Properties

Label 8016.2.a.be.1.2
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 0
Dimension 11
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.11942\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.11942 q^{5} +0.802640 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.11942 q^{5} +0.802640 q^{7} +1.00000 q^{9} +1.53063 q^{11} +6.15404 q^{13} -2.11942 q^{15} +2.02477 q^{17} +8.09372 q^{19} +0.802640 q^{21} +1.69737 q^{23} -0.508068 q^{25} +1.00000 q^{27} +8.39635 q^{29} -1.83232 q^{31} +1.53063 q^{33} -1.70113 q^{35} -9.93315 q^{37} +6.15404 q^{39} -2.89174 q^{41} -2.94539 q^{43} -2.11942 q^{45} +7.81191 q^{47} -6.35577 q^{49} +2.02477 q^{51} +9.25602 q^{53} -3.24405 q^{55} +8.09372 q^{57} -5.76308 q^{59} -0.0936477 q^{61} +0.802640 q^{63} -13.0430 q^{65} +8.66806 q^{67} +1.69737 q^{69} +8.00704 q^{71} +1.52554 q^{73} -0.508068 q^{75} +1.22855 q^{77} -15.5706 q^{79} +1.00000 q^{81} -13.8255 q^{83} -4.29133 q^{85} +8.39635 q^{87} +11.9663 q^{89} +4.93948 q^{91} -1.83232 q^{93} -17.1540 q^{95} -13.7852 q^{97} +1.53063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.11942 −0.947832 −0.473916 0.880570i \(-0.657160\pi\)
−0.473916 + 0.880570i \(0.657160\pi\)
\(6\) 0 0
\(7\) 0.802640 0.303369 0.151685 0.988429i \(-0.451530\pi\)
0.151685 + 0.988429i \(0.451530\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.53063 0.461503 0.230752 0.973013i \(-0.425882\pi\)
0.230752 + 0.973013i \(0.425882\pi\)
\(12\) 0 0
\(13\) 6.15404 1.70682 0.853412 0.521236i \(-0.174529\pi\)
0.853412 + 0.521236i \(0.174529\pi\)
\(14\) 0 0
\(15\) −2.11942 −0.547231
\(16\) 0 0
\(17\) 2.02477 0.491079 0.245539 0.969387i \(-0.421035\pi\)
0.245539 + 0.969387i \(0.421035\pi\)
\(18\) 0 0
\(19\) 8.09372 1.85683 0.928414 0.371548i \(-0.121173\pi\)
0.928414 + 0.371548i \(0.121173\pi\)
\(20\) 0 0
\(21\) 0.802640 0.175150
\(22\) 0 0
\(23\) 1.69737 0.353927 0.176963 0.984217i \(-0.443373\pi\)
0.176963 + 0.984217i \(0.443373\pi\)
\(24\) 0 0
\(25\) −0.508068 −0.101614
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 8.39635 1.55916 0.779582 0.626301i \(-0.215432\pi\)
0.779582 + 0.626301i \(0.215432\pi\)
\(30\) 0 0
\(31\) −1.83232 −0.329095 −0.164548 0.986369i \(-0.552616\pi\)
−0.164548 + 0.986369i \(0.552616\pi\)
\(32\) 0 0
\(33\) 1.53063 0.266449
\(34\) 0 0
\(35\) −1.70113 −0.287543
\(36\) 0 0
\(37\) −9.93315 −1.63300 −0.816500 0.577345i \(-0.804089\pi\)
−0.816500 + 0.577345i \(0.804089\pi\)
\(38\) 0 0
\(39\) 6.15404 0.985436
\(40\) 0 0
\(41\) −2.89174 −0.451614 −0.225807 0.974172i \(-0.572502\pi\)
−0.225807 + 0.974172i \(0.572502\pi\)
\(42\) 0 0
\(43\) −2.94539 −0.449168 −0.224584 0.974455i \(-0.572102\pi\)
−0.224584 + 0.974455i \(0.572102\pi\)
\(44\) 0 0
\(45\) −2.11942 −0.315944
\(46\) 0 0
\(47\) 7.81191 1.13948 0.569742 0.821823i \(-0.307043\pi\)
0.569742 + 0.821823i \(0.307043\pi\)
\(48\) 0 0
\(49\) −6.35577 −0.907967
\(50\) 0 0
\(51\) 2.02477 0.283524
\(52\) 0 0
\(53\) 9.25602 1.27141 0.635706 0.771931i \(-0.280709\pi\)
0.635706 + 0.771931i \(0.280709\pi\)
\(54\) 0 0
\(55\) −3.24405 −0.437428
\(56\) 0 0
\(57\) 8.09372 1.07204
\(58\) 0 0
\(59\) −5.76308 −0.750289 −0.375144 0.926966i \(-0.622407\pi\)
−0.375144 + 0.926966i \(0.622407\pi\)
\(60\) 0 0
\(61\) −0.0936477 −0.0119904 −0.00599518 0.999982i \(-0.501908\pi\)
−0.00599518 + 0.999982i \(0.501908\pi\)
\(62\) 0 0
\(63\) 0.802640 0.101123
\(64\) 0 0
\(65\) −13.0430 −1.61778
\(66\) 0 0
\(67\) 8.66806 1.05897 0.529486 0.848319i \(-0.322385\pi\)
0.529486 + 0.848319i \(0.322385\pi\)
\(68\) 0 0
\(69\) 1.69737 0.204340
\(70\) 0 0
\(71\) 8.00704 0.950261 0.475130 0.879915i \(-0.342401\pi\)
0.475130 + 0.879915i \(0.342401\pi\)
\(72\) 0 0
\(73\) 1.52554 0.178552 0.0892758 0.996007i \(-0.471545\pi\)
0.0892758 + 0.996007i \(0.471545\pi\)
\(74\) 0 0
\(75\) −0.508068 −0.0586667
\(76\) 0 0
\(77\) 1.22855 0.140006
\(78\) 0 0
\(79\) −15.5706 −1.75183 −0.875917 0.482461i \(-0.839743\pi\)
−0.875917 + 0.482461i \(0.839743\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.8255 −1.51755 −0.758775 0.651352i \(-0.774202\pi\)
−0.758775 + 0.651352i \(0.774202\pi\)
\(84\) 0 0
\(85\) −4.29133 −0.465460
\(86\) 0 0
\(87\) 8.39635 0.900183
\(88\) 0 0
\(89\) 11.9663 1.26842 0.634211 0.773160i \(-0.281325\pi\)
0.634211 + 0.773160i \(0.281325\pi\)
\(90\) 0 0
\(91\) 4.93948 0.517798
\(92\) 0 0
\(93\) −1.83232 −0.190003
\(94\) 0 0
\(95\) −17.1540 −1.75996
\(96\) 0 0
\(97\) −13.7852 −1.39968 −0.699840 0.714300i \(-0.746745\pi\)
−0.699840 + 0.714300i \(0.746745\pi\)
\(98\) 0 0
\(99\) 1.53063 0.153834
\(100\) 0 0
\(101\) 13.2301 1.31644 0.658220 0.752825i \(-0.271309\pi\)
0.658220 + 0.752825i \(0.271309\pi\)
\(102\) 0 0
\(103\) 9.58267 0.944209 0.472104 0.881543i \(-0.343495\pi\)
0.472104 + 0.881543i \(0.343495\pi\)
\(104\) 0 0
\(105\) −1.70113 −0.166013
\(106\) 0 0
\(107\) −3.19020 −0.308408 −0.154204 0.988039i \(-0.549281\pi\)
−0.154204 + 0.988039i \(0.549281\pi\)
\(108\) 0 0
\(109\) −13.5473 −1.29760 −0.648800 0.760959i \(-0.724729\pi\)
−0.648800 + 0.760959i \(0.724729\pi\)
\(110\) 0 0
\(111\) −9.93315 −0.942813
\(112\) 0 0
\(113\) 6.42224 0.604154 0.302077 0.953284i \(-0.402320\pi\)
0.302077 + 0.953284i \(0.402320\pi\)
\(114\) 0 0
\(115\) −3.59744 −0.335463
\(116\) 0 0
\(117\) 6.15404 0.568942
\(118\) 0 0
\(119\) 1.62516 0.148978
\(120\) 0 0
\(121\) −8.65716 −0.787015
\(122\) 0 0
\(123\) −2.89174 −0.260740
\(124\) 0 0
\(125\) 11.6739 1.04415
\(126\) 0 0
\(127\) −6.93176 −0.615094 −0.307547 0.951533i \(-0.599508\pi\)
−0.307547 + 0.951533i \(0.599508\pi\)
\(128\) 0 0
\(129\) −2.94539 −0.259327
\(130\) 0 0
\(131\) 5.62848 0.491762 0.245881 0.969300i \(-0.420923\pi\)
0.245881 + 0.969300i \(0.420923\pi\)
\(132\) 0 0
\(133\) 6.49634 0.563304
\(134\) 0 0
\(135\) −2.11942 −0.182410
\(136\) 0 0
\(137\) 1.30884 0.111822 0.0559109 0.998436i \(-0.482194\pi\)
0.0559109 + 0.998436i \(0.482194\pi\)
\(138\) 0 0
\(139\) −16.9293 −1.43593 −0.717963 0.696082i \(-0.754925\pi\)
−0.717963 + 0.696082i \(0.754925\pi\)
\(140\) 0 0
\(141\) 7.81191 0.657882
\(142\) 0 0
\(143\) 9.41959 0.787705
\(144\) 0 0
\(145\) −17.7954 −1.47783
\(146\) 0 0
\(147\) −6.35577 −0.524215
\(148\) 0 0
\(149\) 23.9654 1.96332 0.981660 0.190642i \(-0.0610570\pi\)
0.981660 + 0.190642i \(0.0610570\pi\)
\(150\) 0 0
\(151\) −4.74051 −0.385777 −0.192888 0.981221i \(-0.561786\pi\)
−0.192888 + 0.981221i \(0.561786\pi\)
\(152\) 0 0
\(153\) 2.02477 0.163693
\(154\) 0 0
\(155\) 3.88346 0.311927
\(156\) 0 0
\(157\) 12.2918 0.980991 0.490495 0.871444i \(-0.336816\pi\)
0.490495 + 0.871444i \(0.336816\pi\)
\(158\) 0 0
\(159\) 9.25602 0.734050
\(160\) 0 0
\(161\) 1.36238 0.107371
\(162\) 0 0
\(163\) −14.4990 −1.13565 −0.567823 0.823151i \(-0.692214\pi\)
−0.567823 + 0.823151i \(0.692214\pi\)
\(164\) 0 0
\(165\) −3.24405 −0.252549
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 24.8723 1.91325
\(170\) 0 0
\(171\) 8.09372 0.618943
\(172\) 0 0
\(173\) −14.2287 −1.08179 −0.540893 0.841091i \(-0.681914\pi\)
−0.540893 + 0.841091i \(0.681914\pi\)
\(174\) 0 0
\(175\) −0.407796 −0.0308265
\(176\) 0 0
\(177\) −5.76308 −0.433180
\(178\) 0 0
\(179\) −5.46854 −0.408738 −0.204369 0.978894i \(-0.565514\pi\)
−0.204369 + 0.978894i \(0.565514\pi\)
\(180\) 0 0
\(181\) 8.71174 0.647538 0.323769 0.946136i \(-0.395050\pi\)
0.323769 + 0.946136i \(0.395050\pi\)
\(182\) 0 0
\(183\) −0.0936477 −0.00692263
\(184\) 0 0
\(185\) 21.0525 1.54781
\(186\) 0 0
\(187\) 3.09918 0.226634
\(188\) 0 0
\(189\) 0.802640 0.0583834
\(190\) 0 0
\(191\) 6.84326 0.495161 0.247580 0.968867i \(-0.420365\pi\)
0.247580 + 0.968867i \(0.420365\pi\)
\(192\) 0 0
\(193\) 11.6905 0.841499 0.420750 0.907177i \(-0.361767\pi\)
0.420750 + 0.907177i \(0.361767\pi\)
\(194\) 0 0
\(195\) −13.0430 −0.934028
\(196\) 0 0
\(197\) 20.4537 1.45727 0.728633 0.684904i \(-0.240156\pi\)
0.728633 + 0.684904i \(0.240156\pi\)
\(198\) 0 0
\(199\) −19.5826 −1.38817 −0.694086 0.719892i \(-0.744191\pi\)
−0.694086 + 0.719892i \(0.744191\pi\)
\(200\) 0 0
\(201\) 8.66806 0.611398
\(202\) 0 0
\(203\) 6.73924 0.473002
\(204\) 0 0
\(205\) 6.12881 0.428055
\(206\) 0 0
\(207\) 1.69737 0.117976
\(208\) 0 0
\(209\) 12.3885 0.856932
\(210\) 0 0
\(211\) 12.0070 0.826598 0.413299 0.910595i \(-0.364376\pi\)
0.413299 + 0.910595i \(0.364376\pi\)
\(212\) 0 0
\(213\) 8.00704 0.548633
\(214\) 0 0
\(215\) 6.24252 0.425736
\(216\) 0 0
\(217\) −1.47070 −0.0998373
\(218\) 0 0
\(219\) 1.52554 0.103087
\(220\) 0 0
\(221\) 12.4605 0.838185
\(222\) 0 0
\(223\) −20.0988 −1.34591 −0.672957 0.739681i \(-0.734976\pi\)
−0.672957 + 0.739681i \(0.734976\pi\)
\(224\) 0 0
\(225\) −0.508068 −0.0338712
\(226\) 0 0
\(227\) −14.1963 −0.942242 −0.471121 0.882068i \(-0.656151\pi\)
−0.471121 + 0.882068i \(0.656151\pi\)
\(228\) 0 0
\(229\) 19.7750 1.30677 0.653386 0.757025i \(-0.273348\pi\)
0.653386 + 0.757025i \(0.273348\pi\)
\(230\) 0 0
\(231\) 1.22855 0.0808324
\(232\) 0 0
\(233\) 9.37536 0.614200 0.307100 0.951677i \(-0.400641\pi\)
0.307100 + 0.951677i \(0.400641\pi\)
\(234\) 0 0
\(235\) −16.5567 −1.08004
\(236\) 0 0
\(237\) −15.5706 −1.01142
\(238\) 0 0
\(239\) 11.0467 0.714551 0.357276 0.933999i \(-0.383706\pi\)
0.357276 + 0.933999i \(0.383706\pi\)
\(240\) 0 0
\(241\) 3.14465 0.202565 0.101282 0.994858i \(-0.467705\pi\)
0.101282 + 0.994858i \(0.467705\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 13.4705 0.860601
\(246\) 0 0
\(247\) 49.8091 3.16928
\(248\) 0 0
\(249\) −13.8255 −0.876158
\(250\) 0 0
\(251\) −19.4249 −1.22609 −0.613044 0.790049i \(-0.710055\pi\)
−0.613044 + 0.790049i \(0.710055\pi\)
\(252\) 0 0
\(253\) 2.59806 0.163338
\(254\) 0 0
\(255\) −4.29133 −0.268734
\(256\) 0 0
\(257\) 24.3783 1.52068 0.760338 0.649528i \(-0.225033\pi\)
0.760338 + 0.649528i \(0.225033\pi\)
\(258\) 0 0
\(259\) −7.97274 −0.495402
\(260\) 0 0
\(261\) 8.39635 0.519721
\(262\) 0 0
\(263\) 19.1381 1.18010 0.590051 0.807366i \(-0.299107\pi\)
0.590051 + 0.807366i \(0.299107\pi\)
\(264\) 0 0
\(265\) −19.6174 −1.20509
\(266\) 0 0
\(267\) 11.9663 0.732324
\(268\) 0 0
\(269\) −31.8583 −1.94244 −0.971218 0.238192i \(-0.923445\pi\)
−0.971218 + 0.238192i \(0.923445\pi\)
\(270\) 0 0
\(271\) 27.6866 1.68184 0.840922 0.541157i \(-0.182014\pi\)
0.840922 + 0.541157i \(0.182014\pi\)
\(272\) 0 0
\(273\) 4.93948 0.298951
\(274\) 0 0
\(275\) −0.777666 −0.0468951
\(276\) 0 0
\(277\) 16.5531 0.994582 0.497291 0.867584i \(-0.334328\pi\)
0.497291 + 0.867584i \(0.334328\pi\)
\(278\) 0 0
\(279\) −1.83232 −0.109698
\(280\) 0 0
\(281\) −16.1221 −0.961766 −0.480883 0.876785i \(-0.659684\pi\)
−0.480883 + 0.876785i \(0.659684\pi\)
\(282\) 0 0
\(283\) 15.4620 0.919118 0.459559 0.888147i \(-0.348008\pi\)
0.459559 + 0.888147i \(0.348008\pi\)
\(284\) 0 0
\(285\) −17.1540 −1.01611
\(286\) 0 0
\(287\) −2.32103 −0.137006
\(288\) 0 0
\(289\) −12.9003 −0.758842
\(290\) 0 0
\(291\) −13.7852 −0.808105
\(292\) 0 0
\(293\) −13.3824 −0.781806 −0.390903 0.920432i \(-0.627837\pi\)
−0.390903 + 0.920432i \(0.627837\pi\)
\(294\) 0 0
\(295\) 12.2144 0.711148
\(296\) 0 0
\(297\) 1.53063 0.0888164
\(298\) 0 0
\(299\) 10.4457 0.604091
\(300\) 0 0
\(301\) −2.36409 −0.136264
\(302\) 0 0
\(303\) 13.2301 0.760048
\(304\) 0 0
\(305\) 0.198479 0.0113648
\(306\) 0 0
\(307\) 10.3905 0.593018 0.296509 0.955030i \(-0.404178\pi\)
0.296509 + 0.955030i \(0.404178\pi\)
\(308\) 0 0
\(309\) 9.58267 0.545139
\(310\) 0 0
\(311\) −5.04038 −0.285814 −0.142907 0.989736i \(-0.545645\pi\)
−0.142907 + 0.989736i \(0.545645\pi\)
\(312\) 0 0
\(313\) 12.2609 0.693025 0.346513 0.938045i \(-0.387366\pi\)
0.346513 + 0.938045i \(0.387366\pi\)
\(314\) 0 0
\(315\) −1.70113 −0.0958477
\(316\) 0 0
\(317\) −15.7166 −0.882731 −0.441365 0.897327i \(-0.645506\pi\)
−0.441365 + 0.897327i \(0.645506\pi\)
\(318\) 0 0
\(319\) 12.8517 0.719559
\(320\) 0 0
\(321\) −3.19020 −0.178059
\(322\) 0 0
\(323\) 16.3879 0.911848
\(324\) 0 0
\(325\) −3.12668 −0.173437
\(326\) 0 0
\(327\) −13.5473 −0.749169
\(328\) 0 0
\(329\) 6.27015 0.345685
\(330\) 0 0
\(331\) 18.2687 1.00414 0.502069 0.864827i \(-0.332572\pi\)
0.502069 + 0.864827i \(0.332572\pi\)
\(332\) 0 0
\(333\) −9.93315 −0.544334
\(334\) 0 0
\(335\) −18.3712 −1.00373
\(336\) 0 0
\(337\) 20.6321 1.12390 0.561951 0.827171i \(-0.310051\pi\)
0.561951 + 0.827171i \(0.310051\pi\)
\(338\) 0 0
\(339\) 6.42224 0.348808
\(340\) 0 0
\(341\) −2.80462 −0.151878
\(342\) 0 0
\(343\) −10.7199 −0.578819
\(344\) 0 0
\(345\) −3.59744 −0.193680
\(346\) 0 0
\(347\) −7.45323 −0.400110 −0.200055 0.979785i \(-0.564112\pi\)
−0.200055 + 0.979785i \(0.564112\pi\)
\(348\) 0 0
\(349\) 20.1869 1.08058 0.540289 0.841480i \(-0.318315\pi\)
0.540289 + 0.841480i \(0.318315\pi\)
\(350\) 0 0
\(351\) 6.15404 0.328479
\(352\) 0 0
\(353\) 5.40011 0.287419 0.143709 0.989620i \(-0.454097\pi\)
0.143709 + 0.989620i \(0.454097\pi\)
\(354\) 0 0
\(355\) −16.9703 −0.900688
\(356\) 0 0
\(357\) 1.62516 0.0860126
\(358\) 0 0
\(359\) −14.1097 −0.744680 −0.372340 0.928096i \(-0.621445\pi\)
−0.372340 + 0.928096i \(0.621445\pi\)
\(360\) 0 0
\(361\) 46.5084 2.44781
\(362\) 0 0
\(363\) −8.65716 −0.454383
\(364\) 0 0
\(365\) −3.23327 −0.169237
\(366\) 0 0
\(367\) −8.40423 −0.438697 −0.219349 0.975647i \(-0.570393\pi\)
−0.219349 + 0.975647i \(0.570393\pi\)
\(368\) 0 0
\(369\) −2.89174 −0.150538
\(370\) 0 0
\(371\) 7.42925 0.385707
\(372\) 0 0
\(373\) −23.3605 −1.20956 −0.604780 0.796393i \(-0.706739\pi\)
−0.604780 + 0.796393i \(0.706739\pi\)
\(374\) 0 0
\(375\) 11.6739 0.602837
\(376\) 0 0
\(377\) 51.6715 2.66122
\(378\) 0 0
\(379\) −35.8583 −1.84192 −0.920959 0.389659i \(-0.872593\pi\)
−0.920959 + 0.389659i \(0.872593\pi\)
\(380\) 0 0
\(381\) −6.93176 −0.355125
\(382\) 0 0
\(383\) 1.69504 0.0866123 0.0433061 0.999062i \(-0.486211\pi\)
0.0433061 + 0.999062i \(0.486211\pi\)
\(384\) 0 0
\(385\) −2.60380 −0.132702
\(386\) 0 0
\(387\) −2.94539 −0.149723
\(388\) 0 0
\(389\) 14.2244 0.721203 0.360602 0.932720i \(-0.382571\pi\)
0.360602 + 0.932720i \(0.382571\pi\)
\(390\) 0 0
\(391\) 3.43679 0.173806
\(392\) 0 0
\(393\) 5.62848 0.283919
\(394\) 0 0
\(395\) 33.0007 1.66045
\(396\) 0 0
\(397\) −13.0556 −0.655240 −0.327620 0.944810i \(-0.606247\pi\)
−0.327620 + 0.944810i \(0.606247\pi\)
\(398\) 0 0
\(399\) 6.49634 0.325224
\(400\) 0 0
\(401\) 32.8074 1.63832 0.819162 0.573563i \(-0.194439\pi\)
0.819162 + 0.573563i \(0.194439\pi\)
\(402\) 0 0
\(403\) −11.2762 −0.561708
\(404\) 0 0
\(405\) −2.11942 −0.105315
\(406\) 0 0
\(407\) −15.2040 −0.753635
\(408\) 0 0
\(409\) −15.4482 −0.763865 −0.381932 0.924190i \(-0.624741\pi\)
−0.381932 + 0.924190i \(0.624741\pi\)
\(410\) 0 0
\(411\) 1.30884 0.0645603
\(412\) 0 0
\(413\) −4.62567 −0.227615
\(414\) 0 0
\(415\) 29.3021 1.43838
\(416\) 0 0
\(417\) −16.9293 −0.829032
\(418\) 0 0
\(419\) 1.69199 0.0826592 0.0413296 0.999146i \(-0.486841\pi\)
0.0413296 + 0.999146i \(0.486841\pi\)
\(420\) 0 0
\(421\) 28.1615 1.37251 0.686254 0.727362i \(-0.259254\pi\)
0.686254 + 0.727362i \(0.259254\pi\)
\(422\) 0 0
\(423\) 7.81191 0.379828
\(424\) 0 0
\(425\) −1.02872 −0.0499003
\(426\) 0 0
\(427\) −0.0751653 −0.00363750
\(428\) 0 0
\(429\) 9.41959 0.454782
\(430\) 0 0
\(431\) 15.1892 0.731636 0.365818 0.930686i \(-0.380789\pi\)
0.365818 + 0.930686i \(0.380789\pi\)
\(432\) 0 0
\(433\) −8.76398 −0.421170 −0.210585 0.977576i \(-0.567537\pi\)
−0.210585 + 0.977576i \(0.567537\pi\)
\(434\) 0 0
\(435\) −17.7954 −0.853223
\(436\) 0 0
\(437\) 13.7381 0.657181
\(438\) 0 0
\(439\) 32.6631 1.55892 0.779462 0.626450i \(-0.215493\pi\)
0.779462 + 0.626450i \(0.215493\pi\)
\(440\) 0 0
\(441\) −6.35577 −0.302656
\(442\) 0 0
\(443\) −10.5636 −0.501894 −0.250947 0.968001i \(-0.580742\pi\)
−0.250947 + 0.968001i \(0.580742\pi\)
\(444\) 0 0
\(445\) −25.3615 −1.20225
\(446\) 0 0
\(447\) 23.9654 1.13352
\(448\) 0 0
\(449\) 4.46969 0.210938 0.105469 0.994423i \(-0.466366\pi\)
0.105469 + 0.994423i \(0.466366\pi\)
\(450\) 0 0
\(451\) −4.42620 −0.208421
\(452\) 0 0
\(453\) −4.74051 −0.222728
\(454\) 0 0
\(455\) −10.4688 −0.490786
\(456\) 0 0
\(457\) 22.9914 1.07549 0.537745 0.843107i \(-0.319276\pi\)
0.537745 + 0.843107i \(0.319276\pi\)
\(458\) 0 0
\(459\) 2.02477 0.0945081
\(460\) 0 0
\(461\) 7.77260 0.362006 0.181003 0.983483i \(-0.442066\pi\)
0.181003 + 0.983483i \(0.442066\pi\)
\(462\) 0 0
\(463\) 18.5847 0.863705 0.431853 0.901944i \(-0.357860\pi\)
0.431853 + 0.901944i \(0.357860\pi\)
\(464\) 0 0
\(465\) 3.88346 0.180091
\(466\) 0 0
\(467\) −16.4040 −0.759088 −0.379544 0.925174i \(-0.623919\pi\)
−0.379544 + 0.925174i \(0.623919\pi\)
\(468\) 0 0
\(469\) 6.95733 0.321260
\(470\) 0 0
\(471\) 12.2918 0.566375
\(472\) 0 0
\(473\) −4.50832 −0.207293
\(474\) 0 0
\(475\) −4.11217 −0.188679
\(476\) 0 0
\(477\) 9.25602 0.423804
\(478\) 0 0
\(479\) −4.17459 −0.190742 −0.0953709 0.995442i \(-0.530404\pi\)
−0.0953709 + 0.995442i \(0.530404\pi\)
\(480\) 0 0
\(481\) −61.1291 −2.78725
\(482\) 0 0
\(483\) 1.36238 0.0619904
\(484\) 0 0
\(485\) 29.2167 1.32666
\(486\) 0 0
\(487\) 8.01182 0.363050 0.181525 0.983386i \(-0.441897\pi\)
0.181525 + 0.983386i \(0.441897\pi\)
\(488\) 0 0
\(489\) −14.4990 −0.655666
\(490\) 0 0
\(491\) −19.5821 −0.883730 −0.441865 0.897082i \(-0.645683\pi\)
−0.441865 + 0.897082i \(0.645683\pi\)
\(492\) 0 0
\(493\) 17.0007 0.765672
\(494\) 0 0
\(495\) −3.24405 −0.145809
\(496\) 0 0
\(497\) 6.42677 0.288280
\(498\) 0 0
\(499\) −1.25191 −0.0560432 −0.0280216 0.999607i \(-0.508921\pi\)
−0.0280216 + 0.999607i \(0.508921\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 20.5341 0.915572 0.457786 0.889062i \(-0.348643\pi\)
0.457786 + 0.889062i \(0.348643\pi\)
\(504\) 0 0
\(505\) −28.0400 −1.24777
\(506\) 0 0
\(507\) 24.8723 1.10462
\(508\) 0 0
\(509\) −21.7060 −0.962102 −0.481051 0.876693i \(-0.659745\pi\)
−0.481051 + 0.876693i \(0.659745\pi\)
\(510\) 0 0
\(511\) 1.22446 0.0541670
\(512\) 0 0
\(513\) 8.09372 0.357347
\(514\) 0 0
\(515\) −20.3097 −0.894952
\(516\) 0 0
\(517\) 11.9572 0.525876
\(518\) 0 0
\(519\) −14.2287 −0.624570
\(520\) 0 0
\(521\) 31.3324 1.37270 0.686350 0.727272i \(-0.259212\pi\)
0.686350 + 0.727272i \(0.259212\pi\)
\(522\) 0 0
\(523\) −13.8582 −0.605979 −0.302989 0.952994i \(-0.597985\pi\)
−0.302989 + 0.952994i \(0.597985\pi\)
\(524\) 0 0
\(525\) −0.407796 −0.0177977
\(526\) 0 0
\(527\) −3.71003 −0.161612
\(528\) 0 0
\(529\) −20.1189 −0.874736
\(530\) 0 0
\(531\) −5.76308 −0.250096
\(532\) 0 0
\(533\) −17.7959 −0.770826
\(534\) 0 0
\(535\) 6.76136 0.292319
\(536\) 0 0
\(537\) −5.46854 −0.235985
\(538\) 0 0
\(539\) −9.72835 −0.419030
\(540\) 0 0
\(541\) 8.41986 0.361998 0.180999 0.983483i \(-0.442067\pi\)
0.180999 + 0.983483i \(0.442067\pi\)
\(542\) 0 0
\(543\) 8.71174 0.373856
\(544\) 0 0
\(545\) 28.7125 1.22991
\(546\) 0 0
\(547\) 32.8513 1.40462 0.702310 0.711871i \(-0.252152\pi\)
0.702310 + 0.711871i \(0.252152\pi\)
\(548\) 0 0
\(549\) −0.0936477 −0.00399679
\(550\) 0 0
\(551\) 67.9577 2.89510
\(552\) 0 0
\(553\) −12.4976 −0.531453
\(554\) 0 0
\(555\) 21.0525 0.893629
\(556\) 0 0
\(557\) −41.3326 −1.75132 −0.875659 0.482929i \(-0.839573\pi\)
−0.875659 + 0.482929i \(0.839573\pi\)
\(558\) 0 0
\(559\) −18.1261 −0.766651
\(560\) 0 0
\(561\) 3.09918 0.130847
\(562\) 0 0
\(563\) −29.5494 −1.24536 −0.622680 0.782477i \(-0.713956\pi\)
−0.622680 + 0.782477i \(0.713956\pi\)
\(564\) 0 0
\(565\) −13.6114 −0.572637
\(566\) 0 0
\(567\) 0.802640 0.0337077
\(568\) 0 0
\(569\) 28.3368 1.18794 0.593971 0.804487i \(-0.297559\pi\)
0.593971 + 0.804487i \(0.297559\pi\)
\(570\) 0 0
\(571\) −26.1544 −1.09453 −0.547265 0.836960i \(-0.684331\pi\)
−0.547265 + 0.836960i \(0.684331\pi\)
\(572\) 0 0
\(573\) 6.84326 0.285881
\(574\) 0 0
\(575\) −0.862382 −0.0359638
\(576\) 0 0
\(577\) 7.89822 0.328807 0.164404 0.986393i \(-0.447430\pi\)
0.164404 + 0.986393i \(0.447430\pi\)
\(578\) 0 0
\(579\) 11.6905 0.485840
\(580\) 0 0
\(581\) −11.0969 −0.460378
\(582\) 0 0
\(583\) 14.1676 0.586761
\(584\) 0 0
\(585\) −13.0430 −0.539261
\(586\) 0 0
\(587\) −35.8279 −1.47878 −0.739388 0.673280i \(-0.764885\pi\)
−0.739388 + 0.673280i \(0.764885\pi\)
\(588\) 0 0
\(589\) −14.8303 −0.611073
\(590\) 0 0
\(591\) 20.4537 0.841353
\(592\) 0 0
\(593\) −21.5505 −0.884974 −0.442487 0.896775i \(-0.645904\pi\)
−0.442487 + 0.896775i \(0.645904\pi\)
\(594\) 0 0
\(595\) −3.44439 −0.141206
\(596\) 0 0
\(597\) −19.5826 −0.801462
\(598\) 0 0
\(599\) 16.3883 0.669608 0.334804 0.942288i \(-0.391330\pi\)
0.334804 + 0.942288i \(0.391330\pi\)
\(600\) 0 0
\(601\) −17.5147 −0.714439 −0.357220 0.934020i \(-0.616275\pi\)
−0.357220 + 0.934020i \(0.616275\pi\)
\(602\) 0 0
\(603\) 8.66806 0.352991
\(604\) 0 0
\(605\) 18.3481 0.745958
\(606\) 0 0
\(607\) −6.07723 −0.246667 −0.123334 0.992365i \(-0.539359\pi\)
−0.123334 + 0.992365i \(0.539359\pi\)
\(608\) 0 0
\(609\) 6.73924 0.273088
\(610\) 0 0
\(611\) 48.0749 1.94490
\(612\) 0 0
\(613\) −18.9440 −0.765140 −0.382570 0.923927i \(-0.624961\pi\)
−0.382570 + 0.923927i \(0.624961\pi\)
\(614\) 0 0
\(615\) 6.12881 0.247137
\(616\) 0 0
\(617\) −24.1057 −0.970458 −0.485229 0.874387i \(-0.661264\pi\)
−0.485229 + 0.874387i \(0.661264\pi\)
\(618\) 0 0
\(619\) −10.4384 −0.419555 −0.209777 0.977749i \(-0.567274\pi\)
−0.209777 + 0.977749i \(0.567274\pi\)
\(620\) 0 0
\(621\) 1.69737 0.0681133
\(622\) 0 0
\(623\) 9.60460 0.384800
\(624\) 0 0
\(625\) −22.2015 −0.888061
\(626\) 0 0
\(627\) 12.3885 0.494750
\(628\) 0 0
\(629\) −20.1123 −0.801932
\(630\) 0 0
\(631\) 7.14705 0.284519 0.142260 0.989829i \(-0.454563\pi\)
0.142260 + 0.989829i \(0.454563\pi\)
\(632\) 0 0
\(633\) 12.0070 0.477237
\(634\) 0 0
\(635\) 14.6913 0.583006
\(636\) 0 0
\(637\) −39.1137 −1.54974
\(638\) 0 0
\(639\) 8.00704 0.316754
\(640\) 0 0
\(641\) −41.9265 −1.65600 −0.827998 0.560731i \(-0.810520\pi\)
−0.827998 + 0.560731i \(0.810520\pi\)
\(642\) 0 0
\(643\) −41.0956 −1.62065 −0.810327 0.585978i \(-0.800711\pi\)
−0.810327 + 0.585978i \(0.800711\pi\)
\(644\) 0 0
\(645\) 6.24252 0.245799
\(646\) 0 0
\(647\) −44.0967 −1.73362 −0.866810 0.498638i \(-0.833834\pi\)
−0.866810 + 0.498638i \(0.833834\pi\)
\(648\) 0 0
\(649\) −8.82116 −0.346261
\(650\) 0 0
\(651\) −1.47070 −0.0576411
\(652\) 0 0
\(653\) −18.0236 −0.705318 −0.352659 0.935752i \(-0.614722\pi\)
−0.352659 + 0.935752i \(0.614722\pi\)
\(654\) 0 0
\(655\) −11.9291 −0.466108
\(656\) 0 0
\(657\) 1.52554 0.0595172
\(658\) 0 0
\(659\) 3.10967 0.121135 0.0605677 0.998164i \(-0.480709\pi\)
0.0605677 + 0.998164i \(0.480709\pi\)
\(660\) 0 0
\(661\) 49.6200 1.93000 0.964998 0.262259i \(-0.0844674\pi\)
0.964998 + 0.262259i \(0.0844674\pi\)
\(662\) 0 0
\(663\) 12.4605 0.483926
\(664\) 0 0
\(665\) −13.7685 −0.533918
\(666\) 0 0
\(667\) 14.2517 0.551830
\(668\) 0 0
\(669\) −20.0988 −0.777064
\(670\) 0 0
\(671\) −0.143340 −0.00553359
\(672\) 0 0
\(673\) 15.6182 0.602039 0.301019 0.953618i \(-0.402673\pi\)
0.301019 + 0.953618i \(0.402673\pi\)
\(674\) 0 0
\(675\) −0.508068 −0.0195556
\(676\) 0 0
\(677\) 49.8253 1.91494 0.957471 0.288529i \(-0.0931663\pi\)
0.957471 + 0.288529i \(0.0931663\pi\)
\(678\) 0 0
\(679\) −11.0646 −0.424620
\(680\) 0 0
\(681\) −14.1963 −0.544004
\(682\) 0 0
\(683\) −11.6091 −0.444210 −0.222105 0.975023i \(-0.571293\pi\)
−0.222105 + 0.975023i \(0.571293\pi\)
\(684\) 0 0
\(685\) −2.77398 −0.105988
\(686\) 0 0
\(687\) 19.7750 0.754465
\(688\) 0 0
\(689\) 56.9620 2.17008
\(690\) 0 0
\(691\) 18.2300 0.693501 0.346751 0.937957i \(-0.387285\pi\)
0.346751 + 0.937957i \(0.387285\pi\)
\(692\) 0 0
\(693\) 1.22855 0.0466686
\(694\) 0 0
\(695\) 35.8803 1.36102
\(696\) 0 0
\(697\) −5.85511 −0.221778
\(698\) 0 0
\(699\) 9.37536 0.354609
\(700\) 0 0
\(701\) 22.9534 0.866937 0.433468 0.901169i \(-0.357290\pi\)
0.433468 + 0.901169i \(0.357290\pi\)
\(702\) 0 0
\(703\) −80.3962 −3.03220
\(704\) 0 0
\(705\) −16.5567 −0.623562
\(706\) 0 0
\(707\) 10.6190 0.399368
\(708\) 0 0
\(709\) −43.5154 −1.63425 −0.817127 0.576458i \(-0.804434\pi\)
−0.817127 + 0.576458i \(0.804434\pi\)
\(710\) 0 0
\(711\) −15.5706 −0.583945
\(712\) 0 0
\(713\) −3.11014 −0.116476
\(714\) 0 0
\(715\) −19.9640 −0.746613
\(716\) 0 0
\(717\) 11.0467 0.412546
\(718\) 0 0
\(719\) −50.0902 −1.86805 −0.934026 0.357206i \(-0.883729\pi\)
−0.934026 + 0.357206i \(0.883729\pi\)
\(720\) 0 0
\(721\) 7.69143 0.286444
\(722\) 0 0
\(723\) 3.14465 0.116951
\(724\) 0 0
\(725\) −4.26592 −0.158432
\(726\) 0 0
\(727\) 25.8400 0.958354 0.479177 0.877718i \(-0.340935\pi\)
0.479177 + 0.877718i \(0.340935\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.96374 −0.220577
\(732\) 0 0
\(733\) 12.2488 0.452420 0.226210 0.974079i \(-0.427366\pi\)
0.226210 + 0.974079i \(0.427366\pi\)
\(734\) 0 0
\(735\) 13.4705 0.496868
\(736\) 0 0
\(737\) 13.2676 0.488719
\(738\) 0 0
\(739\) 47.4080 1.74393 0.871966 0.489567i \(-0.162845\pi\)
0.871966 + 0.489567i \(0.162845\pi\)
\(740\) 0 0
\(741\) 49.8091 1.82978
\(742\) 0 0
\(743\) −0.720168 −0.0264204 −0.0132102 0.999913i \(-0.504205\pi\)
−0.0132102 + 0.999913i \(0.504205\pi\)
\(744\) 0 0
\(745\) −50.7926 −1.86090
\(746\) 0 0
\(747\) −13.8255 −0.505850
\(748\) 0 0
\(749\) −2.56058 −0.0935614
\(750\) 0 0
\(751\) −16.7424 −0.610940 −0.305470 0.952202i \(-0.598814\pi\)
−0.305470 + 0.952202i \(0.598814\pi\)
\(752\) 0 0
\(753\) −19.4249 −0.707882
\(754\) 0 0
\(755\) 10.0471 0.365652
\(756\) 0 0
\(757\) −36.0703 −1.31100 −0.655498 0.755197i \(-0.727541\pi\)
−0.655498 + 0.755197i \(0.727541\pi\)
\(758\) 0 0
\(759\) 2.59806 0.0943035
\(760\) 0 0
\(761\) −10.3511 −0.375226 −0.187613 0.982243i \(-0.560075\pi\)
−0.187613 + 0.982243i \(0.560075\pi\)
\(762\) 0 0
\(763\) −10.8736 −0.393652
\(764\) 0 0
\(765\) −4.29133 −0.155153
\(766\) 0 0
\(767\) −35.4662 −1.28061
\(768\) 0 0
\(769\) −27.2909 −0.984134 −0.492067 0.870557i \(-0.663758\pi\)
−0.492067 + 0.870557i \(0.663758\pi\)
\(770\) 0 0
\(771\) 24.3783 0.877962
\(772\) 0 0
\(773\) 44.8338 1.61256 0.806279 0.591535i \(-0.201478\pi\)
0.806279 + 0.591535i \(0.201478\pi\)
\(774\) 0 0
\(775\) 0.930946 0.0334406
\(776\) 0 0
\(777\) −7.97274 −0.286021
\(778\) 0 0
\(779\) −23.4050 −0.838570
\(780\) 0 0
\(781\) 12.2558 0.438548
\(782\) 0 0
\(783\) 8.39635 0.300061
\(784\) 0 0
\(785\) −26.0514 −0.929815
\(786\) 0 0
\(787\) 21.8489 0.778830 0.389415 0.921062i \(-0.372677\pi\)
0.389415 + 0.921062i \(0.372677\pi\)
\(788\) 0 0
\(789\) 19.1381 0.681333
\(790\) 0 0
\(791\) 5.15475 0.183282
\(792\) 0 0
\(793\) −0.576312 −0.0204654
\(794\) 0 0
\(795\) −19.6174 −0.695756
\(796\) 0 0
\(797\) 19.1416 0.678030 0.339015 0.940781i \(-0.389906\pi\)
0.339015 + 0.940781i \(0.389906\pi\)
\(798\) 0 0
\(799\) 15.8173 0.559577
\(800\) 0 0
\(801\) 11.9663 0.422807
\(802\) 0 0
\(803\) 2.33505 0.0824021
\(804\) 0 0
\(805\) −2.88745 −0.101769
\(806\) 0 0
\(807\) −31.8583 −1.12147
\(808\) 0 0
\(809\) −47.0992 −1.65592 −0.827960 0.560787i \(-0.810499\pi\)
−0.827960 + 0.560787i \(0.810499\pi\)
\(810\) 0 0
\(811\) −31.1864 −1.09510 −0.547552 0.836772i \(-0.684440\pi\)
−0.547552 + 0.836772i \(0.684440\pi\)
\(812\) 0 0
\(813\) 27.6866 0.971013
\(814\) 0 0
\(815\) 30.7294 1.07640
\(816\) 0 0
\(817\) −23.8392 −0.834028
\(818\) 0 0
\(819\) 4.93948 0.172599
\(820\) 0 0
\(821\) −26.0414 −0.908851 −0.454425 0.890785i \(-0.650155\pi\)
−0.454425 + 0.890785i \(0.650155\pi\)
\(822\) 0 0
\(823\) 32.8099 1.14368 0.571841 0.820364i \(-0.306229\pi\)
0.571841 + 0.820364i \(0.306229\pi\)
\(824\) 0 0
\(825\) −0.777666 −0.0270749
\(826\) 0 0
\(827\) 7.60622 0.264494 0.132247 0.991217i \(-0.457781\pi\)
0.132247 + 0.991217i \(0.457781\pi\)
\(828\) 0 0
\(829\) 20.5841 0.714917 0.357458 0.933929i \(-0.383643\pi\)
0.357458 + 0.933929i \(0.383643\pi\)
\(830\) 0 0
\(831\) 16.5531 0.574222
\(832\) 0 0
\(833\) −12.8690 −0.445883
\(834\) 0 0
\(835\) 2.11942 0.0733455
\(836\) 0 0
\(837\) −1.83232 −0.0633344
\(838\) 0 0
\(839\) 51.8511 1.79010 0.895050 0.445966i \(-0.147140\pi\)
0.895050 + 0.445966i \(0.147140\pi\)
\(840\) 0 0
\(841\) 41.4987 1.43099
\(842\) 0 0
\(843\) −16.1221 −0.555276
\(844\) 0 0
\(845\) −52.7147 −1.81344
\(846\) 0 0
\(847\) −6.94858 −0.238756
\(848\) 0 0
\(849\) 15.4620 0.530653
\(850\) 0 0
\(851\) −16.8603 −0.577963
\(852\) 0 0
\(853\) −39.0857 −1.33827 −0.669135 0.743141i \(-0.733335\pi\)
−0.669135 + 0.743141i \(0.733335\pi\)
\(854\) 0 0
\(855\) −17.1540 −0.586654
\(856\) 0 0
\(857\) −28.2522 −0.965077 −0.482538 0.875875i \(-0.660285\pi\)
−0.482538 + 0.875875i \(0.660285\pi\)
\(858\) 0 0
\(859\) 51.1161 1.74406 0.872030 0.489453i \(-0.162804\pi\)
0.872030 + 0.489453i \(0.162804\pi\)
\(860\) 0 0
\(861\) −2.32103 −0.0791004
\(862\) 0 0
\(863\) 5.24574 0.178567 0.0892835 0.996006i \(-0.471542\pi\)
0.0892835 + 0.996006i \(0.471542\pi\)
\(864\) 0 0
\(865\) 30.1565 1.02535
\(866\) 0 0
\(867\) −12.9003 −0.438118
\(868\) 0 0
\(869\) −23.8330 −0.808478
\(870\) 0 0
\(871\) 53.3437 1.80748
\(872\) 0 0
\(873\) −13.7852 −0.466560
\(874\) 0 0
\(875\) 9.36993 0.316762
\(876\) 0 0
\(877\) −3.27093 −0.110451 −0.0552257 0.998474i \(-0.517588\pi\)
−0.0552257 + 0.998474i \(0.517588\pi\)
\(878\) 0 0
\(879\) −13.3824 −0.451376
\(880\) 0 0
\(881\) 7.23440 0.243733 0.121867 0.992546i \(-0.461112\pi\)
0.121867 + 0.992546i \(0.461112\pi\)
\(882\) 0 0
\(883\) −5.28825 −0.177964 −0.0889820 0.996033i \(-0.528361\pi\)
−0.0889820 + 0.996033i \(0.528361\pi\)
\(884\) 0 0
\(885\) 12.2144 0.410582
\(886\) 0 0
\(887\) 4.41900 0.148376 0.0741878 0.997244i \(-0.476364\pi\)
0.0741878 + 0.997244i \(0.476364\pi\)
\(888\) 0 0
\(889\) −5.56370 −0.186601
\(890\) 0 0
\(891\) 1.53063 0.0512781
\(892\) 0 0
\(893\) 63.2275 2.11583
\(894\) 0 0
\(895\) 11.5901 0.387415
\(896\) 0 0
\(897\) 10.4457 0.348772
\(898\) 0 0
\(899\) −15.3848 −0.513113
\(900\) 0 0
\(901\) 18.7413 0.624363
\(902\) 0 0
\(903\) −2.36409 −0.0786719
\(904\) 0 0
\(905\) −18.4638 −0.613758
\(906\) 0 0
\(907\) −27.3464 −0.908022 −0.454011 0.890996i \(-0.650007\pi\)
−0.454011 + 0.890996i \(0.650007\pi\)
\(908\) 0 0
\(909\) 13.2301 0.438814
\(910\) 0 0
\(911\) −21.3819 −0.708415 −0.354207 0.935167i \(-0.615249\pi\)
−0.354207 + 0.935167i \(0.615249\pi\)
\(912\) 0 0
\(913\) −21.1618 −0.700355
\(914\) 0 0
\(915\) 0.198479 0.00656150
\(916\) 0 0
\(917\) 4.51764 0.149186
\(918\) 0 0
\(919\) −50.1624 −1.65471 −0.827353 0.561682i \(-0.810154\pi\)
−0.827353 + 0.561682i \(0.810154\pi\)
\(920\) 0 0
\(921\) 10.3905 0.342379
\(922\) 0 0
\(923\) 49.2757 1.62193
\(924\) 0 0
\(925\) 5.04672 0.165935
\(926\) 0 0
\(927\) 9.58267 0.314736
\(928\) 0 0
\(929\) −46.5655 −1.52777 −0.763883 0.645355i \(-0.776709\pi\)
−0.763883 + 0.645355i \(0.776709\pi\)
\(930\) 0 0
\(931\) −51.4418 −1.68594
\(932\) 0 0
\(933\) −5.04038 −0.165015
\(934\) 0 0
\(935\) −6.56845 −0.214811
\(936\) 0 0
\(937\) 23.1861 0.757457 0.378728 0.925508i \(-0.376361\pi\)
0.378728 + 0.925508i \(0.376361\pi\)
\(938\) 0 0
\(939\) 12.2609 0.400118
\(940\) 0 0
\(941\) −28.8102 −0.939186 −0.469593 0.882883i \(-0.655599\pi\)
−0.469593 + 0.882883i \(0.655599\pi\)
\(942\) 0 0
\(943\) −4.90837 −0.159838
\(944\) 0 0
\(945\) −1.70113 −0.0553377
\(946\) 0 0
\(947\) −27.1110 −0.880989 −0.440495 0.897755i \(-0.645197\pi\)
−0.440495 + 0.897755i \(0.645197\pi\)
\(948\) 0 0
\(949\) 9.38827 0.304756
\(950\) 0 0
\(951\) −15.7166 −0.509645
\(952\) 0 0
\(953\) 54.3342 1.76006 0.880028 0.474922i \(-0.157524\pi\)
0.880028 + 0.474922i \(0.157524\pi\)
\(954\) 0 0
\(955\) −14.5037 −0.469329
\(956\) 0 0
\(957\) 12.8517 0.415438
\(958\) 0 0
\(959\) 1.05053 0.0339233
\(960\) 0 0
\(961\) −27.6426 −0.891696
\(962\) 0 0
\(963\) −3.19020 −0.102803
\(964\) 0 0
\(965\) −24.7770 −0.797600
\(966\) 0 0
\(967\) −33.3646 −1.07293 −0.536466 0.843922i \(-0.680241\pi\)
−0.536466 + 0.843922i \(0.680241\pi\)
\(968\) 0 0
\(969\) 16.3879 0.526456
\(970\) 0 0
\(971\) −56.5247 −1.81396 −0.906982 0.421170i \(-0.861620\pi\)
−0.906982 + 0.421170i \(0.861620\pi\)
\(972\) 0 0
\(973\) −13.5881 −0.435616
\(974\) 0 0
\(975\) −3.12668 −0.100134
\(976\) 0 0
\(977\) 15.7001 0.502292 0.251146 0.967949i \(-0.419193\pi\)
0.251146 + 0.967949i \(0.419193\pi\)
\(978\) 0 0
\(979\) 18.3160 0.585381
\(980\) 0 0
\(981\) −13.5473 −0.432533
\(982\) 0 0
\(983\) −16.5877 −0.529066 −0.264533 0.964377i \(-0.585218\pi\)
−0.264533 + 0.964377i \(0.585218\pi\)
\(984\) 0 0
\(985\) −43.3500 −1.38124
\(986\) 0 0
\(987\) 6.27015 0.199581
\(988\) 0 0
\(989\) −4.99943 −0.158973
\(990\) 0 0
\(991\) 34.8301 1.10641 0.553207 0.833044i \(-0.313404\pi\)
0.553207 + 0.833044i \(0.313404\pi\)
\(992\) 0 0
\(993\) 18.2687 0.579740
\(994\) 0 0
\(995\) 41.5037 1.31576
\(996\) 0 0
\(997\) −45.7106 −1.44767 −0.723834 0.689974i \(-0.757622\pi\)
−0.723834 + 0.689974i \(0.757622\pi\)
\(998\) 0 0
\(999\) −9.93315 −0.314271
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 8016.2.a.be.1.2 11
4.3 odd 2 4008.2.a.k.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.2 11 4.3 odd 2
8016.2.a.be.1.2 11 1.1 even 1 trivial