Properties

Label 7360.2.a.ch.1.1
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.21208.1
Defining polynomial: \(x^{4} - x^{3} - 8 x^{2} + 13 x - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3680)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.07664\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58604 q^{3} +1.00000 q^{5} -2.07664 q^{7} +3.68758 q^{9} +O(q^{10})\) \(q-2.58604 q^{3} +1.00000 q^{5} -2.07664 q^{7} +3.68758 q^{9} +3.19698 q^{11} -5.95629 q^{13} -2.58604 q^{15} -6.46569 q^{17} +6.07664 q^{19} +5.37026 q^{21} +1.00000 q^{23} +1.00000 q^{25} -1.77811 q^{27} -3.87966 q^{29} -7.56233 q^{31} -8.26751 q^{33} -2.07664 q^{35} -2.64387 q^{37} +15.4032 q^{39} -0.979997 q^{41} +5.66267 q^{43} +3.68758 q^{45} -4.86086 q^{47} -2.68758 q^{49} +16.7205 q^{51} +8.53742 q^{53} +3.19698 q^{55} -15.7144 q^{57} -3.13447 q^{59} +3.38785 q^{61} -7.65777 q^{63} -5.95629 q^{65} +1.11544 q^{67} -2.58604 q^{69} +9.85475 q^{71} -12.3303 q^{73} -2.58604 q^{75} -6.63897 q^{77} +0.874749 q^{79} -6.46449 q^{81} -12.5096 q^{83} -6.46569 q^{85} +10.0329 q^{87} +10.4506 q^{89} +12.3691 q^{91} +19.5565 q^{93} +6.07664 q^{95} +5.54353 q^{97} +11.7891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} + 4 q^{5} + 5 q^{7} + 9 q^{9} + O(q^{10}) \) \( 4 q - q^{3} + 4 q^{5} + 5 q^{7} + 9 q^{9} + 11 q^{11} + q^{13} - q^{15} - 5 q^{17} + 11 q^{19} + 6 q^{21} + 4 q^{23} + 4 q^{25} + 8 q^{27} - 4 q^{29} - 9 q^{31} - 9 q^{33} + 5 q^{35} + 20 q^{37} + 8 q^{39} + 9 q^{41} + 9 q^{45} - 5 q^{49} + 23 q^{51} - 4 q^{53} + 11 q^{55} - 10 q^{57} + 22 q^{59} + q^{61} - 4 q^{63} + q^{65} + 12 q^{67} - q^{69} + 11 q^{71} - 8 q^{73} - q^{75} + 8 q^{77} - 12 q^{79} - 4 q^{83} - 5 q^{85} + 2 q^{87} + 12 q^{89} + 29 q^{91} - 2 q^{93} + 11 q^{95} - 7 q^{97} + 45 q^{99} + O(q^{100}) \)

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
\(3\) −2.58604 −1.49305 −0.746524 0.665358i \(-0.768279\pi\)
−0.746524 + 0.665358i \(0.768279\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.07664 −0.784895 −0.392447 0.919774i \(-0.628371\pi\)
−0.392447 + 0.919774i \(0.628371\pi\)
\(8\) 0 0
\(9\) 3.68758 1.22919
\(10\) 0 0
\(11\) 3.19698 0.963926 0.481963 0.876192i \(-0.339924\pi\)
0.481963 + 0.876192i \(0.339924\pi\)
\(12\) 0 0
\(13\) −5.95629 −1.65198 −0.825989 0.563686i \(-0.809383\pi\)
−0.825989 + 0.563686i \(0.809383\pi\)
\(14\) 0 0
\(15\) −2.58604 −0.667712
\(16\) 0 0
\(17\) −6.46569 −1.56816 −0.784080 0.620659i \(-0.786865\pi\)
−0.784080 + 0.620659i \(0.786865\pi\)
\(18\) 0 0
\(19\) 6.07664 1.39408 0.697038 0.717034i \(-0.254501\pi\)
0.697038 + 0.717034i \(0.254501\pi\)
\(20\) 0 0
\(21\) 5.37026 1.17189
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.77811 −0.342197
\(28\) 0 0
\(29\) −3.87966 −0.720434 −0.360217 0.932869i \(-0.617297\pi\)
−0.360217 + 0.932869i \(0.617297\pi\)
\(30\) 0 0
\(31\) −7.56233 −1.35823 −0.679117 0.734030i \(-0.737637\pi\)
−0.679117 + 0.734030i \(0.737637\pi\)
\(32\) 0 0
\(33\) −8.26751 −1.43919
\(34\) 0 0
\(35\) −2.07664 −0.351016
\(36\) 0 0
\(37\) −2.64387 −0.434650 −0.217325 0.976099i \(-0.569733\pi\)
−0.217325 + 0.976099i \(0.569733\pi\)
\(38\) 0 0
\(39\) 15.4032 2.46648
\(40\) 0 0
\(41\) −0.979997 −0.153050 −0.0765249 0.997068i \(-0.524382\pi\)
−0.0765249 + 0.997068i \(0.524382\pi\)
\(42\) 0 0
\(43\) 5.66267 0.863549 0.431775 0.901981i \(-0.357888\pi\)
0.431775 + 0.901981i \(0.357888\pi\)
\(44\) 0 0
\(45\) 3.68758 0.549712
\(46\) 0 0
\(47\) −4.86086 −0.709029 −0.354514 0.935051i \(-0.615354\pi\)
−0.354514 + 0.935051i \(0.615354\pi\)
\(48\) 0 0
\(49\) −2.68758 −0.383940
\(50\) 0 0
\(51\) 16.7205 2.34134
\(52\) 0 0
\(53\) 8.53742 1.17270 0.586352 0.810056i \(-0.300563\pi\)
0.586352 + 0.810056i \(0.300563\pi\)
\(54\) 0 0
\(55\) 3.19698 0.431081
\(56\) 0 0
\(57\) −15.7144 −2.08142
\(58\) 0 0
\(59\) −3.13447 −0.408074 −0.204037 0.978963i \(-0.565406\pi\)
−0.204037 + 0.978963i \(0.565406\pi\)
\(60\) 0 0
\(61\) 3.38785 0.433770 0.216885 0.976197i \(-0.430410\pi\)
0.216885 + 0.976197i \(0.430410\pi\)
\(62\) 0 0
\(63\) −7.65777 −0.964788
\(64\) 0 0
\(65\) −5.95629 −0.738787
\(66\) 0 0
\(67\) 1.11544 0.136272 0.0681362 0.997676i \(-0.478295\pi\)
0.0681362 + 0.997676i \(0.478295\pi\)
\(68\) 0 0
\(69\) −2.58604 −0.311322
\(70\) 0 0
\(71\) 9.85475 1.16954 0.584772 0.811198i \(-0.301184\pi\)
0.584772 + 0.811198i \(0.301184\pi\)
\(72\) 0 0
\(73\) −12.3303 −1.44315 −0.721573 0.692338i \(-0.756581\pi\)
−0.721573 + 0.692338i \(0.756581\pi\)
\(74\) 0 0
\(75\) −2.58604 −0.298610
\(76\) 0 0
\(77\) −6.63897 −0.756580
\(78\) 0 0
\(79\) 0.874749 0.0984169 0.0492085 0.998789i \(-0.484330\pi\)
0.0492085 + 0.998789i \(0.484330\pi\)
\(80\) 0 0
\(81\) −6.46449 −0.718276
\(82\) 0 0
\(83\) −12.5096 −1.37311 −0.686555 0.727077i \(-0.740878\pi\)
−0.686555 + 0.727077i \(0.740878\pi\)
\(84\) 0 0
\(85\) −6.46569 −0.701303
\(86\) 0 0
\(87\) 10.0329 1.07564
\(88\) 0 0
\(89\) 10.4506 1.10776 0.553880 0.832596i \(-0.313146\pi\)
0.553880 + 0.832596i \(0.313146\pi\)
\(90\) 0 0
\(91\) 12.3691 1.29663
\(92\) 0 0
\(93\) 19.5565 2.02791
\(94\) 0 0
\(95\) 6.07664 0.623450
\(96\) 0 0
\(97\) 5.54353 0.562860 0.281430 0.959582i \(-0.409191\pi\)
0.281430 + 0.959582i \(0.409191\pi\)
\(98\) 0 0
\(99\) 11.7891 1.18485
\(100\) 0 0
\(101\) 0.153273 0.0152512 0.00762560 0.999971i \(-0.497573\pi\)
0.00762560 + 0.999971i \(0.497573\pi\)
\(102\) 0 0
\(103\) −3.09053 −0.304519 −0.152259 0.988341i \(-0.548655\pi\)
−0.152259 + 0.988341i \(0.548655\pi\)
\(104\) 0 0
\(105\) 5.37026 0.524083
\(106\) 0 0
\(107\) 5.26871 0.509345 0.254673 0.967027i \(-0.418032\pi\)
0.254673 + 0.967027i \(0.418032\pi\)
\(108\) 0 0
\(109\) −10.6615 −1.02118 −0.510592 0.859823i \(-0.670574\pi\)
−0.510592 + 0.859823i \(0.670574\pi\)
\(110\) 0 0
\(111\) 6.83715 0.648954
\(112\) 0 0
\(113\) −6.68147 −0.628540 −0.314270 0.949334i \(-0.601760\pi\)
−0.314270 + 0.949334i \(0.601760\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) −21.9643 −2.03060
\(118\) 0 0
\(119\) 13.4269 1.23084
\(120\) 0 0
\(121\) −0.779314 −0.0708467
\(122\) 0 0
\(123\) 2.53431 0.228511
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.90827 −0.613010 −0.306505 0.951869i \(-0.599160\pi\)
−0.306505 + 0.951869i \(0.599160\pi\)
\(128\) 0 0
\(129\) −14.6439 −1.28932
\(130\) 0 0
\(131\) 9.35146 0.817041 0.408520 0.912749i \(-0.366045\pi\)
0.408520 + 0.912749i \(0.366045\pi\)
\(132\) 0 0
\(133\) −12.6190 −1.09420
\(134\) 0 0
\(135\) −1.77811 −0.153035
\(136\) 0 0
\(137\) −8.92360 −0.762395 −0.381197 0.924494i \(-0.624488\pi\)
−0.381197 + 0.924494i \(0.624488\pi\)
\(138\) 0 0
\(139\) 19.4949 1.65354 0.826769 0.562542i \(-0.190177\pi\)
0.826769 + 0.562542i \(0.190177\pi\)
\(140\) 0 0
\(141\) 12.5703 1.05861
\(142\) 0 0
\(143\) −19.0422 −1.59238
\(144\) 0 0
\(145\) −3.87966 −0.322188
\(146\) 0 0
\(147\) 6.95018 0.573241
\(148\) 0 0
\(149\) −16.9114 −1.38543 −0.692717 0.721209i \(-0.743587\pi\)
−0.692717 + 0.721209i \(0.743587\pi\)
\(150\) 0 0
\(151\) −17.4232 −1.41788 −0.708939 0.705269i \(-0.750826\pi\)
−0.708939 + 0.705269i \(0.750826\pi\)
\(152\) 0 0
\(153\) −23.8428 −1.92757
\(154\) 0 0
\(155\) −7.56233 −0.607421
\(156\) 0 0
\(157\) 22.5565 1.80020 0.900101 0.435682i \(-0.143493\pi\)
0.900101 + 0.435682i \(0.143493\pi\)
\(158\) 0 0
\(159\) −22.0781 −1.75091
\(160\) 0 0
\(161\) −2.07664 −0.163662
\(162\) 0 0
\(163\) 9.31242 0.729405 0.364702 0.931124i \(-0.381171\pi\)
0.364702 + 0.931124i \(0.381171\pi\)
\(164\) 0 0
\(165\) −8.26751 −0.643625
\(166\) 0 0
\(167\) 6.77811 0.524506 0.262253 0.964999i \(-0.415535\pi\)
0.262253 + 0.964999i \(0.415535\pi\)
\(168\) 0 0
\(169\) 22.4774 1.72903
\(170\) 0 0
\(171\) 22.4081 1.71359
\(172\) 0 0
\(173\) −23.7910 −1.80880 −0.904399 0.426687i \(-0.859681\pi\)
−0.904399 + 0.426687i \(0.859681\pi\)
\(174\) 0 0
\(175\) −2.07664 −0.156979
\(176\) 0 0
\(177\) 8.10586 0.609274
\(178\) 0 0
\(179\) 2.45767 0.183695 0.0918475 0.995773i \(-0.470723\pi\)
0.0918475 + 0.995773i \(0.470723\pi\)
\(180\) 0 0
\(181\) −3.28871 −0.244448 −0.122224 0.992503i \(-0.539003\pi\)
−0.122224 + 0.992503i \(0.539003\pi\)
\(182\) 0 0
\(183\) −8.76111 −0.647640
\(184\) 0 0
\(185\) −2.64387 −0.194381
\(186\) 0 0
\(187\) −20.6707 −1.51159
\(188\) 0 0
\(189\) 3.69249 0.268589
\(190\) 0 0
\(191\) 5.36535 0.388223 0.194112 0.980979i \(-0.437818\pi\)
0.194112 + 0.980979i \(0.437818\pi\)
\(192\) 0 0
\(193\) 19.4671 1.40127 0.700637 0.713517i \(-0.252899\pi\)
0.700637 + 0.713517i \(0.252899\pi\)
\(194\) 0 0
\(195\) 15.4032 1.10304
\(196\) 0 0
\(197\) −8.05543 −0.573926 −0.286963 0.957942i \(-0.592646\pi\)
−0.286963 + 0.957942i \(0.592646\pi\)
\(198\) 0 0
\(199\) −21.4596 −1.52123 −0.760615 0.649204i \(-0.775102\pi\)
−0.760615 + 0.649204i \(0.775102\pi\)
\(200\) 0 0
\(201\) −2.88456 −0.203461
\(202\) 0 0
\(203\) 8.05663 0.565465
\(204\) 0 0
\(205\) −0.979997 −0.0684460
\(206\) 0 0
\(207\) 3.68758 0.256305
\(208\) 0 0
\(209\) 19.4269 1.34379
\(210\) 0 0
\(211\) 2.43397 0.167561 0.0837806 0.996484i \(-0.473301\pi\)
0.0837806 + 0.996484i \(0.473301\pi\)
\(212\) 0 0
\(213\) −25.4847 −1.74618
\(214\) 0 0
\(215\) 5.66267 0.386191
\(216\) 0 0
\(217\) 15.7042 1.06607
\(218\) 0 0
\(219\) 31.8865 2.15469
\(220\) 0 0
\(221\) 38.5115 2.59057
\(222\) 0 0
\(223\) 8.33433 0.558108 0.279054 0.960275i \(-0.409979\pi\)
0.279054 + 0.960275i \(0.409979\pi\)
\(224\) 0 0
\(225\) 3.68758 0.245839
\(226\) 0 0
\(227\) 15.1789 1.00746 0.503729 0.863862i \(-0.331961\pi\)
0.503729 + 0.863862i \(0.331961\pi\)
\(228\) 0 0
\(229\) 14.0590 0.929048 0.464524 0.885561i \(-0.346226\pi\)
0.464524 + 0.885561i \(0.346226\pi\)
\(230\) 0 0
\(231\) 17.1686 1.12961
\(232\) 0 0
\(233\) 9.31145 0.610014 0.305007 0.952350i \(-0.401341\pi\)
0.305007 + 0.952350i \(0.401341\pi\)
\(234\) 0 0
\(235\) −4.86086 −0.317087
\(236\) 0 0
\(237\) −2.26213 −0.146941
\(238\) 0 0
\(239\) −5.14837 −0.333020 −0.166510 0.986040i \(-0.553250\pi\)
−0.166510 + 0.986040i \(0.553250\pi\)
\(240\) 0 0
\(241\) −15.9526 −1.02760 −0.513798 0.857911i \(-0.671762\pi\)
−0.513798 + 0.857911i \(0.671762\pi\)
\(242\) 0 0
\(243\) 22.0517 1.41462
\(244\) 0 0
\(245\) −2.68758 −0.171703
\(246\) 0 0
\(247\) −36.1942 −2.30298
\(248\) 0 0
\(249\) 32.3504 2.05012
\(250\) 0 0
\(251\) −25.6021 −1.61599 −0.807994 0.589190i \(-0.799447\pi\)
−0.807994 + 0.589190i \(0.799447\pi\)
\(252\) 0 0
\(253\) 3.19698 0.200992
\(254\) 0 0
\(255\) 16.7205 1.04708
\(256\) 0 0
\(257\) 9.33924 0.582566 0.291283 0.956637i \(-0.405918\pi\)
0.291283 + 0.956637i \(0.405918\pi\)
\(258\) 0 0
\(259\) 5.49036 0.341155
\(260\) 0 0
\(261\) −14.3065 −0.885553
\(262\) 0 0
\(263\) 0.612149 0.0377467 0.0188733 0.999822i \(-0.493992\pi\)
0.0188733 + 0.999822i \(0.493992\pi\)
\(264\) 0 0
\(265\) 8.53742 0.524450
\(266\) 0 0
\(267\) −27.0256 −1.65394
\(268\) 0 0
\(269\) −6.70518 −0.408822 −0.204411 0.978885i \(-0.565528\pi\)
−0.204411 + 0.978885i \(0.565528\pi\)
\(270\) 0 0
\(271\) 31.2277 1.89695 0.948475 0.316852i \(-0.102626\pi\)
0.948475 + 0.316852i \(0.102626\pi\)
\(272\) 0 0
\(273\) −31.9868 −1.93593
\(274\) 0 0
\(275\) 3.19698 0.192785
\(276\) 0 0
\(277\) 29.8513 1.79359 0.896795 0.442447i \(-0.145889\pi\)
0.896795 + 0.442447i \(0.145889\pi\)
\(278\) 0 0
\(279\) −27.8867 −1.66953
\(280\) 0 0
\(281\) 18.3910 1.09711 0.548556 0.836114i \(-0.315178\pi\)
0.548556 + 0.836114i \(0.315178\pi\)
\(282\) 0 0
\(283\) −21.6319 −1.28588 −0.642941 0.765916i \(-0.722286\pi\)
−0.642941 + 0.765916i \(0.722286\pi\)
\(284\) 0 0
\(285\) −15.7144 −0.930841
\(286\) 0 0
\(287\) 2.03510 0.120128
\(288\) 0 0
\(289\) 24.8052 1.45913
\(290\) 0 0
\(291\) −14.3358 −0.840378
\(292\) 0 0
\(293\) −9.83451 −0.574538 −0.287269 0.957850i \(-0.592747\pi\)
−0.287269 + 0.957850i \(0.592747\pi\)
\(294\) 0 0
\(295\) −3.13447 −0.182496
\(296\) 0 0
\(297\) −5.68458 −0.329853
\(298\) 0 0
\(299\) −5.95629 −0.344461
\(300\) 0 0
\(301\) −11.7593 −0.677795
\(302\) 0 0
\(303\) −0.396369 −0.0227708
\(304\) 0 0
\(305\) 3.38785 0.193988
\(306\) 0 0
\(307\) −23.0031 −1.31286 −0.656428 0.754388i \(-0.727934\pi\)
−0.656428 + 0.754388i \(0.727934\pi\)
\(308\) 0 0
\(309\) 7.99222 0.454661
\(310\) 0 0
\(311\) −12.7144 −0.720967 −0.360484 0.932766i \(-0.617388\pi\)
−0.360484 + 0.932766i \(0.617388\pi\)
\(312\) 0 0
\(313\) −17.5583 −0.992451 −0.496226 0.868194i \(-0.665281\pi\)
−0.496226 + 0.868194i \(0.665281\pi\)
\(314\) 0 0
\(315\) −7.65777 −0.431466
\(316\) 0 0
\(317\) 23.0924 1.29700 0.648500 0.761214i \(-0.275397\pi\)
0.648500 + 0.761214i \(0.275397\pi\)
\(318\) 0 0
\(319\) −12.4032 −0.694445
\(320\) 0 0
\(321\) −13.6251 −0.760477
\(322\) 0 0
\(323\) −39.2897 −2.18613
\(324\) 0 0
\(325\) −5.95629 −0.330396
\(326\) 0 0
\(327\) 27.5709 1.52468
\(328\) 0 0
\(329\) 10.0942 0.556513
\(330\) 0 0
\(331\) 7.51454 0.413037 0.206518 0.978443i \(-0.433787\pi\)
0.206518 + 0.978443i \(0.433787\pi\)
\(332\) 0 0
\(333\) −9.74950 −0.534269
\(334\) 0 0
\(335\) 1.11544 0.0609429
\(336\) 0 0
\(337\) 25.3996 1.38360 0.691801 0.722088i \(-0.256817\pi\)
0.691801 + 0.722088i \(0.256817\pi\)
\(338\) 0 0
\(339\) 17.2785 0.938441
\(340\) 0 0
\(341\) −24.1766 −1.30924
\(342\) 0 0
\(343\) 20.1176 1.08625
\(344\) 0 0
\(345\) −2.58604 −0.139227
\(346\) 0 0
\(347\) 15.1964 0.815785 0.407892 0.913030i \(-0.366264\pi\)
0.407892 + 0.913030i \(0.366264\pi\)
\(348\) 0 0
\(349\) 2.32103 0.124242 0.0621209 0.998069i \(-0.480214\pi\)
0.0621209 + 0.998069i \(0.480214\pi\)
\(350\) 0 0
\(351\) 10.5909 0.565303
\(352\) 0 0
\(353\) −10.5113 −0.559460 −0.279730 0.960079i \(-0.590245\pi\)
−0.279730 + 0.960079i \(0.590245\pi\)
\(354\) 0 0
\(355\) 9.85475 0.523036
\(356\) 0 0
\(357\) −34.7224 −1.83771
\(358\) 0 0
\(359\) −11.6153 −0.613030 −0.306515 0.951866i \(-0.599163\pi\)
−0.306515 + 0.951866i \(0.599163\pi\)
\(360\) 0 0
\(361\) 17.9255 0.943448
\(362\) 0 0
\(363\) 2.01533 0.105778
\(364\) 0 0
\(365\) −12.3303 −0.645395
\(366\) 0 0
\(367\) 28.0381 1.46358 0.731788 0.681533i \(-0.238686\pi\)
0.731788 + 0.681533i \(0.238686\pi\)
\(368\) 0 0
\(369\) −3.61382 −0.188128
\(370\) 0 0
\(371\) −17.7291 −0.920450
\(372\) 0 0
\(373\) 27.9224 1.44577 0.722883 0.690970i \(-0.242816\pi\)
0.722883 + 0.690970i \(0.242816\pi\)
\(374\) 0 0
\(375\) −2.58604 −0.133542
\(376\) 0 0
\(377\) 23.1084 1.19014
\(378\) 0 0
\(379\) 17.5978 0.903936 0.451968 0.892034i \(-0.350722\pi\)
0.451968 + 0.892034i \(0.350722\pi\)
\(380\) 0 0
\(381\) 17.8650 0.915253
\(382\) 0 0
\(383\) 3.24333 0.165727 0.0828633 0.996561i \(-0.473594\pi\)
0.0828633 + 0.996561i \(0.473594\pi\)
\(384\) 0 0
\(385\) −6.63897 −0.338353
\(386\) 0 0
\(387\) 20.8816 1.06147
\(388\) 0 0
\(389\) −21.1964 −1.07470 −0.537350 0.843359i \(-0.680575\pi\)
−0.537350 + 0.843359i \(0.680575\pi\)
\(390\) 0 0
\(391\) −6.46569 −0.326984
\(392\) 0 0
\(393\) −24.1832 −1.21988
\(394\) 0 0
\(395\) 0.874749 0.0440134
\(396\) 0 0
\(397\) −27.6263 −1.38652 −0.693262 0.720686i \(-0.743827\pi\)
−0.693262 + 0.720686i \(0.743827\pi\)
\(398\) 0 0
\(399\) 32.6331 1.63370
\(400\) 0 0
\(401\) 36.2093 1.80821 0.904103 0.427314i \(-0.140540\pi\)
0.904103 + 0.427314i \(0.140540\pi\)
\(402\) 0 0
\(403\) 45.0434 2.24377
\(404\) 0 0
\(405\) −6.46449 −0.321223
\(406\) 0 0
\(407\) −8.45241 −0.418971
\(408\) 0 0
\(409\) 33.9231 1.67739 0.838695 0.544602i \(-0.183319\pi\)
0.838695 + 0.544602i \(0.183319\pi\)
\(410\) 0 0
\(411\) 23.0768 1.13829
\(412\) 0 0
\(413\) 6.50916 0.320295
\(414\) 0 0
\(415\) −12.5096 −0.614074
\(416\) 0 0
\(417\) −50.4146 −2.46881
\(418\) 0 0
\(419\) −6.40318 −0.312816 −0.156408 0.987693i \(-0.549991\pi\)
−0.156408 + 0.987693i \(0.549991\pi\)
\(420\) 0 0
\(421\) 11.2013 0.545918 0.272959 0.962026i \(-0.411998\pi\)
0.272959 + 0.962026i \(0.411998\pi\)
\(422\) 0 0
\(423\) −17.9248 −0.871534
\(424\) 0 0
\(425\) −6.46569 −0.313632
\(426\) 0 0
\(427\) −7.03534 −0.340464
\(428\) 0 0
\(429\) 49.2437 2.37751
\(430\) 0 0
\(431\) 25.0002 1.20422 0.602110 0.798414i \(-0.294327\pi\)
0.602110 + 0.798414i \(0.294327\pi\)
\(432\) 0 0
\(433\) −19.2955 −0.927284 −0.463642 0.886023i \(-0.653458\pi\)
−0.463642 + 0.886023i \(0.653458\pi\)
\(434\) 0 0
\(435\) 10.0329 0.481042
\(436\) 0 0
\(437\) 6.07664 0.290685
\(438\) 0 0
\(439\) 38.7725 1.85051 0.925255 0.379347i \(-0.123851\pi\)
0.925255 + 0.379347i \(0.123851\pi\)
\(440\) 0 0
\(441\) −9.91067 −0.471937
\(442\) 0 0
\(443\) 38.7915 1.84304 0.921520 0.388331i \(-0.126948\pi\)
0.921520 + 0.388331i \(0.126948\pi\)
\(444\) 0 0
\(445\) 10.4506 0.495406
\(446\) 0 0
\(447\) 43.7334 2.06852
\(448\) 0 0
\(449\) −37.7398 −1.78105 −0.890525 0.454934i \(-0.849663\pi\)
−0.890525 + 0.454934i \(0.849663\pi\)
\(450\) 0 0
\(451\) −3.13303 −0.147529
\(452\) 0 0
\(453\) 45.0570 2.11696
\(454\) 0 0
\(455\) 12.3691 0.579870
\(456\) 0 0
\(457\) 27.6973 1.29562 0.647812 0.761800i \(-0.275684\pi\)
0.647812 + 0.761800i \(0.275684\pi\)
\(458\) 0 0
\(459\) 11.4967 0.536621
\(460\) 0 0
\(461\) 33.5590 1.56300 0.781498 0.623907i \(-0.214456\pi\)
0.781498 + 0.623907i \(0.214456\pi\)
\(462\) 0 0
\(463\) −16.7259 −0.777318 −0.388659 0.921382i \(-0.627062\pi\)
−0.388659 + 0.921382i \(0.627062\pi\)
\(464\) 0 0
\(465\) 19.5565 0.906909
\(466\) 0 0
\(467\) 8.79033 0.406768 0.203384 0.979099i \(-0.434806\pi\)
0.203384 + 0.979099i \(0.434806\pi\)
\(468\) 0 0
\(469\) −2.31636 −0.106960
\(470\) 0 0
\(471\) −58.3318 −2.68779
\(472\) 0 0
\(473\) 18.1035 0.832398
\(474\) 0 0
\(475\) 6.07664 0.278815
\(476\) 0 0
\(477\) 31.4824 1.44148
\(478\) 0 0
\(479\) −17.8726 −0.816619 −0.408309 0.912844i \(-0.633882\pi\)
−0.408309 + 0.912844i \(0.633882\pi\)
\(480\) 0 0
\(481\) 15.7477 0.718032
\(482\) 0 0
\(483\) 5.37026 0.244355
\(484\) 0 0
\(485\) 5.54353 0.251719
\(486\) 0 0
\(487\) 14.1481 0.641113 0.320556 0.947229i \(-0.396130\pi\)
0.320556 + 0.947229i \(0.396130\pi\)
\(488\) 0 0
\(489\) −24.0822 −1.08904
\(490\) 0 0
\(491\) 0.829600 0.0374393 0.0187197 0.999825i \(-0.494041\pi\)
0.0187197 + 0.999825i \(0.494041\pi\)
\(492\) 0 0
\(493\) 25.0847 1.12976
\(494\) 0 0
\(495\) 11.7891 0.529882
\(496\) 0 0
\(497\) −20.4647 −0.917968
\(498\) 0 0
\(499\) 39.0634 1.74872 0.874358 0.485281i \(-0.161283\pi\)
0.874358 + 0.485281i \(0.161283\pi\)
\(500\) 0 0
\(501\) −17.5284 −0.783113
\(502\) 0 0
\(503\) 24.4202 1.08884 0.544421 0.838812i \(-0.316749\pi\)
0.544421 + 0.838812i \(0.316749\pi\)
\(504\) 0 0
\(505\) 0.153273 0.00682055
\(506\) 0 0
\(507\) −58.1274 −2.58153
\(508\) 0 0
\(509\) −21.6488 −0.959565 −0.479783 0.877387i \(-0.659284\pi\)
−0.479783 + 0.877387i \(0.659284\pi\)
\(510\) 0 0
\(511\) 25.6054 1.13272
\(512\) 0 0
\(513\) −10.8049 −0.477049
\(514\) 0 0
\(515\) −3.09053 −0.136185
\(516\) 0 0
\(517\) −15.5401 −0.683451
\(518\) 0 0
\(519\) 61.5245 2.70062
\(520\) 0 0
\(521\) 18.2788 0.800807 0.400404 0.916339i \(-0.368870\pi\)
0.400404 + 0.916339i \(0.368870\pi\)
\(522\) 0 0
\(523\) −0.671658 −0.0293695 −0.0146848 0.999892i \(-0.504674\pi\)
−0.0146848 + 0.999892i \(0.504674\pi\)
\(524\) 0 0
\(525\) 5.37026 0.234377
\(526\) 0 0
\(527\) 48.8957 2.12993
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −11.5586 −0.501602
\(532\) 0 0
\(533\) 5.83715 0.252835
\(534\) 0 0
\(535\) 5.26871 0.227786
\(536\) 0 0
\(537\) −6.35563 −0.274266
\(538\) 0 0
\(539\) −8.59215 −0.370090
\(540\) 0 0
\(541\) 27.2309 1.17075 0.585373 0.810764i \(-0.300948\pi\)
0.585373 + 0.810764i \(0.300948\pi\)
\(542\) 0 0
\(543\) 8.50473 0.364973
\(544\) 0 0
\(545\) −10.6615 −0.456687
\(546\) 0 0
\(547\) 7.12155 0.304495 0.152248 0.988342i \(-0.451349\pi\)
0.152248 + 0.988342i \(0.451349\pi\)
\(548\) 0 0
\(549\) 12.4930 0.533187
\(550\) 0 0
\(551\) −23.5753 −1.00434
\(552\) 0 0
\(553\) −1.81654 −0.0772469
\(554\) 0 0
\(555\) 6.83715 0.290221
\(556\) 0 0
\(557\) 5.32834 0.225769 0.112885 0.993608i \(-0.463991\pi\)
0.112885 + 0.993608i \(0.463991\pi\)
\(558\) 0 0
\(559\) −33.7285 −1.42656
\(560\) 0 0
\(561\) 53.4551 2.25688
\(562\) 0 0
\(563\) 36.1317 1.52277 0.761385 0.648300i \(-0.224520\pi\)
0.761385 + 0.648300i \(0.224520\pi\)
\(564\) 0 0
\(565\) −6.68147 −0.281092
\(566\) 0 0
\(567\) 13.4244 0.563771
\(568\) 0 0
\(569\) 35.4566 1.48642 0.743209 0.669060i \(-0.233303\pi\)
0.743209 + 0.669060i \(0.233303\pi\)
\(570\) 0 0
\(571\) 3.95365 0.165455 0.0827275 0.996572i \(-0.473637\pi\)
0.0827275 + 0.996572i \(0.473637\pi\)
\(572\) 0 0
\(573\) −13.8750 −0.579636
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 35.7234 1.48718 0.743592 0.668634i \(-0.233121\pi\)
0.743592 + 0.668634i \(0.233121\pi\)
\(578\) 0 0
\(579\) −50.3427 −2.09217
\(580\) 0 0
\(581\) 25.9780 1.07775
\(582\) 0 0
\(583\) 27.2940 1.13040
\(584\) 0 0
\(585\) −21.9643 −0.908112
\(586\) 0 0
\(587\) 42.0407 1.73520 0.867602 0.497259i \(-0.165660\pi\)
0.867602 + 0.497259i \(0.165660\pi\)
\(588\) 0 0
\(589\) −45.9535 −1.89348
\(590\) 0 0
\(591\) 20.8316 0.856899
\(592\) 0 0
\(593\) 4.71848 0.193765 0.0968823 0.995296i \(-0.469113\pi\)
0.0968823 + 0.995296i \(0.469113\pi\)
\(594\) 0 0
\(595\) 13.4269 0.550449
\(596\) 0 0
\(597\) 55.4952 2.27127
\(598\) 0 0
\(599\) −28.0976 −1.14804 −0.574018 0.818843i \(-0.694616\pi\)
−0.574018 + 0.818843i \(0.694616\pi\)
\(600\) 0 0
\(601\) 16.3995 0.668949 0.334474 0.942405i \(-0.391441\pi\)
0.334474 + 0.942405i \(0.391441\pi\)
\(602\) 0 0
\(603\) 4.11327 0.167505
\(604\) 0 0
\(605\) −0.779314 −0.0316836
\(606\) 0 0
\(607\) 41.6973 1.69244 0.846220 0.532834i \(-0.178873\pi\)
0.846220 + 0.532834i \(0.178873\pi\)
\(608\) 0 0
\(609\) −20.8347 −0.844266
\(610\) 0 0
\(611\) 28.9527 1.17130
\(612\) 0 0
\(613\) −21.5660 −0.871044 −0.435522 0.900178i \(-0.643436\pi\)
−0.435522 + 0.900178i \(0.643436\pi\)
\(614\) 0 0
\(615\) 2.53431 0.102193
\(616\) 0 0
\(617\) 11.5035 0.463115 0.231557 0.972821i \(-0.425618\pi\)
0.231557 + 0.972821i \(0.425618\pi\)
\(618\) 0 0
\(619\) −36.9470 −1.48503 −0.742514 0.669831i \(-0.766367\pi\)
−0.742514 + 0.669831i \(0.766367\pi\)
\(620\) 0 0
\(621\) −1.77811 −0.0713531
\(622\) 0 0
\(623\) −21.7021 −0.869476
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −50.2386 −2.00634
\(628\) 0 0
\(629\) 17.0945 0.681601
\(630\) 0 0
\(631\) −36.6839 −1.46036 −0.730181 0.683254i \(-0.760564\pi\)
−0.730181 + 0.683254i \(0.760564\pi\)
\(632\) 0 0
\(633\) −6.29433 −0.250177
\(634\) 0 0
\(635\) −6.90827 −0.274146
\(636\) 0 0
\(637\) 16.0080 0.634261
\(638\) 0 0
\(639\) 36.3402 1.43760
\(640\) 0 0
\(641\) −31.7187 −1.25281 −0.626407 0.779496i \(-0.715475\pi\)
−0.626407 + 0.779496i \(0.715475\pi\)
\(642\) 0 0
\(643\) −49.6953 −1.95979 −0.979896 0.199507i \(-0.936066\pi\)
−0.979896 + 0.199507i \(0.936066\pi\)
\(644\) 0 0
\(645\) −14.6439 −0.576602
\(646\) 0 0
\(647\) 17.9197 0.704495 0.352247 0.935907i \(-0.385418\pi\)
0.352247 + 0.935907i \(0.385418\pi\)
\(648\) 0 0
\(649\) −10.0209 −0.393353
\(650\) 0 0
\(651\) −40.6117 −1.59170
\(652\) 0 0
\(653\) 31.8591 1.24674 0.623371 0.781926i \(-0.285763\pi\)
0.623371 + 0.781926i \(0.285763\pi\)
\(654\) 0 0
\(655\) 9.35146 0.365392
\(656\) 0 0
\(657\) −45.4688 −1.77391
\(658\) 0 0
\(659\) 42.2689 1.64656 0.823282 0.567632i \(-0.192140\pi\)
0.823282 + 0.567632i \(0.192140\pi\)
\(660\) 0 0
\(661\) −25.0251 −0.973365 −0.486683 0.873579i \(-0.661793\pi\)
−0.486683 + 0.873579i \(0.661793\pi\)
\(662\) 0 0
\(663\) −99.5922 −3.86784
\(664\) 0 0
\(665\) −12.6190 −0.489342
\(666\) 0 0
\(667\) −3.87966 −0.150221
\(668\) 0 0
\(669\) −21.5529 −0.833282
\(670\) 0 0
\(671\) 10.8309 0.418122
\(672\) 0 0
\(673\) −25.6058 −0.987030 −0.493515 0.869737i \(-0.664288\pi\)
−0.493515 + 0.869737i \(0.664288\pi\)
\(674\) 0 0
\(675\) −1.77811 −0.0684395
\(676\) 0 0
\(677\) 12.2689 0.471534 0.235767 0.971810i \(-0.424240\pi\)
0.235767 + 0.971810i \(0.424240\pi\)
\(678\) 0 0
\(679\) −11.5119 −0.441786
\(680\) 0 0
\(681\) −39.2531 −1.50418
\(682\) 0 0
\(683\) −38.0788 −1.45704 −0.728522 0.685022i \(-0.759792\pi\)
−0.728522 + 0.685022i \(0.759792\pi\)
\(684\) 0 0
\(685\) −8.92360 −0.340953
\(686\) 0 0
\(687\) −36.3572 −1.38711
\(688\) 0 0
\(689\) −50.8514 −1.93728
\(690\) 0 0
\(691\) −18.9788 −0.721987 −0.360994 0.932568i \(-0.617562\pi\)
−0.360994 + 0.932568i \(0.617562\pi\)
\(692\) 0 0
\(693\) −24.4817 −0.929984
\(694\) 0 0
\(695\) 19.4949 0.739484
\(696\) 0 0
\(697\) 6.33636 0.240007
\(698\) 0 0
\(699\) −24.0797 −0.910780
\(700\) 0 0
\(701\) −5.75834 −0.217490 −0.108745 0.994070i \(-0.534683\pi\)
−0.108745 + 0.994070i \(0.534683\pi\)
\(702\) 0 0
\(703\) −16.0659 −0.605935
\(704\) 0 0
\(705\) 12.5703 0.473427
\(706\) 0 0
\(707\) −0.318292 −0.0119706
\(708\) 0 0
\(709\) 38.6356 1.45099 0.725495 0.688227i \(-0.241611\pi\)
0.725495 + 0.688227i \(0.241611\pi\)
\(710\) 0 0
\(711\) 3.22571 0.120973
\(712\) 0 0
\(713\) −7.56233 −0.283211
\(714\) 0 0
\(715\) −19.0422 −0.712136
\(716\) 0 0
\(717\) 13.3139 0.497215
\(718\) 0 0
\(719\) −3.30293 −0.123179 −0.0615893 0.998102i \(-0.519617\pi\)
−0.0615893 + 0.998102i \(0.519617\pi\)
\(720\) 0 0
\(721\) 6.41790 0.239015
\(722\) 0 0
\(723\) 41.2540 1.53425
\(724\) 0 0
\(725\) −3.87966 −0.144087
\(726\) 0 0
\(727\) 9.74362 0.361371 0.180686 0.983541i \(-0.442168\pi\)
0.180686 + 0.983541i \(0.442168\pi\)
\(728\) 0 0
\(729\) −37.6331 −1.39382
\(730\) 0 0
\(731\) −36.6131 −1.35418
\(732\) 0 0
\(733\) 11.4152 0.421629 0.210814 0.977526i \(-0.432388\pi\)
0.210814 + 0.977526i \(0.432388\pi\)
\(734\) 0 0
\(735\) 6.95018 0.256361
\(736\) 0 0
\(737\) 3.56603 0.131357
\(738\) 0 0
\(739\) 53.6434 1.97330 0.986652 0.162845i \(-0.0520669\pi\)
0.986652 + 0.162845i \(0.0520669\pi\)
\(740\) 0 0
\(741\) 93.5996 3.43847
\(742\) 0 0
\(743\) −24.5457 −0.900494 −0.450247 0.892904i \(-0.648664\pi\)
−0.450247 + 0.892904i \(0.648664\pi\)
\(744\) 0 0
\(745\) −16.9114 −0.619585
\(746\) 0 0
\(747\) −46.1303 −1.68782
\(748\) 0 0
\(749\) −10.9412 −0.399783
\(750\) 0 0
\(751\) −30.1797 −1.10127 −0.550637 0.834745i \(-0.685615\pi\)
−0.550637 + 0.834745i \(0.685615\pi\)
\(752\) 0 0
\(753\) 66.2079 2.41275
\(754\) 0 0
\(755\) −17.4232 −0.634095
\(756\) 0 0
\(757\) −13.1432 −0.477699 −0.238849 0.971057i \(-0.576770\pi\)
−0.238849 + 0.971057i \(0.576770\pi\)
\(758\) 0 0
\(759\) −8.26751 −0.300091
\(760\) 0 0
\(761\) 4.39467 0.159307 0.0796533 0.996823i \(-0.474619\pi\)
0.0796533 + 0.996823i \(0.474619\pi\)
\(762\) 0 0
\(763\) 22.1400 0.801522
\(764\) 0 0
\(765\) −23.8428 −0.862037
\(766\) 0 0
\(767\) 18.6698 0.674129
\(768\) 0 0
\(769\) −27.9380 −1.00747 −0.503734 0.863859i \(-0.668041\pi\)
−0.503734 + 0.863859i \(0.668041\pi\)
\(770\) 0 0
\(771\) −24.1516 −0.869799
\(772\) 0 0
\(773\) −43.2096 −1.55414 −0.777070 0.629414i \(-0.783295\pi\)
−0.777070 + 0.629414i \(0.783295\pi\)
\(774\) 0 0
\(775\) −7.56233 −0.271647
\(776\) 0 0
\(777\) −14.1983 −0.509360
\(778\) 0 0
\(779\) −5.95509 −0.213363
\(780\) 0 0
\(781\) 31.5054 1.12735
\(782\) 0 0
\(783\) 6.89845 0.246531
\(784\) 0 0
\(785\) 22.5565 0.805074
\(786\) 0 0
\(787\) 51.0255 1.81886 0.909431 0.415854i \(-0.136517\pi\)
0.909431 + 0.415854i \(0.136517\pi\)
\(788\) 0 0
\(789\) −1.58304 −0.0563577
\(790\) 0 0
\(791\) 13.8750 0.493338
\(792\) 0 0
\(793\) −20.1790 −0.716578
\(794\) 0 0
\(795\) −22.0781 −0.783029
\(796\) 0 0
\(797\) 19.6701 0.696750 0.348375 0.937355i \(-0.386734\pi\)
0.348375 + 0.937355i \(0.386734\pi\)
\(798\) 0 0
\(799\) 31.4288 1.11187
\(800\) 0 0
\(801\) 38.5374 1.36165
\(802\) 0 0
\(803\) −39.4196 −1.39109
\(804\) 0 0
\(805\) −2.07664 −0.0731918
\(806\) 0 0
\(807\) 17.3398 0.610391
\(808\) 0 0
\(809\) −45.8691 −1.61267 −0.806336 0.591458i \(-0.798553\pi\)
−0.806336 + 0.591458i \(0.798553\pi\)
\(810\) 0 0
\(811\) 1.97629 0.0693971 0.0346985 0.999398i \(-0.488953\pi\)
0.0346985 + 0.999398i \(0.488953\pi\)
\(812\) 0 0
\(813\) −80.7561 −2.83224
\(814\) 0 0
\(815\) 9.31242 0.326200
\(816\) 0 0
\(817\) 34.4100 1.20385
\(818\) 0 0
\(819\) 45.6119 1.59381
\(820\) 0 0
\(821\) −33.7778 −1.17885 −0.589426 0.807822i \(-0.700646\pi\)
−0.589426 + 0.807822i \(0.700646\pi\)
\(822\) 0 0
\(823\) −1.97189 −0.0687356 −0.0343678 0.999409i \(-0.510942\pi\)
−0.0343678 + 0.999409i \(0.510942\pi\)
\(824\) 0 0
\(825\) −8.26751 −0.287838
\(826\) 0 0
\(827\) −2.06779 −0.0719041 −0.0359520 0.999354i \(-0.511446\pi\)
−0.0359520 + 0.999354i \(0.511446\pi\)
\(828\) 0 0
\(829\) −30.0659 −1.04423 −0.522115 0.852875i \(-0.674857\pi\)
−0.522115 + 0.852875i \(0.674857\pi\)
\(830\) 0 0
\(831\) −77.1965 −2.67792
\(832\) 0 0
\(833\) 17.3771 0.602080
\(834\) 0 0
\(835\) 6.77811 0.234566
\(836\) 0 0
\(837\) 13.4467 0.464784
\(838\) 0 0
\(839\) 28.4008 0.980504 0.490252 0.871581i \(-0.336905\pi\)
0.490252 + 0.871581i \(0.336905\pi\)
\(840\) 0 0
\(841\) −13.9483 −0.480975
\(842\) 0 0
\(843\) −47.5597 −1.63804
\(844\) 0 0
\(845\) 22.4774 0.773247
\(846\) 0 0
\(847\) 1.61835 0.0556072
\(848\) 0 0
\(849\) 55.9408 1.91988
\(850\) 0 0
\(851\) −2.64387 −0.0906308
\(852\) 0 0
\(853\) 23.0965 0.790809 0.395405 0.918507i \(-0.370604\pi\)
0.395405 + 0.918507i \(0.370604\pi\)
\(854\) 0 0
\(855\) 22.4081 0.766341
\(856\) 0 0
\(857\) 18.1530 0.620095 0.310048 0.950721i \(-0.399655\pi\)
0.310048 + 0.950721i \(0.399655\pi\)
\(858\) 0 0
\(859\) 49.6082 1.69261 0.846305 0.532699i \(-0.178822\pi\)
0.846305 + 0.532699i \(0.178822\pi\)
\(860\) 0 0
\(861\) −5.26284 −0.179357
\(862\) 0 0
\(863\) 24.3893 0.830221 0.415111 0.909771i \(-0.363743\pi\)
0.415111 + 0.909771i \(0.363743\pi\)
\(864\) 0 0
\(865\) −23.7910 −0.808919
\(866\) 0 0
\(867\) −64.1470 −2.17855
\(868\) 0 0
\(869\) 2.79656 0.0948666
\(870\) 0 0
\(871\) −6.64387 −0.225119
\(872\) 0 0
\(873\) 20.4422 0.691864
\(874\) 0 0
\(875\) −2.07664 −0.0702031
\(876\) 0 0
\(877\) 3.19639 0.107934 0.0539672 0.998543i \(-0.482813\pi\)
0.0539672 + 0.998543i \(0.482813\pi\)
\(878\) 0 0
\(879\) 25.4324 0.857813
\(880\) 0 0
\(881\) −18.8440 −0.634869 −0.317435 0.948280i \(-0.602821\pi\)
−0.317435 + 0.948280i \(0.602821\pi\)
\(882\) 0 0
\(883\) −4.74254 −0.159599 −0.0797996 0.996811i \(-0.525428\pi\)
−0.0797996 + 0.996811i \(0.525428\pi\)
\(884\) 0 0
\(885\) 8.10586 0.272476
\(886\) 0 0
\(887\) −2.69296 −0.0904206 −0.0452103 0.998977i \(-0.514396\pi\)
−0.0452103 + 0.998977i \(0.514396\pi\)
\(888\) 0 0
\(889\) 14.3460 0.481148
\(890\) 0 0
\(891\) −20.6668 −0.692365
\(892\) 0 0
\(893\) −29.5377 −0.988440
\(894\) 0 0
\(895\) 2.45767 0.0821509
\(896\) 0 0
\(897\) 15.4032 0.514297
\(898\) 0 0
\(899\) 29.3392 0.978518
\(900\) 0 0
\(901\) −55.2003 −1.83899
\(902\) 0 0
\(903\) 30.4100 1.01198
\(904\) 0 0
\(905\) −3.28871 −0.109321
\(906\) 0 0
\(907\) −36.1879 −1.20160 −0.600799 0.799400i \(-0.705151\pi\)
−0.600799 + 0.799400i \(0.705151\pi\)
\(908\) 0 0
\(909\) 0.565206 0.0187467
\(910\) 0 0
\(911\) 40.2537 1.33367 0.666833 0.745207i \(-0.267650\pi\)
0.666833 + 0.745207i \(0.267650\pi\)
\(912\) 0 0
\(913\) −39.9931 −1.32358
\(914\) 0 0
\(915\) −8.76111 −0.289633
\(916\) 0 0
\(917\) −19.4196 −0.641291
\(918\) 0 0
\(919\) 9.92181 0.327290 0.163645 0.986519i \(-0.447675\pi\)
0.163645 + 0.986519i \(0.447675\pi\)
\(920\) 0 0
\(921\) 59.4869 1.96016
\(922\) 0 0
\(923\) −58.6977 −1.93206
\(924\) 0 0
\(925\) −2.64387 −0.0869300
\(926\) 0 0
\(927\) −11.3966 −0.374313
\(928\) 0 0
\(929\) −32.3155 −1.06024 −0.530119 0.847923i \(-0.677853\pi\)
−0.530119 + 0.847923i \(0.677853\pi\)
\(930\) 0 0
\(931\) −16.3315 −0.535242
\(932\) 0 0
\(933\) 32.8799 1.07644
\(934\) 0 0
\(935\) −20.6707 −0.676004
\(936\) 0 0
\(937\) −30.1049 −0.983484 −0.491742 0.870741i \(-0.663640\pi\)
−0.491742 + 0.870741i \(0.663640\pi\)
\(938\) 0 0
\(939\) 45.4063 1.48178
\(940\) 0 0
\(941\) 6.37205 0.207723 0.103861 0.994592i \(-0.466880\pi\)
0.103861 + 0.994592i \(0.466880\pi\)
\(942\) 0 0
\(943\) −0.979997 −0.0319131
\(944\) 0 0
\(945\) 3.69249 0.120117
\(946\) 0 0
\(947\) −38.5664 −1.25324 −0.626620 0.779325i \(-0.715562\pi\)
−0.626620 + 0.779325i \(0.715562\pi\)
\(948\) 0 0
\(949\) 73.4426 2.38405
\(950\) 0 0
\(951\) −59.7179 −1.93648
\(952\) 0 0
\(953\) 44.0322 1.42634 0.713171 0.700990i \(-0.247258\pi\)
0.713171 + 0.700990i \(0.247258\pi\)
\(954\) 0 0
\(955\) 5.36535 0.173619
\(956\) 0 0
\(957\) 32.0751 1.03684
\(958\) 0 0
\(959\) 18.5311 0.598400
\(960\) 0 0
\(961\) 26.1888 0.844801
\(962\) 0 0
\(963\) 19.4288 0.626084
\(964\) 0 0
\(965\) 19.4671 0.626669
\(966\) 0 0
\(967\) −23.3837 −0.751967 −0.375984 0.926626i \(-0.622695\pi\)
−0.375984 + 0.926626i \(0.622695\pi\)
\(968\) 0 0
\(969\) 101.604 3.26401
\(970\) 0 0
\(971\) 47.4327 1.52219 0.761095 0.648641i \(-0.224662\pi\)
0.761095 + 0.648641i \(0.224662\pi\)
\(972\) 0 0
\(973\) −40.4839 −1.29785
\(974\) 0 0
\(975\) 15.4032 0.493297
\(976\) 0 0
\(977\) −27.2961 −0.873280 −0.436640 0.899636i \(-0.643832\pi\)
−0.436640 + 0.899636i \(0.643832\pi\)
\(978\) 0 0
\(979\) 33.4104 1.06780
\(980\) 0 0
\(981\) −39.3150 −1.25523
\(982\) 0 0
\(983\) −7.17601 −0.228879 −0.114440 0.993430i \(-0.536507\pi\)
−0.114440 + 0.993430i \(0.536507\pi\)
\(984\) 0 0
\(985\) −8.05543 −0.256667
\(986\) 0 0
\(987\) −26.1040 −0.830901
\(988\) 0 0
\(989\) 5.66267 0.180063
\(990\) 0 0
\(991\) −38.6824 −1.22879 −0.614394 0.789000i \(-0.710599\pi\)
−0.614394 + 0.789000i \(0.710599\pi\)
\(992\) 0 0
\(993\) −19.4329 −0.616684
\(994\) 0 0
\(995\) −21.4596 −0.680314
\(996\) 0 0
\(997\) 22.0184 0.697331 0.348666 0.937247i \(-0.386635\pi\)
0.348666 + 0.937247i \(0.386635\pi\)
\(998\) 0 0
\(999\) 4.70110 0.148736
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 7360.2.a.ch.1.1 4
4.3 odd 2 7360.2.a.ci.1.4 4
8.3 odd 2 3680.2.a.s.1.1 4
8.5 even 2 3680.2.a.t.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.s.1.1 4 8.3 odd 2
3680.2.a.t.1.4 yes 4 8.5 even 2
7360.2.a.ch.1.1 4 1.1 even 1 trivial
7360.2.a.ci.1.4 4 4.3 odd 2