Properties

Label 950.2.a.l.1.2
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.993.1
Defining polynomial: \(x^{3} - x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.480031\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +0.960061 q^{11} +0.519969 q^{12} +2.24960 q^{13} +4.76957 q^{14} +1.00000 q^{16} -0.249601 q^{17} -2.72963 q^{18} +1.00000 q^{19} +2.48003 q^{21} +0.960061 q^{22} -9.01917 q^{23} +0.519969 q^{24} +2.24960 q^{26} -2.97923 q^{27} +4.76957 q^{28} +6.24960 q^{29} +2.96006 q^{31} +1.00000 q^{32} +0.499202 q^{33} -0.249601 q^{34} -2.72963 q^{36} -0.0399387 q^{37} +1.00000 q^{38} +1.16972 q^{39} +2.48003 q^{42} -4.96006 q^{43} +0.960061 q^{44} -9.01917 q^{46} +9.49920 q^{47} +0.519969 q^{48} +15.7488 q^{49} -0.129785 q^{51} +2.24960 q^{52} -6.84945 q^{53} -2.97923 q^{54} +4.76957 q^{56} +0.519969 q^{57} +6.24960 q^{58} -14.5583 q^{59} +7.53914 q^{61} +2.96006 q^{62} -13.0192 q^{63} +1.00000 q^{64} +0.499202 q^{66} +5.72963 q^{67} -0.249601 q^{68} -4.68969 q^{69} -9.61902 q^{71} -2.72963 q^{72} -12.0591 q^{73} -0.0399387 q^{74} +1.00000 q^{76} +4.57908 q^{77} +1.16972 q^{78} +6.07988 q^{79} +6.63979 q^{81} +7.45926 q^{83} +2.48003 q^{84} -4.96006 q^{86} +3.24960 q^{87} +0.960061 q^{88} +4.07988 q^{89} +10.7296 q^{91} -9.01917 q^{92} +1.53914 q^{93} +9.49920 q^{94} +0.519969 q^{96} -18.4193 q^{97} +15.7488 q^{98} -2.62061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + 2q^{11} + 2q^{12} - 6q^{13} + 2q^{14} + 3q^{16} + 12q^{17} + 5q^{18} + 3q^{19} + 7q^{21} + 2q^{22} - 2q^{23} + 2q^{24} - 6q^{26} + 17q^{27} + 2q^{28} + 6q^{29} + 8q^{31} + 3q^{32} - 24q^{33} + 12q^{34} + 5q^{36} - q^{37} + 3q^{38} - 11q^{39} + 7q^{42} - 14q^{43} + 2q^{44} - 2q^{46} + 3q^{47} + 2q^{48} + 9q^{49} + 15q^{51} - 6q^{52} - 10q^{53} + 17q^{54} + 2q^{56} + 2q^{57} + 6q^{58} + 6q^{59} - 2q^{61} + 8q^{62} - 14q^{63} + 3q^{64} - 24q^{66} + 4q^{67} + 12q^{68} - 6q^{71} + 5q^{72} - 12q^{73} - q^{74} + 3q^{76} - 10q^{77} - 11q^{78} + 20q^{79} + 23q^{81} - 4q^{83} + 7q^{84} - 14q^{86} - 3q^{87} + 2q^{88} + 14q^{89} + 19q^{91} - 2q^{92} - 20q^{93} + 3q^{94} + 2q^{96} - 28q^{97} + 9q^{98} - 36q^{99} + O(q^{100}) \)

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
\(3\) 0.519969 0.300204 0.150102 0.988670i \(-0.452040\pi\)
0.150102 + 0.988670i \(0.452040\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0.519969 0.212277
\(7\) 4.76957 1.80273 0.901364 0.433062i \(-0.142567\pi\)
0.901364 + 0.433062i \(0.142567\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.72963 −0.909877
\(10\) 0 0
\(11\) 0.960061 0.289469 0.144735 0.989471i \(-0.453767\pi\)
0.144735 + 0.989471i \(0.453767\pi\)
\(12\) 0.519969 0.150102
\(13\) 2.24960 0.623927 0.311964 0.950094i \(-0.399013\pi\)
0.311964 + 0.950094i \(0.399013\pi\)
\(14\) 4.76957 1.27472
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.249601 −0.0605372 −0.0302686 0.999542i \(-0.509636\pi\)
−0.0302686 + 0.999542i \(0.509636\pi\)
\(18\) −2.72963 −0.643380
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 2.48003 0.541187
\(22\) 0.960061 0.204686
\(23\) −9.01917 −1.88063 −0.940314 0.340309i \(-0.889468\pi\)
−0.940314 + 0.340309i \(0.889468\pi\)
\(24\) 0.519969 0.106138
\(25\) 0 0
\(26\) 2.24960 0.441183
\(27\) −2.97923 −0.573354
\(28\) 4.76957 0.901364
\(29\) 6.24960 1.16052 0.580261 0.814431i \(-0.302951\pi\)
0.580261 + 0.814431i \(0.302951\pi\)
\(30\) 0 0
\(31\) 2.96006 0.531643 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.499202 0.0869000
\(34\) −0.249601 −0.0428063
\(35\) 0 0
\(36\) −2.72963 −0.454939
\(37\) −0.0399387 −0.00656589 −0.00328294 0.999995i \(-0.501045\pi\)
−0.00328294 + 0.999995i \(0.501045\pi\)
\(38\) 1.00000 0.162221
\(39\) 1.16972 0.187306
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 2.48003 0.382677
\(43\) −4.96006 −0.756402 −0.378201 0.925723i \(-0.623457\pi\)
−0.378201 + 0.925723i \(0.623457\pi\)
\(44\) 0.960061 0.144735
\(45\) 0 0
\(46\) −9.01917 −1.32980
\(47\) 9.49920 1.38560 0.692801 0.721129i \(-0.256377\pi\)
0.692801 + 0.721129i \(0.256377\pi\)
\(48\) 0.519969 0.0750511
\(49\) 15.7488 2.24983
\(50\) 0 0
\(51\) −0.129785 −0.0181735
\(52\) 2.24960 0.311964
\(53\) −6.84945 −0.940844 −0.470422 0.882442i \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(54\) −2.97923 −0.405422
\(55\) 0 0
\(56\) 4.76957 0.637361
\(57\) 0.519969 0.0688716
\(58\) 6.24960 0.820613
\(59\) −14.5583 −1.89533 −0.947665 0.319265i \(-0.896564\pi\)
−0.947665 + 0.319265i \(0.896564\pi\)
\(60\) 0 0
\(61\) 7.53914 0.965288 0.482644 0.875817i \(-0.339676\pi\)
0.482644 + 0.875817i \(0.339676\pi\)
\(62\) 2.96006 0.375928
\(63\) −13.0192 −1.64026
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.499202 0.0614476
\(67\) 5.72963 0.699986 0.349993 0.936752i \(-0.386184\pi\)
0.349993 + 0.936752i \(0.386184\pi\)
\(68\) −0.249601 −0.0302686
\(69\) −4.68969 −0.564573
\(70\) 0 0
\(71\) −9.61902 −1.14157 −0.570784 0.821100i \(-0.693361\pi\)
−0.570784 + 0.821100i \(0.693361\pi\)
\(72\) −2.72963 −0.321690
\(73\) −12.0591 −1.41141 −0.705706 0.708505i \(-0.749370\pi\)
−0.705706 + 0.708505i \(0.749370\pi\)
\(74\) −0.0399387 −0.00464278
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 4.57908 0.521835
\(78\) 1.16972 0.132445
\(79\) 6.07988 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(80\) 0 0
\(81\) 6.63979 0.737754
\(82\) 0 0
\(83\) 7.45926 0.818761 0.409380 0.912364i \(-0.365745\pi\)
0.409380 + 0.912364i \(0.365745\pi\)
\(84\) 2.48003 0.270594
\(85\) 0 0
\(86\) −4.96006 −0.534857
\(87\) 3.24960 0.348394
\(88\) 0.960061 0.102343
\(89\) 4.07988 0.432466 0.216233 0.976342i \(-0.430623\pi\)
0.216233 + 0.976342i \(0.430623\pi\)
\(90\) 0 0
\(91\) 10.7296 1.12477
\(92\) −9.01917 −0.940314
\(93\) 1.53914 0.159602
\(94\) 9.49920 0.979768
\(95\) 0 0
\(96\) 0.519969 0.0530692
\(97\) −18.4193 −1.87020 −0.935100 0.354385i \(-0.884690\pi\)
−0.935100 + 0.354385i \(0.884690\pi\)
\(98\) 15.7488 1.59087
\(99\) −2.62061 −0.263382
\(100\) 0 0
\(101\) 5.53914 0.551165 0.275583 0.961277i \(-0.411129\pi\)
0.275583 + 0.961277i \(0.411129\pi\)
\(102\) −0.129785 −0.0128506
\(103\) 6.57908 0.648256 0.324128 0.946013i \(-0.394929\pi\)
0.324128 + 0.946013i \(0.394929\pi\)
\(104\) 2.24960 0.220592
\(105\) 0 0
\(106\) −6.84945 −0.665277
\(107\) −14.9086 −1.44126 −0.720632 0.693317i \(-0.756148\pi\)
−0.720632 + 0.693317i \(0.756148\pi\)
\(108\) −2.97923 −0.286677
\(109\) 4.76957 0.456842 0.228421 0.973562i \(-0.426644\pi\)
0.228421 + 0.973562i \(0.426644\pi\)
\(110\) 0 0
\(111\) −0.0207669 −0.00197111
\(112\) 4.76957 0.450682
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0.519969 0.0486996
\(115\) 0 0
\(116\) 6.24960 0.580261
\(117\) −6.14058 −0.567697
\(118\) −14.5583 −1.34020
\(119\) −1.19049 −0.109132
\(120\) 0 0
\(121\) −10.0783 −0.916207
\(122\) 7.53914 0.682562
\(123\) 0 0
\(124\) 2.96006 0.265821
\(125\) 0 0
\(126\) −13.0192 −1.15984
\(127\) −17.9585 −1.59356 −0.796778 0.604272i \(-0.793464\pi\)
−0.796778 + 0.604272i \(0.793464\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.57908 −0.227075
\(130\) 0 0
\(131\) −6.96006 −0.608103 −0.304052 0.952656i \(-0.598340\pi\)
−0.304052 + 0.952656i \(0.598340\pi\)
\(132\) 0.499202 0.0434500
\(133\) 4.76957 0.413574
\(134\) 5.72963 0.494965
\(135\) 0 0
\(136\) −0.249601 −0.0214031
\(137\) −7.80951 −0.667211 −0.333606 0.942713i \(-0.608265\pi\)
−0.333606 + 0.942713i \(0.608265\pi\)
\(138\) −4.68969 −0.399213
\(139\) −16.0383 −1.36035 −0.680177 0.733048i \(-0.738097\pi\)
−0.680177 + 0.733048i \(0.738097\pi\)
\(140\) 0 0
\(141\) 4.93929 0.415964
\(142\) −9.61902 −0.807210
\(143\) 2.15975 0.180608
\(144\) −2.72963 −0.227469
\(145\) 0 0
\(146\) −12.0591 −0.998019
\(147\) 8.18890 0.675409
\(148\) −0.0399387 −0.00328294
\(149\) −8.41932 −0.689738 −0.344869 0.938651i \(-0.612077\pi\)
−0.344869 + 0.938651i \(0.612077\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 1.00000 0.0811107
\(153\) 0.681319 0.0550814
\(154\) 4.57908 0.368993
\(155\) 0 0
\(156\) 1.16972 0.0936529
\(157\) −4.96006 −0.395856 −0.197928 0.980217i \(-0.563421\pi\)
−0.197928 + 0.980217i \(0.563421\pi\)
\(158\) 6.07988 0.483689
\(159\) −3.56150 −0.282446
\(160\) 0 0
\(161\) −43.0176 −3.39026
\(162\) 6.63979 0.521671
\(163\) 21.4593 1.68082 0.840410 0.541952i \(-0.182314\pi\)
0.840410 + 0.541952i \(0.182314\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 7.45926 0.578951
\(167\) 11.0399 0.854296 0.427148 0.904182i \(-0.359518\pi\)
0.427148 + 0.904182i \(0.359518\pi\)
\(168\) 2.48003 0.191339
\(169\) −7.93929 −0.610715
\(170\) 0 0
\(171\) −2.72963 −0.208740
\(172\) −4.96006 −0.378201
\(173\) −16.9585 −1.28933 −0.644664 0.764466i \(-0.723003\pi\)
−0.644664 + 0.764466i \(0.723003\pi\)
\(174\) 3.24960 0.246352
\(175\) 0 0
\(176\) 0.960061 0.0723673
\(177\) −7.56988 −0.568987
\(178\) 4.07988 0.305800
\(179\) 2.53914 0.189784 0.0948922 0.995488i \(-0.469749\pi\)
0.0948922 + 0.995488i \(0.469749\pi\)
\(180\) 0 0
\(181\) −3.88018 −0.288412 −0.144206 0.989548i \(-0.546063\pi\)
−0.144206 + 0.989548i \(0.546063\pi\)
\(182\) 10.7296 0.795333
\(183\) 3.92012 0.289784
\(184\) −9.01917 −0.664902
\(185\) 0 0
\(186\) 1.53914 0.112855
\(187\) −0.239632 −0.0175237
\(188\) 9.49920 0.692801
\(189\) −14.2097 −1.03360
\(190\) 0 0
\(191\) 2.05911 0.148992 0.0744960 0.997221i \(-0.476265\pi\)
0.0744960 + 0.997221i \(0.476265\pi\)
\(192\) 0.519969 0.0375256
\(193\) 8.46086 0.609026 0.304513 0.952508i \(-0.401506\pi\)
0.304513 + 0.952508i \(0.401506\pi\)
\(194\) −18.4193 −1.32243
\(195\) 0 0
\(196\) 15.7488 1.12491
\(197\) −13.9201 −0.991768 −0.495884 0.868389i \(-0.665156\pi\)
−0.495884 + 0.868389i \(0.665156\pi\)
\(198\) −2.62061 −0.186239
\(199\) −9.15055 −0.648665 −0.324333 0.945943i \(-0.605140\pi\)
−0.324333 + 0.945943i \(0.605140\pi\)
\(200\) 0 0
\(201\) 2.97923 0.210139
\(202\) 5.53914 0.389733
\(203\) 29.8079 2.09211
\(204\) −0.129785 −0.00908677
\(205\) 0 0
\(206\) 6.57908 0.458386
\(207\) 24.6190 1.71114
\(208\) 2.24960 0.155982
\(209\) 0.960061 0.0664088
\(210\) 0 0
\(211\) 16.5200 1.13728 0.568641 0.822586i \(-0.307469\pi\)
0.568641 + 0.822586i \(0.307469\pi\)
\(212\) −6.84945 −0.470422
\(213\) −5.00160 −0.342704
\(214\) −14.9086 −1.01913
\(215\) 0 0
\(216\) −2.97923 −0.202711
\(217\) 14.1182 0.958407
\(218\) 4.76957 0.323036
\(219\) −6.27037 −0.423712
\(220\) 0 0
\(221\) −0.561503 −0.0377708
\(222\) −0.0207669 −0.00139378
\(223\) −9.03994 −0.605359 −0.302680 0.953092i \(-0.597881\pi\)
−0.302680 + 0.953092i \(0.597881\pi\)
\(224\) 4.76957 0.318680
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −0.350246 −0.0232466 −0.0116233 0.999932i \(-0.503700\pi\)
−0.0116233 + 0.999932i \(0.503700\pi\)
\(228\) 0.519969 0.0344358
\(229\) −8.07988 −0.533933 −0.266967 0.963706i \(-0.586021\pi\)
−0.266967 + 0.963706i \(0.586021\pi\)
\(230\) 0 0
\(231\) 2.38098 0.156657
\(232\) 6.24960 0.410306
\(233\) 4.92012 0.322328 0.161164 0.986928i \(-0.448475\pi\)
0.161164 + 0.986928i \(0.448475\pi\)
\(234\) −6.14058 −0.401422
\(235\) 0 0
\(236\) −14.5583 −0.947665
\(237\) 3.16135 0.205352
\(238\) −1.19049 −0.0771680
\(239\) 2.98083 0.192814 0.0964069 0.995342i \(-0.469265\pi\)
0.0964069 + 0.995342i \(0.469265\pi\)
\(240\) 0 0
\(241\) 20.0383 1.29078 0.645392 0.763852i \(-0.276694\pi\)
0.645392 + 0.763852i \(0.276694\pi\)
\(242\) −10.0783 −0.647857
\(243\) 12.3902 0.794831
\(244\) 7.53914 0.482644
\(245\) 0 0
\(246\) 0 0
\(247\) 2.24960 0.143139
\(248\) 2.96006 0.187964
\(249\) 3.87859 0.245796
\(250\) 0 0
\(251\) −14.8802 −0.939229 −0.469614 0.882872i \(-0.655607\pi\)
−0.469614 + 0.882872i \(0.655607\pi\)
\(252\) −13.0192 −0.820131
\(253\) −8.65896 −0.544384
\(254\) −17.9585 −1.12681
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.0399 0.688652 0.344326 0.938850i \(-0.388107\pi\)
0.344326 + 0.938850i \(0.388107\pi\)
\(258\) −2.57908 −0.160567
\(259\) −0.190491 −0.0118365
\(260\) 0 0
\(261\) −17.0591 −1.05593
\(262\) −6.96006 −0.429994
\(263\) 3.84025 0.236800 0.118400 0.992966i \(-0.462224\pi\)
0.118400 + 0.992966i \(0.462224\pi\)
\(264\) 0.499202 0.0307238
\(265\) 0 0
\(266\) 4.76957 0.292441
\(267\) 2.12141 0.129828
\(268\) 5.72963 0.349993
\(269\) 23.1981 1.41441 0.707207 0.707007i \(-0.249955\pi\)
0.707207 + 0.707007i \(0.249955\pi\)
\(270\) 0 0
\(271\) 23.9792 1.45663 0.728317 0.685240i \(-0.240303\pi\)
0.728317 + 0.685240i \(0.240303\pi\)
\(272\) −0.249601 −0.0151343
\(273\) 5.57908 0.337661
\(274\) −7.80951 −0.471790
\(275\) 0 0
\(276\) −4.68969 −0.282286
\(277\) −24.6590 −1.48161 −0.740807 0.671718i \(-0.765556\pi\)
−0.740807 + 0.671718i \(0.765556\pi\)
\(278\) −16.0383 −0.961916
\(279\) −8.07988 −0.483730
\(280\) 0 0
\(281\) −18.9984 −1.13335 −0.566675 0.823941i \(-0.691770\pi\)
−0.566675 + 0.823941i \(0.691770\pi\)
\(282\) 4.93929 0.294131
\(283\) −29.0367 −1.72606 −0.863028 0.505156i \(-0.831435\pi\)
−0.863028 + 0.505156i \(0.831435\pi\)
\(284\) −9.61902 −0.570784
\(285\) 0 0
\(286\) 2.15975 0.127709
\(287\) 0 0
\(288\) −2.72963 −0.160845
\(289\) −16.9377 −0.996335
\(290\) 0 0
\(291\) −9.57748 −0.561442
\(292\) −12.0591 −0.705706
\(293\) −6.24960 −0.365106 −0.182553 0.983196i \(-0.558436\pi\)
−0.182553 + 0.983196i \(0.558436\pi\)
\(294\) 8.18890 0.477586
\(295\) 0 0
\(296\) −0.0399387 −0.00232139
\(297\) −2.86025 −0.165968
\(298\) −8.41932 −0.487718
\(299\) −20.2895 −1.17337
\(300\) 0 0
\(301\) −23.6574 −1.36359
\(302\) 20.0000 1.15087
\(303\) 2.88018 0.165462
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 0.681319 0.0389484
\(307\) −12.5391 −0.715647 −0.357823 0.933789i \(-0.616481\pi\)
−0.357823 + 0.933789i \(0.616481\pi\)
\(308\) 4.57908 0.260917
\(309\) 3.42092 0.194609
\(310\) 0 0
\(311\) 7.84785 0.445011 0.222505 0.974931i \(-0.428576\pi\)
0.222505 + 0.974931i \(0.428576\pi\)
\(312\) 1.16972 0.0662226
\(313\) −10.9884 −0.621103 −0.310552 0.950557i \(-0.600514\pi\)
−0.310552 + 0.950557i \(0.600514\pi\)
\(314\) −4.96006 −0.279912
\(315\) 0 0
\(316\) 6.07988 0.342020
\(317\) 21.5567 1.21075 0.605373 0.795942i \(-0.293024\pi\)
0.605373 + 0.795942i \(0.293024\pi\)
\(318\) −3.56150 −0.199719
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) −7.75199 −0.432674
\(322\) −43.0176 −2.39728
\(323\) −0.249601 −0.0138882
\(324\) 6.63979 0.368877
\(325\) 0 0
\(326\) 21.4593 1.18852
\(327\) 2.48003 0.137146
\(328\) 0 0
\(329\) 45.3071 2.49786
\(330\) 0 0
\(331\) 33.4876 1.84065 0.920324 0.391158i \(-0.127925\pi\)
0.920324 + 0.391158i \(0.127925\pi\)
\(332\) 7.45926 0.409380
\(333\) 0.109018 0.00597415
\(334\) 11.0399 0.604079
\(335\) 0 0
\(336\) 2.48003 0.135297
\(337\) −5.69890 −0.310439 −0.155219 0.987880i \(-0.549608\pi\)
−0.155219 + 0.987880i \(0.549608\pi\)
\(338\) −7.93929 −0.431841
\(339\) −3.11982 −0.169445
\(340\) 0 0
\(341\) 2.84184 0.153894
\(342\) −2.72963 −0.147602
\(343\) 41.7280 2.25310
\(344\) −4.96006 −0.267429
\(345\) 0 0
\(346\) −16.9585 −0.911693
\(347\) 0.239632 0.0128641 0.00643207 0.999979i \(-0.497953\pi\)
0.00643207 + 0.999979i \(0.497953\pi\)
\(348\) 3.24960 0.174197
\(349\) −17.2380 −0.922731 −0.461365 0.887210i \(-0.652640\pi\)
−0.461365 + 0.887210i \(0.652640\pi\)
\(350\) 0 0
\(351\) −6.70209 −0.357731
\(352\) 0.960061 0.0511714
\(353\) 34.7280 1.84839 0.924193 0.381925i \(-0.124739\pi\)
0.924193 + 0.381925i \(0.124739\pi\)
\(354\) −7.56988 −0.402334
\(355\) 0 0
\(356\) 4.07988 0.216233
\(357\) −0.619019 −0.0327619
\(358\) 2.53914 0.134198
\(359\) 26.6689 1.40753 0.703766 0.710432i \(-0.251500\pi\)
0.703766 + 0.710432i \(0.251500\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −3.88018 −0.203938
\(363\) −5.24040 −0.275050
\(364\) 10.7296 0.562386
\(365\) 0 0
\(366\) 3.92012 0.204908
\(367\) 15.2380 0.795419 0.397710 0.917511i \(-0.369805\pi\)
0.397710 + 0.917511i \(0.369805\pi\)
\(368\) −9.01917 −0.470157
\(369\) 0 0
\(370\) 0 0
\(371\) −32.6689 −1.69609
\(372\) 1.53914 0.0798008
\(373\) 26.6382 1.37927 0.689637 0.724156i \(-0.257770\pi\)
0.689637 + 0.724156i \(0.257770\pi\)
\(374\) −0.239632 −0.0123911
\(375\) 0 0
\(376\) 9.49920 0.489884
\(377\) 14.0591 0.724081
\(378\) −14.2097 −0.730866
\(379\) 11.9693 0.614820 0.307410 0.951577i \(-0.400538\pi\)
0.307410 + 0.951577i \(0.400538\pi\)
\(380\) 0 0
\(381\) −9.33785 −0.478393
\(382\) 2.05911 0.105353
\(383\) 9.84025 0.502813 0.251407 0.967882i \(-0.419107\pi\)
0.251407 + 0.967882i \(0.419107\pi\)
\(384\) 0.519969 0.0265346
\(385\) 0 0
\(386\) 8.46086 0.430646
\(387\) 13.5391 0.688233
\(388\) −18.4193 −0.935100
\(389\) −8.65896 −0.439027 −0.219513 0.975610i \(-0.570447\pi\)
−0.219513 + 0.975610i \(0.570447\pi\)
\(390\) 0 0
\(391\) 2.25120 0.113848
\(392\) 15.7488 0.795435
\(393\) −3.61902 −0.182555
\(394\) −13.9201 −0.701286
\(395\) 0 0
\(396\) −2.62061 −0.131691
\(397\) −28.9984 −1.45539 −0.727694 0.685902i \(-0.759408\pi\)
−0.727694 + 0.685902i \(0.759408\pi\)
\(398\) −9.15055 −0.458676
\(399\) 2.48003 0.124157
\(400\) 0 0
\(401\) 22.6174 1.12946 0.564730 0.825276i \(-0.308980\pi\)
0.564730 + 0.825276i \(0.308980\pi\)
\(402\) 2.97923 0.148591
\(403\) 6.65896 0.331706
\(404\) 5.53914 0.275583
\(405\) 0 0
\(406\) 29.8079 1.47934
\(407\) −0.0383436 −0.00190062
\(408\) −0.129785 −0.00642531
\(409\) 5.34104 0.264098 0.132049 0.991243i \(-0.457844\pi\)
0.132049 + 0.991243i \(0.457844\pi\)
\(410\) 0 0
\(411\) −4.06071 −0.200300
\(412\) 6.57908 0.324128
\(413\) −69.4369 −3.41677
\(414\) 24.6190 1.20996
\(415\) 0 0
\(416\) 2.24960 0.110296
\(417\) −8.33945 −0.408384
\(418\) 0.960061 0.0469581
\(419\) −22.1566 −1.08242 −0.541210 0.840888i \(-0.682033\pi\)
−0.541210 + 0.840888i \(0.682033\pi\)
\(420\) 0 0
\(421\) 29.2787 1.42696 0.713479 0.700676i \(-0.247118\pi\)
0.713479 + 0.700676i \(0.247118\pi\)
\(422\) 16.5200 0.804180
\(423\) −25.9293 −1.26073
\(424\) −6.84945 −0.332639
\(425\) 0 0
\(426\) −5.00160 −0.242328
\(427\) 35.9585 1.74015
\(428\) −14.9086 −0.720632
\(429\) 1.12301 0.0542193
\(430\) 0 0
\(431\) 21.3794 1.02981 0.514904 0.857248i \(-0.327827\pi\)
0.514904 + 0.857248i \(0.327827\pi\)
\(432\) −2.97923 −0.143338
\(433\) 36.1182 1.73573 0.867865 0.496799i \(-0.165491\pi\)
0.867865 + 0.496799i \(0.165491\pi\)
\(434\) 14.1182 0.677696
\(435\) 0 0
\(436\) 4.76957 0.228421
\(437\) −9.01917 −0.431445
\(438\) −6.27037 −0.299610
\(439\) 20.9984 1.00220 0.501100 0.865390i \(-0.332929\pi\)
0.501100 + 0.865390i \(0.332929\pi\)
\(440\) 0 0
\(441\) −42.9884 −2.04707
\(442\) −0.561503 −0.0267080
\(443\) 31.4976 1.49650 0.748248 0.663419i \(-0.230895\pi\)
0.748248 + 0.663419i \(0.230895\pi\)
\(444\) −0.0207669 −0.000985555 0
\(445\) 0 0
\(446\) −9.03994 −0.428054
\(447\) −4.37779 −0.207062
\(448\) 4.76957 0.225341
\(449\) 18.9601 0.894781 0.447390 0.894339i \(-0.352353\pi\)
0.447390 + 0.894339i \(0.352353\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 10.3994 0.488606
\(454\) −0.350246 −0.0164378
\(455\) 0 0
\(456\) 0.519969 0.0243498
\(457\) 6.32948 0.296081 0.148040 0.988981i \(-0.452703\pi\)
0.148040 + 0.988981i \(0.452703\pi\)
\(458\) −8.07988 −0.377548
\(459\) 0.743620 0.0347092
\(460\) 0 0
\(461\) −6.49920 −0.302698 −0.151349 0.988480i \(-0.548362\pi\)
−0.151349 + 0.988480i \(0.548362\pi\)
\(462\) 2.38098 0.110773
\(463\) −28.4177 −1.32068 −0.660342 0.750965i \(-0.729589\pi\)
−0.660342 + 0.750965i \(0.729589\pi\)
\(464\) 6.24960 0.290130
\(465\) 0 0
\(466\) 4.92012 0.227920
\(467\) −17.5775 −0.813389 −0.406694 0.913564i \(-0.633319\pi\)
−0.406694 + 0.913564i \(0.633319\pi\)
\(468\) −6.14058 −0.283849
\(469\) 27.3279 1.26188
\(470\) 0 0
\(471\) −2.57908 −0.118838
\(472\) −14.5583 −0.670101
\(473\) −4.76196 −0.218955
\(474\) 3.16135 0.145206
\(475\) 0 0
\(476\) −1.19049 −0.0545660
\(477\) 18.6965 0.856053
\(478\) 2.98083 0.136340
\(479\) 22.7372 1.03889 0.519446 0.854504i \(-0.326139\pi\)
0.519446 + 0.854504i \(0.326139\pi\)
\(480\) 0 0
\(481\) −0.0898462 −0.00409664
\(482\) 20.0383 0.912722
\(483\) −22.3678 −1.01777
\(484\) −10.0783 −0.458104
\(485\) 0 0
\(486\) 12.3902 0.562030
\(487\) 22.1981 1.00589 0.502946 0.864318i \(-0.332249\pi\)
0.502946 + 0.864318i \(0.332249\pi\)
\(488\) 7.53914 0.341281
\(489\) 11.1582 0.504589
\(490\) 0 0
\(491\) −24.9984 −1.12816 −0.564081 0.825719i \(-0.690769\pi\)
−0.564081 + 0.825719i \(0.690769\pi\)
\(492\) 0 0
\(493\) −1.55991 −0.0702547
\(494\) 2.24960 0.101214
\(495\) 0 0
\(496\) 2.96006 0.132911
\(497\) −45.8786 −2.05794
\(498\) 3.87859 0.173804
\(499\) 11.6574 0.521855 0.260928 0.965358i \(-0.415972\pi\)
0.260928 + 0.965358i \(0.415972\pi\)
\(500\) 0 0
\(501\) 5.74043 0.256463
\(502\) −14.8802 −0.664135
\(503\) −11.7504 −0.523924 −0.261962 0.965078i \(-0.584370\pi\)
−0.261962 + 0.965078i \(0.584370\pi\)
\(504\) −13.0192 −0.579920
\(505\) 0 0
\(506\) −8.65896 −0.384938
\(507\) −4.12819 −0.183339
\(508\) −17.9585 −0.796778
\(509\) 29.9569 1.32781 0.663907 0.747815i \(-0.268897\pi\)
0.663907 + 0.747815i \(0.268897\pi\)
\(510\) 0 0
\(511\) −57.5168 −2.54439
\(512\) 1.00000 0.0441942
\(513\) −2.97923 −0.131536
\(514\) 11.0399 0.486951
\(515\) 0 0
\(516\) −2.57908 −0.113538
\(517\) 9.11982 0.401089
\(518\) −0.190491 −0.00836968
\(519\) −8.81788 −0.387062
\(520\) 0 0
\(521\) −15.1198 −0.662411 −0.331206 0.943559i \(-0.607455\pi\)
−0.331206 + 0.943559i \(0.607455\pi\)
\(522\) −17.0591 −0.746657
\(523\) −15.6498 −0.684316 −0.342158 0.939642i \(-0.611158\pi\)
−0.342158 + 0.939642i \(0.611158\pi\)
\(524\) −6.96006 −0.304052
\(525\) 0 0
\(526\) 3.84025 0.167443
\(527\) −0.738835 −0.0321842
\(528\) 0.499202 0.0217250
\(529\) 58.3455 2.53676
\(530\) 0 0
\(531\) 39.7388 1.72452
\(532\) 4.76957 0.206787
\(533\) 0 0
\(534\) 2.12141 0.0918024
\(535\) 0 0
\(536\) 5.72963 0.247482
\(537\) 1.32028 0.0569741
\(538\) 23.1981 1.00014
\(539\) 15.1198 0.651257
\(540\) 0 0
\(541\) −27.2995 −1.17370 −0.586849 0.809697i \(-0.699632\pi\)
−0.586849 + 0.809697i \(0.699632\pi\)
\(542\) 23.9792 1.03000
\(543\) −2.01758 −0.0865825
\(544\) −0.249601 −0.0107016
\(545\) 0 0
\(546\) 5.57908 0.238763
\(547\) 33.9968 1.45360 0.726799 0.686850i \(-0.241007\pi\)
0.726799 + 0.686850i \(0.241007\pi\)
\(548\) −7.80951 −0.333606
\(549\) −20.5791 −0.878294
\(550\) 0 0
\(551\) 6.24960 0.266242
\(552\) −4.68969 −0.199607
\(553\) 28.9984 1.23314
\(554\) −24.6590 −1.04766
\(555\) 0 0
\(556\) −16.0383 −0.680177
\(557\) −33.8786 −1.43548 −0.717741 0.696310i \(-0.754824\pi\)
−0.717741 + 0.696310i \(0.754824\pi\)
\(558\) −8.07988 −0.342048
\(559\) −11.1582 −0.471940
\(560\) 0 0
\(561\) −0.124602 −0.00526068
\(562\) −18.9984 −0.801399
\(563\) −32.2995 −1.36126 −0.680631 0.732626i \(-0.738294\pi\)
−0.680631 + 0.732626i \(0.738294\pi\)
\(564\) 4.93929 0.207982
\(565\) 0 0
\(566\) −29.0367 −1.22051
\(567\) 31.6689 1.32997
\(568\) −9.61902 −0.403605
\(569\) −6.73883 −0.282507 −0.141253 0.989973i \(-0.545113\pi\)
−0.141253 + 0.989973i \(0.545113\pi\)
\(570\) 0 0
\(571\) 34.4193 1.44040 0.720202 0.693764i \(-0.244049\pi\)
0.720202 + 0.693764i \(0.244049\pi\)
\(572\) 2.15975 0.0903039
\(573\) 1.07067 0.0447281
\(574\) 0 0
\(575\) 0 0
\(576\) −2.72963 −0.113735
\(577\) −28.1773 −1.17304 −0.586519 0.809936i \(-0.699502\pi\)
−0.586519 + 0.809936i \(0.699502\pi\)
\(578\) −16.9377 −0.704515
\(579\) 4.39939 0.182832
\(580\) 0 0
\(581\) 35.5775 1.47600
\(582\) −9.57748 −0.397000
\(583\) −6.57589 −0.272346
\(584\) −12.0591 −0.499010
\(585\) 0 0
\(586\) −6.24960 −0.258169
\(587\) 34.6174 1.42881 0.714407 0.699730i \(-0.246697\pi\)
0.714407 + 0.699730i \(0.246697\pi\)
\(588\) 8.18890 0.337704
\(589\) 2.96006 0.121967
\(590\) 0 0
\(591\) −7.23804 −0.297733
\(592\) −0.0399387 −0.00164147
\(593\) 3.99840 0.164195 0.0820974 0.996624i \(-0.473838\pi\)
0.0820974 + 0.996624i \(0.473838\pi\)
\(594\) −2.86025 −0.117357
\(595\) 0 0
\(596\) −8.41932 −0.344869
\(597\) −4.75801 −0.194732
\(598\) −20.2895 −0.829701
\(599\) −42.5759 −1.73960 −0.869802 0.493401i \(-0.835753\pi\)
−0.869802 + 0.493401i \(0.835753\pi\)
\(600\) 0 0
\(601\) −18.4577 −0.752904 −0.376452 0.926436i \(-0.622856\pi\)
−0.376452 + 0.926436i \(0.622856\pi\)
\(602\) −23.6574 −0.964202
\(603\) −15.6398 −0.636901
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) 2.88018 0.116999
\(607\) 12.5791 0.510569 0.255285 0.966866i \(-0.417831\pi\)
0.255285 + 0.966866i \(0.417831\pi\)
\(608\) 1.00000 0.0405554
\(609\) 15.4992 0.628059
\(610\) 0 0
\(611\) 21.3694 0.864514
\(612\) 0.681319 0.0275407
\(613\) 26.5759 1.07339 0.536695 0.843776i \(-0.319673\pi\)
0.536695 + 0.843776i \(0.319673\pi\)
\(614\) −12.5391 −0.506039
\(615\) 0 0
\(616\) 4.57908 0.184496
\(617\) 37.8386 1.52333 0.761663 0.647973i \(-0.224383\pi\)
0.761663 + 0.647973i \(0.224383\pi\)
\(618\) 3.42092 0.137610
\(619\) 30.1566 1.21209 0.606047 0.795429i \(-0.292754\pi\)
0.606047 + 0.795429i \(0.292754\pi\)
\(620\) 0 0
\(621\) 26.8702 1.07826
\(622\) 7.84785 0.314670
\(623\) 19.4593 0.779619
\(624\) 1.16972 0.0468264
\(625\) 0 0
\(626\) −10.9884 −0.439186
\(627\) 0.499202 0.0199362
\(628\) −4.96006 −0.197928
\(629\) 0.00996876 0.000397480 0
\(630\) 0 0
\(631\) −25.4992 −1.01511 −0.507554 0.861620i \(-0.669450\pi\)
−0.507554 + 0.861620i \(0.669450\pi\)
\(632\) 6.07988 0.241845
\(633\) 8.58988 0.341417
\(634\) 21.5567 0.856127
\(635\) 0 0
\(636\) −3.56150 −0.141223
\(637\) 35.4285 1.40373
\(638\) 6.00000 0.237542
\(639\) 26.2564 1.03869
\(640\) 0 0
\(641\) 39.1965 1.54817 0.774084 0.633082i \(-0.218211\pi\)
0.774084 + 0.633082i \(0.218211\pi\)
\(642\) −7.75199 −0.305947
\(643\) 36.3778 1.43460 0.717300 0.696764i \(-0.245378\pi\)
0.717300 + 0.696764i \(0.245378\pi\)
\(644\) −43.0176 −1.69513
\(645\) 0 0
\(646\) −0.249601 −0.00982043
\(647\) 10.6897 0.420255 0.210128 0.977674i \(-0.432612\pi\)
0.210128 + 0.977674i \(0.432612\pi\)
\(648\) 6.63979 0.260835
\(649\) −13.9769 −0.548640
\(650\) 0 0
\(651\) 7.34104 0.287718
\(652\) 21.4593 0.840410
\(653\) −36.0383 −1.41029 −0.705145 0.709063i \(-0.749118\pi\)
−0.705145 + 0.709063i \(0.749118\pi\)
\(654\) 2.48003 0.0969769
\(655\) 0 0
\(656\) 0 0
\(657\) 32.9169 1.28421
\(658\) 45.3071 1.76626
\(659\) 17.1889 0.669584 0.334792 0.942292i \(-0.391334\pi\)
0.334792 + 0.942292i \(0.391334\pi\)
\(660\) 0 0
\(661\) 48.9054 1.90220 0.951099 0.308886i \(-0.0999560\pi\)
0.951099 + 0.308886i \(0.0999560\pi\)
\(662\) 33.4876 1.30153
\(663\) −0.291964 −0.0113390
\(664\) 7.45926 0.289476
\(665\) 0 0
\(666\) 0.109018 0.00422436
\(667\) −56.3662 −2.18251
\(668\) 11.0399 0.427148
\(669\) −4.70049 −0.181731
\(670\) 0 0
\(671\) 7.23804 0.279421
\(672\) 2.48003 0.0956693
\(673\) 6.57908 0.253605 0.126802 0.991928i \(-0.459529\pi\)
0.126802 + 0.991928i \(0.459529\pi\)
\(674\) −5.69890 −0.219513
\(675\) 0 0
\(676\) −7.93929 −0.305357
\(677\) −38.3087 −1.47232 −0.736162 0.676806i \(-0.763364\pi\)
−0.736162 + 0.676806i \(0.763364\pi\)
\(678\) −3.11982 −0.119816
\(679\) −87.8523 −3.37146
\(680\) 0 0
\(681\) −0.182117 −0.00697874
\(682\) 2.84184 0.108820
\(683\) 7.54074 0.288538 0.144269 0.989538i \(-0.453917\pi\)
0.144269 + 0.989538i \(0.453917\pi\)
\(684\) −2.72963 −0.104370
\(685\) 0 0
\(686\) 41.7280 1.59318
\(687\) −4.20129 −0.160289
\(688\) −4.96006 −0.189101
\(689\) −15.4085 −0.587018
\(690\) 0 0
\(691\) 28.4193 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(692\) −16.9585 −0.644664
\(693\) −12.4992 −0.474805
\(694\) 0.239632 0.00909632
\(695\) 0 0
\(696\) 3.24960 0.123176
\(697\) 0 0
\(698\) −17.2380 −0.652469
\(699\) 2.55831 0.0967643
\(700\) 0 0
\(701\) −24.2596 −0.916271 −0.458136 0.888882i \(-0.651483\pi\)
−0.458136 + 0.888882i \(0.651483\pi\)
\(702\) −6.70209 −0.252954
\(703\) −0.0399387 −0.00150632
\(704\) 0.960061 0.0361837
\(705\) 0 0
\(706\) 34.7280 1.30701
\(707\) 26.4193 0.993601
\(708\) −7.56988 −0.284493
\(709\) 21.7372 0.816359 0.408180 0.912902i \(-0.366164\pi\)
0.408180 + 0.912902i \(0.366164\pi\)
\(710\) 0 0
\(711\) −16.5958 −0.622392
\(712\) 4.07988 0.152900
\(713\) −26.6973 −0.999822
\(714\) −0.619019 −0.0231662
\(715\) 0 0
\(716\) 2.53914 0.0948922
\(717\) 1.54994 0.0578835
\(718\) 26.6689 0.995275
\(719\) −48.9361 −1.82501 −0.912504 0.409067i \(-0.865854\pi\)
−0.912504 + 0.409067i \(0.865854\pi\)
\(720\) 0 0
\(721\) 31.3794 1.16863
\(722\) 1.00000 0.0372161
\(723\) 10.4193 0.387499
\(724\) −3.88018 −0.144206
\(725\) 0 0
\(726\) −5.24040 −0.194489
\(727\) 4.29874 0.159432 0.0797158 0.996818i \(-0.474599\pi\)
0.0797158 + 0.996818i \(0.474599\pi\)
\(728\) 10.7296 0.397667
\(729\) −13.4768 −0.499142
\(730\) 0 0
\(731\) 1.23804 0.0457905
\(732\) 3.92012 0.144892
\(733\) 12.0415 0.444764 0.222382 0.974960i \(-0.428617\pi\)
0.222382 + 0.974960i \(0.428617\pi\)
\(734\) 15.2380 0.562446
\(735\) 0 0
\(736\) −9.01917 −0.332451
\(737\) 5.50080 0.202624
\(738\) 0 0
\(739\) 6.61742 0.243426 0.121713 0.992565i \(-0.461161\pi\)
0.121713 + 0.992565i \(0.461161\pi\)
\(740\) 0 0
\(741\) 1.16972 0.0429709
\(742\) −32.6689 −1.19931
\(743\) 47.6158 1.74686 0.873428 0.486954i \(-0.161892\pi\)
0.873428 + 0.486954i \(0.161892\pi\)
\(744\) 1.53914 0.0564277
\(745\) 0 0
\(746\) 26.6382 0.975293
\(747\) −20.3610 −0.744972
\(748\) −0.239632 −0.00876183
\(749\) −71.1074 −2.59821
\(750\) 0 0
\(751\) −25.6574 −0.936250 −0.468125 0.883662i \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(752\) 9.49920 0.346400
\(753\) −7.73724 −0.281961
\(754\) 14.0591 0.512003
\(755\) 0 0
\(756\) −14.2097 −0.516800
\(757\) −8.83865 −0.321246 −0.160623 0.987016i \(-0.551350\pi\)
−0.160623 + 0.987016i \(0.551350\pi\)
\(758\) 11.9693 0.434743
\(759\) −4.50239 −0.163426
\(760\) 0 0
\(761\) −9.40776 −0.341031 −0.170516 0.985355i \(-0.554543\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(762\) −9.33785 −0.338275
\(763\) 22.7488 0.823562
\(764\) 2.05911 0.0744960
\(765\) 0 0
\(766\) 9.84025 0.355543
\(767\) −32.7504 −1.18255
\(768\) 0.519969 0.0187628
\(769\) 7.32788 0.264250 0.132125 0.991233i \(-0.457820\pi\)
0.132125 + 0.991233i \(0.457820\pi\)
\(770\) 0 0
\(771\) 5.74043 0.206737
\(772\) 8.46086 0.304513
\(773\) −54.4369 −1.95796 −0.978980 0.203958i \(-0.934619\pi\)
−0.978980 + 0.203958i \(0.934619\pi\)
\(774\) 13.5391 0.486654
\(775\) 0 0
\(776\) −18.4193 −0.661215
\(777\) −0.0990493 −0.00355337
\(778\) −8.65896 −0.310439
\(779\) 0 0
\(780\) 0 0
\(781\) −9.23485 −0.330449
\(782\) 2.25120 0.0805026
\(783\) −18.6190 −0.665389
\(784\) 15.7488 0.562457
\(785\) 0 0
\(786\) −3.61902 −0.129086
\(787\) 27.6705 0.986348 0.493174 0.869931i \(-0.335837\pi\)
0.493174 + 0.869931i \(0.335837\pi\)
\(788\) −13.9201 −0.495884
\(789\) 1.99681 0.0710883
\(790\) 0 0
\(791\) −28.6174 −1.01752
\(792\) −2.62061 −0.0931195
\(793\) 16.9601 0.602269
\(794\) −28.9984 −1.02911
\(795\) 0 0
\(796\) −9.15055 −0.324333
\(797\) −21.5906 −0.764780 −0.382390 0.924001i \(-0.624899\pi\)
−0.382390 + 0.924001i \(0.624899\pi\)
\(798\) 2.48003 0.0877921
\(799\) −2.37101 −0.0838804
\(800\) 0 0
\(801\) −11.1366 −0.393491
\(802\) 22.6174 0.798649
\(803\) −11.5775 −0.408561
\(804\) 2.97923 0.105069
\(805\) 0 0
\(806\) 6.65896 0.234552
\(807\) 12.0623 0.424613
\(808\) 5.53914 0.194866
\(809\) 9.72963 0.342076 0.171038 0.985264i \(-0.445288\pi\)
0.171038 + 0.985264i \(0.445288\pi\)
\(810\) 0 0
\(811\) −38.7280 −1.35993 −0.679963 0.733247i \(-0.738004\pi\)
−0.679963 + 0.733247i \(0.738004\pi\)
\(812\) 29.8079 1.04605
\(813\) 12.4685 0.437288
\(814\) −0.0383436 −0.00134394
\(815\) 0 0
\(816\) −0.129785 −0.00454338
\(817\) −4.96006 −0.173531
\(818\) 5.34104 0.186745
\(819\) −29.2879 −1.02340
\(820\) 0 0
\(821\) −30.2780 −1.05671 −0.528354 0.849024i \(-0.677191\pi\)
−0.528354 + 0.849024i \(0.677191\pi\)
\(822\) −4.06071 −0.141633
\(823\) 7.93770 0.276691 0.138345 0.990384i \(-0.455822\pi\)
0.138345 + 0.990384i \(0.455822\pi\)
\(824\) 6.57908 0.229193
\(825\) 0 0
\(826\) −69.4369 −2.41602
\(827\) −30.2496 −1.05188 −0.525941 0.850521i \(-0.676287\pi\)
−0.525941 + 0.850521i \(0.676287\pi\)
\(828\) 24.6190 0.855570
\(829\) −40.6765 −1.41275 −0.706377 0.707836i \(-0.749672\pi\)
−0.706377 + 0.707836i \(0.749672\pi\)
\(830\) 0 0
\(831\) −12.8219 −0.444787
\(832\) 2.24960 0.0779909
\(833\) −3.93092 −0.136198
\(834\) −8.33945 −0.288771
\(835\) 0 0
\(836\) 0.960061 0.0332044
\(837\) −8.81871 −0.304819
\(838\) −22.1566 −0.765386
\(839\) 45.9553 1.58655 0.793276 0.608862i \(-0.208374\pi\)
0.793276 + 0.608862i \(0.208374\pi\)
\(840\) 0 0
\(841\) 10.0575 0.346811
\(842\) 29.2787 1.00901
\(843\) −9.87859 −0.340237
\(844\) 16.5200 0.568641
\(845\) 0 0
\(846\) −25.9293 −0.891469
\(847\) −48.0691 −1.65167
\(848\) −6.84945 −0.235211
\(849\) −15.0982 −0.518170
\(850\) 0 0
\(851\) 0.360214 0.0123480
\(852\) −5.00160 −0.171352
\(853\) −17.2196 −0.589589 −0.294794 0.955561i \(-0.595251\pi\)
−0.294794 + 0.955561i \(0.595251\pi\)
\(854\) 35.9585 1.23047
\(855\) 0 0
\(856\) −14.9086 −0.509564
\(857\) −17.2995 −0.590940 −0.295470 0.955352i \(-0.595476\pi\)
−0.295470 + 0.955352i \(0.595476\pi\)
\(858\) 1.12301 0.0383388
\(859\) 17.6190 0.601153 0.300577 0.953758i \(-0.402821\pi\)
0.300577 + 0.953758i \(0.402821\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 21.3794 0.728185
\(863\) 4.07988 0.138881 0.0694403 0.997586i \(-0.477879\pi\)
0.0694403 + 0.997586i \(0.477879\pi\)
\(864\) −2.97923 −0.101356
\(865\) 0 0
\(866\) 36.1182 1.22735
\(867\) −8.80708 −0.299104
\(868\) 14.1182 0.479204
\(869\) 5.83705 0.198009
\(870\) 0 0
\(871\) 12.8894 0.436740
\(872\) 4.76957 0.161518
\(873\) 50.2780 1.70165
\(874\) −9.01917 −0.305078
\(875\) 0 0
\(876\) −6.27037 −0.211856
\(877\) −25.2787 −0.853602 −0.426801 0.904345i \(-0.640360\pi\)
−0.426801 + 0.904345i \(0.640360\pi\)
\(878\) 20.9984 0.708662
\(879\) −3.24960 −0.109606
\(880\) 0 0
\(881\) −0.0814726 −0.00274488 −0.00137244 0.999999i \(-0.500437\pi\)
−0.00137244 + 0.999999i \(0.500437\pi\)
\(882\) −42.9884 −1.44750
\(883\) −19.3410 −0.650878 −0.325439 0.945563i \(-0.605512\pi\)
−0.325439 + 0.945563i \(0.605512\pi\)
\(884\) −0.561503 −0.0188854
\(885\) 0 0
\(886\) 31.4976 1.05818
\(887\) −5.53914 −0.185986 −0.0929931 0.995667i \(-0.529643\pi\)
−0.0929931 + 0.995667i \(0.529643\pi\)
\(888\) −0.0207669 −0.000696892 0
\(889\) −85.6542 −2.87275
\(890\) 0 0
\(891\) 6.37460 0.213557
\(892\) −9.03994 −0.302680
\(893\) 9.49920 0.317879
\(894\) −4.37779 −0.146415
\(895\) 0 0
\(896\) 4.76957 0.159340
\(897\) −10.5499 −0.352252
\(898\) 18.9601 0.632705
\(899\) 18.4992 0.616983
\(900\) 0 0
\(901\) 1.70963 0.0569561
\(902\) 0 0
\(903\) −12.3011 −0.409355
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 10.3994 0.345497
\(907\) −10.8111 −0.358977 −0.179488 0.983760i \(-0.557444\pi\)
−0.179488 + 0.983760i \(0.557444\pi\)
\(908\) −0.350246 −0.0116233
\(909\) −15.1198 −0.501493
\(910\) 0 0
\(911\) 35.1166 1.16347 0.581733 0.813380i \(-0.302375\pi\)
0.581733 + 0.813380i \(0.302375\pi\)
\(912\) 0.519969 0.0172179
\(913\) 7.16135 0.237006
\(914\) 6.32948 0.209361
\(915\) 0 0
\(916\) −8.07988 −0.266967
\(917\) −33.1965 −1.09625
\(918\) 0.743620 0.0245431
\(919\) 30.8287 1.01694 0.508472 0.861078i \(-0.330210\pi\)
0.508472 + 0.861078i \(0.330210\pi\)
\(920\) 0 0
\(921\) −6.51997 −0.214840
\(922\) −6.49920 −0.214040
\(923\) −21.6390 −0.712255
\(924\) 2.38098 0.0783285
\(925\) 0 0
\(926\) −28.4177 −0.933865
\(927\) −17.9585 −0.589833
\(928\) 6.24960 0.205153
\(929\) −45.0575 −1.47829 −0.739145 0.673547i \(-0.764770\pi\)
−0.739145 + 0.673547i \(0.764770\pi\)
\(930\) 0 0
\(931\) 15.7488 0.516146
\(932\) 4.92012 0.161164
\(933\) 4.08064 0.133594
\(934\) −17.5775 −0.575153
\(935\) 0 0
\(936\) −6.14058 −0.200711
\(937\) 22.2464 0.726759 0.363379 0.931641i \(-0.381623\pi\)
0.363379 + 0.931641i \(0.381623\pi\)
\(938\) 27.3279 0.892287
\(939\) −5.71365 −0.186458
\(940\) 0 0
\(941\) −53.9277 −1.75799 −0.878997 0.476828i \(-0.841787\pi\)
−0.878997 + 0.476828i \(0.841787\pi\)
\(942\) −2.57908 −0.0840310
\(943\) 0 0
\(944\) −14.5583 −0.473833
\(945\) 0 0
\(946\) −4.76196 −0.154825
\(947\) −4.76196 −0.154743 −0.0773715 0.997002i \(-0.524653\pi\)
−0.0773715 + 0.997002i \(0.524653\pi\)
\(948\) 3.16135 0.102676
\(949\) −27.1282 −0.880618
\(950\) 0 0
\(951\) 11.2088 0.363471
\(952\) −1.19049 −0.0385840
\(953\) 4.37779 0.141811 0.0709053 0.997483i \(-0.477411\pi\)
0.0709053 + 0.997483i \(0.477411\pi\)
\(954\) 18.6965 0.605321
\(955\) 0 0
\(956\) 2.98083 0.0964069
\(957\) 3.11982 0.100849
\(958\) 22.7372 0.734607
\(959\) −37.2480 −1.20280
\(960\) 0 0
\(961\) −22.2380 −0.717356
\(962\) −0.0898462 −0.00289676
\(963\) 40.6949 1.31137
\(964\) 20.0383 0.645392
\(965\) 0 0
\(966\) −22.3678 −0.719673
\(967\) −13.1582 −0.423138 −0.211569 0.977363i \(-0.567857\pi\)
−0.211569 + 0.977363i \(0.567857\pi\)
\(968\) −10.0783 −0.323928
\(969\) −0.129785 −0.00416929
\(970\) 0 0
\(971\) 25.9201 0.831816 0.415908 0.909407i \(-0.363464\pi\)
0.415908 + 0.909407i \(0.363464\pi\)
\(972\) 12.3902 0.397415
\(973\) −76.4960 −2.45235
\(974\) 22.1981 0.711273
\(975\) 0 0
\(976\) 7.53914 0.241322
\(977\) 31.2764 1.00062 0.500310 0.865846i \(-0.333219\pi\)
0.500310 + 0.865846i \(0.333219\pi\)
\(978\) 11.1582 0.356799
\(979\) 3.91693 0.125186
\(980\) 0 0
\(981\) −13.0192 −0.415670
\(982\) −24.9984 −0.797731
\(983\) 26.2364 0.836813 0.418406 0.908260i \(-0.362589\pi\)
0.418406 + 0.908260i \(0.362589\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −1.55991 −0.0496776
\(987\) 23.5583 0.749869
\(988\) 2.24960 0.0715693
\(989\) 44.7356 1.42251
\(990\) 0 0
\(991\) 39.2764 1.24766 0.623828 0.781562i \(-0.285577\pi\)
0.623828 + 0.781562i \(0.285577\pi\)
\(992\) 2.96006 0.0939820
\(993\) 17.4125 0.552570
\(994\) −45.8786 −1.45518
\(995\) 0 0
\(996\) 3.87859 0.122898
\(997\) 14.4609 0.457980 0.228990 0.973429i \(-0.426458\pi\)
0.228990 + 0.973429i \(0.426458\pi\)
\(998\) 11.6574 0.369007
\(999\) 0.118987 0.00376458
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 950.2.a.l.1.2 yes 3
3.2 odd 2 8550.2.a.ci.1.3 3
4.3 odd 2 7600.2.a.bk.1.2 3
5.2 odd 4 950.2.b.h.799.5 6
5.3 odd 4 950.2.b.h.799.2 6
5.4 even 2 950.2.a.j.1.2 3
15.14 odd 2 8550.2.a.cp.1.1 3
20.19 odd 2 7600.2.a.bz.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.2 3 5.4 even 2
950.2.a.l.1.2 yes 3 1.1 even 1 trivial
950.2.b.h.799.2 6 5.3 odd 4
950.2.b.h.799.5 6 5.2 odd 4
7600.2.a.bk.1.2 3 4.3 odd 2
7600.2.a.bz.1.2 3 20.19 odd 2
8550.2.a.ci.1.3 3 3.2 odd 2
8550.2.a.cp.1.1 3 15.14 odd 2