Properties

Label 7800.2.a.bv.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.10304.1
Defining polynomial: \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.16053\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -2.82843 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -2.82843 q^{7} +1.00000 q^{9} -6.46967 q^{11} +1.00000 q^{13} -3.49264 q^{17} -2.21016 q^{19} +2.82843 q^{21} +7.14949 q^{23} -1.00000 q^{27} +4.82843 q^{29} -9.65685 q^{31} +6.46967 q^{33} -6.93933 q^{37} -1.00000 q^{39} -0.148604 q^{41} -3.03858 q^{43} -6.79073 q^{47} +1.00000 q^{49} +3.49264 q^{51} -1.70279 q^{53} +2.21016 q^{57} -6.46967 q^{59} +2.66421 q^{61} -2.82843 q^{63} +7.70279 q^{67} -7.14949 q^{69} -11.0879 q^{71} -5.76776 q^{73} +18.2990 q^{77} -10.0239 q^{79} +1.00000 q^{81} +2.27171 q^{83} -4.82843 q^{87} -9.21104 q^{89} -2.82843 q^{91} +9.65685 q^{93} +8.11091 q^{97} -6.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{9} - 8 q^{11} + 4 q^{13} - 4 q^{17} - 12 q^{19} - 4 q^{23} - 4 q^{27} + 8 q^{29} - 16 q^{31} + 8 q^{33} + 8 q^{37} - 4 q^{39} - 4 q^{41} - 4 q^{43} + 12 q^{47} + 4 q^{49} + 4 q^{51} + 12 q^{57} - 8 q^{59} + 12 q^{61} + 24 q^{67} + 4 q^{69} - 12 q^{71} + 24 q^{73} + 8 q^{77} - 12 q^{79} + 4 q^{81} + 12 q^{83} - 8 q^{87} - 4 q^{89} + 16 q^{93} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.82843 −1.06904 −0.534522 0.845154i \(-0.679509\pi\)
−0.534522 + 0.845154i \(0.679509\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −6.46967 −1.95068 −0.975339 0.220713i \(-0.929162\pi\)
−0.975339 + 0.220713i \(0.929162\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.49264 −0.847089 −0.423544 0.905875i \(-0.639214\pi\)
−0.423544 + 0.905875i \(0.639214\pi\)
\(18\) 0 0
\(19\) −2.21016 −0.507045 −0.253522 0.967330i \(-0.581589\pi\)
−0.253522 + 0.967330i \(0.581589\pi\)
\(20\) 0 0
\(21\) 2.82843 0.617213
\(22\) 0 0
\(23\) 7.14949 1.49077 0.745386 0.666633i \(-0.232265\pi\)
0.745386 + 0.666633i \(0.232265\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.82843 0.896616 0.448308 0.893879i \(-0.352027\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(30\) 0 0
\(31\) −9.65685 −1.73442 −0.867211 0.497941i \(-0.834090\pi\)
−0.867211 + 0.497941i \(0.834090\pi\)
\(32\) 0 0
\(33\) 6.46967 1.12622
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.93933 −1.14082 −0.570410 0.821360i \(-0.693216\pi\)
−0.570410 + 0.821360i \(0.693216\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −0.148604 −0.0232080 −0.0116040 0.999933i \(-0.503694\pi\)
−0.0116040 + 0.999933i \(0.503694\pi\)
\(42\) 0 0
\(43\) −3.03858 −0.463380 −0.231690 0.972790i \(-0.574425\pi\)
−0.231690 + 0.972790i \(0.574425\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.79073 −0.990530 −0.495265 0.868742i \(-0.664929\pi\)
−0.495265 + 0.868742i \(0.664929\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 3.49264 0.489067
\(52\) 0 0
\(53\) −1.70279 −0.233897 −0.116948 0.993138i \(-0.537311\pi\)
−0.116948 + 0.993138i \(0.537311\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.21016 0.292742
\(58\) 0 0
\(59\) −6.46967 −0.842279 −0.421139 0.906996i \(-0.638370\pi\)
−0.421139 + 0.906996i \(0.638370\pi\)
\(60\) 0 0
\(61\) 2.66421 0.341117 0.170558 0.985348i \(-0.445443\pi\)
0.170558 + 0.985348i \(0.445443\pi\)
\(62\) 0 0
\(63\) −2.82843 −0.356348
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.70279 0.941046 0.470523 0.882388i \(-0.344065\pi\)
0.470523 + 0.882388i \(0.344065\pi\)
\(68\) 0 0
\(69\) −7.14949 −0.860697
\(70\) 0 0
\(71\) −11.0879 −1.31590 −0.657948 0.753063i \(-0.728575\pi\)
−0.657948 + 0.753063i \(0.728575\pi\)
\(72\) 0 0
\(73\) −5.76776 −0.675065 −0.337533 0.941314i \(-0.609592\pi\)
−0.337533 + 0.941314i \(0.609592\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18.2990 2.08536
\(78\) 0 0
\(79\) −10.0239 −1.12777 −0.563886 0.825853i \(-0.690694\pi\)
−0.563886 + 0.825853i \(0.690694\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.27171 0.249353 0.124676 0.992197i \(-0.460211\pi\)
0.124676 + 0.992197i \(0.460211\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.82843 −0.517662
\(88\) 0 0
\(89\) −9.21104 −0.976369 −0.488184 0.872741i \(-0.662341\pi\)
−0.488184 + 0.872741i \(0.662341\pi\)
\(90\) 0 0
\(91\) −2.82843 −0.296500
\(92\) 0 0
\(93\) 9.65685 1.00137
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.11091 0.823538 0.411769 0.911288i \(-0.364911\pi\)
0.411769 + 0.911288i \(0.364911\pi\)
\(98\) 0 0
\(99\) −6.46967 −0.650226
\(100\) 0 0
\(101\) −16.1421 −1.60620 −0.803101 0.595843i \(-0.796818\pi\)
−0.803101 + 0.595843i \(0.796818\pi\)
\(102\) 0 0
\(103\) 19.5815 1.92942 0.964709 0.263318i \(-0.0848167\pi\)
0.964709 + 0.263318i \(0.0848167\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.35965 −0.131442 −0.0657210 0.997838i \(-0.520935\pi\)
−0.0657210 + 0.997838i \(0.520935\pi\)
\(108\) 0 0
\(109\) 3.49264 0.334534 0.167267 0.985912i \(-0.446506\pi\)
0.167267 + 0.985912i \(0.446506\pi\)
\(110\) 0 0
\(111\) 6.93933 0.658652
\(112\) 0 0
\(113\) 12.4320 1.16950 0.584751 0.811213i \(-0.301192\pi\)
0.584751 + 0.811213i \(0.301192\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 9.87867 0.905576
\(120\) 0 0
\(121\) 30.8566 2.80514
\(122\) 0 0
\(123\) 0.148604 0.0133991
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −18.6200 −1.65226 −0.826131 0.563478i \(-0.809463\pi\)
−0.826131 + 0.563478i \(0.809463\pi\)
\(128\) 0 0
\(129\) 3.03858 0.267532
\(130\) 0 0
\(131\) −0.751258 −0.0656378 −0.0328189 0.999461i \(-0.510448\pi\)
−0.0328189 + 0.999461i \(0.510448\pi\)
\(132\) 0 0
\(133\) 6.25127 0.542054
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.08794 −0.0929487 −0.0464743 0.998919i \(-0.514799\pi\)
−0.0464743 + 0.998919i \(0.514799\pi\)
\(138\) 0 0
\(139\) 0.420314 0.0356506 0.0178253 0.999841i \(-0.494326\pi\)
0.0178253 + 0.999841i \(0.494326\pi\)
\(140\) 0 0
\(141\) 6.79073 0.571883
\(142\) 0 0
\(143\) −6.46967 −0.541021
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.00000 −0.0824786
\(148\) 0 0
\(149\) −14.1265 −1.15729 −0.578645 0.815580i \(-0.696418\pi\)
−0.578645 + 0.815580i \(0.696418\pi\)
\(150\) 0 0
\(151\) 6.07717 0.494553 0.247276 0.968945i \(-0.420464\pi\)
0.247276 + 0.968945i \(0.420464\pi\)
\(152\) 0 0
\(153\) −3.49264 −0.282363
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.7266 0.935888 0.467944 0.883758i \(-0.344995\pi\)
0.467944 + 0.883758i \(0.344995\pi\)
\(158\) 0 0
\(159\) 1.70279 0.135040
\(160\) 0 0
\(161\) −20.2218 −1.59370
\(162\) 0 0
\(163\) −7.31371 −0.572854 −0.286427 0.958102i \(-0.592468\pi\)
−0.286427 + 0.958102i \(0.592468\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.0420 1.62828 0.814139 0.580670i \(-0.197209\pi\)
0.814139 + 0.580670i \(0.197209\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.21016 −0.169015
\(172\) 0 0
\(173\) 18.9706 1.44231 0.721153 0.692776i \(-0.243613\pi\)
0.721153 + 0.692776i \(0.243613\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.46967 0.486290
\(178\) 0 0
\(179\) 20.4099 1.52551 0.762753 0.646690i \(-0.223847\pi\)
0.762753 + 0.646690i \(0.223847\pi\)
\(180\) 0 0
\(181\) 24.8934 1.85031 0.925156 0.379588i \(-0.123934\pi\)
0.925156 + 0.379588i \(0.123934\pi\)
\(182\) 0 0
\(183\) −2.66421 −0.196944
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 22.5962 1.65240
\(188\) 0 0
\(189\) 2.82843 0.205738
\(190\) 0 0
\(191\) −14.9853 −1.08430 −0.542148 0.840283i \(-0.682389\pi\)
−0.542148 + 0.840283i \(0.682389\pi\)
\(192\) 0 0
\(193\) 18.7990 1.35318 0.676590 0.736360i \(-0.263457\pi\)
0.676590 + 0.736360i \(0.263457\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.92857 −0.137405 −0.0687023 0.997637i \(-0.521886\pi\)
−0.0687023 + 0.997637i \(0.521886\pi\)
\(198\) 0 0
\(199\) −10.0239 −0.710572 −0.355286 0.934758i \(-0.615617\pi\)
−0.355286 + 0.934758i \(0.615617\pi\)
\(200\) 0 0
\(201\) −7.70279 −0.543313
\(202\) 0 0
\(203\) −13.6569 −0.958523
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 7.14949 0.496924
\(208\) 0 0
\(209\) 14.2990 0.989081
\(210\) 0 0
\(211\) 20.2751 1.39580 0.697899 0.716197i \(-0.254119\pi\)
0.697899 + 0.716197i \(0.254119\pi\)
\(212\) 0 0
\(213\) 11.0879 0.759733
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 27.3137 1.85418
\(218\) 0 0
\(219\) 5.76776 0.389749
\(220\) 0 0
\(221\) −3.49264 −0.234940
\(222\) 0 0
\(223\) −16.1881 −1.08403 −0.542017 0.840368i \(-0.682339\pi\)
−0.542017 + 0.840368i \(0.682339\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 23.0879 1.53240 0.766200 0.642602i \(-0.222145\pi\)
0.766200 + 0.642602i \(0.222145\pi\)
\(228\) 0 0
\(229\) −4.30886 −0.284738 −0.142369 0.989814i \(-0.545472\pi\)
−0.142369 + 0.989814i \(0.545472\pi\)
\(230\) 0 0
\(231\) −18.2990 −1.20398
\(232\) 0 0
\(233\) 1.53857 0.100795 0.0503977 0.998729i \(-0.483951\pi\)
0.0503977 + 0.998729i \(0.483951\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.0239 0.651119
\(238\) 0 0
\(239\) −17.8514 −1.15471 −0.577355 0.816493i \(-0.695915\pi\)
−0.577355 + 0.816493i \(0.695915\pi\)
\(240\) 0 0
\(241\) 3.95406 0.254703 0.127352 0.991858i \(-0.459352\pi\)
0.127352 + 0.991858i \(0.459352\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.21016 −0.140629
\(248\) 0 0
\(249\) −2.27171 −0.143964
\(250\) 0 0
\(251\) 3.42284 0.216048 0.108024 0.994148i \(-0.465548\pi\)
0.108024 + 0.994148i \(0.465548\pi\)
\(252\) 0 0
\(253\) −46.2548 −2.90802
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.14772 0.196349 0.0981746 0.995169i \(-0.468700\pi\)
0.0981746 + 0.995169i \(0.468700\pi\)
\(258\) 0 0
\(259\) 19.6274 1.21959
\(260\) 0 0
\(261\) 4.82843 0.298872
\(262\) 0 0
\(263\) −13.7144 −0.845669 −0.422835 0.906207i \(-0.638965\pi\)
−0.422835 + 0.906207i \(0.638965\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.21104 0.563707
\(268\) 0 0
\(269\) 9.84316 0.600148 0.300074 0.953916i \(-0.402989\pi\)
0.300074 + 0.953916i \(0.402989\pi\)
\(270\) 0 0
\(271\) −2.86216 −0.173864 −0.0869320 0.996214i \(-0.527706\pi\)
−0.0869320 + 0.996214i \(0.527706\pi\)
\(272\) 0 0
\(273\) 2.82843 0.171184
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6.24389 −0.375159 −0.187580 0.982249i \(-0.560064\pi\)
−0.187580 + 0.982249i \(0.560064\pi\)
\(278\) 0 0
\(279\) −9.65685 −0.578141
\(280\) 0 0
\(281\) −31.3869 −1.87239 −0.936193 0.351486i \(-0.885677\pi\)
−0.936193 + 0.351486i \(0.885677\pi\)
\(282\) 0 0
\(283\) −2.56496 −0.152471 −0.0762354 0.997090i \(-0.524290\pi\)
−0.0762354 + 0.997090i \(0.524290\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.420314 0.0248104
\(288\) 0 0
\(289\) −4.80150 −0.282441
\(290\) 0 0
\(291\) −8.11091 −0.475470
\(292\) 0 0
\(293\) 0.834895 0.0487751 0.0243875 0.999703i \(-0.492236\pi\)
0.0243875 + 0.999703i \(0.492236\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.46967 0.375408
\(298\) 0 0
\(299\) 7.14949 0.413466
\(300\) 0 0
\(301\) 8.59441 0.495374
\(302\) 0 0
\(303\) 16.1421 0.927341
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 17.7556 1.01336 0.506682 0.862133i \(-0.330872\pi\)
0.506682 + 0.862133i \(0.330872\pi\)
\(308\) 0 0
\(309\) −19.5815 −1.11395
\(310\) 0 0
\(311\) −1.35965 −0.0770985 −0.0385493 0.999257i \(-0.512274\pi\)
−0.0385493 + 0.999257i \(0.512274\pi\)
\(312\) 0 0
\(313\) 7.75611 0.438401 0.219201 0.975680i \(-0.429655\pi\)
0.219201 + 0.975680i \(0.429655\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.38514 0.527122 0.263561 0.964643i \(-0.415103\pi\)
0.263561 + 0.964643i \(0.415103\pi\)
\(318\) 0 0
\(319\) −31.2383 −1.74901
\(320\) 0 0
\(321\) 1.35965 0.0758881
\(322\) 0 0
\(323\) 7.71927 0.429512
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.49264 −0.193143
\(328\) 0 0
\(329\) 19.2071 1.05892
\(330\) 0 0
\(331\) 16.0576 0.882605 0.441303 0.897358i \(-0.354517\pi\)
0.441303 + 0.897358i \(0.354517\pi\)
\(332\) 0 0
\(333\) −6.93933 −0.380273
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.0698 −0.603011 −0.301506 0.953464i \(-0.597489\pi\)
−0.301506 + 0.953464i \(0.597489\pi\)
\(338\) 0 0
\(339\) −12.4320 −0.675212
\(340\) 0 0
\(341\) 62.4766 3.38330
\(342\) 0 0
\(343\) 16.9706 0.916324
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −29.6127 −1.58969 −0.794846 0.606811i \(-0.792449\pi\)
−0.794846 + 0.606811i \(0.792449\pi\)
\(348\) 0 0
\(349\) 17.1183 0.916319 0.458160 0.888870i \(-0.348509\pi\)
0.458160 + 0.888870i \(0.348509\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −18.3245 −0.975313 −0.487657 0.873035i \(-0.662148\pi\)
−0.487657 + 0.873035i \(0.662148\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.87867 −0.522834
\(358\) 0 0
\(359\) 27.1356 1.43216 0.716082 0.698016i \(-0.245933\pi\)
0.716082 + 0.698016i \(0.245933\pi\)
\(360\) 0 0
\(361\) −14.1152 −0.742906
\(362\) 0 0
\(363\) −30.8566 −1.61955
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 15.1855 0.792679 0.396340 0.918104i \(-0.370280\pi\)
0.396340 + 0.918104i \(0.370280\pi\)
\(368\) 0 0
\(369\) −0.148604 −0.00773599
\(370\) 0 0
\(371\) 4.81623 0.250046
\(372\) 0 0
\(373\) −22.1776 −1.14831 −0.574157 0.818745i \(-0.694670\pi\)
−0.574157 + 0.818745i \(0.694670\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.82843 0.248677
\(378\) 0 0
\(379\) 14.7604 0.758191 0.379096 0.925358i \(-0.376235\pi\)
0.379096 + 0.925358i \(0.376235\pi\)
\(380\) 0 0
\(381\) 18.6200 0.953934
\(382\) 0 0
\(383\) 9.33238 0.476862 0.238431 0.971159i \(-0.423367\pi\)
0.238431 + 0.971159i \(0.423367\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.03858 −0.154460
\(388\) 0 0
\(389\) −3.09618 −0.156982 −0.0784912 0.996915i \(-0.525010\pi\)
−0.0784912 + 0.996915i \(0.525010\pi\)
\(390\) 0 0
\(391\) −24.9706 −1.26282
\(392\) 0 0
\(393\) 0.751258 0.0378960
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.26777 −0.364759 −0.182379 0.983228i \(-0.558380\pi\)
−0.182379 + 0.983228i \(0.558380\pi\)
\(398\) 0 0
\(399\) −6.25127 −0.312955
\(400\) 0 0
\(401\) −8.40164 −0.419558 −0.209779 0.977749i \(-0.567274\pi\)
−0.209779 + 0.977749i \(0.567274\pi\)
\(402\) 0 0
\(403\) −9.65685 −0.481042
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 44.8952 2.22537
\(408\) 0 0
\(409\) 11.5815 0.572666 0.286333 0.958130i \(-0.407564\pi\)
0.286333 + 0.958130i \(0.407564\pi\)
\(410\) 0 0
\(411\) 1.08794 0.0536639
\(412\) 0 0
\(413\) 18.2990 0.900434
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.420314 −0.0205829
\(418\) 0 0
\(419\) −24.7071 −1.20702 −0.603510 0.797355i \(-0.706232\pi\)
−0.603510 + 0.797355i \(0.706232\pi\)
\(420\) 0 0
\(421\) −20.7769 −1.01260 −0.506302 0.862356i \(-0.668988\pi\)
−0.506302 + 0.862356i \(0.668988\pi\)
\(422\) 0 0
\(423\) −6.79073 −0.330177
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.53552 −0.364669
\(428\) 0 0
\(429\) 6.46967 0.312358
\(430\) 0 0
\(431\) 16.6694 0.802936 0.401468 0.915873i \(-0.368500\pi\)
0.401468 + 0.915873i \(0.368500\pi\)
\(432\) 0 0
\(433\) −12.8860 −0.619263 −0.309631 0.950857i \(-0.600206\pi\)
−0.309631 + 0.950857i \(0.600206\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.8015 −0.755888
\(438\) 0 0
\(439\) 37.1924 1.77510 0.887548 0.460716i \(-0.152407\pi\)
0.887548 + 0.460716i \(0.152407\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 33.0693 1.57117 0.785584 0.618755i \(-0.212363\pi\)
0.785584 + 0.618755i \(0.212363\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 14.1265 0.668161
\(448\) 0 0
\(449\) −10.7448 −0.507078 −0.253539 0.967325i \(-0.581595\pi\)
−0.253539 + 0.967325i \(0.581595\pi\)
\(450\) 0 0
\(451\) 0.961416 0.0452713
\(452\) 0 0
\(453\) −6.07717 −0.285530
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 21.9419 1.02640 0.513198 0.858270i \(-0.328460\pi\)
0.513198 + 0.858270i \(0.328460\pi\)
\(458\) 0 0
\(459\) 3.49264 0.163022
\(460\) 0 0
\(461\) 22.0034 1.02480 0.512401 0.858747i \(-0.328756\pi\)
0.512401 + 0.858747i \(0.328756\pi\)
\(462\) 0 0
\(463\) 32.0208 1.48813 0.744066 0.668106i \(-0.232895\pi\)
0.744066 + 0.668106i \(0.232895\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.3596 1.17350 0.586752 0.809767i \(-0.300406\pi\)
0.586752 + 0.809767i \(0.300406\pi\)
\(468\) 0 0
\(469\) −21.7868 −1.00602
\(470\) 0 0
\(471\) −11.7266 −0.540335
\(472\) 0 0
\(473\) 19.6586 0.903905
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.70279 −0.0779655
\(478\) 0 0
\(479\) 9.46231 0.432344 0.216172 0.976355i \(-0.430643\pi\)
0.216172 + 0.976355i \(0.430643\pi\)
\(480\) 0 0
\(481\) −6.93933 −0.316406
\(482\) 0 0
\(483\) 20.2218 0.920124
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −22.3327 −1.01199 −0.505996 0.862536i \(-0.668875\pi\)
−0.505996 + 0.862536i \(0.668875\pi\)
\(488\) 0 0
\(489\) 7.31371 0.330737
\(490\) 0 0
\(491\) 29.8762 1.34829 0.674146 0.738598i \(-0.264512\pi\)
0.674146 + 0.738598i \(0.264512\pi\)
\(492\) 0 0
\(493\) −16.8639 −0.759513
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 31.3614 1.40675
\(498\) 0 0
\(499\) −24.7145 −1.10637 −0.553186 0.833058i \(-0.686588\pi\)
−0.553186 + 0.833058i \(0.686588\pi\)
\(500\) 0 0
\(501\) −21.0420 −0.940087
\(502\) 0 0
\(503\) −17.2267 −0.768099 −0.384049 0.923313i \(-0.625471\pi\)
−0.384049 + 0.923313i \(0.625471\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 26.1430 1.15877 0.579384 0.815055i \(-0.303293\pi\)
0.579384 + 0.815055i \(0.303293\pi\)
\(510\) 0 0
\(511\) 16.3137 0.721675
\(512\) 0 0
\(513\) 2.21016 0.0975808
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 43.9338 1.93220
\(518\) 0 0
\(519\) −18.9706 −0.832715
\(520\) 0 0
\(521\) −33.0165 −1.44648 −0.723240 0.690597i \(-0.757348\pi\)
−0.723240 + 0.690597i \(0.757348\pi\)
\(522\) 0 0
\(523\) 32.2751 1.41129 0.705646 0.708564i \(-0.250657\pi\)
0.705646 + 0.708564i \(0.250657\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 33.7279 1.46921
\(528\) 0 0
\(529\) 28.1152 1.22240
\(530\) 0 0
\(531\) −6.46967 −0.280760
\(532\) 0 0
\(533\) −0.148604 −0.00643674
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −20.4099 −0.880752
\(538\) 0 0
\(539\) −6.46967 −0.278668
\(540\) 0 0
\(541\) −2.21193 −0.0950983 −0.0475491 0.998869i \(-0.515141\pi\)
−0.0475491 + 0.998869i \(0.515141\pi\)
\(542\) 0 0
\(543\) −24.8934 −1.06828
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −31.4822 −1.34608 −0.673041 0.739605i \(-0.735012\pi\)
−0.673041 + 0.739605i \(0.735012\pi\)
\(548\) 0 0
\(549\) 2.66421 0.113706
\(550\) 0 0
\(551\) −10.6716 −0.454625
\(552\) 0 0
\(553\) 28.3517 1.20564
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −35.1209 −1.48812 −0.744061 0.668112i \(-0.767103\pi\)
−0.744061 + 0.668112i \(0.767103\pi\)
\(558\) 0 0
\(559\) −3.03858 −0.128518
\(560\) 0 0
\(561\) −22.5962 −0.954012
\(562\) 0 0
\(563\) −30.3467 −1.27896 −0.639480 0.768808i \(-0.720850\pi\)
−0.639480 + 0.768808i \(0.720850\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.82843 −0.118783
\(568\) 0 0
\(569\) 30.8327 1.29257 0.646287 0.763094i \(-0.276321\pi\)
0.646287 + 0.763094i \(0.276321\pi\)
\(570\) 0 0
\(571\) 21.1832 0.886490 0.443245 0.896400i \(-0.353827\pi\)
0.443245 + 0.896400i \(0.353827\pi\)
\(572\) 0 0
\(573\) 14.9853 0.626019
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 22.6594 0.943322 0.471661 0.881780i \(-0.343655\pi\)
0.471661 + 0.881780i \(0.343655\pi\)
\(578\) 0 0
\(579\) −18.7990 −0.781259
\(580\) 0 0
\(581\) −6.42537 −0.266569
\(582\) 0 0
\(583\) 11.0165 0.456257
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.6529 −0.563515 −0.281758 0.959486i \(-0.590917\pi\)
−0.281758 + 0.959486i \(0.590917\pi\)
\(588\) 0 0
\(589\) 21.3432 0.879430
\(590\) 0 0
\(591\) 1.92857 0.0793306
\(592\) 0 0
\(593\) −18.7448 −0.769756 −0.384878 0.922967i \(-0.625757\pi\)
−0.384878 + 0.922967i \(0.625757\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.0239 0.410249
\(598\) 0 0
\(599\) −48.7885 −1.99345 −0.996723 0.0808922i \(-0.974223\pi\)
−0.996723 + 0.0808922i \(0.974223\pi\)
\(600\) 0 0
\(601\) 16.5870 0.676599 0.338300 0.941038i \(-0.390148\pi\)
0.338300 + 0.941038i \(0.390148\pi\)
\(602\) 0 0
\(603\) 7.70279 0.313682
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 29.0642 1.17968 0.589840 0.807520i \(-0.299191\pi\)
0.589840 + 0.807520i \(0.299191\pi\)
\(608\) 0 0
\(609\) 13.6569 0.553404
\(610\) 0 0
\(611\) −6.79073 −0.274723
\(612\) 0 0
\(613\) 22.3926 0.904430 0.452215 0.891909i \(-0.350634\pi\)
0.452215 + 0.891909i \(0.350634\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.63136 −0.0656760 −0.0328380 0.999461i \(-0.510455\pi\)
−0.0328380 + 0.999461i \(0.510455\pi\)
\(618\) 0 0
\(619\) −37.4485 −1.50518 −0.752591 0.658489i \(-0.771196\pi\)
−0.752591 + 0.658489i \(0.771196\pi\)
\(620\) 0 0
\(621\) −7.14949 −0.286899
\(622\) 0 0
\(623\) 26.0528 1.04378
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −14.2990 −0.571046
\(628\) 0 0
\(629\) 24.2366 0.966375
\(630\) 0 0
\(631\) 10.7193 0.426728 0.213364 0.976973i \(-0.431558\pi\)
0.213364 + 0.976973i \(0.431558\pi\)
\(632\) 0 0
\(633\) −20.2751 −0.805864
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −11.0879 −0.438632
\(640\) 0 0
\(641\) −31.0183 −1.22515 −0.612574 0.790413i \(-0.709866\pi\)
−0.612574 + 0.790413i \(0.709866\pi\)
\(642\) 0 0
\(643\) −12.4515 −0.491041 −0.245520 0.969391i \(-0.578959\pi\)
−0.245520 + 0.969391i \(0.578959\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 41.6538 1.63758 0.818790 0.574093i \(-0.194645\pi\)
0.818790 + 0.574093i \(0.194645\pi\)
\(648\) 0 0
\(649\) 41.8566 1.64301
\(650\) 0 0
\(651\) −27.3137 −1.07051
\(652\) 0 0
\(653\) 3.83095 0.149917 0.0749584 0.997187i \(-0.476118\pi\)
0.0749584 + 0.997187i \(0.476118\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.76776 −0.225022
\(658\) 0 0
\(659\) −41.8926 −1.63191 −0.815953 0.578119i \(-0.803787\pi\)
−0.815953 + 0.578119i \(0.803787\pi\)
\(660\) 0 0
\(661\) 40.8523 1.58897 0.794485 0.607284i \(-0.207741\pi\)
0.794485 + 0.607284i \(0.207741\pi\)
\(662\) 0 0
\(663\) 3.49264 0.135643
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 34.5208 1.33665
\(668\) 0 0
\(669\) 16.1881 0.625867
\(670\) 0 0
\(671\) −17.2365 −0.665409
\(672\) 0 0
\(673\) 45.2401 1.74388 0.871939 0.489615i \(-0.162863\pi\)
0.871939 + 0.489615i \(0.162863\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.58146 0.137647 0.0688233 0.997629i \(-0.478076\pi\)
0.0688233 + 0.997629i \(0.478076\pi\)
\(678\) 0 0
\(679\) −22.9411 −0.880399
\(680\) 0 0
\(681\) −23.0879 −0.884732
\(682\) 0 0
\(683\) −44.8402 −1.71576 −0.857882 0.513848i \(-0.828220\pi\)
−0.857882 + 0.513848i \(0.828220\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.30886 0.164393
\(688\) 0 0
\(689\) −1.70279 −0.0648712
\(690\) 0 0
\(691\) 18.2891 0.695750 0.347875 0.937541i \(-0.386903\pi\)
0.347875 + 0.937541i \(0.386903\pi\)
\(692\) 0 0
\(693\) 18.2990 0.695121
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.519018 0.0196592
\(698\) 0 0
\(699\) −1.53857 −0.0581942
\(700\) 0 0
\(701\) 36.0667 1.36222 0.681111 0.732180i \(-0.261497\pi\)
0.681111 + 0.732180i \(0.261497\pi\)
\(702\) 0 0
\(703\) 15.3370 0.578447
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 45.6569 1.71710
\(708\) 0 0
\(709\) −11.7769 −0.442291 −0.221146 0.975241i \(-0.570980\pi\)
−0.221146 + 0.975241i \(0.570980\pi\)
\(710\) 0 0
\(711\) −10.0239 −0.375924
\(712\) 0 0
\(713\) −69.0416 −2.58563
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 17.8514 0.666673
\(718\) 0 0
\(719\) −46.7261 −1.74259 −0.871295 0.490759i \(-0.836719\pi\)
−0.871295 + 0.490759i \(0.836719\pi\)
\(720\) 0 0
\(721\) −55.3847 −2.06264
\(722\) 0 0
\(723\) −3.95406 −0.147053
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −37.8038 −1.40207 −0.701033 0.713129i \(-0.747277\pi\)
−0.701033 + 0.713129i \(0.747277\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 10.6127 0.392524
\(732\) 0 0
\(733\) 20.9411 0.773477 0.386739 0.922189i \(-0.373602\pi\)
0.386739 + 0.922189i \(0.373602\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −49.8345 −1.83568
\(738\) 0 0
\(739\) 31.5012 1.15879 0.579396 0.815046i \(-0.303289\pi\)
0.579396 + 0.815046i \(0.303289\pi\)
\(740\) 0 0
\(741\) 2.21016 0.0811922
\(742\) 0 0
\(743\) −2.96483 −0.108769 −0.0543845 0.998520i \(-0.517320\pi\)
−0.0543845 + 0.998520i \(0.517320\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.27171 0.0831176
\(748\) 0 0
\(749\) 3.84566 0.140517
\(750\) 0 0
\(751\) 10.0295 0.365980 0.182990 0.983115i \(-0.441422\pi\)
0.182990 + 0.983115i \(0.441422\pi\)
\(752\) 0 0
\(753\) −3.42284 −0.124735
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 36.4731 1.32564 0.662818 0.748780i \(-0.269360\pi\)
0.662818 + 0.748780i \(0.269360\pi\)
\(758\) 0 0
\(759\) 46.2548 1.67894
\(760\) 0 0
\(761\) −9.88085 −0.358181 −0.179090 0.983833i \(-0.557315\pi\)
−0.179090 + 0.983833i \(0.557315\pi\)
\(762\) 0 0
\(763\) −9.87867 −0.357632
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.46967 −0.233606
\(768\) 0 0
\(769\) 32.6274 1.17657 0.588287 0.808652i \(-0.299802\pi\)
0.588287 + 0.808652i \(0.299802\pi\)
\(770\) 0 0
\(771\) −3.14772 −0.113362
\(772\) 0 0
\(773\) 44.2950 1.59318 0.796591 0.604519i \(-0.206635\pi\)
0.796591 + 0.604519i \(0.206635\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −19.6274 −0.704129
\(778\) 0 0
\(779\) 0.328437 0.0117675
\(780\) 0 0
\(781\) 71.7352 2.56689
\(782\) 0 0
\(783\) −4.82843 −0.172554
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −24.0068 −0.855751 −0.427875 0.903838i \(-0.640738\pi\)
−0.427875 + 0.903838i \(0.640738\pi\)
\(788\) 0 0
\(789\) 13.7144 0.488247
\(790\) 0 0
\(791\) −35.1629 −1.25025
\(792\) 0 0
\(793\) 2.66421 0.0946088
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.4271 −1.50285 −0.751423 0.659821i \(-0.770632\pi\)
−0.751423 + 0.659821i \(0.770632\pi\)
\(798\) 0 0
\(799\) 23.7175 0.839066
\(800\) 0 0
\(801\) −9.21104 −0.325456
\(802\) 0 0
\(803\) 37.3155 1.31683
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9.84316 −0.346495
\(808\) 0 0
\(809\) −12.0495 −0.423637 −0.211819 0.977309i \(-0.567939\pi\)
−0.211819 + 0.977309i \(0.567939\pi\)
\(810\) 0 0
\(811\) −34.5619 −1.21363 −0.606816 0.794842i \(-0.707554\pi\)
−0.606816 + 0.794842i \(0.707554\pi\)
\(812\) 0 0
\(813\) 2.86216 0.100380
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.71575 0.234954
\(818\) 0 0
\(819\) −2.82843 −0.0988332
\(820\) 0 0
\(821\) −1.92119 −0.0670500 −0.0335250 0.999438i \(-0.510673\pi\)
−0.0335250 + 0.999438i \(0.510673\pi\)
\(822\) 0 0
\(823\) 36.9246 1.28711 0.643556 0.765399i \(-0.277458\pi\)
0.643556 + 0.765399i \(0.277458\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.9501 −0.728507 −0.364254 0.931300i \(-0.618676\pi\)
−0.364254 + 0.931300i \(0.618676\pi\)
\(828\) 0 0
\(829\) −3.55255 −0.123385 −0.0616926 0.998095i \(-0.519650\pi\)
−0.0616926 + 0.998095i \(0.519650\pi\)
\(830\) 0 0
\(831\) 6.24389 0.216598
\(832\) 0 0
\(833\) −3.49264 −0.121013
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.65685 0.333790
\(838\) 0 0
\(839\) −12.2768 −0.423841 −0.211920 0.977287i \(-0.567972\pi\)
−0.211920 + 0.977287i \(0.567972\pi\)
\(840\) 0 0
\(841\) −5.68629 −0.196079
\(842\) 0 0
\(843\) 31.3869 1.08102
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −87.2756 −2.99882
\(848\) 0 0
\(849\) 2.56496 0.0880291
\(850\) 0 0
\(851\) −49.6127 −1.70070
\(852\) 0 0
\(853\) 10.6734 0.365449 0.182724 0.983164i \(-0.441508\pi\)
0.182724 + 0.983164i \(0.441508\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −54.5324 −1.86279 −0.931396 0.364006i \(-0.881409\pi\)
−0.931396 + 0.364006i \(0.881409\pi\)
\(858\) 0 0
\(859\) −45.6218 −1.55660 −0.778298 0.627894i \(-0.783917\pi\)
−0.778298 + 0.627894i \(0.783917\pi\)
\(860\) 0 0
\(861\) −0.420314 −0.0143243
\(862\) 0 0
\(863\) 18.1798 0.618849 0.309424 0.950924i \(-0.399864\pi\)
0.309424 + 0.950924i \(0.399864\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 4.80150 0.163067
\(868\) 0 0
\(869\) 64.8510 2.19992
\(870\) 0 0
\(871\) 7.70279 0.260999
\(872\) 0 0
\(873\) 8.11091 0.274513
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 23.1611 0.782096 0.391048 0.920370i \(-0.372113\pi\)
0.391048 + 0.920370i \(0.372113\pi\)
\(878\) 0 0
\(879\) −0.834895 −0.0281603
\(880\) 0 0
\(881\) 16.7358 0.563843 0.281921 0.959438i \(-0.409028\pi\)
0.281921 + 0.959438i \(0.409028\pi\)
\(882\) 0 0
\(883\) −20.3959 −0.686377 −0.343189 0.939267i \(-0.611507\pi\)
−0.343189 + 0.939267i \(0.611507\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −58.7395 −1.97228 −0.986140 0.165912i \(-0.946943\pi\)
−0.986140 + 0.165912i \(0.946943\pi\)
\(888\) 0 0
\(889\) 52.6654 1.76634
\(890\) 0 0
\(891\) −6.46967 −0.216742
\(892\) 0 0
\(893\) 15.0086 0.502243
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −7.14949 −0.238715
\(898\) 0 0
\(899\) −46.6274 −1.55511
\(900\) 0 0
\(901\) 5.94723 0.198131
\(902\) 0 0
\(903\) −8.59441 −0.286004
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 17.9853 0.597192 0.298596 0.954380i \(-0.403482\pi\)
0.298596 + 0.954380i \(0.403482\pi\)
\(908\) 0 0
\(909\) −16.1421 −0.535401
\(910\) 0 0
\(911\) 55.0269 1.82312 0.911561 0.411165i \(-0.134878\pi\)
0.911561 + 0.411165i \(0.134878\pi\)
\(912\) 0 0
\(913\) −14.6972 −0.486407
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.12488 0.0701697
\(918\) 0 0
\(919\) 1.00913 0.0332880 0.0166440 0.999861i \(-0.494702\pi\)
0.0166440 + 0.999861i \(0.494702\pi\)
\(920\) 0 0
\(921\) −17.7556 −0.585066
\(922\) 0 0
\(923\) −11.0879 −0.364964
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 19.5815 0.643139
\(928\) 0 0
\(929\) −23.1407 −0.759222 −0.379611 0.925146i \(-0.623942\pi\)
−0.379611 + 0.925146i \(0.623942\pi\)
\(930\) 0 0
\(931\) −2.21016 −0.0724350
\(932\) 0 0
\(933\) 1.35965 0.0445128
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8.72667 0.285088 0.142544 0.989788i \(-0.454472\pi\)
0.142544 + 0.989788i \(0.454472\pi\)
\(938\) 0 0
\(939\) −7.75611 −0.253111
\(940\) 0 0
\(941\) 5.24965 0.171134 0.0855668 0.996332i \(-0.472730\pi\)
0.0855668 + 0.996332i \(0.472730\pi\)
\(942\) 0 0
\(943\) −1.06244 −0.0345978
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17.0420 0.553791 0.276895 0.960900i \(-0.410694\pi\)
0.276895 + 0.960900i \(0.410694\pi\)
\(948\) 0 0
\(949\) −5.76776 −0.187229
\(950\) 0 0
\(951\) −9.38514 −0.304334
\(952\) 0 0
\(953\) −5.16243 −0.167227 −0.0836137 0.996498i \(-0.526646\pi\)
−0.0836137 + 0.996498i \(0.526646\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 31.2383 1.00979
\(958\) 0 0
\(959\) 3.07715 0.0993663
\(960\) 0 0
\(961\) 62.2548 2.00822
\(962\) 0 0
\(963\) −1.35965 −0.0438140
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −40.3657 −1.29807 −0.649037 0.760757i \(-0.724828\pi\)
−0.649037 + 0.760757i \(0.724828\pi\)
\(968\) 0 0
\(969\) −7.71927 −0.247979
\(970\) 0 0
\(971\) −20.2322 −0.649283 −0.324642 0.945837i \(-0.605244\pi\)
−0.324642 + 0.945837i \(0.605244\pi\)
\(972\) 0 0
\(973\) −1.18883 −0.0381121
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.4034 0.972691 0.486346 0.873766i \(-0.338330\pi\)
0.486346 + 0.873766i \(0.338330\pi\)
\(978\) 0 0
\(979\) 59.5924 1.90458
\(980\) 0 0
\(981\) 3.49264 0.111511
\(982\) 0 0
\(983\) 50.4250 1.60831 0.804153 0.594422i \(-0.202619\pi\)
0.804153 + 0.594422i \(0.202619\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −19.2071 −0.611368
\(988\) 0 0
\(989\) −21.7243 −0.690793
\(990\) 0 0
\(991\) 54.1005 1.71856 0.859279 0.511507i \(-0.170913\pi\)
0.859279 + 0.511507i \(0.170913\pi\)
\(992\) 0 0
\(993\) −16.0576 −0.509572
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −39.3921 −1.24756 −0.623780 0.781600i \(-0.714404\pi\)
−0.623780 + 0.781600i \(0.714404\pi\)
\(998\) 0 0
\(999\) 6.93933 0.219551
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 7800.2.a.bv.1.1 4
5.2 odd 4 1560.2.l.e.1249.8 yes 8
5.3 odd 4 1560.2.l.e.1249.4 8
5.4 even 2 7800.2.a.bw.1.3 4
15.2 even 4 4680.2.l.f.2809.1 8
15.8 even 4 4680.2.l.f.2809.2 8
20.3 even 4 3120.2.l.o.1249.8 8
20.7 even 4 3120.2.l.o.1249.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.e.1249.4 8 5.3 odd 4
1560.2.l.e.1249.8 yes 8 5.2 odd 4
3120.2.l.o.1249.4 8 20.7 even 4
3120.2.l.o.1249.8 8 20.3 even 4
4680.2.l.f.2809.1 8 15.2 even 4
4680.2.l.f.2809.2 8 15.8 even 4
7800.2.a.bv.1.1 4 1.1 even 1 trivial
7800.2.a.bw.1.3 4 5.4 even 2