Properties

Label 950.2.b.h.799.2
Level $950$
Weight $2$
Character 950.799
Analytic conductor $7.586$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.63107136.1
Defining polynomial: \(x^{6} + 13 x^{4} + 42 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 799.2
Root \(-0.480031i\) of defining polynomial
Character \(\chi\) \(=\) 950.799
Dual form 950.2.b.h.799.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +0.960061 q^{11} -0.519969i q^{12} +2.24960i q^{13} -4.76957 q^{14} +1.00000 q^{16} +0.249601i q^{17} -2.72963i q^{18} -1.00000 q^{19} +2.48003 q^{21} -0.960061i q^{22} -9.01917i q^{23} -0.519969 q^{24} +2.24960 q^{26} +2.97923i q^{27} +4.76957i q^{28} -6.24960 q^{29} +2.96006 q^{31} -1.00000i q^{32} +0.499202i q^{33} +0.249601 q^{34} -2.72963 q^{36} +0.0399387i q^{37} +1.00000i q^{38} -1.16972 q^{39} -2.48003i q^{42} -4.96006i q^{43} -0.960061 q^{44} -9.01917 q^{46} -9.49920i q^{47} +0.519969i q^{48} -15.7488 q^{49} -0.129785 q^{51} -2.24960i q^{52} -6.84945i q^{53} +2.97923 q^{54} +4.76957 q^{56} -0.519969i q^{57} +6.24960i q^{58} +14.5583 q^{59} +7.53914 q^{61} -2.96006i q^{62} -13.0192i q^{63} -1.00000 q^{64} +0.499202 q^{66} -5.72963i q^{67} -0.249601i q^{68} +4.68969 q^{69} -9.61902 q^{71} +2.72963i q^{72} -12.0591i q^{73} +0.0399387 q^{74} +1.00000 q^{76} -4.57908i q^{77} +1.16972i q^{78} -6.07988 q^{79} +6.63979 q^{81} +7.45926i q^{83} -2.48003 q^{84} -4.96006 q^{86} -3.24960i q^{87} +0.960061i q^{88} -4.07988 q^{89} +10.7296 q^{91} +9.01917i q^{92} +1.53914i q^{93} -9.49920 q^{94} +0.519969 q^{96} +18.4193i q^{97} +15.7488i q^{98} +2.62061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 4q^{6} - 10q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 4q^{6} - 10q^{9} + 4q^{11} - 4q^{14} + 6q^{16} - 6q^{19} + 14q^{21} - 4q^{24} - 12q^{26} - 12q^{29} + 16q^{31} - 24q^{34} + 10q^{36} + 22q^{39} - 4q^{44} - 4q^{46} - 18q^{49} + 30q^{51} - 34q^{54} + 4q^{56} - 12q^{59} - 4q^{61} - 6q^{64} - 48q^{66} - 12q^{71} + 2q^{74} + 6q^{76} - 40q^{79} + 46q^{81} - 14q^{84} - 28q^{86} - 28q^{89} + 38q^{91} - 6q^{94} + 4q^{96} + 72q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 1.00000i − 0.707107i
\(3\) 0.519969i 0.300204i 0.988670 + 0.150102i \(0.0479603\pi\)
−0.988670 + 0.150102i \(0.952040\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 0.519969 0.212277
\(7\) − 4.76957i − 1.80273i −0.433062 0.901364i \(-0.642567\pi\)
0.433062 0.901364i \(-0.357433\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.72963 0.909877
\(10\) 0 0
\(11\) 0.960061 0.289469 0.144735 0.989471i \(-0.453767\pi\)
0.144735 + 0.989471i \(0.453767\pi\)
\(12\) − 0.519969i − 0.150102i
\(13\) 2.24960i 0.623927i 0.950094 + 0.311964i \(0.100987\pi\)
−0.950094 + 0.311964i \(0.899013\pi\)
\(14\) −4.76957 −1.27472
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.249601i 0.0605372i 0.999542 + 0.0302686i \(0.00963626\pi\)
−0.999542 + 0.0302686i \(0.990364\pi\)
\(18\) − 2.72963i − 0.643380i
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.48003 0.541187
\(22\) − 0.960061i − 0.204686i
\(23\) − 9.01917i − 1.88063i −0.340309 0.940314i \(-0.610532\pi\)
0.340309 0.940314i \(-0.389468\pi\)
\(24\) −0.519969 −0.106138
\(25\) 0 0
\(26\) 2.24960 0.441183
\(27\) 2.97923i 0.573354i
\(28\) 4.76957i 0.901364i
\(29\) −6.24960 −1.16052 −0.580261 0.814431i \(-0.697049\pi\)
−0.580261 + 0.814431i \(0.697049\pi\)
\(30\) 0 0
\(31\) 2.96006 0.531643 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(32\) − 1.00000i − 0.176777i
\(33\) 0.499202i 0.0869000i
\(34\) 0.249601 0.0428063
\(35\) 0 0
\(36\) −2.72963 −0.454939
\(37\) 0.0399387i 0.00656589i 0.999995 + 0.00328294i \(0.00104500\pi\)
−0.999995 + 0.00328294i \(0.998955\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −1.16972 −0.187306
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) − 2.48003i − 0.382677i
\(43\) − 4.96006i − 0.756402i −0.925723 0.378201i \(-0.876543\pi\)
0.925723 0.378201i \(-0.123457\pi\)
\(44\) −0.960061 −0.144735
\(45\) 0 0
\(46\) −9.01917 −1.32980
\(47\) − 9.49920i − 1.38560i −0.721129 0.692801i \(-0.756377\pi\)
0.721129 0.692801i \(-0.243623\pi\)
\(48\) 0.519969i 0.0750511i
\(49\) −15.7488 −2.24983
\(50\) 0 0
\(51\) −0.129785 −0.0181735
\(52\) − 2.24960i − 0.311964i
\(53\) − 6.84945i − 0.940844i −0.882442 0.470422i \(-0.844102\pi\)
0.882442 0.470422i \(-0.155898\pi\)
\(54\) 2.97923 0.405422
\(55\) 0 0
\(56\) 4.76957 0.637361
\(57\) − 0.519969i − 0.0688716i
\(58\) 6.24960i 0.820613i
\(59\) 14.5583 1.89533 0.947665 0.319265i \(-0.103436\pi\)
0.947665 + 0.319265i \(0.103436\pi\)
\(60\) 0 0
\(61\) 7.53914 0.965288 0.482644 0.875817i \(-0.339676\pi\)
0.482644 + 0.875817i \(0.339676\pi\)
\(62\) − 2.96006i − 0.375928i
\(63\) − 13.0192i − 1.64026i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0.499202 0.0614476
\(67\) − 5.72963i − 0.699986i −0.936752 0.349993i \(-0.886184\pi\)
0.936752 0.349993i \(-0.113816\pi\)
\(68\) − 0.249601i − 0.0302686i
\(69\) 4.68969 0.564573
\(70\) 0 0
\(71\) −9.61902 −1.14157 −0.570784 0.821100i \(-0.693361\pi\)
−0.570784 + 0.821100i \(0.693361\pi\)
\(72\) 2.72963i 0.321690i
\(73\) − 12.0591i − 1.41141i −0.708505 0.705706i \(-0.750630\pi\)
0.708505 0.705706i \(-0.249370\pi\)
\(74\) 0.0399387 0.00464278
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) − 4.57908i − 0.521835i
\(78\) 1.16972i 0.132445i
\(79\) −6.07988 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(80\) 0 0
\(81\) 6.63979 0.737754
\(82\) 0 0
\(83\) 7.45926i 0.818761i 0.912364 + 0.409380i \(0.134255\pi\)
−0.912364 + 0.409380i \(0.865745\pi\)
\(84\) −2.48003 −0.270594
\(85\) 0 0
\(86\) −4.96006 −0.534857
\(87\) − 3.24960i − 0.348394i
\(88\) 0.960061i 0.102343i
\(89\) −4.07988 −0.432466 −0.216233 0.976342i \(-0.569377\pi\)
−0.216233 + 0.976342i \(0.569377\pi\)
\(90\) 0 0
\(91\) 10.7296 1.12477
\(92\) 9.01917i 0.940314i
\(93\) 1.53914i 0.159602i
\(94\) −9.49920 −0.979768
\(95\) 0 0
\(96\) 0.519969 0.0530692
\(97\) 18.4193i 1.87020i 0.354385 + 0.935100i \(0.384690\pi\)
−0.354385 + 0.935100i \(0.615310\pi\)
\(98\) 15.7488i 1.59087i
\(99\) 2.62061 0.263382
\(100\) 0 0
\(101\) 5.53914 0.551165 0.275583 0.961277i \(-0.411129\pi\)
0.275583 + 0.961277i \(0.411129\pi\)
\(102\) 0.129785i 0.0128506i
\(103\) 6.57908i 0.648256i 0.946013 + 0.324128i \(0.105071\pi\)
−0.946013 + 0.324128i \(0.894929\pi\)
\(104\) −2.24960 −0.220592
\(105\) 0 0
\(106\) −6.84945 −0.665277
\(107\) 14.9086i 1.44126i 0.693317 + 0.720632i \(0.256148\pi\)
−0.693317 + 0.720632i \(0.743852\pi\)
\(108\) − 2.97923i − 0.286677i
\(109\) −4.76957 −0.456842 −0.228421 0.973562i \(-0.573356\pi\)
−0.228421 + 0.973562i \(0.573356\pi\)
\(110\) 0 0
\(111\) −0.0207669 −0.00197111
\(112\) − 4.76957i − 0.450682i
\(113\) − 6.00000i − 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −0.519969 −0.0486996
\(115\) 0 0
\(116\) 6.24960 0.580261
\(117\) 6.14058i 0.567697i
\(118\) − 14.5583i − 1.34020i
\(119\) 1.19049 0.109132
\(120\) 0 0
\(121\) −10.0783 −0.916207
\(122\) − 7.53914i − 0.682562i
\(123\) 0 0
\(124\) −2.96006 −0.265821
\(125\) 0 0
\(126\) −13.0192 −1.15984
\(127\) 17.9585i 1.59356i 0.604272 + 0.796778i \(0.293464\pi\)
−0.604272 + 0.796778i \(0.706536\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.57908 0.227075
\(130\) 0 0
\(131\) −6.96006 −0.608103 −0.304052 0.952656i \(-0.598340\pi\)
−0.304052 + 0.952656i \(0.598340\pi\)
\(132\) − 0.499202i − 0.0434500i
\(133\) 4.76957i 0.413574i
\(134\) −5.72963 −0.494965
\(135\) 0 0
\(136\) −0.249601 −0.0214031
\(137\) 7.80951i 0.667211i 0.942713 + 0.333606i \(0.108265\pi\)
−0.942713 + 0.333606i \(0.891735\pi\)
\(138\) − 4.68969i − 0.399213i
\(139\) 16.0383 1.36035 0.680177 0.733048i \(-0.261903\pi\)
0.680177 + 0.733048i \(0.261903\pi\)
\(140\) 0 0
\(141\) 4.93929 0.415964
\(142\) 9.61902i 0.807210i
\(143\) 2.15975i 0.180608i
\(144\) 2.72963 0.227469
\(145\) 0 0
\(146\) −12.0591 −0.998019
\(147\) − 8.18890i − 0.675409i
\(148\) − 0.0399387i − 0.00328294i
\(149\) 8.41932 0.689738 0.344869 0.938651i \(-0.387923\pi\)
0.344869 + 0.938651i \(0.387923\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) − 1.00000i − 0.0811107i
\(153\) 0.681319i 0.0550814i
\(154\) −4.57908 −0.368993
\(155\) 0 0
\(156\) 1.16972 0.0936529
\(157\) 4.96006i 0.395856i 0.980217 + 0.197928i \(0.0634212\pi\)
−0.980217 + 0.197928i \(0.936579\pi\)
\(158\) 6.07988i 0.483689i
\(159\) 3.56150 0.282446
\(160\) 0 0
\(161\) −43.0176 −3.39026
\(162\) − 6.63979i − 0.521671i
\(163\) 21.4593i 1.68082i 0.541952 + 0.840410i \(0.317686\pi\)
−0.541952 + 0.840410i \(0.682314\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 7.45926 0.578951
\(167\) − 11.0399i − 0.854296i −0.904182 0.427148i \(-0.859518\pi\)
0.904182 0.427148i \(-0.140482\pi\)
\(168\) 2.48003i 0.191339i
\(169\) 7.93929 0.610715
\(170\) 0 0
\(171\) −2.72963 −0.208740
\(172\) 4.96006i 0.378201i
\(173\) − 16.9585i − 1.28933i −0.764466 0.644664i \(-0.776997\pi\)
0.764466 0.644664i \(-0.223003\pi\)
\(174\) −3.24960 −0.246352
\(175\) 0 0
\(176\) 0.960061 0.0723673
\(177\) 7.56988i 0.568987i
\(178\) 4.07988i 0.305800i
\(179\) −2.53914 −0.189784 −0.0948922 0.995488i \(-0.530251\pi\)
−0.0948922 + 0.995488i \(0.530251\pi\)
\(180\) 0 0
\(181\) −3.88018 −0.288412 −0.144206 0.989548i \(-0.546063\pi\)
−0.144206 + 0.989548i \(0.546063\pi\)
\(182\) − 10.7296i − 0.795333i
\(183\) 3.92012i 0.289784i
\(184\) 9.01917 0.664902
\(185\) 0 0
\(186\) 1.53914 0.112855
\(187\) 0.239632i 0.0175237i
\(188\) 9.49920i 0.692801i
\(189\) 14.2097 1.03360
\(190\) 0 0
\(191\) 2.05911 0.148992 0.0744960 0.997221i \(-0.476265\pi\)
0.0744960 + 0.997221i \(0.476265\pi\)
\(192\) − 0.519969i − 0.0375256i
\(193\) 8.46086i 0.609026i 0.952508 + 0.304513i \(0.0984937\pi\)
−0.952508 + 0.304513i \(0.901506\pi\)
\(194\) 18.4193 1.32243
\(195\) 0 0
\(196\) 15.7488 1.12491
\(197\) 13.9201i 0.991768i 0.868389 + 0.495884i \(0.165156\pi\)
−0.868389 + 0.495884i \(0.834844\pi\)
\(198\) − 2.62061i − 0.186239i
\(199\) 9.15055 0.648665 0.324333 0.945943i \(-0.394860\pi\)
0.324333 + 0.945943i \(0.394860\pi\)
\(200\) 0 0
\(201\) 2.97923 0.210139
\(202\) − 5.53914i − 0.389733i
\(203\) 29.8079i 2.09211i
\(204\) 0.129785 0.00908677
\(205\) 0 0
\(206\) 6.57908 0.458386
\(207\) − 24.6190i − 1.71114i
\(208\) 2.24960i 0.155982i
\(209\) −0.960061 −0.0664088
\(210\) 0 0
\(211\) 16.5200 1.13728 0.568641 0.822586i \(-0.307469\pi\)
0.568641 + 0.822586i \(0.307469\pi\)
\(212\) 6.84945i 0.470422i
\(213\) − 5.00160i − 0.342704i
\(214\) 14.9086 1.01913
\(215\) 0 0
\(216\) −2.97923 −0.202711
\(217\) − 14.1182i − 0.958407i
\(218\) 4.76957i 0.323036i
\(219\) 6.27037 0.423712
\(220\) 0 0
\(221\) −0.561503 −0.0377708
\(222\) 0.0207669i 0.00139378i
\(223\) − 9.03994i − 0.605359i −0.953092 0.302680i \(-0.902119\pi\)
0.953092 0.302680i \(-0.0978812\pi\)
\(224\) −4.76957 −0.318680
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 0.350246i 0.0232466i 0.999932 + 0.0116233i \(0.00369990\pi\)
−0.999932 + 0.0116233i \(0.996300\pi\)
\(228\) 0.519969i 0.0344358i
\(229\) 8.07988 0.533933 0.266967 0.963706i \(-0.413979\pi\)
0.266967 + 0.963706i \(0.413979\pi\)
\(230\) 0 0
\(231\) 2.38098 0.156657
\(232\) − 6.24960i − 0.410306i
\(233\) 4.92012i 0.322328i 0.986928 + 0.161164i \(0.0515248\pi\)
−0.986928 + 0.161164i \(0.948475\pi\)
\(234\) 6.14058 0.401422
\(235\) 0 0
\(236\) −14.5583 −0.947665
\(237\) − 3.16135i − 0.205352i
\(238\) − 1.19049i − 0.0771680i
\(239\) −2.98083 −0.192814 −0.0964069 0.995342i \(-0.530735\pi\)
−0.0964069 + 0.995342i \(0.530735\pi\)
\(240\) 0 0
\(241\) 20.0383 1.29078 0.645392 0.763852i \(-0.276694\pi\)
0.645392 + 0.763852i \(0.276694\pi\)
\(242\) 10.0783i 0.647857i
\(243\) 12.3902i 0.794831i
\(244\) −7.53914 −0.482644
\(245\) 0 0
\(246\) 0 0
\(247\) − 2.24960i − 0.143139i
\(248\) 2.96006i 0.187964i
\(249\) −3.87859 −0.245796
\(250\) 0 0
\(251\) −14.8802 −0.939229 −0.469614 0.882872i \(-0.655607\pi\)
−0.469614 + 0.882872i \(0.655607\pi\)
\(252\) 13.0192i 0.820131i
\(253\) − 8.65896i − 0.544384i
\(254\) 17.9585 1.12681
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) − 11.0399i − 0.688652i −0.938850 0.344326i \(-0.888107\pi\)
0.938850 0.344326i \(-0.111893\pi\)
\(258\) − 2.57908i − 0.160567i
\(259\) 0.190491 0.0118365
\(260\) 0 0
\(261\) −17.0591 −1.05593
\(262\) 6.96006i 0.429994i
\(263\) 3.84025i 0.236800i 0.992966 + 0.118400i \(0.0377764\pi\)
−0.992966 + 0.118400i \(0.962224\pi\)
\(264\) −0.499202 −0.0307238
\(265\) 0 0
\(266\) 4.76957 0.292441
\(267\) − 2.12141i − 0.129828i
\(268\) 5.72963i 0.349993i
\(269\) −23.1981 −1.41441 −0.707207 0.707007i \(-0.750045\pi\)
−0.707207 + 0.707007i \(0.750045\pi\)
\(270\) 0 0
\(271\) 23.9792 1.45663 0.728317 0.685240i \(-0.240303\pi\)
0.728317 + 0.685240i \(0.240303\pi\)
\(272\) 0.249601i 0.0151343i
\(273\) 5.57908i 0.337661i
\(274\) 7.80951 0.471790
\(275\) 0 0
\(276\) −4.68969 −0.282286
\(277\) 24.6590i 1.48161i 0.671718 + 0.740807i \(0.265556\pi\)
−0.671718 + 0.740807i \(0.734444\pi\)
\(278\) − 16.0383i − 0.961916i
\(279\) 8.07988 0.483730
\(280\) 0 0
\(281\) −18.9984 −1.13335 −0.566675 0.823941i \(-0.691770\pi\)
−0.566675 + 0.823941i \(0.691770\pi\)
\(282\) − 4.93929i − 0.294131i
\(283\) − 29.0367i − 1.72606i −0.505156 0.863028i \(-0.668565\pi\)
0.505156 0.863028i \(-0.331435\pi\)
\(284\) 9.61902 0.570784
\(285\) 0 0
\(286\) 2.15975 0.127709
\(287\) 0 0
\(288\) − 2.72963i − 0.160845i
\(289\) 16.9377 0.996335
\(290\) 0 0
\(291\) −9.57748 −0.561442
\(292\) 12.0591i 0.705706i
\(293\) − 6.24960i − 0.365106i −0.983196 0.182553i \(-0.941564\pi\)
0.983196 0.182553i \(-0.0584360\pi\)
\(294\) −8.18890 −0.477586
\(295\) 0 0
\(296\) −0.0399387 −0.00232139
\(297\) 2.86025i 0.165968i
\(298\) − 8.41932i − 0.487718i
\(299\) 20.2895 1.17337
\(300\) 0 0
\(301\) −23.6574 −1.36359
\(302\) − 20.0000i − 1.15087i
\(303\) 2.88018i 0.165462i
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 0.681319 0.0389484
\(307\) 12.5391i 0.715647i 0.933789 + 0.357823i \(0.116481\pi\)
−0.933789 + 0.357823i \(0.883519\pi\)
\(308\) 4.57908i 0.260917i
\(309\) −3.42092 −0.194609
\(310\) 0 0
\(311\) 7.84785 0.445011 0.222505 0.974931i \(-0.428576\pi\)
0.222505 + 0.974931i \(0.428576\pi\)
\(312\) − 1.16972i − 0.0662226i
\(313\) − 10.9884i − 0.621103i −0.950557 0.310552i \(-0.899486\pi\)
0.950557 0.310552i \(-0.100514\pi\)
\(314\) 4.96006 0.279912
\(315\) 0 0
\(316\) 6.07988 0.342020
\(317\) − 21.5567i − 1.21075i −0.795942 0.605373i \(-0.793024\pi\)
0.795942 0.605373i \(-0.206976\pi\)
\(318\) − 3.56150i − 0.199719i
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −7.75199 −0.432674
\(322\) 43.0176i 2.39728i
\(323\) − 0.249601i − 0.0138882i
\(324\) −6.63979 −0.368877
\(325\) 0 0
\(326\) 21.4593 1.18852
\(327\) − 2.48003i − 0.137146i
\(328\) 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 \(0.127925\pi\)
\(332\) − 7.45926i − 0.409380i
\(333\) 0.109018i 0.00597415i
\(334\) −11.0399 −0.604079
\(335\) 0 0
\(336\) 2.48003 0.135297
\(337\) 5.69890i 0.310439i 0.987880 + 0.155219i \(0.0496084\pi\)
−0.987880 + 0.155219i \(0.950392\pi\)
\(338\) − 7.93929i − 0.431841i
\(339\) 3.11982 0.169445
\(340\) 0 0
\(341\) 2.84184 0.153894
\(342\) 2.72963i 0.147602i
\(343\) 41.7280i 2.25310i
\(344\) 4.96006 0.267429
\(345\) 0 0
\(346\) −16.9585 −0.911693
\(347\) − 0.239632i − 0.0128641i −0.999979 0.00643207i \(-0.997953\pi\)
0.999979 0.00643207i \(-0.00204741\pi\)
\(348\) 3.24960i 0.174197i
\(349\) 17.2380 0.922731 0.461365 0.887210i \(-0.347360\pi\)
0.461365 + 0.887210i \(0.347360\pi\)
\(350\) 0 0
\(351\) −6.70209 −0.357731
\(352\) − 0.960061i − 0.0511714i
\(353\) 34.7280i 1.84839i 0.381925 + 0.924193i \(0.375261\pi\)
−0.381925 + 0.924193i \(0.624739\pi\)
\(354\) 7.56988 0.402334
\(355\) 0 0
\(356\) 4.07988 0.216233
\(357\) 0.619019i 0.0327619i
\(358\) 2.53914i 0.134198i
\(359\) −26.6689 −1.40753 −0.703766 0.710432i \(-0.748500\pi\)
−0.703766 + 0.710432i \(0.748500\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 3.88018i 0.203938i
\(363\) − 5.24040i − 0.275050i
\(364\) −10.7296 −0.562386
\(365\) 0 0
\(366\) 3.92012 0.204908
\(367\) − 15.2380i − 0.795419i −0.917511 0.397710i \(-0.869805\pi\)
0.917511 0.397710i \(-0.130195\pi\)
\(368\) − 9.01917i − 0.470157i
\(369\) 0 0
\(370\) 0 0
\(371\) −32.6689 −1.69609
\(372\) − 1.53914i − 0.0798008i
\(373\) 26.6382i 1.37927i 0.724156 + 0.689637i \(0.242230\pi\)
−0.724156 + 0.689637i \(0.757770\pi\)
\(374\) 0.239632 0.0123911
\(375\) 0 0
\(376\) 9.49920 0.489884
\(377\) − 14.0591i − 0.724081i
\(378\) − 14.2097i − 0.730866i
\(379\) −11.9693 −0.614820 −0.307410 0.951577i \(-0.599462\pi\)
−0.307410 + 0.951577i \(0.599462\pi\)
\(380\) 0 0
\(381\) −9.33785 −0.478393
\(382\) − 2.05911i − 0.105353i
\(383\) 9.84025i 0.502813i 0.967882 + 0.251407i \(0.0808931\pi\)
−0.967882 + 0.251407i \(0.919107\pi\)
\(384\) −0.519969 −0.0265346
\(385\) 0 0
\(386\) 8.46086 0.430646
\(387\) − 13.5391i − 0.688233i
\(388\) − 18.4193i − 0.935100i
\(389\) 8.65896 0.439027 0.219513 0.975610i \(-0.429553\pi\)
0.219513 + 0.975610i \(0.429553\pi\)
\(390\) 0 0
\(391\) 2.25120 0.113848
\(392\) − 15.7488i − 0.795435i
\(393\) − 3.61902i − 0.182555i
\(394\) 13.9201 0.701286
\(395\) 0 0
\(396\) −2.62061 −0.131691
\(397\) 28.9984i 1.45539i 0.685902 + 0.727694i \(0.259408\pi\)
−0.685902 + 0.727694i \(0.740592\pi\)
\(398\) − 9.15055i − 0.458676i
\(399\) −2.48003 −0.124157
\(400\) 0 0
\(401\) 22.6174 1.12946 0.564730 0.825276i \(-0.308980\pi\)
0.564730 + 0.825276i \(0.308980\pi\)
\(402\) − 2.97923i − 0.148591i
\(403\) 6.65896i 0.331706i
\(404\) −5.53914 −0.275583
\(405\) 0 0
\(406\) 29.8079 1.47934
\(407\) 0.0383436i 0.00190062i
\(408\) − 0.129785i − 0.00642531i
\(409\) −5.34104 −0.264098 −0.132049 0.991243i \(-0.542156\pi\)
−0.132049 + 0.991243i \(0.542156\pi\)
\(410\) 0 0
\(411\) −4.06071 −0.200300
\(412\) − 6.57908i − 0.324128i
\(413\) − 69.4369i − 3.41677i
\(414\) −24.6190 −1.20996
\(415\) 0 0
\(416\) 2.24960 0.110296
\(417\) 8.33945i 0.408384i
\(418\) 0.960061i 0.0469581i
\(419\) 22.1566 1.08242 0.541210 0.840888i \(-0.317967\pi\)
0.541210 + 0.840888i \(0.317967\pi\)
\(420\) 0 0
\(421\) 29.2787 1.42696 0.713479 0.700676i \(-0.247118\pi\)
0.713479 + 0.700676i \(0.247118\pi\)
\(422\) − 16.5200i − 0.804180i
\(423\) − 25.9293i − 1.26073i
\(424\) 6.84945 0.332639
\(425\) 0 0
\(426\) −5.00160 −0.242328
\(427\) − 35.9585i − 1.74015i
\(428\) − 14.9086i − 0.720632i
\(429\) −1.12301 −0.0542193
\(430\) 0 0
\(431\) 21.3794 1.02981 0.514904 0.857248i \(-0.327827\pi\)
0.514904 + 0.857248i \(0.327827\pi\)
\(432\) 2.97923i 0.143338i
\(433\) 36.1182i 1.73573i 0.496799 + 0.867865i \(0.334509\pi\)
−0.496799 + 0.867865i \(0.665491\pi\)
\(434\) −14.1182 −0.677696
\(435\) 0 0
\(436\) 4.76957 0.228421
\(437\) 9.01917i 0.431445i
\(438\) − 6.27037i − 0.299610i
\(439\) −20.9984 −1.00220 −0.501100 0.865390i \(-0.667071\pi\)
−0.501100 + 0.865390i \(0.667071\pi\)
\(440\) 0 0
\(441\) −42.9884 −2.04707
\(442\) 0.561503i 0.0267080i
\(443\) 31.4976i 1.49650i 0.663419 + 0.748248i \(0.269105\pi\)
−0.663419 + 0.748248i \(0.730895\pi\)
\(444\) 0.0207669 0.000985555 0
\(445\) 0 0
\(446\) −9.03994 −0.428054
\(447\) 4.37779i 0.207062i
\(448\) 4.76957i 0.225341i
\(449\) −18.9601 −0.894781 −0.447390 0.894339i \(-0.647647\pi\)
−0.447390 + 0.894339i \(0.647647\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000i 0.282216i
\(453\) 10.3994i 0.488606i
\(454\) 0.350246 0.0164378
\(455\) 0 0
\(456\) 0.519969 0.0243498
\(457\) − 6.32948i − 0.296081i −0.988981 0.148040i \(-0.952703\pi\)
0.988981 0.148040i \(-0.0472965\pi\)
\(458\) − 8.07988i − 0.377548i
\(459\) −0.743620 −0.0347092
\(460\) 0 0
\(461\) −6.49920 −0.302698 −0.151349 0.988480i \(-0.548362\pi\)
−0.151349 + 0.988480i \(0.548362\pi\)
\(462\) − 2.38098i − 0.110773i
\(463\) − 28.4177i − 1.32068i −0.750965 0.660342i \(-0.770411\pi\)
0.750965 0.660342i \(-0.229589\pi\)
\(464\) −6.24960 −0.290130
\(465\) 0 0
\(466\) 4.92012 0.227920
\(467\) 17.5775i 0.813389i 0.913564 + 0.406694i \(0.133319\pi\)
−0.913564 + 0.406694i \(0.866681\pi\)
\(468\) − 6.14058i − 0.283849i
\(469\) −27.3279 −1.26188
\(470\) 0 0
\(471\) −2.57908 −0.118838
\(472\) 14.5583i 0.670101i
\(473\) − 4.76196i − 0.218955i
\(474\) −3.16135 −0.145206
\(475\) 0 0
\(476\) −1.19049 −0.0545660
\(477\) − 18.6965i − 0.856053i
\(478\) 2.98083i 0.136340i
\(479\) −22.7372 −1.03889 −0.519446 0.854504i \(-0.673861\pi\)
−0.519446 + 0.854504i \(0.673861\pi\)
\(480\) 0 0
\(481\) −0.0898462 −0.00409664
\(482\) − 20.0383i − 0.912722i
\(483\) − 22.3678i − 1.01777i
\(484\) 10.0783 0.458104
\(485\) 0 0
\(486\) 12.3902 0.562030
\(487\) − 22.1981i − 1.00589i −0.864318 0.502946i \(-0.832249\pi\)
0.864318 0.502946i \(-0.167751\pi\)
\(488\) 7.53914i 0.341281i
\(489\) −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
\(493\) − 1.55991i − 0.0702547i
\(494\) −2.24960 −0.101214
\(495\) 0 0
\(496\) 2.96006 0.132911
\(497\) 45.8786i 2.05794i
\(498\) 3.87859i 0.173804i
\(499\) −11.6574 −0.521855 −0.260928 0.965358i \(-0.584028\pi\)
−0.260928 + 0.965358i \(0.584028\pi\)
\(500\) 0 0
\(501\) 5.74043 0.256463
\(502\) 14.8802i 0.664135i
\(503\) − 11.7504i − 0.523924i −0.965078 0.261962i \(-0.915630\pi\)
0.965078 0.261962i \(-0.0843696\pi\)
\(504\) 13.0192 0.579920
\(505\) 0 0
\(506\) −8.65896 −0.384938
\(507\) 4.12819i 0.183339i
\(508\) − 17.9585i − 0.796778i
\(509\) −29.9569 −1.32781 −0.663907 0.747815i \(-0.731103\pi\)
−0.663907 + 0.747815i \(0.731103\pi\)
\(510\) 0 0
\(511\) −57.5168 −2.54439
\(512\) − 1.00000i − 0.0441942i
\(513\) − 2.97923i − 0.131536i
\(514\) −11.0399 −0.486951
\(515\) 0 0
\(516\) −2.57908 −0.113538
\(517\) − 9.11982i − 0.401089i
\(518\) − 0.190491i − 0.00836968i
\(519\) 8.81788 0.387062
\(520\) 0 0
\(521\) −15.1198 −0.662411 −0.331206 0.943559i \(-0.607455\pi\)
−0.331206 + 0.943559i \(0.607455\pi\)
\(522\) 17.0591i 0.746657i
\(523\) − 15.6498i − 0.684316i −0.939642 0.342158i \(-0.888842\pi\)
0.939642 0.342158i \(-0.111158\pi\)
\(524\) 6.96006 0.304052
\(525\) 0 0
\(526\) 3.84025 0.167443
\(527\) 0.738835i 0.0321842i
\(528\) 0.499202i 0.0217250i
\(529\) −58.3455 −2.53676
\(530\) 0 0
\(531\) 39.7388 1.72452
\(532\) − 4.76957i − 0.206787i
\(533\) 0 0
\(534\) −2.12141 −0.0918024
\(535\) 0 0
\(536\) 5.72963 0.247482
\(537\) − 1.32028i − 0.0569741i
\(538\) 23.1981i 1.00014i
\(539\) −15.1198 −0.651257
\(540\) 0 0
\(541\) −27.2995 −1.17370 −0.586849 0.809697i \(-0.699632\pi\)
−0.586849 + 0.809697i \(0.699632\pi\)
\(542\) − 23.9792i − 1.03000i
\(543\) − 2.01758i − 0.0865825i
\(544\) 0.249601 0.0107016
\(545\) 0 0
\(546\) 5.57908 0.238763
\(547\) − 33.9968i − 1.45360i −0.686850 0.726799i \(-0.741007\pi\)
0.686850 0.726799i \(-0.258993\pi\)
\(548\) − 7.80951i − 0.333606i
\(549\) 20.5791 0.878294
\(550\) 0 0
\(551\) 6.24960 0.266242
\(552\) 4.68969i 0.199607i
\(553\) 28.9984i 1.23314i
\(554\) 24.6590 1.04766
\(555\) 0 0
\(556\) −16.0383 −0.680177
\(557\) 33.8786i 1.43548i 0.696310 + 0.717741i \(0.254824\pi\)
−0.696310 + 0.717741i \(0.745176\pi\)
\(558\) − 8.07988i − 0.342048i
\(559\) 11.1582 0.471940
\(560\) 0 0
\(561\) −0.124602 −0.00526068
\(562\) 18.9984i 0.801399i
\(563\) − 32.2995i − 1.36126i −0.732626 0.680631i \(-0.761706\pi\)
0.732626 0.680631i \(-0.238294\pi\)
\(564\) −4.93929 −0.207982
\(565\) 0 0
\(566\) −29.0367 −1.22051
\(567\) − 31.6689i − 1.32997i
\(568\) − 9.61902i − 0.403605i
\(569\) 6.73883 0.282507 0.141253 0.989973i \(-0.454887\pi\)
0.141253 + 0.989973i \(0.454887\pi\)
\(570\) 0 0
\(571\) 34.4193 1.44040 0.720202 0.693764i \(-0.244049\pi\)
0.720202 + 0.693764i \(0.244049\pi\)
\(572\) − 2.15975i − 0.0903039i
\(573\) 1.07067i 0.0447281i
\(574\) 0 0
\(575\) 0 0
\(576\) −2.72963 −0.113735
\(577\) 28.1773i 1.17304i 0.809936 + 0.586519i \(0.199502\pi\)
−0.809936 + 0.586519i \(0.800498\pi\)
\(578\) − 16.9377i − 0.704515i
\(579\) −4.39939 −0.182832
\(580\) 0 0
\(581\) 35.5775 1.47600
\(582\) 9.57748i 0.397000i
\(583\) − 6.57589i − 0.272346i
\(584\) 12.0591 0.499010
\(585\) 0 0
\(586\) −6.24960 −0.258169
\(587\) − 34.6174i − 1.42881i −0.699730 0.714407i \(-0.746697\pi\)
0.699730 0.714407i \(-0.253303\pi\)
\(588\) 8.18890i 0.337704i
\(589\) −2.96006 −0.121967
\(590\) 0 0
\(591\) −7.23804 −0.297733
\(592\) 0.0399387i 0.00164147i
\(593\) 3.99840i 0.164195i 0.996624 + 0.0820974i \(0.0261619\pi\)
−0.996624 + 0.0820974i \(0.973838\pi\)
\(594\) 2.86025 0.117357
\(595\) 0 0
\(596\) −8.41932 −0.344869
\(597\) 4.75801i 0.194732i
\(598\) − 20.2895i − 0.829701i
\(599\) 42.5759 1.73960 0.869802 0.493401i \(-0.164247\pi\)
0.869802 + 0.493401i \(0.164247\pi\)
\(600\) 0 0
\(601\) −18.4577 −0.752904 −0.376452 0.926436i \(-0.622856\pi\)
−0.376452 + 0.926436i \(0.622856\pi\)
\(602\) 23.6574i 0.964202i
\(603\) − 15.6398i − 0.636901i
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) 2.88018 0.116999
\(607\) − 12.5791i − 0.510569i −0.966866 0.255285i \(-0.917831\pi\)
0.966866 0.255285i \(-0.0821691\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −15.4992 −0.628059
\(610\) 0 0
\(611\) 21.3694 0.864514
\(612\) − 0.681319i − 0.0275407i
\(613\) 26.5759i 1.07339i 0.843776 + 0.536695i \(0.180327\pi\)
−0.843776 + 0.536695i \(0.819673\pi\)
\(614\) 12.5391 0.506039
\(615\) 0 0
\(616\) 4.57908 0.184496
\(617\) − 37.8386i − 1.52333i −0.647973 0.761663i \(-0.724383\pi\)
0.647973 0.761663i \(-0.275617\pi\)
\(618\) 3.42092i 0.137610i
\(619\) −30.1566 −1.21209 −0.606047 0.795429i \(-0.707246\pi\)
−0.606047 + 0.795429i \(0.707246\pi\)
\(620\) 0 0
\(621\) 26.8702 1.07826
\(622\) − 7.84785i − 0.314670i
\(623\) 19.4593i 0.779619i
\(624\) −1.16972 −0.0468264
\(625\) 0 0
\(626\) −10.9884 −0.439186
\(627\) − 0.499202i − 0.0199362i
\(628\) − 4.96006i − 0.197928i
\(629\) −0.00996876 −0.000397480 0
\(630\) 0 0
\(631\) −25.4992 −1.01511 −0.507554 0.861620i \(-0.669450\pi\)
−0.507554 + 0.861620i \(0.669450\pi\)
\(632\) − 6.07988i − 0.241845i
\(633\) 8.58988i 0.341417i
\(634\) −21.5567 −0.856127
\(635\) 0 0
\(636\) −3.56150 −0.141223
\(637\) − 35.4285i − 1.40373i
\(638\) 6.00000i 0.237542i
\(639\) −26.2564 −1.03869
\(640\) 0 0
\(641\) 39.1965 1.54817 0.774084 0.633082i \(-0.218211\pi\)
0.774084 + 0.633082i \(0.218211\pi\)
\(642\) 7.75199i 0.305947i
\(643\) 36.3778i 1.43460i 0.696764 + 0.717300i \(0.254622\pi\)
−0.696764 + 0.717300i \(0.745378\pi\)
\(644\) 43.0176 1.69513
\(645\) 0 0
\(646\) −0.249601 −0.00982043
\(647\) − 10.6897i − 0.420255i −0.977674 0.210128i \(-0.932612\pi\)
0.977674 0.210128i \(-0.0673879\pi\)
\(648\) 6.63979i 0.260835i
\(649\) 13.9769 0.548640
\(650\) 0 0
\(651\) 7.34104 0.287718
\(652\) − 21.4593i − 0.840410i
\(653\) − 36.0383i − 1.41029i −0.709063 0.705145i \(-0.750882\pi\)
0.709063 0.705145i \(-0.249118\pi\)
\(654\) −2.48003 −0.0969769
\(655\) 0 0
\(656\) 0 0
\(657\) − 32.9169i − 1.28421i
\(658\) 45.3071i 1.76626i
\(659\) −17.1889 −0.669584 −0.334792 0.942292i \(-0.608666\pi\)
−0.334792 + 0.942292i \(0.608666\pi\)
\(660\) 0 0
\(661\) 48.9054 1.90220 0.951099 0.308886i \(-0.0999560\pi\)
0.951099 + 0.308886i \(0.0999560\pi\)
\(662\) − 33.4876i − 1.30153i
\(663\) − 0.291964i − 0.0113390i
\(664\) −7.45926 −0.289476
\(665\) 0 0
\(666\) 0.109018 0.00422436
\(667\) 56.3662i 2.18251i
\(668\) 11.0399i 0.427148i
\(669\) 4.70049 0.181731
\(670\) 0 0
\(671\) 7.23804 0.279421
\(672\) − 2.48003i − 0.0956693i
\(673\) 6.57908i 0.253605i 0.991928 + 0.126802i \(0.0404714\pi\)
−0.991928 + 0.126802i \(0.959529\pi\)
\(674\) 5.69890 0.219513
\(675\) 0 0
\(676\) −7.93929 −0.305357
\(677\) 38.3087i 1.47232i 0.676806 + 0.736162i \(0.263364\pi\)
−0.676806 + 0.736162i \(0.736636\pi\)
\(678\) − 3.11982i − 0.119816i
\(679\) 87.8523 3.37146
\(680\) 0 0
\(681\) −0.182117 −0.00697874
\(682\) − 2.84184i − 0.108820i
\(683\) 7.54074i 0.288538i 0.989538 + 0.144269i \(0.0460831\pi\)
−0.989538 + 0.144269i \(0.953917\pi\)
\(684\) 2.72963 0.104370
\(685\) 0 0
\(686\) 41.7280 1.59318
\(687\) 4.20129i 0.160289i
\(688\) − 4.96006i − 0.189101i
\(689\) 15.4085 0.587018
\(690\) 0 0
\(691\) 28.4193 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(692\) 16.9585i 0.644664i
\(693\) − 12.4992i − 0.474805i
\(694\) −0.239632 −0.00909632
\(695\) 0 0
\(696\) 3.24960 0.123176
\(697\) 0 0
\(698\) − 17.2380i − 0.652469i
\(699\) −2.55831 −0.0967643
\(700\) 0 0
\(701\) −24.2596 −0.916271 −0.458136 0.888882i \(-0.651483\pi\)
−0.458136 + 0.888882i \(0.651483\pi\)
\(702\) 6.70209i 0.252954i
\(703\) − 0.0399387i − 0.00150632i
\(704\) −0.960061 −0.0361837
\(705\) 0 0
\(706\) 34.7280 1.30701
\(707\) − 26.4193i − 0.993601i
\(708\) − 7.56988i − 0.284493i
\(709\) −21.7372 −0.816359 −0.408180 0.912902i \(-0.633836\pi\)
−0.408180 + 0.912902i \(0.633836\pi\)
\(710\) 0 0
\(711\) −16.5958 −0.622392
\(712\) − 4.07988i − 0.152900i
\(713\) − 26.6973i − 0.999822i
\(714\) 0.619019 0.0231662
\(715\) 0 0
\(716\) 2.53914 0.0948922
\(717\) − 1.54994i − 0.0578835i
\(718\) 26.6689i 0.995275i
\(719\) 48.9361 1.82501 0.912504 0.409067i \(-0.134146\pi\)
0.912504 + 0.409067i \(0.134146\pi\)
\(720\) 0 0
\(721\) 31.3794 1.16863
\(722\) − 1.00000i − 0.0372161i
\(723\) 10.4193i 0.387499i
\(724\) 3.88018 0.144206
\(725\) 0 0
\(726\) −5.24040 −0.194489
\(727\) − 4.29874i − 0.159432i −0.996818 0.0797158i \(-0.974599\pi\)
0.996818 0.0797158i \(-0.0254013\pi\)
\(728\) 10.7296i 0.397667i
\(729\) 13.4768 0.499142
\(730\) 0 0
\(731\) 1.23804 0.0457905
\(732\) − 3.92012i − 0.144892i
\(733\) 12.0415i 0.444764i 0.974960 + 0.222382i \(0.0713832\pi\)
−0.974960 + 0.222382i \(0.928617\pi\)
\(734\) −15.2380 −0.562446
\(735\) 0 0
\(736\) −9.01917 −0.332451
\(737\) − 5.50080i − 0.202624i
\(738\) 0 0
\(739\) −6.61742 −0.243426 −0.121713 0.992565i \(-0.538839\pi\)
−0.121713 + 0.992565i \(0.538839\pi\)
\(740\) 0 0
\(741\) 1.16972 0.0429709
\(742\) 32.6689i 1.19931i
\(743\) 47.6158i 1.74686i 0.486954 + 0.873428i \(0.338108\pi\)
−0.486954 + 0.873428i \(0.661892\pi\)
\(744\) −1.53914 −0.0564277
\(745\) 0 0
\(746\) 26.6382 0.975293
\(747\) 20.3610i 0.744972i
\(748\) − 0.239632i − 0.00876183i
\(749\) 71.1074 2.59821
\(750\) 0 0
\(751\) −25.6574 −0.936250 −0.468125 0.883662i \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(752\) − 9.49920i − 0.346400i
\(753\) − 7.73724i − 0.281961i
\(754\) −14.0591 −0.512003
\(755\) 0 0
\(756\) −14.2097 −0.516800
\(757\) 8.83865i 0.321246i 0.987016 + 0.160623i \(0.0513504\pi\)
−0.987016 + 0.160623i \(0.948650\pi\)
\(758\) 11.9693i 0.434743i
\(759\) 4.50239 0.163426
\(760\) 0 0
\(761\) −9.40776 −0.341031 −0.170516 0.985355i \(-0.554543\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(762\) 9.33785i 0.338275i
\(763\) 22.7488i 0.823562i
\(764\) −2.05911 −0.0744960
\(765\) 0 0
\(766\) 9.84025 0.355543
\(767\) 32.7504i 1.18255i
\(768\) 0.519969i 0.0187628i
\(769\) −7.32788 −0.264250 −0.132125 0.991233i \(-0.542180\pi\)
−0.132125 + 0.991233i \(0.542180\pi\)
\(770\) 0 0
\(771\) 5.74043 0.206737
\(772\) − 8.46086i − 0.304513i
\(773\) − 54.4369i − 1.95796i −0.203958 0.978980i \(-0.565381\pi\)
0.203958 0.978980i \(-0.434619\pi\)
\(774\) −13.5391 −0.486654
\(775\) 0 0
\(776\) −18.4193 −0.661215
\(777\) 0.0990493i 0.00355337i
\(778\) − 8.65896i − 0.310439i
\(779\) 0 0
\(780\) 0 0
\(781\) −9.23485 −0.330449
\(782\) − 2.25120i − 0.0805026i
\(783\) − 18.6190i − 0.665389i
\(784\) −15.7488 −0.562457
\(785\) 0 0
\(786\) −3.61902 −0.129086
\(787\) − 27.6705i − 0.986348i −0.869931 0.493174i \(-0.835837\pi\)
0.869931 0.493174i \(-0.164163\pi\)
\(788\) − 13.9201i − 0.495884i
\(789\) −1.99681 −0.0710883
\(790\) 0 0
\(791\) −28.6174 −1.01752
\(792\) 2.62061i 0.0931195i
\(793\) 16.9601i 0.602269i
\(794\) 28.9984 1.02911
\(795\) 0 0
\(796\) −9.15055 −0.324333
\(797\) 21.5906i 0.764780i 0.924001 + 0.382390i \(0.124899\pi\)
−0.924001 + 0.382390i \(0.875101\pi\)
\(798\) 2.48003i 0.0877921i
\(799\) 2.37101 0.0838804
\(800\) 0 0
\(801\) −11.1366 −0.393491
\(802\) − 22.6174i − 0.798649i
\(803\) − 11.5775i − 0.408561i
\(804\) −2.97923 −0.105069
\(805\) 0 0
\(806\) 6.65896 0.234552
\(807\) − 12.0623i − 0.424613i
\(808\) 5.53914i 0.194866i
\(809\) −9.72963 −0.342076 −0.171038 0.985264i \(-0.554712\pi\)
−0.171038 + 0.985264i \(0.554712\pi\)
\(810\) 0 0
\(811\) −38.7280 −1.35993 −0.679963 0.733247i \(-0.738004\pi\)
−0.679963 + 0.733247i \(0.738004\pi\)
\(812\) − 29.8079i − 1.04605i
\(813\) 12.4685i 0.437288i
\(814\) 0.0383436 0.00134394
\(815\) 0 0
\(816\) −0.129785 −0.00454338
\(817\) 4.96006i 0.173531i
\(818\) 5.34104i 0.186745i
\(819\) 29.2879 1.02340
\(820\) 0 0
\(821\) −30.2780 −1.05671 −0.528354 0.849024i \(-0.677191\pi\)
−0.528354 + 0.849024i \(0.677191\pi\)
\(822\) 4.06071i 0.141633i
\(823\) 7.93770i 0.276691i 0.990384 + 0.138345i \(0.0441784\pi\)
−0.990384 + 0.138345i \(0.955822\pi\)
\(824\) −6.57908 −0.229193
\(825\) 0 0
\(826\) −69.4369 −2.41602
\(827\) 30.2496i 1.05188i 0.850521 + 0.525941i \(0.176287\pi\)
−0.850521 + 0.525941i \(0.823713\pi\)
\(828\) 24.6190i 0.855570i
\(829\) 40.6765 1.41275 0.706377 0.707836i \(-0.250328\pi\)
0.706377 + 0.707836i \(0.250328\pi\)
\(830\) 0 0
\(831\) −12.8219 −0.444787
\(832\) − 2.24960i − 0.0779909i
\(833\) − 3.93092i − 0.136198i
\(834\) 8.33945 0.288771
\(835\) 0 0
\(836\) 0.960061 0.0332044
\(837\) 8.81871i 0.304819i
\(838\) − 22.1566i − 0.765386i
\(839\) −45.9553 −1.58655 −0.793276 0.608862i \(-0.791626\pi\)
−0.793276 + 0.608862i \(0.791626\pi\)
\(840\) 0 0
\(841\) 10.0575 0.346811
\(842\) − 29.2787i − 1.00901i
\(843\) − 9.87859i − 0.340237i
\(844\) −16.5200 −0.568641
\(845\) 0 0
\(846\) −25.9293 −0.891469
\(847\) 48.0691i 1.65167i
\(848\) − 6.84945i − 0.235211i
\(849\) 15.0982 0.518170
\(850\) 0 0
\(851\) 0.360214 0.0123480
\(852\) 5.00160i 0.171352i
\(853\) − 17.2196i − 0.589589i −0.955561 0.294794i \(-0.904749\pi\)
0.955561 0.294794i \(-0.0952512\pi\)
\(854\) −35.9585 −1.23047
\(855\) 0 0
\(856\) −14.9086 −0.509564
\(857\) 17.2995i 0.590940i 0.955352 + 0.295470i \(0.0954762\pi\)
−0.955352 + 0.295470i \(0.904524\pi\)
\(858\) 1.12301i 0.0383388i
\(859\) −17.6190 −0.601153 −0.300577 0.953758i \(-0.597179\pi\)
−0.300577 + 0.953758i \(0.597179\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) − 21.3794i − 0.728185i
\(863\) 4.07988i 0.138881i 0.997586 + 0.0694403i \(0.0221213\pi\)
−0.997586 + 0.0694403i \(0.977879\pi\)
\(864\) 2.97923 0.101356
\(865\) 0 0
\(866\) 36.1182 1.22735
\(867\) 8.80708i 0.299104i
\(868\) 14.1182i 0.479204i
\(869\) −5.83705 −0.198009
\(870\) 0 0
\(871\) 12.8894 0.436740
\(872\) − 4.76957i − 0.161518i
\(873\) 50.2780i 1.70165i
\(874\) 9.01917 0.305078
\(875\) 0 0
\(876\) −6.27037 −0.211856
\(877\) 25.2787i 0.853602i 0.904345 + 0.426801i \(0.140360\pi\)
−0.904345 + 0.426801i \(0.859640\pi\)
\(878\) 20.9984i 0.708662i
\(879\) 3.24960 0.109606
\(880\) 0 0
\(881\) −0.0814726 −0.00274488 −0.00137244 0.999999i \(-0.500437\pi\)
−0.00137244 + 0.999999i \(0.500437\pi\)
\(882\) 42.9884i 1.44750i
\(883\) − 19.3410i − 0.650878i −0.945563 0.325439i \(-0.894488\pi\)
0.945563 0.325439i \(-0.105512\pi\)
\(884\) 0.561503 0.0188854
\(885\) 0 0
\(886\) 31.4976 1.05818
\(887\) 5.53914i 0.185986i 0.995667 + 0.0929931i \(0.0296434\pi\)
−0.995667 + 0.0929931i \(0.970357\pi\)
\(888\) − 0.0207669i 0 0.000696892i
\(889\) 85.6542 2.87275
\(890\) 0 0
\(891\) 6.37460 0.213557
\(892\) 9.03994i 0.302680i
\(893\) 9.49920i 0.317879i
\(894\) 4.37779 0.146415
\(895\) 0 0
\(896\) 4.76957 0.159340
\(897\) 10.5499i 0.352252i
\(898\) 18.9601i 0.632705i
\(899\) −18.4992 −0.616983
\(900\) 0 0
\(901\) 1.70963 0.0569561
\(902\) 0 0
\(903\) − 12.3011i − 0.409355i
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) 10.3994 0.345497
\(907\) 10.8111i 0.358977i 0.983760 + 0.179488i \(0.0574442\pi\)
−0.983760 + 0.179488i \(0.942556\pi\)
\(908\) − 0.350246i − 0.0116233i
\(909\) 15.1198 0.501493
\(910\) 0 0
\(911\) 35.1166 1.16347 0.581733 0.813380i \(-0.302375\pi\)
0.581733 + 0.813380i \(0.302375\pi\)
\(912\) − 0.519969i − 0.0172179i
\(913\) 7.16135i 0.237006i
\(914\) −6.32948 −0.209361
\(915\) 0 0
\(916\) −8.07988 −0.266967
\(917\) 33.1965i 1.09625i
\(918\) 0.743620i 0.0245431i
\(919\) −30.8287 −1.01694 −0.508472 0.861078i \(-0.669790\pi\)
−0.508472 + 0.861078i \(0.669790\pi\)
\(920\) 0 0
\(921\) −6.51997 −0.214840
\(922\) 6.49920i 0.214040i
\(923\) − 21.6390i − 0.712255i
\(924\) −2.38098 −0.0783285
\(925\) 0 0
\(926\) −28.4177 −0.933865
\(927\) 17.9585i 0.589833i
\(928\) 6.24960i 0.205153i
\(929\) 45.0575 1.47829 0.739145 0.673547i \(-0.235230\pi\)
0.739145 + 0.673547i \(0.235230\pi\)
\(930\) 0 0
\(931\) 15.7488 0.516146
\(932\) − 4.92012i − 0.161164i
\(933\) 4.08064i 0.133594i
\(934\) 17.5775 0.575153
\(935\) 0 0
\(936\) −6.14058 −0.200711
\(937\) − 22.2464i − 0.726759i −0.931641 0.363379i \(-0.881623\pi\)
0.931641 0.363379i \(-0.118377\pi\)
\(938\) 27.3279i 0.892287i
\(939\) 5.71365 0.186458
\(940\) 0 0
\(941\) −53.9277 −1.75799 −0.878997 0.476828i \(-0.841787\pi\)
−0.878997 + 0.476828i \(0.841787\pi\)
\(942\) 2.57908i 0.0840310i
\(943\) 0 0
\(944\) 14.5583 0.473833
\(945\) 0 0
\(946\) −4.76196 −0.154825
\(947\) 4.76196i 0.154743i 0.997002 + 0.0773715i \(0.0246528\pi\)
−0.997002 + 0.0773715i \(0.975347\pi\)
\(948\) 3.16135i 0.102676i
\(949\) 27.1282 0.880618
\(950\) 0 0
\(951\) 11.2088 0.363471
\(952\) 1.19049i 0.0385840i
\(953\) 4.37779i 0.141811i 0.997483 + 0.0709053i \(0.0225888\pi\)
−0.997483 + 0.0709053i \(0.977411\pi\)
\(954\) −18.6965 −0.605321
\(955\) 0 0
\(956\) 2.98083 0.0964069
\(957\) − 3.11982i − 0.100849i
\(958\) 22.7372i 0.734607i
\(959\) 37.2480 1.20280
\(960\) 0 0
\(961\) −22.2380 −0.717356
\(962\) 0.0898462i 0.00289676i
\(963\) 40.6949i 1.31137i
\(964\) −20.0383 −0.645392
\(965\) 0 0
\(966\) −22.3678 −0.719673
\(967\) 13.1582i 0.423138i 0.977363 + 0.211569i \(0.0678573\pi\)
−0.977363 + 0.211569i \(0.932143\pi\)
\(968\) − 10.0783i − 0.323928i
\(969\) 0.129785 0.00416929
\(970\) 0 0
\(971\) 25.9201 0.831816 0.415908 0.909407i \(-0.363464\pi\)
0.415908 + 0.909407i \(0.363464\pi\)
\(972\) − 12.3902i − 0.397415i
\(973\) − 76.4960i − 2.45235i
\(974\) −22.1981 −0.711273
\(975\) 0 0
\(976\) 7.53914 0.241322
\(977\) − 31.2764i − 1.00062i −0.865846 0.500310i \(-0.833219\pi\)
0.865846 0.500310i \(-0.166781\pi\)
\(978\) 11.1582i 0.356799i
\(979\) −3.91693 −0.125186
\(980\) 0 0
\(981\) −13.0192 −0.415670
\(982\) 24.9984i 0.797731i
\(983\) 26.2364i 0.836813i 0.908260 + 0.418406i \(0.137411\pi\)
−0.908260 + 0.418406i \(0.862589\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −1.55991 −0.0496776
\(987\) − 23.5583i − 0.749869i
\(988\) 2.24960i 0.0715693i
\(989\) −44.7356 −1.42251
\(990\) 0 0
\(991\) 39.2764 1.24766 0.623828 0.781562i \(-0.285577\pi\)
0.623828 + 0.781562i \(0.285577\pi\)
\(992\) − 2.96006i − 0.0939820i
\(993\) 17.4125i 0.552570i
\(994\) 45.8786 1.45518
\(995\) 0 0
\(996\) 3.87859 0.122898
\(997\) − 14.4609i − 0.457980i −0.973429 0.228990i \(-0.926458\pi\)
0.973429 0.228990i \(-0.0735423\pi\)
\(998\) 11.6574i 0.369007i
\(999\) −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.b.h.799.2 6
5.2 odd 4 950.2.a.l.1.2 yes 3
5.3 odd 4 950.2.a.j.1.2 3
5.4 even 2 inner 950.2.b.h.799.5 6
15.2 even 4 8550.2.a.ci.1.3 3
15.8 even 4 8550.2.a.cp.1.1 3
20.3 even 4 7600.2.a.bz.1.2 3
20.7 even 4 7600.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.2 3 5.3 odd 4
950.2.a.l.1.2 yes 3 5.2 odd 4
950.2.b.h.799.2 6 1.1 even 1 trivial
950.2.b.h.799.5 6 5.4 even 2 inner
7600.2.a.bk.1.2 3 20.7 even 4
7600.2.a.bz.1.2 3 20.3 even 4
8550.2.a.ci.1.3 3 15.2 even 4
8550.2.a.cp.1.1 3 15.8 even 4