Properties

Label 3150.2.a.bj.1.1
Level 3150
Weight 2
Character 3150.1
Self dual yes
Analytic conductor 25.153
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 3150.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -4.00000 q^{11} +6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -4.00000 q^{22} +6.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} +8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +10.0000 q^{37} -2.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} +8.00000 q^{47} +1.00000 q^{49} +6.00000 q^{52} -2.00000 q^{53} +1.00000 q^{56} -6.00000 q^{58} +8.00000 q^{59} -14.0000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +12.0000 q^{67} +2.00000 q^{68} +16.0000 q^{71} -2.00000 q^{73} +10.0000 q^{74} -4.00000 q^{77} -8.00000 q^{79} -2.00000 q^{82} +8.00000 q^{83} -4.00000 q^{86} -4.00000 q^{88} -10.0000 q^{89} +6.00000 q^{91} +8.00000 q^{94} -2.00000 q^{97} +1.00000 q^{98} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 6.00000 0.832050
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 10.0000 1.16248
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2.00000 −0.220863
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −14.0000 −1.26750
\(123\) 0 0
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 16.0000 1.39793 0.698963 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 16.0000 1.34269
\(143\) −24.0000 −2.00698
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 8.00000 0.620920
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 6.00000 0.444750
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −8.00000 −0.585018
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 14.0000 0.997459 0.498729 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 2.00000 0.133038
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 2.00000 0.129641
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 5.00000 0.321412
\(243\) 0 0
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 8.00000 0.508001
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 0 0
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) 0 0
\(262\) 16.0000 0.988483
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 12.0000 0.733017
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) 18.0000 1.08152 0.540758 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 16.0000 0.959616
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) −32.0000 −1.90220 −0.951101 0.308879i \(-0.900046\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) 16.0000 0.949425
\(285\) 0 0
\(286\) −24.0000 −1.41915
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) −2.00000 −0.117041
\(293\) 10.0000 0.584206 0.292103 0.956387i \(-0.405645\pi\)
0.292103 + 0.956387i \(0.405645\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −4.00000 −0.227921
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 22.0000 1.23564 0.617822 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 0 0
\(319\) 24.0000 1.34374
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) −2.00000 −0.110432
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 8.00000 0.439057
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 23.0000 1.25104
\(339\) 0 0
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −22.0000 −1.18273
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) 6.00000 0.314485
\(365\) 0 0
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) −8.00000 −0.413670
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −24.0000 −1.22795
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 14.0000 0.705310
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0000 −0.501886 −0.250943 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 0 0
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 0 0
\(403\) 48.0000 2.39105
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) 8.00000 0.393654
\(414\) 0 0
\(415\) 0 0
\(416\) 6.00000 0.294174
\(417\) 0 0
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) −2.00000 −0.0971286
\(425\) 0 0
\(426\) 0 0
\(427\) −14.0000 −0.677507
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 8.00000 0.384012
\(435\) 0 0
\(436\) 6.00000 0.287348
\(437\) 0 0
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −16.0000 −0.757622
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −40.0000 −1.85098 −0.925490 0.378773i \(-0.876346\pi\)
−0.925490 + 0.378773i \(0.876346\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 8.00000 0.368230
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 0 0
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) −16.0000 −0.731823
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 60.0000 2.73576
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) −14.0000 −0.633750
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) −12.0000 −0.537194 −0.268597 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −10.0000 −0.443242 −0.221621 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −22.0000 −0.970378
\(515\) 0 0
\(516\) 0 0
\(517\) −32.0000 −1.40736
\(518\) 10.0000 0.439375
\(519\) 0 0
\(520\) 0 0
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 16.0000 0.698963
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 6.00000 0.258678
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 18.0000 0.764747
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) −26.0000 −1.09674
\(563\) −16.0000 −0.674320 −0.337160 0.941447i \(-0.609466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −32.0000 −1.34506
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) −24.0000 −1.00349
\(573\) 0 0
\(574\) −2.00000 −0.0834784
\(575\) 0 0
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −13.0000 −0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) 8.00000 0.331896
\(582\) 0 0
\(583\) 8.00000 0.331326
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 10.0000 0.413096
\(587\) 8.00000 0.330195 0.165098 0.986277i \(-0.447206\pi\)
0.165098 + 0.986277i \(0.447206\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 10.0000 0.410997
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 8.00000 0.322854
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −10.0000 −0.400642
\(624\) 0 0
\(625\) 0 0
\(626\) 22.0000 0.879297
\(627\) 0 0
\(628\) −10.0000 −0.399043
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 −0.318223
\(633\) 0 0
\(634\) 22.0000 0.873732
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) 24.0000 0.950169
\(639\) 0 0
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.0000 0.629025 0.314512 0.949253i \(-0.398159\pi\)
0.314512 + 0.949253i \(0.398159\pi\)
\(648\) 0 0
\(649\) −32.0000 −1.25611
\(650\) 0 0
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 8.00000 0.311872
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 56.0000 2.16186
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) 0 0
\(681\) 0 0
\(682\) −32.0000 −1.22534
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 10.0000 0.378506
\(699\) 0 0
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 6.00000 0.225653
\(708\) 0 0
\(709\) −2.00000 −0.0751116 −0.0375558 0.999295i \(-0.511957\pi\)
−0.0375558 + 0.999295i \(0.511957\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.0000 −0.374766
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) −8.00000 −0.298557
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) −14.0000 −0.520306
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 6.00000 0.222375
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 0 0
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −14.0000 −0.512576
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 8.00000 0.291730
\(753\) 0 0
\(754\) −36.0000 −1.31104
\(755\) 0 0
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −12.0000 −0.435860
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 48.0000 1.73318
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 −0.0719816
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) 0 0
\(780\) 0 0
\(781\) −64.0000 −2.29010
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) 14.0000 0.498729
\(789\) 0 0
\(790\) 0 0
\(791\) 2.00000 0.0711118
\(792\) 0 0
\(793\) −84.0000 −2.98293
\(794\) −10.0000 −0.354887
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 0 0
\(802\) 14.0000 0.494357
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) 48.0000 1.69073
\(807\) 0 0
\(808\) 6.00000 0.211079
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) −6.00000 −0.210559
\(813\) 0 0
\(814\) −40.0000 −1.40200
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −30.0000 −1.04893
\(819\) 0 0
\(820\) 0 0
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 0 0
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) 8.00000 0.278356
\(827\) 44.0000 1.53003 0.765015 0.644013i \(-0.222732\pi\)
0.765015 + 0.644013i \(0.222732\pi\)
\(828\) 0 0
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 6.00000 0.208013
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −24.0000 −0.829066
\(839\) 16.0000 0.552381 0.276191 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −10.0000 −0.344623
\(843\) 0 0
\(844\) 4.00000 0.137686
\(845\) 0 0
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) −2.00000 −0.0686803
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 46.0000 1.57501 0.787505 0.616308i \(-0.211372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) −14.0000 −0.479070
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −54.0000 −1.84460 −0.922302 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) −48.0000 −1.63774 −0.818869 0.573980i \(-0.805399\pi\)
−0.818869 + 0.573980i \(0.805399\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 0 0
\(868\) 8.00000 0.271538
\(869\) 32.0000 1.08553
\(870\) 0 0
\(871\) 72.0000 2.43963
\(872\) 6.00000 0.203186
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −14.0000 −0.472746 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) −8.00000 −0.269987
\(879\) 0 0
\(880\) 0 0
\(881\) −2.00000 −0.0673817 −0.0336909 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) −20.0000 −0.671913
\(887\) −16.0000 −0.537227 −0.268614 0.963248i \(-0.586566\pi\)
−0.268614 + 0.963248i \(0.586566\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) −48.0000 −1.60089
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 8.00000 0.266371
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 0 0
\(906\) 0 0
\(907\) 52.0000 1.72663 0.863316 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) 8.00000 0.265489
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −32.0000 −1.05905
\(914\) −10.0000 −0.330771
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 16.0000 0.528367
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −10.0000 −0.329332
\(923\) 96.0000 3.15988
\(924\) 0 0
\(925\) 0 0
\(926\) 16.0000 0.525793
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) −58.0000 −1.90292 −0.951459 0.307775i \(-0.900416\pi\)
−0.951459 + 0.307775i \(0.900416\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) −40.0000 −1.30884
\(935\) 0 0
\(936\) 0 0
\(937\) −50.0000 −1.63343 −0.816714 0.577042i \(-0.804207\pi\)
−0.816714 + 0.577042i \(0.804207\pi\)
\(938\) 12.0000 0.391814
\(939\) 0 0
\(940\) 0 0
\(941\) −2.00000 −0.0651981 −0.0325991 0.999469i \(-0.510378\pi\)
−0.0325991 + 0.999469i \(0.510378\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) 44.0000 1.42981 0.714904 0.699223i \(-0.246470\pi\)
0.714904 + 0.699223i \(0.246470\pi\)
\(948\) 0 0
\(949\) −12.0000 −0.389536
\(950\) 0 0
\(951\) 0 0
\(952\) 2.00000 0.0648204
\(953\) −54.0000 −1.74923 −0.874616 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 60.0000 1.93448
\(963\) 0 0
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) −32.0000 −1.02535
\(975\) 0 0
\(976\) −14.0000 −0.448129
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) 40.0000 1.27841
\(980\) 0 0
\(981\) 0 0
\(982\) −12.0000 −0.382935
\(983\) −16.0000 −0.510321 −0.255160 0.966899i \(-0.582128\pi\)
−0.255160 + 0.966899i \(0.582128\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −12.0000 −0.382158
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) 8.00000 0.254000
\(993\) 0 0
\(994\) 16.0000 0.507489
\(995\) 0 0
\(996\) 0 0
\(997\) 22.0000 0.696747 0.348373 0.937356i \(-0.386734\pi\)
0.348373 + 0.937356i \(0.386734\pi\)
\(998\) −12.0000 −0.379853
\(999\) 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 3150.2.a.bj.1.1 1
3.2 odd 2 350.2.a.b.1.1 1
5.2 odd 4 3150.2.g.c.2899.2 2
5.3 odd 4 3150.2.g.c.2899.1 2
5.4 even 2 630.2.a.d.1.1 1
12.11 even 2 2800.2.a.m.1.1 1
15.2 even 4 350.2.c.b.99.1 2
15.8 even 4 350.2.c.b.99.2 2
15.14 odd 2 70.2.a.a.1.1 1
20.19 odd 2 5040.2.a.bm.1.1 1
21.20 even 2 2450.2.a.l.1.1 1
35.34 odd 2 4410.2.a.b.1.1 1
60.23 odd 4 2800.2.g.n.449.2 2
60.47 odd 4 2800.2.g.n.449.1 2
60.59 even 2 560.2.a.d.1.1 1
105.44 odd 6 490.2.e.d.361.1 2
105.59 even 6 490.2.e.c.471.1 2
105.62 odd 4 2450.2.c.k.99.1 2
105.74 odd 6 490.2.e.d.471.1 2
105.83 odd 4 2450.2.c.k.99.2 2
105.89 even 6 490.2.e.c.361.1 2
105.104 even 2 490.2.a.h.1.1 1
120.29 odd 2 2240.2.a.n.1.1 1
120.59 even 2 2240.2.a.q.1.1 1
165.164 even 2 8470.2.a.j.1.1 1
420.419 odd 2 3920.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.a.a.1.1 1 15.14 odd 2
350.2.a.b.1.1 1 3.2 odd 2
350.2.c.b.99.1 2 15.2 even 4
350.2.c.b.99.2 2 15.8 even 4
490.2.a.h.1.1 1 105.104 even 2
490.2.e.c.361.1 2 105.89 even 6
490.2.e.c.471.1 2 105.59 even 6
490.2.e.d.361.1 2 105.44 odd 6
490.2.e.d.471.1 2 105.74 odd 6
560.2.a.d.1.1 1 60.59 even 2
630.2.a.d.1.1 1 5.4 even 2
2240.2.a.n.1.1 1 120.29 odd 2
2240.2.a.q.1.1 1 120.59 even 2
2450.2.a.l.1.1 1 21.20 even 2
2450.2.c.k.99.1 2 105.62 odd 4
2450.2.c.k.99.2 2 105.83 odd 4
2800.2.a.m.1.1 1 12.11 even 2
2800.2.g.n.449.1 2 60.47 odd 4
2800.2.g.n.449.2 2 60.23 odd 4
3150.2.a.bj.1.1 1 1.1 even 1 trivial
3150.2.g.c.2899.1 2 5.3 odd 4
3150.2.g.c.2899.2 2 5.2 odd 4
3920.2.a.t.1.1 1 420.419 odd 2
4410.2.a.b.1.1 1 35.34 odd 2
5040.2.a.bm.1.1 1 20.19 odd 2
8470.2.a.j.1.1 1 165.164 even 2