Properties

Label 7360.2.a.cl.1.4
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $1$
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: \(1\)
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 1.4
Root \(1.63675\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.706809 q^{3} -1.00000 q^{5} -5.21261 q^{7} -2.50042 q^{9} +O(q^{10})\) \(q+0.706809 q^{3} -1.00000 q^{5} -5.21261 q^{7} -2.50042 q^{9} +4.73273 q^{11} +0.250999 q^{13} -0.706809 q^{15} -2.11467 q^{17} +5.84398 q^{19} -3.68431 q^{21} -1.00000 q^{23} +1.00000 q^{25} -3.88775 q^{27} +6.19011 q^{29} +3.60888 q^{31} +3.34513 q^{33} +5.21261 q^{35} -10.8474 q^{37} +0.177408 q^{39} +1.02054 q^{41} +11.6670 q^{43} +2.50042 q^{45} -0.134372 q^{47} +20.1713 q^{49} -1.49467 q^{51} +9.78309 q^{53} -4.73273 q^{55} +4.13057 q^{57} -10.3695 q^{59} -1.05036 q^{61} +13.0337 q^{63} -0.250999 q^{65} -11.2602 q^{67} -0.706809 q^{69} -10.4582 q^{71} -6.98568 q^{73} +0.706809 q^{75} -24.6698 q^{77} +6.07590 q^{79} +4.75337 q^{81} -17.6987 q^{83} +2.11467 q^{85} +4.37522 q^{87} +0.300413 q^{89} -1.30836 q^{91} +2.55079 q^{93} -5.84398 q^{95} +0.307515 q^{97} -11.8338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - q^{3} - 5 q^{5} + q^{7} + 6 q^{9} + O(q^{10}) \) \( 5 q - q^{3} - 5 q^{5} + q^{7} + 6 q^{9} - 3 q^{11} - 7 q^{13} + q^{15} + 9 q^{17} - q^{19} - 20 q^{21} - 5 q^{23} + 5 q^{25} - 4 q^{27} + 10 q^{29} + 21 q^{31} + 7 q^{33} - q^{35} - 8 q^{37} - 24 q^{39} - 13 q^{41} + 6 q^{43} - 6 q^{45} + 24 q^{49} + 17 q^{51} + 6 q^{53} + 3 q^{55} + 26 q^{57} - 18 q^{59} + 11 q^{61} + 4 q^{63} + 7 q^{65} - 38 q^{67} + q^{69} - 21 q^{71} - 12 q^{73} - q^{75} - 46 q^{77} - 18 q^{79} + 9 q^{81} - 20 q^{83} - 9 q^{85} - 6 q^{87} - 16 q^{89} + 3 q^{91} - 22 q^{93} + q^{95} + 29 q^{97} - 29 q^{99} + O(q^{100}) \)

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
\(3\) 0.706809 0.408076 0.204038 0.978963i \(-0.434593\pi\)
0.204038 + 0.978963i \(0.434593\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −5.21261 −1.97018 −0.985090 0.172041i \(-0.944964\pi\)
−0.985090 + 0.172041i \(0.944964\pi\)
\(8\) 0 0
\(9\) −2.50042 −0.833474
\(10\) 0 0
\(11\) 4.73273 1.42697 0.713485 0.700670i \(-0.247116\pi\)
0.713485 + 0.700670i \(0.247116\pi\)
\(12\) 0 0
\(13\) 0.250999 0.0696145 0.0348073 0.999394i \(-0.488918\pi\)
0.0348073 + 0.999394i \(0.488918\pi\)
\(14\) 0 0
\(15\) −0.706809 −0.182497
\(16\) 0 0
\(17\) −2.11467 −0.512884 −0.256442 0.966560i \(-0.582550\pi\)
−0.256442 + 0.966560i \(0.582550\pi\)
\(18\) 0 0
\(19\) 5.84398 1.34070 0.670350 0.742045i \(-0.266144\pi\)
0.670350 + 0.742045i \(0.266144\pi\)
\(20\) 0 0
\(21\) −3.68431 −0.803983
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −3.88775 −0.748197
\(28\) 0 0
\(29\) 6.19011 1.14947 0.574737 0.818338i \(-0.305104\pi\)
0.574737 + 0.818338i \(0.305104\pi\)
\(30\) 0 0
\(31\) 3.60888 0.648173 0.324087 0.946027i \(-0.394943\pi\)
0.324087 + 0.946027i \(0.394943\pi\)
\(32\) 0 0
\(33\) 3.34513 0.582313
\(34\) 0 0
\(35\) 5.21261 0.881091
\(36\) 0 0
\(37\) −10.8474 −1.78330 −0.891651 0.452724i \(-0.850452\pi\)
−0.891651 + 0.452724i \(0.850452\pi\)
\(38\) 0 0
\(39\) 0.177408 0.0284080
\(40\) 0 0
\(41\) 1.02054 0.159382 0.0796909 0.996820i \(-0.474607\pi\)
0.0796909 + 0.996820i \(0.474607\pi\)
\(42\) 0 0
\(43\) 11.6670 1.77921 0.889603 0.456734i \(-0.150981\pi\)
0.889603 + 0.456734i \(0.150981\pi\)
\(44\) 0 0
\(45\) 2.50042 0.372741
\(46\) 0 0
\(47\) −0.134372 −0.0196002 −0.00980011 0.999952i \(-0.503120\pi\)
−0.00980011 + 0.999952i \(0.503120\pi\)
\(48\) 0 0
\(49\) 20.1713 2.88161
\(50\) 0 0
\(51\) −1.49467 −0.209296
\(52\) 0 0
\(53\) 9.78309 1.34381 0.671905 0.740637i \(-0.265476\pi\)
0.671905 + 0.740637i \(0.265476\pi\)
\(54\) 0 0
\(55\) −4.73273 −0.638161
\(56\) 0 0
\(57\) 4.13057 0.547108
\(58\) 0 0
\(59\) −10.3695 −1.34999 −0.674995 0.737822i \(-0.735854\pi\)
−0.674995 + 0.737822i \(0.735854\pi\)
\(60\) 0 0
\(61\) −1.05036 −0.134485 −0.0672426 0.997737i \(-0.521420\pi\)
−0.0672426 + 0.997737i \(0.521420\pi\)
\(62\) 0 0
\(63\) 13.0337 1.64209
\(64\) 0 0
\(65\) −0.250999 −0.0311326
\(66\) 0 0
\(67\) −11.2602 −1.37565 −0.687825 0.725877i \(-0.741434\pi\)
−0.687825 + 0.725877i \(0.741434\pi\)
\(68\) 0 0
\(69\) −0.706809 −0.0850898
\(70\) 0 0
\(71\) −10.4582 −1.24116 −0.620582 0.784142i \(-0.713103\pi\)
−0.620582 + 0.784142i \(0.713103\pi\)
\(72\) 0 0
\(73\) −6.98568 −0.817612 −0.408806 0.912621i \(-0.634055\pi\)
−0.408806 + 0.912621i \(0.634055\pi\)
\(74\) 0 0
\(75\) 0.706809 0.0816152
\(76\) 0 0
\(77\) −24.6698 −2.81139
\(78\) 0 0
\(79\) 6.07590 0.683593 0.341796 0.939774i \(-0.388965\pi\)
0.341796 + 0.939774i \(0.388965\pi\)
\(80\) 0 0
\(81\) 4.75337 0.528153
\(82\) 0 0
\(83\) −17.6987 −1.94269 −0.971343 0.237684i \(-0.923612\pi\)
−0.971343 + 0.237684i \(0.923612\pi\)
\(84\) 0 0
\(85\) 2.11467 0.229369
\(86\) 0 0
\(87\) 4.37522 0.469073
\(88\) 0 0
\(89\) 0.300413 0.0318438 0.0159219 0.999873i \(-0.494932\pi\)
0.0159219 + 0.999873i \(0.494932\pi\)
\(90\) 0 0
\(91\) −1.30836 −0.137153
\(92\) 0 0
\(93\) 2.55079 0.264504
\(94\) 0 0
\(95\) −5.84398 −0.599579
\(96\) 0 0
\(97\) 0.307515 0.0312234 0.0156117 0.999878i \(-0.495030\pi\)
0.0156117 + 0.999878i \(0.495030\pi\)
\(98\) 0 0
\(99\) −11.8338 −1.18934
\(100\) 0 0
\(101\) −2.12937 −0.211881 −0.105940 0.994372i \(-0.533785\pi\)
−0.105940 + 0.994372i \(0.533785\pi\)
\(102\) 0 0
\(103\) −12.4734 −1.22904 −0.614520 0.788901i \(-0.710650\pi\)
−0.614520 + 0.788901i \(0.710650\pi\)
\(104\) 0 0
\(105\) 3.68431 0.359552
\(106\) 0 0
\(107\) 3.33381 0.322291 0.161146 0.986931i \(-0.448481\pi\)
0.161146 + 0.986931i \(0.448481\pi\)
\(108\) 0 0
\(109\) 8.67046 0.830479 0.415240 0.909712i \(-0.363698\pi\)
0.415240 + 0.909712i \(0.363698\pi\)
\(110\) 0 0
\(111\) −7.66704 −0.727723
\(112\) 0 0
\(113\) 2.49258 0.234483 0.117241 0.993103i \(-0.462595\pi\)
0.117241 + 0.993103i \(0.462595\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) −0.627603 −0.0580219
\(118\) 0 0
\(119\) 11.0230 1.01047
\(120\) 0 0
\(121\) 11.3987 1.03624
\(122\) 0 0
\(123\) 0.721328 0.0650399
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −2.54715 −0.226023 −0.113011 0.993594i \(-0.536050\pi\)
−0.113011 + 0.993594i \(0.536050\pi\)
\(128\) 0 0
\(129\) 8.24636 0.726052
\(130\) 0 0
\(131\) 10.3878 0.907585 0.453793 0.891107i \(-0.350071\pi\)
0.453793 + 0.891107i \(0.350071\pi\)
\(132\) 0 0
\(133\) −30.4623 −2.64142
\(134\) 0 0
\(135\) 3.88775 0.334604
\(136\) 0 0
\(137\) −2.14830 −0.183541 −0.0917706 0.995780i \(-0.529253\pi\)
−0.0917706 + 0.995780i \(0.529253\pi\)
\(138\) 0 0
\(139\) −3.69753 −0.313620 −0.156810 0.987629i \(-0.550121\pi\)
−0.156810 + 0.987629i \(0.550121\pi\)
\(140\) 0 0
\(141\) −0.0949755 −0.00799838
\(142\) 0 0
\(143\) 1.18791 0.0993379
\(144\) 0 0
\(145\) −6.19011 −0.514061
\(146\) 0 0
\(147\) 14.2572 1.17592
\(148\) 0 0
\(149\) 8.33265 0.682638 0.341319 0.939948i \(-0.389126\pi\)
0.341319 + 0.939948i \(0.389126\pi\)
\(150\) 0 0
\(151\) −15.1453 −1.23251 −0.616255 0.787547i \(-0.711351\pi\)
−0.616255 + 0.787547i \(0.711351\pi\)
\(152\) 0 0
\(153\) 5.28758 0.427475
\(154\) 0 0
\(155\) −3.60888 −0.289872
\(156\) 0 0
\(157\) 1.97518 0.157636 0.0788181 0.996889i \(-0.474885\pi\)
0.0788181 + 0.996889i \(0.474885\pi\)
\(158\) 0 0
\(159\) 6.91477 0.548377
\(160\) 0 0
\(161\) 5.21261 0.410811
\(162\) 0 0
\(163\) −15.7337 −1.23236 −0.616178 0.787607i \(-0.711320\pi\)
−0.616178 + 0.787607i \(0.711320\pi\)
\(164\) 0 0
\(165\) −3.34513 −0.260418
\(166\) 0 0
\(167\) 20.2115 1.56401 0.782005 0.623273i \(-0.214197\pi\)
0.782005 + 0.623273i \(0.214197\pi\)
\(168\) 0 0
\(169\) −12.9370 −0.995154
\(170\) 0 0
\(171\) −14.6124 −1.11744
\(172\) 0 0
\(173\) 0.579282 0.0440420 0.0220210 0.999758i \(-0.492990\pi\)
0.0220210 + 0.999758i \(0.492990\pi\)
\(174\) 0 0
\(175\) −5.21261 −0.394036
\(176\) 0 0
\(177\) −7.32923 −0.550899
\(178\) 0 0
\(179\) 6.22178 0.465038 0.232519 0.972592i \(-0.425303\pi\)
0.232519 + 0.972592i \(0.425303\pi\)
\(180\) 0 0
\(181\) 11.1175 0.826355 0.413178 0.910651i \(-0.364419\pi\)
0.413178 + 0.910651i \(0.364419\pi\)
\(182\) 0 0
\(183\) −0.742406 −0.0548802
\(184\) 0 0
\(185\) 10.8474 0.797517
\(186\) 0 0
\(187\) −10.0082 −0.731870
\(188\) 0 0
\(189\) 20.2653 1.47408
\(190\) 0 0
\(191\) −24.2812 −1.75692 −0.878462 0.477812i \(-0.841430\pi\)
−0.878462 + 0.477812i \(0.841430\pi\)
\(192\) 0 0
\(193\) −18.1931 −1.30957 −0.654785 0.755815i \(-0.727241\pi\)
−0.654785 + 0.755815i \(0.727241\pi\)
\(194\) 0 0
\(195\) −0.177408 −0.0127045
\(196\) 0 0
\(197\) −27.7099 −1.97425 −0.987125 0.159950i \(-0.948867\pi\)
−0.987125 + 0.159950i \(0.948867\pi\)
\(198\) 0 0
\(199\) −15.9434 −1.13020 −0.565098 0.825024i \(-0.691162\pi\)
−0.565098 + 0.825024i \(0.691162\pi\)
\(200\) 0 0
\(201\) −7.95879 −0.561370
\(202\) 0 0
\(203\) −32.2666 −2.26467
\(204\) 0 0
\(205\) −1.02054 −0.0712777
\(206\) 0 0
\(207\) 2.50042 0.173791
\(208\) 0 0
\(209\) 27.6579 1.91314
\(210\) 0 0
\(211\) −6.00559 −0.413442 −0.206721 0.978400i \(-0.566279\pi\)
−0.206721 + 0.978400i \(0.566279\pi\)
\(212\) 0 0
\(213\) −7.39197 −0.506489
\(214\) 0 0
\(215\) −11.6670 −0.795685
\(216\) 0 0
\(217\) −18.8117 −1.27702
\(218\) 0 0
\(219\) −4.93754 −0.333648
\(220\) 0 0
\(221\) −0.530781 −0.0357042
\(222\) 0 0
\(223\) 2.90571 0.194581 0.0972903 0.995256i \(-0.468982\pi\)
0.0972903 + 0.995256i \(0.468982\pi\)
\(224\) 0 0
\(225\) −2.50042 −0.166695
\(226\) 0 0
\(227\) −10.8063 −0.717240 −0.358620 0.933484i \(-0.616753\pi\)
−0.358620 + 0.933484i \(0.616753\pi\)
\(228\) 0 0
\(229\) −23.6384 −1.56207 −0.781034 0.624488i \(-0.785308\pi\)
−0.781034 + 0.624488i \(0.785308\pi\)
\(230\) 0 0
\(231\) −17.4368 −1.14726
\(232\) 0 0
\(233\) 13.4845 0.883400 0.441700 0.897163i \(-0.354375\pi\)
0.441700 + 0.897163i \(0.354375\pi\)
\(234\) 0 0
\(235\) 0.134372 0.00876548
\(236\) 0 0
\(237\) 4.29450 0.278958
\(238\) 0 0
\(239\) −21.6295 −1.39910 −0.699548 0.714586i \(-0.746615\pi\)
−0.699548 + 0.714586i \(0.746615\pi\)
\(240\) 0 0
\(241\) −15.0901 −0.972037 −0.486018 0.873949i \(-0.661551\pi\)
−0.486018 + 0.873949i \(0.661551\pi\)
\(242\) 0 0
\(243\) 15.0230 0.963723
\(244\) 0 0
\(245\) −20.1713 −1.28869
\(246\) 0 0
\(247\) 1.46683 0.0933322
\(248\) 0 0
\(249\) −12.5096 −0.792763
\(250\) 0 0
\(251\) −2.91589 −0.184049 −0.0920245 0.995757i \(-0.529334\pi\)
−0.0920245 + 0.995757i \(0.529334\pi\)
\(252\) 0 0
\(253\) −4.73273 −0.297544
\(254\) 0 0
\(255\) 1.49467 0.0935998
\(256\) 0 0
\(257\) 15.5613 0.970688 0.485344 0.874323i \(-0.338694\pi\)
0.485344 + 0.874323i \(0.338694\pi\)
\(258\) 0 0
\(259\) 56.5432 3.51342
\(260\) 0 0
\(261\) −15.4779 −0.958057
\(262\) 0 0
\(263\) 0.342206 0.0211013 0.0105507 0.999944i \(-0.496642\pi\)
0.0105507 + 0.999944i \(0.496642\pi\)
\(264\) 0 0
\(265\) −9.78309 −0.600970
\(266\) 0 0
\(267\) 0.212335 0.0129947
\(268\) 0 0
\(269\) 14.5603 0.887759 0.443880 0.896086i \(-0.353602\pi\)
0.443880 + 0.896086i \(0.353602\pi\)
\(270\) 0 0
\(271\) −1.17019 −0.0710837 −0.0355419 0.999368i \(-0.511316\pi\)
−0.0355419 + 0.999368i \(0.511316\pi\)
\(272\) 0 0
\(273\) −0.924758 −0.0559689
\(274\) 0 0
\(275\) 4.73273 0.285394
\(276\) 0 0
\(277\) −24.3954 −1.46578 −0.732888 0.680349i \(-0.761828\pi\)
−0.732888 + 0.680349i \(0.761828\pi\)
\(278\) 0 0
\(279\) −9.02371 −0.540236
\(280\) 0 0
\(281\) 2.83106 0.168887 0.0844434 0.996428i \(-0.473089\pi\)
0.0844434 + 0.996428i \(0.473089\pi\)
\(282\) 0 0
\(283\) −6.81964 −0.405385 −0.202693 0.979242i \(-0.564969\pi\)
−0.202693 + 0.979242i \(0.564969\pi\)
\(284\) 0 0
\(285\) −4.13057 −0.244674
\(286\) 0 0
\(287\) −5.31968 −0.314011
\(288\) 0 0
\(289\) −12.5282 −0.736950
\(290\) 0 0
\(291\) 0.217354 0.0127415
\(292\) 0 0
\(293\) 29.0172 1.69520 0.847601 0.530634i \(-0.178046\pi\)
0.847601 + 0.530634i \(0.178046\pi\)
\(294\) 0 0
\(295\) 10.3695 0.603734
\(296\) 0 0
\(297\) −18.3996 −1.06765
\(298\) 0 0
\(299\) −0.250999 −0.0145156
\(300\) 0 0
\(301\) −60.8157 −3.50536
\(302\) 0 0
\(303\) −1.50506 −0.0864634
\(304\) 0 0
\(305\) 1.05036 0.0601437
\(306\) 0 0
\(307\) −9.24320 −0.527538 −0.263769 0.964586i \(-0.584966\pi\)
−0.263769 + 0.964586i \(0.584966\pi\)
\(308\) 0 0
\(309\) −8.81630 −0.501542
\(310\) 0 0
\(311\) 14.2166 0.806151 0.403075 0.915167i \(-0.367941\pi\)
0.403075 + 0.915167i \(0.367941\pi\)
\(312\) 0 0
\(313\) 3.45918 0.195524 0.0977622 0.995210i \(-0.468832\pi\)
0.0977622 + 0.995210i \(0.468832\pi\)
\(314\) 0 0
\(315\) −13.0337 −0.734366
\(316\) 0 0
\(317\) −15.9776 −0.897393 −0.448696 0.893684i \(-0.648112\pi\)
−0.448696 + 0.893684i \(0.648112\pi\)
\(318\) 0 0
\(319\) 29.2961 1.64027
\(320\) 0 0
\(321\) 2.35636 0.131519
\(322\) 0 0
\(323\) −12.3581 −0.687623
\(324\) 0 0
\(325\) 0.250999 0.0139229
\(326\) 0 0
\(327\) 6.12835 0.338899
\(328\) 0 0
\(329\) 0.700430 0.0386159
\(330\) 0 0
\(331\) −8.63455 −0.474598 −0.237299 0.971437i \(-0.576262\pi\)
−0.237299 + 0.971437i \(0.576262\pi\)
\(332\) 0 0
\(333\) 27.1231 1.48634
\(334\) 0 0
\(335\) 11.2602 0.615209
\(336\) 0 0
\(337\) 31.9718 1.74161 0.870807 0.491624i \(-0.163597\pi\)
0.870807 + 0.491624i \(0.163597\pi\)
\(338\) 0 0
\(339\) 1.76178 0.0956867
\(340\) 0 0
\(341\) 17.0798 0.924924
\(342\) 0 0
\(343\) −68.6566 −3.70711
\(344\) 0 0
\(345\) 0.706809 0.0380533
\(346\) 0 0
\(347\) 12.3122 0.660955 0.330477 0.943814i \(-0.392790\pi\)
0.330477 + 0.943814i \(0.392790\pi\)
\(348\) 0 0
\(349\) 10.5094 0.562557 0.281279 0.959626i \(-0.409241\pi\)
0.281279 + 0.959626i \(0.409241\pi\)
\(350\) 0 0
\(351\) −0.975819 −0.0520854
\(352\) 0 0
\(353\) −11.1250 −0.592127 −0.296063 0.955168i \(-0.595674\pi\)
−0.296063 + 0.955168i \(0.595674\pi\)
\(354\) 0 0
\(355\) 10.4582 0.555065
\(356\) 0 0
\(357\) 7.79112 0.412350
\(358\) 0 0
\(359\) −24.2718 −1.28101 −0.640507 0.767952i \(-0.721276\pi\)
−0.640507 + 0.767952i \(0.721276\pi\)
\(360\) 0 0
\(361\) 15.1521 0.797477
\(362\) 0 0
\(363\) 8.05669 0.422867
\(364\) 0 0
\(365\) 6.98568 0.365647
\(366\) 0 0
\(367\) 8.78708 0.458682 0.229341 0.973346i \(-0.426343\pi\)
0.229341 + 0.973346i \(0.426343\pi\)
\(368\) 0 0
\(369\) −2.55178 −0.132841
\(370\) 0 0
\(371\) −50.9954 −2.64755
\(372\) 0 0
\(373\) −6.53233 −0.338231 −0.169116 0.985596i \(-0.554091\pi\)
−0.169116 + 0.985596i \(0.554091\pi\)
\(374\) 0 0
\(375\) −0.706809 −0.0364994
\(376\) 0 0
\(377\) 1.55371 0.0800202
\(378\) 0 0
\(379\) −19.4920 −1.00124 −0.500620 0.865667i \(-0.666894\pi\)
−0.500620 + 0.865667i \(0.666894\pi\)
\(380\) 0 0
\(381\) −1.80034 −0.0922345
\(382\) 0 0
\(383\) 26.0604 1.33163 0.665813 0.746118i \(-0.268085\pi\)
0.665813 + 0.746118i \(0.268085\pi\)
\(384\) 0 0
\(385\) 24.6698 1.25729
\(386\) 0 0
\(387\) −29.1725 −1.48292
\(388\) 0 0
\(389\) 14.4470 0.732490 0.366245 0.930518i \(-0.380643\pi\)
0.366245 + 0.930518i \(0.380643\pi\)
\(390\) 0 0
\(391\) 2.11467 0.106944
\(392\) 0 0
\(393\) 7.34218 0.370364
\(394\) 0 0
\(395\) −6.07590 −0.305712
\(396\) 0 0
\(397\) −20.9996 −1.05394 −0.526970 0.849884i \(-0.676672\pi\)
−0.526970 + 0.849884i \(0.676672\pi\)
\(398\) 0 0
\(399\) −21.5310 −1.07790
\(400\) 0 0
\(401\) −28.2831 −1.41239 −0.706195 0.708018i \(-0.749590\pi\)
−0.706195 + 0.708018i \(0.749590\pi\)
\(402\) 0 0
\(403\) 0.905824 0.0451223
\(404\) 0 0
\(405\) −4.75337 −0.236197
\(406\) 0 0
\(407\) −51.3378 −2.54472
\(408\) 0 0
\(409\) 23.0734 1.14091 0.570454 0.821329i \(-0.306767\pi\)
0.570454 + 0.821329i \(0.306767\pi\)
\(410\) 0 0
\(411\) −1.51843 −0.0748988
\(412\) 0 0
\(413\) 54.0520 2.65972
\(414\) 0 0
\(415\) 17.6987 0.868795
\(416\) 0 0
\(417\) −2.61344 −0.127981
\(418\) 0 0
\(419\) −27.4805 −1.34251 −0.671254 0.741227i \(-0.734244\pi\)
−0.671254 + 0.741227i \(0.734244\pi\)
\(420\) 0 0
\(421\) 10.9524 0.533787 0.266893 0.963726i \(-0.414003\pi\)
0.266893 + 0.963726i \(0.414003\pi\)
\(422\) 0 0
\(423\) 0.335987 0.0163363
\(424\) 0 0
\(425\) −2.11467 −0.102577
\(426\) 0 0
\(427\) 5.47513 0.264960
\(428\) 0 0
\(429\) 0.839624 0.0405374
\(430\) 0 0
\(431\) 13.7335 0.661521 0.330760 0.943715i \(-0.392695\pi\)
0.330760 + 0.943715i \(0.392695\pi\)
\(432\) 0 0
\(433\) 35.5907 1.71038 0.855190 0.518315i \(-0.173441\pi\)
0.855190 + 0.518315i \(0.173441\pi\)
\(434\) 0 0
\(435\) −4.37522 −0.209776
\(436\) 0 0
\(437\) −5.84398 −0.279555
\(438\) 0 0
\(439\) 32.1827 1.53600 0.767999 0.640451i \(-0.221252\pi\)
0.767999 + 0.640451i \(0.221252\pi\)
\(440\) 0 0
\(441\) −50.4366 −2.40174
\(442\) 0 0
\(443\) −32.5678 −1.54734 −0.773670 0.633588i \(-0.781581\pi\)
−0.773670 + 0.633588i \(0.781581\pi\)
\(444\) 0 0
\(445\) −0.300413 −0.0142410
\(446\) 0 0
\(447\) 5.88959 0.278568
\(448\) 0 0
\(449\) −16.9995 −0.802257 −0.401128 0.916022i \(-0.631382\pi\)
−0.401128 + 0.916022i \(0.631382\pi\)
\(450\) 0 0
\(451\) 4.82994 0.227433
\(452\) 0 0
\(453\) −10.7049 −0.502958
\(454\) 0 0
\(455\) 1.30836 0.0613368
\(456\) 0 0
\(457\) 16.0768 0.752040 0.376020 0.926611i \(-0.377292\pi\)
0.376020 + 0.926611i \(0.377292\pi\)
\(458\) 0 0
\(459\) 8.22131 0.383738
\(460\) 0 0
\(461\) −14.2977 −0.665910 −0.332955 0.942943i \(-0.608046\pi\)
−0.332955 + 0.942943i \(0.608046\pi\)
\(462\) 0 0
\(463\) −32.5700 −1.51365 −0.756827 0.653615i \(-0.773252\pi\)
−0.756827 + 0.653615i \(0.773252\pi\)
\(464\) 0 0
\(465\) −2.55079 −0.118290
\(466\) 0 0
\(467\) 4.31563 0.199704 0.0998518 0.995002i \(-0.468163\pi\)
0.0998518 + 0.995002i \(0.468163\pi\)
\(468\) 0 0
\(469\) 58.6948 2.71028
\(470\) 0 0
\(471\) 1.39607 0.0643276
\(472\) 0 0
\(473\) 55.2169 2.53887
\(474\) 0 0
\(475\) 5.84398 0.268140
\(476\) 0 0
\(477\) −24.4618 −1.12003
\(478\) 0 0
\(479\) −19.0248 −0.869265 −0.434632 0.900608i \(-0.643122\pi\)
−0.434632 + 0.900608i \(0.643122\pi\)
\(480\) 0 0
\(481\) −2.72268 −0.124144
\(482\) 0 0
\(483\) 3.68431 0.167642
\(484\) 0 0
\(485\) −0.307515 −0.0139635
\(486\) 0 0
\(487\) 4.21675 0.191079 0.0955396 0.995426i \(-0.469542\pi\)
0.0955396 + 0.995426i \(0.469542\pi\)
\(488\) 0 0
\(489\) −11.1207 −0.502895
\(490\) 0 0
\(491\) −35.6441 −1.60860 −0.804299 0.594225i \(-0.797459\pi\)
−0.804299 + 0.594225i \(0.797459\pi\)
\(492\) 0 0
\(493\) −13.0901 −0.589547
\(494\) 0 0
\(495\) 11.8338 0.531890
\(496\) 0 0
\(497\) 54.5146 2.44531
\(498\) 0 0
\(499\) 16.5025 0.738754 0.369377 0.929280i \(-0.379571\pi\)
0.369377 + 0.929280i \(0.379571\pi\)
\(500\) 0 0
\(501\) 14.2856 0.638235
\(502\) 0 0
\(503\) −22.4530 −1.00113 −0.500564 0.865699i \(-0.666874\pi\)
−0.500564 + 0.865699i \(0.666874\pi\)
\(504\) 0 0
\(505\) 2.12937 0.0947559
\(506\) 0 0
\(507\) −9.14398 −0.406099
\(508\) 0 0
\(509\) −12.8789 −0.570848 −0.285424 0.958401i \(-0.592134\pi\)
−0.285424 + 0.958401i \(0.592134\pi\)
\(510\) 0 0
\(511\) 36.4136 1.61084
\(512\) 0 0
\(513\) −22.7199 −1.00311
\(514\) 0 0
\(515\) 12.4734 0.549643
\(516\) 0 0
\(517\) −0.635947 −0.0279689
\(518\) 0 0
\(519\) 0.409441 0.0179725
\(520\) 0 0
\(521\) 20.6355 0.904058 0.452029 0.892003i \(-0.350700\pi\)
0.452029 + 0.892003i \(0.350700\pi\)
\(522\) 0 0
\(523\) 16.6823 0.729467 0.364734 0.931112i \(-0.381160\pi\)
0.364734 + 0.931112i \(0.381160\pi\)
\(524\) 0 0
\(525\) −3.68431 −0.160797
\(526\) 0 0
\(527\) −7.63160 −0.332438
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 25.9281 1.12518
\(532\) 0 0
\(533\) 0.256155 0.0110953
\(534\) 0 0
\(535\) −3.33381 −0.144133
\(536\) 0 0
\(537\) 4.39761 0.189771
\(538\) 0 0
\(539\) 95.4650 4.11197
\(540\) 0 0
\(541\) 21.1313 0.908506 0.454253 0.890873i \(-0.349906\pi\)
0.454253 + 0.890873i \(0.349906\pi\)
\(542\) 0 0
\(543\) 7.85792 0.337216
\(544\) 0 0
\(545\) −8.67046 −0.371402
\(546\) 0 0
\(547\) 21.7265 0.928959 0.464480 0.885584i \(-0.346241\pi\)
0.464480 + 0.885584i \(0.346241\pi\)
\(548\) 0 0
\(549\) 2.62635 0.112090
\(550\) 0 0
\(551\) 36.1749 1.54110
\(552\) 0 0
\(553\) −31.6713 −1.34680
\(554\) 0 0
\(555\) 7.66704 0.325448
\(556\) 0 0
\(557\) 44.8821 1.90172 0.950858 0.309628i \(-0.100205\pi\)
0.950858 + 0.309628i \(0.100205\pi\)
\(558\) 0 0
\(559\) 2.92841 0.123859
\(560\) 0 0
\(561\) −7.07386 −0.298659
\(562\) 0 0
\(563\) −19.5584 −0.824287 −0.412143 0.911119i \(-0.635220\pi\)
−0.412143 + 0.911119i \(0.635220\pi\)
\(564\) 0 0
\(565\) −2.49258 −0.104864
\(566\) 0 0
\(567\) −24.7775 −1.04056
\(568\) 0 0
\(569\) −20.5392 −0.861047 −0.430524 0.902579i \(-0.641671\pi\)
−0.430524 + 0.902579i \(0.641671\pi\)
\(570\) 0 0
\(571\) −12.8879 −0.539340 −0.269670 0.962953i \(-0.586915\pi\)
−0.269670 + 0.962953i \(0.586915\pi\)
\(572\) 0 0
\(573\) −17.1621 −0.716959
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 18.2883 0.761351 0.380675 0.924709i \(-0.375692\pi\)
0.380675 + 0.924709i \(0.375692\pi\)
\(578\) 0 0
\(579\) −12.8591 −0.534404
\(580\) 0 0
\(581\) 92.2564 3.82744
\(582\) 0 0
\(583\) 46.3007 1.91758
\(584\) 0 0
\(585\) 0.627603 0.0259482
\(586\) 0 0
\(587\) −42.1035 −1.73780 −0.868898 0.494991i \(-0.835171\pi\)
−0.868898 + 0.494991i \(0.835171\pi\)
\(588\) 0 0
\(589\) 21.0902 0.869006
\(590\) 0 0
\(591\) −19.5856 −0.805644
\(592\) 0 0
\(593\) 34.5902 1.42045 0.710225 0.703975i \(-0.248593\pi\)
0.710225 + 0.703975i \(0.248593\pi\)
\(594\) 0 0
\(595\) −11.0230 −0.451897
\(596\) 0 0
\(597\) −11.2689 −0.461206
\(598\) 0 0
\(599\) 10.4714 0.427849 0.213925 0.976850i \(-0.431375\pi\)
0.213925 + 0.976850i \(0.431375\pi\)
\(600\) 0 0
\(601\) −41.2450 −1.68242 −0.841210 0.540708i \(-0.818156\pi\)
−0.841210 + 0.540708i \(0.818156\pi\)
\(602\) 0 0
\(603\) 28.1552 1.14657
\(604\) 0 0
\(605\) −11.3987 −0.463423
\(606\) 0 0
\(607\) 17.5933 0.714091 0.357045 0.934087i \(-0.383784\pi\)
0.357045 + 0.934087i \(0.383784\pi\)
\(608\) 0 0
\(609\) −22.8063 −0.924159
\(610\) 0 0
\(611\) −0.0337273 −0.00136446
\(612\) 0 0
\(613\) −20.8066 −0.840370 −0.420185 0.907439i \(-0.638035\pi\)
−0.420185 + 0.907439i \(0.638035\pi\)
\(614\) 0 0
\(615\) −0.721328 −0.0290867
\(616\) 0 0
\(617\) −35.4765 −1.42823 −0.714115 0.700028i \(-0.753171\pi\)
−0.714115 + 0.700028i \(0.753171\pi\)
\(618\) 0 0
\(619\) −20.2405 −0.813533 −0.406766 0.913532i \(-0.633344\pi\)
−0.406766 + 0.913532i \(0.633344\pi\)
\(620\) 0 0
\(621\) 3.88775 0.156010
\(622\) 0 0
\(623\) −1.56594 −0.0627379
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 19.5489 0.780707
\(628\) 0 0
\(629\) 22.9387 0.914626
\(630\) 0 0
\(631\) −7.40468 −0.294776 −0.147388 0.989079i \(-0.547087\pi\)
−0.147388 + 0.989079i \(0.547087\pi\)
\(632\) 0 0
\(633\) −4.24480 −0.168716
\(634\) 0 0
\(635\) 2.54715 0.101080
\(636\) 0 0
\(637\) 5.06296 0.200602
\(638\) 0 0
\(639\) 26.1500 1.03448
\(640\) 0 0
\(641\) 16.0313 0.633200 0.316600 0.948559i \(-0.397459\pi\)
0.316600 + 0.948559i \(0.397459\pi\)
\(642\) 0 0
\(643\) 3.77825 0.149000 0.0744998 0.997221i \(-0.476264\pi\)
0.0744998 + 0.997221i \(0.476264\pi\)
\(644\) 0 0
\(645\) −8.24636 −0.324700
\(646\) 0 0
\(647\) −43.1818 −1.69765 −0.848826 0.528672i \(-0.822690\pi\)
−0.848826 + 0.528672i \(0.822690\pi\)
\(648\) 0 0
\(649\) −49.0759 −1.92640
\(650\) 0 0
\(651\) −13.2962 −0.521121
\(652\) 0 0
\(653\) 29.8519 1.16819 0.584097 0.811684i \(-0.301449\pi\)
0.584097 + 0.811684i \(0.301449\pi\)
\(654\) 0 0
\(655\) −10.3878 −0.405885
\(656\) 0 0
\(657\) 17.4671 0.681458
\(658\) 0 0
\(659\) 15.9212 0.620202 0.310101 0.950704i \(-0.399637\pi\)
0.310101 + 0.950704i \(0.399637\pi\)
\(660\) 0 0
\(661\) 27.1121 1.05454 0.527269 0.849699i \(-0.323216\pi\)
0.527269 + 0.849699i \(0.323216\pi\)
\(662\) 0 0
\(663\) −0.375160 −0.0145700
\(664\) 0 0
\(665\) 30.4623 1.18128
\(666\) 0 0
\(667\) −6.19011 −0.239682
\(668\) 0 0
\(669\) 2.05378 0.0794037
\(670\) 0 0
\(671\) −4.97108 −0.191907
\(672\) 0 0
\(673\) −35.6258 −1.37327 −0.686637 0.727001i \(-0.740914\pi\)
−0.686637 + 0.727001i \(0.740914\pi\)
\(674\) 0 0
\(675\) −3.88775 −0.149639
\(676\) 0 0
\(677\) 48.4246 1.86111 0.930554 0.366154i \(-0.119326\pi\)
0.930554 + 0.366154i \(0.119326\pi\)
\(678\) 0 0
\(679\) −1.60295 −0.0615156
\(680\) 0 0
\(681\) −7.63800 −0.292689
\(682\) 0 0
\(683\) −14.8433 −0.567965 −0.283982 0.958829i \(-0.591656\pi\)
−0.283982 + 0.958829i \(0.591656\pi\)
\(684\) 0 0
\(685\) 2.14830 0.0820821
\(686\) 0 0
\(687\) −16.7078 −0.637443
\(688\) 0 0
\(689\) 2.45554 0.0935488
\(690\) 0 0
\(691\) −24.3369 −0.925820 −0.462910 0.886405i \(-0.653195\pi\)
−0.462910 + 0.886405i \(0.653195\pi\)
\(692\) 0 0
\(693\) 61.6850 2.34322
\(694\) 0 0
\(695\) 3.69753 0.140255
\(696\) 0 0
\(697\) −2.15811 −0.0817443
\(698\) 0 0
\(699\) 9.53098 0.360495
\(700\) 0 0
\(701\) −19.0235 −0.718509 −0.359255 0.933240i \(-0.616969\pi\)
−0.359255 + 0.933240i \(0.616969\pi\)
\(702\) 0 0
\(703\) −63.3919 −2.39087
\(704\) 0 0
\(705\) 0.0949755 0.00357698
\(706\) 0 0
\(707\) 11.0996 0.417443
\(708\) 0 0
\(709\) 10.7681 0.404405 0.202202 0.979344i \(-0.435190\pi\)
0.202202 + 0.979344i \(0.435190\pi\)
\(710\) 0 0
\(711\) −15.1923 −0.569757
\(712\) 0 0
\(713\) −3.60888 −0.135154
\(714\) 0 0
\(715\) −1.18791 −0.0444253
\(716\) 0 0
\(717\) −15.2879 −0.570937
\(718\) 0 0
\(719\) 17.3605 0.647436 0.323718 0.946154i \(-0.395067\pi\)
0.323718 + 0.946154i \(0.395067\pi\)
\(720\) 0 0
\(721\) 65.0189 2.42143
\(722\) 0 0
\(723\) −10.6658 −0.396665
\(724\) 0 0
\(725\) 6.19011 0.229895
\(726\) 0 0
\(727\) −4.28344 −0.158864 −0.0794321 0.996840i \(-0.525311\pi\)
−0.0794321 + 0.996840i \(0.525311\pi\)
\(728\) 0 0
\(729\) −3.64176 −0.134880
\(730\) 0 0
\(731\) −24.6720 −0.912526
\(732\) 0 0
\(733\) 29.7449 1.09865 0.549327 0.835607i \(-0.314884\pi\)
0.549327 + 0.835607i \(0.314884\pi\)
\(734\) 0 0
\(735\) −14.2572 −0.525885
\(736\) 0 0
\(737\) −53.2913 −1.96301
\(738\) 0 0
\(739\) −19.9696 −0.734592 −0.367296 0.930104i \(-0.619716\pi\)
−0.367296 + 0.930104i \(0.619716\pi\)
\(740\) 0 0
\(741\) 1.03677 0.0380867
\(742\) 0 0
\(743\) −12.3943 −0.454703 −0.227351 0.973813i \(-0.573007\pi\)
−0.227351 + 0.973813i \(0.573007\pi\)
\(744\) 0 0
\(745\) −8.33265 −0.305285
\(746\) 0 0
\(747\) 44.2542 1.61918
\(748\) 0 0
\(749\) −17.3778 −0.634972
\(750\) 0 0
\(751\) 35.0772 1.27999 0.639993 0.768381i \(-0.278937\pi\)
0.639993 + 0.768381i \(0.278937\pi\)
\(752\) 0 0
\(753\) −2.06097 −0.0751060
\(754\) 0 0
\(755\) 15.1453 0.551195
\(756\) 0 0
\(757\) 2.91074 0.105793 0.0528963 0.998600i \(-0.483155\pi\)
0.0528963 + 0.998600i \(0.483155\pi\)
\(758\) 0 0
\(759\) −3.34513 −0.121421
\(760\) 0 0
\(761\) 20.6494 0.748542 0.374271 0.927319i \(-0.377893\pi\)
0.374271 + 0.927319i \(0.377893\pi\)
\(762\) 0 0
\(763\) −45.1957 −1.63619
\(764\) 0 0
\(765\) −5.28758 −0.191173
\(766\) 0 0
\(767\) −2.60272 −0.0939790
\(768\) 0 0
\(769\) −31.0441 −1.11948 −0.559739 0.828669i \(-0.689099\pi\)
−0.559739 + 0.828669i \(0.689099\pi\)
\(770\) 0 0
\(771\) 10.9989 0.396115
\(772\) 0 0
\(773\) 1.64944 0.0593262 0.0296631 0.999560i \(-0.490557\pi\)
0.0296631 + 0.999560i \(0.490557\pi\)
\(774\) 0 0
\(775\) 3.60888 0.129635
\(776\) 0 0
\(777\) 39.9652 1.43374
\(778\) 0 0
\(779\) 5.96402 0.213683
\(780\) 0 0
\(781\) −49.4959 −1.77110
\(782\) 0 0
\(783\) −24.0656 −0.860034
\(784\) 0 0
\(785\) −1.97518 −0.0704971
\(786\) 0 0
\(787\) 23.0488 0.821600 0.410800 0.911725i \(-0.365249\pi\)
0.410800 + 0.911725i \(0.365249\pi\)
\(788\) 0 0
\(789\) 0.241874 0.00861095
\(790\) 0 0
\(791\) −12.9929 −0.461973
\(792\) 0 0
\(793\) −0.263640 −0.00936213
\(794\) 0 0
\(795\) −6.91477 −0.245242
\(796\) 0 0
\(797\) −7.69319 −0.272507 −0.136253 0.990674i \(-0.543506\pi\)
−0.136253 + 0.990674i \(0.543506\pi\)
\(798\) 0 0
\(799\) 0.284154 0.0100526
\(800\) 0 0
\(801\) −0.751160 −0.0265409
\(802\) 0 0
\(803\) −33.0613 −1.16671
\(804\) 0 0
\(805\) −5.21261 −0.183720
\(806\) 0 0
\(807\) 10.2914 0.362273
\(808\) 0 0
\(809\) −8.02914 −0.282290 −0.141145 0.989989i \(-0.545078\pi\)
−0.141145 + 0.989989i \(0.545078\pi\)
\(810\) 0 0
\(811\) 10.5287 0.369712 0.184856 0.982766i \(-0.440818\pi\)
0.184856 + 0.982766i \(0.440818\pi\)
\(812\) 0 0
\(813\) −0.827098 −0.0290076
\(814\) 0 0
\(815\) 15.7337 0.551127
\(816\) 0 0
\(817\) 68.1819 2.38538
\(818\) 0 0
\(819\) 3.27145 0.114314
\(820\) 0 0
\(821\) 17.5562 0.612715 0.306357 0.951917i \(-0.400890\pi\)
0.306357 + 0.951917i \(0.400890\pi\)
\(822\) 0 0
\(823\) 26.7749 0.933316 0.466658 0.884438i \(-0.345458\pi\)
0.466658 + 0.884438i \(0.345458\pi\)
\(824\) 0 0
\(825\) 3.34513 0.116463
\(826\) 0 0
\(827\) 11.8652 0.412592 0.206296 0.978490i \(-0.433859\pi\)
0.206296 + 0.978490i \(0.433859\pi\)
\(828\) 0 0
\(829\) −49.0687 −1.70423 −0.852113 0.523358i \(-0.824679\pi\)
−0.852113 + 0.523358i \(0.824679\pi\)
\(830\) 0 0
\(831\) −17.2429 −0.598149
\(832\) 0 0
\(833\) −42.6556 −1.47793
\(834\) 0 0
\(835\) −20.2115 −0.699446
\(836\) 0 0
\(837\) −14.0304 −0.484961
\(838\) 0 0
\(839\) −18.1610 −0.626989 −0.313494 0.949590i \(-0.601500\pi\)
−0.313494 + 0.949590i \(0.601500\pi\)
\(840\) 0 0
\(841\) 9.31748 0.321292
\(842\) 0 0
\(843\) 2.00102 0.0689186
\(844\) 0 0
\(845\) 12.9370 0.445046
\(846\) 0 0
\(847\) −59.4169 −2.04159
\(848\) 0 0
\(849\) −4.82018 −0.165428
\(850\) 0 0
\(851\) 10.8474 0.371844
\(852\) 0 0
\(853\) 35.3535 1.21048 0.605241 0.796042i \(-0.293077\pi\)
0.605241 + 0.796042i \(0.293077\pi\)
\(854\) 0 0
\(855\) 14.6124 0.499734
\(856\) 0 0
\(857\) −26.2249 −0.895827 −0.447913 0.894077i \(-0.647833\pi\)
−0.447913 + 0.894077i \(0.647833\pi\)
\(858\) 0 0
\(859\) −34.7616 −1.18605 −0.593026 0.805184i \(-0.702067\pi\)
−0.593026 + 0.805184i \(0.702067\pi\)
\(860\) 0 0
\(861\) −3.76000 −0.128140
\(862\) 0 0
\(863\) 18.7005 0.636571 0.318286 0.947995i \(-0.396893\pi\)
0.318286 + 0.947995i \(0.396893\pi\)
\(864\) 0 0
\(865\) −0.579282 −0.0196962
\(866\) 0 0
\(867\) −8.85501 −0.300732
\(868\) 0 0
\(869\) 28.7556 0.975466
\(870\) 0 0
\(871\) −2.82629 −0.0957652
\(872\) 0 0
\(873\) −0.768916 −0.0260239
\(874\) 0 0
\(875\) 5.21261 0.176218
\(876\) 0 0
\(877\) −22.1856 −0.749155 −0.374577 0.927196i \(-0.622212\pi\)
−0.374577 + 0.927196i \(0.622212\pi\)
\(878\) 0 0
\(879\) 20.5096 0.691772
\(880\) 0 0
\(881\) −34.8580 −1.17440 −0.587198 0.809443i \(-0.699769\pi\)
−0.587198 + 0.809443i \(0.699769\pi\)
\(882\) 0 0
\(883\) 42.7441 1.43845 0.719227 0.694775i \(-0.244496\pi\)
0.719227 + 0.694775i \(0.244496\pi\)
\(884\) 0 0
\(885\) 7.32923 0.246369
\(886\) 0 0
\(887\) −47.9301 −1.60934 −0.804668 0.593725i \(-0.797657\pi\)
−0.804668 + 0.593725i \(0.797657\pi\)
\(888\) 0 0
\(889\) 13.2773 0.445305
\(890\) 0 0
\(891\) 22.4964 0.753658
\(892\) 0 0
\(893\) −0.785269 −0.0262780
\(894\) 0 0
\(895\) −6.22178 −0.207971
\(896\) 0 0
\(897\) −0.177408 −0.00592348
\(898\) 0 0
\(899\) 22.3394 0.745059
\(900\) 0 0
\(901\) −20.6880 −0.689219
\(902\) 0 0
\(903\) −42.9850 −1.43045
\(904\) 0 0
\(905\) −11.1175 −0.369557
\(906\) 0 0
\(907\) 4.88310 0.162141 0.0810704 0.996708i \(-0.474166\pi\)
0.0810704 + 0.996708i \(0.474166\pi\)
\(908\) 0 0
\(909\) 5.32433 0.176597
\(910\) 0 0
\(911\) −2.83697 −0.0939930 −0.0469965 0.998895i \(-0.514965\pi\)
−0.0469965 + 0.998895i \(0.514965\pi\)
\(912\) 0 0
\(913\) −83.7631 −2.77215
\(914\) 0 0
\(915\) 0.742406 0.0245432
\(916\) 0 0
\(917\) −54.1475 −1.78811
\(918\) 0 0
\(919\) 13.2430 0.436847 0.218424 0.975854i \(-0.429909\pi\)
0.218424 + 0.975854i \(0.429909\pi\)
\(920\) 0 0
\(921\) −6.53318 −0.215275
\(922\) 0 0
\(923\) −2.62500 −0.0864030
\(924\) 0 0
\(925\) −10.8474 −0.356660
\(926\) 0 0
\(927\) 31.1887 1.02437
\(928\) 0 0
\(929\) −57.7862 −1.89590 −0.947952 0.318413i \(-0.896850\pi\)
−0.947952 + 0.318413i \(0.896850\pi\)
\(930\) 0 0
\(931\) 117.880 3.86337
\(932\) 0 0
\(933\) 10.0484 0.328971
\(934\) 0 0
\(935\) 10.0082 0.327302
\(936\) 0 0
\(937\) −26.8345 −0.876646 −0.438323 0.898818i \(-0.644427\pi\)
−0.438323 + 0.898818i \(0.644427\pi\)
\(938\) 0 0
\(939\) 2.44498 0.0797888
\(940\) 0 0
\(941\) 13.8892 0.452776 0.226388 0.974037i \(-0.427308\pi\)
0.226388 + 0.974037i \(0.427308\pi\)
\(942\) 0 0
\(943\) −1.02054 −0.0332334
\(944\) 0 0
\(945\) −20.2653 −0.659230
\(946\) 0 0
\(947\) 15.4571 0.502289 0.251144 0.967950i \(-0.419193\pi\)
0.251144 + 0.967950i \(0.419193\pi\)
\(948\) 0 0
\(949\) −1.75340 −0.0569177
\(950\) 0 0
\(951\) −11.2931 −0.366205
\(952\) 0 0
\(953\) 46.9863 1.52203 0.761017 0.648731i \(-0.224700\pi\)
0.761017 + 0.648731i \(0.224700\pi\)
\(954\) 0 0
\(955\) 24.2812 0.785721
\(956\) 0 0
\(957\) 20.7067 0.669354
\(958\) 0 0
\(959\) 11.1982 0.361609
\(960\) 0 0
\(961\) −17.9760 −0.579871
\(962\) 0 0
\(963\) −8.33593 −0.268621
\(964\) 0 0
\(965\) 18.1931 0.585658
\(966\) 0 0
\(967\) 11.0807 0.356331 0.178165 0.984001i \(-0.442984\pi\)
0.178165 + 0.984001i \(0.442984\pi\)
\(968\) 0 0
\(969\) −8.73481 −0.280603
\(970\) 0 0
\(971\) −28.3401 −0.909478 −0.454739 0.890625i \(-0.650267\pi\)
−0.454739 + 0.890625i \(0.650267\pi\)
\(972\) 0 0
\(973\) 19.2738 0.617888
\(974\) 0 0
\(975\) 0.177408 0.00568161
\(976\) 0 0
\(977\) −11.9491 −0.382286 −0.191143 0.981562i \(-0.561219\pi\)
−0.191143 + 0.981562i \(0.561219\pi\)
\(978\) 0 0
\(979\) 1.42177 0.0454401
\(980\) 0 0
\(981\) −21.6798 −0.692183
\(982\) 0 0
\(983\) 51.9566 1.65716 0.828579 0.559873i \(-0.189150\pi\)
0.828579 + 0.559873i \(0.189150\pi\)
\(984\) 0 0
\(985\) 27.7099 0.882912
\(986\) 0 0
\(987\) 0.495070 0.0157582
\(988\) 0 0
\(989\) −11.6670 −0.370990
\(990\) 0 0
\(991\) 40.7230 1.29361 0.646804 0.762656i \(-0.276105\pi\)
0.646804 + 0.762656i \(0.276105\pi\)
\(992\) 0 0
\(993\) −6.10298 −0.193672
\(994\) 0 0
\(995\) 15.9434 0.505439
\(996\) 0 0
\(997\) 14.4242 0.456820 0.228410 0.973565i \(-0.426647\pi\)
0.228410 + 0.973565i \(0.426647\pi\)
\(998\) 0 0
\(999\) 42.1719 1.33426
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.cl.1.4 5
4.3 odd 2 7360.2.a.cq.1.2 5
8.3 odd 2 3680.2.a.x.1.4 5
8.5 even 2 3680.2.a.ba.1.2 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.x.1.4 5 8.3 odd 2
3680.2.a.ba.1.2 yes 5 8.5 even 2
7360.2.a.cl.1.4 5 1.1 even 1 trivial
7360.2.a.cq.1.2 5 4.3 odd 2