Properties

Label 7360.2.a.bm.1.2
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{3} -1.00000 q^{5} -5.12311 q^{7} +3.56155 q^{9} +O(q^{10})\) \(q+2.56155 q^{3} -1.00000 q^{5} -5.12311 q^{7} +3.56155 q^{9} -4.00000 q^{11} +0.561553 q^{13} -2.56155 q^{15} -3.12311 q^{17} +4.00000 q^{19} -13.1231 q^{21} -1.00000 q^{23} +1.00000 q^{25} +1.43845 q^{27} +8.56155 q^{29} -1.43845 q^{31} -10.2462 q^{33} +5.12311 q^{35} +7.12311 q^{37} +1.43845 q^{39} +0.561553 q^{41} -9.12311 q^{43} -3.56155 q^{45} +3.68466 q^{47} +19.2462 q^{49} -8.00000 q^{51} +4.24621 q^{53} +4.00000 q^{55} +10.2462 q^{57} -6.24621 q^{59} -11.1231 q^{61} -18.2462 q^{63} -0.561553 q^{65} +6.24621 q^{67} -2.56155 q^{69} -3.68466 q^{71} +16.5616 q^{73} +2.56155 q^{75} +20.4924 q^{77} +10.2462 q^{79} -7.00000 q^{81} +12.0000 q^{83} +3.12311 q^{85} +21.9309 q^{87} +10.0000 q^{89} -2.87689 q^{91} -3.68466 q^{93} -4.00000 q^{95} -16.2462 q^{97} -14.2462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 2q^{5} - 2q^{7} + 3q^{9} + O(q^{10}) \) \( 2q + q^{3} - 2q^{5} - 2q^{7} + 3q^{9} - 8q^{11} - 3q^{13} - q^{15} + 2q^{17} + 8q^{19} - 18q^{21} - 2q^{23} + 2q^{25} + 7q^{27} + 13q^{29} - 7q^{31} - 4q^{33} + 2q^{35} + 6q^{37} + 7q^{39} - 3q^{41} - 10q^{43} - 3q^{45} - 5q^{47} + 22q^{49} - 16q^{51} - 8q^{53} + 8q^{55} + 4q^{57} + 4q^{59} - 14q^{61} - 20q^{63} + 3q^{65} - 4q^{67} - q^{69} + 5q^{71} + 29q^{73} + q^{75} + 8q^{77} + 4q^{79} - 14q^{81} + 24q^{83} - 2q^{85} + 15q^{87} + 20q^{89} - 14q^{91} + 5q^{93} - 8q^{95} - 16q^{97} - 12q^{99} + O(q^{100}) \)

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
\(3\) 2.56155 1.47891 0.739457 0.673204i \(-0.235083\pi\)
0.739457 + 0.673204i \(0.235083\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −5.12311 −1.93635 −0.968176 0.250270i \(-0.919480\pi\)
−0.968176 + 0.250270i \(0.919480\pi\)
\(8\) 0 0
\(9\) 3.56155 1.18718
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 0.561553 0.155747 0.0778734 0.996963i \(-0.475187\pi\)
0.0778734 + 0.996963i \(0.475187\pi\)
\(14\) 0 0
\(15\) −2.56155 −0.661390
\(16\) 0 0
\(17\) −3.12311 −0.757464 −0.378732 0.925506i \(-0.623640\pi\)
−0.378732 + 0.925506i \(0.623640\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −13.1231 −2.86370
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.43845 0.276829
\(28\) 0 0
\(29\) 8.56155 1.58984 0.794920 0.606714i \(-0.207513\pi\)
0.794920 + 0.606714i \(0.207513\pi\)
\(30\) 0 0
\(31\) −1.43845 −0.258353 −0.129176 0.991622i \(-0.541233\pi\)
−0.129176 + 0.991622i \(0.541233\pi\)
\(32\) 0 0
\(33\) −10.2462 −1.78364
\(34\) 0 0
\(35\) 5.12311 0.865963
\(36\) 0 0
\(37\) 7.12311 1.17103 0.585516 0.810661i \(-0.300892\pi\)
0.585516 + 0.810661i \(0.300892\pi\)
\(38\) 0 0
\(39\) 1.43845 0.230336
\(40\) 0 0
\(41\) 0.561553 0.0876998 0.0438499 0.999038i \(-0.486038\pi\)
0.0438499 + 0.999038i \(0.486038\pi\)
\(42\) 0 0
\(43\) −9.12311 −1.39126 −0.695630 0.718400i \(-0.744875\pi\)
−0.695630 + 0.718400i \(0.744875\pi\)
\(44\) 0 0
\(45\) −3.56155 −0.530925
\(46\) 0 0
\(47\) 3.68466 0.537463 0.268731 0.963215i \(-0.413396\pi\)
0.268731 + 0.963215i \(0.413396\pi\)
\(48\) 0 0
\(49\) 19.2462 2.74946
\(50\) 0 0
\(51\) −8.00000 −1.12022
\(52\) 0 0
\(53\) 4.24621 0.583262 0.291631 0.956531i \(-0.405802\pi\)
0.291631 + 0.956531i \(0.405802\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 10.2462 1.35714
\(58\) 0 0
\(59\) −6.24621 −0.813187 −0.406594 0.913609i \(-0.633284\pi\)
−0.406594 + 0.913609i \(0.633284\pi\)
\(60\) 0 0
\(61\) −11.1231 −1.42417 −0.712084 0.702094i \(-0.752248\pi\)
−0.712084 + 0.702094i \(0.752248\pi\)
\(62\) 0 0
\(63\) −18.2462 −2.29881
\(64\) 0 0
\(65\) −0.561553 −0.0696521
\(66\) 0 0
\(67\) 6.24621 0.763096 0.381548 0.924349i \(-0.375391\pi\)
0.381548 + 0.924349i \(0.375391\pi\)
\(68\) 0 0
\(69\) −2.56155 −0.308375
\(70\) 0 0
\(71\) −3.68466 −0.437289 −0.218644 0.975805i \(-0.570163\pi\)
−0.218644 + 0.975805i \(0.570163\pi\)
\(72\) 0 0
\(73\) 16.5616 1.93838 0.969192 0.246308i \(-0.0792175\pi\)
0.969192 + 0.246308i \(0.0792175\pi\)
\(74\) 0 0
\(75\) 2.56155 0.295783
\(76\) 0 0
\(77\) 20.4924 2.33533
\(78\) 0 0
\(79\) 10.2462 1.15279 0.576394 0.817172i \(-0.304459\pi\)
0.576394 + 0.817172i \(0.304459\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 3.12311 0.338748
\(86\) 0 0
\(87\) 21.9309 2.35124
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) −2.87689 −0.301580
\(92\) 0 0
\(93\) −3.68466 −0.382081
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) −16.2462 −1.64955 −0.824776 0.565459i \(-0.808699\pi\)
−0.824776 + 0.565459i \(0.808699\pi\)
\(98\) 0 0
\(99\) −14.2462 −1.43180
\(100\) 0 0
\(101\) −0.246211 −0.0244989 −0.0122495 0.999925i \(-0.503899\pi\)
−0.0122495 + 0.999925i \(0.503899\pi\)
\(102\) 0 0
\(103\) 2.24621 0.221326 0.110663 0.993858i \(-0.464703\pi\)
0.110663 + 0.993858i \(0.464703\pi\)
\(104\) 0 0
\(105\) 13.1231 1.28068
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −8.24621 −0.789844 −0.394922 0.918715i \(-0.629228\pi\)
−0.394922 + 0.918715i \(0.629228\pi\)
\(110\) 0 0
\(111\) 18.2462 1.73185
\(112\) 0 0
\(113\) 20.2462 1.90460 0.952302 0.305158i \(-0.0987093\pi\)
0.952302 + 0.305158i \(0.0987093\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 16.0000 1.46672
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 1.43845 0.129700
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.8078 1.49145 0.745724 0.666255i \(-0.232104\pi\)
0.745724 + 0.666255i \(0.232104\pi\)
\(128\) 0 0
\(129\) −23.3693 −2.05755
\(130\) 0 0
\(131\) 9.93087 0.867664 0.433832 0.900994i \(-0.357161\pi\)
0.433832 + 0.900994i \(0.357161\pi\)
\(132\) 0 0
\(133\) −20.4924 −1.77692
\(134\) 0 0
\(135\) −1.43845 −0.123802
\(136\) 0 0
\(137\) 15.1231 1.29205 0.646027 0.763315i \(-0.276429\pi\)
0.646027 + 0.763315i \(0.276429\pi\)
\(138\) 0 0
\(139\) 0.315342 0.0267469 0.0133735 0.999911i \(-0.495743\pi\)
0.0133735 + 0.999911i \(0.495743\pi\)
\(140\) 0 0
\(141\) 9.43845 0.794861
\(142\) 0 0
\(143\) −2.24621 −0.187838
\(144\) 0 0
\(145\) −8.56155 −0.710998
\(146\) 0 0
\(147\) 49.3002 4.06621
\(148\) 0 0
\(149\) 4.24621 0.347863 0.173932 0.984758i \(-0.444353\pi\)
0.173932 + 0.984758i \(0.444353\pi\)
\(150\) 0 0
\(151\) 16.8078 1.36780 0.683898 0.729577i \(-0.260283\pi\)
0.683898 + 0.729577i \(0.260283\pi\)
\(152\) 0 0
\(153\) −11.1231 −0.899250
\(154\) 0 0
\(155\) 1.43845 0.115539
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 10.8769 0.862594
\(160\) 0 0
\(161\) 5.12311 0.403757
\(162\) 0 0
\(163\) −0.315342 −0.0246995 −0.0123497 0.999924i \(-0.503931\pi\)
−0.0123497 + 0.999924i \(0.503931\pi\)
\(164\) 0 0
\(165\) 10.2462 0.797666
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −12.6847 −0.975743
\(170\) 0 0
\(171\) 14.2462 1.08944
\(172\) 0 0
\(173\) −10.4924 −0.797724 −0.398862 0.917011i \(-0.630595\pi\)
−0.398862 + 0.917011i \(0.630595\pi\)
\(174\) 0 0
\(175\) −5.12311 −0.387270
\(176\) 0 0
\(177\) −16.0000 −1.20263
\(178\) 0 0
\(179\) −7.68466 −0.574378 −0.287189 0.957874i \(-0.592721\pi\)
−0.287189 + 0.957874i \(0.592721\pi\)
\(180\) 0 0
\(181\) −3.12311 −0.232139 −0.116069 0.993241i \(-0.537029\pi\)
−0.116069 + 0.993241i \(0.537029\pi\)
\(182\) 0 0
\(183\) −28.4924 −2.10622
\(184\) 0 0
\(185\) −7.12311 −0.523701
\(186\) 0 0
\(187\) 12.4924 0.913536
\(188\) 0 0
\(189\) −7.36932 −0.536039
\(190\) 0 0
\(191\) 2.87689 0.208165 0.104082 0.994569i \(-0.466809\pi\)
0.104082 + 0.994569i \(0.466809\pi\)
\(192\) 0 0
\(193\) 24.5616 1.76798 0.883990 0.467507i \(-0.154848\pi\)
0.883990 + 0.467507i \(0.154848\pi\)
\(194\) 0 0
\(195\) −1.43845 −0.103009
\(196\) 0 0
\(197\) 11.4384 0.814956 0.407478 0.913215i \(-0.366408\pi\)
0.407478 + 0.913215i \(0.366408\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) 16.0000 1.12855
\(202\) 0 0
\(203\) −43.8617 −3.07849
\(204\) 0 0
\(205\) −0.561553 −0.0392205
\(206\) 0 0
\(207\) −3.56155 −0.247545
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) −14.2462 −0.980750 −0.490375 0.871512i \(-0.663140\pi\)
−0.490375 + 0.871512i \(0.663140\pi\)
\(212\) 0 0
\(213\) −9.43845 −0.646712
\(214\) 0 0
\(215\) 9.12311 0.622191
\(216\) 0 0
\(217\) 7.36932 0.500262
\(218\) 0 0
\(219\) 42.4233 2.86670
\(220\) 0 0
\(221\) −1.75379 −0.117973
\(222\) 0 0
\(223\) 20.4924 1.37227 0.686137 0.727472i \(-0.259305\pi\)
0.686137 + 0.727472i \(0.259305\pi\)
\(224\) 0 0
\(225\) 3.56155 0.237437
\(226\) 0 0
\(227\) 9.12311 0.605522 0.302761 0.953067i \(-0.402092\pi\)
0.302761 + 0.953067i \(0.402092\pi\)
\(228\) 0 0
\(229\) −0.246211 −0.0162701 −0.00813505 0.999967i \(-0.502589\pi\)
−0.00813505 + 0.999967i \(0.502589\pi\)
\(230\) 0 0
\(231\) 52.4924 3.45375
\(232\) 0 0
\(233\) −12.5616 −0.822935 −0.411467 0.911425i \(-0.634984\pi\)
−0.411467 + 0.911425i \(0.634984\pi\)
\(234\) 0 0
\(235\) −3.68466 −0.240361
\(236\) 0 0
\(237\) 26.2462 1.70487
\(238\) 0 0
\(239\) 8.80776 0.569727 0.284863 0.958568i \(-0.408052\pi\)
0.284863 + 0.958568i \(0.408052\pi\)
\(240\) 0 0
\(241\) −18.4924 −1.19120 −0.595601 0.803281i \(-0.703086\pi\)
−0.595601 + 0.803281i \(0.703086\pi\)
\(242\) 0 0
\(243\) −22.2462 −1.42710
\(244\) 0 0
\(245\) −19.2462 −1.22960
\(246\) 0 0
\(247\) 2.24621 0.142923
\(248\) 0 0
\(249\) 30.7386 1.94798
\(250\) 0 0
\(251\) 6.24621 0.394257 0.197129 0.980378i \(-0.436838\pi\)
0.197129 + 0.980378i \(0.436838\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 8.00000 0.500979
\(256\) 0 0
\(257\) −9.05398 −0.564771 −0.282386 0.959301i \(-0.591126\pi\)
−0.282386 + 0.959301i \(0.591126\pi\)
\(258\) 0 0
\(259\) −36.4924 −2.26753
\(260\) 0 0
\(261\) 30.4924 1.88743
\(262\) 0 0
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) −4.24621 −0.260843
\(266\) 0 0
\(267\) 25.6155 1.56764
\(268\) 0 0
\(269\) 23.3002 1.42064 0.710319 0.703880i \(-0.248551\pi\)
0.710319 + 0.703880i \(0.248551\pi\)
\(270\) 0 0
\(271\) 2.24621 0.136448 0.0682238 0.997670i \(-0.478267\pi\)
0.0682238 + 0.997670i \(0.478267\pi\)
\(272\) 0 0
\(273\) −7.36932 −0.446011
\(274\) 0 0
\(275\) −4.00000 −0.241209
\(276\) 0 0
\(277\) 11.4384 0.687270 0.343635 0.939103i \(-0.388342\pi\)
0.343635 + 0.939103i \(0.388342\pi\)
\(278\) 0 0
\(279\) −5.12311 −0.306712
\(280\) 0 0
\(281\) 30.4924 1.81903 0.909513 0.415676i \(-0.136455\pi\)
0.909513 + 0.415676i \(0.136455\pi\)
\(282\) 0 0
\(283\) 22.8769 1.35989 0.679945 0.733263i \(-0.262004\pi\)
0.679945 + 0.733263i \(0.262004\pi\)
\(284\) 0 0
\(285\) −10.2462 −0.606933
\(286\) 0 0
\(287\) −2.87689 −0.169818
\(288\) 0 0
\(289\) −7.24621 −0.426248
\(290\) 0 0
\(291\) −41.6155 −2.43955
\(292\) 0 0
\(293\) 12.8769 0.752276 0.376138 0.926564i \(-0.377252\pi\)
0.376138 + 0.926564i \(0.377252\pi\)
\(294\) 0 0
\(295\) 6.24621 0.363668
\(296\) 0 0
\(297\) −5.75379 −0.333869
\(298\) 0 0
\(299\) −0.561553 −0.0324754
\(300\) 0 0
\(301\) 46.7386 2.69397
\(302\) 0 0
\(303\) −0.630683 −0.0362318
\(304\) 0 0
\(305\) 11.1231 0.636907
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 5.75379 0.327322
\(310\) 0 0
\(311\) −13.9309 −0.789947 −0.394974 0.918692i \(-0.629246\pi\)
−0.394974 + 0.918692i \(0.629246\pi\)
\(312\) 0 0
\(313\) 15.1231 0.854808 0.427404 0.904061i \(-0.359428\pi\)
0.427404 + 0.904061i \(0.359428\pi\)
\(314\) 0 0
\(315\) 18.2462 1.02806
\(316\) 0 0
\(317\) −20.7386 −1.16480 −0.582399 0.812903i \(-0.697886\pi\)
−0.582399 + 0.812903i \(0.697886\pi\)
\(318\) 0 0
\(319\) −34.2462 −1.91742
\(320\) 0 0
\(321\) −30.7386 −1.71566
\(322\) 0 0
\(323\) −12.4924 −0.695097
\(324\) 0 0
\(325\) 0.561553 0.0311493
\(326\) 0 0
\(327\) −21.1231 −1.16811
\(328\) 0 0
\(329\) −18.8769 −1.04072
\(330\) 0 0
\(331\) 10.5616 0.580515 0.290258 0.956949i \(-0.406259\pi\)
0.290258 + 0.956949i \(0.406259\pi\)
\(332\) 0 0
\(333\) 25.3693 1.39023
\(334\) 0 0
\(335\) −6.24621 −0.341267
\(336\) 0 0
\(337\) 15.7538 0.858164 0.429082 0.903266i \(-0.358837\pi\)
0.429082 + 0.903266i \(0.358837\pi\)
\(338\) 0 0
\(339\) 51.8617 2.81674
\(340\) 0 0
\(341\) 5.75379 0.311585
\(342\) 0 0
\(343\) −62.7386 −3.38757
\(344\) 0 0
\(345\) 2.56155 0.137909
\(346\) 0 0
\(347\) −16.4924 −0.885360 −0.442680 0.896680i \(-0.645972\pi\)
−0.442680 + 0.896680i \(0.645972\pi\)
\(348\) 0 0
\(349\) 2.80776 0.150296 0.0751481 0.997172i \(-0.476057\pi\)
0.0751481 + 0.997172i \(0.476057\pi\)
\(350\) 0 0
\(351\) 0.807764 0.0431153
\(352\) 0 0
\(353\) 34.8078 1.85263 0.926315 0.376750i \(-0.122958\pi\)
0.926315 + 0.376750i \(0.122958\pi\)
\(354\) 0 0
\(355\) 3.68466 0.195561
\(356\) 0 0
\(357\) 40.9848 2.16915
\(358\) 0 0
\(359\) 13.7538 0.725897 0.362949 0.931809i \(-0.381770\pi\)
0.362949 + 0.931809i \(0.381770\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 12.8078 0.672233
\(364\) 0 0
\(365\) −16.5616 −0.866871
\(366\) 0 0
\(367\) −20.4924 −1.06970 −0.534848 0.844948i \(-0.679631\pi\)
−0.534848 + 0.844948i \(0.679631\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) −21.7538 −1.12940
\(372\) 0 0
\(373\) 24.7386 1.28092 0.640459 0.767992i \(-0.278744\pi\)
0.640459 + 0.767992i \(0.278744\pi\)
\(374\) 0 0
\(375\) −2.56155 −0.132278
\(376\) 0 0
\(377\) 4.80776 0.247612
\(378\) 0 0
\(379\) −14.2462 −0.731779 −0.365889 0.930658i \(-0.619235\pi\)
−0.365889 + 0.930658i \(0.619235\pi\)
\(380\) 0 0
\(381\) 43.0540 2.20572
\(382\) 0 0
\(383\) −33.6155 −1.71767 −0.858837 0.512250i \(-0.828812\pi\)
−0.858837 + 0.512250i \(0.828812\pi\)
\(384\) 0 0
\(385\) −20.4924 −1.04439
\(386\) 0 0
\(387\) −32.4924 −1.65168
\(388\) 0 0
\(389\) −7.61553 −0.386123 −0.193061 0.981187i \(-0.561842\pi\)
−0.193061 + 0.981187i \(0.561842\pi\)
\(390\) 0 0
\(391\) 3.12311 0.157942
\(392\) 0 0
\(393\) 25.4384 1.28320
\(394\) 0 0
\(395\) −10.2462 −0.515543
\(396\) 0 0
\(397\) −3.93087 −0.197285 −0.0986423 0.995123i \(-0.531450\pi\)
−0.0986423 + 0.995123i \(0.531450\pi\)
\(398\) 0 0
\(399\) −52.4924 −2.62791
\(400\) 0 0
\(401\) −28.7386 −1.43514 −0.717569 0.696487i \(-0.754745\pi\)
−0.717569 + 0.696487i \(0.754745\pi\)
\(402\) 0 0
\(403\) −0.807764 −0.0402376
\(404\) 0 0
\(405\) 7.00000 0.347833
\(406\) 0 0
\(407\) −28.4924 −1.41232
\(408\) 0 0
\(409\) −2.31534 −0.114486 −0.0572431 0.998360i \(-0.518231\pi\)
−0.0572431 + 0.998360i \(0.518231\pi\)
\(410\) 0 0
\(411\) 38.7386 1.91084
\(412\) 0 0
\(413\) 32.0000 1.57462
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 0.807764 0.0395564
\(418\) 0 0
\(419\) −9.12311 −0.445693 −0.222846 0.974854i \(-0.571535\pi\)
−0.222846 + 0.974854i \(0.571535\pi\)
\(420\) 0 0
\(421\) −26.4924 −1.29116 −0.645581 0.763692i \(-0.723385\pi\)
−0.645581 + 0.763692i \(0.723385\pi\)
\(422\) 0 0
\(423\) 13.1231 0.638067
\(424\) 0 0
\(425\) −3.12311 −0.151493
\(426\) 0 0
\(427\) 56.9848 2.75769
\(428\) 0 0
\(429\) −5.75379 −0.277796
\(430\) 0 0
\(431\) 33.6155 1.61920 0.809602 0.586980i \(-0.199683\pi\)
0.809602 + 0.586980i \(0.199683\pi\)
\(432\) 0 0
\(433\) 24.7386 1.18886 0.594431 0.804146i \(-0.297377\pi\)
0.594431 + 0.804146i \(0.297377\pi\)
\(434\) 0 0
\(435\) −21.9309 −1.05150
\(436\) 0 0
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) −21.3002 −1.01660 −0.508301 0.861179i \(-0.669726\pi\)
−0.508301 + 0.861179i \(0.669726\pi\)
\(440\) 0 0
\(441\) 68.5464 3.26411
\(442\) 0 0
\(443\) −15.6847 −0.745201 −0.372600 0.927992i \(-0.621534\pi\)
−0.372600 + 0.927992i \(0.621534\pi\)
\(444\) 0 0
\(445\) −10.0000 −0.474045
\(446\) 0 0
\(447\) 10.8769 0.514459
\(448\) 0 0
\(449\) 16.7386 0.789945 0.394972 0.918693i \(-0.370754\pi\)
0.394972 + 0.918693i \(0.370754\pi\)
\(450\) 0 0
\(451\) −2.24621 −0.105770
\(452\) 0 0
\(453\) 43.0540 2.02285
\(454\) 0 0
\(455\) 2.87689 0.134871
\(456\) 0 0
\(457\) −0.876894 −0.0410194 −0.0205097 0.999790i \(-0.506529\pi\)
−0.0205097 + 0.999790i \(0.506529\pi\)
\(458\) 0 0
\(459\) −4.49242 −0.209688
\(460\) 0 0
\(461\) −23.4384 −1.09164 −0.545819 0.837903i \(-0.683781\pi\)
−0.545819 + 0.837903i \(0.683781\pi\)
\(462\) 0 0
\(463\) −10.2462 −0.476182 −0.238091 0.971243i \(-0.576522\pi\)
−0.238091 + 0.971243i \(0.576522\pi\)
\(464\) 0 0
\(465\) 3.68466 0.170872
\(466\) 0 0
\(467\) 35.3693 1.63670 0.818348 0.574722i \(-0.194890\pi\)
0.818348 + 0.574722i \(0.194890\pi\)
\(468\) 0 0
\(469\) −32.0000 −1.47762
\(470\) 0 0
\(471\) 5.12311 0.236060
\(472\) 0 0
\(473\) 36.4924 1.67792
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 15.1231 0.692439
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 0 0
\(483\) 13.1231 0.597122
\(484\) 0 0
\(485\) 16.2462 0.737702
\(486\) 0 0
\(487\) 3.05398 0.138389 0.0691944 0.997603i \(-0.477957\pi\)
0.0691944 + 0.997603i \(0.477957\pi\)
\(488\) 0 0
\(489\) −0.807764 −0.0365284
\(490\) 0 0
\(491\) 10.5616 0.476636 0.238318 0.971187i \(-0.423404\pi\)
0.238318 + 0.971187i \(0.423404\pi\)
\(492\) 0 0
\(493\) −26.7386 −1.20425
\(494\) 0 0
\(495\) 14.2462 0.640320
\(496\) 0 0
\(497\) 18.8769 0.846744
\(498\) 0 0
\(499\) 0.946025 0.0423499 0.0211749 0.999776i \(-0.493259\pi\)
0.0211749 + 0.999776i \(0.493259\pi\)
\(500\) 0 0
\(501\) 20.4924 0.915534
\(502\) 0 0
\(503\) −25.6155 −1.14214 −0.571070 0.820901i \(-0.693472\pi\)
−0.571070 + 0.820901i \(0.693472\pi\)
\(504\) 0 0
\(505\) 0.246211 0.0109563
\(506\) 0 0
\(507\) −32.4924 −1.44304
\(508\) 0 0
\(509\) 8.56155 0.379484 0.189742 0.981834i \(-0.439235\pi\)
0.189742 + 0.981834i \(0.439235\pi\)
\(510\) 0 0
\(511\) −84.8466 −3.75339
\(512\) 0 0
\(513\) 5.75379 0.254036
\(514\) 0 0
\(515\) −2.24621 −0.0989799
\(516\) 0 0
\(517\) −14.7386 −0.648204
\(518\) 0 0
\(519\) −26.8769 −1.17976
\(520\) 0 0
\(521\) −17.8617 −0.782537 −0.391269 0.920277i \(-0.627964\pi\)
−0.391269 + 0.920277i \(0.627964\pi\)
\(522\) 0 0
\(523\) −23.8617 −1.04340 −0.521701 0.853129i \(-0.674702\pi\)
−0.521701 + 0.853129i \(0.674702\pi\)
\(524\) 0 0
\(525\) −13.1231 −0.572739
\(526\) 0 0
\(527\) 4.49242 0.195693
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −22.2462 −0.965403
\(532\) 0 0
\(533\) 0.315342 0.0136590
\(534\) 0 0
\(535\) 12.0000 0.518805
\(536\) 0 0
\(537\) −19.6847 −0.849456
\(538\) 0 0
\(539\) −76.9848 −3.31597
\(540\) 0 0
\(541\) −33.6847 −1.44822 −0.724108 0.689686i \(-0.757748\pi\)
−0.724108 + 0.689686i \(0.757748\pi\)
\(542\) 0 0
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 8.24621 0.353229
\(546\) 0 0
\(547\) 0.946025 0.0404491 0.0202245 0.999795i \(-0.493562\pi\)
0.0202245 + 0.999795i \(0.493562\pi\)
\(548\) 0 0
\(549\) −39.6155 −1.69075
\(550\) 0 0
\(551\) 34.2462 1.45894
\(552\) 0 0
\(553\) −52.4924 −2.23220
\(554\) 0 0
\(555\) −18.2462 −0.774509
\(556\) 0 0
\(557\) 7.75379 0.328539 0.164269 0.986416i \(-0.447473\pi\)
0.164269 + 0.986416i \(0.447473\pi\)
\(558\) 0 0
\(559\) −5.12311 −0.216684
\(560\) 0 0
\(561\) 32.0000 1.35104
\(562\) 0 0
\(563\) −39.2311 −1.65339 −0.826696 0.562649i \(-0.809782\pi\)
−0.826696 + 0.562649i \(0.809782\pi\)
\(564\) 0 0
\(565\) −20.2462 −0.851765
\(566\) 0 0
\(567\) 35.8617 1.50605
\(568\) 0 0
\(569\) −20.7386 −0.869409 −0.434704 0.900573i \(-0.643147\pi\)
−0.434704 + 0.900573i \(0.643147\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 7.36932 0.307858
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −32.4233 −1.34980 −0.674900 0.737910i \(-0.735813\pi\)
−0.674900 + 0.737910i \(0.735813\pi\)
\(578\) 0 0
\(579\) 62.9157 2.61469
\(580\) 0 0
\(581\) −61.4773 −2.55051
\(582\) 0 0
\(583\) −16.9848 −0.703440
\(584\) 0 0
\(585\) −2.00000 −0.0826898
\(586\) 0 0
\(587\) −36.1771 −1.49319 −0.746594 0.665280i \(-0.768312\pi\)
−0.746594 + 0.665280i \(0.768312\pi\)
\(588\) 0 0
\(589\) −5.75379 −0.237081
\(590\) 0 0
\(591\) 29.3002 1.20525
\(592\) 0 0
\(593\) 26.9848 1.10813 0.554067 0.832472i \(-0.313075\pi\)
0.554067 + 0.832472i \(0.313075\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 0 0
\(597\) −61.4773 −2.51610
\(598\) 0 0
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) 18.1771 0.741459 0.370729 0.928741i \(-0.379108\pi\)
0.370729 + 0.928741i \(0.379108\pi\)
\(602\) 0 0
\(603\) 22.2462 0.905936
\(604\) 0 0
\(605\) −5.00000 −0.203279
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) −112.354 −4.55282
\(610\) 0 0
\(611\) 2.06913 0.0837081
\(612\) 0 0
\(613\) −3.12311 −0.126141 −0.0630705 0.998009i \(-0.520089\pi\)
−0.0630705 + 0.998009i \(0.520089\pi\)
\(614\) 0 0
\(615\) −1.43845 −0.0580038
\(616\) 0 0
\(617\) 35.6155 1.43383 0.716914 0.697162i \(-0.245554\pi\)
0.716914 + 0.697162i \(0.245554\pi\)
\(618\) 0 0
\(619\) −28.9848 −1.16500 −0.582500 0.812831i \(-0.697925\pi\)
−0.582500 + 0.812831i \(0.697925\pi\)
\(620\) 0 0
\(621\) −1.43845 −0.0577229
\(622\) 0 0
\(623\) −51.2311 −2.05253
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −40.9848 −1.63678
\(628\) 0 0
\(629\) −22.2462 −0.887015
\(630\) 0 0
\(631\) 31.3693 1.24879 0.624396 0.781108i \(-0.285345\pi\)
0.624396 + 0.781108i \(0.285345\pi\)
\(632\) 0 0
\(633\) −36.4924 −1.45044
\(634\) 0 0
\(635\) −16.8078 −0.666996
\(636\) 0 0
\(637\) 10.8078 0.428219
\(638\) 0 0
\(639\) −13.1231 −0.519142
\(640\) 0 0
\(641\) 23.7538 0.938218 0.469109 0.883140i \(-0.344575\pi\)
0.469109 + 0.883140i \(0.344575\pi\)
\(642\) 0 0
\(643\) 44.3542 1.74916 0.874579 0.484884i \(-0.161138\pi\)
0.874579 + 0.484884i \(0.161138\pi\)
\(644\) 0 0
\(645\) 23.3693 0.920166
\(646\) 0 0
\(647\) 1.43845 0.0565512 0.0282756 0.999600i \(-0.490998\pi\)
0.0282756 + 0.999600i \(0.490998\pi\)
\(648\) 0 0
\(649\) 24.9848 0.980741
\(650\) 0 0
\(651\) 18.8769 0.739844
\(652\) 0 0
\(653\) 35.7926 1.40067 0.700337 0.713813i \(-0.253033\pi\)
0.700337 + 0.713813i \(0.253033\pi\)
\(654\) 0 0
\(655\) −9.93087 −0.388031
\(656\) 0 0
\(657\) 58.9848 2.30122
\(658\) 0 0
\(659\) 14.2462 0.554954 0.277477 0.960732i \(-0.410502\pi\)
0.277477 + 0.960732i \(0.410502\pi\)
\(660\) 0 0
\(661\) −10.4924 −0.408108 −0.204054 0.978960i \(-0.565412\pi\)
−0.204054 + 0.978960i \(0.565412\pi\)
\(662\) 0 0
\(663\) −4.49242 −0.174471
\(664\) 0 0
\(665\) 20.4924 0.794662
\(666\) 0 0
\(667\) −8.56155 −0.331505
\(668\) 0 0
\(669\) 52.4924 2.02947
\(670\) 0 0
\(671\) 44.4924 1.71761
\(672\) 0 0
\(673\) −4.56155 −0.175835 −0.0879175 0.996128i \(-0.528021\pi\)
−0.0879175 + 0.996128i \(0.528021\pi\)
\(674\) 0 0
\(675\) 1.43845 0.0553659
\(676\) 0 0
\(677\) −20.7386 −0.797050 −0.398525 0.917157i \(-0.630478\pi\)
−0.398525 + 0.917157i \(0.630478\pi\)
\(678\) 0 0
\(679\) 83.2311 3.19411
\(680\) 0 0
\(681\) 23.3693 0.895514
\(682\) 0 0
\(683\) −18.5616 −0.710238 −0.355119 0.934821i \(-0.615560\pi\)
−0.355119 + 0.934821i \(0.615560\pi\)
\(684\) 0 0
\(685\) −15.1231 −0.577824
\(686\) 0 0
\(687\) −0.630683 −0.0240621
\(688\) 0 0
\(689\) 2.38447 0.0908411
\(690\) 0 0
\(691\) 6.24621 0.237617 0.118809 0.992917i \(-0.462093\pi\)
0.118809 + 0.992917i \(0.462093\pi\)
\(692\) 0 0
\(693\) 72.9848 2.77247
\(694\) 0 0
\(695\) −0.315342 −0.0119616
\(696\) 0 0
\(697\) −1.75379 −0.0664295
\(698\) 0 0
\(699\) −32.1771 −1.21705
\(700\) 0 0
\(701\) −38.9848 −1.47244 −0.736219 0.676744i \(-0.763390\pi\)
−0.736219 + 0.676744i \(0.763390\pi\)
\(702\) 0 0
\(703\) 28.4924 1.07461
\(704\) 0 0
\(705\) −9.43845 −0.355472
\(706\) 0 0
\(707\) 1.26137 0.0474386
\(708\) 0 0
\(709\) 40.7386 1.52997 0.764986 0.644047i \(-0.222746\pi\)
0.764986 + 0.644047i \(0.222746\pi\)
\(710\) 0 0
\(711\) 36.4924 1.36857
\(712\) 0 0
\(713\) 1.43845 0.0538703
\(714\) 0 0
\(715\) 2.24621 0.0840035
\(716\) 0 0
\(717\) 22.5616 0.842577
\(718\) 0 0
\(719\) −38.7386 −1.44471 −0.722354 0.691524i \(-0.756940\pi\)
−0.722354 + 0.691524i \(0.756940\pi\)
\(720\) 0 0
\(721\) −11.5076 −0.428565
\(722\) 0 0
\(723\) −47.3693 −1.76168
\(724\) 0 0
\(725\) 8.56155 0.317968
\(726\) 0 0
\(727\) −37.1231 −1.37682 −0.688410 0.725322i \(-0.741691\pi\)
−0.688410 + 0.725322i \(0.741691\pi\)
\(728\) 0 0
\(729\) −35.9848 −1.33277
\(730\) 0 0
\(731\) 28.4924 1.05383
\(732\) 0 0
\(733\) −11.1231 −0.410841 −0.205421 0.978674i \(-0.565856\pi\)
−0.205421 + 0.978674i \(0.565856\pi\)
\(734\) 0 0
\(735\) −49.3002 −1.81846
\(736\) 0 0
\(737\) −24.9848 −0.920329
\(738\) 0 0
\(739\) 27.5464 1.01331 0.506655 0.862149i \(-0.330882\pi\)
0.506655 + 0.862149i \(0.330882\pi\)
\(740\) 0 0
\(741\) 5.75379 0.211371
\(742\) 0 0
\(743\) 13.7538 0.504578 0.252289 0.967652i \(-0.418817\pi\)
0.252289 + 0.967652i \(0.418817\pi\)
\(744\) 0 0
\(745\) −4.24621 −0.155569
\(746\) 0 0
\(747\) 42.7386 1.56372
\(748\) 0 0
\(749\) 61.4773 2.24633
\(750\) 0 0
\(751\) −49.6155 −1.81050 −0.905248 0.424883i \(-0.860315\pi\)
−0.905248 + 0.424883i \(0.860315\pi\)
\(752\) 0 0
\(753\) 16.0000 0.583072
\(754\) 0 0
\(755\) −16.8078 −0.611697
\(756\) 0 0
\(757\) −24.8769 −0.904166 −0.452083 0.891976i \(-0.649319\pi\)
−0.452083 + 0.891976i \(0.649319\pi\)
\(758\) 0 0
\(759\) 10.2462 0.371914
\(760\) 0 0
\(761\) −11.3002 −0.409631 −0.204816 0.978801i \(-0.565660\pi\)
−0.204816 + 0.978801i \(0.565660\pi\)
\(762\) 0 0
\(763\) 42.2462 1.52942
\(764\) 0 0
\(765\) 11.1231 0.402157
\(766\) 0 0
\(767\) −3.50758 −0.126651
\(768\) 0 0
\(769\) 38.4924 1.38807 0.694036 0.719940i \(-0.255831\pi\)
0.694036 + 0.719940i \(0.255831\pi\)
\(770\) 0 0
\(771\) −23.1922 −0.835248
\(772\) 0 0
\(773\) 4.24621 0.152726 0.0763628 0.997080i \(-0.475669\pi\)
0.0763628 + 0.997080i \(0.475669\pi\)
\(774\) 0 0
\(775\) −1.43845 −0.0516705
\(776\) 0 0
\(777\) −93.4773 −3.35348
\(778\) 0 0
\(779\) 2.24621 0.0804789
\(780\) 0 0
\(781\) 14.7386 0.527390
\(782\) 0 0
\(783\) 12.3153 0.440114
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −46.2462 −1.64850 −0.824250 0.566226i \(-0.808403\pi\)
−0.824250 + 0.566226i \(0.808403\pi\)
\(788\) 0 0
\(789\) 20.4924 0.729550
\(790\) 0 0
\(791\) −103.723 −3.68798
\(792\) 0 0
\(793\) −6.24621 −0.221809
\(794\) 0 0
\(795\) −10.8769 −0.385764
\(796\) 0 0
\(797\) −27.1231 −0.960750 −0.480375 0.877063i \(-0.659499\pi\)
−0.480375 + 0.877063i \(0.659499\pi\)
\(798\) 0 0
\(799\) −11.5076 −0.407109
\(800\) 0 0
\(801\) 35.6155 1.25841
\(802\) 0 0
\(803\) −66.2462 −2.33778
\(804\) 0 0
\(805\) −5.12311 −0.180566
\(806\) 0 0
\(807\) 59.6847 2.10100
\(808\) 0 0
\(809\) −10.4924 −0.368894 −0.184447 0.982842i \(-0.559049\pi\)
−0.184447 + 0.982842i \(0.559049\pi\)
\(810\) 0 0
\(811\) −8.31534 −0.291991 −0.145996 0.989285i \(-0.546639\pi\)
−0.145996 + 0.989285i \(0.546639\pi\)
\(812\) 0 0
\(813\) 5.75379 0.201794
\(814\) 0 0
\(815\) 0.315342 0.0110459
\(816\) 0 0
\(817\) −36.4924 −1.27671
\(818\) 0 0
\(819\) −10.2462 −0.358032
\(820\) 0 0
\(821\) 31.7538 1.10821 0.554107 0.832445i \(-0.313060\pi\)
0.554107 + 0.832445i \(0.313060\pi\)
\(822\) 0 0
\(823\) 17.4384 0.607866 0.303933 0.952693i \(-0.401700\pi\)
0.303933 + 0.952693i \(0.401700\pi\)
\(824\) 0 0
\(825\) −10.2462 −0.356727
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −50.4924 −1.75367 −0.876837 0.480787i \(-0.840351\pi\)
−0.876837 + 0.480787i \(0.840351\pi\)
\(830\) 0 0
\(831\) 29.3002 1.01641
\(832\) 0 0
\(833\) −60.1080 −2.08262
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) −2.06913 −0.0715196
\(838\) 0 0
\(839\) −9.61553 −0.331965 −0.165982 0.986129i \(-0.553080\pi\)
−0.165982 + 0.986129i \(0.553080\pi\)
\(840\) 0 0
\(841\) 44.3002 1.52759
\(842\) 0 0
\(843\) 78.1080 2.69018
\(844\) 0 0
\(845\) 12.6847 0.436366
\(846\) 0 0
\(847\) −25.6155 −0.880160
\(848\) 0 0
\(849\) 58.6004 2.01116
\(850\) 0 0
\(851\) −7.12311 −0.244177
\(852\) 0 0
\(853\) −22.9848 −0.786986 −0.393493 0.919328i \(-0.628733\pi\)
−0.393493 + 0.919328i \(0.628733\pi\)
\(854\) 0 0
\(855\) −14.2462 −0.487210
\(856\) 0 0
\(857\) 34.1771 1.16747 0.583733 0.811945i \(-0.301591\pi\)
0.583733 + 0.811945i \(0.301591\pi\)
\(858\) 0 0
\(859\) 38.4233 1.31099 0.655493 0.755201i \(-0.272461\pi\)
0.655493 + 0.755201i \(0.272461\pi\)
\(860\) 0 0
\(861\) −7.36932 −0.251146
\(862\) 0 0
\(863\) −18.4233 −0.627136 −0.313568 0.949566i \(-0.601524\pi\)
−0.313568 + 0.949566i \(0.601524\pi\)
\(864\) 0 0
\(865\) 10.4924 0.356753
\(866\) 0 0
\(867\) −18.5616 −0.630383
\(868\) 0 0
\(869\) −40.9848 −1.39032
\(870\) 0 0
\(871\) 3.50758 0.118850
\(872\) 0 0
\(873\) −57.8617 −1.95832
\(874\) 0 0
\(875\) 5.12311 0.173193
\(876\) 0 0
\(877\) 40.7386 1.37565 0.687823 0.725878i \(-0.258567\pi\)
0.687823 + 0.725878i \(0.258567\pi\)
\(878\) 0 0
\(879\) 32.9848 1.11255
\(880\) 0 0
\(881\) 24.1080 0.812217 0.406109 0.913825i \(-0.366885\pi\)
0.406109 + 0.913825i \(0.366885\pi\)
\(882\) 0 0
\(883\) −40.4924 −1.36268 −0.681339 0.731968i \(-0.738602\pi\)
−0.681339 + 0.731968i \(0.738602\pi\)
\(884\) 0 0
\(885\) 16.0000 0.537834
\(886\) 0 0
\(887\) 33.4384 1.12275 0.561377 0.827560i \(-0.310272\pi\)
0.561377 + 0.827560i \(0.310272\pi\)
\(888\) 0 0
\(889\) −86.1080 −2.88797
\(890\) 0 0
\(891\) 28.0000 0.938035
\(892\) 0 0
\(893\) 14.7386 0.493210
\(894\) 0 0
\(895\) 7.68466 0.256870
\(896\) 0 0
\(897\) −1.43845 −0.0480284
\(898\) 0 0
\(899\) −12.3153 −0.410740
\(900\) 0 0
\(901\) −13.2614 −0.441800
\(902\) 0 0
\(903\) 119.723 3.98415
\(904\) 0 0
\(905\) 3.12311 0.103816
\(906\) 0 0
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 0 0
\(909\) −0.876894 −0.0290848
\(910\) 0 0
\(911\) 20.4924 0.678944 0.339472 0.940616i \(-0.389752\pi\)
0.339472 + 0.940616i \(0.389752\pi\)
\(912\) 0 0
\(913\) −48.0000 −1.58857
\(914\) 0 0
\(915\) 28.4924 0.941930
\(916\) 0 0
\(917\) −50.8769 −1.68010
\(918\) 0 0
\(919\) 35.8617 1.18297 0.591485 0.806316i \(-0.298542\pi\)
0.591485 + 0.806316i \(0.298542\pi\)
\(920\) 0 0
\(921\) 30.7386 1.01287
\(922\) 0 0
\(923\) −2.06913 −0.0681063
\(924\) 0 0
\(925\) 7.12311 0.234206
\(926\) 0 0
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 13.0540 0.428287 0.214144 0.976802i \(-0.431304\pi\)
0.214144 + 0.976802i \(0.431304\pi\)
\(930\) 0 0
\(931\) 76.9848 2.52308
\(932\) 0 0
\(933\) −35.6847 −1.16826
\(934\) 0 0
\(935\) −12.4924 −0.408546
\(936\) 0 0
\(937\) 41.3693 1.35148 0.675738 0.737142i \(-0.263825\pi\)
0.675738 + 0.737142i \(0.263825\pi\)
\(938\) 0 0
\(939\) 38.7386 1.26419
\(940\) 0 0
\(941\) 60.6004 1.97552 0.987758 0.155995i \(-0.0498584\pi\)
0.987758 + 0.155995i \(0.0498584\pi\)
\(942\) 0 0
\(943\) −0.561553 −0.0182867
\(944\) 0 0
\(945\) 7.36932 0.239724
\(946\) 0 0
\(947\) −35.1922 −1.14359 −0.571797 0.820395i \(-0.693754\pi\)
−0.571797 + 0.820395i \(0.693754\pi\)
\(948\) 0 0
\(949\) 9.30019 0.301897
\(950\) 0 0
\(951\) −53.1231 −1.72263
\(952\) 0 0
\(953\) 13.5076 0.437553 0.218777 0.975775i \(-0.429793\pi\)
0.218777 + 0.975775i \(0.429793\pi\)
\(954\) 0 0
\(955\) −2.87689 −0.0930941
\(956\) 0 0
\(957\) −87.7235 −2.83570
\(958\) 0 0
\(959\) −77.4773 −2.50187
\(960\) 0 0
\(961\) −28.9309 −0.933254
\(962\) 0 0
\(963\) −42.7386 −1.37723
\(964\) 0 0
\(965\) −24.5616 −0.790664
\(966\) 0 0
\(967\) −0.177081 −0.00569454 −0.00284727 0.999996i \(-0.500906\pi\)
−0.00284727 + 0.999996i \(0.500906\pi\)
\(968\) 0 0
\(969\) −32.0000 −1.02799
\(970\) 0 0
\(971\) 3.36932 0.108127 0.0540633 0.998538i \(-0.482783\pi\)
0.0540633 + 0.998538i \(0.482783\pi\)
\(972\) 0 0
\(973\) −1.61553 −0.0517915
\(974\) 0 0
\(975\) 1.43845 0.0460672
\(976\) 0 0
\(977\) 48.1080 1.53911 0.769555 0.638581i \(-0.220478\pi\)
0.769555 + 0.638581i \(0.220478\pi\)
\(978\) 0 0
\(979\) −40.0000 −1.27841
\(980\) 0 0
\(981\) −29.3693 −0.937690
\(982\) 0 0
\(983\) −37.1231 −1.18404 −0.592022 0.805922i \(-0.701670\pi\)
−0.592022 + 0.805922i \(0.701670\pi\)
\(984\) 0 0
\(985\) −11.4384 −0.364459
\(986\) 0 0
\(987\) −48.3542 −1.53913
\(988\) 0 0
\(989\) 9.12311 0.290098
\(990\) 0 0
\(991\) 12.4924 0.396835 0.198417 0.980118i \(-0.436420\pi\)
0.198417 + 0.980118i \(0.436420\pi\)
\(992\) 0 0
\(993\) 27.0540 0.858532
\(994\) 0 0
\(995\) 24.0000 0.760851
\(996\) 0 0
\(997\) 48.7386 1.54357 0.771784 0.635885i \(-0.219365\pi\)
0.771784 + 0.635885i \(0.219365\pi\)
\(998\) 0 0
\(999\) 10.2462 0.324176
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.bm.1.2 2
4.3 odd 2 7360.2.a.bj.1.1 2
8.3 odd 2 920.2.a.f.1.2 2
8.5 even 2 1840.2.a.k.1.1 2
24.11 even 2 8280.2.a.bb.1.2 2
40.3 even 4 4600.2.e.m.4049.4 4
40.19 odd 2 4600.2.a.r.1.1 2
40.27 even 4 4600.2.e.m.4049.1 4
40.29 even 2 9200.2.a.bx.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.f.1.2 2 8.3 odd 2
1840.2.a.k.1.1 2 8.5 even 2
4600.2.a.r.1.1 2 40.19 odd 2
4600.2.e.m.4049.1 4 40.27 even 4
4600.2.e.m.4049.4 4 40.3 even 4
7360.2.a.bj.1.1 2 4.3 odd 2
7360.2.a.bm.1.2 2 1.1 even 1 trivial
8280.2.a.bb.1.2 2 24.11 even 2
9200.2.a.bx.1.2 2 40.29 even 2