Properties

Label 4600.2.a.bi.1.4
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.356372\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.356372 q^{3} -2.46376 q^{7} -2.87300 q^{9} +O(q^{10})\) \(q+0.356372 q^{3} -2.46376 q^{7} -2.87300 q^{9} +1.61574 q^{11} +2.62553 q^{13} +2.58924 q^{17} +4.02550 q^{19} -0.878013 q^{21} -1.00000 q^{23} -2.09297 q^{27} -7.08580 q^{29} -4.58371 q^{31} +0.575803 q^{33} -2.96054 q^{37} +0.935665 q^{39} -5.71155 q^{41} +2.30448 q^{43} -6.88317 q^{47} -0.929907 q^{49} +0.922731 q^{51} +6.76467 q^{53} +1.43457 q^{57} +2.53432 q^{59} +9.25564 q^{61} +7.07837 q^{63} +15.7285 q^{67} -0.356372 q^{69} -5.25113 q^{71} -6.03858 q^{73} -3.98078 q^{77} -1.35712 q^{79} +7.87312 q^{81} +8.59500 q^{83} -2.52518 q^{87} -8.84084 q^{89} -6.46867 q^{91} -1.63350 q^{93} -8.01314 q^{97} -4.64201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q + 3q^{3} + 4q^{7} + 2q^{9} - 7q^{11} - 7q^{13} - 7q^{19} - 6q^{21} - 7q^{23} - 11q^{29} - 10q^{31} - 19q^{33} - 19q^{37} - 24q^{39} - 16q^{41} + 6q^{43} + 6q^{47} - 17q^{49} - 7q^{51} - 15q^{53} - 8q^{57} - 11q^{59} + 5q^{61} + 13q^{63} + 9q^{67} - 3q^{69} - 14q^{71} - 10q^{73} - 6q^{77} - 32q^{79} - 5q^{81} + q^{83} + 10q^{87} - 24q^{89} - 7q^{91} - 26q^{93} + 7q^{97} - 61q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.356372 0.205751 0.102876 0.994694i \(-0.467196\pi\)
0.102876 + 0.994694i \(0.467196\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.46376 −0.931212 −0.465606 0.884992i \(-0.654164\pi\)
−0.465606 + 0.884992i \(0.654164\pi\)
\(8\) 0 0
\(9\) −2.87300 −0.957666
\(10\) 0 0
\(11\) 1.61574 0.487163 0.243581 0.969880i \(-0.421678\pi\)
0.243581 + 0.969880i \(0.421678\pi\)
\(12\) 0 0
\(13\) 2.62553 0.728191 0.364096 0.931362i \(-0.381378\pi\)
0.364096 + 0.931362i \(0.381378\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.58924 0.627982 0.313991 0.949426i \(-0.398334\pi\)
0.313991 + 0.949426i \(0.398334\pi\)
\(18\) 0 0
\(19\) 4.02550 0.923512 0.461756 0.887007i \(-0.347220\pi\)
0.461756 + 0.887007i \(0.347220\pi\)
\(20\) 0 0
\(21\) −0.878013 −0.191598
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.09297 −0.402793
\(28\) 0 0
\(29\) −7.08580 −1.31580 −0.657900 0.753106i \(-0.728555\pi\)
−0.657900 + 0.753106i \(0.728555\pi\)
\(30\) 0 0
\(31\) −4.58371 −0.823258 −0.411629 0.911352i \(-0.635040\pi\)
−0.411629 + 0.911352i \(0.635040\pi\)
\(32\) 0 0
\(33\) 0.575803 0.100234
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.96054 −0.486710 −0.243355 0.969937i \(-0.578248\pi\)
−0.243355 + 0.969937i \(0.578248\pi\)
\(38\) 0 0
\(39\) 0.935665 0.149826
\(40\) 0 0
\(41\) −5.71155 −0.891995 −0.445997 0.895034i \(-0.647151\pi\)
−0.445997 + 0.895034i \(0.647151\pi\)
\(42\) 0 0
\(43\) 2.30448 0.351430 0.175715 0.984441i \(-0.443776\pi\)
0.175715 + 0.984441i \(0.443776\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.88317 −1.00401 −0.502007 0.864864i \(-0.667405\pi\)
−0.502007 + 0.864864i \(0.667405\pi\)
\(48\) 0 0
\(49\) −0.929907 −0.132844
\(50\) 0 0
\(51\) 0.922731 0.129208
\(52\) 0 0
\(53\) 6.76467 0.929199 0.464600 0.885521i \(-0.346198\pi\)
0.464600 + 0.885521i \(0.346198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.43457 0.190014
\(58\) 0 0
\(59\) 2.53432 0.329941 0.164970 0.986299i \(-0.447247\pi\)
0.164970 + 0.986299i \(0.447247\pi\)
\(60\) 0 0
\(61\) 9.25564 1.18506 0.592532 0.805547i \(-0.298129\pi\)
0.592532 + 0.805547i \(0.298129\pi\)
\(62\) 0 0
\(63\) 7.07837 0.891791
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.7285 1.92154 0.960770 0.277347i \(-0.0894550\pi\)
0.960770 + 0.277347i \(0.0894550\pi\)
\(68\) 0 0
\(69\) −0.356372 −0.0429021
\(70\) 0 0
\(71\) −5.25113 −0.623194 −0.311597 0.950214i \(-0.600864\pi\)
−0.311597 + 0.950214i \(0.600864\pi\)
\(72\) 0 0
\(73\) −6.03858 −0.706762 −0.353381 0.935479i \(-0.614968\pi\)
−0.353381 + 0.935479i \(0.614968\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.98078 −0.453652
\(78\) 0 0
\(79\) −1.35712 −0.152688 −0.0763439 0.997082i \(-0.524325\pi\)
−0.0763439 + 0.997082i \(0.524325\pi\)
\(80\) 0 0
\(81\) 7.87312 0.874791
\(82\) 0 0
\(83\) 8.59500 0.943423 0.471712 0.881753i \(-0.343636\pi\)
0.471712 + 0.881753i \(0.343636\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.52518 −0.270727
\(88\) 0 0
\(89\) −8.84084 −0.937127 −0.468564 0.883430i \(-0.655228\pi\)
−0.468564 + 0.883430i \(0.655228\pi\)
\(90\) 0 0
\(91\) −6.46867 −0.678100
\(92\) 0 0
\(93\) −1.63350 −0.169386
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.01314 −0.813611 −0.406806 0.913515i \(-0.633357\pi\)
−0.406806 + 0.913515i \(0.633357\pi\)
\(98\) 0 0
\(99\) −4.64201 −0.466539
\(100\) 0 0
\(101\) −6.33185 −0.630043 −0.315021 0.949085i \(-0.602012\pi\)
−0.315021 + 0.949085i \(0.602012\pi\)
\(102\) 0 0
\(103\) −13.1901 −1.29966 −0.649831 0.760078i \(-0.725161\pi\)
−0.649831 + 0.760078i \(0.725161\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.54923 −0.923159 −0.461580 0.887099i \(-0.652717\pi\)
−0.461580 + 0.887099i \(0.652717\pi\)
\(108\) 0 0
\(109\) −17.5622 −1.68215 −0.841077 0.540915i \(-0.818078\pi\)
−0.841077 + 0.540915i \(0.818078\pi\)
\(110\) 0 0
\(111\) −1.05505 −0.100141
\(112\) 0 0
\(113\) 1.54267 0.145122 0.0725611 0.997364i \(-0.476883\pi\)
0.0725611 + 0.997364i \(0.476883\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −7.54315 −0.697364
\(118\) 0 0
\(119\) −6.37925 −0.584785
\(120\) 0 0
\(121\) −8.38940 −0.762673
\(122\) 0 0
\(123\) −2.03544 −0.183529
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.4256 1.10260 0.551299 0.834308i \(-0.314132\pi\)
0.551299 + 0.834308i \(0.314132\pi\)
\(128\) 0 0
\(129\) 0.821251 0.0723071
\(130\) 0 0
\(131\) −11.3191 −0.988957 −0.494479 0.869190i \(-0.664641\pi\)
−0.494479 + 0.869190i \(0.664641\pi\)
\(132\) 0 0
\(133\) −9.91784 −0.859986
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.94093 0.422132 0.211066 0.977472i \(-0.432306\pi\)
0.211066 + 0.977472i \(0.432306\pi\)
\(138\) 0 0
\(139\) −2.93101 −0.248605 −0.124303 0.992244i \(-0.539669\pi\)
−0.124303 + 0.992244i \(0.539669\pi\)
\(140\) 0 0
\(141\) −2.45297 −0.206577
\(142\) 0 0
\(143\) 4.24216 0.354748
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.331393 −0.0273328
\(148\) 0 0
\(149\) −5.09023 −0.417008 −0.208504 0.978022i \(-0.566859\pi\)
−0.208504 + 0.978022i \(0.566859\pi\)
\(150\) 0 0
\(151\) −14.3645 −1.16897 −0.584485 0.811405i \(-0.698703\pi\)
−0.584485 + 0.811405i \(0.698703\pi\)
\(152\) 0 0
\(153\) −7.43888 −0.601398
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.34146 −0.585912 −0.292956 0.956126i \(-0.594639\pi\)
−0.292956 + 0.956126i \(0.594639\pi\)
\(158\) 0 0
\(159\) 2.41074 0.191184
\(160\) 0 0
\(161\) 2.46376 0.194171
\(162\) 0 0
\(163\) −2.12762 −0.166648 −0.0833240 0.996523i \(-0.526554\pi\)
−0.0833240 + 0.996523i \(0.526554\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.16080 0.167208 0.0836039 0.996499i \(-0.473357\pi\)
0.0836039 + 0.996499i \(0.473357\pi\)
\(168\) 0 0
\(169\) −6.10659 −0.469738
\(170\) 0 0
\(171\) −11.5652 −0.884417
\(172\) 0 0
\(173\) −18.6210 −1.41573 −0.707863 0.706350i \(-0.750341\pi\)
−0.707863 + 0.706350i \(0.750341\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.903162 0.0678858
\(178\) 0 0
\(179\) −13.4670 −1.00657 −0.503287 0.864119i \(-0.667876\pi\)
−0.503287 + 0.864119i \(0.667876\pi\)
\(180\) 0 0
\(181\) 12.2927 0.913706 0.456853 0.889542i \(-0.348977\pi\)
0.456853 + 0.889542i \(0.348977\pi\)
\(182\) 0 0
\(183\) 3.29845 0.243828
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 4.18352 0.305930
\(188\) 0 0
\(189\) 5.15657 0.375085
\(190\) 0 0
\(191\) −2.07099 −0.149852 −0.0749258 0.997189i \(-0.523872\pi\)
−0.0749258 + 0.997189i \(0.523872\pi\)
\(192\) 0 0
\(193\) −25.7996 −1.85710 −0.928549 0.371209i \(-0.878943\pi\)
−0.928549 + 0.371209i \(0.878943\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.21443 0.300266 0.150133 0.988666i \(-0.452030\pi\)
0.150133 + 0.988666i \(0.452030\pi\)
\(198\) 0 0
\(199\) −22.0428 −1.56257 −0.781285 0.624175i \(-0.785435\pi\)
−0.781285 + 0.624175i \(0.785435\pi\)
\(200\) 0 0
\(201\) 5.60519 0.395359
\(202\) 0 0
\(203\) 17.4577 1.22529
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.87300 0.199687
\(208\) 0 0
\(209\) 6.50414 0.449901
\(210\) 0 0
\(211\) 28.9217 1.99105 0.995524 0.0945049i \(-0.0301268\pi\)
0.995524 + 0.0945049i \(0.0301268\pi\)
\(212\) 0 0
\(213\) −1.87135 −0.128223
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 11.2931 0.766628
\(218\) 0 0
\(219\) −2.15198 −0.145417
\(220\) 0 0
\(221\) 6.79812 0.457291
\(222\) 0 0
\(223\) −6.63731 −0.444467 −0.222234 0.974993i \(-0.571335\pi\)
−0.222234 + 0.974993i \(0.571335\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.370367 −0.0245821 −0.0122911 0.999924i \(-0.503912\pi\)
−0.0122911 + 0.999924i \(0.503912\pi\)
\(228\) 0 0
\(229\) −11.5625 −0.764073 −0.382036 0.924147i \(-0.624777\pi\)
−0.382036 + 0.924147i \(0.624777\pi\)
\(230\) 0 0
\(231\) −1.41864 −0.0933395
\(232\) 0 0
\(233\) −16.8534 −1.10410 −0.552051 0.833810i \(-0.686155\pi\)
−0.552051 + 0.833810i \(0.686155\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.483639 −0.0314157
\(238\) 0 0
\(239\) −17.7742 −1.14972 −0.574859 0.818252i \(-0.694943\pi\)
−0.574859 + 0.818252i \(0.694943\pi\)
\(240\) 0 0
\(241\) −26.6318 −1.71551 −0.857754 0.514061i \(-0.828141\pi\)
−0.857754 + 0.514061i \(0.828141\pi\)
\(242\) 0 0
\(243\) 9.08467 0.582782
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 10.5691 0.672493
\(248\) 0 0
\(249\) 3.06301 0.194111
\(250\) 0 0
\(251\) 16.8599 1.06419 0.532094 0.846685i \(-0.321405\pi\)
0.532094 + 0.846685i \(0.321405\pi\)
\(252\) 0 0
\(253\) −1.61574 −0.101580
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.33024 0.519626 0.259813 0.965659i \(-0.416339\pi\)
0.259813 + 0.965659i \(0.416339\pi\)
\(258\) 0 0
\(259\) 7.29405 0.453230
\(260\) 0 0
\(261\) 20.3575 1.26010
\(262\) 0 0
\(263\) 15.0389 0.927337 0.463669 0.886009i \(-0.346533\pi\)
0.463669 + 0.886009i \(0.346533\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3.15063 −0.192815
\(268\) 0 0
\(269\) −7.01922 −0.427969 −0.213985 0.976837i \(-0.568644\pi\)
−0.213985 + 0.976837i \(0.568644\pi\)
\(270\) 0 0
\(271\) 4.40129 0.267359 0.133680 0.991025i \(-0.457321\pi\)
0.133680 + 0.991025i \(0.457321\pi\)
\(272\) 0 0
\(273\) −2.30525 −0.139520
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.41544 0.505634 0.252817 0.967514i \(-0.418643\pi\)
0.252817 + 0.967514i \(0.418643\pi\)
\(278\) 0 0
\(279\) 13.1690 0.788406
\(280\) 0 0
\(281\) −15.0068 −0.895233 −0.447617 0.894226i \(-0.647727\pi\)
−0.447617 + 0.894226i \(0.647727\pi\)
\(282\) 0 0
\(283\) −7.09122 −0.421529 −0.210765 0.977537i \(-0.567595\pi\)
−0.210765 + 0.977537i \(0.567595\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.0719 0.830637
\(288\) 0 0
\(289\) −10.2958 −0.605638
\(290\) 0 0
\(291\) −2.85566 −0.167402
\(292\) 0 0
\(293\) 28.0567 1.63909 0.819545 0.573015i \(-0.194226\pi\)
0.819545 + 0.573015i \(0.194226\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.38169 −0.196225
\(298\) 0 0
\(299\) −2.62553 −0.151838
\(300\) 0 0
\(301\) −5.67767 −0.327256
\(302\) 0 0
\(303\) −2.25649 −0.129632
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 29.2707 1.67057 0.835283 0.549820i \(-0.185304\pi\)
0.835283 + 0.549820i \(0.185304\pi\)
\(308\) 0 0
\(309\) −4.70059 −0.267407
\(310\) 0 0
\(311\) −15.8111 −0.896563 −0.448281 0.893893i \(-0.647964\pi\)
−0.448281 + 0.893893i \(0.647964\pi\)
\(312\) 0 0
\(313\) 9.98602 0.564443 0.282222 0.959349i \(-0.408929\pi\)
0.282222 + 0.959349i \(0.408929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.7683 −0.773302 −0.386651 0.922226i \(-0.626368\pi\)
−0.386651 + 0.922226i \(0.626368\pi\)
\(318\) 0 0
\(319\) −11.4488 −0.641008
\(320\) 0 0
\(321\) −3.40308 −0.189941
\(322\) 0 0
\(323\) 10.4230 0.579950
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.25868 −0.346106
\(328\) 0 0
\(329\) 16.9584 0.934950
\(330\) 0 0
\(331\) 18.6765 1.02656 0.513278 0.858223i \(-0.328431\pi\)
0.513278 + 0.858223i \(0.328431\pi\)
\(332\) 0 0
\(333\) 8.50564 0.466106
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.8915 −0.756716 −0.378358 0.925659i \(-0.623511\pi\)
−0.378358 + 0.925659i \(0.623511\pi\)
\(338\) 0 0
\(339\) 0.549764 0.0298591
\(340\) 0 0
\(341\) −7.40606 −0.401060
\(342\) 0 0
\(343\) 19.5374 1.05492
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.706854 0.0379459 0.0189730 0.999820i \(-0.493960\pi\)
0.0189730 + 0.999820i \(0.493960\pi\)
\(348\) 0 0
\(349\) 6.93817 0.371392 0.185696 0.982607i \(-0.440546\pi\)
0.185696 + 0.982607i \(0.440546\pi\)
\(350\) 0 0
\(351\) −5.49516 −0.293310
\(352\) 0 0
\(353\) 0.413170 0.0219908 0.0109954 0.999940i \(-0.496500\pi\)
0.0109954 + 0.999940i \(0.496500\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.27338 −0.120320
\(358\) 0 0
\(359\) −32.6209 −1.72167 −0.860834 0.508886i \(-0.830057\pi\)
−0.860834 + 0.508886i \(0.830057\pi\)
\(360\) 0 0
\(361\) −2.79537 −0.147125
\(362\) 0 0
\(363\) −2.98974 −0.156921
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 13.5293 0.706223 0.353112 0.935581i \(-0.385124\pi\)
0.353112 + 0.935581i \(0.385124\pi\)
\(368\) 0 0
\(369\) 16.4093 0.854234
\(370\) 0 0
\(371\) −16.6665 −0.865282
\(372\) 0 0
\(373\) −20.7690 −1.07538 −0.537689 0.843143i \(-0.680703\pi\)
−0.537689 + 0.843143i \(0.680703\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −18.6040 −0.958153
\(378\) 0 0
\(379\) −25.0528 −1.28688 −0.643438 0.765498i \(-0.722493\pi\)
−0.643438 + 0.765498i \(0.722493\pi\)
\(380\) 0 0
\(381\) 4.42815 0.226861
\(382\) 0 0
\(383\) 4.51677 0.230796 0.115398 0.993319i \(-0.463186\pi\)
0.115398 + 0.993319i \(0.463186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.62076 −0.336552
\(388\) 0 0
\(389\) 0.455188 0.0230789 0.0115395 0.999933i \(-0.496327\pi\)
0.0115395 + 0.999933i \(0.496327\pi\)
\(390\) 0 0
\(391\) −2.58924 −0.130943
\(392\) 0 0
\(393\) −4.03382 −0.203479
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 15.0798 0.756832 0.378416 0.925636i \(-0.376469\pi\)
0.378416 + 0.925636i \(0.376469\pi\)
\(398\) 0 0
\(399\) −3.53444 −0.176943
\(400\) 0 0
\(401\) −38.0845 −1.90185 −0.950924 0.309424i \(-0.899864\pi\)
−0.950924 + 0.309424i \(0.899864\pi\)
\(402\) 0 0
\(403\) −12.0347 −0.599489
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.78345 −0.237107
\(408\) 0 0
\(409\) 16.3672 0.809305 0.404653 0.914470i \(-0.367392\pi\)
0.404653 + 0.914470i \(0.367392\pi\)
\(410\) 0 0
\(411\) 1.76081 0.0868543
\(412\) 0 0
\(413\) −6.24396 −0.307245
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.04453 −0.0511509
\(418\) 0 0
\(419\) −5.32621 −0.260202 −0.130101 0.991501i \(-0.541530\pi\)
−0.130101 + 0.991501i \(0.541530\pi\)
\(420\) 0 0
\(421\) −11.3000 −0.550730 −0.275365 0.961340i \(-0.588799\pi\)
−0.275365 + 0.961340i \(0.588799\pi\)
\(422\) 0 0
\(423\) 19.7753 0.961510
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −22.8036 −1.10355
\(428\) 0 0
\(429\) 1.51179 0.0729898
\(430\) 0 0
\(431\) 33.6364 1.62021 0.810105 0.586285i \(-0.199410\pi\)
0.810105 + 0.586285i \(0.199410\pi\)
\(432\) 0 0
\(433\) 18.3932 0.883920 0.441960 0.897035i \(-0.354283\pi\)
0.441960 + 0.897035i \(0.354283\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.02550 −0.192566
\(438\) 0 0
\(439\) 28.7628 1.37277 0.686387 0.727236i \(-0.259196\pi\)
0.686387 + 0.727236i \(0.259196\pi\)
\(440\) 0 0
\(441\) 2.67162 0.127220
\(442\) 0 0
\(443\) 22.2359 1.05646 0.528229 0.849102i \(-0.322856\pi\)
0.528229 + 0.849102i \(0.322856\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.81401 −0.0857999
\(448\) 0 0
\(449\) 28.4538 1.34282 0.671409 0.741087i \(-0.265689\pi\)
0.671409 + 0.741087i \(0.265689\pi\)
\(450\) 0 0
\(451\) −9.22836 −0.434547
\(452\) 0 0
\(453\) −5.11912 −0.240517
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.58512 0.354817 0.177408 0.984137i \(-0.443229\pi\)
0.177408 + 0.984137i \(0.443229\pi\)
\(458\) 0 0
\(459\) −5.41920 −0.252947
\(460\) 0 0
\(461\) 6.02951 0.280822 0.140411 0.990093i \(-0.455158\pi\)
0.140411 + 0.990093i \(0.455158\pi\)
\(462\) 0 0
\(463\) 24.2763 1.12821 0.564107 0.825701i \(-0.309220\pi\)
0.564107 + 0.825701i \(0.309220\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.99614 0.277468 0.138734 0.990330i \(-0.455697\pi\)
0.138734 + 0.990330i \(0.455697\pi\)
\(468\) 0 0
\(469\) −38.7511 −1.78936
\(470\) 0 0
\(471\) −2.61629 −0.120552
\(472\) 0 0
\(473\) 3.72343 0.171203
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −19.4349 −0.889863
\(478\) 0 0
\(479\) −17.5065 −0.799892 −0.399946 0.916539i \(-0.630971\pi\)
−0.399946 + 0.916539i \(0.630971\pi\)
\(480\) 0 0
\(481\) −7.77299 −0.354418
\(482\) 0 0
\(483\) 0.878013 0.0399510
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.6269 −1.43315 −0.716576 0.697509i \(-0.754292\pi\)
−0.716576 + 0.697509i \(0.754292\pi\)
\(488\) 0 0
\(489\) −0.758224 −0.0342881
\(490\) 0 0
\(491\) 24.7642 1.11759 0.558797 0.829305i \(-0.311263\pi\)
0.558797 + 0.829305i \(0.311263\pi\)
\(492\) 0 0
\(493\) −18.3468 −0.826299
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.9375 0.580326
\(498\) 0 0
\(499\) 37.7906 1.69174 0.845871 0.533388i \(-0.179081\pi\)
0.845871 + 0.533388i \(0.179081\pi\)
\(500\) 0 0
\(501\) 0.770049 0.0344032
\(502\) 0 0
\(503\) 1.40481 0.0626376 0.0313188 0.999509i \(-0.490029\pi\)
0.0313188 + 0.999509i \(0.490029\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.17622 −0.0966492
\(508\) 0 0
\(509\) 30.4044 1.34765 0.673825 0.738891i \(-0.264650\pi\)
0.673825 + 0.738891i \(0.264650\pi\)
\(510\) 0 0
\(511\) 14.8776 0.658146
\(512\) 0 0
\(513\) −8.42525 −0.371984
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −11.1214 −0.489118
\(518\) 0 0
\(519\) −6.63599 −0.291288
\(520\) 0 0
\(521\) −13.3500 −0.584873 −0.292437 0.956285i \(-0.594466\pi\)
−0.292437 + 0.956285i \(0.594466\pi\)
\(522\) 0 0
\(523\) 8.71026 0.380873 0.190437 0.981699i \(-0.439010\pi\)
0.190437 + 0.981699i \(0.439010\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.8683 −0.516991
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −7.28111 −0.315973
\(532\) 0 0
\(533\) −14.9959 −0.649543
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.79927 −0.207104
\(538\) 0 0
\(539\) −1.50248 −0.0647166
\(540\) 0 0
\(541\) 21.2922 0.915423 0.457711 0.889101i \(-0.348669\pi\)
0.457711 + 0.889101i \(0.348669\pi\)
\(542\) 0 0
\(543\) 4.38075 0.187996
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.27222 0.310937 0.155469 0.987841i \(-0.450311\pi\)
0.155469 + 0.987841i \(0.450311\pi\)
\(548\) 0 0
\(549\) −26.5914 −1.13490
\(550\) 0 0
\(551\) −28.5238 −1.21516
\(552\) 0 0
\(553\) 3.34361 0.142185
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −27.0665 −1.14684 −0.573422 0.819260i \(-0.694384\pi\)
−0.573422 + 0.819260i \(0.694384\pi\)
\(558\) 0 0
\(559\) 6.05048 0.255908
\(560\) 0 0
\(561\) 1.49089 0.0629454
\(562\) 0 0
\(563\) 12.7921 0.539124 0.269562 0.962983i \(-0.413121\pi\)
0.269562 + 0.962983i \(0.413121\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −19.3974 −0.814616
\(568\) 0 0
\(569\) −13.3013 −0.557621 −0.278810 0.960346i \(-0.589940\pi\)
−0.278810 + 0.960346i \(0.589940\pi\)
\(570\) 0 0
\(571\) 31.8239 1.33179 0.665894 0.746046i \(-0.268050\pi\)
0.665894 + 0.746046i \(0.268050\pi\)
\(572\) 0 0
\(573\) −0.738043 −0.0308322
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 26.0091 1.08277 0.541386 0.840774i \(-0.317900\pi\)
0.541386 + 0.840774i \(0.317900\pi\)
\(578\) 0 0
\(579\) −9.19426 −0.382101
\(580\) 0 0
\(581\) −21.1760 −0.878527
\(582\) 0 0
\(583\) 10.9299 0.452671
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −39.4259 −1.62728 −0.813641 0.581367i \(-0.802518\pi\)
−0.813641 + 0.581367i \(0.802518\pi\)
\(588\) 0 0
\(589\) −18.4517 −0.760289
\(590\) 0 0
\(591\) 1.50191 0.0617801
\(592\) 0 0
\(593\) 20.8918 0.857922 0.428961 0.903323i \(-0.358880\pi\)
0.428961 + 0.903323i \(0.358880\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.85542 −0.321501
\(598\) 0 0
\(599\) 12.7986 0.522938 0.261469 0.965212i \(-0.415793\pi\)
0.261469 + 0.965212i \(0.415793\pi\)
\(600\) 0 0
\(601\) −18.7566 −0.765099 −0.382550 0.923935i \(-0.624954\pi\)
−0.382550 + 0.923935i \(0.624954\pi\)
\(602\) 0 0
\(603\) −45.1879 −1.84019
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.51153 −0.0613512 −0.0306756 0.999529i \(-0.509766\pi\)
−0.0306756 + 0.999529i \(0.509766\pi\)
\(608\) 0 0
\(609\) 6.22142 0.252105
\(610\) 0 0
\(611\) −18.0720 −0.731114
\(612\) 0 0
\(613\) −39.5673 −1.59811 −0.799054 0.601259i \(-0.794666\pi\)
−0.799054 + 0.601259i \(0.794666\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 41.0023 1.65069 0.825345 0.564629i \(-0.190981\pi\)
0.825345 + 0.564629i \(0.190981\pi\)
\(618\) 0 0
\(619\) 10.9089 0.438464 0.219232 0.975673i \(-0.429645\pi\)
0.219232 + 0.975673i \(0.429645\pi\)
\(620\) 0 0
\(621\) 2.09297 0.0839880
\(622\) 0 0
\(623\) 21.7817 0.872664
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.31789 0.0925677
\(628\) 0 0
\(629\) −7.66555 −0.305645
\(630\) 0 0
\(631\) −24.7516 −0.985347 −0.492674 0.870214i \(-0.663980\pi\)
−0.492674 + 0.870214i \(0.663980\pi\)
\(632\) 0 0
\(633\) 10.3069 0.409661
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −2.44150 −0.0967357
\(638\) 0 0
\(639\) 15.0865 0.596812
\(640\) 0 0
\(641\) 33.5110 1.32360 0.661802 0.749679i \(-0.269792\pi\)
0.661802 + 0.749679i \(0.269792\pi\)
\(642\) 0 0
\(643\) 9.15767 0.361143 0.180572 0.983562i \(-0.442205\pi\)
0.180572 + 0.983562i \(0.442205\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.8011 1.21092 0.605458 0.795877i \(-0.292990\pi\)
0.605458 + 0.795877i \(0.292990\pi\)
\(648\) 0 0
\(649\) 4.09480 0.160735
\(650\) 0 0
\(651\) 4.02455 0.157735
\(652\) 0 0
\(653\) 25.4779 0.997026 0.498513 0.866882i \(-0.333880\pi\)
0.498513 + 0.866882i \(0.333880\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 17.3488 0.676843
\(658\) 0 0
\(659\) 2.34417 0.0913159 0.0456580 0.998957i \(-0.485462\pi\)
0.0456580 + 0.998957i \(0.485462\pi\)
\(660\) 0 0
\(661\) 43.4164 1.68870 0.844351 0.535791i \(-0.179987\pi\)
0.844351 + 0.535791i \(0.179987\pi\)
\(662\) 0 0
\(663\) 2.42266 0.0940883
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.08580 0.274363
\(668\) 0 0
\(669\) −2.36535 −0.0914498
\(670\) 0 0
\(671\) 14.9547 0.577319
\(672\) 0 0
\(673\) −48.4902 −1.86916 −0.934580 0.355754i \(-0.884224\pi\)
−0.934580 + 0.355754i \(0.884224\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −46.9213 −1.80333 −0.901665 0.432435i \(-0.857655\pi\)
−0.901665 + 0.432435i \(0.857655\pi\)
\(678\) 0 0
\(679\) 19.7424 0.757645
\(680\) 0 0
\(681\) −0.131988 −0.00505780
\(682\) 0 0
\(683\) −15.3660 −0.587965 −0.293983 0.955811i \(-0.594981\pi\)
−0.293983 + 0.955811i \(0.594981\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −4.12056 −0.157209
\(688\) 0 0
\(689\) 17.7609 0.676635
\(690\) 0 0
\(691\) −40.0235 −1.52257 −0.761283 0.648419i \(-0.775430\pi\)
−0.761283 + 0.648419i \(0.775430\pi\)
\(692\) 0 0
\(693\) 11.4368 0.434447
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −14.7886 −0.560157
\(698\) 0 0
\(699\) −6.00607 −0.227171
\(700\) 0 0
\(701\) −28.2943 −1.06866 −0.534331 0.845276i \(-0.679436\pi\)
−0.534331 + 0.845276i \(0.679436\pi\)
\(702\) 0 0
\(703\) −11.9177 −0.449483
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.6001 0.586703
\(708\) 0 0
\(709\) 26.8823 1.00959 0.504793 0.863240i \(-0.331569\pi\)
0.504793 + 0.863240i \(0.331569\pi\)
\(710\) 0 0
\(711\) 3.89900 0.146224
\(712\) 0 0
\(713\) 4.58371 0.171661
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.33423 −0.236556
\(718\) 0 0
\(719\) 11.2624 0.420015 0.210008 0.977700i \(-0.432651\pi\)
0.210008 + 0.977700i \(0.432651\pi\)
\(720\) 0 0
\(721\) 32.4973 1.21026
\(722\) 0 0
\(723\) −9.49084 −0.352968
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.07629 −0.0770054 −0.0385027 0.999258i \(-0.512259\pi\)
−0.0385027 + 0.999258i \(0.512259\pi\)
\(728\) 0 0
\(729\) −20.3818 −0.754883
\(730\) 0 0
\(731\) 5.96684 0.220692
\(732\) 0 0
\(733\) −16.6294 −0.614221 −0.307111 0.951674i \(-0.599362\pi\)
−0.307111 + 0.951674i \(0.599362\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.4131 0.936103
\(738\) 0 0
\(739\) 50.8052 1.86890 0.934450 0.356095i \(-0.115892\pi\)
0.934450 + 0.356095i \(0.115892\pi\)
\(740\) 0 0
\(741\) 3.76652 0.138366
\(742\) 0 0
\(743\) −31.3667 −1.15073 −0.575366 0.817896i \(-0.695141\pi\)
−0.575366 + 0.817896i \(0.695141\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −24.6934 −0.903485
\(748\) 0 0
\(749\) 23.5270 0.859657
\(750\) 0 0
\(751\) 41.2551 1.50542 0.752711 0.658351i \(-0.228746\pi\)
0.752711 + 0.658351i \(0.228746\pi\)
\(752\) 0 0
\(753\) 6.00839 0.218958
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −11.3081 −0.411000 −0.205500 0.978657i \(-0.565882\pi\)
−0.205500 + 0.978657i \(0.565882\pi\)
\(758\) 0 0
\(759\) −0.575803 −0.0209003
\(760\) 0 0
\(761\) −4.32880 −0.156919 −0.0784594 0.996917i \(-0.525000\pi\)
−0.0784594 + 0.996917i \(0.525000\pi\)
\(762\) 0 0
\(763\) 43.2690 1.56644
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.65395 0.240260
\(768\) 0 0
\(769\) 40.6517 1.46594 0.732968 0.680263i \(-0.238134\pi\)
0.732968 + 0.680263i \(0.238134\pi\)
\(770\) 0 0
\(771\) 2.96866 0.106914
\(772\) 0 0
\(773\) −37.9716 −1.36574 −0.682872 0.730538i \(-0.739269\pi\)
−0.682872 + 0.730538i \(0.739269\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.59940 0.0932528
\(778\) 0 0
\(779\) −22.9918 −0.823768
\(780\) 0 0
\(781\) −8.48443 −0.303597
\(782\) 0 0
\(783\) 14.8304 0.529994
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 55.1654 1.96643 0.983216 0.182443i \(-0.0584006\pi\)
0.983216 + 0.182443i \(0.0584006\pi\)
\(788\) 0 0
\(789\) 5.35944 0.190801
\(790\) 0 0
\(791\) −3.80076 −0.135140
\(792\) 0 0
\(793\) 24.3010 0.862952
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.0601 −1.17105 −0.585524 0.810655i \(-0.699111\pi\)
−0.585524 + 0.810655i \(0.699111\pi\)
\(798\) 0 0
\(799\) −17.8222 −0.630503
\(800\) 0 0
\(801\) 25.3997 0.897455
\(802\) 0 0
\(803\) −9.75675 −0.344308
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2.50145 −0.0880553
\(808\) 0 0
\(809\) −26.4318 −0.929291 −0.464646 0.885497i \(-0.653818\pi\)
−0.464646 + 0.885497i \(0.653818\pi\)
\(810\) 0 0
\(811\) 5.49057 0.192800 0.0964000 0.995343i \(-0.469267\pi\)
0.0964000 + 0.995343i \(0.469267\pi\)
\(812\) 0 0
\(813\) 1.56850 0.0550096
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.27667 0.324550
\(818\) 0 0
\(819\) 18.5845 0.649394
\(820\) 0 0
\(821\) −42.2732 −1.47534 −0.737672 0.675160i \(-0.764075\pi\)
−0.737672 + 0.675160i \(0.764075\pi\)
\(822\) 0 0
\(823\) −52.2599 −1.82167 −0.910833 0.412774i \(-0.864560\pi\)
−0.910833 + 0.412774i \(0.864560\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 46.7667 1.62624 0.813119 0.582097i \(-0.197768\pi\)
0.813119 + 0.582097i \(0.197768\pi\)
\(828\) 0 0
\(829\) 15.2175 0.528525 0.264262 0.964451i \(-0.414871\pi\)
0.264262 + 0.964451i \(0.414871\pi\)
\(830\) 0 0
\(831\) 2.99902 0.104035
\(832\) 0 0
\(833\) −2.40775 −0.0834236
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.59356 0.331602
\(838\) 0 0
\(839\) 54.7388 1.88979 0.944897 0.327369i \(-0.106162\pi\)
0.944897 + 0.327369i \(0.106162\pi\)
\(840\) 0 0
\(841\) 21.2085 0.731328
\(842\) 0 0
\(843\) −5.34802 −0.184195
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 20.6694 0.710210
\(848\) 0 0
\(849\) −2.52711 −0.0867302
\(850\) 0 0
\(851\) 2.96054 0.101486
\(852\) 0 0
\(853\) −16.8683 −0.577559 −0.288779 0.957396i \(-0.593249\pi\)
−0.288779 + 0.957396i \(0.593249\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 39.9513 1.36471 0.682355 0.731021i \(-0.260956\pi\)
0.682355 + 0.731021i \(0.260956\pi\)
\(858\) 0 0
\(859\) 21.5728 0.736053 0.368027 0.929815i \(-0.380034\pi\)
0.368027 + 0.929815i \(0.380034\pi\)
\(860\) 0 0
\(861\) 5.01482 0.170905
\(862\) 0 0
\(863\) 2.71384 0.0923803 0.0461902 0.998933i \(-0.485292\pi\)
0.0461902 + 0.998933i \(0.485292\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −3.66915 −0.124611
\(868\) 0 0
\(869\) −2.19275 −0.0743838
\(870\) 0 0
\(871\) 41.2956 1.39925
\(872\) 0 0
\(873\) 23.0217 0.779168
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −40.8294 −1.37871 −0.689355 0.724423i \(-0.742106\pi\)
−0.689355 + 0.724423i \(0.742106\pi\)
\(878\) 0 0
\(879\) 9.99862 0.337245
\(880\) 0 0
\(881\) 36.3676 1.22525 0.612627 0.790372i \(-0.290113\pi\)
0.612627 + 0.790372i \(0.290113\pi\)
\(882\) 0 0
\(883\) 18.2495 0.614146 0.307073 0.951686i \(-0.400650\pi\)
0.307073 + 0.951686i \(0.400650\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.33546 0.111994 0.0559968 0.998431i \(-0.482166\pi\)
0.0559968 + 0.998431i \(0.482166\pi\)
\(888\) 0 0
\(889\) −30.6138 −1.02675
\(890\) 0 0
\(891\) 12.7209 0.426166
\(892\) 0 0
\(893\) −27.7082 −0.927219
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.935665 −0.0312409
\(898\) 0 0
\(899\) 32.4792 1.08324
\(900\) 0 0
\(901\) 17.5153 0.583521
\(902\) 0 0
\(903\) −2.02336 −0.0673333
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 5.50057 0.182643 0.0913217 0.995821i \(-0.470891\pi\)
0.0913217 + 0.995821i \(0.470891\pi\)
\(908\) 0 0
\(909\) 18.1914 0.603371
\(910\) 0 0
\(911\) 11.9531 0.396024 0.198012 0.980200i \(-0.436551\pi\)
0.198012 + 0.980200i \(0.436551\pi\)
\(912\) 0 0
\(913\) 13.8872 0.459601
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 27.8876 0.920929
\(918\) 0 0
\(919\) 22.3756 0.738102 0.369051 0.929409i \(-0.379683\pi\)
0.369051 + 0.929409i \(0.379683\pi\)
\(920\) 0 0
\(921\) 10.4312 0.343721
\(922\) 0 0
\(923\) −13.7870 −0.453804
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 37.8953 1.24464
\(928\) 0 0
\(929\) −42.9751 −1.40997 −0.704983 0.709224i \(-0.749045\pi\)
−0.704983 + 0.709224i \(0.749045\pi\)
\(930\) 0 0
\(931\) −3.74334 −0.122683
\(932\) 0 0
\(933\) −5.63461 −0.184469
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 3.76556 0.123015 0.0615077 0.998107i \(-0.480409\pi\)
0.0615077 + 0.998107i \(0.480409\pi\)
\(938\) 0 0
\(939\) 3.55874 0.116135
\(940\) 0 0
\(941\) −15.9193 −0.518953 −0.259477 0.965749i \(-0.583550\pi\)
−0.259477 + 0.965749i \(0.583550\pi\)
\(942\) 0 0
\(943\) 5.71155 0.185994
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −51.8553 −1.68507 −0.842535 0.538642i \(-0.818938\pi\)
−0.842535 + 0.538642i \(0.818938\pi\)
\(948\) 0 0
\(949\) −15.8545 −0.514658
\(950\) 0 0
\(951\) −4.90662 −0.159108
\(952\) 0 0
\(953\) −44.6848 −1.44748 −0.723741 0.690072i \(-0.757579\pi\)
−0.723741 + 0.690072i \(0.757579\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −4.08002 −0.131888
\(958\) 0 0
\(959\) −12.1733 −0.393095
\(960\) 0 0
\(961\) −9.98964 −0.322247
\(962\) 0 0
\(963\) 27.4349 0.884079
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 31.5594 1.01488 0.507440 0.861687i \(-0.330592\pi\)
0.507440 + 0.861687i \(0.330592\pi\)
\(968\) 0 0
\(969\) 3.71445 0.119325
\(970\) 0 0
\(971\) −20.6291 −0.662018 −0.331009 0.943628i \(-0.607389\pi\)
−0.331009 + 0.943628i \(0.607389\pi\)
\(972\) 0 0
\(973\) 7.22130 0.231504
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.76933 0.0566058 0.0283029 0.999599i \(-0.490990\pi\)
0.0283029 + 0.999599i \(0.490990\pi\)
\(978\) 0 0
\(979\) −14.2845 −0.456533
\(980\) 0 0
\(981\) 50.4562 1.61094
\(982\) 0 0
\(983\) −43.4073 −1.38448 −0.692239 0.721668i \(-0.743376\pi\)
−0.692239 + 0.721668i \(0.743376\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6.04351 0.192367
\(988\) 0 0
\(989\) −2.30448 −0.0732781
\(990\) 0 0
\(991\) 16.2222 0.515317 0.257658 0.966236i \(-0.417049\pi\)
0.257658 + 0.966236i \(0.417049\pi\)
\(992\) 0 0
\(993\) 6.65579 0.211215
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −2.61347 −0.0827695 −0.0413847 0.999143i \(-0.513177\pi\)
−0.0413847 + 0.999143i \(0.513177\pi\)
\(998\) 0 0
\(999\) 6.19633 0.196043
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 4600.2.a.bi.1.4 7
4.3 odd 2 9200.2.a.cz.1.4 7
5.2 odd 4 920.2.e.b.369.6 14
5.3 odd 4 920.2.e.b.369.9 yes 14
5.4 even 2 4600.2.a.bh.1.4 7
20.3 even 4 1840.2.e.g.369.6 14
20.7 even 4 1840.2.e.g.369.9 14
20.19 odd 2 9200.2.a.dc.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.6 14 5.2 odd 4
920.2.e.b.369.9 yes 14 5.3 odd 4
1840.2.e.g.369.6 14 20.3 even 4
1840.2.e.g.369.9 14 20.7 even 4
4600.2.a.bh.1.4 7 5.4 even 2
4600.2.a.bi.1.4 7 1.1 even 1 trivial
9200.2.a.cz.1.4 7 4.3 odd 2
9200.2.a.dc.1.4 7 20.19 odd 2