Properties

Label 1666.2.a.m.1.1
Level $1666$
Weight $2$
Character 1666.1
Self dual yes
Analytic conductor $13.303$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.3030769767\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 34)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1666.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +6.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +6.00000 q^{22} +2.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} -4.00000 q^{27} +4.00000 q^{31} +1.00000 q^{32} +12.0000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +4.00000 q^{38} -4.00000 q^{39} -6.00000 q^{41} +8.00000 q^{43} +6.00000 q^{44} +2.00000 q^{48} -5.00000 q^{50} +2.00000 q^{51} -2.00000 q^{52} -6.00000 q^{53} -4.00000 q^{54} +8.00000 q^{57} +4.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +12.0000 q^{66} +8.00000 q^{67} +1.00000 q^{68} +1.00000 q^{72} -2.00000 q^{73} -4.00000 q^{74} -10.0000 q^{75} +4.00000 q^{76} -4.00000 q^{78} +8.00000 q^{79} -11.0000 q^{81} -6.00000 q^{82} +8.00000 q^{86} +6.00000 q^{88} +6.00000 q^{89} +8.00000 q^{93} +2.00000 q^{96} -14.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 2.00000 0.577350
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.00000 0.408248
\(25\) −5.00000 −1.00000
\(26\) −2.00000 −0.392232
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.0000 2.08893
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 4.00000 0.648886
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 2.00000 0.288675
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 2.00000 0.280056
\(52\) −2.00000 −0.277350
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −4.00000 −0.544331
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000 1.05963
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 4.00000 0.512148 0.256074 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 12.0000 1.47710
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −4.00000 −0.464991
\(75\) −10.0000 −1.15470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) −6.00000 −0.662589
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) 6.00000 0.639602
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 0 0
\(95\) 0 0
\(96\) 2.00000 0.204124
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) −5.00000 −0.500000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 2.00000 0.198030
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) −4.00000 −0.384900
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 8.00000 0.749269
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 4.00000 0.362143
\(123\) −12.0000 −1.08200
\(124\) 4.00000 0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) 16.0000 1.40872
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 12.0000 1.04447
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 1.00000 0.0857493
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −10.0000 −0.816497
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 4.00000 0.324443
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 8.00000 0.636446
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) −11.0000 −0.864242
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 8.00000 0.609994
\(173\) −24.0000 −1.82469 −0.912343 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 4.00000 0.297318 0.148659 0.988889i \(-0.452504\pi\)
0.148659 + 0.988889i \(0.452504\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) 0 0
\(186\) 8.00000 0.586588
\(187\) 6.00000 0.438763
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 2.00000 0.144338
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 6.00000 0.426401
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) −5.00000 −0.353553
\(201\) 16.0000 1.12855
\(202\) −18.0000 −1.26648
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) −2.00000 −0.138675
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −6.00000 −0.410152
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) −8.00000 −0.536925
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) −6.00000 −0.399114
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 8.00000 0.529813
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 25.0000 1.60706
\(243\) −10.0000 −0.641500
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) −12.0000 −0.765092
\(247\) −8.00000 −0.509028
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 16.0000 0.996116
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 12.0000 0.738549
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 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
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −30.0000 −1.80907
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −2.00000 −0.119952
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −28.0000 −1.64139
\(292\) −2.00000 −0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) −24.0000 −1.39262
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) −10.0000 −0.577350
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −36.0000 −2.06815
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) 1.00000 0.0571662
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 32.0000 1.82042
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −4.00000 −0.226455
\(313\) 34.0000 1.92179 0.960897 0.276907i \(-0.0893093\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) −11.0000 −0.611111
\(325\) 10.0000 0.554700
\(326\) 2.00000 0.110770
\(327\) −32.0000 −1.76960
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −16.0000 −0.879440 −0.439720 0.898135i \(-0.644922\pi\)
−0.439720 + 0.898135i \(0.644922\pi\)
\(332\) 0 0
\(333\) −4.00000 −0.219199
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −9.00000 −0.489535
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −24.0000 −1.29025
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 6.00000 0.319801
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 4.00000 0.210235
\(363\) 50.0000 2.62432
\(364\) 0 0
\(365\) 0 0
\(366\) 8.00000 0.418167
\(367\) 16.0000 0.835193 0.417597 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 14.0000 0.719132 0.359566 0.933120i \(-0.382925\pi\)
0.359566 + 0.933120i \(0.382925\pi\)
\(380\) 0 0
\(381\) −32.0000 −1.63941
\(382\) −24.0000 −1.22795
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 8.00000 0.406663
\(388\) −14.0000 −0.710742
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) −12.0000 −0.604551
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) −20.0000 −1.00377 −0.501886 0.864934i \(-0.667360\pi\)
−0.501886 + 0.864934i \(0.667360\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 16.0000 0.798007
\(403\) −8.00000 −0.398508
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 2.00000 0.0990148
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) −4.00000 −0.195881
\(418\) 24.0000 1.17388
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −10.0000 −0.486792
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) −5.00000 −0.242536
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 −0.290021
\(429\) −24.0000 −1.15873
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) −4.00000 −0.192450
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2.00000 −0.0951303
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −8.00000 −0.379663
\(445\) 0 0
\(446\) −8.00000 −0.378811
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) −5.00000 −0.235702
\(451\) −36.0000 −1.69517
\(452\) −6.00000 −0.282216
\(453\) −32.0000 −1.50349
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) 8.00000 0.374634
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −14.0000 −0.654177
\(459\) −4.00000 −0.186704
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) −28.0000 −1.29017
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 16.0000 0.734904
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 24.0000 1.09773
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) 0 0
\(486\) −10.0000 −0.453609
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 4.00000 0.181071
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −12.0000 −0.541002
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) 24.0000 1.07117
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −18.0000 −0.799408
\(508\) −16.0000 −0.709885
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −16.0000 −0.706417
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) 16.0000 0.704361
\(517\) 0 0
\(518\) 0 0
\(519\) −48.0000 −2.10697
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 4.00000 0.174243
\(528\) 12.0000 0.522233
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 12.0000 0.519291
\(535\) 0 0
\(536\) 8.00000 0.345547
\(537\) 24.0000 1.03568
\(538\) 24.0000 1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −8.00000 −0.343629
\(543\) 8.00000 0.343313
\(544\) 1.00000 0.0428746
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 6.00000 0.256307
\(549\) 4.00000 0.170716
\(550\) −30.0000 −1.27920
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 4.00000 0.169334
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) 6.00000 0.253095
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 0 0
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) −12.0000 −0.501745
\(573\) −48.0000 −2.00523
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 1.00000 0.0415945
\(579\) −20.0000 −0.831172
\(580\) 0 0
\(581\) 0 0
\(582\) −28.0000 −1.16064
\(583\) −36.0000 −1.49097
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −24.0000 −0.987228
\(592\) −4.00000 −0.164399
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) −24.0000 −0.984732
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 32.0000 1.30967
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −10.0000 −0.408248
\(601\) 46.0000 1.87638 0.938190 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) −36.0000 −1.46240
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 32.0000 1.28723
\(619\) −26.0000 −1.04503 −0.522514 0.852631i \(-0.675006\pi\)
−0.522514 + 0.852631i \(0.675006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 25.0000 1.00000
\(626\) 34.0000 1.35891
\(627\) 48.0000 1.91694
\(628\) −14.0000 −0.558661
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 8.00000 0.318223
\(633\) −20.0000 −0.794929
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −12.0000 −0.473602
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) −11.0000 −0.432121
\(649\) 0 0
\(650\) 10.0000 0.392232
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) −32.0000 −1.25130
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 46.0000 1.78919 0.894596 0.446875i \(-0.147463\pi\)
0.894596 + 0.446875i \(0.147463\pi\)
\(662\) −16.0000 −0.621858
\(663\) −4.00000 −0.155347
\(664\) 0 0
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) −16.0000 −0.618596
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 38.0000 1.46479 0.732396 0.680879i \(-0.238402\pi\)
0.732396 + 0.680879i \(0.238402\pi\)
\(674\) −22.0000 −0.847408
\(675\) 20.0000 0.769800
\(676\) −9.00000 −0.346154
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −12.0000 −0.460857
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 24.0000 0.919007
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) 4.00000 0.152944
\(685\) 0 0
\(686\) 0 0
\(687\) −28.0000 −1.06827
\(688\) 8.00000 0.304997
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) −24.0000 −0.912343
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) −26.0000 −0.984115
\(699\) 36.0000 1.36165
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 8.00000 0.301941
\(703\) −16.0000 −0.603451
\(704\) 6.00000 0.226134
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −16.0000 −0.600893 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 48.0000 1.79259
\(718\) 24.0000 0.895672
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 20.0000 0.743808
\(724\) 4.00000 0.148659
\(725\) 0 0
\(726\) 50.0000 1.85567
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 8.00000 0.295689
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) 0 0
\(737\) 48.0000 1.76810
\(738\) −6.00000 −0.220863
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) −16.0000 −0.587775
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 8.00000 0.293294
\(745\) 0 0
\(746\) −22.0000 −0.805477
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 0 0
\(753\) 48.0000 1.74922
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 14.0000 0.508503
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −32.0000 −1.15924
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 0 0
\(768\) 2.00000 0.0721688
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −10.0000 −0.359908
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 8.00000 0.287554
\(775\) −20.0000 −0.718421
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) 46.0000 1.63972 0.819861 0.572562i \(-0.194050\pi\)
0.819861 + 0.572562i \(0.194050\pi\)
\(788\) −12.0000 −0.427482
\(789\) 48.0000 1.70885
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000 0.213201
\(793\) −8.00000 −0.284088
\(794\) −20.0000 −0.709773
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 6.00000 0.212000
\(802\) 30.0000 1.05934
\(803\) −12.0000 −0.423471
\(804\) 16.0000 0.564276
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) 48.0000 1.68968
\(808\) −18.0000 −0.633238
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 0 0
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) −24.0000 −0.841200
\(815\) 0 0
\(816\) 2.00000 0.0700140
\(817\) 32.0000 1.11954
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 0 0
\(821\) 36.0000 1.25641 0.628204 0.778048i \(-0.283790\pi\)
0.628204 + 0.778048i \(0.283790\pi\)
\(822\) 12.0000 0.418548
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 16.0000 0.557386
\(825\) −60.0000 −2.08893
\(826\) 0 0
\(827\) 6.00000 0.208640 0.104320 0.994544i \(-0.466733\pi\)
0.104320 + 0.994544i \(0.466733\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 16.0000 0.555034
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) 24.0000 0.830057
\(837\) −16.0000 −0.553041
\(838\) 30.0000 1.03633
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 2.00000 0.0689246
\(843\) 12.0000 0.413302
\(844\) −10.0000 −0.344214
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −28.0000 −0.960958
\(850\) −5.00000 −0.171499
\(851\) 0 0
\(852\) 0 0
\(853\) 40.0000 1.36957 0.684787 0.728743i \(-0.259895\pi\)
0.684787 + 0.728743i \(0.259895\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −6.00000 −0.205076
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) −24.0000 −0.819346
\(859\) 16.0000 0.545913 0.272956 0.962026i \(-0.411998\pi\)
0.272956 + 0.962026i \(0.411998\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) −4.00000 −0.136083
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 2.00000 0.0679236
\(868\) 0 0
\(869\) 48.0000 1.62829
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) −16.0000 −0.541828
\(873\) −14.0000 −0.473828
\(874\) 0 0
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) 32.0000 1.08056 0.540282 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) −8.00000 −0.269987
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) −24.0000 −0.806296
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) −8.00000 −0.268462
\(889\) 0 0
\(890\) 0 0
\(891\) −66.0000 −2.21108
\(892\) −8.00000 −0.267860
\(893\) 0 0
\(894\) 12.0000 0.401340
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −18.0000 −0.600668
\(899\) 0 0
\(900\) −5.00000 −0.166667
\(901\) −6.00000 −0.199889
\(902\) −36.0000 −1.19867
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) −32.0000 −1.06313
\(907\) −58.0000 −1.92586 −0.962929 0.269754i \(-0.913058\pi\)
−0.962929 + 0.269754i \(0.913058\pi\)
\(908\) 6.00000 0.199117
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 8.00000 0.264906
\(913\) 0 0
\(914\) 26.0000 0.860004
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 0 0
\(918\) −4.00000 −0.132020
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 0 0
\(921\) −40.0000 −1.31804
\(922\) 6.00000 0.197599
\(923\) 0 0
\(924\) 0 0
\(925\) 20.0000 0.657596
\(926\) −16.0000 −0.525793
\(927\) 16.0000 0.525509
\(928\) 0 0
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 18.0000 0.589610
\(933\) −24.0000 −0.785725
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 58.0000 1.89478 0.947389 0.320085i \(-0.103712\pi\)
0.947389 + 0.320085i \(0.103712\pi\)
\(938\) 0 0
\(939\) 68.0000 2.21910
\(940\) 0 0
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) −28.0000 −0.912289
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 48.0000 1.56061
\(947\) 18.0000 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(948\) 16.0000 0.519656
\(949\) 4.00000 0.129845
\(950\) −20.0000 −0.648886
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 8.00000 0.257930
\(963\) −6.00000 −0.193347
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 25.0000 0.803530
\(969\) 8.00000 0.256997
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) −10.0000 −0.320750
\(973\) 0 0
\(974\) 8.00000 0.256337
\(975\) 20.0000 0.640513
\(976\) 4.00000 0.128037
\(977\) 42.0000 1.34370 0.671850 0.740688i \(-0.265500\pi\)
0.671850 + 0.740688i \(0.265500\pi\)
\(978\) 4.00000 0.127906
\(979\) 36.0000 1.15056
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) −12.0000 −0.382935
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −12.0000 −0.382546
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 0 0
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 4.00000 0.127000
\(993\) −32.0000 −1.01549
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 28.0000 0.886769 0.443384 0.896332i \(-0.353778\pi\)
0.443384 + 0.896332i \(0.353778\pi\)
\(998\) 14.0000 0.443162
\(999\) 16.0000 0.506218
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 1666.2.a.m.1.1 1
7.6 odd 2 34.2.a.a.1.1 1
21.20 even 2 306.2.a.a.1.1 1
28.27 even 2 272.2.a.d.1.1 1
35.13 even 4 850.2.c.b.749.1 2
35.27 even 4 850.2.c.b.749.2 2
35.34 odd 2 850.2.a.e.1.1 1
56.13 odd 2 1088.2.a.l.1.1 1
56.27 even 2 1088.2.a.d.1.1 1
77.76 even 2 4114.2.a.a.1.1 1
84.83 odd 2 2448.2.a.k.1.1 1
91.90 odd 2 5746.2.a.b.1.1 1
105.104 even 2 7650.2.a.ci.1.1 1
119.6 even 16 578.2.d.e.155.1 8
119.13 odd 4 578.2.b.a.577.1 2
119.20 even 16 578.2.d.e.179.1 8
119.27 even 16 578.2.d.e.423.1 8
119.41 even 16 578.2.d.e.423.2 8
119.48 even 16 578.2.d.e.179.2 8
119.55 odd 4 578.2.b.a.577.2 2
119.62 even 16 578.2.d.e.155.2 8
119.76 odd 8 578.2.c.e.251.2 4
119.83 odd 8 578.2.c.e.327.2 4
119.90 even 16 578.2.d.e.399.2 8
119.97 even 16 578.2.d.e.399.1 8
119.104 odd 8 578.2.c.e.327.1 4
119.111 odd 8 578.2.c.e.251.1 4
119.118 odd 2 578.2.a.a.1.1 1
140.139 even 2 6800.2.a.b.1.1 1
168.83 odd 2 9792.2.a.bj.1.1 1
168.125 even 2 9792.2.a.y.1.1 1
357.356 even 2 5202.2.a.d.1.1 1
476.475 even 2 4624.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
34.2.a.a.1.1 1 7.6 odd 2
272.2.a.d.1.1 1 28.27 even 2
306.2.a.a.1.1 1 21.20 even 2
578.2.a.a.1.1 1 119.118 odd 2
578.2.b.a.577.1 2 119.13 odd 4
578.2.b.a.577.2 2 119.55 odd 4
578.2.c.e.251.1 4 119.111 odd 8
578.2.c.e.251.2 4 119.76 odd 8
578.2.c.e.327.1 4 119.104 odd 8
578.2.c.e.327.2 4 119.83 odd 8
578.2.d.e.155.1 8 119.6 even 16
578.2.d.e.155.2 8 119.62 even 16
578.2.d.e.179.1 8 119.20 even 16
578.2.d.e.179.2 8 119.48 even 16
578.2.d.e.399.1 8 119.97 even 16
578.2.d.e.399.2 8 119.90 even 16
578.2.d.e.423.1 8 119.27 even 16
578.2.d.e.423.2 8 119.41 even 16
850.2.a.e.1.1 1 35.34 odd 2
850.2.c.b.749.1 2 35.13 even 4
850.2.c.b.749.2 2 35.27 even 4
1088.2.a.d.1.1 1 56.27 even 2
1088.2.a.l.1.1 1 56.13 odd 2
1666.2.a.m.1.1 1 1.1 even 1 trivial
2448.2.a.k.1.1 1 84.83 odd 2
4114.2.a.a.1.1 1 77.76 even 2
4624.2.a.a.1.1 1 476.475 even 2
5202.2.a.d.1.1 1 357.356 even 2
5746.2.a.b.1.1 1 91.90 odd 2
6800.2.a.b.1.1 1 140.139 even 2
7650.2.a.ci.1.1 1 105.104 even 2
9792.2.a.y.1.1 1 168.125 even 2
9792.2.a.bj.1.1 1 168.83 odd 2