Properties

Label 1932.2.a.g.1.2
Level $1932$
Weight $2$
Character 1932.1
Self dual yes
Analytic conductor $15.427$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.4270976705\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 1932.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +0.618034 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +0.618034 q^{5} -1.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} -1.61803 q^{13} +0.618034 q^{15} -6.70820 q^{17} +0.236068 q^{19} -1.00000 q^{21} -1.00000 q^{23} -4.61803 q^{25} +1.00000 q^{27} -6.23607 q^{29} -3.00000 q^{31} -3.00000 q^{33} -0.618034 q^{35} +0.527864 q^{37} -1.61803 q^{39} +5.94427 q^{41} +2.09017 q^{43} +0.618034 q^{45} -4.76393 q^{47} +1.00000 q^{49} -6.70820 q^{51} +6.32624 q^{53} -1.85410 q^{55} +0.236068 q^{57} -7.38197 q^{59} -0.854102 q^{61} -1.00000 q^{63} -1.00000 q^{65} -13.5623 q^{67} -1.00000 q^{69} -2.38197 q^{71} +6.23607 q^{73} -4.61803 q^{75} +3.00000 q^{77} +6.70820 q^{79} +1.00000 q^{81} +1.47214 q^{83} -4.14590 q^{85} -6.23607 q^{87} +7.79837 q^{89} +1.61803 q^{91} -3.00000 q^{93} +0.145898 q^{95} +14.4164 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - q^{5} - 2 q^{7} + 2 q^{9} - 6 q^{11} - q^{13} - q^{15} - 4 q^{19} - 2 q^{21} - 2 q^{23} - 7 q^{25} + 2 q^{27} - 8 q^{29} - 6 q^{31} - 6 q^{33} + q^{35} + 10 q^{37} - q^{39} - 6 q^{41} - 7 q^{43} - q^{45} - 14 q^{47} + 2 q^{49} - 3 q^{53} + 3 q^{55} - 4 q^{57} - 17 q^{59} + 5 q^{61} - 2 q^{63} - 2 q^{65} - 7 q^{67} - 2 q^{69} - 7 q^{71} + 8 q^{73} - 7 q^{75} + 6 q^{77} + 2 q^{81} - 6 q^{83} - 15 q^{85} - 8 q^{87} - 9 q^{89} + q^{91} - 6 q^{93} + 7 q^{95} + 2 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.618034 0.276393 0.138197 0.990405i \(-0.455869\pi\)
0.138197 + 0.990405i \(0.455869\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −1.61803 −0.448762 −0.224381 0.974502i \(-0.572036\pi\)
−0.224381 + 0.974502i \(0.572036\pi\)
\(14\) 0 0
\(15\) 0.618034 0.159576
\(16\) 0 0
\(17\) −6.70820 −1.62698 −0.813489 0.581580i \(-0.802435\pi\)
−0.813489 + 0.581580i \(0.802435\pi\)
\(18\) 0 0
\(19\) 0.236068 0.0541577 0.0270789 0.999633i \(-0.491379\pi\)
0.0270789 + 0.999633i \(0.491379\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −4.61803 −0.923607
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.23607 −1.15801 −0.579004 0.815324i \(-0.696559\pi\)
−0.579004 + 0.815324i \(0.696559\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) −0.618034 −0.104467
\(36\) 0 0
\(37\) 0.527864 0.0867803 0.0433902 0.999058i \(-0.486184\pi\)
0.0433902 + 0.999058i \(0.486184\pi\)
\(38\) 0 0
\(39\) −1.61803 −0.259093
\(40\) 0 0
\(41\) 5.94427 0.928339 0.464170 0.885746i \(-0.346353\pi\)
0.464170 + 0.885746i \(0.346353\pi\)
\(42\) 0 0
\(43\) 2.09017 0.318748 0.159374 0.987218i \(-0.449052\pi\)
0.159374 + 0.987218i \(0.449052\pi\)
\(44\) 0 0
\(45\) 0.618034 0.0921311
\(46\) 0 0
\(47\) −4.76393 −0.694891 −0.347445 0.937700i \(-0.612951\pi\)
−0.347445 + 0.937700i \(0.612951\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −6.70820 −0.939336
\(52\) 0 0
\(53\) 6.32624 0.868976 0.434488 0.900678i \(-0.356929\pi\)
0.434488 + 0.900678i \(0.356929\pi\)
\(54\) 0 0
\(55\) −1.85410 −0.250007
\(56\) 0 0
\(57\) 0.236068 0.0312680
\(58\) 0 0
\(59\) −7.38197 −0.961050 −0.480525 0.876981i \(-0.659554\pi\)
−0.480525 + 0.876981i \(0.659554\pi\)
\(60\) 0 0
\(61\) −0.854102 −0.109357 −0.0546783 0.998504i \(-0.517413\pi\)
−0.0546783 + 0.998504i \(0.517413\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −13.5623 −1.65690 −0.828450 0.560063i \(-0.810777\pi\)
−0.828450 + 0.560063i \(0.810777\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −2.38197 −0.282687 −0.141344 0.989961i \(-0.545142\pi\)
−0.141344 + 0.989961i \(0.545142\pi\)
\(72\) 0 0
\(73\) 6.23607 0.729877 0.364938 0.931032i \(-0.381090\pi\)
0.364938 + 0.931032i \(0.381090\pi\)
\(74\) 0 0
\(75\) −4.61803 −0.533245
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 6.70820 0.754732 0.377366 0.926064i \(-0.376830\pi\)
0.377366 + 0.926064i \(0.376830\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 1.47214 0.161588 0.0807940 0.996731i \(-0.474254\pi\)
0.0807940 + 0.996731i \(0.474254\pi\)
\(84\) 0 0
\(85\) −4.14590 −0.449686
\(86\) 0 0
\(87\) −6.23607 −0.668577
\(88\) 0 0
\(89\) 7.79837 0.826626 0.413313 0.910589i \(-0.364372\pi\)
0.413313 + 0.910589i \(0.364372\pi\)
\(90\) 0 0
\(91\) 1.61803 0.169616
\(92\) 0 0
\(93\) −3.00000 −0.311086
\(94\) 0 0
\(95\) 0.145898 0.0149688
\(96\) 0 0
\(97\) 14.4164 1.46376 0.731882 0.681431i \(-0.238642\pi\)
0.731882 + 0.681431i \(0.238642\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −10.3262 −1.02750 −0.513750 0.857940i \(-0.671744\pi\)
−0.513750 + 0.857940i \(0.671744\pi\)
\(102\) 0 0
\(103\) −7.41641 −0.730760 −0.365380 0.930858i \(-0.619061\pi\)
−0.365380 + 0.930858i \(0.619061\pi\)
\(104\) 0 0
\(105\) −0.618034 −0.0603139
\(106\) 0 0
\(107\) 8.38197 0.810315 0.405158 0.914247i \(-0.367217\pi\)
0.405158 + 0.914247i \(0.367217\pi\)
\(108\) 0 0
\(109\) 9.09017 0.870680 0.435340 0.900266i \(-0.356628\pi\)
0.435340 + 0.900266i \(0.356628\pi\)
\(110\) 0 0
\(111\) 0.527864 0.0501026
\(112\) 0 0
\(113\) −12.3262 −1.15955 −0.579777 0.814775i \(-0.696861\pi\)
−0.579777 + 0.814775i \(0.696861\pi\)
\(114\) 0 0
\(115\) −0.618034 −0.0576320
\(116\) 0 0
\(117\) −1.61803 −0.149587
\(118\) 0 0
\(119\) 6.70820 0.614940
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 5.94427 0.535977
\(124\) 0 0
\(125\) −5.94427 −0.531672
\(126\) 0 0
\(127\) −14.5623 −1.29220 −0.646098 0.763255i \(-0.723600\pi\)
−0.646098 + 0.763255i \(0.723600\pi\)
\(128\) 0 0
\(129\) 2.09017 0.184029
\(130\) 0 0
\(131\) −11.9443 −1.04358 −0.521788 0.853075i \(-0.674735\pi\)
−0.521788 + 0.853075i \(0.674735\pi\)
\(132\) 0 0
\(133\) −0.236068 −0.0204697
\(134\) 0 0
\(135\) 0.618034 0.0531919
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) 0.145898 0.0123749 0.00618745 0.999981i \(-0.498030\pi\)
0.00618745 + 0.999981i \(0.498030\pi\)
\(140\) 0 0
\(141\) −4.76393 −0.401195
\(142\) 0 0
\(143\) 4.85410 0.405920
\(144\) 0 0
\(145\) −3.85410 −0.320066
\(146\) 0 0
\(147\) 1.00000 0.0824786
\(148\) 0 0
\(149\) 3.23607 0.265109 0.132555 0.991176i \(-0.457682\pi\)
0.132555 + 0.991176i \(0.457682\pi\)
\(150\) 0 0
\(151\) 21.1246 1.71910 0.859548 0.511055i \(-0.170745\pi\)
0.859548 + 0.511055i \(0.170745\pi\)
\(152\) 0 0
\(153\) −6.70820 −0.542326
\(154\) 0 0
\(155\) −1.85410 −0.148925
\(156\) 0 0
\(157\) 13.2361 1.05635 0.528177 0.849135i \(-0.322876\pi\)
0.528177 + 0.849135i \(0.322876\pi\)
\(158\) 0 0
\(159\) 6.32624 0.501703
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 4.14590 0.324732 0.162366 0.986731i \(-0.448088\pi\)
0.162366 + 0.986731i \(0.448088\pi\)
\(164\) 0 0
\(165\) −1.85410 −0.144342
\(166\) 0 0
\(167\) −19.4721 −1.50680 −0.753400 0.657563i \(-0.771587\pi\)
−0.753400 + 0.657563i \(0.771587\pi\)
\(168\) 0 0
\(169\) −10.3820 −0.798613
\(170\) 0 0
\(171\) 0.236068 0.0180526
\(172\) 0 0
\(173\) 4.52786 0.344247 0.172124 0.985075i \(-0.444937\pi\)
0.172124 + 0.985075i \(0.444937\pi\)
\(174\) 0 0
\(175\) 4.61803 0.349091
\(176\) 0 0
\(177\) −7.38197 −0.554863
\(178\) 0 0
\(179\) −18.0344 −1.34796 −0.673979 0.738751i \(-0.735416\pi\)
−0.673979 + 0.738751i \(0.735416\pi\)
\(180\) 0 0
\(181\) 8.52786 0.633871 0.316936 0.948447i \(-0.397346\pi\)
0.316936 + 0.948447i \(0.397346\pi\)
\(182\) 0 0
\(183\) −0.854102 −0.0631370
\(184\) 0 0
\(185\) 0.326238 0.0239855
\(186\) 0 0
\(187\) 20.1246 1.47166
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 10.6525 0.770786 0.385393 0.922753i \(-0.374066\pi\)
0.385393 + 0.922753i \(0.374066\pi\)
\(192\) 0 0
\(193\) 7.70820 0.554849 0.277424 0.960747i \(-0.410519\pi\)
0.277424 + 0.960747i \(0.410519\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) 3.61803 0.257774 0.128887 0.991659i \(-0.458860\pi\)
0.128887 + 0.991659i \(0.458860\pi\)
\(198\) 0 0
\(199\) 2.43769 0.172804 0.0864018 0.996260i \(-0.472463\pi\)
0.0864018 + 0.996260i \(0.472463\pi\)
\(200\) 0 0
\(201\) −13.5623 −0.956611
\(202\) 0 0
\(203\) 6.23607 0.437686
\(204\) 0 0
\(205\) 3.67376 0.256587
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) −0.708204 −0.0489875
\(210\) 0 0
\(211\) 14.1246 0.972378 0.486189 0.873854i \(-0.338387\pi\)
0.486189 + 0.873854i \(0.338387\pi\)
\(212\) 0 0
\(213\) −2.38197 −0.163210
\(214\) 0 0
\(215\) 1.29180 0.0880998
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) 0 0
\(219\) 6.23607 0.421394
\(220\) 0 0
\(221\) 10.8541 0.730126
\(222\) 0 0
\(223\) −12.7984 −0.857043 −0.428521 0.903532i \(-0.640965\pi\)
−0.428521 + 0.903532i \(0.640965\pi\)
\(224\) 0 0
\(225\) −4.61803 −0.307869
\(226\) 0 0
\(227\) −29.4508 −1.95472 −0.977361 0.211580i \(-0.932139\pi\)
−0.977361 + 0.211580i \(0.932139\pi\)
\(228\) 0 0
\(229\) −9.27051 −0.612613 −0.306306 0.951933i \(-0.599093\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(230\) 0 0
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) −0.909830 −0.0596049 −0.0298025 0.999556i \(-0.509488\pi\)
−0.0298025 + 0.999556i \(0.509488\pi\)
\(234\) 0 0
\(235\) −2.94427 −0.192063
\(236\) 0 0
\(237\) 6.70820 0.435745
\(238\) 0 0
\(239\) −15.3820 −0.994977 −0.497488 0.867471i \(-0.665744\pi\)
−0.497488 + 0.867471i \(0.665744\pi\)
\(240\) 0 0
\(241\) 21.0000 1.35273 0.676364 0.736567i \(-0.263554\pi\)
0.676364 + 0.736567i \(0.263554\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.618034 0.0394847
\(246\) 0 0
\(247\) −0.381966 −0.0243039
\(248\) 0 0
\(249\) 1.47214 0.0932928
\(250\) 0 0
\(251\) 8.65248 0.546139 0.273070 0.961994i \(-0.411961\pi\)
0.273070 + 0.961994i \(0.411961\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) −4.14590 −0.259626
\(256\) 0 0
\(257\) −14.6525 −0.913996 −0.456998 0.889468i \(-0.651075\pi\)
−0.456998 + 0.889468i \(0.651075\pi\)
\(258\) 0 0
\(259\) −0.527864 −0.0327999
\(260\) 0 0
\(261\) −6.23607 −0.386003
\(262\) 0 0
\(263\) −7.18034 −0.442759 −0.221379 0.975188i \(-0.571056\pi\)
−0.221379 + 0.975188i \(0.571056\pi\)
\(264\) 0 0
\(265\) 3.90983 0.240179
\(266\) 0 0
\(267\) 7.79837 0.477253
\(268\) 0 0
\(269\) 1.79837 0.109649 0.0548244 0.998496i \(-0.482540\pi\)
0.0548244 + 0.998496i \(0.482540\pi\)
\(270\) 0 0
\(271\) 1.18034 0.0717005 0.0358503 0.999357i \(-0.488586\pi\)
0.0358503 + 0.999357i \(0.488586\pi\)
\(272\) 0 0
\(273\) 1.61803 0.0979279
\(274\) 0 0
\(275\) 13.8541 0.835434
\(276\) 0 0
\(277\) −5.03444 −0.302490 −0.151245 0.988496i \(-0.548328\pi\)
−0.151245 + 0.988496i \(0.548328\pi\)
\(278\) 0 0
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) −17.2361 −1.02822 −0.514109 0.857725i \(-0.671877\pi\)
−0.514109 + 0.857725i \(0.671877\pi\)
\(282\) 0 0
\(283\) −8.14590 −0.484223 −0.242112 0.970248i \(-0.577840\pi\)
−0.242112 + 0.970248i \(0.577840\pi\)
\(284\) 0 0
\(285\) 0.145898 0.00864225
\(286\) 0 0
\(287\) −5.94427 −0.350879
\(288\) 0 0
\(289\) 28.0000 1.64706
\(290\) 0 0
\(291\) 14.4164 0.845105
\(292\) 0 0
\(293\) 16.9443 0.989895 0.494947 0.868923i \(-0.335187\pi\)
0.494947 + 0.868923i \(0.335187\pi\)
\(294\) 0 0
\(295\) −4.56231 −0.265628
\(296\) 0 0
\(297\) −3.00000 −0.174078
\(298\) 0 0
\(299\) 1.61803 0.0935733
\(300\) 0 0
\(301\) −2.09017 −0.120475
\(302\) 0 0
\(303\) −10.3262 −0.593227
\(304\) 0 0
\(305\) −0.527864 −0.0302254
\(306\) 0 0
\(307\) −1.58359 −0.0903804 −0.0451902 0.998978i \(-0.514389\pi\)
−0.0451902 + 0.998978i \(0.514389\pi\)
\(308\) 0 0
\(309\) −7.41641 −0.421905
\(310\) 0 0
\(311\) 18.2705 1.03603 0.518013 0.855373i \(-0.326672\pi\)
0.518013 + 0.855373i \(0.326672\pi\)
\(312\) 0 0
\(313\) 26.4721 1.49629 0.748147 0.663533i \(-0.230944\pi\)
0.748147 + 0.663533i \(0.230944\pi\)
\(314\) 0 0
\(315\) −0.618034 −0.0348223
\(316\) 0 0
\(317\) 3.38197 0.189950 0.0949751 0.995480i \(-0.469723\pi\)
0.0949751 + 0.995480i \(0.469723\pi\)
\(318\) 0 0
\(319\) 18.7082 1.04746
\(320\) 0 0
\(321\) 8.38197 0.467836
\(322\) 0 0
\(323\) −1.58359 −0.0881134
\(324\) 0 0
\(325\) 7.47214 0.414480
\(326\) 0 0
\(327\) 9.09017 0.502688
\(328\) 0 0
\(329\) 4.76393 0.262644
\(330\) 0 0
\(331\) −27.8885 −1.53289 −0.766447 0.642308i \(-0.777977\pi\)
−0.766447 + 0.642308i \(0.777977\pi\)
\(332\) 0 0
\(333\) 0.527864 0.0289268
\(334\) 0 0
\(335\) −8.38197 −0.457956
\(336\) 0 0
\(337\) −10.3820 −0.565542 −0.282771 0.959187i \(-0.591254\pi\)
−0.282771 + 0.959187i \(0.591254\pi\)
\(338\) 0 0
\(339\) −12.3262 −0.669469
\(340\) 0 0
\(341\) 9.00000 0.487377
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −0.618034 −0.0332738
\(346\) 0 0
\(347\) −4.52786 −0.243068 −0.121534 0.992587i \(-0.538781\pi\)
−0.121534 + 0.992587i \(0.538781\pi\)
\(348\) 0 0
\(349\) 19.8541 1.06277 0.531383 0.847132i \(-0.321673\pi\)
0.531383 + 0.847132i \(0.321673\pi\)
\(350\) 0 0
\(351\) −1.61803 −0.0863643
\(352\) 0 0
\(353\) −15.0000 −0.798369 −0.399185 0.916871i \(-0.630707\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(354\) 0 0
\(355\) −1.47214 −0.0781329
\(356\) 0 0
\(357\) 6.70820 0.355036
\(358\) 0 0
\(359\) −2.03444 −0.107374 −0.0536869 0.998558i \(-0.517097\pi\)
−0.0536869 + 0.998558i \(0.517097\pi\)
\(360\) 0 0
\(361\) −18.9443 −0.997067
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 3.85410 0.201733
\(366\) 0 0
\(367\) −6.20163 −0.323722 −0.161861 0.986814i \(-0.551750\pi\)
−0.161861 + 0.986814i \(0.551750\pi\)
\(368\) 0 0
\(369\) 5.94427 0.309446
\(370\) 0 0
\(371\) −6.32624 −0.328442
\(372\) 0 0
\(373\) 28.8885 1.49579 0.747896 0.663816i \(-0.231064\pi\)
0.747896 + 0.663816i \(0.231064\pi\)
\(374\) 0 0
\(375\) −5.94427 −0.306961
\(376\) 0 0
\(377\) 10.0902 0.519670
\(378\) 0 0
\(379\) −5.52786 −0.283947 −0.141974 0.989870i \(-0.545345\pi\)
−0.141974 + 0.989870i \(0.545345\pi\)
\(380\) 0 0
\(381\) −14.5623 −0.746050
\(382\) 0 0
\(383\) 29.9443 1.53008 0.765040 0.643982i \(-0.222719\pi\)
0.765040 + 0.643982i \(0.222719\pi\)
\(384\) 0 0
\(385\) 1.85410 0.0944938
\(386\) 0 0
\(387\) 2.09017 0.106249
\(388\) 0 0
\(389\) 9.65248 0.489400 0.244700 0.969599i \(-0.421311\pi\)
0.244700 + 0.969599i \(0.421311\pi\)
\(390\) 0 0
\(391\) 6.70820 0.339248
\(392\) 0 0
\(393\) −11.9443 −0.602509
\(394\) 0 0
\(395\) 4.14590 0.208603
\(396\) 0 0
\(397\) 25.1246 1.26097 0.630484 0.776202i \(-0.282856\pi\)
0.630484 + 0.776202i \(0.282856\pi\)
\(398\) 0 0
\(399\) −0.236068 −0.0118182
\(400\) 0 0
\(401\) −11.7639 −0.587463 −0.293731 0.955888i \(-0.594897\pi\)
−0.293731 + 0.955888i \(0.594897\pi\)
\(402\) 0 0
\(403\) 4.85410 0.241800
\(404\) 0 0
\(405\) 0.618034 0.0307104
\(406\) 0 0
\(407\) −1.58359 −0.0784957
\(408\) 0 0
\(409\) 9.58359 0.473878 0.236939 0.971525i \(-0.423856\pi\)
0.236939 + 0.971525i \(0.423856\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) 0 0
\(413\) 7.38197 0.363243
\(414\) 0 0
\(415\) 0.909830 0.0446618
\(416\) 0 0
\(417\) 0.145898 0.00714466
\(418\) 0 0
\(419\) −24.2148 −1.18297 −0.591485 0.806316i \(-0.701458\pi\)
−0.591485 + 0.806316i \(0.701458\pi\)
\(420\) 0 0
\(421\) −15.6180 −0.761176 −0.380588 0.924745i \(-0.624278\pi\)
−0.380588 + 0.924745i \(0.624278\pi\)
\(422\) 0 0
\(423\) −4.76393 −0.231630
\(424\) 0 0
\(425\) 30.9787 1.50269
\(426\) 0 0
\(427\) 0.854102 0.0413329
\(428\) 0 0
\(429\) 4.85410 0.234358
\(430\) 0 0
\(431\) 25.1459 1.21124 0.605618 0.795756i \(-0.292926\pi\)
0.605618 + 0.795756i \(0.292926\pi\)
\(432\) 0 0
\(433\) 27.7082 1.33157 0.665786 0.746143i \(-0.268097\pi\)
0.665786 + 0.746143i \(0.268097\pi\)
\(434\) 0 0
\(435\) −3.85410 −0.184790
\(436\) 0 0
\(437\) −0.236068 −0.0112927
\(438\) 0 0
\(439\) 30.8885 1.47423 0.737115 0.675767i \(-0.236188\pi\)
0.737115 + 0.675767i \(0.236188\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −19.4164 −0.922501 −0.461251 0.887270i \(-0.652599\pi\)
−0.461251 + 0.887270i \(0.652599\pi\)
\(444\) 0 0
\(445\) 4.81966 0.228474
\(446\) 0 0
\(447\) 3.23607 0.153061
\(448\) 0 0
\(449\) 0.909830 0.0429375 0.0214688 0.999770i \(-0.493166\pi\)
0.0214688 + 0.999770i \(0.493166\pi\)
\(450\) 0 0
\(451\) −17.8328 −0.839714
\(452\) 0 0
\(453\) 21.1246 0.992521
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) −6.97871 −0.326450 −0.163225 0.986589i \(-0.552190\pi\)
−0.163225 + 0.986589i \(0.552190\pi\)
\(458\) 0 0
\(459\) −6.70820 −0.313112
\(460\) 0 0
\(461\) 7.20163 0.335413 0.167707 0.985837i \(-0.446364\pi\)
0.167707 + 0.985837i \(0.446364\pi\)
\(462\) 0 0
\(463\) −37.8328 −1.75824 −0.879120 0.476600i \(-0.841869\pi\)
−0.879120 + 0.476600i \(0.841869\pi\)
\(464\) 0 0
\(465\) −1.85410 −0.0859819
\(466\) 0 0
\(467\) −24.8885 −1.15170 −0.575852 0.817554i \(-0.695330\pi\)
−0.575852 + 0.817554i \(0.695330\pi\)
\(468\) 0 0
\(469\) 13.5623 0.626249
\(470\) 0 0
\(471\) 13.2361 0.609886
\(472\) 0 0
\(473\) −6.27051 −0.288318
\(474\) 0 0
\(475\) −1.09017 −0.0500204
\(476\) 0 0
\(477\) 6.32624 0.289659
\(478\) 0 0
\(479\) 13.7639 0.628890 0.314445 0.949276i \(-0.398182\pi\)
0.314445 + 0.949276i \(0.398182\pi\)
\(480\) 0 0
\(481\) −0.854102 −0.0389437
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) 8.90983 0.404575
\(486\) 0 0
\(487\) −29.0000 −1.31412 −0.657058 0.753840i \(-0.728199\pi\)
−0.657058 + 0.753840i \(0.728199\pi\)
\(488\) 0 0
\(489\) 4.14590 0.187484
\(490\) 0 0
\(491\) 6.09017 0.274846 0.137423 0.990512i \(-0.456118\pi\)
0.137423 + 0.990512i \(0.456118\pi\)
\(492\) 0 0
\(493\) 41.8328 1.88406
\(494\) 0 0
\(495\) −1.85410 −0.0833357
\(496\) 0 0
\(497\) 2.38197 0.106846
\(498\) 0 0
\(499\) 34.5066 1.54473 0.772363 0.635181i \(-0.219075\pi\)
0.772363 + 0.635181i \(0.219075\pi\)
\(500\) 0 0
\(501\) −19.4721 −0.869951
\(502\) 0 0
\(503\) 40.2148 1.79309 0.896544 0.442954i \(-0.146070\pi\)
0.896544 + 0.442954i \(0.146070\pi\)
\(504\) 0 0
\(505\) −6.38197 −0.283994
\(506\) 0 0
\(507\) −10.3820 −0.461079
\(508\) 0 0
\(509\) 16.7639 0.743048 0.371524 0.928423i \(-0.378835\pi\)
0.371524 + 0.928423i \(0.378835\pi\)
\(510\) 0 0
\(511\) −6.23607 −0.275867
\(512\) 0 0
\(513\) 0.236068 0.0104227
\(514\) 0 0
\(515\) −4.58359 −0.201977
\(516\) 0 0
\(517\) 14.2918 0.628552
\(518\) 0 0
\(519\) 4.52786 0.198751
\(520\) 0 0
\(521\) −22.3607 −0.979639 −0.489820 0.871824i \(-0.662937\pi\)
−0.489820 + 0.871824i \(0.662937\pi\)
\(522\) 0 0
\(523\) 18.0000 0.787085 0.393543 0.919306i \(-0.371249\pi\)
0.393543 + 0.919306i \(0.371249\pi\)
\(524\) 0 0
\(525\) 4.61803 0.201548
\(526\) 0 0
\(527\) 20.1246 0.876642
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −7.38197 −0.320350
\(532\) 0 0
\(533\) −9.61803 −0.416603
\(534\) 0 0
\(535\) 5.18034 0.223966
\(536\) 0 0
\(537\) −18.0344 −0.778244
\(538\) 0 0
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) 37.1246 1.59611 0.798056 0.602583i \(-0.205862\pi\)
0.798056 + 0.602583i \(0.205862\pi\)
\(542\) 0 0
\(543\) 8.52786 0.365966
\(544\) 0 0
\(545\) 5.61803 0.240650
\(546\) 0 0
\(547\) −17.8541 −0.763386 −0.381693 0.924289i \(-0.624659\pi\)
−0.381693 + 0.924289i \(0.624659\pi\)
\(548\) 0 0
\(549\) −0.854102 −0.0364522
\(550\) 0 0
\(551\) −1.47214 −0.0627151
\(552\) 0 0
\(553\) −6.70820 −0.285262
\(554\) 0 0
\(555\) 0.326238 0.0138480
\(556\) 0 0
\(557\) 18.7639 0.795053 0.397527 0.917591i \(-0.369869\pi\)
0.397527 + 0.917591i \(0.369869\pi\)
\(558\) 0 0
\(559\) −3.38197 −0.143042
\(560\) 0 0
\(561\) 20.1246 0.849662
\(562\) 0 0
\(563\) −28.3820 −1.19616 −0.598079 0.801437i \(-0.704069\pi\)
−0.598079 + 0.801437i \(0.704069\pi\)
\(564\) 0 0
\(565\) −7.61803 −0.320493
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) −4.58359 −0.192154 −0.0960771 0.995374i \(-0.530630\pi\)
−0.0960771 + 0.995374i \(0.530630\pi\)
\(570\) 0 0
\(571\) 0.708204 0.0296374 0.0148187 0.999890i \(-0.495283\pi\)
0.0148187 + 0.999890i \(0.495283\pi\)
\(572\) 0 0
\(573\) 10.6525 0.445014
\(574\) 0 0
\(575\) 4.61803 0.192585
\(576\) 0 0
\(577\) 37.7771 1.57268 0.786340 0.617794i \(-0.211973\pi\)
0.786340 + 0.617794i \(0.211973\pi\)
\(578\) 0 0
\(579\) 7.70820 0.320342
\(580\) 0 0
\(581\) −1.47214 −0.0610745
\(582\) 0 0
\(583\) −18.9787 −0.786018
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) 0 0
\(587\) 22.3820 0.923803 0.461901 0.886931i \(-0.347167\pi\)
0.461901 + 0.886931i \(0.347167\pi\)
\(588\) 0 0
\(589\) −0.708204 −0.0291810
\(590\) 0 0
\(591\) 3.61803 0.148826
\(592\) 0 0
\(593\) −24.6525 −1.01236 −0.506178 0.862429i \(-0.668942\pi\)
−0.506178 + 0.862429i \(0.668942\pi\)
\(594\) 0 0
\(595\) 4.14590 0.169965
\(596\) 0 0
\(597\) 2.43769 0.0997682
\(598\) 0 0
\(599\) −8.74265 −0.357215 −0.178607 0.983920i \(-0.557159\pi\)
−0.178607 + 0.983920i \(0.557159\pi\)
\(600\) 0 0
\(601\) 5.20163 0.212179 0.106089 0.994357i \(-0.466167\pi\)
0.106089 + 0.994357i \(0.466167\pi\)
\(602\) 0 0
\(603\) −13.5623 −0.552300
\(604\) 0 0
\(605\) −1.23607 −0.0502533
\(606\) 0 0
\(607\) −4.56231 −0.185178 −0.0925891 0.995704i \(-0.529514\pi\)
−0.0925891 + 0.995704i \(0.529514\pi\)
\(608\) 0 0
\(609\) 6.23607 0.252698
\(610\) 0 0
\(611\) 7.70820 0.311841
\(612\) 0 0
\(613\) −9.29180 −0.375292 −0.187646 0.982237i \(-0.560086\pi\)
−0.187646 + 0.982237i \(0.560086\pi\)
\(614\) 0 0
\(615\) 3.67376 0.148140
\(616\) 0 0
\(617\) 22.8541 0.920072 0.460036 0.887900i \(-0.347837\pi\)
0.460036 + 0.887900i \(0.347837\pi\)
\(618\) 0 0
\(619\) −31.1459 −1.25186 −0.625930 0.779880i \(-0.715280\pi\)
−0.625930 + 0.779880i \(0.715280\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) −7.79837 −0.312435
\(624\) 0 0
\(625\) 19.4164 0.776656
\(626\) 0 0
\(627\) −0.708204 −0.0282829
\(628\) 0 0
\(629\) −3.54102 −0.141190
\(630\) 0 0
\(631\) −40.7771 −1.62331 −0.811655 0.584137i \(-0.801433\pi\)
−0.811655 + 0.584137i \(0.801433\pi\)
\(632\) 0 0
\(633\) 14.1246 0.561403
\(634\) 0 0
\(635\) −9.00000 −0.357154
\(636\) 0 0
\(637\) −1.61803 −0.0641088
\(638\) 0 0
\(639\) −2.38197 −0.0942291
\(640\) 0 0
\(641\) −24.6738 −0.974555 −0.487278 0.873247i \(-0.662010\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(642\) 0 0
\(643\) 7.32624 0.288919 0.144459 0.989511i \(-0.453856\pi\)
0.144459 + 0.989511i \(0.453856\pi\)
\(644\) 0 0
\(645\) 1.29180 0.0508644
\(646\) 0 0
\(647\) 26.3951 1.03770 0.518850 0.854866i \(-0.326360\pi\)
0.518850 + 0.854866i \(0.326360\pi\)
\(648\) 0 0
\(649\) 22.1459 0.869303
\(650\) 0 0
\(651\) 3.00000 0.117579
\(652\) 0 0
\(653\) −25.8541 −1.01175 −0.505875 0.862607i \(-0.668830\pi\)
−0.505875 + 0.862607i \(0.668830\pi\)
\(654\) 0 0
\(655\) −7.38197 −0.288437
\(656\) 0 0
\(657\) 6.23607 0.243292
\(658\) 0 0
\(659\) 22.3050 0.868878 0.434439 0.900701i \(-0.356947\pi\)
0.434439 + 0.900701i \(0.356947\pi\)
\(660\) 0 0
\(661\) −28.7771 −1.11930 −0.559649 0.828729i \(-0.689064\pi\)
−0.559649 + 0.828729i \(0.689064\pi\)
\(662\) 0 0
\(663\) 10.8541 0.421538
\(664\) 0 0
\(665\) −0.145898 −0.00565768
\(666\) 0 0
\(667\) 6.23607 0.241462
\(668\) 0 0
\(669\) −12.7984 −0.494814
\(670\) 0 0
\(671\) 2.56231 0.0989167
\(672\) 0 0
\(673\) −44.3050 −1.70783 −0.853915 0.520412i \(-0.825778\pi\)
−0.853915 + 0.520412i \(0.825778\pi\)
\(674\) 0 0
\(675\) −4.61803 −0.177748
\(676\) 0 0
\(677\) 0.0901699 0.00346551 0.00173276 0.999998i \(-0.499448\pi\)
0.00173276 + 0.999998i \(0.499448\pi\)
\(678\) 0 0
\(679\) −14.4164 −0.553251
\(680\) 0 0
\(681\) −29.4508 −1.12856
\(682\) 0 0
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 0 0
\(685\) −5.56231 −0.212525
\(686\) 0 0
\(687\) −9.27051 −0.353692
\(688\) 0 0
\(689\) −10.2361 −0.389963
\(690\) 0 0
\(691\) 19.6180 0.746305 0.373153 0.927770i \(-0.378277\pi\)
0.373153 + 0.927770i \(0.378277\pi\)
\(692\) 0 0
\(693\) 3.00000 0.113961
\(694\) 0 0
\(695\) 0.0901699 0.00342034
\(696\) 0 0
\(697\) −39.8754 −1.51039
\(698\) 0 0
\(699\) −0.909830 −0.0344129
\(700\) 0 0
\(701\) 13.0902 0.494409 0.247204 0.968963i \(-0.420488\pi\)
0.247204 + 0.968963i \(0.420488\pi\)
\(702\) 0 0
\(703\) 0.124612 0.00469982
\(704\) 0 0
\(705\) −2.94427 −0.110888
\(706\) 0 0
\(707\) 10.3262 0.388358
\(708\) 0 0
\(709\) 0.0901699 0.00338640 0.00169320 0.999999i \(-0.499461\pi\)
0.00169320 + 0.999999i \(0.499461\pi\)
\(710\) 0 0
\(711\) 6.70820 0.251577
\(712\) 0 0
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) 0 0
\(717\) −15.3820 −0.574450
\(718\) 0 0
\(719\) −3.65248 −0.136214 −0.0681072 0.997678i \(-0.521696\pi\)
−0.0681072 + 0.997678i \(0.521696\pi\)
\(720\) 0 0
\(721\) 7.41641 0.276201
\(722\) 0 0
\(723\) 21.0000 0.780998
\(724\) 0 0
\(725\) 28.7984 1.06954
\(726\) 0 0
\(727\) −19.2918 −0.715493 −0.357747 0.933819i \(-0.616455\pi\)
−0.357747 + 0.933819i \(0.616455\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −14.0213 −0.518596
\(732\) 0 0
\(733\) −1.59675 −0.0589772 −0.0294886 0.999565i \(-0.509388\pi\)
−0.0294886 + 0.999565i \(0.509388\pi\)
\(734\) 0 0
\(735\) 0.618034 0.0227965
\(736\) 0 0
\(737\) 40.6869 1.49872
\(738\) 0 0
\(739\) 15.2918 0.562518 0.281259 0.959632i \(-0.409248\pi\)
0.281259 + 0.959632i \(0.409248\pi\)
\(740\) 0 0
\(741\) −0.381966 −0.0140319
\(742\) 0 0
\(743\) −22.6180 −0.829775 −0.414888 0.909873i \(-0.636179\pi\)
−0.414888 + 0.909873i \(0.636179\pi\)
\(744\) 0 0
\(745\) 2.00000 0.0732743
\(746\) 0 0
\(747\) 1.47214 0.0538626
\(748\) 0 0
\(749\) −8.38197 −0.306270
\(750\) 0 0
\(751\) 4.72949 0.172582 0.0862908 0.996270i \(-0.472499\pi\)
0.0862908 + 0.996270i \(0.472499\pi\)
\(752\) 0 0
\(753\) 8.65248 0.315314
\(754\) 0 0
\(755\) 13.0557 0.475147
\(756\) 0 0
\(757\) −8.52786 −0.309950 −0.154975 0.987918i \(-0.549530\pi\)
−0.154975 + 0.987918i \(0.549530\pi\)
\(758\) 0 0
\(759\) 3.00000 0.108893
\(760\) 0 0
\(761\) −17.5279 −0.635385 −0.317692 0.948194i \(-0.602908\pi\)
−0.317692 + 0.948194i \(0.602908\pi\)
\(762\) 0 0
\(763\) −9.09017 −0.329086
\(764\) 0 0
\(765\) −4.14590 −0.149895
\(766\) 0 0
\(767\) 11.9443 0.431283
\(768\) 0 0
\(769\) −35.1246 −1.26663 −0.633313 0.773896i \(-0.718305\pi\)
−0.633313 + 0.773896i \(0.718305\pi\)
\(770\) 0 0
\(771\) −14.6525 −0.527696
\(772\) 0 0
\(773\) −33.9443 −1.22089 −0.610445 0.792058i \(-0.709009\pi\)
−0.610445 + 0.792058i \(0.709009\pi\)
\(774\) 0 0
\(775\) 13.8541 0.497654
\(776\) 0 0
\(777\) −0.527864 −0.0189370
\(778\) 0 0
\(779\) 1.40325 0.0502767
\(780\) 0 0
\(781\) 7.14590 0.255700
\(782\) 0 0
\(783\) −6.23607 −0.222859
\(784\) 0 0
\(785\) 8.18034 0.291969
\(786\) 0 0
\(787\) 12.9098 0.460186 0.230093 0.973169i \(-0.426097\pi\)
0.230093 + 0.973169i \(0.426097\pi\)
\(788\) 0 0
\(789\) −7.18034 −0.255627
\(790\) 0 0
\(791\) 12.3262 0.438271
\(792\) 0 0
\(793\) 1.38197 0.0490751
\(794\) 0 0
\(795\) 3.90983 0.138667
\(796\) 0 0
\(797\) 44.1803 1.56495 0.782474 0.622683i \(-0.213957\pi\)
0.782474 + 0.622683i \(0.213957\pi\)
\(798\) 0 0
\(799\) 31.9574 1.13057
\(800\) 0 0
\(801\) 7.79837 0.275542
\(802\) 0 0
\(803\) −18.7082 −0.660198
\(804\) 0 0
\(805\) 0.618034 0.0217828
\(806\) 0 0
\(807\) 1.79837 0.0633058
\(808\) 0 0
\(809\) 9.21478 0.323974 0.161987 0.986793i \(-0.448210\pi\)
0.161987 + 0.986793i \(0.448210\pi\)
\(810\) 0 0
\(811\) −27.2918 −0.958345 −0.479172 0.877721i \(-0.659063\pi\)
−0.479172 + 0.877721i \(0.659063\pi\)
\(812\) 0 0
\(813\) 1.18034 0.0413963
\(814\) 0 0
\(815\) 2.56231 0.0897537
\(816\) 0 0
\(817\) 0.493422 0.0172627
\(818\) 0 0
\(819\) 1.61803 0.0565387
\(820\) 0 0
\(821\) −38.2918 −1.33639 −0.668196 0.743985i \(-0.732933\pi\)
−0.668196 + 0.743985i \(0.732933\pi\)
\(822\) 0 0
\(823\) −39.0902 −1.36260 −0.681299 0.732005i \(-0.738585\pi\)
−0.681299 + 0.732005i \(0.738585\pi\)
\(824\) 0 0
\(825\) 13.8541 0.482338
\(826\) 0 0
\(827\) −13.9230 −0.484150 −0.242075 0.970258i \(-0.577828\pi\)
−0.242075 + 0.970258i \(0.577828\pi\)
\(828\) 0 0
\(829\) 7.00000 0.243120 0.121560 0.992584i \(-0.461210\pi\)
0.121560 + 0.992584i \(0.461210\pi\)
\(830\) 0 0
\(831\) −5.03444 −0.174643
\(832\) 0 0
\(833\) −6.70820 −0.232425
\(834\) 0 0
\(835\) −12.0344 −0.416469
\(836\) 0 0
\(837\) −3.00000 −0.103695
\(838\) 0 0
\(839\) 0.0901699 0.00311301 0.00155651 0.999999i \(-0.499505\pi\)
0.00155651 + 0.999999i \(0.499505\pi\)
\(840\) 0 0
\(841\) 9.88854 0.340984
\(842\) 0 0
\(843\) −17.2361 −0.593642
\(844\) 0 0
\(845\) −6.41641 −0.220731
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) −8.14590 −0.279566
\(850\) 0 0
\(851\) −0.527864 −0.0180949
\(852\) 0 0
\(853\) 15.7082 0.537839 0.268919 0.963163i \(-0.413333\pi\)
0.268919 + 0.963163i \(0.413333\pi\)
\(854\) 0 0
\(855\) 0.145898 0.00498961
\(856\) 0 0
\(857\) 10.1803 0.347754 0.173877 0.984767i \(-0.444371\pi\)
0.173877 + 0.984767i \(0.444371\pi\)
\(858\) 0 0
\(859\) 27.3050 0.931633 0.465816 0.884881i \(-0.345761\pi\)
0.465816 + 0.884881i \(0.345761\pi\)
\(860\) 0 0
\(861\) −5.94427 −0.202580
\(862\) 0 0
\(863\) 19.3475 0.658597 0.329299 0.944226i \(-0.393188\pi\)
0.329299 + 0.944226i \(0.393188\pi\)
\(864\) 0 0
\(865\) 2.79837 0.0951476
\(866\) 0 0
\(867\) 28.0000 0.950930
\(868\) 0 0
\(869\) −20.1246 −0.682681
\(870\) 0 0
\(871\) 21.9443 0.743553
\(872\) 0 0
\(873\) 14.4164 0.487921
\(874\) 0 0
\(875\) 5.94427 0.200953
\(876\) 0 0
\(877\) 23.4164 0.790716 0.395358 0.918527i \(-0.370621\pi\)
0.395358 + 0.918527i \(0.370621\pi\)
\(878\) 0 0
\(879\) 16.9443 0.571516
\(880\) 0 0
\(881\) 3.70820 0.124933 0.0624663 0.998047i \(-0.480103\pi\)
0.0624663 + 0.998047i \(0.480103\pi\)
\(882\) 0 0
\(883\) −37.3262 −1.25613 −0.628064 0.778162i \(-0.716152\pi\)
−0.628064 + 0.778162i \(0.716152\pi\)
\(884\) 0 0
\(885\) −4.56231 −0.153360
\(886\) 0 0
\(887\) 30.2705 1.01638 0.508192 0.861244i \(-0.330314\pi\)
0.508192 + 0.861244i \(0.330314\pi\)
\(888\) 0 0
\(889\) 14.5623 0.488404
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 0 0
\(893\) −1.12461 −0.0376337
\(894\) 0 0
\(895\) −11.1459 −0.372566
\(896\) 0 0
\(897\) 1.61803 0.0540246
\(898\) 0 0
\(899\) 18.7082 0.623954
\(900\) 0 0
\(901\) −42.4377 −1.41380
\(902\) 0 0
\(903\) −2.09017 −0.0695565
\(904\) 0 0
\(905\) 5.27051 0.175198
\(906\) 0 0
\(907\) −32.4377 −1.07708 −0.538538 0.842601i \(-0.681023\pi\)
−0.538538 + 0.842601i \(0.681023\pi\)
\(908\) 0 0
\(909\) −10.3262 −0.342500
\(910\) 0 0
\(911\) −56.1803 −1.86134 −0.930669 0.365863i \(-0.880774\pi\)
−0.930669 + 0.365863i \(0.880774\pi\)
\(912\) 0 0
\(913\) −4.41641 −0.146162
\(914\) 0 0
\(915\) −0.527864 −0.0174506
\(916\) 0 0
\(917\) 11.9443 0.394435
\(918\) 0 0
\(919\) 36.3050 1.19759 0.598795 0.800902i \(-0.295646\pi\)
0.598795 + 0.800902i \(0.295646\pi\)
\(920\) 0 0
\(921\) −1.58359 −0.0521811
\(922\) 0 0
\(923\) 3.85410 0.126859
\(924\) 0 0
\(925\) −2.43769 −0.0801509
\(926\) 0 0
\(927\) −7.41641 −0.243587
\(928\) 0 0
\(929\) −36.0344 −1.18225 −0.591126 0.806579i \(-0.701316\pi\)
−0.591126 + 0.806579i \(0.701316\pi\)
\(930\) 0 0
\(931\) 0.236068 0.00773682
\(932\) 0 0
\(933\) 18.2705 0.598150
\(934\) 0 0
\(935\) 12.4377 0.406756
\(936\) 0 0
\(937\) −40.7082 −1.32988 −0.664940 0.746897i \(-0.731543\pi\)
−0.664940 + 0.746897i \(0.731543\pi\)
\(938\) 0 0
\(939\) 26.4721 0.863886
\(940\) 0 0
\(941\) −36.0000 −1.17357 −0.586783 0.809744i \(-0.699606\pi\)
−0.586783 + 0.809744i \(0.699606\pi\)
\(942\) 0 0
\(943\) −5.94427 −0.193572
\(944\) 0 0
\(945\) −0.618034 −0.0201046
\(946\) 0 0
\(947\) −55.3050 −1.79717 −0.898585 0.438800i \(-0.855404\pi\)
−0.898585 + 0.438800i \(0.855404\pi\)
\(948\) 0 0
\(949\) −10.0902 −0.327541
\(950\) 0 0
\(951\) 3.38197 0.109668
\(952\) 0 0
\(953\) −30.0902 −0.974716 −0.487358 0.873202i \(-0.662039\pi\)
−0.487358 + 0.873202i \(0.662039\pi\)
\(954\) 0 0
\(955\) 6.58359 0.213040
\(956\) 0 0
\(957\) 18.7082 0.604750
\(958\) 0 0
\(959\) 9.00000 0.290625
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 8.38197 0.270105
\(964\) 0 0
\(965\) 4.76393 0.153356
\(966\) 0 0
\(967\) −54.0000 −1.73652 −0.868261 0.496107i \(-0.834762\pi\)
−0.868261 + 0.496107i \(0.834762\pi\)
\(968\) 0 0
\(969\) −1.58359 −0.0508723
\(970\) 0 0
\(971\) 19.7984 0.635360 0.317680 0.948198i \(-0.397096\pi\)
0.317680 + 0.948198i \(0.397096\pi\)
\(972\) 0 0
\(973\) −0.145898 −0.00467728
\(974\) 0 0
\(975\) 7.47214 0.239300
\(976\) 0 0
\(977\) −59.2837 −1.89665 −0.948326 0.317297i \(-0.897225\pi\)
−0.948326 + 0.317297i \(0.897225\pi\)
\(978\) 0 0
\(979\) −23.3951 −0.747711
\(980\) 0 0
\(981\) 9.09017 0.290227
\(982\) 0 0
\(983\) −45.4721 −1.45034 −0.725168 0.688572i \(-0.758238\pi\)
−0.725168 + 0.688572i \(0.758238\pi\)
\(984\) 0 0
\(985\) 2.23607 0.0712470
\(986\) 0 0
\(987\) 4.76393 0.151638
\(988\) 0 0
\(989\) −2.09017 −0.0664635
\(990\) 0 0
\(991\) −59.6869 −1.89602 −0.948009 0.318244i \(-0.896907\pi\)
−0.948009 + 0.318244i \(0.896907\pi\)
\(992\) 0 0
\(993\) −27.8885 −0.885016
\(994\) 0 0
\(995\) 1.50658 0.0477617
\(996\) 0 0
\(997\) −15.4721 −0.490007 −0.245004 0.969522i \(-0.578789\pi\)
−0.245004 + 0.969522i \(0.578789\pi\)
\(998\) 0 0
\(999\) 0.527864 0.0167009
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 1932.2.a.g.1.2 2
3.2 odd 2 5796.2.a.l.1.1 2
4.3 odd 2 7728.2.a.ba.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.2.a.g.1.2 2 1.1 even 1 trivial
5796.2.a.l.1.1 2 3.2 odd 2
7728.2.a.ba.1.2 2 4.3 odd 2