(980\) −4.00000 −0.127775
\(981\) 0 0
\(982\) 32.0000 1.02116
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) −100.000 −3.18465
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) 39.0000 1.23888 0.619438 0.785046i \(-0.287361\pi\)
0.619438 + 0.785046i \(0.287361\pi\)
\(992\) −16.0000 −0.508001
\(993\) 0 0
\(994\) −90.0000 −2.85463
\(995\) −4.00000 −0.126809
\(996\) 0 0
\(997\) −16.0000 −0.506725 −0.253363 0.967371i \(-0.581537\pi\)
−0.253363 + 0.967371i \(0.581537\pi\)
\(998\) −68.0000 −2.15250
\(999\) 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 585.2.a.a.1.1 1
3.2 odd 2 195.2.a.d.1.1 1
4.3 odd 2 9360.2.a.w.1.1 1
5.2 odd 4 2925.2.c.d.2224.1 2
5.3 odd 4 2925.2.c.d.2224.2 2
5.4 even 2 2925.2.a.t.1.1 1
12.11 even 2 3120.2.a.n.1.1 1
13.12 even 2 7605.2.a.v.1.1 1
15.2 even 4 975.2.c.b.274.2 2
15.8 even 4 975.2.c.b.274.1 2
15.14 odd 2 975.2.a.b.1.1 1
21.20 even 2 9555.2.a.t.1.1 1
39.38 odd 2 2535.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.d.1.1 1 3.2 odd 2
585.2.a.a.1.1 1 1.1 even 1 trivial
975.2.a.b.1.1 1 15.14 odd 2
975.2.c.b.274.1 2 15.8 even 4
975.2.c.b.274.2 2 15.2 even 4
2535.2.a.b.1.1 1 39.38 odd 2
2925.2.a.t.1.1 1 5.4 even 2
2925.2.c.d.2224.1 2 5.2 odd 4
2925.2.c.d.2224.2 2 5.3 odd 4
3120.2.a.n.1.1 1 12.11 even 2
7605.2.a.v.1.1 1 13.12 even 2
9360.2.a.w.1.1 1 4.3 odd 2
9555.2.a.t.1.1 1 21.20 even 2