Properties

Label 585.2.a.c.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

\(f(q)\) \(=\) \(q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{10} -5.00000 q^{11} -1.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} +7.00000 q^{17} -6.00000 q^{19} +2.00000 q^{20} +10.0000 q^{22} -3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -2.00000 q^{28} -2.00000 q^{29} +2.00000 q^{31} +8.00000 q^{32} -14.0000 q^{34} -1.00000 q^{35} +7.00000 q^{37} +12.0000 q^{38} -9.00000 q^{41} -8.00000 q^{43} -10.0000 q^{44} +6.00000 q^{46} -10.0000 q^{47} -6.00000 q^{49} -2.00000 q^{50} -2.00000 q^{52} -5.00000 q^{53} -5.00000 q^{55} +4.00000 q^{58} +5.00000 q^{61} -4.00000 q^{62} -8.00000 q^{64} -1.00000 q^{65} -4.00000 q^{67} +14.0000 q^{68} +2.00000 q^{70} -9.00000 q^{71} -6.00000 q^{73} -14.0000 q^{74} -12.0000 q^{76} +5.00000 q^{77} -3.00000 q^{79} -4.00000 q^{80} +18.0000 q^{82} +4.00000 q^{83} +7.00000 q^{85} +16.0000 q^{86} -11.0000 q^{89} +1.00000 q^{91} -6.00000 q^{92} +20.0000 q^{94} -6.00000 q^{95} -11.0000 q^{97} +12.0000 q^{98} +O(q^{100})\)

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
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) −2.00000 −0.632456
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 10.0000 2.13201
\(23\) −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
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 8.00000 1.41421
\(33\) 0 0
\(34\) −14.0000 −2.40098
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 12.0000 1.94666
\(39\) 0 0
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −10.0000 −1.50756
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) −2.00000 −0.282843
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −5.00000 −0.686803 −0.343401 0.939189i \(-0.611579\pi\)
−0.343401 + 0.939189i \(0.611579\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) −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 \(0.578571\pi\)
\(68\) 14.0000 1.69775
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −14.0000 −1.62747
\(75\) 0 0
\(76\) −12.0000 −1.37649
\(77\) 5.00000 0.569803
\(78\) 0 0
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) 18.0000 1.98777
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 7.00000 0.759257
\(86\) 16.0000 1.72532
\(87\) 0 0
\(88\) 0 0
\(89\) −11.0000 −1.16600 −0.582999 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 20.0000 2.06284
\(95\) −6.00000 −0.615587
\(96\) 0 0
\(97\) −11.0000 −1.11688 −0.558440 0.829545i \(-0.688600\pi\)
−0.558440 + 0.829545i \(0.688600\pi\)
\(98\) 12.0000 1.21218
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 10.0000 0.953463
\(111\) 0 0
\(112\) 4.00000 0.377964
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −3.00000 −0.279751
\(116\) −4.00000 −0.371391
\(117\) 0 0
\(118\) 0 0
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 2.00000 0.175412
\(131\) 22.0000 1.92215 0.961074 0.276289i \(-0.0891049\pi\)
0.961074 + 0.276289i \(0.0891049\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) −2.00000 −0.169031
\(141\) 0 0
\(142\) 18.0000 1.51053
\(143\) 5.00000 0.418121
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) 14.0000 1.15079
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −10.0000 −0.805823
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 6.00000 0.477334
\(159\) 0 0
\(160\) 8.00000 0.632456
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) 15.0000 1.17489 0.587445 0.809264i \(-0.300134\pi\)
0.587445 + 0.809264i \(0.300134\pi\)
\(164\) −18.0000 −1.40556
\(165\) 0 0
\(166\) −8.00000 −0.620920
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −14.0000 −1.07375
\(171\) 0 0
\(172\) −16.0000 −1.21999
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 20.0000 1.50756
\(177\) 0 0
\(178\) 22.0000 1.64897
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −2.00000 −0.148250
\(183\) 0 0
\(184\) 0 0
\(185\) 7.00000 0.514650
\(186\) 0 0
\(187\) −35.0000 −2.55945
\(188\) −20.0000 −1.45865
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) 22.0000 1.57951
\(195\) 0 0
\(196\) −12.0000 −0.857143
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) −28.0000 −1.98487 −0.992434 0.122782i \(-0.960818\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.00000 0.140372
\(204\) 0 0
\(205\) −9.00000 −0.628587
\(206\) 8.00000 0.557386
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 30.0000 2.07514
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −10.0000 −0.686803
\(213\) 0 0
\(214\) −34.0000 −2.32419
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) −8.00000 −0.541828
\(219\) 0 0
\(220\) −10.0000 −0.674200
\(221\) −7.00000 −0.470871
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −8.00000 −0.534522
\(225\) 0 0
\(226\) 20.0000 1.33038
\(227\) 2.00000 0.132745 0.0663723 0.997795i \(-0.478857\pi\)
0.0663723 + 0.997795i \(0.478857\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 0 0
\(233\) −19.0000 −1.24473 −0.622366 0.782727i \(-0.713828\pi\)
−0.622366 + 0.782727i \(0.713828\pi\)
\(234\) 0 0
\(235\) −10.0000 −0.652328
\(236\) 0 0
\(237\) 0 0
\(238\) 14.0000 0.907485
\(239\) −9.00000 −0.582162 −0.291081 0.956698i \(-0.594015\pi\)
−0.291081 + 0.956698i \(0.594015\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) −28.0000 −1.79991
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) 0 0
\(250\) −2.00000 −0.126491
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 4.00000 0.250982
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) −7.00000 −0.434959
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −44.0000 −2.71833
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) −5.00000 −0.307148
\(266\) −12.0000 −0.735767
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) −28.0000 −1.69775
\(273\) 0 0
\(274\) −28.0000 −1.69154
\(275\) −5.00000 −0.301511
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −30.0000 −1.79928
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −18.0000 −1.06810
\(285\) 0 0
\(286\) −10.0000 −0.591312
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 4.00000 0.234888
\(291\) 0 0
\(292\) −12.0000 −0.702247
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 30.0000 1.73785
\(299\) 3.00000 0.173494
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 16.0000 0.920697
\(303\) 0 0
\(304\) 24.0000 1.37649
\(305\) 5.00000 0.286299
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 10.0000 0.569803
\(309\) 0 0
\(310\) −4.00000 −0.227185
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −36.0000 −2.03160
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) 24.0000 1.34797 0.673987 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 0 0
\(319\) 10.0000 0.559893
\(320\) −8.00000 −0.447214
\(321\) 0 0
\(322\) −6.00000 −0.334367
\(323\) −42.0000 −2.33694
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −30.0000 −1.66155
\(327\) 0 0
\(328\) 0 0
\(329\) 10.0000 0.551318
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 8.00000 0.439057
\(333\) 0 0
\(334\) −48.0000 −2.62644
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −2.00000 −0.108786
\(339\) 0 0
\(340\) 14.0000 0.759257
\(341\) −10.0000 −0.541530
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) −36.0000 −1.93537
\(347\) −11.0000 −0.590511 −0.295255 0.955418i \(-0.595405\pi\)
−0.295255 + 0.955418i \(0.595405\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) −40.0000 −2.13201
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) −22.0000 −1.16600
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) 2.00000 0.104828
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 4.00000 0.208798 0.104399 0.994535i \(-0.466708\pi\)
0.104399 + 0.994535i \(0.466708\pi\)
\(368\) 12.0000 0.625543
\(369\) 0 0
\(370\) −14.0000 −0.727825
\(371\) 5.00000 0.259587
\(372\) 0 0
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) 70.0000 3.61961
\(375\) 0 0
\(376\) 0 0
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) −12.0000 −0.615587
\(381\) 0 0
\(382\) −24.0000 −1.22795
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 5.00000 0.254824
\(386\) 34.0000 1.73055
\(387\) 0 0
\(388\) −22.0000 −1.11688
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 0 0
\(393\) 0 0
\(394\) 48.0000 2.41821
\(395\) −3.00000 −0.150946
\(396\) 0 0
\(397\) 15.0000 0.752828 0.376414 0.926451i \(-0.377157\pi\)
0.376414 + 0.926451i \(0.377157\pi\)
\(398\) 56.0000 2.80703
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 0 0
\(406\) −4.00000 −0.198517
\(407\) −35.0000 −1.73489
\(408\) 0 0
\(409\) 30.0000 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) 18.0000 0.888957
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) −8.00000 −0.392232
\(417\) 0 0
\(418\) −60.0000 −2.93470
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 24.0000 1.16830
\(423\) 0 0
\(424\) 0 0
\(425\) 7.00000 0.339550
\(426\) 0 0
\(427\) −5.00000 −0.241967
\(428\) 34.0000 1.64345
\(429\) 0 0
\(430\) 16.0000 0.771589
\(431\) 40.0000 1.92673 0.963366 0.268190i \(-0.0864254\pi\)
0.963366 + 0.268190i \(0.0864254\pi\)
\(432\) 0 0
\(433\) −20.0000 −0.961139 −0.480569 0.876957i \(-0.659570\pi\)
−0.480569 + 0.876957i \(0.659570\pi\)
\(434\) 4.00000 0.192006
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) 18.0000 0.861057
\(438\) 0 0
\(439\) 15.0000 0.715911 0.357955 0.933739i \(-0.383474\pi\)
0.357955 + 0.933739i \(0.383474\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 14.0000 0.665912
\(443\) 1.00000 0.0475114 0.0237557 0.999718i \(-0.492438\pi\)
0.0237557 + 0.999718i \(0.492438\pi\)
\(444\) 0 0
\(445\) −11.0000 −0.521450
\(446\) 16.0000 0.757622
\(447\) 0 0
\(448\) 8.00000 0.377964
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 45.0000 2.11897
\(452\) −20.0000 −0.940721
\(453\) 0 0
\(454\) −4.00000 −0.187729
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) −28.0000 −1.30835
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) −37.0000 −1.72326 −0.861631 0.507535i \(-0.830557\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(462\) 0 0
\(463\) 15.0000 0.697109 0.348555 0.937288i \(-0.386673\pi\)
0.348555 + 0.937288i \(0.386673\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 38.0000 1.76032
\(467\) 1.00000 0.0462745 0.0231372 0.999732i \(-0.492635\pi\)
0.0231372 + 0.999732i \(0.492635\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 20.0000 0.922531
\(471\) 0 0
\(472\) 0 0
\(473\) 40.0000 1.83920
\(474\) 0 0
\(475\) −6.00000 −0.275299
\(476\) −14.0000 −0.641689
\(477\) 0 0
\(478\) 18.0000 0.823301
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) −44.0000 −2.00415
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) −11.0000 −0.499484
\(486\) 0 0
\(487\) 5.00000 0.226572 0.113286 0.993562i \(-0.463862\pi\)
0.113286 + 0.993562i \(0.463862\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 12.0000 0.542105
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −14.0000 −0.630528
\(494\) −12.0000 −0.539906
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 9.00000 0.403705
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 2.00000 0.0894427
\(501\) 0 0
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −30.0000 −1.33366
\(507\) 0 0
\(508\) −4.00000 −0.177471
\(509\) −27.0000 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 4.00000 0.176432
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) 50.0000 2.19900
\(518\) 14.0000 0.615125
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 44.0000 1.92215
\(525\) 0 0
\(526\) −32.0000 −1.39527
\(527\) 14.0000 0.609850
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 10.0000 0.434372
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) 9.00000 0.389833
\(534\) 0 0
\(535\) 17.0000 0.734974
\(536\) 0 0
\(537\) 0 0
\(538\) −48.0000 −2.06943
\(539\) 30.0000 1.29219
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 44.0000 1.88996
\(543\) 0 0
\(544\) 56.0000 2.40098
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 28.0000 1.19610
\(549\) 0 0
\(550\) 10.0000 0.426401
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 3.00000 0.127573
\(554\) 4.00000 0.169944
\(555\) 0 0
\(556\) 30.0000 1.27228
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) 36.0000 1.51857
\(563\) −11.0000 −0.463595 −0.231797 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 0 0
\(565\) −10.0000 −0.420703
\(566\) −40.0000 −1.68133
\(567\) 0 0
\(568\) 0 0
\(569\) 20.0000 0.838444 0.419222 0.907884i \(-0.362303\pi\)
0.419222 + 0.907884i \(0.362303\pi\)
\(570\) 0 0
\(571\) −39.0000 −1.63210 −0.816050 0.577982i \(-0.803840\pi\)
−0.816050 + 0.577982i \(0.803840\pi\)
\(572\) 10.0000 0.418121
\(573\) 0 0
\(574\) −18.0000 −0.751305
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) −64.0000 −2.66205
\(579\) 0 0
\(580\) −4.00000 −0.166091
\(581\) −4.00000 −0.165948
\(582\) 0 0
\(583\) 25.0000 1.03539
\(584\) 0 0
\(585\) 0 0
\(586\) 8.00000 0.330477
\(587\) 2.00000 0.0825488 0.0412744 0.999148i \(-0.486858\pi\)
0.0412744 + 0.999148i \(0.486858\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −28.0000 −1.15079
\(593\) 16.0000 0.657041 0.328521 0.944497i \(-0.393450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) 0 0
\(595\) −7.00000 −0.286972
\(596\) −30.0000 −1.22885
\(597\) 0 0
\(598\) −6.00000 −0.245358
\(599\) −20.0000 −0.817178 −0.408589 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) −16.0000 −0.652111
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) 14.0000 0.569181
\(606\) 0 0
\(607\) −32.0000 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) −48.0000 −1.94666
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 10.0000 0.404557
\(612\) 0 0
\(613\) 9.00000 0.363507 0.181753 0.983344i \(-0.441823\pi\)
0.181753 + 0.983344i \(0.441823\pi\)
\(614\) −46.0000 −1.85641
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) −38.0000 −1.52735 −0.763674 0.645601i \(-0.776607\pi\)
−0.763674 + 0.645601i \(0.776607\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 40.0000 1.60385
\(623\) 11.0000 0.440706
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 44.0000 1.75859
\(627\) 0 0
\(628\) 36.0000 1.43656
\(629\) 49.0000 1.95376
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −48.0000 −1.90632
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) −20.0000 −0.791808
\(639\) 0 0
\(640\) 0 0
\(641\) −20.0000 −0.789953 −0.394976 0.918691i \(-0.629247\pi\)
−0.394976 + 0.918691i \(0.629247\pi\)
\(642\) 0 0
\(643\) −37.0000 −1.45914 −0.729569 0.683907i \(-0.760279\pi\)
−0.729569 + 0.683907i \(0.760279\pi\)
\(644\) 6.00000 0.236433
\(645\) 0 0
\(646\) 84.0000 3.30494
\(647\) −17.0000 −0.668339 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 30.0000 1.17489
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 0 0
\(655\) 22.0000 0.859611
\(656\) 36.0000 1.40556
\(657\) 0 0
\(658\) −20.0000 −0.779681
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6.00000 0.232670
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) 48.0000 1.85718
\(669\) 0 0
\(670\) 8.00000 0.309067
\(671\) −25.0000 −0.965114
\(672\) 0 0
\(673\) 42.0000 1.61898 0.809491 0.587133i \(-0.199743\pi\)
0.809491 + 0.587133i \(0.199743\pi\)
\(674\) −16.0000 −0.616297
\(675\) 0 0
\(676\) 2.00000 0.0769231
\(677\) −21.0000 −0.807096 −0.403548 0.914959i \(-0.632223\pi\)
−0.403548 + 0.914959i \(0.632223\pi\)
\(678\) 0 0
\(679\) 11.0000 0.422141
\(680\) 0 0
\(681\) 0 0
\(682\) 20.0000 0.765840
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) 0 0
\(685\) 14.0000 0.534913
\(686\) −26.0000 −0.992685
\(687\) 0 0
\(688\) 32.0000 1.21999
\(689\) 5.00000 0.190485
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) 36.0000 1.36851
\(693\) 0 0
\(694\) 22.0000 0.835109
\(695\) 15.0000 0.568982
\(696\) 0 0
\(697\) −63.0000 −2.38630
\(698\) −48.0000 −1.81683
\(699\) 0 0
\(700\) −2.00000 −0.0755929
\(701\) −28.0000 −1.05755 −0.528773 0.848763i \(-0.677348\pi\)
−0.528773 + 0.848763i \(0.677348\pi\)
\(702\) 0 0
\(703\) −42.0000 −1.58406
\(704\) 40.0000 1.50756
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) 0 0
\(708\) 0 0
\(709\) −44.0000 −1.65245 −0.826227 0.563337i \(-0.809517\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 18.0000 0.675528
\(711\) 0 0
\(712\) 0 0
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 5.00000 0.186989
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) −32.0000 −1.19423
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) −34.0000 −1.26535
\(723\) 0 0
\(724\) −14.0000 −0.520306
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) −56.0000 −2.07123
\(732\) 0 0
\(733\) 43.0000 1.58824 0.794121 0.607760i \(-0.207932\pi\)
0.794121 + 0.607760i \(0.207932\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −24.0000 −0.884652
\(737\) 20.0000 0.736709
\(738\) 0 0
\(739\) −6.00000 −0.220714 −0.110357 0.993892i \(-0.535199\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(740\) 14.0000 0.514650
\(741\) 0 0
\(742\) −10.0000 −0.367112
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) 0 0
\(745\) −15.0000 −0.549557
\(746\) 64.0000 2.34321
\(747\) 0 0
\(748\) −70.0000 −2.55945
\(749\) −17.0000 −0.621166
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 40.0000 1.45865
\(753\) 0 0
\(754\) −4.00000 −0.145671
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) 20.0000 0.726912 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) −4.00000 −0.144810
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) 0 0
\(768\) 0 0
\(769\) −28.0000 −1.00971 −0.504853 0.863205i \(-0.668453\pi\)
−0.504853 + 0.863205i \(0.668453\pi\)
\(770\) −10.0000 −0.360375
\(771\) 0 0
\(772\) −34.0000 −1.22369
\(773\) 20.0000 0.719350 0.359675 0.933078i \(-0.382888\pi\)
0.359675 + 0.933078i \(0.382888\pi\)
\(774\) 0 0
\(775\) 2.00000 0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) −8.00000 −0.286814
\(779\) 54.0000 1.93475
\(780\) 0 0
\(781\) 45.0000 1.61023
\(782\) 42.0000 1.50192
\(783\) 0 0
\(784\) 24.0000 0.857143
\(785\) 18.0000 0.642448
\(786\) 0 0
\(787\) 44.0000 1.56843 0.784215 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) −48.0000 −1.70993
\(789\) 0 0
\(790\) 6.00000 0.213470
\(791\) 10.0000 0.355559
\(792\) 0 0
\(793\) −5.00000 −0.177555
\(794\) −30.0000 −1.06466
\(795\) 0 0
\(796\) −56.0000 −1.98487
\(797\) −39.0000 −1.38145 −0.690725 0.723117i \(-0.742709\pi\)
−0.690725 + 0.723117i \(0.742709\pi\)
\(798\) 0 0
\(799\) −70.0000 −2.47642
\(800\) 8.00000 0.282843
\(801\) 0 0
\(802\) −28.0000 −0.988714
\(803\) 30.0000 1.05868
\(804\) 0 0
\(805\) 3.00000 0.105736
\(806\) 4.00000 0.140894
\(807\) 0 0
\(808\) 0 0
\(809\) 50.0000 1.75791 0.878953 0.476908i \(-0.158243\pi\)
0.878953 + 0.476908i \(0.158243\pi\)
\(810\) 0 0
\(811\) 24.0000 0.842754 0.421377 0.906886i \(-0.361547\pi\)
0.421377 + 0.906886i \(0.361547\pi\)
\(812\) 4.00000 0.140372
\(813\) 0 0
\(814\) 70.0000 2.45350
\(815\) 15.0000 0.525427
\(816\) 0 0
\(817\) 48.0000 1.67931
\(818\) −60.0000 −2.09785
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) −17.0000 −0.593304 −0.296652 0.954986i \(-0.595870\pi\)
−0.296652 + 0.954986i \(0.595870\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26.0000 0.904109 0.452054 0.891990i \(-0.350691\pi\)
0.452054 + 0.891990i \(0.350691\pi\)
\(828\) 0 0
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) −8.00000 −0.277684
\(831\) 0 0
\(832\) 8.00000 0.277350
\(833\) −42.0000 −1.45521
\(834\) 0 0
\(835\) 24.0000 0.830554
\(836\) 60.0000 2.07514
\(837\) 0 0
\(838\) 52.0000 1.79631
\(839\) −17.0000 −0.586905 −0.293453 0.955974i \(-0.594804\pi\)
−0.293453 + 0.955974i \(0.594804\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 40.0000 1.37849
\(843\) 0 0
\(844\) −24.0000 −0.826114
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −14.0000 −0.481046
\(848\) 20.0000 0.686803
\(849\) 0 0
\(850\) −14.0000 −0.480196
\(851\) −21.0000 −0.719871
\(852\) 0 0
\(853\) −39.0000 −1.33533 −0.667667 0.744460i \(-0.732707\pi\)
−0.667667 + 0.744460i \(0.732707\pi\)
\(854\) 10.0000 0.342193
\(855\) 0 0
\(856\) 0 0
\(857\) 45.0000 1.53717 0.768585 0.639747i \(-0.220961\pi\)
0.768585 + 0.639747i \(0.220961\pi\)
\(858\) 0 0
\(859\) 19.0000 0.648272 0.324136 0.946011i \(-0.394927\pi\)
0.324136 + 0.946011i \(0.394927\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −80.0000 −2.72481
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 40.0000 1.35926
\(867\) 0 0
\(868\) −4.00000 −0.135769
\(869\) 15.0000 0.508840
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) 0 0
\(874\) −36.0000 −1.21772
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −30.0000 −1.01245
\(879\) 0 0
\(880\) 20.0000 0.674200
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) −14.0000 −0.470871
\(885\) 0 0
\(886\) −2.00000 −0.0671913
\(887\) −13.0000 −0.436497 −0.218249 0.975893i \(-0.570034\pi\)
−0.218249 + 0.975893i \(0.570034\pi\)
\(888\) 0 0
\(889\) 2.00000 0.0670778
\(890\) 22.0000 0.737442
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 60.0000 2.00782
\(894\) 0 0
\(895\) −6.00000 −0.200558
\(896\) 0 0
\(897\) 0 0
\(898\) 18.0000 0.600668
\(899\) −4.00000 −0.133407
\(900\) 0 0
\(901\) −35.0000 −1.16602
\(902\) −90.0000 −2.99667
\(903\) 0 0
\(904\) 0 0
\(905\) −7.00000 −0.232688
\(906\) 0 0
\(907\) 38.0000 1.26177 0.630885 0.775877i \(-0.282692\pi\)
0.630885 + 0.775877i \(0.282692\pi\)
\(908\) 4.00000 0.132745
\(909\) 0 0
\(910\) −2.00000 −0.0662994
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −20.0000 −0.661903
\(914\) 14.0000 0.463079
\(915\) 0 0
\(916\) 28.0000 0.925146
\(917\) −22.0000 −0.726504
\(918\) 0 0
\(919\) −19.0000 −0.626752 −0.313376 0.949629i \(-0.601460\pi\)
−0.313376 + 0.949629i \(0.601460\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 74.0000 2.43706
\(923\) 9.00000 0.296239
\(924\) 0 0
\(925\) 7.00000 0.230159
\(926\) −30.0000 −0.985861
\(927\) 0 0
\(928\) −16.0000 −0.525226
\(929\) 29.0000 0.951459 0.475730 0.879592i \(-0.342184\pi\)
0.475730 + 0.879592i \(0.342184\pi\)
\(930\) 0 0
\(931\) 36.0000 1.17985
\(932\) −38.0000 −1.24473
\(933\) 0 0
\(934\) −2.00000 −0.0654420
\(935\) −35.0000 −1.14462
\(936\) 0 0
\(937\) −6.00000 −0.196011 −0.0980057 0.995186i \(-0.531246\pi\)
−0.0980057 + 0.995186i \(0.531246\pi\)
\(938\) −8.00000 −0.261209
\(939\) 0 0
\(940\) −20.0000 −0.652328
\(941\) −15.0000 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(942\) 0 0
\(943\) 27.0000 0.879241
\(944\) 0 0
\(945\) 0 0
\(946\) −80.0000 −2.60102
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 12.0000 0.389331
\(951\) 0 0
\(952\) 0 0
\(953\) 15.0000 0.485898 0.242949 0.970039i \(-0.421885\pi\)
0.242949 + 0.970039i \(0.421885\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) −18.0000 −0.582162
\(957\) 0 0
\(958\) 6.00000 0.193851
\(959\) −14.0000 −0.452084
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 14.0000 0.451378
\(963\) 0 0
\(964\) 44.0000 1.41714
\(965\) −17.0000 −0.547249
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 22.0000 0.706377
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) 0 0
\(973\) −15.0000 −0.480878
\(974\) −10.0000 −0.320421
\(975\) 0 0
\(976\) −20.0000 −0.640184
\(977\) 12.0000 0.383914 0.191957 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 0 0
\(979\) 55.0000 1.75781
\(980\) −12.0000 −0.383326
\(981\) 0 0
\(982\) 0 0
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) −24.0000 −0.764704
\(986\) 28.0000 0.891702
\(987\) 0 0
\(988\) 12.0000 0.381771
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −57.0000 −1.81066 −0.905332 0.424704i \(-0.860378\pi\)
−0.905332 + 0.424704i \(0.860378\pi\)
\(992\) 16.0000 0.508001
\(993\) 0 0
\(994\) −18.0000 −0.570925
\(995\) −28.0000 −0.887660
\(996\) 0 0
\(997\) 8.00000 0.253363 0.126681 0.991943i \(-0.459567\pi\)
0.126681 + 0.991943i \(0.459567\pi\)
\(998\) 28.0000 0.886325
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 585.2.a.c.1.1 1
3.2 odd 2 195.2.a.c.1.1 1
4.3 odd 2 9360.2.a.bv.1.1 1
5.2 odd 4 2925.2.c.a.2224.1 2
5.3 odd 4 2925.2.c.a.2224.2 2
5.4 even 2 2925.2.a.s.1.1 1
12.11 even 2 3120.2.a.d.1.1 1
13.12 even 2 7605.2.a.t.1.1 1
15.2 even 4 975.2.c.c.274.2 2
15.8 even 4 975.2.c.c.274.1 2
15.14 odd 2 975.2.a.a.1.1 1
21.20 even 2 9555.2.a.u.1.1 1
39.38 odd 2 2535.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.c.1.1 1 3.2 odd 2
585.2.a.c.1.1 1 1.1 even 1 trivial
975.2.a.a.1.1 1 15.14 odd 2
975.2.c.c.274.1 2 15.8 even 4
975.2.c.c.274.2 2 15.2 even 4
2535.2.a.d.1.1 1 39.38 odd 2
2925.2.a.s.1.1 1 5.4 even 2
2925.2.c.a.2224.1 2 5.2 odd 4
2925.2.c.a.2224.2 2 5.3 odd 4
3120.2.a.d.1.1 1 12.11 even 2
7605.2.a.t.1.1 1 13.12 even 2
9360.2.a.bv.1.1 1 4.3 odd 2
9555.2.a.u.1.1 1 21.20 even 2