Properties

Label 7360.2.a.cq.1.5
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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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: \(5\)
Coefficient field: 5.5.876604.1
Defining polynomial: \(x^{5} - x^{4} - 9 x^{3} + 8 x^{2} + 18 x - 16\)
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 1.5
Root \(0.895130\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.94825 q^{3} -1.00000 q^{5} -2.13809 q^{7} +5.69219 q^{9} +O(q^{10})\) \(q+2.94825 q^{3} -1.00000 q^{5} -2.13809 q^{7} +5.69219 q^{9} +5.67228 q^{11} +5.04212 q^{13} -2.94825 q^{15} +0.545195 q^{17} +6.74531 q^{19} -6.30361 q^{21} +1.00000 q^{23} +1.00000 q^{25} +7.93725 q^{27} +5.11378 q^{29} -4.64464 q^{31} +16.7233 q^{33} +2.13809 q^{35} +2.21748 q^{37} +14.8655 q^{39} -10.2264 q^{41} -10.5377 q^{43} -5.69219 q^{45} +2.61280 q^{47} -2.42859 q^{49} +1.60737 q^{51} -8.67366 q^{53} -5.67228 q^{55} +19.8869 q^{57} -0.777152 q^{59} +7.00137 q^{61} -12.1704 q^{63} -5.04212 q^{65} +7.27040 q^{67} +2.94825 q^{69} +3.40168 q^{71} -6.34436 q^{73} +2.94825 q^{75} -12.1278 q^{77} -4.07651 q^{79} +6.32446 q^{81} +1.51409 q^{83} -0.545195 q^{85} +15.0767 q^{87} -9.79799 q^{89} -10.7805 q^{91} -13.6936 q^{93} -6.74531 q^{95} +4.60389 q^{97} +32.2877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + q^{3} - 5 q^{5} - q^{7} + 6 q^{9} + O(q^{10}) \) \( 5 q + q^{3} - 5 q^{5} - q^{7} + 6 q^{9} + 3 q^{11} - 7 q^{13} - q^{15} + 9 q^{17} + q^{19} - 20 q^{21} + 5 q^{23} + 5 q^{25} + 4 q^{27} + 10 q^{29} - 21 q^{31} + 7 q^{33} + q^{35} - 8 q^{37} + 24 q^{39} - 13 q^{41} - 6 q^{43} - 6 q^{45} + 24 q^{49} - 17 q^{51} + 6 q^{53} - 3 q^{55} + 26 q^{57} + 18 q^{59} + 11 q^{61} - 4 q^{63} + 7 q^{65} + 38 q^{67} + q^{69} + 21 q^{71} - 12 q^{73} + q^{75} - 46 q^{77} + 18 q^{79} + 9 q^{81} + 20 q^{83} - 9 q^{85} + 6 q^{87} - 16 q^{89} - 3 q^{91} - 22 q^{93} - q^{95} + 29 q^{97} + 29 q^{99} + O(q^{100}) \)

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
\(3\) 2.94825 1.70217 0.851087 0.525025i \(-0.175944\pi\)
0.851087 + 0.525025i \(0.175944\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.13809 −0.808120 −0.404060 0.914732i \(-0.632401\pi\)
−0.404060 + 0.914732i \(0.632401\pi\)
\(8\) 0 0
\(9\) 5.69219 1.89740
\(10\) 0 0
\(11\) 5.67228 1.71026 0.855129 0.518416i \(-0.173478\pi\)
0.855129 + 0.518416i \(0.173478\pi\)
\(12\) 0 0
\(13\) 5.04212 1.39843 0.699217 0.714910i \(-0.253532\pi\)
0.699217 + 0.714910i \(0.253532\pi\)
\(14\) 0 0
\(15\) −2.94825 −0.761235
\(16\) 0 0
\(17\) 0.545195 0.132229 0.0661146 0.997812i \(-0.478940\pi\)
0.0661146 + 0.997812i \(0.478940\pi\)
\(18\) 0 0
\(19\) 6.74531 1.54748 0.773740 0.633503i \(-0.218383\pi\)
0.773740 + 0.633503i \(0.218383\pi\)
\(20\) 0 0
\(21\) −6.30361 −1.37556
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 7.93725 1.52753
\(28\) 0 0
\(29\) 5.11378 0.949605 0.474803 0.880092i \(-0.342519\pi\)
0.474803 + 0.880092i \(0.342519\pi\)
\(30\) 0 0
\(31\) −4.64464 −0.834202 −0.417101 0.908860i \(-0.636954\pi\)
−0.417101 + 0.908860i \(0.636954\pi\)
\(32\) 0 0
\(33\) 16.7233 2.91116
\(34\) 0 0
\(35\) 2.13809 0.361402
\(36\) 0 0
\(37\) 2.21748 0.364551 0.182275 0.983248i \(-0.441654\pi\)
0.182275 + 0.983248i \(0.441654\pi\)
\(38\) 0 0
\(39\) 14.8655 2.38038
\(40\) 0 0
\(41\) −10.2264 −1.59709 −0.798547 0.601933i \(-0.794397\pi\)
−0.798547 + 0.601933i \(0.794397\pi\)
\(42\) 0 0
\(43\) −10.5377 −1.60698 −0.803491 0.595317i \(-0.797026\pi\)
−0.803491 + 0.595317i \(0.797026\pi\)
\(44\) 0 0
\(45\) −5.69219 −0.848542
\(46\) 0 0
\(47\) 2.61280 0.381116 0.190558 0.981676i \(-0.438970\pi\)
0.190558 + 0.981676i \(0.438970\pi\)
\(48\) 0 0
\(49\) −2.42859 −0.346942
\(50\) 0 0
\(51\) 1.60737 0.225077
\(52\) 0 0
\(53\) −8.67366 −1.19142 −0.595709 0.803200i \(-0.703129\pi\)
−0.595709 + 0.803200i \(0.703129\pi\)
\(54\) 0 0
\(55\) −5.67228 −0.764850
\(56\) 0 0
\(57\) 19.8869 2.63408
\(58\) 0 0
\(59\) −0.777152 −0.101177 −0.0505883 0.998720i \(-0.516110\pi\)
−0.0505883 + 0.998720i \(0.516110\pi\)
\(60\) 0 0
\(61\) 7.00137 0.896434 0.448217 0.893925i \(-0.352059\pi\)
0.448217 + 0.893925i \(0.352059\pi\)
\(62\) 0 0
\(63\) −12.1704 −1.53332
\(64\) 0 0
\(65\) −5.04212 −0.625399
\(66\) 0 0
\(67\) 7.27040 0.888221 0.444110 0.895972i \(-0.353520\pi\)
0.444110 + 0.895972i \(0.353520\pi\)
\(68\) 0 0
\(69\) 2.94825 0.354928
\(70\) 0 0
\(71\) 3.40168 0.403705 0.201853 0.979416i \(-0.435304\pi\)
0.201853 + 0.979416i \(0.435304\pi\)
\(72\) 0 0
\(73\) −6.34436 −0.742552 −0.371276 0.928523i \(-0.621080\pi\)
−0.371276 + 0.928523i \(0.621080\pi\)
\(74\) 0 0
\(75\) 2.94825 0.340435
\(76\) 0 0
\(77\) −12.1278 −1.38209
\(78\) 0 0
\(79\) −4.07651 −0.458644 −0.229322 0.973351i \(-0.573651\pi\)
−0.229322 + 0.973351i \(0.573651\pi\)
\(80\) 0 0
\(81\) 6.32446 0.702717
\(82\) 0 0
\(83\) 1.51409 0.166193 0.0830964 0.996542i \(-0.473519\pi\)
0.0830964 + 0.996542i \(0.473519\pi\)
\(84\) 0 0
\(85\) −0.545195 −0.0591347
\(86\) 0 0
\(87\) 15.0767 1.61639
\(88\) 0 0
\(89\) −9.79799 −1.03859 −0.519293 0.854596i \(-0.673805\pi\)
−0.519293 + 0.854596i \(0.673805\pi\)
\(90\) 0 0
\(91\) −10.7805 −1.13010
\(92\) 0 0
\(93\) −13.6936 −1.41996
\(94\) 0 0
\(95\) −6.74531 −0.692054
\(96\) 0 0
\(97\) 4.60389 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(98\) 0 0
\(99\) 32.2877 3.24504
\(100\) 0 0
\(101\) 12.6915 1.26285 0.631425 0.775437i \(-0.282471\pi\)
0.631425 + 0.775437i \(0.282471\pi\)
\(102\) 0 0
\(103\) −10.3271 −1.01756 −0.508778 0.860898i \(-0.669903\pi\)
−0.508778 + 0.860898i \(0.669903\pi\)
\(104\) 0 0
\(105\) 6.30361 0.615170
\(106\) 0 0
\(107\) 11.9221 1.15255 0.576275 0.817256i \(-0.304506\pi\)
0.576275 + 0.817256i \(0.304506\pi\)
\(108\) 0 0
\(109\) 7.06552 0.676754 0.338377 0.941011i \(-0.390122\pi\)
0.338377 + 0.941011i \(0.390122\pi\)
\(110\) 0 0
\(111\) 6.53768 0.620529
\(112\) 0 0
\(113\) 19.5134 1.83567 0.917835 0.396963i \(-0.129936\pi\)
0.917835 + 0.396963i \(0.129936\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 28.7007 2.65338
\(118\) 0 0
\(119\) −1.16567 −0.106857
\(120\) 0 0
\(121\) 21.1748 1.92498
\(122\) 0 0
\(123\) −30.1500 −2.71853
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.1007 1.25123 0.625616 0.780131i \(-0.284848\pi\)
0.625616 + 0.780131i \(0.284848\pi\)
\(128\) 0 0
\(129\) −31.0677 −2.73536
\(130\) 0 0
\(131\) −19.0470 −1.66414 −0.832071 0.554669i \(-0.812845\pi\)
−0.832071 + 0.554669i \(0.812845\pi\)
\(132\) 0 0
\(133\) −14.4221 −1.25055
\(134\) 0 0
\(135\) −7.93725 −0.683130
\(136\) 0 0
\(137\) 10.5943 0.905129 0.452565 0.891732i \(-0.350509\pi\)
0.452565 + 0.891732i \(0.350509\pi\)
\(138\) 0 0
\(139\) −14.3997 −1.22136 −0.610681 0.791877i \(-0.709104\pi\)
−0.610681 + 0.791877i \(0.709104\pi\)
\(140\) 0 0
\(141\) 7.70319 0.648725
\(142\) 0 0
\(143\) 28.6004 2.39168
\(144\) 0 0
\(145\) −5.11378 −0.424676
\(146\) 0 0
\(147\) −7.16010 −0.590555
\(148\) 0 0
\(149\) 2.81908 0.230948 0.115474 0.993311i \(-0.463161\pi\)
0.115474 + 0.993311i \(0.463161\pi\)
\(150\) 0 0
\(151\) −0.704562 −0.0573365 −0.0286682 0.999589i \(-0.509127\pi\)
−0.0286682 + 0.999589i \(0.509127\pi\)
\(152\) 0 0
\(153\) 3.10335 0.250891
\(154\) 0 0
\(155\) 4.64464 0.373066
\(156\) 0 0
\(157\) 16.0793 1.28326 0.641632 0.767012i \(-0.278257\pi\)
0.641632 + 0.767012i \(0.278257\pi\)
\(158\) 0 0
\(159\) −25.5721 −2.02800
\(160\) 0 0
\(161\) −2.13809 −0.168505
\(162\) 0 0
\(163\) 12.1665 0.952951 0.476475 0.879188i \(-0.341914\pi\)
0.476475 + 0.879188i \(0.341914\pi\)
\(164\) 0 0
\(165\) −16.7233 −1.30191
\(166\) 0 0
\(167\) −22.6031 −1.74908 −0.874538 0.484956i \(-0.838835\pi\)
−0.874538 + 0.484956i \(0.838835\pi\)
\(168\) 0 0
\(169\) 12.4230 0.955617
\(170\) 0 0
\(171\) 38.3956 2.93618
\(172\) 0 0
\(173\) −6.50538 −0.494595 −0.247297 0.968940i \(-0.579542\pi\)
−0.247297 + 0.968940i \(0.579542\pi\)
\(174\) 0 0
\(175\) −2.13809 −0.161624
\(176\) 0 0
\(177\) −2.29124 −0.172220
\(178\) 0 0
\(179\) 9.90981 0.740694 0.370347 0.928893i \(-0.379239\pi\)
0.370347 + 0.928893i \(0.379239\pi\)
\(180\) 0 0
\(181\) −2.95505 −0.219647 −0.109824 0.993951i \(-0.535029\pi\)
−0.109824 + 0.993951i \(0.535029\pi\)
\(182\) 0 0
\(183\) 20.6418 1.52589
\(184\) 0 0
\(185\) −2.21748 −0.163032
\(186\) 0 0
\(187\) 3.09250 0.226146
\(188\) 0 0
\(189\) −16.9705 −1.23442
\(190\) 0 0
\(191\) 5.46155 0.395184 0.197592 0.980284i \(-0.436688\pi\)
0.197592 + 0.980284i \(0.436688\pi\)
\(192\) 0 0
\(193\) −0.778917 −0.0560677 −0.0280338 0.999607i \(-0.508925\pi\)
−0.0280338 + 0.999607i \(0.508925\pi\)
\(194\) 0 0
\(195\) −14.8655 −1.06454
\(196\) 0 0
\(197\) −16.9363 −1.20666 −0.603332 0.797490i \(-0.706161\pi\)
−0.603332 + 0.797490i \(0.706161\pi\)
\(198\) 0 0
\(199\) −6.78489 −0.480968 −0.240484 0.970653i \(-0.577306\pi\)
−0.240484 + 0.970653i \(0.577306\pi\)
\(200\) 0 0
\(201\) 21.4350 1.51191
\(202\) 0 0
\(203\) −10.9337 −0.767395
\(204\) 0 0
\(205\) 10.2264 0.714242
\(206\) 0 0
\(207\) 5.69219 0.395635
\(208\) 0 0
\(209\) 38.2613 2.64659
\(210\) 0 0
\(211\) −16.8197 −1.15792 −0.578959 0.815357i \(-0.696541\pi\)
−0.578959 + 0.815357i \(0.696541\pi\)
\(212\) 0 0
\(213\) 10.0290 0.687177
\(214\) 0 0
\(215\) 10.5377 0.718664
\(216\) 0 0
\(217\) 9.93063 0.674135
\(218\) 0 0
\(219\) −18.7048 −1.26395
\(220\) 0 0
\(221\) 2.74894 0.184914
\(222\) 0 0
\(223\) 20.2013 1.35278 0.676391 0.736543i \(-0.263543\pi\)
0.676391 + 0.736543i \(0.263543\pi\)
\(224\) 0 0
\(225\) 5.69219 0.379479
\(226\) 0 0
\(227\) 20.2353 1.34306 0.671532 0.740976i \(-0.265637\pi\)
0.671532 + 0.740976i \(0.265637\pi\)
\(228\) 0 0
\(229\) −21.2264 −1.40268 −0.701340 0.712827i \(-0.747415\pi\)
−0.701340 + 0.712827i \(0.747415\pi\)
\(230\) 0 0
\(231\) −35.7559 −2.35256
\(232\) 0 0
\(233\) −13.1243 −0.859799 −0.429900 0.902877i \(-0.641451\pi\)
−0.429900 + 0.902877i \(0.641451\pi\)
\(234\) 0 0
\(235\) −2.61280 −0.170440
\(236\) 0 0
\(237\) −12.0186 −0.780691
\(238\) 0 0
\(239\) −8.02691 −0.519218 −0.259609 0.965714i \(-0.583594\pi\)
−0.259609 + 0.965714i \(0.583594\pi\)
\(240\) 0 0
\(241\) 0.788006 0.0507599 0.0253800 0.999678i \(-0.491920\pi\)
0.0253800 + 0.999678i \(0.491920\pi\)
\(242\) 0 0
\(243\) −5.16567 −0.331378
\(244\) 0 0
\(245\) 2.42859 0.155157
\(246\) 0 0
\(247\) 34.0107 2.16405
\(248\) 0 0
\(249\) 4.46392 0.282889
\(250\) 0 0
\(251\) −30.8373 −1.94643 −0.973216 0.229891i \(-0.926163\pi\)
−0.973216 + 0.229891i \(0.926163\pi\)
\(252\) 0 0
\(253\) 5.67228 0.356613
\(254\) 0 0
\(255\) −1.60737 −0.100658
\(256\) 0 0
\(257\) 13.2362 0.825649 0.412824 0.910811i \(-0.364542\pi\)
0.412824 + 0.910811i \(0.364542\pi\)
\(258\) 0 0
\(259\) −4.74115 −0.294601
\(260\) 0 0
\(261\) 29.1086 1.80178
\(262\) 0 0
\(263\) 26.7546 1.64976 0.824879 0.565310i \(-0.191243\pi\)
0.824879 + 0.565310i \(0.191243\pi\)
\(264\) 0 0
\(265\) 8.67366 0.532818
\(266\) 0 0
\(267\) −28.8870 −1.76785
\(268\) 0 0
\(269\) −23.2672 −1.41863 −0.709313 0.704893i \(-0.750995\pi\)
−0.709313 + 0.704893i \(0.750995\pi\)
\(270\) 0 0
\(271\) −0.119207 −0.00724133 −0.00362067 0.999993i \(-0.501152\pi\)
−0.00362067 + 0.999993i \(0.501152\pi\)
\(272\) 0 0
\(273\) −31.7836 −1.92363
\(274\) 0 0
\(275\) 5.67228 0.342051
\(276\) 0 0
\(277\) −6.49882 −0.390476 −0.195238 0.980756i \(-0.562548\pi\)
−0.195238 + 0.980756i \(0.562548\pi\)
\(278\) 0 0
\(279\) −26.4382 −1.58281
\(280\) 0 0
\(281\) 3.59753 0.214610 0.107305 0.994226i \(-0.465778\pi\)
0.107305 + 0.994226i \(0.465778\pi\)
\(282\) 0 0
\(283\) 18.7552 1.11488 0.557439 0.830218i \(-0.311784\pi\)
0.557439 + 0.830218i \(0.311784\pi\)
\(284\) 0 0
\(285\) −19.8869 −1.17800
\(286\) 0 0
\(287\) 21.8649 1.29064
\(288\) 0 0
\(289\) −16.7028 −0.982515
\(290\) 0 0
\(291\) 13.5734 0.795688
\(292\) 0 0
\(293\) −1.19938 −0.0700687 −0.0350344 0.999386i \(-0.511154\pi\)
−0.0350344 + 0.999386i \(0.511154\pi\)
\(294\) 0 0
\(295\) 0.777152 0.0452476
\(296\) 0 0
\(297\) 45.0223 2.61246
\(298\) 0 0
\(299\) 5.04212 0.291594
\(300\) 0 0
\(301\) 22.5305 1.29863
\(302\) 0 0
\(303\) 37.4177 2.14959
\(304\) 0 0
\(305\) −7.00137 −0.400898
\(306\) 0 0
\(307\) 8.14771 0.465014 0.232507 0.972595i \(-0.425307\pi\)
0.232507 + 0.972595i \(0.425307\pi\)
\(308\) 0 0
\(309\) −30.4468 −1.73206
\(310\) 0 0
\(311\) 33.7342 1.91289 0.956447 0.291907i \(-0.0942898\pi\)
0.956447 + 0.291907i \(0.0942898\pi\)
\(312\) 0 0
\(313\) 3.24043 0.183160 0.0915799 0.995798i \(-0.470808\pi\)
0.0915799 + 0.995798i \(0.470808\pi\)
\(314\) 0 0
\(315\) 12.1704 0.685724
\(316\) 0 0
\(317\) 5.89626 0.331167 0.165584 0.986196i \(-0.447049\pi\)
0.165584 + 0.986196i \(0.447049\pi\)
\(318\) 0 0
\(319\) 29.0068 1.62407
\(320\) 0 0
\(321\) 35.1492 1.96184
\(322\) 0 0
\(323\) 3.67751 0.204622
\(324\) 0 0
\(325\) 5.04212 0.279687
\(326\) 0 0
\(327\) 20.8309 1.15195
\(328\) 0 0
\(329\) −5.58638 −0.307987
\(330\) 0 0
\(331\) 1.57807 0.0867383 0.0433691 0.999059i \(-0.486191\pi\)
0.0433691 + 0.999059i \(0.486191\pi\)
\(332\) 0 0
\(333\) 12.6223 0.691698
\(334\) 0 0
\(335\) −7.27040 −0.397224
\(336\) 0 0
\(337\) −1.55835 −0.0848888 −0.0424444 0.999099i \(-0.513515\pi\)
−0.0424444 + 0.999099i \(0.513515\pi\)
\(338\) 0 0
\(339\) 57.5305 3.12463
\(340\) 0 0
\(341\) −26.3457 −1.42670
\(342\) 0 0
\(343\) 20.1591 1.08849
\(344\) 0 0
\(345\) −2.94825 −0.158729
\(346\) 0 0
\(347\) 32.4997 1.74468 0.872339 0.488902i \(-0.162603\pi\)
0.872339 + 0.488902i \(0.162603\pi\)
\(348\) 0 0
\(349\) −20.9841 −1.12325 −0.561626 0.827391i \(-0.689824\pi\)
−0.561626 + 0.827391i \(0.689824\pi\)
\(350\) 0 0
\(351\) 40.0206 2.13614
\(352\) 0 0
\(353\) −30.2614 −1.61065 −0.805327 0.592831i \(-0.798010\pi\)
−0.805327 + 0.592831i \(0.798010\pi\)
\(354\) 0 0
\(355\) −3.40168 −0.180543
\(356\) 0 0
\(357\) −3.43670 −0.181889
\(358\) 0 0
\(359\) 12.8907 0.680347 0.340173 0.940363i \(-0.389514\pi\)
0.340173 + 0.940363i \(0.389514\pi\)
\(360\) 0 0
\(361\) 26.4992 1.39470
\(362\) 0 0
\(363\) 62.4286 3.27665
\(364\) 0 0
\(365\) 6.34436 0.332079
\(366\) 0 0
\(367\) −9.49484 −0.495627 −0.247813 0.968808i \(-0.579712\pi\)
−0.247813 + 0.968808i \(0.579712\pi\)
\(368\) 0 0
\(369\) −58.2105 −3.03032
\(370\) 0 0
\(371\) 18.5450 0.962809
\(372\) 0 0
\(373\) 15.3732 0.795996 0.397998 0.917386i \(-0.369705\pi\)
0.397998 + 0.917386i \(0.369705\pi\)
\(374\) 0 0
\(375\) −2.94825 −0.152247
\(376\) 0 0
\(377\) 25.7843 1.32796
\(378\) 0 0
\(379\) 34.7952 1.78731 0.893655 0.448756i \(-0.148133\pi\)
0.893655 + 0.448756i \(0.148133\pi\)
\(380\) 0 0
\(381\) 41.5723 2.12982
\(382\) 0 0
\(383\) 26.6026 1.35933 0.679666 0.733522i \(-0.262125\pi\)
0.679666 + 0.733522i \(0.262125\pi\)
\(384\) 0 0
\(385\) 12.1278 0.618091
\(386\) 0 0
\(387\) −59.9825 −3.04908
\(388\) 0 0
\(389\) 33.0795 1.67720 0.838598 0.544751i \(-0.183376\pi\)
0.838598 + 0.544751i \(0.183376\pi\)
\(390\) 0 0
\(391\) 0.545195 0.0275717
\(392\) 0 0
\(393\) −56.1553 −2.83266
\(394\) 0 0
\(395\) 4.07651 0.205112
\(396\) 0 0
\(397\) −33.8019 −1.69647 −0.848235 0.529620i \(-0.822334\pi\)
−0.848235 + 0.529620i \(0.822334\pi\)
\(398\) 0 0
\(399\) −42.5198 −2.12865
\(400\) 0 0
\(401\) −23.1390 −1.15551 −0.577754 0.816211i \(-0.696071\pi\)
−0.577754 + 0.816211i \(0.696071\pi\)
\(402\) 0 0
\(403\) −23.4188 −1.16658
\(404\) 0 0
\(405\) −6.32446 −0.314265
\(406\) 0 0
\(407\) 12.5782 0.623476
\(408\) 0 0
\(409\) −22.9838 −1.13648 −0.568239 0.822864i \(-0.692375\pi\)
−0.568239 + 0.822864i \(0.692375\pi\)
\(410\) 0 0
\(411\) 31.2346 1.54069
\(412\) 0 0
\(413\) 1.66162 0.0817629
\(414\) 0 0
\(415\) −1.51409 −0.0743237
\(416\) 0 0
\(417\) −42.4538 −2.07897
\(418\) 0 0
\(419\) −23.5935 −1.15262 −0.576308 0.817233i \(-0.695507\pi\)
−0.576308 + 0.817233i \(0.695507\pi\)
\(420\) 0 0
\(421\) −35.0768 −1.70954 −0.854769 0.519009i \(-0.826301\pi\)
−0.854769 + 0.519009i \(0.826301\pi\)
\(422\) 0 0
\(423\) 14.8725 0.723128
\(424\) 0 0
\(425\) 0.545195 0.0264458
\(426\) 0 0
\(427\) −14.9695 −0.724427
\(428\) 0 0
\(429\) 84.3210 4.07106
\(430\) 0 0
\(431\) −18.0434 −0.869119 −0.434559 0.900643i \(-0.643096\pi\)
−0.434559 + 0.900643i \(0.643096\pi\)
\(432\) 0 0
\(433\) −22.0698 −1.06061 −0.530304 0.847808i \(-0.677922\pi\)
−0.530304 + 0.847808i \(0.677922\pi\)
\(434\) 0 0
\(435\) −15.0767 −0.722873
\(436\) 0 0
\(437\) 6.74531 0.322672
\(438\) 0 0
\(439\) 21.0314 1.00377 0.501887 0.864933i \(-0.332639\pi\)
0.501887 + 0.864933i \(0.332639\pi\)
\(440\) 0 0
\(441\) −13.8240 −0.658286
\(442\) 0 0
\(443\) 13.4291 0.638037 0.319019 0.947748i \(-0.396647\pi\)
0.319019 + 0.947748i \(0.396647\pi\)
\(444\) 0 0
\(445\) 9.79799 0.464469
\(446\) 0 0
\(447\) 8.31135 0.393113
\(448\) 0 0
\(449\) −6.57879 −0.310472 −0.155236 0.987877i \(-0.549614\pi\)
−0.155236 + 0.987877i \(0.549614\pi\)
\(450\) 0 0
\(451\) −58.0069 −2.73144
\(452\) 0 0
\(453\) −2.07723 −0.0975966
\(454\) 0 0
\(455\) 10.7805 0.505397
\(456\) 0 0
\(457\) 40.3604 1.88798 0.943990 0.329973i \(-0.107040\pi\)
0.943990 + 0.329973i \(0.107040\pi\)
\(458\) 0 0
\(459\) 4.32735 0.201983
\(460\) 0 0
\(461\) 3.83330 0.178534 0.0892672 0.996008i \(-0.471547\pi\)
0.0892672 + 0.996008i \(0.471547\pi\)
\(462\) 0 0
\(463\) −31.6251 −1.46974 −0.734871 0.678207i \(-0.762757\pi\)
−0.734871 + 0.678207i \(0.762757\pi\)
\(464\) 0 0
\(465\) 13.6936 0.635024
\(466\) 0 0
\(467\) −10.3994 −0.481225 −0.240612 0.970621i \(-0.577348\pi\)
−0.240612 + 0.970621i \(0.577348\pi\)
\(468\) 0 0
\(469\) −15.5447 −0.717789
\(470\) 0 0
\(471\) 47.4057 2.18434
\(472\) 0 0
\(473\) −59.7727 −2.74835
\(474\) 0 0
\(475\) 6.74531 0.309496
\(476\) 0 0
\(477\) −49.3721 −2.26059
\(478\) 0 0
\(479\) −37.7475 −1.72473 −0.862365 0.506288i \(-0.831017\pi\)
−0.862365 + 0.506288i \(0.831017\pi\)
\(480\) 0 0
\(481\) 11.1808 0.509800
\(482\) 0 0
\(483\) −6.30361 −0.286824
\(484\) 0 0
\(485\) −4.60389 −0.209052
\(486\) 0 0
\(487\) −8.15350 −0.369470 −0.184735 0.982788i \(-0.559143\pi\)
−0.184735 + 0.982788i \(0.559143\pi\)
\(488\) 0 0
\(489\) 35.8698 1.62209
\(490\) 0 0
\(491\) 24.9268 1.12493 0.562466 0.826820i \(-0.309853\pi\)
0.562466 + 0.826820i \(0.309853\pi\)
\(492\) 0 0
\(493\) 2.78801 0.125565
\(494\) 0 0
\(495\) −32.2877 −1.45122
\(496\) 0 0
\(497\) −7.27309 −0.326243
\(498\) 0 0
\(499\) 8.59825 0.384911 0.192455 0.981306i \(-0.438355\pi\)
0.192455 + 0.981306i \(0.438355\pi\)
\(500\) 0 0
\(501\) −66.6395 −2.97723
\(502\) 0 0
\(503\) −39.6459 −1.76772 −0.883861 0.467750i \(-0.845065\pi\)
−0.883861 + 0.467750i \(0.845065\pi\)
\(504\) 0 0
\(505\) −12.6915 −0.564763
\(506\) 0 0
\(507\) 36.6262 1.62663
\(508\) 0 0
\(509\) 29.7612 1.31914 0.659572 0.751642i \(-0.270738\pi\)
0.659572 + 0.751642i \(0.270738\pi\)
\(510\) 0 0
\(511\) 13.5648 0.600071
\(512\) 0 0
\(513\) 53.5393 2.36382
\(514\) 0 0
\(515\) 10.3271 0.455065
\(516\) 0 0
\(517\) 14.8205 0.651806
\(518\) 0 0
\(519\) −19.1795 −0.841886
\(520\) 0 0
\(521\) −30.9544 −1.35614 −0.678069 0.734998i \(-0.737183\pi\)
−0.678069 + 0.734998i \(0.737183\pi\)
\(522\) 0 0
\(523\) 28.3392 1.23919 0.619593 0.784923i \(-0.287298\pi\)
0.619593 + 0.784923i \(0.287298\pi\)
\(524\) 0 0
\(525\) −6.30361 −0.275112
\(526\) 0 0
\(527\) −2.53223 −0.110306
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −4.42370 −0.191972
\(532\) 0 0
\(533\) −51.5627 −2.23343
\(534\) 0 0
\(535\) −11.9221 −0.515436
\(536\) 0 0
\(537\) 29.2166 1.26079
\(538\) 0 0
\(539\) −13.7757 −0.593360
\(540\) 0 0
\(541\) −2.72062 −0.116969 −0.0584844 0.998288i \(-0.518627\pi\)
−0.0584844 + 0.998288i \(0.518627\pi\)
\(542\) 0 0
\(543\) −8.71224 −0.373878
\(544\) 0 0
\(545\) −7.06552 −0.302653
\(546\) 0 0
\(547\) −34.8646 −1.49070 −0.745352 0.666671i \(-0.767718\pi\)
−0.745352 + 0.666671i \(0.767718\pi\)
\(548\) 0 0
\(549\) 39.8532 1.70089
\(550\) 0 0
\(551\) 34.4940 1.46950
\(552\) 0 0
\(553\) 8.71593 0.370639
\(554\) 0 0
\(555\) −6.53768 −0.277509
\(556\) 0 0
\(557\) 0.424068 0.0179684 0.00898418 0.999960i \(-0.497140\pi\)
0.00898418 + 0.999960i \(0.497140\pi\)
\(558\) 0 0
\(559\) −53.1323 −2.24726
\(560\) 0 0
\(561\) 9.11746 0.384940
\(562\) 0 0
\(563\) −37.2454 −1.56971 −0.784853 0.619682i \(-0.787262\pi\)
−0.784853 + 0.619682i \(0.787262\pi\)
\(564\) 0 0
\(565\) −19.5134 −0.820936
\(566\) 0 0
\(567\) −13.5222 −0.567880
\(568\) 0 0
\(569\) 2.31757 0.0971574 0.0485787 0.998819i \(-0.484531\pi\)
0.0485787 + 0.998819i \(0.484531\pi\)
\(570\) 0 0
\(571\) −33.6079 −1.40645 −0.703224 0.710968i \(-0.748257\pi\)
−0.703224 + 0.710968i \(0.748257\pi\)
\(572\) 0 0
\(573\) 16.1020 0.672672
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 7.59589 0.316221 0.158110 0.987421i \(-0.449460\pi\)
0.158110 + 0.987421i \(0.449460\pi\)
\(578\) 0 0
\(579\) −2.29644 −0.0954369
\(580\) 0 0
\(581\) −3.23725 −0.134304
\(582\) 0 0
\(583\) −49.1994 −2.03763
\(584\) 0 0
\(585\) −28.7007 −1.18663
\(586\) 0 0
\(587\) 31.6838 1.30773 0.653864 0.756612i \(-0.273147\pi\)
0.653864 + 0.756612i \(0.273147\pi\)
\(588\) 0 0
\(589\) −31.3295 −1.29091
\(590\) 0 0
\(591\) −49.9326 −2.05395
\(592\) 0 0
\(593\) −33.4910 −1.37531 −0.687656 0.726037i \(-0.741360\pi\)
−0.687656 + 0.726037i \(0.741360\pi\)
\(594\) 0 0
\(595\) 1.16567 0.0477879
\(596\) 0 0
\(597\) −20.0036 −0.818691
\(598\) 0 0
\(599\) 8.59861 0.351330 0.175665 0.984450i \(-0.443792\pi\)
0.175665 + 0.984450i \(0.443792\pi\)
\(600\) 0 0
\(601\) 2.84676 0.116122 0.0580608 0.998313i \(-0.481508\pi\)
0.0580608 + 0.998313i \(0.481508\pi\)
\(602\) 0 0
\(603\) 41.3845 1.68531
\(604\) 0 0
\(605\) −21.1748 −0.860877
\(606\) 0 0
\(607\) −33.1716 −1.34639 −0.673197 0.739463i \(-0.735080\pi\)
−0.673197 + 0.739463i \(0.735080\pi\)
\(608\) 0 0
\(609\) −32.2353 −1.30624
\(610\) 0 0
\(611\) 13.1741 0.532965
\(612\) 0 0
\(613\) −43.2327 −1.74615 −0.873076 0.487583i \(-0.837879\pi\)
−0.873076 + 0.487583i \(0.837879\pi\)
\(614\) 0 0
\(615\) 30.1500 1.21576
\(616\) 0 0
\(617\) −5.55753 −0.223738 −0.111869 0.993723i \(-0.535684\pi\)
−0.111869 + 0.993723i \(0.535684\pi\)
\(618\) 0 0
\(619\) −2.89126 −0.116210 −0.0581048 0.998310i \(-0.518506\pi\)
−0.0581048 + 0.998310i \(0.518506\pi\)
\(620\) 0 0
\(621\) 7.93725 0.318511
\(622\) 0 0
\(623\) 20.9489 0.839302
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 112.804 4.50496
\(628\) 0 0
\(629\) 1.20896 0.0482043
\(630\) 0 0
\(631\) 10.2178 0.406763 0.203381 0.979100i \(-0.434807\pi\)
0.203381 + 0.979100i \(0.434807\pi\)
\(632\) 0 0
\(633\) −49.5888 −1.97098
\(634\) 0 0
\(635\) −14.1007 −0.559568
\(636\) 0 0
\(637\) −12.2453 −0.485175
\(638\) 0 0
\(639\) 19.3630 0.765989
\(640\) 0 0
\(641\) −28.0639 −1.10846 −0.554229 0.832364i \(-0.686987\pi\)
−0.554229 + 0.832364i \(0.686987\pi\)
\(642\) 0 0
\(643\) 17.4578 0.688467 0.344234 0.938884i \(-0.388139\pi\)
0.344234 + 0.938884i \(0.388139\pi\)
\(644\) 0 0
\(645\) 31.0677 1.22329
\(646\) 0 0
\(647\) 46.1560 1.81458 0.907290 0.420506i \(-0.138147\pi\)
0.907290 + 0.420506i \(0.138147\pi\)
\(648\) 0 0
\(649\) −4.40823 −0.173038
\(650\) 0 0
\(651\) 29.2780 1.14750
\(652\) 0 0
\(653\) −33.6636 −1.31736 −0.658680 0.752423i \(-0.728885\pi\)
−0.658680 + 0.752423i \(0.728885\pi\)
\(654\) 0 0
\(655\) 19.0470 0.744227
\(656\) 0 0
\(657\) −36.1133 −1.40891
\(658\) 0 0
\(659\) 4.63197 0.180436 0.0902180 0.995922i \(-0.471244\pi\)
0.0902180 + 0.995922i \(0.471244\pi\)
\(660\) 0 0
\(661\) −11.7286 −0.456191 −0.228095 0.973639i \(-0.573250\pi\)
−0.228095 + 0.973639i \(0.573250\pi\)
\(662\) 0 0
\(663\) 8.10457 0.314755
\(664\) 0 0
\(665\) 14.4221 0.559263
\(666\) 0 0
\(667\) 5.11378 0.198006
\(668\) 0 0
\(669\) 59.5587 2.30267
\(670\) 0 0
\(671\) 39.7138 1.53313
\(672\) 0 0
\(673\) −42.4703 −1.63711 −0.818555 0.574428i \(-0.805224\pi\)
−0.818555 + 0.574428i \(0.805224\pi\)
\(674\) 0 0
\(675\) 7.93725 0.305505
\(676\) 0 0
\(677\) 20.4373 0.785471 0.392735 0.919651i \(-0.371529\pi\)
0.392735 + 0.919651i \(0.371529\pi\)
\(678\) 0 0
\(679\) −9.84350 −0.377759
\(680\) 0 0
\(681\) 59.6588 2.28613
\(682\) 0 0
\(683\) −0.289606 −0.0110815 −0.00554073 0.999985i \(-0.501764\pi\)
−0.00554073 + 0.999985i \(0.501764\pi\)
\(684\) 0 0
\(685\) −10.5943 −0.404786
\(686\) 0 0
\(687\) −62.5808 −2.38761
\(688\) 0 0
\(689\) −43.7337 −1.66612
\(690\) 0 0
\(691\) 1.96253 0.0746583 0.0373291 0.999303i \(-0.488115\pi\)
0.0373291 + 0.999303i \(0.488115\pi\)
\(692\) 0 0
\(693\) −69.0339 −2.62238
\(694\) 0 0
\(695\) 14.3997 0.546210
\(696\) 0 0
\(697\) −5.57537 −0.211182
\(698\) 0 0
\(699\) −38.6936 −1.46353
\(700\) 0 0
\(701\) 37.2259 1.40600 0.703001 0.711189i \(-0.251843\pi\)
0.703001 + 0.711189i \(0.251843\pi\)
\(702\) 0 0
\(703\) 14.9576 0.564136
\(704\) 0 0
\(705\) −7.70319 −0.290119
\(706\) 0 0
\(707\) −27.1355 −1.02053
\(708\) 0 0
\(709\) 18.1006 0.679782 0.339891 0.940465i \(-0.389610\pi\)
0.339891 + 0.940465i \(0.389610\pi\)
\(710\) 0 0
\(711\) −23.2043 −0.870229
\(712\) 0 0
\(713\) −4.64464 −0.173943
\(714\) 0 0
\(715\) −28.6004 −1.06959
\(716\) 0 0
\(717\) −23.6654 −0.883799
\(718\) 0 0
\(719\) −29.5147 −1.10071 −0.550357 0.834930i \(-0.685508\pi\)
−0.550357 + 0.834930i \(0.685508\pi\)
\(720\) 0 0
\(721\) 22.0801 0.822307
\(722\) 0 0
\(723\) 2.32324 0.0864023
\(724\) 0 0
\(725\) 5.11378 0.189921
\(726\) 0 0
\(727\) −2.92069 −0.108322 −0.0541611 0.998532i \(-0.517248\pi\)
−0.0541611 + 0.998532i \(0.517248\pi\)
\(728\) 0 0
\(729\) −34.2031 −1.26678
\(730\) 0 0
\(731\) −5.74509 −0.212490
\(732\) 0 0
\(733\) 22.8857 0.845304 0.422652 0.906292i \(-0.361099\pi\)
0.422652 + 0.906292i \(0.361099\pi\)
\(734\) 0 0
\(735\) 7.16010 0.264104
\(736\) 0 0
\(737\) 41.2398 1.51909
\(738\) 0 0
\(739\) 3.48850 0.128327 0.0641633 0.997939i \(-0.479562\pi\)
0.0641633 + 0.997939i \(0.479562\pi\)
\(740\) 0 0
\(741\) 100.272 3.68359
\(742\) 0 0
\(743\) 9.54065 0.350013 0.175006 0.984567i \(-0.444005\pi\)
0.175006 + 0.984567i \(0.444005\pi\)
\(744\) 0 0
\(745\) −2.81908 −0.103283
\(746\) 0 0
\(747\) 8.61848 0.315334
\(748\) 0 0
\(749\) −25.4904 −0.931398
\(750\) 0 0
\(751\) −6.84212 −0.249673 −0.124836 0.992177i \(-0.539841\pi\)
−0.124836 + 0.992177i \(0.539841\pi\)
\(752\) 0 0
\(753\) −90.9161 −3.31317
\(754\) 0 0
\(755\) 0.704562 0.0256416
\(756\) 0 0
\(757\) −40.2647 −1.46344 −0.731722 0.681603i \(-0.761283\pi\)
−0.731722 + 0.681603i \(0.761283\pi\)
\(758\) 0 0
\(759\) 16.7233 0.607018
\(760\) 0 0
\(761\) −46.1615 −1.67335 −0.836677 0.547697i \(-0.815505\pi\)
−0.836677 + 0.547697i \(0.815505\pi\)
\(762\) 0 0
\(763\) −15.1067 −0.546898
\(764\) 0 0
\(765\) −3.10335 −0.112202
\(766\) 0 0
\(767\) −3.91850 −0.141489
\(768\) 0 0
\(769\) 50.4559 1.81949 0.909744 0.415171i \(-0.136278\pi\)
0.909744 + 0.415171i \(0.136278\pi\)
\(770\) 0 0
\(771\) 39.0235 1.40540
\(772\) 0 0
\(773\) −7.52270 −0.270573 −0.135286 0.990807i \(-0.543195\pi\)
−0.135286 + 0.990807i \(0.543195\pi\)
\(774\) 0 0
\(775\) −4.64464 −0.166840
\(776\) 0 0
\(777\) −13.9781 −0.501462
\(778\) 0 0
\(779\) −68.9802 −2.47147
\(780\) 0 0
\(781\) 19.2953 0.690440
\(782\) 0 0
\(783\) 40.5894 1.45055
\(784\) 0 0
\(785\) −16.0793 −0.573893
\(786\) 0 0
\(787\) 16.7815 0.598195 0.299098 0.954223i \(-0.403314\pi\)
0.299098 + 0.954223i \(0.403314\pi\)
\(788\) 0 0
\(789\) 78.8792 2.80817
\(790\) 0 0
\(791\) −41.7214 −1.48344
\(792\) 0 0
\(793\) 35.3018 1.25360
\(794\) 0 0
\(795\) 25.5721 0.906950
\(796\) 0 0
\(797\) −8.89231 −0.314982 −0.157491 0.987520i \(-0.550341\pi\)
−0.157491 + 0.987520i \(0.550341\pi\)
\(798\) 0 0
\(799\) 1.42448 0.0503946
\(800\) 0 0
\(801\) −55.7720 −1.97061
\(802\) 0 0
\(803\) −35.9870 −1.26995
\(804\) 0 0
\(805\) 2.13809 0.0753576
\(806\) 0 0
\(807\) −68.5976 −2.41475
\(808\) 0 0
\(809\) 31.6388 1.11236 0.556180 0.831062i \(-0.312266\pi\)
0.556180 + 0.831062i \(0.312266\pi\)
\(810\) 0 0
\(811\) 12.2436 0.429932 0.214966 0.976622i \(-0.431036\pi\)
0.214966 + 0.976622i \(0.431036\pi\)
\(812\) 0 0
\(813\) −0.351453 −0.0123260
\(814\) 0 0
\(815\) −12.1665 −0.426173
\(816\) 0 0
\(817\) −71.0799 −2.48677
\(818\) 0 0
\(819\) −61.3646 −2.14425
\(820\) 0 0
\(821\) −53.9559 −1.88307 −0.941536 0.336912i \(-0.890618\pi\)
−0.941536 + 0.336912i \(0.890618\pi\)
\(822\) 0 0
\(823\) −26.8887 −0.937282 −0.468641 0.883389i \(-0.655256\pi\)
−0.468641 + 0.883389i \(0.655256\pi\)
\(824\) 0 0
\(825\) 16.7233 0.582231
\(826\) 0 0
\(827\) −10.6209 −0.369324 −0.184662 0.982802i \(-0.559119\pi\)
−0.184662 + 0.982802i \(0.559119\pi\)
\(828\) 0 0
\(829\) 23.6878 0.822710 0.411355 0.911475i \(-0.365056\pi\)
0.411355 + 0.911475i \(0.365056\pi\)
\(830\) 0 0
\(831\) −19.1602 −0.664658
\(832\) 0 0
\(833\) −1.32406 −0.0458758
\(834\) 0 0
\(835\) 22.6031 0.782211
\(836\) 0 0
\(837\) −36.8657 −1.27426
\(838\) 0 0
\(839\) −11.7151 −0.404449 −0.202225 0.979339i \(-0.564817\pi\)
−0.202225 + 0.979339i \(0.564817\pi\)
\(840\) 0 0
\(841\) −2.84925 −0.0982499
\(842\) 0 0
\(843\) 10.6064 0.365304
\(844\) 0 0
\(845\) −12.4230 −0.427365
\(846\) 0 0
\(847\) −45.2735 −1.55562
\(848\) 0 0
\(849\) 55.2949 1.89772
\(850\) 0 0
\(851\) 2.21748 0.0760141
\(852\) 0 0
\(853\) −36.8775 −1.26266 −0.631331 0.775513i \(-0.717491\pi\)
−0.631331 + 0.775513i \(0.717491\pi\)
\(854\) 0 0
\(855\) −38.3956 −1.31310
\(856\) 0 0
\(857\) −45.6431 −1.55914 −0.779569 0.626317i \(-0.784562\pi\)
−0.779569 + 0.626317i \(0.784562\pi\)
\(858\) 0 0
\(859\) 32.3689 1.10441 0.552206 0.833708i \(-0.313786\pi\)
0.552206 + 0.833708i \(0.313786\pi\)
\(860\) 0 0
\(861\) 64.4632 2.19690
\(862\) 0 0
\(863\) 24.9540 0.849443 0.424722 0.905324i \(-0.360372\pi\)
0.424722 + 0.905324i \(0.360372\pi\)
\(864\) 0 0
\(865\) 6.50538 0.221190
\(866\) 0 0
\(867\) −49.2440 −1.67241
\(868\) 0 0
\(869\) −23.1231 −0.784399
\(870\) 0 0
\(871\) 36.6583 1.24212
\(872\) 0 0
\(873\) 26.2062 0.886946
\(874\) 0 0
\(875\) 2.13809 0.0722805
\(876\) 0 0
\(877\) 37.1405 1.25415 0.627073 0.778960i \(-0.284253\pi\)
0.627073 + 0.778960i \(0.284253\pi\)
\(878\) 0 0
\(879\) −3.53608 −0.119269
\(880\) 0 0
\(881\) 21.1005 0.710894 0.355447 0.934696i \(-0.384329\pi\)
0.355447 + 0.934696i \(0.384329\pi\)
\(882\) 0 0
\(883\) 3.57577 0.120334 0.0601672 0.998188i \(-0.480837\pi\)
0.0601672 + 0.998188i \(0.480837\pi\)
\(884\) 0 0
\(885\) 2.29124 0.0770192
\(886\) 0 0
\(887\) 54.6213 1.83401 0.917003 0.398881i \(-0.130601\pi\)
0.917003 + 0.398881i \(0.130601\pi\)
\(888\) 0 0
\(889\) −30.1484 −1.01115
\(890\) 0 0
\(891\) 35.8741 1.20183
\(892\) 0 0
\(893\) 17.6241 0.589769
\(894\) 0 0
\(895\) −9.90981 −0.331248
\(896\) 0 0
\(897\) 14.8655 0.496343
\(898\) 0 0
\(899\) −23.7517 −0.792162
\(900\) 0 0
\(901\) −4.72883 −0.157540
\(902\) 0 0
\(903\) 66.4255 2.21050
\(904\) 0 0
\(905\) 2.95505 0.0982293
\(906\) 0 0
\(907\) −38.5957 −1.28155 −0.640775 0.767729i \(-0.721387\pi\)
−0.640775 + 0.767729i \(0.721387\pi\)
\(908\) 0 0
\(909\) 72.2423 2.39613
\(910\) 0 0
\(911\) 9.81812 0.325289 0.162644 0.986685i \(-0.447998\pi\)
0.162644 + 0.986685i \(0.447998\pi\)
\(912\) 0 0
\(913\) 8.58834 0.284233
\(914\) 0 0
\(915\) −20.6418 −0.682397
\(916\) 0 0
\(917\) 40.7241 1.34483
\(918\) 0 0
\(919\) 8.64000 0.285007 0.142504 0.989794i \(-0.454485\pi\)
0.142504 + 0.989794i \(0.454485\pi\)
\(920\) 0 0
\(921\) 24.0215 0.791535
\(922\) 0 0
\(923\) 17.1517 0.564555
\(924\) 0 0
\(925\) 2.21748 0.0729102
\(926\) 0 0
\(927\) −58.7836 −1.93071
\(928\) 0 0
\(929\) −21.4687 −0.704367 −0.352183 0.935931i \(-0.614561\pi\)
−0.352183 + 0.935931i \(0.614561\pi\)
\(930\) 0 0
\(931\) −16.3816 −0.536886
\(932\) 0 0
\(933\) 99.4570 3.25608
\(934\) 0 0
\(935\) −3.09250 −0.101136
\(936\) 0 0
\(937\) 20.9844 0.685531 0.342765 0.939421i \(-0.388636\pi\)
0.342765 + 0.939421i \(0.388636\pi\)
\(938\) 0 0
\(939\) 9.55360 0.311770
\(940\) 0 0
\(941\) 26.4942 0.863687 0.431844 0.901948i \(-0.357863\pi\)
0.431844 + 0.901948i \(0.357863\pi\)
\(942\) 0 0
\(943\) −10.2264 −0.333017
\(944\) 0 0
\(945\) 16.9705 0.552051
\(946\) 0 0
\(947\) 12.9572 0.421053 0.210527 0.977588i \(-0.432482\pi\)
0.210527 + 0.977588i \(0.432482\pi\)
\(948\) 0 0
\(949\) −31.9891 −1.03841
\(950\) 0 0
\(951\) 17.3837 0.563704
\(952\) 0 0
\(953\) 3.87158 0.125413 0.0627064 0.998032i \(-0.480027\pi\)
0.0627064 + 0.998032i \(0.480027\pi\)
\(954\) 0 0
\(955\) −5.46155 −0.176732
\(956\) 0 0
\(957\) 85.5194 2.76445
\(958\) 0 0
\(959\) −22.6514 −0.731453
\(960\) 0 0
\(961\) −9.42733 −0.304108
\(962\) 0 0
\(963\) 67.8626 2.18684
\(964\) 0 0
\(965\) 0.778917 0.0250742
\(966\) 0 0
\(967\) 34.7264 1.11673 0.558363 0.829597i \(-0.311430\pi\)
0.558363 + 0.829597i \(0.311430\pi\)
\(968\) 0 0
\(969\) 10.8422 0.348302
\(970\) 0 0
\(971\) 10.4154 0.334245 0.167123 0.985936i \(-0.446552\pi\)
0.167123 + 0.985936i \(0.446552\pi\)
\(972\) 0 0
\(973\) 30.7877 0.987008
\(974\) 0 0
\(975\) 14.8655 0.476076
\(976\) 0 0
\(977\) −40.6802 −1.30148 −0.650738 0.759303i \(-0.725540\pi\)
−0.650738 + 0.759303i \(0.725540\pi\)
\(978\) 0 0
\(979\) −55.5770 −1.77625
\(980\) 0 0
\(981\) 40.2183 1.28407
\(982\) 0 0
\(983\) 22.5016 0.717688 0.358844 0.933397i \(-0.383171\pi\)
0.358844 + 0.933397i \(0.383171\pi\)
\(984\) 0 0
\(985\) 16.9363 0.539637
\(986\) 0 0
\(987\) −16.4701 −0.524248
\(988\) 0 0
\(989\) −10.5377 −0.335079
\(990\) 0 0
\(991\) −8.71659 −0.276892 −0.138446 0.990370i \(-0.544211\pi\)
−0.138446 + 0.990370i \(0.544211\pi\)
\(992\) 0 0
\(993\) 4.65253 0.147644
\(994\) 0 0
\(995\) 6.78489 0.215095
\(996\) 0 0
\(997\) −21.1186 −0.668832 −0.334416 0.942426i \(-0.608539\pi\)
−0.334416 + 0.942426i \(0.608539\pi\)
\(998\) 0 0
\(999\) 17.6007 0.556861
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.cq.1.5 5
4.3 odd 2 7360.2.a.cl.1.1 5
8.3 odd 2 3680.2.a.ba.1.5 yes 5
8.5 even 2 3680.2.a.x.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.x.1.1 5 8.5 even 2
3680.2.a.ba.1.5 yes 5 8.3 odd 2
7360.2.a.cl.1.1 5 4.3 odd 2
7360.2.a.cq.1.5 5 1.1 even 1 trivial