Properties

Label 966.2.a.h.1.1
Level $966$
Weight $2$
Character 966.1
Self dual yes
Analytic conductor $7.714$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{29} -1.00000 q^{30} +10.0000 q^{31} +1.00000 q^{32} +4.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -5.00000 q^{37} +4.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} +7.00000 q^{41} -1.00000 q^{42} -3.00000 q^{43} +1.00000 q^{45} +1.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.00000 q^{50} -4.00000 q^{51} -1.00000 q^{52} -1.00000 q^{54} +1.00000 q^{56} -4.00000 q^{57} -1.00000 q^{58} +6.00000 q^{59} -1.00000 q^{60} -6.00000 q^{61} +10.0000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} +4.00000 q^{67} +4.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} -2.00000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -5.00000 q^{74} +4.00000 q^{75} +4.00000 q^{76} +1.00000 q^{78} +12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.00000 q^{82} +4.00000 q^{83} -1.00000 q^{84} +4.00000 q^{85} -3.00000 q^{86} +1.00000 q^{87} -6.00000 q^{89} +1.00000 q^{90} -1.00000 q^{91} +1.00000 q^{92} -10.0000 q^{93} +3.00000 q^{94} +4.00000 q^{95} -1.00000 q^{96} -1.00000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) −1.00000 −0.204124
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) −1.00000 −0.182574
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 4.00000 0.648886
\(39\) 1.00000 0.160128
\(40\) 1.00000 0.158114
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) −1.00000 −0.154303
\(43\) −3.00000 −0.457496 −0.228748 0.973486i \(-0.573463\pi\)
−0.228748 + 0.973486i \(0.573463\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 1.00000 0.147442
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −4.00000 −0.565685
\(51\) −4.00000 −0.560112
\(52\) −1.00000 −0.138675
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −4.00000 −0.529813
\(58\) −1.00000 −0.131306
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) −1.00000 −0.129099
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 10.0000 1.27000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 4.00000 0.485071
\(69\) −1.00000 −0.120386
\(70\) 1.00000 0.119523
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 1.00000 0.117851
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −5.00000 −0.581238
\(75\) 4.00000 0.461880
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 7.00000 0.773021
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) −1.00000 −0.109109
\(85\) 4.00000 0.433861
\(86\) −3.00000 −0.323498
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.00000 0.105409
\(91\) −1.00000 −0.104828
\(92\) 1.00000 0.104257
\(93\) −10.0000 −1.03695
\(94\) 3.00000 0.309426
\(95\) 4.00000 0.410391
\(96\) −1.00000 −0.102062
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −4.00000 −0.396059
\(103\) −17.0000 −1.67506 −0.837530 0.546392i \(-0.816001\pi\)
−0.837530 + 0.546392i \(0.816001\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −1.00000 −0.0975900
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −17.0000 −1.62830 −0.814152 0.580651i \(-0.802798\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 1.00000 0.0944911
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) −4.00000 −0.374634
\(115\) 1.00000 0.0932505
\(116\) −1.00000 −0.0928477
\(117\) −1.00000 −0.0924500
\(118\) 6.00000 0.552345
\(119\) 4.00000 0.366679
\(120\) −1.00000 −0.0912871
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) −7.00000 −0.631169
\(124\) 10.0000 0.898027
\(125\) −9.00000 −0.804984
\(126\) 1.00000 0.0890871
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.00000 0.264135
\(130\) −1.00000 −0.0877058
\(131\) −14.0000 −1.22319 −0.611593 0.791173i \(-0.709471\pi\)
−0.611593 + 0.791173i \(0.709471\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 4.00000 0.345547
\(135\) −1.00000 −0.0860663
\(136\) 4.00000 0.342997
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −1.00000 −0.0848189 −0.0424094 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) 1.00000 0.0845154
\(141\) −3.00000 −0.252646
\(142\) −2.00000 −0.167836
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −1.00000 −0.0830455
\(146\) −4.00000 −0.331042
\(147\) −1.00000 −0.0824786
\(148\) −5.00000 −0.410997
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 4.00000 0.326599
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 4.00000 0.324443
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 10.0000 0.803219
\(156\) 1.00000 0.0800641
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 12.0000 0.954669
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 1.00000 0.0788110
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 7.00000 0.546608
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.0000 −0.923077
\(170\) 4.00000 0.306786
\(171\) 4.00000 0.305888
\(172\) −3.00000 −0.228748
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 1.00000 0.0758098
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) −6.00000 −0.449719
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 1.00000 0.0745356
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −1.00000 −0.0741249
\(183\) 6.00000 0.443533
\(184\) 1.00000 0.0737210
\(185\) −5.00000 −0.367607
\(186\) −10.0000 −0.733236
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) −1.00000 −0.0727393
\(190\) 4.00000 0.290191
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 1.00000 0.0716115
\(196\) 1.00000 0.0714286
\(197\) 5.00000 0.356235 0.178118 0.984009i \(-0.442999\pi\)
0.178118 + 0.984009i \(0.442999\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) −4.00000 −0.282843
\(201\) −4.00000 −0.282138
\(202\) 2.00000 0.140720
\(203\) −1.00000 −0.0701862
\(204\) −4.00000 −0.280056
\(205\) 7.00000 0.488901
\(206\) −17.0000 −1.18445
\(207\) 1.00000 0.0695048
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) −1.00000 −0.0690066
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 2.00000 0.137038
\(214\) 0 0
\(215\) −3.00000 −0.204598
\(216\) −1.00000 −0.0680414
\(217\) 10.0000 0.678844
\(218\) −17.0000 −1.15139
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 5.00000 0.335578
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 1.00000 0.0668153
\(225\) −4.00000 −0.266667
\(226\) 1.00000 0.0665190
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) −4.00000 −0.264906
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 1.00000 0.0659380
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 3.00000 0.195698
\(236\) 6.00000 0.390567
\(237\) −12.0000 −0.779484
\(238\) 4.00000 0.259281
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −3.00000 −0.193247 −0.0966235 0.995321i \(-0.530804\pi\)
−0.0966235 + 0.995321i \(0.530804\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −6.00000 −0.384111
\(245\) 1.00000 0.0638877
\(246\) −7.00000 −0.446304
\(247\) −4.00000 −0.254514
\(248\) 10.0000 0.635001
\(249\) −4.00000 −0.253490
\(250\) −9.00000 −0.569210
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −13.0000 −0.815693
\(255\) −4.00000 −0.250490
\(256\) 1.00000 0.0625000
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 3.00000 0.186772
\(259\) −5.00000 −0.310685
\(260\) −1.00000 −0.0620174
\(261\) −1.00000 −0.0618984
\(262\) −14.0000 −0.864923
\(263\) 25.0000 1.54157 0.770783 0.637098i \(-0.219865\pi\)
0.770783 + 0.637098i \(0.219865\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 0.245256
\(267\) 6.00000 0.367194
\(268\) 4.00000 0.244339
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 4.00000 0.242536
\(273\) 1.00000 0.0605228
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) −1.00000 −0.0601929
\(277\) −32.0000 −1.92269 −0.961347 0.275340i \(-0.911209\pi\)
−0.961347 + 0.275340i \(0.911209\pi\)
\(278\) −1.00000 −0.0599760
\(279\) 10.0000 0.598684
\(280\) 1.00000 0.0597614
\(281\) 23.0000 1.37206 0.686032 0.727571i \(-0.259351\pi\)
0.686032 + 0.727571i \(0.259351\pi\)
\(282\) −3.00000 −0.178647
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) −2.00000 −0.118678
\(285\) −4.00000 −0.236940
\(286\) 0 0
\(287\) 7.00000 0.413197
\(288\) 1.00000 0.0589256
\(289\) −1.00000 −0.0588235
\(290\) −1.00000 −0.0587220
\(291\) 1.00000 0.0586210
\(292\) −4.00000 −0.234082
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 6.00000 0.349334
\(296\) −5.00000 −0.290619
\(297\) 0 0
\(298\) −4.00000 −0.231714
\(299\) −1.00000 −0.0578315
\(300\) 4.00000 0.230940
\(301\) −3.00000 −0.172917
\(302\) −5.00000 −0.287718
\(303\) −2.00000 −0.114897
\(304\) 4.00000 0.229416
\(305\) −6.00000 −0.343559
\(306\) 4.00000 0.228665
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) 17.0000 0.967096
\(310\) 10.0000 0.567962
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 1.00000 0.0566139
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 12.0000 0.677199
\(315\) 1.00000 0.0563436
\(316\) 12.0000 0.675053
\(317\) 17.0000 0.954815 0.477408 0.878682i \(-0.341577\pi\)
0.477408 + 0.878682i \(0.341577\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 1.00000 0.0557278
\(323\) 16.0000 0.890264
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) −16.0000 −0.886158
\(327\) 17.0000 0.940102
\(328\) 7.00000 0.386510
\(329\) 3.00000 0.165395
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 4.00000 0.219529
\(333\) −5.00000 −0.273998
\(334\) 12.0000 0.656611
\(335\) 4.00000 0.218543
\(336\) −1.00000 −0.0545545
\(337\) 24.0000 1.30736 0.653682 0.756770i \(-0.273224\pi\)
0.653682 + 0.756770i \(0.273224\pi\)
\(338\) −12.0000 −0.652714
\(339\) −1.00000 −0.0543125
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 1.00000 0.0539949
\(344\) −3.00000 −0.161749
\(345\) −1.00000 −0.0538382
\(346\) −18.0000 −0.967686
\(347\) −33.0000 −1.77153 −0.885766 0.464131i \(-0.846367\pi\)
−0.885766 + 0.464131i \(0.846367\pi\)
\(348\) 1.00000 0.0536056
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −4.00000 −0.213809
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) 13.0000 0.691920 0.345960 0.938249i \(-0.387553\pi\)
0.345960 + 0.938249i \(0.387553\pi\)
\(354\) −6.00000 −0.318896
\(355\) −2.00000 −0.106149
\(356\) −6.00000 −0.317999
\(357\) −4.00000 −0.211702
\(358\) 3.00000 0.158555
\(359\) 3.00000 0.158334 0.0791670 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 1.00000 0.0527046
\(361\) −3.00000 −0.157895
\(362\) −14.0000 −0.735824
\(363\) 11.0000 0.577350
\(364\) −1.00000 −0.0524142
\(365\) −4.00000 −0.209370
\(366\) 6.00000 0.313625
\(367\) 13.0000 0.678594 0.339297 0.940679i \(-0.389811\pi\)
0.339297 + 0.940679i \(0.389811\pi\)
\(368\) 1.00000 0.0521286
\(369\) 7.00000 0.364405
\(370\) −5.00000 −0.259938
\(371\) 0 0
\(372\) −10.0000 −0.518476
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 9.00000 0.464758
\(376\) 3.00000 0.154713
\(377\) 1.00000 0.0515026
\(378\) −1.00000 −0.0514344
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 4.00000 0.205196
\(381\) 13.0000 0.666010
\(382\) −20.0000 −1.02329
\(383\) −4.00000 −0.204390 −0.102195 0.994764i \(-0.532587\pi\)
−0.102195 + 0.994764i \(0.532587\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −17.0000 −0.865277
\(387\) −3.00000 −0.152499
\(388\) −1.00000 −0.0507673
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 1.00000 0.0506370
\(391\) 4.00000 0.202289
\(392\) 1.00000 0.0505076
\(393\) 14.0000 0.706207
\(394\) 5.00000 0.251896
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) −7.00000 −0.350878
\(399\) −4.00000 −0.200250
\(400\) −4.00000 −0.200000
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) −4.00000 −0.199502
\(403\) −10.0000 −0.498135
\(404\) 2.00000 0.0995037
\(405\) 1.00000 0.0496904
\(406\) −1.00000 −0.0496292
\(407\) 0 0
\(408\) −4.00000 −0.198030
\(409\) 28.0000 1.38451 0.692255 0.721653i \(-0.256617\pi\)
0.692255 + 0.721653i \(0.256617\pi\)
\(410\) 7.00000 0.345705
\(411\) −9.00000 −0.443937
\(412\) −17.0000 −0.837530
\(413\) 6.00000 0.295241
\(414\) 1.00000 0.0491473
\(415\) 4.00000 0.196352
\(416\) −1.00000 −0.0490290
\(417\) 1.00000 0.0489702
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −9.00000 −0.438633 −0.219317 0.975654i \(-0.570383\pi\)
−0.219317 + 0.975654i \(0.570383\pi\)
\(422\) 0 0
\(423\) 3.00000 0.145865
\(424\) 0 0
\(425\) −16.0000 −0.776114
\(426\) 2.00000 0.0969003
\(427\) −6.00000 −0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) −3.00000 −0.144673
\(431\) 33.0000 1.58955 0.794777 0.606902i \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 10.0000 0.480015
\(435\) 1.00000 0.0479463
\(436\) −17.0000 −0.814152
\(437\) 4.00000 0.191346
\(438\) 4.00000 0.191127
\(439\) −34.0000 −1.62273 −0.811366 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) −4.00000 −0.190261
\(443\) 1.00000 0.0475114 0.0237557 0.999718i \(-0.492438\pi\)
0.0237557 + 0.999718i \(0.492438\pi\)
\(444\) 5.00000 0.237289
\(445\) −6.00000 −0.284427
\(446\) −2.00000 −0.0947027
\(447\) 4.00000 0.189194
\(448\) 1.00000 0.0472456
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −4.00000 −0.188562
\(451\) 0 0
\(452\) 1.00000 0.0470360
\(453\) 5.00000 0.234920
\(454\) 21.0000 0.985579
\(455\) −1.00000 −0.0468807
\(456\) −4.00000 −0.187317
\(457\) −8.00000 −0.374224 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 4.00000 0.186908
\(459\) −4.00000 −0.186704
\(460\) 1.00000 0.0466252
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 25.0000 1.16185 0.580924 0.813958i \(-0.302691\pi\)
0.580924 + 0.813958i \(0.302691\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −10.0000 −0.463739
\(466\) −6.00000 −0.277945
\(467\) −29.0000 −1.34196 −0.670980 0.741475i \(-0.734126\pi\)
−0.670980 + 0.741475i \(0.734126\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 4.00000 0.184703
\(470\) 3.00000 0.138380
\(471\) −12.0000 −0.552931
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) −12.0000 −0.551178
\(475\) −16.0000 −0.734130
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) 10.0000 0.456912 0.228456 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 5.00000 0.227980
\(482\) −3.00000 −0.136646
\(483\) −1.00000 −0.0455016
\(484\) −11.0000 −0.500000
\(485\) −1.00000 −0.0454077
\(486\) −1.00000 −0.0453609
\(487\) −15.0000 −0.679715 −0.339857 0.940477i \(-0.610379\pi\)
−0.339857 + 0.940477i \(0.610379\pi\)
\(488\) −6.00000 −0.271607
\(489\) 16.0000 0.723545
\(490\) 1.00000 0.0451754
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) −7.00000 −0.315584
\(493\) −4.00000 −0.180151
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) −2.00000 −0.0897123
\(498\) −4.00000 −0.179244
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) −9.00000 −0.402492
\(501\) −12.0000 −0.536120
\(502\) 21.0000 0.937276
\(503\) 2.00000 0.0891756 0.0445878 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 1.00000 0.0445435
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −13.0000 −0.576782
\(509\) −16.0000 −0.709188 −0.354594 0.935020i \(-0.615381\pi\)
−0.354594 + 0.935020i \(0.615381\pi\)
\(510\) −4.00000 −0.177123
\(511\) −4.00000 −0.176950
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) −22.0000 −0.970378
\(515\) −17.0000 −0.749110
\(516\) 3.00000 0.132068
\(517\) 0 0
\(518\) −5.00000 −0.219687
\(519\) 18.0000 0.790112
\(520\) −1.00000 −0.0438529
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −1.00000 −0.0437688
\(523\) 6.00000 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) −14.0000 −0.611593
\(525\) 4.00000 0.174574
\(526\) 25.0000 1.09005
\(527\) 40.0000 1.74243
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) 4.00000 0.173422
\(533\) −7.00000 −0.303204
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −3.00000 −0.129460
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 24.0000 1.03089
\(543\) 14.0000 0.600798
\(544\) 4.00000 0.171499
\(545\) −17.0000 −0.728200
\(546\) 1.00000 0.0427960
\(547\) 22.0000 0.940652 0.470326 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) 9.00000 0.384461
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) −4.00000 −0.170406
\(552\) −1.00000 −0.0425628
\(553\) 12.0000 0.510292
\(554\) −32.0000 −1.35955
\(555\) 5.00000 0.212238
\(556\) −1.00000 −0.0424094
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 10.0000 0.423334
\(559\) 3.00000 0.126886
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 23.0000 0.970196
\(563\) −39.0000 −1.64365 −0.821827 0.569737i \(-0.807045\pi\)
−0.821827 + 0.569737i \(0.807045\pi\)
\(564\) −3.00000 −0.126323
\(565\) 1.00000 0.0420703
\(566\) −6.00000 −0.252199
\(567\) 1.00000 0.0419961
\(568\) −2.00000 −0.0839181
\(569\) 27.0000 1.13190 0.565949 0.824440i \(-0.308510\pi\)
0.565949 + 0.824440i \(0.308510\pi\)
\(570\) −4.00000 −0.167542
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 20.0000 0.835512
\(574\) 7.00000 0.292174
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 17.0000 0.706496
\(580\) −1.00000 −0.0415227
\(581\) 4.00000 0.165948
\(582\) 1.00000 0.0414513
\(583\) 0 0
\(584\) −4.00000 −0.165521
\(585\) −1.00000 −0.0413449
\(586\) −14.0000 −0.578335
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 40.0000 1.64817
\(590\) 6.00000 0.247016
\(591\) −5.00000 −0.205673
\(592\) −5.00000 −0.205499
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) −4.00000 −0.163846
\(597\) 7.00000 0.286491
\(598\) −1.00000 −0.0408930
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 4.00000 0.163299
\(601\) −4.00000 −0.163163 −0.0815817 0.996667i \(-0.525997\pi\)
−0.0815817 + 0.996667i \(0.525997\pi\)
\(602\) −3.00000 −0.122271
\(603\) 4.00000 0.162893
\(604\) −5.00000 −0.203447
\(605\) −11.0000 −0.447214
\(606\) −2.00000 −0.0812444
\(607\) 18.0000 0.730597 0.365299 0.930890i \(-0.380967\pi\)
0.365299 + 0.930890i \(0.380967\pi\)
\(608\) 4.00000 0.162221
\(609\) 1.00000 0.0405220
\(610\) −6.00000 −0.242933
\(611\) −3.00000 −0.121367
\(612\) 4.00000 0.161690
\(613\) −27.0000 −1.09052 −0.545260 0.838267i \(-0.683569\pi\)
−0.545260 + 0.838267i \(0.683569\pi\)
\(614\) −23.0000 −0.928204
\(615\) −7.00000 −0.282267
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 17.0000 0.683840
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 10.0000 0.401610
\(621\) −1.00000 −0.0401286
\(622\) 4.00000 0.160385
\(623\) −6.00000 −0.240385
\(624\) 1.00000 0.0400320
\(625\) 11.0000 0.440000
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) 12.0000 0.478852
\(629\) −20.0000 −0.797452
\(630\) 1.00000 0.0398410
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 12.0000 0.477334
\(633\) 0 0
\(634\) 17.0000 0.675156
\(635\) −13.0000 −0.515889
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −2.00000 −0.0791188
\(640\) 1.00000 0.0395285
\(641\) 15.0000 0.592464 0.296232 0.955116i \(-0.404270\pi\)
0.296232 + 0.955116i \(0.404270\pi\)
\(642\) 0 0
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 1.00000 0.0394055
\(645\) 3.00000 0.118125
\(646\) 16.0000 0.629512
\(647\) −16.0000 −0.629025 −0.314512 0.949253i \(-0.601841\pi\)
−0.314512 + 0.949253i \(0.601841\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) −10.0000 −0.391931
\(652\) −16.0000 −0.626608
\(653\) 11.0000 0.430463 0.215232 0.976563i \(-0.430949\pi\)
0.215232 + 0.976563i \(0.430949\pi\)
\(654\) 17.0000 0.664753
\(655\) −14.0000 −0.547025
\(656\) 7.00000 0.273304
\(657\) −4.00000 −0.156055
\(658\) 3.00000 0.116952
\(659\) 16.0000 0.623272 0.311636 0.950202i \(-0.399123\pi\)
0.311636 + 0.950202i \(0.399123\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −8.00000 −0.310929
\(663\) 4.00000 0.155347
\(664\) 4.00000 0.155230
\(665\) 4.00000 0.155113
\(666\) −5.00000 −0.193746
\(667\) −1.00000 −0.0387202
\(668\) 12.0000 0.464294
\(669\) 2.00000 0.0773245
\(670\) 4.00000 0.154533
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 43.0000 1.65753 0.828764 0.559598i \(-0.189045\pi\)
0.828764 + 0.559598i \(0.189045\pi\)
\(674\) 24.0000 0.924445
\(675\) 4.00000 0.153960
\(676\) −12.0000 −0.461538
\(677\) −14.0000 −0.538064 −0.269032 0.963131i \(-0.586704\pi\)
−0.269032 + 0.963131i \(0.586704\pi\)
\(678\) −1.00000 −0.0384048
\(679\) −1.00000 −0.0383765
\(680\) 4.00000 0.153393
\(681\) −21.0000 −0.804722
\(682\) 0 0
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 4.00000 0.152944
\(685\) 9.00000 0.343872
\(686\) 1.00000 0.0381802
\(687\) −4.00000 −0.152610
\(688\) −3.00000 −0.114374
\(689\) 0 0
\(690\) −1.00000 −0.0380693
\(691\) 29.0000 1.10321 0.551606 0.834105i \(-0.314015\pi\)
0.551606 + 0.834105i \(0.314015\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −33.0000 −1.25266
\(695\) −1.00000 −0.0379322
\(696\) 1.00000 0.0379049
\(697\) 28.0000 1.06058
\(698\) 10.0000 0.378506
\(699\) 6.00000 0.226941
\(700\) −4.00000 −0.151186
\(701\) −52.0000 −1.96401 −0.982006 0.188847i \(-0.939525\pi\)
−0.982006 + 0.188847i \(0.939525\pi\)
\(702\) 1.00000 0.0377426
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) −3.00000 −0.112987
\(706\) 13.0000 0.489261
\(707\) 2.00000 0.0752177
\(708\) −6.00000 −0.225494
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −2.00000 −0.0750587
\(711\) 12.0000 0.450035
\(712\) −6.00000 −0.224860
\(713\) 10.0000 0.374503
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) 3.00000 0.112115
\(717\) −12.0000 −0.448148
\(718\) 3.00000 0.111959
\(719\) 51.0000 1.90198 0.950990 0.309223i \(-0.100069\pi\)
0.950990 + 0.309223i \(0.100069\pi\)
\(720\) 1.00000 0.0372678
\(721\) −17.0000 −0.633113
\(722\) −3.00000 −0.111648
\(723\) 3.00000 0.111571
\(724\) −14.0000 −0.520306
\(725\) 4.00000 0.148556
\(726\) 11.0000 0.408248
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 1.00000 0.0370370
\(730\) −4.00000 −0.148047
\(731\) −12.0000 −0.443836
\(732\) 6.00000 0.221766
\(733\) 20.0000 0.738717 0.369358 0.929287i \(-0.379577\pi\)
0.369358 + 0.929287i \(0.379577\pi\)
\(734\) 13.0000 0.479839
\(735\) −1.00000 −0.0368856
\(736\) 1.00000 0.0368605
\(737\) 0 0
\(738\) 7.00000 0.257674
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) −5.00000 −0.183804
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −10.0000 −0.366618
\(745\) −4.00000 −0.146549
\(746\) −10.0000 −0.366126
\(747\) 4.00000 0.146352
\(748\) 0 0
\(749\) 0 0
\(750\) 9.00000 0.328634
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 3.00000 0.109399
\(753\) −21.0000 −0.765283
\(754\) 1.00000 0.0364179
\(755\) −5.00000 −0.181969
\(756\) −1.00000 −0.0363696
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 23.0000 0.835398
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) −54.0000 −1.95750 −0.978749 0.205061i \(-0.934261\pi\)
−0.978749 + 0.205061i \(0.934261\pi\)
\(762\) 13.0000 0.470940
\(763\) −17.0000 −0.615441
\(764\) −20.0000 −0.723575
\(765\) 4.00000 0.144620
\(766\) −4.00000 −0.144526
\(767\) −6.00000 −0.216647
\(768\) −1.00000 −0.0360844
\(769\) 51.0000 1.83911 0.919554 0.392965i \(-0.128551\pi\)
0.919554 + 0.392965i \(0.128551\pi\)
\(770\) 0 0
\(771\) 22.0000 0.792311
\(772\) −17.0000 −0.611843
\(773\) −23.0000 −0.827253 −0.413626 0.910447i \(-0.635738\pi\)
−0.413626 + 0.910447i \(0.635738\pi\)
\(774\) −3.00000 −0.107833
\(775\) −40.0000 −1.43684
\(776\) −1.00000 −0.0358979
\(777\) 5.00000 0.179374
\(778\) 2.00000 0.0717035
\(779\) 28.0000 1.00320
\(780\) 1.00000 0.0358057
\(781\) 0 0
\(782\) 4.00000 0.143040
\(783\) 1.00000 0.0357371
\(784\) 1.00000 0.0357143
\(785\) 12.0000 0.428298
\(786\) 14.0000 0.499363
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 5.00000 0.178118
\(789\) −25.0000 −0.890024
\(790\) 12.0000 0.426941
\(791\) 1.00000 0.0355559
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) −2.00000 −0.0709773
\(795\) 0 0
\(796\) −7.00000 −0.248108
\(797\) −27.0000 −0.956389 −0.478195 0.878254i \(-0.658709\pi\)
−0.478195 + 0.878254i \(0.658709\pi\)
\(798\) −4.00000 −0.141598
\(799\) 12.0000 0.424529
\(800\) −4.00000 −0.141421
\(801\) −6.00000 −0.212000
\(802\) −2.00000 −0.0706225
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 1.00000 0.0352454
\(806\) −10.0000 −0.352235
\(807\) −18.0000 −0.633630
\(808\) 2.00000 0.0703598
\(809\) 20.0000 0.703163 0.351581 0.936157i \(-0.385644\pi\)
0.351581 + 0.936157i \(0.385644\pi\)
\(810\) 1.00000 0.0351364
\(811\) −17.0000 −0.596951 −0.298475 0.954417i \(-0.596478\pi\)
−0.298475 + 0.954417i \(0.596478\pi\)
\(812\) −1.00000 −0.0350931
\(813\) −24.0000 −0.841717
\(814\) 0 0
\(815\) −16.0000 −0.560456
\(816\) −4.00000 −0.140028
\(817\) −12.0000 −0.419827
\(818\) 28.0000 0.978997
\(819\) −1.00000 −0.0349428
\(820\) 7.00000 0.244451
\(821\) −46.0000 −1.60541 −0.802706 0.596376i \(-0.796607\pi\)
−0.802706 + 0.596376i \(0.796607\pi\)
\(822\) −9.00000 −0.313911
\(823\) 19.0000 0.662298 0.331149 0.943578i \(-0.392564\pi\)
0.331149 + 0.943578i \(0.392564\pi\)
\(824\) −17.0000 −0.592223
\(825\) 0 0
\(826\) 6.00000 0.208767
\(827\) −22.0000 −0.765015 −0.382507 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 1.00000 0.0347524
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 4.00000 0.138842
\(831\) 32.0000 1.11007
\(832\) −1.00000 −0.0346688
\(833\) 4.00000 0.138592
\(834\) 1.00000 0.0346272
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) 12.0000 0.414533
\(839\) −2.00000 −0.0690477 −0.0345238 0.999404i \(-0.510991\pi\)
−0.0345238 + 0.999404i \(0.510991\pi\)
\(840\) −1.00000 −0.0345033
\(841\) −28.0000 −0.965517
\(842\) −9.00000 −0.310160
\(843\) −23.0000 −0.792162
\(844\) 0 0
\(845\) −12.0000 −0.412813
\(846\) 3.00000 0.103142
\(847\) −11.0000 −0.377964
\(848\) 0 0
\(849\) 6.00000 0.205919
\(850\) −16.0000 −0.548795
\(851\) −5.00000 −0.171398
\(852\) 2.00000 0.0685189
\(853\) −27.0000 −0.924462 −0.462231 0.886759i \(-0.652951\pi\)
−0.462231 + 0.886759i \(0.652951\pi\)
\(854\) −6.00000 −0.205316
\(855\) 4.00000 0.136797
\(856\) 0 0
\(857\) 7.00000 0.239115 0.119558 0.992827i \(-0.461852\pi\)
0.119558 + 0.992827i \(0.461852\pi\)
\(858\) 0 0
\(859\) 43.0000 1.46714 0.733571 0.679613i \(-0.237852\pi\)
0.733571 + 0.679613i \(0.237852\pi\)
\(860\) −3.00000 −0.102299
\(861\) −7.00000 −0.238559
\(862\) 33.0000 1.12398
\(863\) −48.0000 −1.63394 −0.816970 0.576681i \(-0.804348\pi\)
−0.816970 + 0.576681i \(0.804348\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −18.0000 −0.612018
\(866\) −7.00000 −0.237870
\(867\) 1.00000 0.0339618
\(868\) 10.0000 0.339422
\(869\) 0 0
\(870\) 1.00000 0.0339032
\(871\) −4.00000 −0.135535
\(872\) −17.0000 −0.575693
\(873\) −1.00000 −0.0338449
\(874\) 4.00000 0.135302
\(875\) −9.00000 −0.304256
\(876\) 4.00000 0.135147
\(877\) −52.0000 −1.75592 −0.877958 0.478738i \(-0.841094\pi\)
−0.877958 + 0.478738i \(0.841094\pi\)
\(878\) −34.0000 −1.14744
\(879\) 14.0000 0.472208
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 1.00000 0.0336718
\(883\) −46.0000 −1.54802 −0.774012 0.633171i \(-0.781753\pi\)
−0.774012 + 0.633171i \(0.781753\pi\)
\(884\) −4.00000 −0.134535
\(885\) −6.00000 −0.201688
\(886\) 1.00000 0.0335957
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 5.00000 0.167789
\(889\) −13.0000 −0.436006
\(890\) −6.00000 −0.201120
\(891\) 0 0
\(892\) −2.00000 −0.0669650
\(893\) 12.0000 0.401565
\(894\) 4.00000 0.133780
\(895\) 3.00000 0.100279
\(896\) 1.00000 0.0334077
\(897\) 1.00000 0.0333890
\(898\) 6.00000 0.200223
\(899\) −10.0000 −0.333519
\(900\) −4.00000 −0.133333
\(901\) 0 0
\(902\) 0 0
\(903\) 3.00000 0.0998337
\(904\) 1.00000 0.0332595
\(905\) −14.0000 −0.465376
\(906\) 5.00000 0.166114
\(907\) 19.0000 0.630885 0.315442 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(908\) 21.0000 0.696909
\(909\) 2.00000 0.0663358
\(910\) −1.00000 −0.0331497
\(911\) −5.00000 −0.165657 −0.0828287 0.996564i \(-0.526395\pi\)
−0.0828287 + 0.996564i \(0.526395\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) −8.00000 −0.264616
\(915\) 6.00000 0.198354
\(916\) 4.00000 0.132164
\(917\) −14.0000 −0.462321
\(918\) −4.00000 −0.132020
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 1.00000 0.0329690
\(921\) 23.0000 0.757876
\(922\) 2.00000 0.0658665
\(923\) 2.00000 0.0658308
\(924\) 0 0
\(925\) 20.0000 0.657596
\(926\) 25.0000 0.821551
\(927\) −17.0000 −0.558353
\(928\) −1.00000 −0.0328266
\(929\) −25.0000 −0.820223 −0.410112 0.912035i \(-0.634510\pi\)
−0.410112 + 0.912035i \(0.634510\pi\)
\(930\) −10.0000 −0.327913
\(931\) 4.00000 0.131095
\(932\) −6.00000 −0.196537
\(933\) −4.00000 −0.130954
\(934\) −29.0000 −0.948909
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) −1.00000 −0.0326686 −0.0163343 0.999867i \(-0.505200\pi\)
−0.0163343 + 0.999867i \(0.505200\pi\)
\(938\) 4.00000 0.130605
\(939\) −14.0000 −0.456873
\(940\) 3.00000 0.0978492
\(941\) 57.0000 1.85815 0.929073 0.369895i \(-0.120606\pi\)
0.929073 + 0.369895i \(0.120606\pi\)
\(942\) −12.0000 −0.390981
\(943\) 7.00000 0.227951
\(944\) 6.00000 0.195283
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) 33.0000 1.07236 0.536178 0.844105i \(-0.319868\pi\)
0.536178 + 0.844105i \(0.319868\pi\)
\(948\) −12.0000 −0.389742
\(949\) 4.00000 0.129845
\(950\) −16.0000 −0.519109
\(951\) −17.0000 −0.551263
\(952\) 4.00000 0.129641
\(953\) 34.0000 1.10137 0.550684 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) 0 0
\(955\) −20.0000 −0.647185
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) 10.0000 0.323085
\(959\) 9.00000 0.290625
\(960\) −1.00000 −0.0322749
\(961\) 69.0000 2.22581
\(962\) 5.00000 0.161206
\(963\) 0 0
\(964\) −3.00000 −0.0966235
\(965\) −17.0000 −0.547249
\(966\) −1.00000 −0.0321745
\(967\) −52.0000 −1.67221 −0.836104 0.548572i \(-0.815172\pi\)
−0.836104 + 0.548572i \(0.815172\pi\)
\(968\) −11.0000 −0.353553
\(969\) −16.0000 −0.513994
\(970\) −1.00000 −0.0321081
\(971\) −56.0000 −1.79713 −0.898563 0.438845i \(-0.855388\pi\)
−0.898563 + 0.438845i \(0.855388\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −1.00000 −0.0320585
\(974\) −15.0000 −0.480631
\(975\) −4.00000 −0.128103
\(976\) −6.00000 −0.192055
\(977\) −27.0000 −0.863807 −0.431903 0.901920i \(-0.642158\pi\)
−0.431903 + 0.901920i \(0.642158\pi\)
\(978\) 16.0000 0.511624
\(979\) 0 0
\(980\) 1.00000 0.0319438
\(981\) −17.0000 −0.542768
\(982\) −20.0000 −0.638226
\(983\) 58.0000 1.84991 0.924956 0.380073i \(-0.124101\pi\)
0.924956 + 0.380073i \(0.124101\pi\)
\(984\) −7.00000 −0.223152
\(985\) 5.00000 0.159313
\(986\) −4.00000 −0.127386
\(987\) −3.00000 −0.0954911
\(988\) −4.00000 −0.127257
\(989\) −3.00000 −0.0953945
\(990\) 0 0
\(991\) −12.0000 −0.381193 −0.190596 0.981669i \(-0.561042\pi\)
−0.190596 + 0.981669i \(0.561042\pi\)
\(992\) 10.0000 0.317500
\(993\) 8.00000 0.253872
\(994\) −2.00000 −0.0634361
\(995\) −7.00000 −0.221915
\(996\) −4.00000 −0.126745
\(997\) −42.0000 −1.33015 −0.665077 0.746775i \(-0.731601\pi\)
−0.665077 + 0.746775i \(0.731601\pi\)
\(998\) 18.0000 0.569780
\(999\) 5.00000 0.158193
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 966.2.a.h.1.1 1
3.2 odd 2 2898.2.a.d.1.1 1
4.3 odd 2 7728.2.a.s.1.1 1
7.6 odd 2 6762.2.a.bi.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.a.h.1.1 1 1.1 even 1 trivial
2898.2.a.d.1.1 1 3.2 odd 2
6762.2.a.bi.1.1 1 7.6 odd 2
7728.2.a.s.1.1 1 4.3 odd 2