Properties

Label 6240.2.a.bw.1.3
Level $6240$
Weight $2$
Character 6240.1
Self dual yes
Analytic conductor $49.827$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.8266508613\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.254102\) of defining polynomial
Character \(\chi\) \(=\) 6240.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{5} +0.681331 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -1.00000 q^{5} +0.681331 q^{7} +1.00000 q^{9} +3.18953 q^{11} +1.00000 q^{13} +1.00000 q^{15} +3.69774 q^{17} +3.87086 q^{19} -0.681331 q^{21} +6.04399 q^{23} +1.00000 q^{25} -1.00000 q^{27} +4.85446 q^{29} -4.00000 q^{31} -3.18953 q^{33} -0.681331 q^{35} +5.18953 q^{37} -1.00000 q^{39} +1.18953 q^{41} +6.37907 q^{43} -1.00000 q^{45} -10.7253 q^{47} -6.53579 q^{49} -3.69774 q^{51} -7.56860 q^{53} -3.18953 q^{55} -3.87086 q^{57} -1.01641 q^{59} +6.55220 q^{61} +0.681331 q^{63} -1.00000 q^{65} -6.04399 q^{69} -1.82687 q^{71} +10.2171 q^{73} -1.00000 q^{75} +2.17313 q^{77} -10.1731 q^{79} +1.00000 q^{81} -2.72532 q^{83} -3.69774 q^{85} -4.85446 q^{87} -4.17313 q^{89} +0.681331 q^{91} +4.00000 q^{93} -3.87086 q^{95} +5.31867 q^{97} +3.18953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - 3 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - 3 q^{5} - 5 q^{7} + 3 q^{9} + q^{11} + 3 q^{13} + 3 q^{15} + q^{17} - 4 q^{19} + 5 q^{21} - 3 q^{23} + 3 q^{25} - 3 q^{27} + 2 q^{29} - 12 q^{31} - q^{33} + 5 q^{35} + 7 q^{37} - 3 q^{39} - 5 q^{41} + 2 q^{43} - 3 q^{45} - 4 q^{47} - q^{51} + 3 q^{53} - q^{55} + 4 q^{57} - 3 q^{61} - 5 q^{63} - 3 q^{65} + 3 q^{69} - 11 q^{71} + 4 q^{73} - 3 q^{75} + q^{77} - 25 q^{79} + 3 q^{81} + 20 q^{83} - q^{85} - 2 q^{87} - 7 q^{89} - 5 q^{91} + 12 q^{93} + 4 q^{95} + 23 q^{97} + q^{99}+O(q^{100}) \) 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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.681331 0.257519 0.128759 0.991676i \(-0.458901\pi\)
0.128759 + 0.991676i \(0.458901\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.18953 0.961681 0.480840 0.876808i \(-0.340332\pi\)
0.480840 + 0.876808i \(0.340332\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 3.69774 0.896833 0.448417 0.893825i \(-0.351988\pi\)
0.448417 + 0.893825i \(0.351988\pi\)
\(18\) 0 0
\(19\) 3.87086 0.888037 0.444019 0.896018i \(-0.353552\pi\)
0.444019 + 0.896018i \(0.353552\pi\)
\(20\) 0 0
\(21\) −0.681331 −0.148679
\(22\) 0 0
\(23\) 6.04399 1.26026 0.630130 0.776490i \(-0.283002\pi\)
0.630130 + 0.776490i \(0.283002\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.85446 0.901450 0.450725 0.892663i \(-0.351165\pi\)
0.450725 + 0.892663i \(0.351165\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −3.18953 −0.555227
\(34\) 0 0
\(35\) −0.681331 −0.115166
\(36\) 0 0
\(37\) 5.18953 0.853154 0.426577 0.904451i \(-0.359719\pi\)
0.426577 + 0.904451i \(0.359719\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 1.18953 0.185774 0.0928870 0.995677i \(-0.470390\pi\)
0.0928870 + 0.995677i \(0.470390\pi\)
\(42\) 0 0
\(43\) 6.37907 0.972799 0.486399 0.873737i \(-0.338310\pi\)
0.486399 + 0.873737i \(0.338310\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −10.7253 −1.56445 −0.782225 0.622997i \(-0.785915\pi\)
−0.782225 + 0.622997i \(0.785915\pi\)
\(48\) 0 0
\(49\) −6.53579 −0.933684
\(50\) 0 0
\(51\) −3.69774 −0.517787
\(52\) 0 0
\(53\) −7.56860 −1.03963 −0.519814 0.854280i \(-0.673999\pi\)
−0.519814 + 0.854280i \(0.673999\pi\)
\(54\) 0 0
\(55\) −3.18953 −0.430077
\(56\) 0 0
\(57\) −3.87086 −0.512709
\(58\) 0 0
\(59\) −1.01641 −0.132325 −0.0661624 0.997809i \(-0.521076\pi\)
−0.0661624 + 0.997809i \(0.521076\pi\)
\(60\) 0 0
\(61\) 6.55220 0.838923 0.419461 0.907773i \(-0.362219\pi\)
0.419461 + 0.907773i \(0.362219\pi\)
\(62\) 0 0
\(63\) 0.681331 0.0858396
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) −6.04399 −0.727611
\(70\) 0 0
\(71\) −1.82687 −0.216810 −0.108405 0.994107i \(-0.534574\pi\)
−0.108405 + 0.994107i \(0.534574\pi\)
\(72\) 0 0
\(73\) 10.2171 1.19582 0.597912 0.801562i \(-0.295997\pi\)
0.597912 + 0.801562i \(0.295997\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 2.17313 0.247651
\(78\) 0 0
\(79\) −10.1731 −1.14457 −0.572283 0.820056i \(-0.693942\pi\)
−0.572283 + 0.820056i \(0.693942\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.72532 −0.299143 −0.149572 0.988751i \(-0.547789\pi\)
−0.149572 + 0.988751i \(0.547789\pi\)
\(84\) 0 0
\(85\) −3.69774 −0.401076
\(86\) 0 0
\(87\) −4.85446 −0.520453
\(88\) 0 0
\(89\) −4.17313 −0.442351 −0.221175 0.975234i \(-0.570989\pi\)
−0.221175 + 0.975234i \(0.570989\pi\)
\(90\) 0 0
\(91\) 0.681331 0.0714229
\(92\) 0 0
\(93\) 4.00000 0.414781
\(94\) 0 0
\(95\) −3.87086 −0.397142
\(96\) 0 0
\(97\) 5.31867 0.540029 0.270015 0.962856i \(-0.412971\pi\)
0.270015 + 0.962856i \(0.412971\pi\)
\(98\) 0 0
\(99\) 3.18953 0.320560
\(100\) 0 0
\(101\) 1.87086 0.186158 0.0930790 0.995659i \(-0.470329\pi\)
0.0930790 + 0.995659i \(0.470329\pi\)
\(102\) 0 0
\(103\) −18.7253 −1.84506 −0.922530 0.385924i \(-0.873883\pi\)
−0.922530 + 0.385924i \(0.873883\pi\)
\(104\) 0 0
\(105\) 0.681331 0.0664911
\(106\) 0 0
\(107\) 12.5522 1.21347 0.606733 0.794905i \(-0.292480\pi\)
0.606733 + 0.794905i \(0.292480\pi\)
\(108\) 0 0
\(109\) 14.8873 1.42594 0.712971 0.701194i \(-0.247349\pi\)
0.712971 + 0.701194i \(0.247349\pi\)
\(110\) 0 0
\(111\) −5.18953 −0.492569
\(112\) 0 0
\(113\) 2.47539 0.232865 0.116433 0.993199i \(-0.462854\pi\)
0.116433 + 0.993199i \(0.462854\pi\)
\(114\) 0 0
\(115\) −6.04399 −0.563605
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 2.51938 0.230951
\(120\) 0 0
\(121\) −0.826873 −0.0751702
\(122\) 0 0
\(123\) −1.18953 −0.107257
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 15.4835 1.37393 0.686967 0.726688i \(-0.258942\pi\)
0.686967 + 0.726688i \(0.258942\pi\)
\(128\) 0 0
\(129\) −6.37907 −0.561646
\(130\) 0 0
\(131\) 4.21712 0.368451 0.184226 0.982884i \(-0.441022\pi\)
0.184226 + 0.982884i \(0.441022\pi\)
\(132\) 0 0
\(133\) 2.63734 0.228686
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 11.7089 1.00036 0.500180 0.865921i \(-0.333267\pi\)
0.500180 + 0.865921i \(0.333267\pi\)
\(138\) 0 0
\(139\) −20.2939 −1.72131 −0.860654 0.509190i \(-0.829945\pi\)
−0.860654 + 0.509190i \(0.829945\pi\)
\(140\) 0 0
\(141\) 10.7253 0.903235
\(142\) 0 0
\(143\) 3.18953 0.266722
\(144\) 0 0
\(145\) −4.85446 −0.403141
\(146\) 0 0
\(147\) 6.53579 0.539063
\(148\) 0 0
\(149\) 13.5358 1.10890 0.554448 0.832219i \(-0.312930\pi\)
0.554448 + 0.832219i \(0.312930\pi\)
\(150\) 0 0
\(151\) −6.03281 −0.490943 −0.245472 0.969404i \(-0.578943\pi\)
−0.245472 + 0.969404i \(0.578943\pi\)
\(152\) 0 0
\(153\) 3.69774 0.298944
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −16.4671 −1.31421 −0.657107 0.753797i \(-0.728220\pi\)
−0.657107 + 0.753797i \(0.728220\pi\)
\(158\) 0 0
\(159\) 7.56860 0.600229
\(160\) 0 0
\(161\) 4.11796 0.324540
\(162\) 0 0
\(163\) −5.56860 −0.436167 −0.218083 0.975930i \(-0.569980\pi\)
−0.218083 + 0.975930i \(0.569980\pi\)
\(164\) 0 0
\(165\) 3.18953 0.248305
\(166\) 0 0
\(167\) 5.01641 0.388181 0.194091 0.980984i \(-0.437824\pi\)
0.194091 + 0.980984i \(0.437824\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.87086 0.296012
\(172\) 0 0
\(173\) 3.01641 0.229333 0.114667 0.993404i \(-0.463420\pi\)
0.114667 + 0.993404i \(0.463420\pi\)
\(174\) 0 0
\(175\) 0.681331 0.0515038
\(176\) 0 0
\(177\) 1.01641 0.0763978
\(178\) 0 0
\(179\) 0.129135 0.00965203 0.00482601 0.999988i \(-0.498464\pi\)
0.00482601 + 0.999988i \(0.498464\pi\)
\(180\) 0 0
\(181\) −7.15672 −0.531955 −0.265977 0.963979i \(-0.585695\pi\)
−0.265977 + 0.963979i \(0.585695\pi\)
\(182\) 0 0
\(183\) −6.55220 −0.484352
\(184\) 0 0
\(185\) −5.18953 −0.381542
\(186\) 0 0
\(187\) 11.7941 0.862467
\(188\) 0 0
\(189\) −0.681331 −0.0495595
\(190\) 0 0
\(191\) −4.34625 −0.314484 −0.157242 0.987560i \(-0.550260\pi\)
−0.157242 + 0.987560i \(0.550260\pi\)
\(192\) 0 0
\(193\) 16.7141 1.20311 0.601555 0.798831i \(-0.294548\pi\)
0.601555 + 0.798831i \(0.294548\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 11.0164 0.784886 0.392443 0.919776i \(-0.371630\pi\)
0.392443 + 0.919776i \(0.371630\pi\)
\(198\) 0 0
\(199\) 2.03281 0.144102 0.0720512 0.997401i \(-0.477046\pi\)
0.0720512 + 0.997401i \(0.477046\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.30749 0.232140
\(204\) 0 0
\(205\) −1.18953 −0.0830807
\(206\) 0 0
\(207\) 6.04399 0.420086
\(208\) 0 0
\(209\) 12.3463 0.854008
\(210\) 0 0
\(211\) −14.7253 −1.01373 −0.506867 0.862025i \(-0.669196\pi\)
−0.506867 + 0.862025i \(0.669196\pi\)
\(212\) 0 0
\(213\) 1.82687 0.125175
\(214\) 0 0
\(215\) −6.37907 −0.435049
\(216\) 0 0
\(217\) −2.72532 −0.185007
\(218\) 0 0
\(219\) −10.2171 −0.690409
\(220\) 0 0
\(221\) 3.69774 0.248737
\(222\) 0 0
\(223\) −17.2335 −1.15404 −0.577021 0.816729i \(-0.695785\pi\)
−0.577021 + 0.816729i \(0.695785\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 12.4119 0.823806 0.411903 0.911228i \(-0.364864\pi\)
0.411903 + 0.911228i \(0.364864\pi\)
\(228\) 0 0
\(229\) 25.6126 1.69253 0.846264 0.532764i \(-0.178847\pi\)
0.846264 + 0.532764i \(0.178847\pi\)
\(230\) 0 0
\(231\) −2.17313 −0.142981
\(232\) 0 0
\(233\) −13.4067 −0.878299 −0.439150 0.898414i \(-0.644720\pi\)
−0.439150 + 0.898414i \(0.644720\pi\)
\(234\) 0 0
\(235\) 10.7253 0.699643
\(236\) 0 0
\(237\) 10.1731 0.660816
\(238\) 0 0
\(239\) −0.552195 −0.0357185 −0.0178593 0.999841i \(-0.505685\pi\)
−0.0178593 + 0.999841i \(0.505685\pi\)
\(240\) 0 0
\(241\) −17.1372 −1.10390 −0.551952 0.833876i \(-0.686117\pi\)
−0.551952 + 0.833876i \(0.686117\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 6.53579 0.417556
\(246\) 0 0
\(247\) 3.87086 0.246297
\(248\) 0 0
\(249\) 2.72532 0.172710
\(250\) 0 0
\(251\) 22.5082 1.42071 0.710353 0.703846i \(-0.248535\pi\)
0.710353 + 0.703846i \(0.248535\pi\)
\(252\) 0 0
\(253\) 19.2775 1.21197
\(254\) 0 0
\(255\) 3.69774 0.231561
\(256\) 0 0
\(257\) 30.7170 1.91607 0.958036 0.286646i \(-0.0925405\pi\)
0.958036 + 0.286646i \(0.0925405\pi\)
\(258\) 0 0
\(259\) 3.53579 0.219703
\(260\) 0 0
\(261\) 4.85446 0.300483
\(262\) 0 0
\(263\) 12.5410 0.773312 0.386656 0.922224i \(-0.373630\pi\)
0.386656 + 0.922224i \(0.373630\pi\)
\(264\) 0 0
\(265\) 7.56860 0.464936
\(266\) 0 0
\(267\) 4.17313 0.255391
\(268\) 0 0
\(269\) 22.6290 1.37971 0.689857 0.723945i \(-0.257673\pi\)
0.689857 + 0.723945i \(0.257673\pi\)
\(270\) 0 0
\(271\) −20.4119 −1.23993 −0.619967 0.784628i \(-0.712854\pi\)
−0.619967 + 0.784628i \(0.712854\pi\)
\(272\) 0 0
\(273\) −0.681331 −0.0412360
\(274\) 0 0
\(275\) 3.18953 0.192336
\(276\) 0 0
\(277\) −4.12080 −0.247595 −0.123797 0.992308i \(-0.539507\pi\)
−0.123797 + 0.992308i \(0.539507\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −17.4835 −1.04298 −0.521488 0.853259i \(-0.674623\pi\)
−0.521488 + 0.853259i \(0.674623\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 3.87086 0.229290
\(286\) 0 0
\(287\) 0.810466 0.0478403
\(288\) 0 0
\(289\) −3.32674 −0.195690
\(290\) 0 0
\(291\) −5.31867 −0.311786
\(292\) 0 0
\(293\) 12.6373 0.738281 0.369141 0.929374i \(-0.379652\pi\)
0.369141 + 0.929374i \(0.379652\pi\)
\(294\) 0 0
\(295\) 1.01641 0.0591775
\(296\) 0 0
\(297\) −3.18953 −0.185076
\(298\) 0 0
\(299\) 6.04399 0.349533
\(300\) 0 0
\(301\) 4.34625 0.250514
\(302\) 0 0
\(303\) −1.87086 −0.107478
\(304\) 0 0
\(305\) −6.55220 −0.375178
\(306\) 0 0
\(307\) −24.0357 −1.37179 −0.685894 0.727702i \(-0.740588\pi\)
−0.685894 + 0.727702i \(0.740588\pi\)
\(308\) 0 0
\(309\) 18.7253 1.06525
\(310\) 0 0
\(311\) −17.1044 −0.969901 −0.484951 0.874542i \(-0.661162\pi\)
−0.484951 + 0.874542i \(0.661162\pi\)
\(312\) 0 0
\(313\) 19.7745 1.11772 0.558862 0.829261i \(-0.311238\pi\)
0.558862 + 0.829261i \(0.311238\pi\)
\(314\) 0 0
\(315\) −0.681331 −0.0383886
\(316\) 0 0
\(317\) 5.24186 0.294412 0.147206 0.989106i \(-0.452972\pi\)
0.147206 + 0.989106i \(0.452972\pi\)
\(318\) 0 0
\(319\) 15.4835 0.866907
\(320\) 0 0
\(321\) −12.5522 −0.700595
\(322\) 0 0
\(323\) 14.3134 0.796421
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −14.8873 −0.823268
\(328\) 0 0
\(329\) −7.30749 −0.402875
\(330\) 0 0
\(331\) 26.6618 1.46547 0.732733 0.680516i \(-0.238244\pi\)
0.732733 + 0.680516i \(0.238244\pi\)
\(332\) 0 0
\(333\) 5.18953 0.284385
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 26.4342 1.43996 0.719982 0.693992i \(-0.244150\pi\)
0.719982 + 0.693992i \(0.244150\pi\)
\(338\) 0 0
\(339\) −2.47539 −0.134445
\(340\) 0 0
\(341\) −12.7581 −0.690892
\(342\) 0 0
\(343\) −9.22235 −0.497960
\(344\) 0 0
\(345\) 6.04399 0.325398
\(346\) 0 0
\(347\) 24.2283 1.30064 0.650322 0.759659i \(-0.274634\pi\)
0.650322 + 0.759659i \(0.274634\pi\)
\(348\) 0 0
\(349\) −6.97526 −0.373377 −0.186688 0.982419i \(-0.559775\pi\)
−0.186688 + 0.982419i \(0.559775\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 5.32985 0.283679 0.141840 0.989890i \(-0.454698\pi\)
0.141840 + 0.989890i \(0.454698\pi\)
\(354\) 0 0
\(355\) 1.82687 0.0969603
\(356\) 0 0
\(357\) −2.51938 −0.133340
\(358\) 0 0
\(359\) −6.72532 −0.354949 −0.177474 0.984125i \(-0.556793\pi\)
−0.177474 + 0.984125i \(0.556793\pi\)
\(360\) 0 0
\(361\) −4.01641 −0.211390
\(362\) 0 0
\(363\) 0.826873 0.0433996
\(364\) 0 0
\(365\) −10.2171 −0.534788
\(366\) 0 0
\(367\) 4.34625 0.226873 0.113436 0.993545i \(-0.463814\pi\)
0.113436 + 0.993545i \(0.463814\pi\)
\(368\) 0 0
\(369\) 1.18953 0.0619247
\(370\) 0 0
\(371\) −5.15672 −0.267724
\(372\) 0 0
\(373\) −37.2252 −1.92745 −0.963724 0.266902i \(-0.914000\pi\)
−0.963724 + 0.266902i \(0.914000\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 4.85446 0.250017
\(378\) 0 0
\(379\) −3.45898 −0.177676 −0.0888380 0.996046i \(-0.528315\pi\)
−0.0888380 + 0.996046i \(0.528315\pi\)
\(380\) 0 0
\(381\) −15.4835 −0.793242
\(382\) 0 0
\(383\) −22.1208 −1.13032 −0.565160 0.824981i \(-0.691186\pi\)
−0.565160 + 0.824981i \(0.691186\pi\)
\(384\) 0 0
\(385\) −2.17313 −0.110753
\(386\) 0 0
\(387\) 6.37907 0.324266
\(388\) 0 0
\(389\) −27.0632 −1.37216 −0.686080 0.727526i \(-0.740670\pi\)
−0.686080 + 0.727526i \(0.740670\pi\)
\(390\) 0 0
\(391\) 22.3491 1.13024
\(392\) 0 0
\(393\) −4.21712 −0.212726
\(394\) 0 0
\(395\) 10.1731 0.511866
\(396\) 0 0
\(397\) 34.6402 1.73854 0.869270 0.494337i \(-0.164589\pi\)
0.869270 + 0.494337i \(0.164589\pi\)
\(398\) 0 0
\(399\) −2.63734 −0.132032
\(400\) 0 0
\(401\) 19.7745 0.987494 0.493747 0.869606i \(-0.335627\pi\)
0.493747 + 0.869606i \(0.335627\pi\)
\(402\) 0 0
\(403\) −4.00000 −0.199254
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 16.5522 0.820462
\(408\) 0 0
\(409\) 1.32985 0.0657567 0.0328784 0.999459i \(-0.489533\pi\)
0.0328784 + 0.999459i \(0.489533\pi\)
\(410\) 0 0
\(411\) −11.7089 −0.577558
\(412\) 0 0
\(413\) −0.692509 −0.0340761
\(414\) 0 0
\(415\) 2.72532 0.133781
\(416\) 0 0
\(417\) 20.2939 0.993798
\(418\) 0 0
\(419\) 18.0796 0.883249 0.441624 0.897200i \(-0.354402\pi\)
0.441624 + 0.897200i \(0.354402\pi\)
\(420\) 0 0
\(421\) 23.3215 1.13662 0.568310 0.822814i \(-0.307597\pi\)
0.568310 + 0.822814i \(0.307597\pi\)
\(422\) 0 0
\(423\) −10.7253 −0.521483
\(424\) 0 0
\(425\) 3.69774 0.179367
\(426\) 0 0
\(427\) 4.46421 0.216038
\(428\) 0 0
\(429\) −3.18953 −0.153992
\(430\) 0 0
\(431\) 29.4506 1.41859 0.709294 0.704913i \(-0.249014\pi\)
0.709294 + 0.704913i \(0.249014\pi\)
\(432\) 0 0
\(433\) 15.1924 0.730099 0.365049 0.930988i \(-0.381052\pi\)
0.365049 + 0.930988i \(0.381052\pi\)
\(434\) 0 0
\(435\) 4.85446 0.232753
\(436\) 0 0
\(437\) 23.3955 1.11916
\(438\) 0 0
\(439\) −14.5850 −0.696104 −0.348052 0.937475i \(-0.613157\pi\)
−0.348052 + 0.937475i \(0.613157\pi\)
\(440\) 0 0
\(441\) −6.53579 −0.311228
\(442\) 0 0
\(443\) 30.3267 1.44087 0.720433 0.693524i \(-0.243943\pi\)
0.720433 + 0.693524i \(0.243943\pi\)
\(444\) 0 0
\(445\) 4.17313 0.197825
\(446\) 0 0
\(447\) −13.5358 −0.640221
\(448\) 0 0
\(449\) 12.2388 0.577583 0.288791 0.957392i \(-0.406747\pi\)
0.288791 + 0.957392i \(0.406747\pi\)
\(450\) 0 0
\(451\) 3.79406 0.178655
\(452\) 0 0
\(453\) 6.03281 0.283446
\(454\) 0 0
\(455\) −0.681331 −0.0319413
\(456\) 0 0
\(457\) −21.4067 −1.00136 −0.500681 0.865632i \(-0.666917\pi\)
−0.500681 + 0.865632i \(0.666917\pi\)
\(458\) 0 0
\(459\) −3.69774 −0.172596
\(460\) 0 0
\(461\) −12.5194 −0.583086 −0.291543 0.956558i \(-0.594169\pi\)
−0.291543 + 0.956558i \(0.594169\pi\)
\(462\) 0 0
\(463\) 5.69774 0.264796 0.132398 0.991197i \(-0.457732\pi\)
0.132398 + 0.991197i \(0.457732\pi\)
\(464\) 0 0
\(465\) −4.00000 −0.185496
\(466\) 0 0
\(467\) 31.2775 1.44735 0.723675 0.690140i \(-0.242451\pi\)
0.723675 + 0.690140i \(0.242451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 16.4671 0.758762
\(472\) 0 0
\(473\) 20.3463 0.935522
\(474\) 0 0
\(475\) 3.87086 0.177607
\(476\) 0 0
\(477\) −7.56860 −0.346542
\(478\) 0 0
\(479\) −17.6566 −0.806750 −0.403375 0.915035i \(-0.632163\pi\)
−0.403375 + 0.915035i \(0.632163\pi\)
\(480\) 0 0
\(481\) 5.18953 0.236622
\(482\) 0 0
\(483\) −4.11796 −0.187374
\(484\) 0 0
\(485\) −5.31867 −0.241508
\(486\) 0 0
\(487\) −8.93960 −0.405092 −0.202546 0.979273i \(-0.564922\pi\)
−0.202546 + 0.979273i \(0.564922\pi\)
\(488\) 0 0
\(489\) 5.56860 0.251821
\(490\) 0 0
\(491\) −6.92008 −0.312299 −0.156150 0.987733i \(-0.549908\pi\)
−0.156150 + 0.987733i \(0.549908\pi\)
\(492\) 0 0
\(493\) 17.9505 0.808450
\(494\) 0 0
\(495\) −3.18953 −0.143359
\(496\) 0 0
\(497\) −1.24470 −0.0558326
\(498\) 0 0
\(499\) 17.5798 0.786979 0.393490 0.919329i \(-0.371268\pi\)
0.393490 + 0.919329i \(0.371268\pi\)
\(500\) 0 0
\(501\) −5.01641 −0.224117
\(502\) 0 0
\(503\) 20.0245 0.892847 0.446424 0.894822i \(-0.352697\pi\)
0.446424 + 0.894822i \(0.352697\pi\)
\(504\) 0 0
\(505\) −1.87086 −0.0832524
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −0.865636 −0.0383687 −0.0191843 0.999816i \(-0.506107\pi\)
−0.0191843 + 0.999816i \(0.506107\pi\)
\(510\) 0 0
\(511\) 6.96124 0.307947
\(512\) 0 0
\(513\) −3.87086 −0.170903
\(514\) 0 0
\(515\) 18.7253 0.825136
\(516\) 0 0
\(517\) −34.2088 −1.50450
\(518\) 0 0
\(519\) −3.01641 −0.132406
\(520\) 0 0
\(521\) 10.4342 0.457132 0.228566 0.973528i \(-0.426596\pi\)
0.228566 + 0.973528i \(0.426596\pi\)
\(522\) 0 0
\(523\) −4.92842 −0.215505 −0.107752 0.994178i \(-0.534365\pi\)
−0.107752 + 0.994178i \(0.534365\pi\)
\(524\) 0 0
\(525\) −0.681331 −0.0297357
\(526\) 0 0
\(527\) −14.7909 −0.644304
\(528\) 0 0
\(529\) 13.5298 0.588254
\(530\) 0 0
\(531\) −1.01641 −0.0441083
\(532\) 0 0
\(533\) 1.18953 0.0515244
\(534\) 0 0
\(535\) −12.5522 −0.542679
\(536\) 0 0
\(537\) −0.129135 −0.00557260
\(538\) 0 0
\(539\) −20.8461 −0.897906
\(540\) 0 0
\(541\) −33.2663 −1.43023 −0.715116 0.699006i \(-0.753626\pi\)
−0.715116 + 0.699006i \(0.753626\pi\)
\(542\) 0 0
\(543\) 7.15672 0.307124
\(544\) 0 0
\(545\) −14.8873 −0.637701
\(546\) 0 0
\(547\) −9.45065 −0.404080 −0.202040 0.979377i \(-0.564757\pi\)
−0.202040 + 0.979377i \(0.564757\pi\)
\(548\) 0 0
\(549\) 6.55220 0.279641
\(550\) 0 0
\(551\) 18.7909 0.800521
\(552\) 0 0
\(553\) −6.93126 −0.294747
\(554\) 0 0
\(555\) 5.18953 0.220283
\(556\) 0 0
\(557\) 30.3463 1.28581 0.642906 0.765945i \(-0.277729\pi\)
0.642906 + 0.765945i \(0.277729\pi\)
\(558\) 0 0
\(559\) 6.37907 0.269806
\(560\) 0 0
\(561\) −11.7941 −0.497946
\(562\) 0 0
\(563\) −13.3983 −0.564672 −0.282336 0.959316i \(-0.591109\pi\)
−0.282336 + 0.959316i \(0.591109\pi\)
\(564\) 0 0
\(565\) −2.47539 −0.104140
\(566\) 0 0
\(567\) 0.681331 0.0286132
\(568\) 0 0
\(569\) −3.01641 −0.126454 −0.0632272 0.997999i \(-0.520139\pi\)
−0.0632272 + 0.997999i \(0.520139\pi\)
\(570\) 0 0
\(571\) −10.6730 −0.446651 −0.223325 0.974744i \(-0.571691\pi\)
−0.223325 + 0.974744i \(0.571691\pi\)
\(572\) 0 0
\(573\) 4.34625 0.181567
\(574\) 0 0
\(575\) 6.04399 0.252052
\(576\) 0 0
\(577\) 45.7529 1.90472 0.952359 0.304979i \(-0.0986493\pi\)
0.952359 + 0.304979i \(0.0986493\pi\)
\(578\) 0 0
\(579\) −16.7141 −0.694616
\(580\) 0 0
\(581\) −1.85685 −0.0770349
\(582\) 0 0
\(583\) −24.1403 −0.999790
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) 0 0
\(587\) −20.5878 −0.849751 −0.424876 0.905252i \(-0.639682\pi\)
−0.424876 + 0.905252i \(0.639682\pi\)
\(588\) 0 0
\(589\) −15.4835 −0.637985
\(590\) 0 0
\(591\) −11.0164 −0.453154
\(592\) 0 0
\(593\) −21.8297 −0.896439 −0.448219 0.893924i \(-0.647942\pi\)
−0.448219 + 0.893924i \(0.647942\pi\)
\(594\) 0 0
\(595\) −2.51938 −0.103285
\(596\) 0 0
\(597\) −2.03281 −0.0831975
\(598\) 0 0
\(599\) −9.51627 −0.388824 −0.194412 0.980920i \(-0.562280\pi\)
−0.194412 + 0.980920i \(0.562280\pi\)
\(600\) 0 0
\(601\) 9.94767 0.405774 0.202887 0.979202i \(-0.434968\pi\)
0.202887 + 0.979202i \(0.434968\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.826873 0.0336172
\(606\) 0 0
\(607\) −11.6537 −0.473011 −0.236505 0.971630i \(-0.576002\pi\)
−0.236505 + 0.971630i \(0.576002\pi\)
\(608\) 0 0
\(609\) −3.30749 −0.134026
\(610\) 0 0
\(611\) −10.7253 −0.433900
\(612\) 0 0
\(613\) −25.1895 −1.01740 −0.508698 0.860945i \(-0.669873\pi\)
−0.508698 + 0.860945i \(0.669873\pi\)
\(614\) 0 0
\(615\) 1.18953 0.0479666
\(616\) 0 0
\(617\) −18.4342 −0.742134 −0.371067 0.928606i \(-0.621008\pi\)
−0.371067 + 0.928606i \(0.621008\pi\)
\(618\) 0 0
\(619\) 21.9260 0.881282 0.440641 0.897683i \(-0.354751\pi\)
0.440641 + 0.897683i \(0.354751\pi\)
\(620\) 0 0
\(621\) −6.04399 −0.242537
\(622\) 0 0
\(623\) −2.84328 −0.113914
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −12.3463 −0.493062
\(628\) 0 0
\(629\) 19.1895 0.765137
\(630\) 0 0
\(631\) −29.1267 −1.15952 −0.579759 0.814788i \(-0.696853\pi\)
−0.579759 + 0.814788i \(0.696853\pi\)
\(632\) 0 0
\(633\) 14.7253 0.585279
\(634\) 0 0
\(635\) −15.4835 −0.614442
\(636\) 0 0
\(637\) −6.53579 −0.258957
\(638\) 0 0
\(639\) −1.82687 −0.0722700
\(640\) 0 0
\(641\) −3.27468 −0.129342 −0.0646710 0.997907i \(-0.520600\pi\)
−0.0646710 + 0.997907i \(0.520600\pi\)
\(642\) 0 0
\(643\) −27.2775 −1.07572 −0.537860 0.843034i \(-0.680767\pi\)
−0.537860 + 0.843034i \(0.680767\pi\)
\(644\) 0 0
\(645\) 6.37907 0.251176
\(646\) 0 0
\(647\) 9.43947 0.371104 0.185552 0.982634i \(-0.440593\pi\)
0.185552 + 0.982634i \(0.440593\pi\)
\(648\) 0 0
\(649\) −3.24186 −0.127254
\(650\) 0 0
\(651\) 2.72532 0.106814
\(652\) 0 0
\(653\) 37.6594 1.47373 0.736864 0.676041i \(-0.236306\pi\)
0.736864 + 0.676041i \(0.236306\pi\)
\(654\) 0 0
\(655\) −4.21712 −0.164776
\(656\) 0 0
\(657\) 10.2171 0.398608
\(658\) 0 0
\(659\) −2.44258 −0.0951493 −0.0475746 0.998868i \(-0.515149\pi\)
−0.0475746 + 0.998868i \(0.515149\pi\)
\(660\) 0 0
\(661\) −45.2007 −1.75810 −0.879052 0.476726i \(-0.841823\pi\)
−0.879052 + 0.476726i \(0.841823\pi\)
\(662\) 0 0
\(663\) −3.69774 −0.143608
\(664\) 0 0
\(665\) −2.63734 −0.102272
\(666\) 0 0
\(667\) 29.3403 1.13606
\(668\) 0 0
\(669\) 17.2335 0.666287
\(670\) 0 0
\(671\) 20.8984 0.806776
\(672\) 0 0
\(673\) 11.6209 0.447954 0.223977 0.974594i \(-0.428096\pi\)
0.223977 + 0.974594i \(0.428096\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −5.27752 −0.202831 −0.101416 0.994844i \(-0.532337\pi\)
−0.101416 + 0.994844i \(0.532337\pi\)
\(678\) 0 0
\(679\) 3.62377 0.139068
\(680\) 0 0
\(681\) −12.4119 −0.475624
\(682\) 0 0
\(683\) −16.5878 −0.634716 −0.317358 0.948306i \(-0.602796\pi\)
−0.317358 + 0.948306i \(0.602796\pi\)
\(684\) 0 0
\(685\) −11.7089 −0.447375
\(686\) 0 0
\(687\) −25.6126 −0.977181
\(688\) 0 0
\(689\) −7.56860 −0.288341
\(690\) 0 0
\(691\) 45.5631 1.73330 0.866651 0.498915i \(-0.166268\pi\)
0.866651 + 0.498915i \(0.166268\pi\)
\(692\) 0 0
\(693\) 2.17313 0.0825503
\(694\) 0 0
\(695\) 20.2939 0.769792
\(696\) 0 0
\(697\) 4.39858 0.166608
\(698\) 0 0
\(699\) 13.4067 0.507086
\(700\) 0 0
\(701\) 1.35432 0.0511521 0.0255760 0.999673i \(-0.491858\pi\)
0.0255760 + 0.999673i \(0.491858\pi\)
\(702\) 0 0
\(703\) 20.0880 0.757633
\(704\) 0 0
\(705\) −10.7253 −0.403939
\(706\) 0 0
\(707\) 1.27468 0.0479392
\(708\) 0 0
\(709\) −17.2887 −0.649291 −0.324645 0.945836i \(-0.605245\pi\)
−0.324645 + 0.945836i \(0.605245\pi\)
\(710\) 0 0
\(711\) −10.1731 −0.381522
\(712\) 0 0
\(713\) −24.1760 −0.905397
\(714\) 0 0
\(715\) −3.18953 −0.119282
\(716\) 0 0
\(717\) 0.552195 0.0206221
\(718\) 0 0
\(719\) 34.4671 1.28540 0.642702 0.766116i \(-0.277813\pi\)
0.642702 + 0.766116i \(0.277813\pi\)
\(720\) 0 0
\(721\) −12.7581 −0.475138
\(722\) 0 0
\(723\) 17.1372 0.637339
\(724\) 0 0
\(725\) 4.85446 0.180290
\(726\) 0 0
\(727\) −24.8461 −0.921492 −0.460746 0.887532i \(-0.652418\pi\)
−0.460746 + 0.887532i \(0.652418\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 23.5881 0.872438
\(732\) 0 0
\(733\) −12.8433 −0.474377 −0.237189 0.971464i \(-0.576226\pi\)
−0.237189 + 0.971464i \(0.576226\pi\)
\(734\) 0 0
\(735\) −6.53579 −0.241076
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −23.2887 −0.856689 −0.428344 0.903616i \(-0.640903\pi\)
−0.428344 + 0.903616i \(0.640903\pi\)
\(740\) 0 0
\(741\) −3.87086 −0.142200
\(742\) 0 0
\(743\) 14.8133 0.543448 0.271724 0.962375i \(-0.412406\pi\)
0.271724 + 0.962375i \(0.412406\pi\)
\(744\) 0 0
\(745\) −13.5358 −0.495913
\(746\) 0 0
\(747\) −2.72532 −0.0997143
\(748\) 0 0
\(749\) 8.55220 0.312490
\(750\) 0 0
\(751\) 18.9313 0.690812 0.345406 0.938453i \(-0.387741\pi\)
0.345406 + 0.938453i \(0.387741\pi\)
\(752\) 0 0
\(753\) −22.5082 −0.820245
\(754\) 0 0
\(755\) 6.03281 0.219557
\(756\) 0 0
\(757\) 35.3460 1.28467 0.642336 0.766423i \(-0.277965\pi\)
0.642336 + 0.766423i \(0.277965\pi\)
\(758\) 0 0
\(759\) −19.2775 −0.699730
\(760\) 0 0
\(761\) −9.67610 −0.350758 −0.175379 0.984501i \(-0.556115\pi\)
−0.175379 + 0.984501i \(0.556115\pi\)
\(762\) 0 0
\(763\) 10.1432 0.367207
\(764\) 0 0
\(765\) −3.69774 −0.133692
\(766\) 0 0
\(767\) −1.01641 −0.0367003
\(768\) 0 0
\(769\) 38.2416 1.37903 0.689514 0.724273i \(-0.257824\pi\)
0.689514 + 0.724273i \(0.257824\pi\)
\(770\) 0 0
\(771\) −30.7170 −1.10625
\(772\) 0 0
\(773\) 0.571712 0.0205630 0.0102815 0.999947i \(-0.496727\pi\)
0.0102815 + 0.999947i \(0.496727\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) −3.53579 −0.126846
\(778\) 0 0
\(779\) 4.60453 0.164974
\(780\) 0 0
\(781\) −5.82687 −0.208502
\(782\) 0 0
\(783\) −4.85446 −0.173484
\(784\) 0 0
\(785\) 16.4671 0.587734
\(786\) 0 0
\(787\) 26.4671 0.943449 0.471724 0.881746i \(-0.343632\pi\)
0.471724 + 0.881746i \(0.343632\pi\)
\(788\) 0 0
\(789\) −12.5410 −0.446472
\(790\) 0 0
\(791\) 1.68656 0.0599671
\(792\) 0 0
\(793\) 6.55220 0.232675
\(794\) 0 0
\(795\) −7.56860 −0.268431
\(796\) 0 0
\(797\) −6.46421 −0.228974 −0.114487 0.993425i \(-0.536522\pi\)
−0.114487 + 0.993425i \(0.536522\pi\)
\(798\) 0 0
\(799\) −39.6594 −1.40305
\(800\) 0 0
\(801\) −4.17313 −0.147450
\(802\) 0 0
\(803\) 32.5878 1.15000
\(804\) 0 0
\(805\) −4.11796 −0.145139
\(806\) 0 0
\(807\) −22.6290 −0.796579
\(808\) 0 0
\(809\) 23.4506 0.824481 0.412240 0.911075i \(-0.364746\pi\)
0.412240 + 0.911075i \(0.364746\pi\)
\(810\) 0 0
\(811\) 17.1455 0.602061 0.301031 0.953614i \(-0.402669\pi\)
0.301031 + 0.953614i \(0.402669\pi\)
\(812\) 0 0
\(813\) 20.4119 0.715876
\(814\) 0 0
\(815\) 5.56860 0.195060
\(816\) 0 0
\(817\) 24.6925 0.863882
\(818\) 0 0
\(819\) 0.681331 0.0238076
\(820\) 0 0
\(821\) −38.2939 −1.33647 −0.668234 0.743952i \(-0.732949\pi\)
−0.668234 + 0.743952i \(0.732949\pi\)
\(822\) 0 0
\(823\) −34.7253 −1.21045 −0.605224 0.796055i \(-0.706917\pi\)
−0.605224 + 0.796055i \(0.706917\pi\)
\(824\) 0 0
\(825\) −3.18953 −0.111045
\(826\) 0 0
\(827\) 44.7581 1.55639 0.778196 0.628021i \(-0.216135\pi\)
0.778196 + 0.628021i \(0.216135\pi\)
\(828\) 0 0
\(829\) −10.8238 −0.375925 −0.187962 0.982176i \(-0.560188\pi\)
−0.187962 + 0.982176i \(0.560188\pi\)
\(830\) 0 0
\(831\) 4.12080 0.142949
\(832\) 0 0
\(833\) −24.1676 −0.837359
\(834\) 0 0
\(835\) −5.01641 −0.173600
\(836\) 0 0
\(837\) 4.00000 0.138260
\(838\) 0 0
\(839\) 3.68940 0.127372 0.0636861 0.997970i \(-0.479714\pi\)
0.0636861 + 0.997970i \(0.479714\pi\)
\(840\) 0 0
\(841\) −5.43424 −0.187388
\(842\) 0 0
\(843\) 17.4835 0.602162
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −0.563374 −0.0193578
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 31.3655 1.07520
\(852\) 0 0
\(853\) −8.49702 −0.290933 −0.145466 0.989363i \(-0.546468\pi\)
−0.145466 + 0.989363i \(0.546468\pi\)
\(854\) 0 0
\(855\) −3.87086 −0.132381
\(856\) 0 0
\(857\) −42.5990 −1.45516 −0.727578 0.686025i \(-0.759354\pi\)
−0.727578 + 0.686025i \(0.759354\pi\)
\(858\) 0 0
\(859\) −20.5522 −0.701232 −0.350616 0.936519i \(-0.614028\pi\)
−0.350616 + 0.936519i \(0.614028\pi\)
\(860\) 0 0
\(861\) −0.810466 −0.0276206
\(862\) 0 0
\(863\) 47.5058 1.61712 0.808558 0.588416i \(-0.200248\pi\)
0.808558 + 0.588416i \(0.200248\pi\)
\(864\) 0 0
\(865\) −3.01641 −0.102561
\(866\) 0 0
\(867\) 3.32674 0.112982
\(868\) 0 0
\(869\) −32.4475 −1.10071
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 5.31867 0.180010
\(874\) 0 0
\(875\) −0.681331 −0.0230332
\(876\) 0 0
\(877\) 7.34030 0.247864 0.123932 0.992291i \(-0.460449\pi\)
0.123932 + 0.992291i \(0.460449\pi\)
\(878\) 0 0
\(879\) −12.6373 −0.426247
\(880\) 0 0
\(881\) −28.6373 −0.964816 −0.482408 0.875947i \(-0.660238\pi\)
−0.482408 + 0.875947i \(0.660238\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) −1.01641 −0.0341661
\(886\) 0 0
\(887\) −44.7526 −1.50265 −0.751323 0.659934i \(-0.770584\pi\)
−0.751323 + 0.659934i \(0.770584\pi\)
\(888\) 0 0
\(889\) 10.5494 0.353814
\(890\) 0 0
\(891\) 3.18953 0.106853
\(892\) 0 0
\(893\) −41.5163 −1.38929
\(894\) 0 0
\(895\) −0.129135 −0.00431652
\(896\) 0 0
\(897\) −6.04399 −0.201803
\(898\) 0 0
\(899\) −19.4178 −0.647621
\(900\) 0 0
\(901\) −27.9867 −0.932372
\(902\) 0 0
\(903\) −4.34625 −0.144634
\(904\) 0 0
\(905\) 7.15672 0.237897
\(906\) 0 0
\(907\) 50.4894 1.67647 0.838237 0.545307i \(-0.183587\pi\)
0.838237 + 0.545307i \(0.183587\pi\)
\(908\) 0 0
\(909\) 1.87086 0.0620527
\(910\) 0 0
\(911\) −10.0552 −0.333143 −0.166571 0.986029i \(-0.553270\pi\)
−0.166571 + 0.986029i \(0.553270\pi\)
\(912\) 0 0
\(913\) −8.69251 −0.287680
\(914\) 0 0
\(915\) 6.55220 0.216609
\(916\) 0 0
\(917\) 2.87325 0.0948832
\(918\) 0 0
\(919\) 11.2119 0.369846 0.184923 0.982753i \(-0.440796\pi\)
0.184923 + 0.982753i \(0.440796\pi\)
\(920\) 0 0
\(921\) 24.0357 0.792002
\(922\) 0 0
\(923\) −1.82687 −0.0601322
\(924\) 0 0
\(925\) 5.18953 0.170631
\(926\) 0 0
\(927\) −18.7253 −0.615020
\(928\) 0 0
\(929\) −26.9641 −0.884663 −0.442331 0.896852i \(-0.645848\pi\)
−0.442331 + 0.896852i \(0.645848\pi\)
\(930\) 0 0
\(931\) −25.2992 −0.829146
\(932\) 0 0
\(933\) 17.1044 0.559973
\(934\) 0 0
\(935\) −11.7941 −0.385707
\(936\) 0 0
\(937\) 52.6207 1.71904 0.859521 0.511100i \(-0.170762\pi\)
0.859521 + 0.511100i \(0.170762\pi\)
\(938\) 0 0
\(939\) −19.7745 −0.645318
\(940\) 0 0
\(941\) −44.1565 −1.43946 −0.719730 0.694255i \(-0.755734\pi\)
−0.719730 + 0.694255i \(0.755734\pi\)
\(942\) 0 0
\(943\) 7.18953 0.234123
\(944\) 0 0
\(945\) 0.681331 0.0221637
\(946\) 0 0
\(947\) 8.51654 0.276750 0.138375 0.990380i \(-0.455812\pi\)
0.138375 + 0.990380i \(0.455812\pi\)
\(948\) 0 0
\(949\) 10.2171 0.331662
\(950\) 0 0
\(951\) −5.24186 −0.169979
\(952\) 0 0
\(953\) −9.57694 −0.310228 −0.155114 0.987897i \(-0.549574\pi\)
−0.155114 + 0.987897i \(0.549574\pi\)
\(954\) 0 0
\(955\) 4.34625 0.140641
\(956\) 0 0
\(957\) −15.4835 −0.500509
\(958\) 0 0
\(959\) 7.97764 0.257612
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 12.5522 0.404489
\(964\) 0 0
\(965\) −16.7141 −0.538047
\(966\) 0 0
\(967\) 3.26634 0.105038 0.0525192 0.998620i \(-0.483275\pi\)
0.0525192 + 0.998620i \(0.483275\pi\)
\(968\) 0 0
\(969\) −14.3134 −0.459814
\(970\) 0 0
\(971\) −46.0140 −1.47666 −0.738330 0.674440i \(-0.764385\pi\)
−0.738330 + 0.674440i \(0.764385\pi\)
\(972\) 0 0
\(973\) −13.8269 −0.443269
\(974\) 0 0
\(975\) −1.00000 −0.0320256
\(976\) 0 0
\(977\) −32.7909 −1.04908 −0.524538 0.851387i \(-0.675762\pi\)
−0.524538 + 0.851387i \(0.675762\pi\)
\(978\) 0 0
\(979\) −13.3103 −0.425400
\(980\) 0 0
\(981\) 14.8873 0.475314
\(982\) 0 0
\(983\) 39.9177 1.27318 0.636588 0.771204i \(-0.280345\pi\)
0.636588 + 0.771204i \(0.280345\pi\)
\(984\) 0 0
\(985\) −11.0164 −0.351012
\(986\) 0 0
\(987\) 7.30749 0.232600
\(988\) 0 0
\(989\) 38.5550 1.22598
\(990\) 0 0
\(991\) −45.4863 −1.44492 −0.722460 0.691413i \(-0.756989\pi\)
−0.722460 + 0.691413i \(0.756989\pi\)
\(992\) 0 0
\(993\) −26.6618 −0.846087
\(994\) 0 0
\(995\) −2.03281 −0.0644445
\(996\) 0 0
\(997\) 43.0221 1.36252 0.681262 0.732040i \(-0.261432\pi\)
0.681262 + 0.732040i \(0.261432\pi\)
\(998\) 0 0
\(999\) −5.18953 −0.164190
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 6240.2.a.bw.1.3 3
4.3 odd 2 6240.2.a.cb.1.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6240.2.a.bw.1.3 3 1.1 even 1 trivial
6240.2.a.cb.1.1 yes 3 4.3 odd 2