Properties

Label 7360.2.a.cd.1.3
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.1573.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
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 1.3
Root \(3.06871\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.06871 q^{3} -1.00000 q^{5} +4.06871 q^{7} +6.41697 q^{9} +O(q^{10})\) \(q+3.06871 q^{3} -1.00000 q^{5} +4.06871 q^{7} +6.41697 q^{9} +3.06871 q^{11} -5.41697 q^{13} -3.06871 q^{15} +1.72045 q^{17} -5.41697 q^{19} +12.4857 q^{21} +1.00000 q^{23} +1.00000 q^{25} +10.4857 q^{27} -7.34826 q^{29} +8.06871 q^{31} +9.41697 q^{33} -4.06871 q^{35} +0.789156 q^{37} -16.6231 q^{39} +11.8579 q^{41} +4.00000 q^{43} -6.41697 q^{45} -1.44090 q^{47} +9.55438 q^{49} +5.27955 q^{51} +1.48568 q^{53} -3.06871 q^{55} -16.6231 q^{57} +9.62309 q^{59} +12.0401 q^{61} +26.1088 q^{63} +5.41697 q^{65} -0.514324 q^{67} +3.06871 q^{69} -13.1135 q^{71} +10.1374 q^{73} +3.06871 q^{75} +12.4857 q^{77} -8.00000 q^{79} +12.9266 q^{81} -9.48568 q^{83} -1.72045 q^{85} -22.5497 q^{87} -10.9714 q^{89} -22.0401 q^{91} +24.7605 q^{93} +5.41697 q^{95} -5.20612 q^{97} +19.6918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{3} - 3 q^{5} + 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 3 q + q^{3} - 3 q^{5} + 4 q^{7} + 6 q^{9} + q^{11} - 3 q^{13} - q^{15} + 2 q^{17} - 3 q^{19} + 16 q^{21} + 3 q^{23} + 3 q^{25} + 10 q^{27} - 17 q^{29} + 16 q^{31} + 15 q^{33} - 4 q^{35} - 9 q^{37} - 12 q^{39} + 16 q^{41} + 12 q^{43} - 6 q^{45} + 2 q^{47} - q^{49} + 19 q^{51} - 17 q^{53} - q^{55} - 12 q^{57} - 9 q^{59} - 15 q^{61} + 19 q^{63} + 3 q^{65} - 23 q^{67} + q^{69} - 16 q^{71} + 14 q^{73} + q^{75} + 16 q^{77} - 24 q^{79} + 11 q^{81} - 7 q^{83} - 2 q^{85} - 2 q^{87} + 10 q^{89} - 15 q^{91} + 20 q^{93} + 3 q^{95} + 9 q^{97} + 13 q^{99} + O(q^{100}) \)

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
\(3\) 3.06871 1.77172 0.885860 0.463953i \(-0.153569\pi\)
0.885860 + 0.463953i \(0.153569\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.06871 1.53783 0.768914 0.639353i \(-0.220798\pi\)
0.768914 + 0.639353i \(0.220798\pi\)
\(8\) 0 0
\(9\) 6.41697 2.13899
\(10\) 0 0
\(11\) 3.06871 0.925250 0.462625 0.886554i \(-0.346908\pi\)
0.462625 + 0.886554i \(0.346908\pi\)
\(12\) 0 0
\(13\) −5.41697 −1.50240 −0.751198 0.660077i \(-0.770524\pi\)
−0.751198 + 0.660077i \(0.770524\pi\)
\(14\) 0 0
\(15\) −3.06871 −0.792337
\(16\) 0 0
\(17\) 1.72045 0.417270 0.208635 0.977994i \(-0.433098\pi\)
0.208635 + 0.977994i \(0.433098\pi\)
\(18\) 0 0
\(19\) −5.41697 −1.24274 −0.621369 0.783518i \(-0.713423\pi\)
−0.621369 + 0.783518i \(0.713423\pi\)
\(20\) 0 0
\(21\) 12.4857 2.72460
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 10.4857 2.01797
\(28\) 0 0
\(29\) −7.34826 −1.36454 −0.682269 0.731101i \(-0.739007\pi\)
−0.682269 + 0.731101i \(0.739007\pi\)
\(30\) 0 0
\(31\) 8.06871 1.44918 0.724591 0.689179i \(-0.242029\pi\)
0.724591 + 0.689179i \(0.242029\pi\)
\(32\) 0 0
\(33\) 9.41697 1.63928
\(34\) 0 0
\(35\) −4.06871 −0.687737
\(36\) 0 0
\(37\) 0.789156 0.129736 0.0648682 0.997894i \(-0.479337\pi\)
0.0648682 + 0.997894i \(0.479337\pi\)
\(38\) 0 0
\(39\) −16.6231 −2.66182
\(40\) 0 0
\(41\) 11.8579 1.85189 0.925944 0.377662i \(-0.123272\pi\)
0.925944 + 0.377662i \(0.123272\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −6.41697 −0.956585
\(46\) 0 0
\(47\) −1.44090 −0.210176 −0.105088 0.994463i \(-0.533512\pi\)
−0.105088 + 0.994463i \(0.533512\pi\)
\(48\) 0 0
\(49\) 9.55438 1.36491
\(50\) 0 0
\(51\) 5.27955 0.739285
\(52\) 0 0
\(53\) 1.48568 0.204073 0.102037 0.994781i \(-0.467464\pi\)
0.102037 + 0.994781i \(0.467464\pi\)
\(54\) 0 0
\(55\) −3.06871 −0.413784
\(56\) 0 0
\(57\) −16.6231 −2.20178
\(58\) 0 0
\(59\) 9.62309 1.25282 0.626410 0.779494i \(-0.284524\pi\)
0.626410 + 0.779494i \(0.284524\pi\)
\(60\) 0 0
\(61\) 12.0401 1.54157 0.770786 0.637094i \(-0.219864\pi\)
0.770786 + 0.637094i \(0.219864\pi\)
\(62\) 0 0
\(63\) 26.1088 3.28940
\(64\) 0 0
\(65\) 5.41697 0.671892
\(66\) 0 0
\(67\) −0.514324 −0.0628347 −0.0314174 0.999506i \(-0.510002\pi\)
−0.0314174 + 0.999506i \(0.510002\pi\)
\(68\) 0 0
\(69\) 3.06871 0.369429
\(70\) 0 0
\(71\) −13.1135 −1.55628 −0.778142 0.628088i \(-0.783838\pi\)
−0.778142 + 0.628088i \(0.783838\pi\)
\(72\) 0 0
\(73\) 10.1374 1.18649 0.593247 0.805020i \(-0.297846\pi\)
0.593247 + 0.805020i \(0.297846\pi\)
\(74\) 0 0
\(75\) 3.06871 0.354344
\(76\) 0 0
\(77\) 12.4857 1.42287
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 12.9266 1.43629
\(82\) 0 0
\(83\) −9.48568 −1.04119 −0.520594 0.853804i \(-0.674289\pi\)
−0.520594 + 0.853804i \(0.674289\pi\)
\(84\) 0 0
\(85\) −1.72045 −0.186609
\(86\) 0 0
\(87\) −22.5497 −2.41758
\(88\) 0 0
\(89\) −10.9714 −1.16296 −0.581480 0.813560i \(-0.697526\pi\)
−0.581480 + 0.813560i \(0.697526\pi\)
\(90\) 0 0
\(91\) −22.0401 −2.31043
\(92\) 0 0
\(93\) 24.7605 2.56754
\(94\) 0 0
\(95\) 5.41697 0.555769
\(96\) 0 0
\(97\) −5.20612 −0.528602 −0.264301 0.964440i \(-0.585141\pi\)
−0.264301 + 0.964440i \(0.585141\pi\)
\(98\) 0 0
\(99\) 19.6918 1.97910
\(100\) 0 0
\(101\) 14.0448 1.39751 0.698754 0.715362i \(-0.253738\pi\)
0.698754 + 0.715362i \(0.253738\pi\)
\(102\) 0 0
\(103\) 11.2061 1.10417 0.552086 0.833787i \(-0.313832\pi\)
0.552086 + 0.833787i \(0.313832\pi\)
\(104\) 0 0
\(105\) −12.4857 −1.21848
\(106\) 0 0
\(107\) 12.6517 1.22309 0.611545 0.791210i \(-0.290548\pi\)
0.611545 + 0.791210i \(0.290548\pi\)
\(108\) 0 0
\(109\) 13.4170 1.28511 0.642556 0.766239i \(-0.277874\pi\)
0.642556 + 0.766239i \(0.277874\pi\)
\(110\) 0 0
\(111\) 2.42169 0.229856
\(112\) 0 0
\(113\) 10.7892 1.01496 0.507479 0.861664i \(-0.330577\pi\)
0.507479 + 0.861664i \(0.330577\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) −34.7605 −3.21361
\(118\) 0 0
\(119\) 7.00000 0.641689
\(120\) 0 0
\(121\) −1.58303 −0.143912
\(122\) 0 0
\(123\) 36.3883 3.28102
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.833935 0.0739998 0.0369999 0.999315i \(-0.488220\pi\)
0.0369999 + 0.999315i \(0.488220\pi\)
\(128\) 0 0
\(129\) 12.2748 1.08074
\(130\) 0 0
\(131\) −0.696520 −0.0608552 −0.0304276 0.999537i \(-0.509687\pi\)
−0.0304276 + 0.999537i \(0.509687\pi\)
\(132\) 0 0
\(133\) −22.0401 −1.91112
\(134\) 0 0
\(135\) −10.4857 −0.902463
\(136\) 0 0
\(137\) 16.8579 1.44026 0.720132 0.693837i \(-0.244081\pi\)
0.720132 + 0.693837i \(0.244081\pi\)
\(138\) 0 0
\(139\) −14.7413 −1.25034 −0.625170 0.780488i \(-0.714971\pi\)
−0.625170 + 0.780488i \(0.714971\pi\)
\(140\) 0 0
\(141\) −4.42169 −0.372373
\(142\) 0 0
\(143\) −16.6231 −1.39009
\(144\) 0 0
\(145\) 7.34826 0.610240
\(146\) 0 0
\(147\) 29.3196 2.41824
\(148\) 0 0
\(149\) −8.11349 −0.664683 −0.332341 0.943159i \(-0.607839\pi\)
−0.332341 + 0.943159i \(0.607839\pi\)
\(150\) 0 0
\(151\) 11.9505 0.972518 0.486259 0.873815i \(-0.338361\pi\)
0.486259 + 0.873815i \(0.338361\pi\)
\(152\) 0 0
\(153\) 11.0401 0.892536
\(154\) 0 0
\(155\) −8.06871 −0.648094
\(156\) 0 0
\(157\) −19.3483 −1.54416 −0.772080 0.635526i \(-0.780783\pi\)
−0.772080 + 0.635526i \(0.780783\pi\)
\(158\) 0 0
\(159\) 4.55910 0.361560
\(160\) 0 0
\(161\) 4.06871 0.320659
\(162\) 0 0
\(163\) −8.16134 −0.639246 −0.319623 0.947545i \(-0.603556\pi\)
−0.319623 + 0.947545i \(0.603556\pi\)
\(164\) 0 0
\(165\) −9.41697 −0.733110
\(166\) 0 0
\(167\) −1.39304 −0.107797 −0.0538983 0.998546i \(-0.517165\pi\)
−0.0538983 + 0.998546i \(0.517165\pi\)
\(168\) 0 0
\(169\) 16.3435 1.25720
\(170\) 0 0
\(171\) −34.7605 −2.65820
\(172\) 0 0
\(173\) 2.37219 0.180354 0.0901771 0.995926i \(-0.471257\pi\)
0.0901771 + 0.995926i \(0.471257\pi\)
\(174\) 0 0
\(175\) 4.06871 0.307565
\(176\) 0 0
\(177\) 29.5305 2.21964
\(178\) 0 0
\(179\) 18.8339 1.40771 0.703857 0.710341i \(-0.251459\pi\)
0.703857 + 0.710341i \(0.251459\pi\)
\(180\) 0 0
\(181\) 6.99528 0.519955 0.259978 0.965615i \(-0.416285\pi\)
0.259978 + 0.965615i \(0.416285\pi\)
\(182\) 0 0
\(183\) 36.9474 2.73123
\(184\) 0 0
\(185\) −0.789156 −0.0580199
\(186\) 0 0
\(187\) 5.27955 0.386079
\(188\) 0 0
\(189\) 42.6632 3.10329
\(190\) 0 0
\(191\) −1.86258 −0.134772 −0.0673859 0.997727i \(-0.521466\pi\)
−0.0673859 + 0.997727i \(0.521466\pi\)
\(192\) 0 0
\(193\) −11.7157 −0.843316 −0.421658 0.906755i \(-0.638552\pi\)
−0.421658 + 0.906755i \(0.638552\pi\)
\(194\) 0 0
\(195\) 16.6231 1.19040
\(196\) 0 0
\(197\) 14.1775 1.01010 0.505052 0.863089i \(-0.331473\pi\)
0.505052 + 0.863089i \(0.331473\pi\)
\(198\) 0 0
\(199\) −20.9714 −1.48662 −0.743310 0.668947i \(-0.766745\pi\)
−0.743310 + 0.668947i \(0.766745\pi\)
\(200\) 0 0
\(201\) −1.57831 −0.111326
\(202\) 0 0
\(203\) −29.8979 −2.09842
\(204\) 0 0
\(205\) −11.8579 −0.828189
\(206\) 0 0
\(207\) 6.41697 0.446010
\(208\) 0 0
\(209\) −16.6231 −1.14984
\(210\) 0 0
\(211\) −23.1535 −1.59396 −0.796978 0.604008i \(-0.793569\pi\)
−0.796978 + 0.604008i \(0.793569\pi\)
\(212\) 0 0
\(213\) −40.2415 −2.75730
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) 32.8292 2.22859
\(218\) 0 0
\(219\) 31.1088 2.10214
\(220\) 0 0
\(221\) −9.31961 −0.626905
\(222\) 0 0
\(223\) 10.8818 0.728699 0.364349 0.931262i \(-0.381291\pi\)
0.364349 + 0.931262i \(0.381291\pi\)
\(224\) 0 0
\(225\) 6.41697 0.427798
\(226\) 0 0
\(227\) −19.1088 −1.26829 −0.634147 0.773213i \(-0.718648\pi\)
−0.634147 + 0.773213i \(0.718648\pi\)
\(228\) 0 0
\(229\) −26.5497 −1.75445 −0.877226 0.480078i \(-0.840608\pi\)
−0.877226 + 0.480078i \(0.840608\pi\)
\(230\) 0 0
\(231\) 38.3149 2.52093
\(232\) 0 0
\(233\) −10.1374 −0.664124 −0.332062 0.943258i \(-0.607744\pi\)
−0.332062 + 0.943258i \(0.607744\pi\)
\(234\) 0 0
\(235\) 1.44090 0.0939937
\(236\) 0 0
\(237\) −24.5497 −1.59467
\(238\) 0 0
\(239\) −25.1535 −1.62705 −0.813524 0.581532i \(-0.802454\pi\)
−0.813524 + 0.581532i \(0.802454\pi\)
\(240\) 0 0
\(241\) −21.6679 −1.39575 −0.697875 0.716219i \(-0.745871\pi\)
−0.697875 + 0.716219i \(0.745871\pi\)
\(242\) 0 0
\(243\) 8.21084 0.526726
\(244\) 0 0
\(245\) −9.55438 −0.610407
\(246\) 0 0
\(247\) 29.3435 1.86708
\(248\) 0 0
\(249\) −29.1088 −1.84469
\(250\) 0 0
\(251\) −8.52573 −0.538140 −0.269070 0.963121i \(-0.586716\pi\)
−0.269070 + 0.963121i \(0.586716\pi\)
\(252\) 0 0
\(253\) 3.06871 0.192928
\(254\) 0 0
\(255\) −5.27955 −0.330618
\(256\) 0 0
\(257\) −27.5305 −1.71730 −0.858651 0.512560i \(-0.828697\pi\)
−0.858651 + 0.512560i \(0.828697\pi\)
\(258\) 0 0
\(259\) 3.21084 0.199512
\(260\) 0 0
\(261\) −47.1535 −2.91873
\(262\) 0 0
\(263\) −13.3883 −0.825559 −0.412780 0.910831i \(-0.635442\pi\)
−0.412780 + 0.910831i \(0.635442\pi\)
\(264\) 0 0
\(265\) −1.48568 −0.0912643
\(266\) 0 0
\(267\) −33.6679 −2.06044
\(268\) 0 0
\(269\) 11.6231 0.708672 0.354336 0.935118i \(-0.384707\pi\)
0.354336 + 0.935118i \(0.384707\pi\)
\(270\) 0 0
\(271\) 9.64702 0.586015 0.293007 0.956110i \(-0.405344\pi\)
0.293007 + 0.956110i \(0.405344\pi\)
\(272\) 0 0
\(273\) −67.6345 −4.09343
\(274\) 0 0
\(275\) 3.06871 0.185050
\(276\) 0 0
\(277\) 3.39304 0.203868 0.101934 0.994791i \(-0.467497\pi\)
0.101934 + 0.994791i \(0.467497\pi\)
\(278\) 0 0
\(279\) 51.7766 3.09979
\(280\) 0 0
\(281\) −2.74438 −0.163716 −0.0818579 0.996644i \(-0.526085\pi\)
−0.0818579 + 0.996644i \(0.526085\pi\)
\(282\) 0 0
\(283\) 13.2108 0.785303 0.392652 0.919687i \(-0.371558\pi\)
0.392652 + 0.919687i \(0.371558\pi\)
\(284\) 0 0
\(285\) 16.6231 0.984667
\(286\) 0 0
\(287\) 48.2462 2.84788
\(288\) 0 0
\(289\) −14.0401 −0.825886
\(290\) 0 0
\(291\) −15.9761 −0.936534
\(292\) 0 0
\(293\) −12.0926 −0.706459 −0.353230 0.935537i \(-0.614917\pi\)
−0.353230 + 0.935537i \(0.614917\pi\)
\(294\) 0 0
\(295\) −9.62309 −0.560278
\(296\) 0 0
\(297\) 32.1775 1.86713
\(298\) 0 0
\(299\) −5.41697 −0.313271
\(300\) 0 0
\(301\) 16.2748 0.938066
\(302\) 0 0
\(303\) 43.0993 2.47599
\(304\) 0 0
\(305\) −12.0401 −0.689412
\(306\) 0 0
\(307\) −19.3435 −1.10399 −0.551997 0.833846i \(-0.686134\pi\)
−0.551997 + 0.833846i \(0.686134\pi\)
\(308\) 0 0
\(309\) 34.3883 1.95628
\(310\) 0 0
\(311\) −21.9427 −1.24426 −0.622128 0.782915i \(-0.713732\pi\)
−0.622128 + 0.782915i \(0.713732\pi\)
\(312\) 0 0
\(313\) 9.23477 0.521980 0.260990 0.965341i \(-0.415951\pi\)
0.260990 + 0.965341i \(0.415951\pi\)
\(314\) 0 0
\(315\) −26.1088 −1.47106
\(316\) 0 0
\(317\) −26.9953 −1.51621 −0.758103 0.652135i \(-0.773874\pi\)
−0.758103 + 0.652135i \(0.773874\pi\)
\(318\) 0 0
\(319\) −22.5497 −1.26254
\(320\) 0 0
\(321\) 38.8245 2.16697
\(322\) 0 0
\(323\) −9.31961 −0.518557
\(324\) 0 0
\(325\) −5.41697 −0.300479
\(326\) 0 0
\(327\) 41.1728 2.27686
\(328\) 0 0
\(329\) −5.86258 −0.323215
\(330\) 0 0
\(331\) −9.53353 −0.524010 −0.262005 0.965066i \(-0.584384\pi\)
−0.262005 + 0.965066i \(0.584384\pi\)
\(332\) 0 0
\(333\) 5.06399 0.277505
\(334\) 0 0
\(335\) 0.514324 0.0281005
\(336\) 0 0
\(337\) 8.58303 0.467548 0.233774 0.972291i \(-0.424892\pi\)
0.233774 + 0.972291i \(0.424892\pi\)
\(338\) 0 0
\(339\) 33.1088 1.79822
\(340\) 0 0
\(341\) 24.7605 1.34086
\(342\) 0 0
\(343\) 10.3930 0.561171
\(344\) 0 0
\(345\) −3.06871 −0.165214
\(346\) 0 0
\(347\) −1.20612 −0.0647481 −0.0323741 0.999476i \(-0.510307\pi\)
−0.0323741 + 0.999476i \(0.510307\pi\)
\(348\) 0 0
\(349\) 28.4570 1.52327 0.761635 0.648006i \(-0.224397\pi\)
0.761635 + 0.648006i \(0.224397\pi\)
\(350\) 0 0
\(351\) −56.8006 −3.03179
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 13.1135 0.695992
\(356\) 0 0
\(357\) 21.4810 1.13689
\(358\) 0 0
\(359\) 24.7861 1.30816 0.654080 0.756426i \(-0.273056\pi\)
0.654080 + 0.756426i \(0.273056\pi\)
\(360\) 0 0
\(361\) 10.3435 0.544397
\(362\) 0 0
\(363\) −4.85786 −0.254972
\(364\) 0 0
\(365\) −10.1374 −0.530617
\(366\) 0 0
\(367\) 11.7605 0.613893 0.306947 0.951727i \(-0.400693\pi\)
0.306947 + 0.951727i \(0.400693\pi\)
\(368\) 0 0
\(369\) 76.0915 3.96117
\(370\) 0 0
\(371\) 6.04478 0.313829
\(372\) 0 0
\(373\) −29.3836 −1.52143 −0.760713 0.649089i \(-0.775150\pi\)
−0.760713 + 0.649089i \(0.775150\pi\)
\(374\) 0 0
\(375\) −3.06871 −0.158467
\(376\) 0 0
\(377\) 39.8053 2.05008
\(378\) 0 0
\(379\) −15.0687 −0.774028 −0.387014 0.922074i \(-0.626493\pi\)
−0.387014 + 0.922074i \(0.626493\pi\)
\(380\) 0 0
\(381\) 2.55910 0.131107
\(382\) 0 0
\(383\) 7.48568 0.382500 0.191250 0.981541i \(-0.438746\pi\)
0.191250 + 0.981541i \(0.438746\pi\)
\(384\) 0 0
\(385\) −12.4857 −0.636329
\(386\) 0 0
\(387\) 25.6679 1.30477
\(388\) 0 0
\(389\) −28.3149 −1.43562 −0.717811 0.696238i \(-0.754856\pi\)
−0.717811 + 0.696238i \(0.754856\pi\)
\(390\) 0 0
\(391\) 1.72045 0.0870068
\(392\) 0 0
\(393\) −2.13742 −0.107818
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 12.7844 0.641632 0.320816 0.947141i \(-0.396043\pi\)
0.320816 + 0.947141i \(0.396043\pi\)
\(398\) 0 0
\(399\) −67.6345 −3.38596
\(400\) 0 0
\(401\) 12.8339 0.640896 0.320448 0.947266i \(-0.396167\pi\)
0.320448 + 0.947266i \(0.396167\pi\)
\(402\) 0 0
\(403\) −43.7079 −2.17725
\(404\) 0 0
\(405\) −12.9266 −0.642326
\(406\) 0 0
\(407\) 2.42169 0.120039
\(408\) 0 0
\(409\) −21.4617 −1.06122 −0.530608 0.847618i \(-0.678036\pi\)
−0.530608 + 0.847618i \(0.678036\pi\)
\(410\) 0 0
\(411\) 51.7319 2.55174
\(412\) 0 0
\(413\) 39.1535 1.92662
\(414\) 0 0
\(415\) 9.48568 0.465633
\(416\) 0 0
\(417\) −45.2367 −2.21525
\(418\) 0 0
\(419\) −1.30348 −0.0636792 −0.0318396 0.999493i \(-0.510137\pi\)
−0.0318396 + 0.999493i \(0.510137\pi\)
\(420\) 0 0
\(421\) 14.7204 0.717431 0.358715 0.933447i \(-0.383215\pi\)
0.358715 + 0.933447i \(0.383215\pi\)
\(422\) 0 0
\(423\) −9.24618 −0.449565
\(424\) 0 0
\(425\) 1.72045 0.0834540
\(426\) 0 0
\(427\) 48.9875 2.37067
\(428\) 0 0
\(429\) −51.0114 −2.46285
\(430\) 0 0
\(431\) 29.8053 1.43567 0.717835 0.696213i \(-0.245133\pi\)
0.717835 + 0.696213i \(0.245133\pi\)
\(432\) 0 0
\(433\) −16.3914 −0.787720 −0.393860 0.919170i \(-0.628861\pi\)
−0.393860 + 0.919170i \(0.628861\pi\)
\(434\) 0 0
\(435\) 22.5497 1.08117
\(436\) 0 0
\(437\) −5.41697 −0.259129
\(438\) 0 0
\(439\) 32.9474 1.57249 0.786247 0.617912i \(-0.212021\pi\)
0.786247 + 0.617912i \(0.212021\pi\)
\(440\) 0 0
\(441\) 61.3102 2.91953
\(442\) 0 0
\(443\) 13.5544 0.643988 0.321994 0.946742i \(-0.395647\pi\)
0.321994 + 0.946742i \(0.395647\pi\)
\(444\) 0 0
\(445\) 10.9714 0.520092
\(446\) 0 0
\(447\) −24.8979 −1.17763
\(448\) 0 0
\(449\) −20.4810 −0.966556 −0.483278 0.875467i \(-0.660554\pi\)
−0.483278 + 0.875467i \(0.660554\pi\)
\(450\) 0 0
\(451\) 36.3883 1.71346
\(452\) 0 0
\(453\) 36.6726 1.72303
\(454\) 0 0
\(455\) 22.0401 1.03325
\(456\) 0 0
\(457\) −6.78916 −0.317583 −0.158792 0.987312i \(-0.550760\pi\)
−0.158792 + 0.987312i \(0.550760\pi\)
\(458\) 0 0
\(459\) 18.0401 0.842038
\(460\) 0 0
\(461\) 8.83394 0.411437 0.205719 0.978611i \(-0.434047\pi\)
0.205719 + 0.978611i \(0.434047\pi\)
\(462\) 0 0
\(463\) −16.9714 −0.788726 −0.394363 0.918955i \(-0.629035\pi\)
−0.394363 + 0.918955i \(0.629035\pi\)
\(464\) 0 0
\(465\) −24.7605 −1.14824
\(466\) 0 0
\(467\) 2.83701 0.131281 0.0656406 0.997843i \(-0.479091\pi\)
0.0656406 + 0.997843i \(0.479091\pi\)
\(468\) 0 0
\(469\) −2.09264 −0.0966290
\(470\) 0 0
\(471\) −59.3742 −2.73582
\(472\) 0 0
\(473\) 12.2748 0.564397
\(474\) 0 0
\(475\) −5.41697 −0.248548
\(476\) 0 0
\(477\) 9.53353 0.436510
\(478\) 0 0
\(479\) 9.24618 0.422469 0.211234 0.977435i \(-0.432252\pi\)
0.211234 + 0.977435i \(0.432252\pi\)
\(480\) 0 0
\(481\) −4.27483 −0.194916
\(482\) 0 0
\(483\) 12.4857 0.568118
\(484\) 0 0
\(485\) 5.20612 0.236398
\(486\) 0 0
\(487\) −3.44090 −0.155922 −0.0779609 0.996956i \(-0.524841\pi\)
−0.0779609 + 0.996956i \(0.524841\pi\)
\(488\) 0 0
\(489\) −25.0448 −1.13256
\(490\) 0 0
\(491\) 15.0734 0.680254 0.340127 0.940379i \(-0.389530\pi\)
0.340127 + 0.940379i \(0.389530\pi\)
\(492\) 0 0
\(493\) −12.6423 −0.569380
\(494\) 0 0
\(495\) −19.6918 −0.885081
\(496\) 0 0
\(497\) −53.3549 −2.39330
\(498\) 0 0
\(499\) 14.7319 0.659489 0.329744 0.944070i \(-0.393037\pi\)
0.329744 + 0.944070i \(0.393037\pi\)
\(500\) 0 0
\(501\) −4.27483 −0.190985
\(502\) 0 0
\(503\) 29.9219 1.33415 0.667075 0.744991i \(-0.267546\pi\)
0.667075 + 0.744991i \(0.267546\pi\)
\(504\) 0 0
\(505\) −14.0448 −0.624984
\(506\) 0 0
\(507\) 50.1535 2.22740
\(508\) 0 0
\(509\) 22.7444 1.00813 0.504063 0.863667i \(-0.331838\pi\)
0.504063 + 0.863667i \(0.331838\pi\)
\(510\) 0 0
\(511\) 41.2462 1.82462
\(512\) 0 0
\(513\) −56.8006 −2.50781
\(514\) 0 0
\(515\) −11.2061 −0.493801
\(516\) 0 0
\(517\) −4.42169 −0.194466
\(518\) 0 0
\(519\) 7.27955 0.319537
\(520\) 0 0
\(521\) −23.5783 −1.03298 −0.516492 0.856292i \(-0.672763\pi\)
−0.516492 + 0.856292i \(0.672763\pi\)
\(522\) 0 0
\(523\) 11.3035 0.494267 0.247133 0.968981i \(-0.420511\pi\)
0.247133 + 0.968981i \(0.420511\pi\)
\(524\) 0 0
\(525\) 12.4857 0.544920
\(526\) 0 0
\(527\) 13.8818 0.604700
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 61.7511 2.67977
\(532\) 0 0
\(533\) −64.2337 −2.78227
\(534\) 0 0
\(535\) −12.6517 −0.546982
\(536\) 0 0
\(537\) 57.7958 2.49407
\(538\) 0 0
\(539\) 29.3196 1.26289
\(540\) 0 0
\(541\) −11.8147 −0.507955 −0.253977 0.967210i \(-0.581739\pi\)
−0.253977 + 0.967210i \(0.581739\pi\)
\(542\) 0 0
\(543\) 21.4665 0.921214
\(544\) 0 0
\(545\) −13.4170 −0.574720
\(546\) 0 0
\(547\) −16.5736 −0.708636 −0.354318 0.935125i \(-0.615287\pi\)
−0.354318 + 0.935125i \(0.615287\pi\)
\(548\) 0 0
\(549\) 77.2607 3.29741
\(550\) 0 0
\(551\) 39.8053 1.69576
\(552\) 0 0
\(553\) −32.5497 −1.38415
\(554\) 0 0
\(555\) −2.42169 −0.102795
\(556\) 0 0
\(557\) 11.5752 0.490458 0.245229 0.969465i \(-0.421137\pi\)
0.245229 + 0.969465i \(0.421137\pi\)
\(558\) 0 0
\(559\) −21.6679 −0.916453
\(560\) 0 0
\(561\) 16.2014 0.684024
\(562\) 0 0
\(563\) 14.1822 0.597708 0.298854 0.954299i \(-0.403396\pi\)
0.298854 + 0.954299i \(0.403396\pi\)
\(564\) 0 0
\(565\) −10.7892 −0.453903
\(566\) 0 0
\(567\) 52.5944 2.20876
\(568\) 0 0
\(569\) 25.0609 1.05061 0.525304 0.850915i \(-0.323952\pi\)
0.525304 + 0.850915i \(0.323952\pi\)
\(570\) 0 0
\(571\) 23.0687 0.965395 0.482698 0.875787i \(-0.339657\pi\)
0.482698 + 0.875787i \(0.339657\pi\)
\(572\) 0 0
\(573\) −5.71573 −0.238778
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 11.3930 0.474298 0.237149 0.971473i \(-0.423787\pi\)
0.237149 + 0.971473i \(0.423787\pi\)
\(578\) 0 0
\(579\) −35.9521 −1.49412
\(580\) 0 0
\(581\) −38.5944 −1.60117
\(582\) 0 0
\(583\) 4.55910 0.188819
\(584\) 0 0
\(585\) 34.7605 1.43717
\(586\) 0 0
\(587\) −23.9922 −0.990264 −0.495132 0.868818i \(-0.664880\pi\)
−0.495132 + 0.868818i \(0.664880\pi\)
\(588\) 0 0
\(589\) −43.7079 −1.80095
\(590\) 0 0
\(591\) 43.5065 1.78962
\(592\) 0 0
\(593\) 21.1088 0.866833 0.433417 0.901194i \(-0.357308\pi\)
0.433417 + 0.901194i \(0.357308\pi\)
\(594\) 0 0
\(595\) −7.00000 −0.286972
\(596\) 0 0
\(597\) −64.3549 −2.63387
\(598\) 0 0
\(599\) 24.8740 1.01632 0.508162 0.861262i \(-0.330325\pi\)
0.508162 + 0.861262i \(0.330325\pi\)
\(600\) 0 0
\(601\) −25.5513 −1.04226 −0.521130 0.853477i \(-0.674489\pi\)
−0.521130 + 0.853477i \(0.674489\pi\)
\(602\) 0 0
\(603\) −3.30040 −0.134403
\(604\) 0 0
\(605\) 1.58303 0.0643594
\(606\) 0 0
\(607\) −22.9714 −0.932378 −0.466189 0.884685i \(-0.654373\pi\)
−0.466189 + 0.884685i \(0.654373\pi\)
\(608\) 0 0
\(609\) −91.7480 −3.71782
\(610\) 0 0
\(611\) 7.80529 0.315768
\(612\) 0 0
\(613\) 21.0609 0.850642 0.425321 0.905043i \(-0.360161\pi\)
0.425321 + 0.905043i \(0.360161\pi\)
\(614\) 0 0
\(615\) −36.3883 −1.46732
\(616\) 0 0
\(617\) −45.5257 −1.83280 −0.916399 0.400267i \(-0.868917\pi\)
−0.916399 + 0.400267i \(0.868917\pi\)
\(618\) 0 0
\(619\) 0.113487 0.00456145 0.00228072 0.999997i \(-0.499274\pi\)
0.00228072 + 0.999997i \(0.499274\pi\)
\(620\) 0 0
\(621\) 10.4857 0.420776
\(622\) 0 0
\(623\) −44.6392 −1.78843
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −51.0114 −2.03720
\(628\) 0 0
\(629\) 1.35770 0.0541351
\(630\) 0 0
\(631\) 14.2270 0.566367 0.283183 0.959066i \(-0.408609\pi\)
0.283183 + 0.959066i \(0.408609\pi\)
\(632\) 0 0
\(633\) −71.0515 −2.82404
\(634\) 0 0
\(635\) −0.833935 −0.0330937
\(636\) 0 0
\(637\) −51.7558 −2.05064
\(638\) 0 0
\(639\) −84.1488 −3.32888
\(640\) 0 0
\(641\) 3.81473 0.150673 0.0753363 0.997158i \(-0.475997\pi\)
0.0753363 + 0.997158i \(0.475997\pi\)
\(642\) 0 0
\(643\) −46.4092 −1.83020 −0.915100 0.403228i \(-0.867888\pi\)
−0.915100 + 0.403228i \(0.867888\pi\)
\(644\) 0 0
\(645\) −12.2748 −0.483321
\(646\) 0 0
\(647\) −43.7574 −1.72028 −0.860141 0.510056i \(-0.829625\pi\)
−0.860141 + 0.510056i \(0.829625\pi\)
\(648\) 0 0
\(649\) 29.5305 1.15917
\(650\) 0 0
\(651\) 100.743 3.94844
\(652\) 0 0
\(653\) −22.0562 −0.863125 −0.431563 0.902083i \(-0.642038\pi\)
−0.431563 + 0.902083i \(0.642038\pi\)
\(654\) 0 0
\(655\) 0.696520 0.0272153
\(656\) 0 0
\(657\) 65.0515 2.53790
\(658\) 0 0
\(659\) −6.88179 −0.268077 −0.134038 0.990976i \(-0.542795\pi\)
−0.134038 + 0.990976i \(0.542795\pi\)
\(660\) 0 0
\(661\) −12.7844 −0.497257 −0.248628 0.968599i \(-0.579980\pi\)
−0.248628 + 0.968599i \(0.579980\pi\)
\(662\) 0 0
\(663\) −28.5992 −1.11070
\(664\) 0 0
\(665\) 22.0401 0.854677
\(666\) 0 0
\(667\) −7.34826 −0.284526
\(668\) 0 0
\(669\) 33.3930 1.29105
\(670\) 0 0
\(671\) 36.9474 1.42634
\(672\) 0 0
\(673\) −38.6392 −1.48943 −0.744716 0.667381i \(-0.767415\pi\)
−0.744716 + 0.667381i \(0.767415\pi\)
\(674\) 0 0
\(675\) 10.4857 0.403594
\(676\) 0 0
\(677\) 31.3388 1.20445 0.602224 0.798327i \(-0.294281\pi\)
0.602224 + 0.798327i \(0.294281\pi\)
\(678\) 0 0
\(679\) −21.1822 −0.812898
\(680\) 0 0
\(681\) −58.6392 −2.24706
\(682\) 0 0
\(683\) 33.5065 1.28209 0.641046 0.767503i \(-0.278501\pi\)
0.641046 + 0.767503i \(0.278501\pi\)
\(684\) 0 0
\(685\) −16.8579 −0.644106
\(686\) 0 0
\(687\) −81.4732 −3.10839
\(688\) 0 0
\(689\) −8.04786 −0.306599
\(690\) 0 0
\(691\) −17.1661 −0.653028 −0.326514 0.945192i \(-0.605874\pi\)
−0.326514 + 0.945192i \(0.605874\pi\)
\(692\) 0 0
\(693\) 80.1202 3.04351
\(694\) 0 0
\(695\) 14.7413 0.559169
\(696\) 0 0
\(697\) 20.4008 0.772737
\(698\) 0 0
\(699\) −31.1088 −1.17664
\(700\) 0 0
\(701\) 14.8579 0.561174 0.280587 0.959829i \(-0.409471\pi\)
0.280587 + 0.959829i \(0.409471\pi\)
\(702\) 0 0
\(703\) −4.27483 −0.161228
\(704\) 0 0
\(705\) 4.42169 0.166530
\(706\) 0 0
\(707\) 57.1441 2.14913
\(708\) 0 0
\(709\) 1.35298 0.0508123 0.0254061 0.999677i \(-0.491912\pi\)
0.0254061 + 0.999677i \(0.491912\pi\)
\(710\) 0 0
\(711\) −51.3357 −1.92524
\(712\) 0 0
\(713\) 8.06871 0.302175
\(714\) 0 0
\(715\) 16.6231 0.621668
\(716\) 0 0
\(717\) −77.1889 −2.88267
\(718\) 0 0
\(719\) −4.15827 −0.155077 −0.0775386 0.996989i \(-0.524706\pi\)
−0.0775386 + 0.996989i \(0.524706\pi\)
\(720\) 0 0
\(721\) 45.5944 1.69803
\(722\) 0 0
\(723\) −66.4924 −2.47288
\(724\) 0 0
\(725\) −7.34826 −0.272908
\(726\) 0 0
\(727\) −23.8006 −0.882714 −0.441357 0.897332i \(-0.645503\pi\)
−0.441357 + 0.897332i \(0.645503\pi\)
\(728\) 0 0
\(729\) −13.5830 −0.503075
\(730\) 0 0
\(731\) 6.88179 0.254532
\(732\) 0 0
\(733\) 16.6423 0.614697 0.307349 0.951597i \(-0.400558\pi\)
0.307349 + 0.951597i \(0.400558\pi\)
\(734\) 0 0
\(735\) −29.3196 −1.08147
\(736\) 0 0
\(737\) −1.57831 −0.0581379
\(738\) 0 0
\(739\) 42.9171 1.57873 0.789366 0.613923i \(-0.210409\pi\)
0.789366 + 0.613923i \(0.210409\pi\)
\(740\) 0 0
\(741\) 90.0467 3.30795
\(742\) 0 0
\(743\) 50.9858 1.87049 0.935244 0.354002i \(-0.115180\pi\)
0.935244 + 0.354002i \(0.115180\pi\)
\(744\) 0 0
\(745\) 8.11349 0.297255
\(746\) 0 0
\(747\) −60.8693 −2.22709
\(748\) 0 0
\(749\) 51.4762 1.88090
\(750\) 0 0
\(751\) 39.8053 1.45252 0.726258 0.687422i \(-0.241258\pi\)
0.726258 + 0.687422i \(0.241258\pi\)
\(752\) 0 0
\(753\) −26.1630 −0.953432
\(754\) 0 0
\(755\) −11.9505 −0.434923
\(756\) 0 0
\(757\) −21.3388 −0.775573 −0.387786 0.921749i \(-0.626760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(758\) 0 0
\(759\) 9.41697 0.341814
\(760\) 0 0
\(761\) 33.0306 1.19736 0.598679 0.800989i \(-0.295692\pi\)
0.598679 + 0.800989i \(0.295692\pi\)
\(762\) 0 0
\(763\) 54.5897 1.97628
\(764\) 0 0
\(765\) −11.0401 −0.399154
\(766\) 0 0
\(767\) −52.1280 −1.88223
\(768\) 0 0
\(769\) −13.9104 −0.501623 −0.250812 0.968036i \(-0.580697\pi\)
−0.250812 + 0.968036i \(0.580697\pi\)
\(770\) 0 0
\(771\) −84.4829 −3.04258
\(772\) 0 0
\(773\) 6.14686 0.221087 0.110544 0.993871i \(-0.464741\pi\)
0.110544 + 0.993871i \(0.464741\pi\)
\(774\) 0 0
\(775\) 8.06871 0.289837
\(776\) 0 0
\(777\) 9.85314 0.353480
\(778\) 0 0
\(779\) −64.2337 −2.30141
\(780\) 0 0
\(781\) −40.2415 −1.43995
\(782\) 0 0
\(783\) −77.0515 −2.75359
\(784\) 0 0
\(785\) 19.3483 0.690569
\(786\) 0 0
\(787\) −47.1057 −1.67914 −0.839568 0.543254i \(-0.817192\pi\)
−0.839568 + 0.543254i \(0.817192\pi\)
\(788\) 0 0
\(789\) −41.0848 −1.46266
\(790\) 0 0
\(791\) 43.8979 1.56083
\(792\) 0 0
\(793\) −65.2206 −2.31605
\(794\) 0 0
\(795\) −4.55910 −0.161695
\(796\) 0 0
\(797\) 46.1728 1.63552 0.817761 0.575557i \(-0.195215\pi\)
0.817761 + 0.575557i \(0.195215\pi\)
\(798\) 0 0
\(799\) −2.47899 −0.0877002
\(800\) 0 0
\(801\) −70.4028 −2.48756
\(802\) 0 0
\(803\) 31.1088 1.09780
\(804\) 0 0
\(805\) −4.06871 −0.143403
\(806\) 0 0
\(807\) 35.6679 1.25557
\(808\) 0 0
\(809\) 0.966630 0.0339849 0.0169925 0.999856i \(-0.494591\pi\)
0.0169925 + 0.999856i \(0.494591\pi\)
\(810\) 0 0
\(811\) 30.3196 1.06467 0.532333 0.846535i \(-0.321316\pi\)
0.532333 + 0.846535i \(0.321316\pi\)
\(812\) 0 0
\(813\) 29.6039 1.03825
\(814\) 0 0
\(815\) 8.16134 0.285879
\(816\) 0 0
\(817\) −21.6679 −0.758063
\(818\) 0 0
\(819\) −141.430 −4.94198
\(820\) 0 0
\(821\) −7.39304 −0.258019 −0.129009 0.991643i \(-0.541180\pi\)
−0.129009 + 0.991643i \(0.541180\pi\)
\(822\) 0 0
\(823\) −49.6106 −1.72932 −0.864658 0.502361i \(-0.832465\pi\)
−0.864658 + 0.502361i \(0.832465\pi\)
\(824\) 0 0
\(825\) 9.41697 0.327857
\(826\) 0 0
\(827\) −31.9552 −1.11119 −0.555596 0.831452i \(-0.687510\pi\)
−0.555596 + 0.831452i \(0.687510\pi\)
\(828\) 0 0
\(829\) 43.4284 1.50833 0.754165 0.656685i \(-0.228042\pi\)
0.754165 + 0.656685i \(0.228042\pi\)
\(830\) 0 0
\(831\) 10.4122 0.361197
\(832\) 0 0
\(833\) 16.4378 0.569537
\(834\) 0 0
\(835\) 1.39304 0.0482081
\(836\) 0 0
\(837\) 84.6059 2.92441
\(838\) 0 0
\(839\) −19.9521 −0.688824 −0.344412 0.938819i \(-0.611922\pi\)
−0.344412 + 0.938819i \(0.611922\pi\)
\(840\) 0 0
\(841\) 24.9969 0.861963
\(842\) 0 0
\(843\) −8.42169 −0.290058
\(844\) 0 0
\(845\) −16.3435 −0.562235
\(846\) 0 0
\(847\) −6.44090 −0.221312
\(848\) 0 0
\(849\) 40.5402 1.39134
\(850\) 0 0
\(851\) 0.789156 0.0270519
\(852\) 0 0
\(853\) −54.1936 −1.85555 −0.927777 0.373136i \(-0.878283\pi\)
−0.927777 + 0.373136i \(0.878283\pi\)
\(854\) 0 0
\(855\) 34.7605 1.18878
\(856\) 0 0
\(857\) 20.8818 0.713308 0.356654 0.934236i \(-0.383917\pi\)
0.356654 + 0.934236i \(0.383917\pi\)
\(858\) 0 0
\(859\) −56.7224 −1.93534 −0.967672 0.252212i \(-0.918842\pi\)
−0.967672 + 0.252212i \(0.918842\pi\)
\(860\) 0 0
\(861\) 148.053 5.04565
\(862\) 0 0
\(863\) 23.3452 0.794679 0.397340 0.917672i \(-0.369933\pi\)
0.397340 + 0.917672i \(0.369933\pi\)
\(864\) 0 0
\(865\) −2.37219 −0.0806568
\(866\) 0 0
\(867\) −43.0848 −1.46324
\(868\) 0 0
\(869\) −24.5497 −0.832790
\(870\) 0 0
\(871\) 2.78608 0.0944027
\(872\) 0 0
\(873\) −33.4075 −1.13067
\(874\) 0 0
\(875\) −4.06871 −0.137547
\(876\) 0 0
\(877\) 26.1775 0.883951 0.441975 0.897027i \(-0.354278\pi\)
0.441975 + 0.897027i \(0.354278\pi\)
\(878\) 0 0
\(879\) −37.1088 −1.25165
\(880\) 0 0
\(881\) −15.8147 −0.532812 −0.266406 0.963861i \(-0.585836\pi\)
−0.266406 + 0.963861i \(0.585836\pi\)
\(882\) 0 0
\(883\) −3.83866 −0.129181 −0.0645905 0.997912i \(-0.520574\pi\)
−0.0645905 + 0.997912i \(0.520574\pi\)
\(884\) 0 0
\(885\) −29.5305 −0.992655
\(886\) 0 0
\(887\) −13.6679 −0.458922 −0.229461 0.973318i \(-0.573696\pi\)
−0.229461 + 0.973318i \(0.573696\pi\)
\(888\) 0 0
\(889\) 3.39304 0.113799
\(890\) 0 0
\(891\) 39.6679 1.32892
\(892\) 0 0
\(893\) 7.80529 0.261194
\(894\) 0 0
\(895\) −18.8339 −0.629549
\(896\) 0 0
\(897\) −16.6231 −0.555029
\(898\) 0 0
\(899\) −59.2910 −1.97746
\(900\) 0 0
\(901\) 2.55603 0.0851536
\(902\) 0 0
\(903\) 49.9427 1.66199
\(904\) 0 0
\(905\) −6.99528 −0.232531
\(906\) 0 0
\(907\) 37.4762 1.24438 0.622189 0.782867i \(-0.286244\pi\)
0.622189 + 0.782867i \(0.286244\pi\)
\(908\) 0 0
\(909\) 90.1249 2.98925
\(910\) 0 0
\(911\) −31.1983 −1.03365 −0.516823 0.856092i \(-0.672886\pi\)
−0.516823 + 0.856092i \(0.672886\pi\)
\(912\) 0 0
\(913\) −29.1088 −0.963360
\(914\) 0 0
\(915\) −36.9474 −1.22144
\(916\) 0 0
\(917\) −2.83394 −0.0935848
\(918\) 0 0
\(919\) −12.0896 −0.398798 −0.199399 0.979918i \(-0.563899\pi\)
−0.199399 + 0.979918i \(0.563899\pi\)
\(920\) 0 0
\(921\) −59.3597 −1.95597
\(922\) 0 0
\(923\) 71.0353 2.33816
\(924\) 0 0
\(925\) 0.789156 0.0259473
\(926\) 0 0
\(927\) 71.9093 2.36181
\(928\) 0 0
\(929\) −49.5752 −1.62651 −0.813255 0.581907i \(-0.802307\pi\)
−0.813255 + 0.581907i \(0.802307\pi\)
\(930\) 0 0
\(931\) −51.7558 −1.69623
\(932\) 0 0
\(933\) −67.3357 −2.20447
\(934\) 0 0
\(935\) −5.27955 −0.172660
\(936\) 0 0
\(937\) 27.4648 0.897237 0.448618 0.893723i \(-0.351916\pi\)
0.448618 + 0.893723i \(0.351916\pi\)
\(938\) 0 0
\(939\) 28.3388 0.924802
\(940\) 0 0
\(941\) −2.17747 −0.0709836 −0.0354918 0.999370i \(-0.511300\pi\)
−0.0354918 + 0.999370i \(0.511300\pi\)
\(942\) 0 0
\(943\) 11.8579 0.386145
\(944\) 0 0
\(945\) −42.6632 −1.38783
\(946\) 0 0
\(947\) 18.3082 0.594937 0.297468 0.954732i \(-0.403858\pi\)
0.297468 + 0.954732i \(0.403858\pi\)
\(948\) 0 0
\(949\) −54.9141 −1.78259
\(950\) 0 0
\(951\) −82.8406 −2.68629
\(952\) 0 0
\(953\) 27.6184 0.894647 0.447323 0.894372i \(-0.352377\pi\)
0.447323 + 0.894372i \(0.352377\pi\)
\(954\) 0 0
\(955\) 1.86258 0.0602718
\(956\) 0 0
\(957\) −69.1983 −2.23686
\(958\) 0 0
\(959\) 68.5897 2.21488
\(960\) 0 0
\(961\) 34.1040 1.10013
\(962\) 0 0
\(963\) 81.1858 2.61618
\(964\) 0 0
\(965\) 11.7157 0.377143
\(966\) 0 0
\(967\) −19.2556 −0.619219 −0.309610 0.950864i \(-0.600198\pi\)
−0.309610 + 0.950864i \(0.600198\pi\)
\(968\) 0 0
\(969\) −28.5992 −0.918737
\(970\) 0 0
\(971\) 20.7460 0.665771 0.332886 0.942967i \(-0.391978\pi\)
0.332886 + 0.942967i \(0.391978\pi\)
\(972\) 0 0
\(973\) −59.9780 −1.92281
\(974\) 0 0
\(975\) −16.6231 −0.532365
\(976\) 0 0
\(977\) 23.1775 0.741513 0.370757 0.928730i \(-0.379098\pi\)
0.370757 + 0.928730i \(0.379098\pi\)
\(978\) 0 0
\(979\) −33.6679 −1.07603
\(980\) 0 0
\(981\) 86.0962 2.74884
\(982\) 0 0
\(983\) −35.7110 −1.13900 −0.569502 0.821990i \(-0.692864\pi\)
−0.569502 + 0.821990i \(0.692864\pi\)
\(984\) 0 0
\(985\) −14.1775 −0.451732
\(986\) 0 0
\(987\) −17.9906 −0.572646
\(988\) 0 0
\(989\) 4.00000 0.127193
\(990\) 0 0
\(991\) −44.8292 −1.42405 −0.712023 0.702156i \(-0.752221\pi\)
−0.712023 + 0.702156i \(0.752221\pi\)
\(992\) 0 0
\(993\) −29.2556 −0.928399
\(994\) 0 0
\(995\) 20.9714 0.664837
\(996\) 0 0
\(997\) 29.5210 0.934940 0.467470 0.884009i \(-0.345166\pi\)
0.467470 + 0.884009i \(0.345166\pi\)
\(998\) 0 0
\(999\) 8.27483 0.261804
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.cd.1.3 3
4.3 odd 2 7360.2.a.bx.1.1 3
8.3 odd 2 3680.2.a.r.1.3 yes 3
8.5 even 2 3680.2.a.q.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.q.1.1 3 8.5 even 2
3680.2.a.r.1.3 yes 3 8.3 odd 2
7360.2.a.bx.1.1 3 4.3 odd 2
7360.2.a.cd.1.3 3 1.1 even 1 trivial