Properties

Label 1840.2.a.f.1.1
Level $1840$
Weight $2$
Character 1840.1
Self dual yes
Analytic conductor $14.692$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1840.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +6.00000 q^{11} -2.00000 q^{13} -3.00000 q^{17} +6.00000 q^{19} -1.00000 q^{23} +1.00000 q^{25} +3.00000 q^{29} +3.00000 q^{31} -1.00000 q^{35} +1.00000 q^{37} +9.00000 q^{41} +8.00000 q^{43} -3.00000 q^{45} -4.00000 q^{47} -6.00000 q^{49} +1.00000 q^{53} +6.00000 q^{55} -1.00000 q^{59} +8.00000 q^{61} +3.00000 q^{63} -2.00000 q^{65} +7.00000 q^{67} +5.00000 q^{71} -6.00000 q^{73} -6.00000 q^{77} +9.00000 q^{81} +11.0000 q^{83} -3.00000 q^{85} +4.00000 q^{89} +2.00000 q^{91} +6.00000 q^{95} +6.00000 q^{97} -18.0000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.00000 −0.130189 −0.0650945 0.997879i \(-0.520735\pi\)
−0.0650945 + 0.997879i \(0.520735\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 3.00000 0.377964
\(64\) 0 0
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 7.00000 0.855186 0.427593 0.903971i \(-0.359362\pi\)
0.427593 + 0.903971i \(0.359362\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 0 0
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.00000 −0.483368 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.00000 −0.658505 −0.329252 0.944242i \(-0.606797\pi\)
−0.329252 + 0.944242i \(0.606797\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) −4.00000 −0.325515 −0.162758 0.986666i \(-0.552039\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 0 0
\(153\) 9.00000 0.727607
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) 3.00000 0.239426 0.119713 0.992809i \(-0.461803\pi\)
0.119713 + 0.992809i \(0.461803\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −18.0000 −1.37649
\(172\) 0 0
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) −18.0000 −1.31629
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 22.0000 1.55954 0.779769 0.626067i \(-0.215336\pi\)
0.779769 + 0.626067i \(0.215336\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00000 −0.210559
\(204\) 0 0
\(205\) 9.00000 0.628587
\(206\) 0 0
\(207\) 3.00000 0.208514
\(208\) 0 0
\(209\) 36.0000 2.49017
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 0 0
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) −4.00000 −0.260931
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) −12.0000 −0.763542
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 20.0000 1.24757 0.623783 0.781598i \(-0.285595\pi\)
0.623783 + 0.781598i \(0.285595\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) 0 0
\(263\) −3.00000 −0.184988 −0.0924940 0.995713i \(-0.529484\pi\)
−0.0924940 + 0.995713i \(0.529484\pi\)
\(264\) 0 0
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −31.0000 −1.89010 −0.945052 0.326921i \(-0.893989\pi\)
−0.945052 + 0.326921i \(0.893989\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) −9.00000 −0.538816
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 17.0000 1.01055 0.505273 0.862960i \(-0.331392\pi\)
0.505273 + 0.862960i \(0.331392\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.00000 −0.531253
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) −1.00000 −0.0582223
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) −29.0000 −1.63918 −0.819588 0.572953i \(-0.805798\pi\)
−0.819588 + 0.572953i \(0.805798\pi\)
\(314\) 0 0
\(315\) 3.00000 0.169031
\(316\) 0 0
\(317\) −8.00000 −0.449325 −0.224662 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) 0 0
\(319\) 18.0000 1.00781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −18.0000 −1.00155
\(324\) 0 0
\(325\) −2.00000 −0.110940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) 0 0
\(333\) −3.00000 −0.164399
\(334\) 0 0
\(335\) 7.00000 0.382451
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 18.0000 0.974755
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 0 0
\(349\) −25.0000 −1.33822 −0.669110 0.743164i \(-0.733324\pi\)
−0.669110 + 0.743164i \(0.733324\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.00000 −0.425797 −0.212899 0.977074i \(-0.568290\pi\)
−0.212899 + 0.977074i \(0.568290\pi\)
\(354\) 0 0
\(355\) 5.00000 0.265372
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −36.0000 −1.90001 −0.950004 0.312239i \(-0.898921\pi\)
−0.950004 + 0.312239i \(0.898921\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) −35.0000 −1.82699 −0.913493 0.406855i \(-0.866625\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) 0 0
\(369\) −27.0000 −1.40556
\(370\) 0 0
\(371\) −1.00000 −0.0519174
\(372\) 0 0
\(373\) −38.0000 −1.96757 −0.983783 0.179364i \(-0.942596\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) 0 0
\(385\) −6.00000 −0.305788
\(386\) 0 0
\(387\) −24.0000 −1.21999
\(388\) 0 0
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) −6.00000 −0.298881
\(404\) 0 0
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −35.0000 −1.73064 −0.865319 0.501221i \(-0.832884\pi\)
−0.865319 + 0.501221i \(0.832884\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.00000 0.0492068
\(414\) 0 0
\(415\) 11.0000 0.539969
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14.0000 0.683945 0.341972 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) 12.0000 0.583460
\(424\) 0 0
\(425\) −3.00000 −0.145521
\(426\) 0 0
\(427\) −8.00000 −0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 17.0000 0.816968 0.408484 0.912766i \(-0.366058\pi\)
0.408484 + 0.912766i \(0.366058\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) 4.00000 0.189618
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.00000 0.141579 0.0707894 0.997491i \(-0.477448\pi\)
0.0707894 + 0.997491i \(0.477448\pi\)
\(450\) 0 0
\(451\) 54.0000 2.54276
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.00000 0.0937614
\(456\) 0 0
\(457\) −25.0000 −1.16945 −0.584725 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) −3.00000 −0.137361
\(478\) 0 0
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) 40.0000 1.81257 0.906287 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11.0000 −0.496423 −0.248212 0.968706i \(-0.579843\pi\)
−0.248212 + 0.968706i \(0.579843\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) −18.0000 −0.809040
\(496\) 0 0
\(497\) −5.00000 −0.224281
\(498\) 0 0
\(499\) 13.0000 0.581960 0.290980 0.956729i \(-0.406019\pi\)
0.290980 + 0.956729i \(0.406019\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.0000 0.757993 0.378996 0.925398i \(-0.376269\pi\)
0.378996 + 0.925398i \(0.376269\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) −24.0000 −1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) −12.0000 −0.524723 −0.262362 0.964970i \(-0.584501\pi\)
−0.262362 + 0.964970i \(0.584501\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.00000 −0.392046
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 3.00000 0.130189
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) −5.00000 −0.216169
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −36.0000 −1.55063
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −24.0000 −1.02430
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −31.0000 −1.31351 −0.656756 0.754103i \(-0.728072\pi\)
−0.656756 + 0.754103i \(0.728072\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.0000 −0.463595 −0.231797 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 0 0
\(565\) −7.00000 −0.294492
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 12.0000 0.499567 0.249783 0.968302i \(-0.419641\pi\)
0.249783 + 0.968302i \(0.419641\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.0000 −0.456357
\(582\) 0 0
\(583\) 6.00000 0.248495
\(584\) 0 0
\(585\) 6.00000 0.248069
\(586\) 0 0
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 18.0000 0.741677
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 28.0000 1.14982 0.574911 0.818216i \(-0.305037\pi\)
0.574911 + 0.818216i \(0.305037\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) 0 0
\(603\) −21.0000 −0.855186
\(604\) 0 0
\(605\) 25.0000 1.01639
\(606\) 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
\(611\) 8.00000 0.323645
\(612\) 0 0
\(613\) −22.0000 −0.888572 −0.444286 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.0000 −0.845428 −0.422714 0.906263i \(-0.638923\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.00000 −0.317470
\(636\) 0 0
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) −22.0000 −0.868948 −0.434474 0.900684i \(-0.643066\pi\)
−0.434474 + 0.900684i \(0.643066\pi\)
\(642\) 0 0
\(643\) −37.0000 −1.45914 −0.729569 0.683907i \(-0.760279\pi\)
−0.729569 + 0.683907i \(0.760279\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) 22.0000 0.856998 0.428499 0.903542i \(-0.359042\pi\)
0.428499 + 0.903542i \(0.359042\pi\)
\(660\) 0 0
\(661\) −42.0000 −1.63361 −0.816805 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.00000 −0.232670
\(666\) 0 0
\(667\) −3.00000 −0.116160
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 48.0000 1.85302
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 47.0000 1.80636 0.903178 0.429265i \(-0.141228\pi\)
0.903178 + 0.429265i \(0.141228\pi\)
\(678\) 0 0
\(679\) −6.00000 −0.230259
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 0 0
\(685\) 10.0000 0.382080
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 0 0
\(693\) 18.0000 0.683763
\(694\) 0 0
\(695\) −7.00000 −0.265525
\(696\) 0 0
\(697\) −27.0000 −1.02270
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24.0000 −0.906467 −0.453234 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.00000 0.338480
\(708\) 0 0
\(709\) 8.00000 0.300446 0.150223 0.988652i \(-0.452001\pi\)
0.150223 + 0.988652i \(0.452001\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.00000 −0.112351
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13.0000 −0.484818 −0.242409 0.970174i \(-0.577938\pi\)
−0.242409 + 0.970174i \(0.577938\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.00000 0.111417
\(726\) 0 0
\(727\) 21.0000 0.778847 0.389423 0.921059i \(-0.372674\pi\)
0.389423 + 0.921059i \(0.372674\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) 25.0000 0.923396 0.461698 0.887037i \(-0.347240\pi\)
0.461698 + 0.887037i \(0.347240\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 42.0000 1.54709
\(738\) 0 0
\(739\) 19.0000 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 20.0000 0.732743
\(746\) 0 0
\(747\) −33.0000 −1.20741
\(748\) 0 0
\(749\) 5.00000 0.182696
\(750\) 0 0
\(751\) 14.0000 0.510867 0.255434 0.966827i \(-0.417782\pi\)
0.255434 + 0.966827i \(0.417782\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.00000 −0.145575
\(756\) 0 0
\(757\) 15.0000 0.545184 0.272592 0.962130i \(-0.412119\pi\)
0.272592 + 0.962130i \(0.412119\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 29.0000 1.05125 0.525625 0.850717i \(-0.323832\pi\)
0.525625 + 0.850717i \(0.323832\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) 0 0
\(765\) 9.00000 0.325396
\(766\) 0 0
\(767\) 2.00000 0.0722158
\(768\) 0 0
\(769\) 44.0000 1.58668 0.793340 0.608778i \(-0.208340\pi\)
0.793340 + 0.608778i \(0.208340\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −22.0000 −0.791285 −0.395643 0.918405i \(-0.629478\pi\)
−0.395643 + 0.918405i \(0.629478\pi\)
\(774\) 0 0
\(775\) 3.00000 0.107763
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 54.0000 1.93475
\(780\) 0 0
\(781\) 30.0000 1.07348
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.00000 0.107075
\(786\) 0 0
\(787\) −13.0000 −0.463400 −0.231700 0.972787i \(-0.574429\pi\)
−0.231700 + 0.972787i \(0.574429\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.00000 0.248891
\(792\) 0 0
\(793\) −16.0000 −0.568177
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.0000 −1.16892 −0.584460 0.811423i \(-0.698694\pi\)
−0.584460 + 0.811423i \(0.698694\pi\)
\(798\) 0 0
\(799\) 12.0000 0.424529
\(800\) 0 0
\(801\) −12.0000 −0.423999
\(802\) 0 0
\(803\) −36.0000 −1.27041
\(804\) 0 0
\(805\) 1.00000 0.0352454
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 47.0000 1.65243 0.826216 0.563353i \(-0.190489\pi\)
0.826216 + 0.563353i \(0.190489\pi\)
\(810\) 0 0
\(811\) −37.0000 −1.29925 −0.649623 0.760257i \(-0.725073\pi\)
−0.649623 + 0.760257i \(0.725073\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14.0000 0.490399
\(816\) 0 0
\(817\) 48.0000 1.67931
\(818\) 0 0
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) 42.0000 1.46581 0.732905 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 57.0000 1.98208 0.991042 0.133550i \(-0.0426376\pi\)
0.991042 + 0.133550i \(0.0426376\pi\)
\(828\) 0 0
\(829\) 33.0000 1.14614 0.573069 0.819507i \(-0.305753\pi\)
0.573069 + 0.819507i \(0.305753\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.00000 −0.0342796
\(852\) 0 0
\(853\) −2.00000 −0.0684787 −0.0342393 0.999414i \(-0.510901\pi\)
−0.0342393 + 0.999414i \(0.510901\pi\)
\(854\) 0 0
\(855\) −18.0000 −0.615587
\(856\) 0 0
\(857\) 14.0000 0.478231 0.239115 0.970991i \(-0.423143\pi\)
0.239115 + 0.970991i \(0.423143\pi\)
\(858\) 0 0
\(859\) −1.00000 −0.0341196 −0.0170598 0.999854i \(-0.505431\pi\)
−0.0170598 + 0.999854i \(0.505431\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22.0000 −0.748889 −0.374444 0.927249i \(-0.622167\pi\)
−0.374444 + 0.927249i \(0.622167\pi\)
\(864\) 0 0
\(865\) −16.0000 −0.544016
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −14.0000 −0.474372
\(872\) 0 0
\(873\) −18.0000 −0.609208
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 6.00000 0.202606 0.101303 0.994856i \(-0.467699\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.0000 1.00730 0.503651 0.863907i \(-0.331990\pi\)
0.503651 + 0.863907i \(0.331990\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 54.0000 1.80907
\(892\) 0 0
\(893\) −24.0000 −0.803129
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 9.00000 0.300167
\(900\) 0 0
\(901\) −3.00000 −0.0999445
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 7.00000 0.232431 0.116216 0.993224i \(-0.462924\pi\)
0.116216 + 0.993224i \(0.462924\pi\)
\(908\) 0 0
\(909\) 27.0000 0.895533
\(910\) 0 0
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) 0 0
\(913\) 66.0000 2.18428
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 12.0000 0.396275
\(918\) 0 0
\(919\) 32.0000 1.05558 0.527791 0.849374i \(-0.323020\pi\)
0.527791 + 0.849374i \(0.323020\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −10.0000 −0.329154
\(924\) 0 0
\(925\) 1.00000 0.0328798
\(926\) 0 0
\(927\) −48.0000 −1.57653
\(928\) 0 0
\(929\) −29.0000 −0.951459 −0.475730 0.879592i \(-0.657816\pi\)
−0.475730 + 0.879592i \(0.657816\pi\)
\(930\) 0 0
\(931\) −36.0000 −1.17985
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18.0000 −0.588663
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −24.0000 −0.782378 −0.391189 0.920310i \(-0.627936\pi\)
−0.391189 + 0.920310i \(0.627936\pi\)
\(942\) 0 0
\(943\) −9.00000 −0.293080
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.00000 0.259965 0.129983 0.991516i \(-0.458508\pi\)
0.129983 + 0.991516i \(0.458508\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 0 0
\(955\) −8.00000 −0.258874
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −10.0000 −0.322917
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 15.0000 0.483368
\(964\) 0 0
\(965\) −4.00000 −0.128765
\(966\) 0 0
\(967\) 56.0000 1.80084 0.900419 0.435023i \(-0.143260\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −40.0000 −1.28366 −0.641831 0.766846i \(-0.721825\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(972\) 0 0
\(973\) 7.00000 0.224410
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −33.0000 −1.05576 −0.527882 0.849318i \(-0.677014\pi\)
−0.527882 + 0.849318i \(0.677014\pi\)
\(978\) 0 0
\(979\) 24.0000 0.767043
\(980\) 0 0
\(981\) 18.0000 0.574696
\(982\) 0 0
\(983\) −1.00000 −0.0318950 −0.0159475 0.999873i \(-0.505076\pi\)
−0.0159475 + 0.999873i \(0.505076\pi\)
\(984\) 0 0
\(985\) −18.0000 −0.573528
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 15.0000 0.476491 0.238245 0.971205i \(-0.423428\pi\)
0.238245 + 0.971205i \(0.423428\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 22.0000 0.697447
\(996\) 0 0
\(997\) −32.0000 −1.01345 −0.506725 0.862108i \(-0.669144\pi\)
−0.506725 + 0.862108i \(0.669144\pi\)
\(998\) 0 0
\(999\) 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 1840.2.a.f.1.1 1
4.3 odd 2 920.2.a.c.1.1 1
5.4 even 2 9200.2.a.w.1.1 1
8.3 odd 2 7360.2.a.l.1.1 1
8.5 even 2 7360.2.a.k.1.1 1
12.11 even 2 8280.2.a.j.1.1 1
20.3 even 4 4600.2.e.j.4049.1 2
20.7 even 4 4600.2.e.j.4049.2 2
20.19 odd 2 4600.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.c.1.1 1 4.3 odd 2
1840.2.a.f.1.1 1 1.1 even 1 trivial
4600.2.a.h.1.1 1 20.19 odd 2
4600.2.e.j.4049.1 2 20.3 even 4
4600.2.e.j.4049.2 2 20.7 even 4
7360.2.a.k.1.1 1 8.5 even 2
7360.2.a.l.1.1 1 8.3 odd 2
8280.2.a.j.1.1 1 12.11 even 2
9200.2.a.w.1.1 1 5.4 even 2