Properties

Label 8550.2.a.cw.1.6
Level $8550$
Weight $2$
Character 8550.1
Self dual yes
Analytic conductor $68.272$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8550.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(68.2720937282\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.3356224.1
Defining polynomial: \(x^{6} - 6 x^{4} + 8 x^{2} - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 1710)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.02852\) of defining polynomial
Character \(\chi\) \(=\) 8550.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +4.05705 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +4.05705 q^{7} -1.00000 q^{8} +0.466185 q^{11} +0.985939 q^{13} -4.05705 q^{14} +1.00000 q^{16} -4.94567 q^{17} +1.00000 q^{19} -0.466185 q^{22} +2.22982 q^{23} -0.985939 q^{26} +4.05705 q^{28} -2.43806 q^{29} +0.715853 q^{31} -1.00000 q^{32} +4.94567 q^{34} -10.0324 q^{37} -1.00000 q^{38} -10.1993 q^{41} +0.466185 q^{43} +0.466185 q^{44} -2.22982 q^{46} -8.79811 q^{47} +9.45963 q^{49} +0.985939 q^{52} +3.89134 q^{53} -4.05705 q^{56} +2.43806 q^{58} -7.42748 q^{59} -6.45963 q^{61} -0.715853 q^{62} +1.00000 q^{64} -13.9226 q^{67} -4.94567 q^{68} -6.14222 q^{71} +7.07459 q^{73} +10.0324 q^{74} +1.00000 q^{76} +1.89134 q^{77} +1.85244 q^{79} +10.1993 q^{82} -4.37737 q^{83} -0.466185 q^{86} -0.466185 q^{88} +6.02892 q^{89} +4.00000 q^{91} +2.22982 q^{92} +8.79811 q^{94} +6.60840 q^{97} -9.45963 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{2} + 6q^{4} - 6q^{8} + O(q^{10}) \) \( 6q - 6q^{2} + 6q^{4} - 6q^{8} + 6q^{16} - 8q^{17} + 6q^{19} - 12q^{23} + 8q^{31} - 6q^{32} + 8q^{34} - 6q^{38} + 12q^{46} - 20q^{47} + 6q^{49} - 20q^{53} + 12q^{61} - 8q^{62} + 6q^{64} - 8q^{68} + 6q^{76} - 32q^{77} - 12q^{83} + 24q^{91} - 12q^{92} + 20q^{94} - 6q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 4.05705 1.53342 0.766710 0.641994i \(-0.221893\pi\)
0.766710 + 0.641994i \(0.221893\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0.466185 0.140560 0.0702801 0.997527i \(-0.477611\pi\)
0.0702801 + 0.997527i \(0.477611\pi\)
\(12\) 0 0
\(13\) 0.985939 0.273450 0.136725 0.990609i \(-0.456342\pi\)
0.136725 + 0.990609i \(0.456342\pi\)
\(14\) −4.05705 −1.08429
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.94567 −1.19950 −0.599750 0.800187i \(-0.704733\pi\)
−0.599750 + 0.800187i \(0.704733\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) −0.466185 −0.0993910
\(23\) 2.22982 0.464949 0.232474 0.972603i \(-0.425318\pi\)
0.232474 + 0.972603i \(0.425318\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.985939 −0.193359
\(27\) 0 0
\(28\) 4.05705 0.766710
\(29\) −2.43806 −0.452737 −0.226368 0.974042i \(-0.572685\pi\)
−0.226368 + 0.974042i \(0.572685\pi\)
\(30\) 0 0
\(31\) 0.715853 0.128571 0.0642855 0.997932i \(-0.479523\pi\)
0.0642855 + 0.997932i \(0.479523\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.94567 0.848175
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0324 −1.64932 −0.824658 0.565631i \(-0.808633\pi\)
−0.824658 + 0.565631i \(0.808633\pi\)
\(38\) −1.00000 −0.162221
\(39\) 0 0
\(40\) 0 0
\(41\) −10.1993 −1.59286 −0.796429 0.604732i \(-0.793280\pi\)
−0.796429 + 0.604732i \(0.793280\pi\)
\(42\) 0 0
\(43\) 0.466185 0.0710926 0.0355463 0.999368i \(-0.488683\pi\)
0.0355463 + 0.999368i \(0.488683\pi\)
\(44\) 0.466185 0.0702801
\(45\) 0 0
\(46\) −2.22982 −0.328768
\(47\) −8.79811 −1.28334 −0.641668 0.766982i \(-0.721757\pi\)
−0.641668 + 0.766982i \(0.721757\pi\)
\(48\) 0 0
\(49\) 9.45963 1.35138
\(50\) 0 0
\(51\) 0 0
\(52\) 0.985939 0.136725
\(53\) 3.89134 0.534516 0.267258 0.963625i \(-0.413882\pi\)
0.267258 + 0.963625i \(0.413882\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.05705 −0.542146
\(57\) 0 0
\(58\) 2.43806 0.320133
\(59\) −7.42748 −0.966976 −0.483488 0.875351i \(-0.660630\pi\)
−0.483488 + 0.875351i \(0.660630\pi\)
\(60\) 0 0
\(61\) −6.45963 −0.827071 −0.413535 0.910488i \(-0.635706\pi\)
−0.413535 + 0.910488i \(0.635706\pi\)
\(62\) −0.715853 −0.0909134
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −13.9226 −1.70092 −0.850458 0.526044i \(-0.823675\pi\)
−0.850458 + 0.526044i \(0.823675\pi\)
\(68\) −4.94567 −0.599750
\(69\) 0 0
\(70\) 0 0
\(71\) −6.14222 −0.728947 −0.364473 0.931214i \(-0.618751\pi\)
−0.364473 + 0.931214i \(0.618751\pi\)
\(72\) 0 0
\(73\) 7.07459 0.828018 0.414009 0.910273i \(-0.364128\pi\)
0.414009 + 0.910273i \(0.364128\pi\)
\(74\) 10.0324 1.16624
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 1.89134 0.215538
\(78\) 0 0
\(79\) 1.85244 0.208416 0.104208 0.994556i \(-0.466769\pi\)
0.104208 + 0.994556i \(0.466769\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 10.1993 1.12632
\(83\) −4.37737 −0.480479 −0.240240 0.970714i \(-0.577226\pi\)
−0.240240 + 0.970714i \(0.577226\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.466185 −0.0502701
\(87\) 0 0
\(88\) −0.466185 −0.0496955
\(89\) 6.02892 0.639065 0.319532 0.947575i \(-0.396474\pi\)
0.319532 + 0.947575i \(0.396474\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 2.22982 0.232474
\(93\) 0 0
\(94\) 8.79811 0.907456
\(95\) 0 0
\(96\) 0 0
\(97\) 6.60840 0.670982 0.335491 0.942043i \(-0.391098\pi\)
0.335491 + 0.942043i \(0.391098\pi\)
\(98\) −9.45963 −0.955567
\(99\) 0 0
\(100\) 0 0
\(101\) 5.62246 0.559456 0.279728 0.960079i \(-0.409756\pi\)
0.279728 + 0.960079i \(0.409756\pi\)
\(102\) 0 0
\(103\) −18.9464 −1.86684 −0.933422 0.358780i \(-0.883193\pi\)
−0.933422 + 0.358780i \(0.883193\pi\)
\(104\) −0.985939 −0.0966793
\(105\) 0 0
\(106\) −3.89134 −0.377960
\(107\) −8.00000 −0.773389 −0.386695 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) 4.60719 0.441289 0.220644 0.975354i \(-0.429184\pi\)
0.220644 + 0.975354i \(0.429184\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.05705 0.383355
\(113\) −14.4596 −1.36025 −0.680124 0.733097i \(-0.738074\pi\)
−0.680124 + 0.733097i \(0.738074\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.43806 −0.226368
\(117\) 0 0
\(118\) 7.42748 0.683755
\(119\) −20.0648 −1.83934
\(120\) 0 0
\(121\) −10.7827 −0.980243
\(122\) 6.45963 0.584827
\(123\) 0 0
\(124\) 0.715853 0.0642855
\(125\) 0 0
\(126\) 0 0
\(127\) −4.69009 −0.416178 −0.208089 0.978110i \(-0.566724\pi\)
−0.208089 + 0.978110i \(0.566724\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 9.61979 0.840485 0.420242 0.907412i \(-0.361945\pi\)
0.420242 + 0.907412i \(0.361945\pi\)
\(132\) 0 0
\(133\) 4.05705 0.351791
\(134\) 13.9226 1.20273
\(135\) 0 0
\(136\) 4.94567 0.424088
\(137\) −18.8370 −1.60935 −0.804677 0.593713i \(-0.797661\pi\)
−0.804677 + 0.593713i \(0.797661\pi\)
\(138\) 0 0
\(139\) 14.3510 1.21723 0.608617 0.793465i \(-0.291725\pi\)
0.608617 + 0.793465i \(0.291725\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.14222 0.515443
\(143\) 0.459630 0.0384362
\(144\) 0 0
\(145\) 0 0
\(146\) −7.07459 −0.585497
\(147\) 0 0
\(148\) −10.0324 −0.824658
\(149\) 15.3747 1.25955 0.629773 0.776779i \(-0.283148\pi\)
0.629773 + 0.776779i \(0.283148\pi\)
\(150\) 0 0
\(151\) −5.17548 −0.421175 −0.210587 0.977575i \(-0.567538\pi\)
−0.210587 + 0.977575i \(0.567538\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 0 0
\(154\) −1.89134 −0.152408
\(155\) 0 0
\(156\) 0 0
\(157\) −11.7050 −0.934157 −0.467079 0.884216i \(-0.654693\pi\)
−0.467079 + 0.884216i \(0.654693\pi\)
\(158\) −1.85244 −0.147372
\(159\) 0 0
\(160\) 0 0
\(161\) 9.04646 0.712961
\(162\) 0 0
\(163\) −16.6944 −1.30760 −0.653802 0.756666i \(-0.726827\pi\)
−0.653802 + 0.756666i \(0.726827\pi\)
\(164\) −10.1993 −0.796429
\(165\) 0 0
\(166\) 4.37737 0.339750
\(167\) −19.7827 −1.53083 −0.765415 0.643538i \(-0.777466\pi\)
−0.765415 + 0.643538i \(0.777466\pi\)
\(168\) 0 0
\(169\) −12.0279 −0.925225
\(170\) 0 0
\(171\) 0 0
\(172\) 0.466185 0.0355463
\(173\) 12.3510 0.939027 0.469513 0.882925i \(-0.344429\pi\)
0.469513 + 0.882925i \(0.344429\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.466185 0.0351400
\(177\) 0 0
\(178\) −6.02892 −0.451887
\(179\) −4.52323 −0.338082 −0.169041 0.985609i \(-0.554067\pi\)
−0.169041 + 0.985609i \(0.554067\pi\)
\(180\) 0 0
\(181\) 0.147558 0.0109679 0.00548396 0.999985i \(-0.498254\pi\)
0.00548396 + 0.999985i \(0.498254\pi\)
\(182\) −4.00000 −0.296500
\(183\) 0 0
\(184\) −2.22982 −0.164384
\(185\) 0 0
\(186\) 0 0
\(187\) −2.30560 −0.168602
\(188\) −8.79811 −0.641668
\(189\) 0 0
\(190\) 0 0
\(191\) 1.91831 0.138804 0.0694020 0.997589i \(-0.477891\pi\)
0.0694020 + 0.997589i \(0.477891\pi\)
\(192\) 0 0
\(193\) 26.6732 1.91998 0.959990 0.280035i \(-0.0903461\pi\)
0.959990 + 0.280035i \(0.0903461\pi\)
\(194\) −6.60840 −0.474456
\(195\) 0 0
\(196\) 9.45963 0.675688
\(197\) 6.58078 0.468861 0.234431 0.972133i \(-0.424677\pi\)
0.234431 + 0.972133i \(0.424677\pi\)
\(198\) 0 0
\(199\) −12.4596 −0.883240 −0.441620 0.897202i \(-0.645596\pi\)
−0.441620 + 0.897202i \(0.645596\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −5.62246 −0.395595
\(203\) −9.89134 −0.694236
\(204\) 0 0
\(205\) 0 0
\(206\) 18.9464 1.32006
\(207\) 0 0
\(208\) 0.985939 0.0683626
\(209\) 0.466185 0.0322467
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 3.89134 0.267258
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) 0 0
\(216\) 0 0
\(217\) 2.90425 0.197153
\(218\) −4.60719 −0.312038
\(219\) 0 0
\(220\) 0 0
\(221\) −4.87613 −0.328004
\(222\) 0 0
\(223\) 3.75772 0.251636 0.125818 0.992053i \(-0.459845\pi\)
0.125818 + 0.992053i \(0.459845\pi\)
\(224\) −4.05705 −0.271073
\(225\) 0 0
\(226\) 14.4596 0.961840
\(227\) −17.8913 −1.18749 −0.593745 0.804653i \(-0.702351\pi\)
−0.593745 + 0.804653i \(0.702351\pi\)
\(228\) 0 0
\(229\) −5.32304 −0.351756 −0.175878 0.984412i \(-0.556276\pi\)
−0.175878 + 0.984412i \(0.556276\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.43806 0.160067
\(233\) 3.51396 0.230207 0.115104 0.993353i \(-0.463280\pi\)
0.115104 + 0.993353i \(0.463280\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −7.42748 −0.483488
\(237\) 0 0
\(238\) 20.0648 1.30061
\(239\) 29.4986 1.90810 0.954052 0.299642i \(-0.0968674\pi\)
0.954052 + 0.299642i \(0.0968674\pi\)
\(240\) 0 0
\(241\) 29.2702 1.88546 0.942731 0.333555i \(-0.108248\pi\)
0.942731 + 0.333555i \(0.108248\pi\)
\(242\) 10.7827 0.693136
\(243\) 0 0
\(244\) −6.45963 −0.413535
\(245\) 0 0
\(246\) 0 0
\(247\) 0.985939 0.0627338
\(248\) −0.715853 −0.0454567
\(249\) 0 0
\(250\) 0 0
\(251\) 13.7901 0.870425 0.435212 0.900328i \(-0.356673\pi\)
0.435212 + 0.900328i \(0.356673\pi\)
\(252\) 0 0
\(253\) 1.03951 0.0653532
\(254\) 4.69009 0.294283
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −4.10866 −0.256291 −0.128146 0.991755i \(-0.540903\pi\)
−0.128146 + 0.991755i \(0.540903\pi\)
\(258\) 0 0
\(259\) −40.7019 −2.52909
\(260\) 0 0
\(261\) 0 0
\(262\) −9.61979 −0.594312
\(263\) −2.90677 −0.179239 −0.0896197 0.995976i \(-0.528565\pi\)
−0.0896197 + 0.995976i \(0.528565\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.05705 −0.248754
\(267\) 0 0
\(268\) −13.9226 −0.850458
\(269\) 6.60840 0.402921 0.201461 0.979497i \(-0.435431\pi\)
0.201461 + 0.979497i \(0.435431\pi\)
\(270\) 0 0
\(271\) 29.3789 1.78464 0.892320 0.451403i \(-0.149076\pi\)
0.892320 + 0.451403i \(0.149076\pi\)
\(272\) −4.94567 −0.299875
\(273\) 0 0
\(274\) 18.8370 1.13798
\(275\) 0 0
\(276\) 0 0
\(277\) 17.8472 1.07233 0.536166 0.844112i \(-0.319872\pi\)
0.536166 + 0.844112i \(0.319872\pi\)
\(278\) −14.3510 −0.860714
\(279\) 0 0
\(280\) 0 0
\(281\) 10.9051 0.650541 0.325270 0.945621i \(-0.394545\pi\)
0.325270 + 0.945621i \(0.394545\pi\)
\(282\) 0 0
\(283\) −6.27468 −0.372991 −0.186496 0.982456i \(-0.559713\pi\)
−0.186496 + 0.982456i \(0.559713\pi\)
\(284\) −6.14222 −0.364473
\(285\) 0 0
\(286\) −0.459630 −0.0271785
\(287\) −41.3789 −2.44252
\(288\) 0 0
\(289\) 7.45963 0.438802
\(290\) 0 0
\(291\) 0 0
\(292\) 7.07459 0.414009
\(293\) −22.9193 −1.33896 −0.669479 0.742831i \(-0.733482\pi\)
−0.669479 + 0.742831i \(0.733482\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.0324 0.583122
\(297\) 0 0
\(298\) −15.3747 −0.890633
\(299\) 2.19846 0.127140
\(300\) 0 0
\(301\) 1.89134 0.109015
\(302\) 5.17548 0.297816
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 0 0
\(307\) 4.17034 0.238014 0.119007 0.992893i \(-0.462029\pi\)
0.119007 + 0.992893i \(0.462029\pi\)
\(308\) 1.89134 0.107769
\(309\) 0 0
\(310\) 0 0
\(311\) −12.2309 −0.693549 −0.346774 0.937949i \(-0.612723\pi\)
−0.346774 + 0.937949i \(0.612723\pi\)
\(312\) 0 0
\(313\) −8.71274 −0.492473 −0.246237 0.969210i \(-0.579194\pi\)
−0.246237 + 0.969210i \(0.579194\pi\)
\(314\) 11.7050 0.660549
\(315\) 0 0
\(316\) 1.85244 0.104208
\(317\) 9.78267 0.549450 0.274725 0.961523i \(-0.411413\pi\)
0.274725 + 0.961523i \(0.411413\pi\)
\(318\) 0 0
\(319\) −1.13659 −0.0636368
\(320\) 0 0
\(321\) 0 0
\(322\) −9.04646 −0.504140
\(323\) −4.94567 −0.275184
\(324\) 0 0
\(325\) 0 0
\(326\) 16.6944 0.924616
\(327\) 0 0
\(328\) 10.1993 0.563160
\(329\) −35.6943 −1.96789
\(330\) 0 0
\(331\) 12.4596 0.684843 0.342422 0.939546i \(-0.388753\pi\)
0.342422 + 0.939546i \(0.388753\pi\)
\(332\) −4.37737 −0.240240
\(333\) 0 0
\(334\) 19.7827 1.08246
\(335\) 0 0
\(336\) 0 0
\(337\) 10.5522 0.574813 0.287406 0.957809i \(-0.407207\pi\)
0.287406 + 0.957809i \(0.407207\pi\)
\(338\) 12.0279 0.654233
\(339\) 0 0
\(340\) 0 0
\(341\) 0.333720 0.0180720
\(342\) 0 0
\(343\) 9.97884 0.538806
\(344\) −0.466185 −0.0251350
\(345\) 0 0
\(346\) −12.3510 −0.663992
\(347\) −19.8649 −1.06641 −0.533203 0.845988i \(-0.679012\pi\)
−0.533203 + 0.845988i \(0.679012\pi\)
\(348\) 0 0
\(349\) −32.3510 −1.73171 −0.865854 0.500297i \(-0.833224\pi\)
−0.865854 + 0.500297i \(0.833224\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.466185 −0.0248478
\(353\) 17.4053 0.926391 0.463195 0.886256i \(-0.346703\pi\)
0.463195 + 0.886256i \(0.346703\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.02892 0.319532
\(357\) 0 0
\(358\) 4.52323 0.239060
\(359\) 32.5099 1.71581 0.857905 0.513809i \(-0.171766\pi\)
0.857905 + 0.513809i \(0.171766\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −0.147558 −0.00775549
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 0 0
\(366\) 0 0
\(367\) 35.2473 1.83990 0.919948 0.392041i \(-0.128231\pi\)
0.919948 + 0.392041i \(0.128231\pi\)
\(368\) 2.22982 0.116237
\(369\) 0 0
\(370\) 0 0
\(371\) 15.7873 0.819637
\(372\) 0 0
\(373\) −16.0675 −0.831943 −0.415971 0.909378i \(-0.636558\pi\)
−0.415971 + 0.909378i \(0.636558\pi\)
\(374\) 2.30560 0.119220
\(375\) 0 0
\(376\) 8.79811 0.453728
\(377\) −2.40378 −0.123801
\(378\) 0 0
\(379\) 8.24230 0.423379 0.211689 0.977337i \(-0.432104\pi\)
0.211689 + 0.977337i \(0.432104\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.91831 −0.0981492
\(383\) 12.9193 0.660143 0.330072 0.943956i \(-0.392927\pi\)
0.330072 + 0.943956i \(0.392927\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −26.6732 −1.35763
\(387\) 0 0
\(388\) 6.60840 0.335491
\(389\) 22.7830 1.15515 0.577573 0.816339i \(-0.304000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(390\) 0 0
\(391\) −11.0279 −0.557706
\(392\) −9.45963 −0.477783
\(393\) 0 0
\(394\) −6.58078 −0.331535
\(395\) 0 0
\(396\) 0 0
\(397\) 20.4177 1.02473 0.512367 0.858766i \(-0.328769\pi\)
0.512367 + 0.858766i \(0.328769\pi\)
\(398\) 12.4596 0.624545
\(399\) 0 0
\(400\) 0 0
\(401\) 21.8163 1.08945 0.544726 0.838614i \(-0.316634\pi\)
0.544726 + 0.838614i \(0.316634\pi\)
\(402\) 0 0
\(403\) 0.705787 0.0351578
\(404\) 5.62246 0.279728
\(405\) 0 0
\(406\) 9.89134 0.490899
\(407\) −4.67696 −0.231828
\(408\) 0 0
\(409\) 19.3789 0.958224 0.479112 0.877754i \(-0.340959\pi\)
0.479112 + 0.877754i \(0.340959\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −18.9464 −0.933422
\(413\) −30.1336 −1.48278
\(414\) 0 0
\(415\) 0 0
\(416\) −0.985939 −0.0483396
\(417\) 0 0
\(418\) −0.466185 −0.0228019
\(419\) −28.7522 −1.40464 −0.702319 0.711862i \(-0.747852\pi\)
−0.702319 + 0.711862i \(0.747852\pi\)
\(420\) 0 0
\(421\) −14.7159 −0.717207 −0.358603 0.933490i \(-0.616747\pi\)
−0.358603 + 0.933490i \(0.616747\pi\)
\(422\) −12.0000 −0.584151
\(423\) 0 0
\(424\) −3.89134 −0.188980
\(425\) 0 0
\(426\) 0 0
\(427\) −26.2070 −1.26825
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 0 0
\(431\) 18.2001 0.876666 0.438333 0.898813i \(-0.355569\pi\)
0.438333 + 0.898813i \(0.355569\pi\)
\(432\) 0 0
\(433\) 2.77178 0.133203 0.0666017 0.997780i \(-0.478784\pi\)
0.0666017 + 0.997780i \(0.478784\pi\)
\(434\) −2.90425 −0.139408
\(435\) 0 0
\(436\) 4.60719 0.220644
\(437\) 2.22982 0.106667
\(438\) 0 0
\(439\) −12.2034 −0.582437 −0.291218 0.956657i \(-0.594061\pi\)
−0.291218 + 0.956657i \(0.594061\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.87613 0.231934
\(443\) 21.9736 1.04400 0.521998 0.852946i \(-0.325187\pi\)
0.521998 + 0.852946i \(0.325187\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.75772 −0.177933
\(447\) 0 0
\(448\) 4.05705 0.191677
\(449\) −23.1895 −1.09438 −0.547190 0.837009i \(-0.684302\pi\)
−0.547190 + 0.837009i \(0.684302\pi\)
\(450\) 0 0
\(451\) −4.75475 −0.223892
\(452\) −14.4596 −0.680124
\(453\) 0 0
\(454\) 17.8913 0.839682
\(455\) 0 0
\(456\) 0 0
\(457\) −34.3211 −1.60547 −0.802737 0.596333i \(-0.796624\pi\)
−0.802737 + 0.596333i \(0.796624\pi\)
\(458\) 5.32304 0.248729
\(459\) 0 0
\(460\) 0 0
\(461\) −23.5959 −1.09897 −0.549486 0.835503i \(-0.685177\pi\)
−0.549486 + 0.835503i \(0.685177\pi\)
\(462\) 0 0
\(463\) 3.94991 0.183568 0.0917840 0.995779i \(-0.470743\pi\)
0.0917840 + 0.995779i \(0.470743\pi\)
\(464\) −2.43806 −0.113184
\(465\) 0 0
\(466\) −3.51396 −0.162781
\(467\) −9.51396 −0.440254 −0.220127 0.975471i \(-0.570647\pi\)
−0.220127 + 0.975471i \(0.570647\pi\)
\(468\) 0 0
\(469\) −56.4846 −2.60822
\(470\) 0 0
\(471\) 0 0
\(472\) 7.42748 0.341877
\(473\) 0.217329 0.00999279
\(474\) 0 0
\(475\) 0 0
\(476\) −20.0648 −0.919669
\(477\) 0 0
\(478\) −29.4986 −1.34923
\(479\) −28.4591 −1.30033 −0.650164 0.759794i \(-0.725300\pi\)
−0.650164 + 0.759794i \(0.725300\pi\)
\(480\) 0 0
\(481\) −9.89134 −0.451006
\(482\) −29.2702 −1.33322
\(483\) 0 0
\(484\) −10.7827 −0.490121
\(485\) 0 0
\(486\) 0 0
\(487\) 21.5169 0.975025 0.487513 0.873116i \(-0.337904\pi\)
0.487513 + 0.873116i \(0.337904\pi\)
\(488\) 6.45963 0.292414
\(489\) 0 0
\(490\) 0 0
\(491\) −20.3044 −0.916325 −0.458163 0.888868i \(-0.651492\pi\)
−0.458163 + 0.888868i \(0.651492\pi\)
\(492\) 0 0
\(493\) 12.0578 0.543058
\(494\) −0.985939 −0.0443595
\(495\) 0 0
\(496\) 0.715853 0.0321427
\(497\) −24.9193 −1.11778
\(498\) 0 0
\(499\) −12.9193 −0.578346 −0.289173 0.957277i \(-0.593380\pi\)
−0.289173 + 0.957277i \(0.593380\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −13.7901 −0.615483
\(503\) 18.4721 0.823631 0.411815 0.911267i \(-0.364895\pi\)
0.411815 + 0.911267i \(0.364895\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.03951 −0.0462117
\(507\) 0 0
\(508\) −4.69009 −0.208089
\(509\) −41.2632 −1.82896 −0.914480 0.404630i \(-0.867400\pi\)
−0.914480 + 0.404630i \(0.867400\pi\)
\(510\) 0 0
\(511\) 28.7019 1.26970
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 4.10866 0.181225
\(515\) 0 0
\(516\) 0 0
\(517\) −4.10155 −0.180386
\(518\) 40.7019 1.78834
\(519\) 0 0
\(520\) 0 0
\(521\) −27.3598 −1.19866 −0.599328 0.800504i \(-0.704565\pi\)
−0.599328 + 0.800504i \(0.704565\pi\)
\(522\) 0 0
\(523\) −5.31698 −0.232495 −0.116248 0.993220i \(-0.537087\pi\)
−0.116248 + 0.993220i \(0.537087\pi\)
\(524\) 9.61979 0.420242
\(525\) 0 0
\(526\) 2.90677 0.126741
\(527\) −3.54037 −0.154221
\(528\) 0 0
\(529\) −18.0279 −0.783823
\(530\) 0 0
\(531\) 0 0
\(532\) 4.05705 0.175895
\(533\) −10.0558 −0.435567
\(534\) 0 0
\(535\) 0 0
\(536\) 13.9226 0.601364
\(537\) 0 0
\(538\) −6.60840 −0.284908
\(539\) 4.40994 0.189950
\(540\) 0 0
\(541\) −10.2951 −0.442622 −0.221311 0.975203i \(-0.571034\pi\)
−0.221311 + 0.975203i \(0.571034\pi\)
\(542\) −29.3789 −1.26193
\(543\) 0 0
\(544\) 4.94567 0.212044
\(545\) 0 0
\(546\) 0 0
\(547\) 3.50290 0.149773 0.0748866 0.997192i \(-0.476141\pi\)
0.0748866 + 0.997192i \(0.476141\pi\)
\(548\) −18.8370 −0.804677
\(549\) 0 0
\(550\) 0 0
\(551\) −2.43806 −0.103865
\(552\) 0 0
\(553\) 7.51544 0.319589
\(554\) −17.8472 −0.758254
\(555\) 0 0
\(556\) 14.3510 0.608617
\(557\) 15.2577 0.646491 0.323246 0.946315i \(-0.395226\pi\)
0.323246 + 0.946315i \(0.395226\pi\)
\(558\) 0 0
\(559\) 0.459630 0.0194403
\(560\) 0 0
\(561\) 0 0
\(562\) −10.9051 −0.460002
\(563\) 27.5653 1.16174 0.580870 0.813996i \(-0.302712\pi\)
0.580870 + 0.813996i \(0.302712\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.27468 0.263745
\(567\) 0 0
\(568\) 6.14222 0.257722
\(569\) 27.3598 1.14698 0.573492 0.819211i \(-0.305588\pi\)
0.573492 + 0.819211i \(0.305588\pi\)
\(570\) 0 0
\(571\) −40.1895 −1.68188 −0.840939 0.541130i \(-0.817997\pi\)
−0.840939 + 0.541130i \(0.817997\pi\)
\(572\) 0.459630 0.0192181
\(573\) 0 0
\(574\) 41.3789 1.72712
\(575\) 0 0
\(576\) 0 0
\(577\) 18.7987 0.782601 0.391300 0.920263i \(-0.372025\pi\)
0.391300 + 0.920263i \(0.372025\pi\)
\(578\) −7.45963 −0.310280
\(579\) 0 0
\(580\) 0 0
\(581\) −17.7592 −0.736776
\(582\) 0 0
\(583\) 1.81408 0.0751317
\(584\) −7.07459 −0.292748
\(585\) 0 0
\(586\) 22.9193 0.946786
\(587\) 25.7563 1.06307 0.531537 0.847035i \(-0.321615\pi\)
0.531537 + 0.847035i \(0.321615\pi\)
\(588\) 0 0
\(589\) 0.715853 0.0294962
\(590\) 0 0
\(591\) 0 0
\(592\) −10.0324 −0.412329
\(593\) −36.4332 −1.49613 −0.748067 0.663624i \(-0.769018\pi\)
−0.748067 + 0.663624i \(0.769018\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.3747 0.629773
\(597\) 0 0
\(598\) −2.19846 −0.0899018
\(599\) 11.3521 0.463833 0.231916 0.972736i \(-0.425500\pi\)
0.231916 + 0.972736i \(0.425500\pi\)
\(600\) 0 0
\(601\) −14.9721 −0.610724 −0.305362 0.952236i \(-0.598777\pi\)
−0.305362 + 0.952236i \(0.598777\pi\)
\(602\) −1.89134 −0.0770851
\(603\) 0 0
\(604\) −5.17548 −0.210587
\(605\) 0 0
\(606\) 0 0
\(607\) −28.3649 −1.15130 −0.575649 0.817697i \(-0.695250\pi\)
−0.575649 + 0.817697i \(0.695250\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) 0 0
\(611\) −8.67440 −0.350929
\(612\) 0 0
\(613\) −22.8304 −0.922113 −0.461056 0.887371i \(-0.652529\pi\)
−0.461056 + 0.887371i \(0.652529\pi\)
\(614\) −4.17034 −0.168301
\(615\) 0 0
\(616\) −1.89134 −0.0762041
\(617\) 9.62263 0.387392 0.193696 0.981062i \(-0.437952\pi\)
0.193696 + 0.981062i \(0.437952\pi\)
\(618\) 0 0
\(619\) 2.56829 0.103228 0.0516142 0.998667i \(-0.483563\pi\)
0.0516142 + 0.998667i \(0.483563\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.2309 0.490413
\(623\) 24.4596 0.979954
\(624\) 0 0
\(625\) 0 0
\(626\) 8.71274 0.348231
\(627\) 0 0
\(628\) −11.7050 −0.467079
\(629\) 49.6169 1.97836
\(630\) 0 0
\(631\) −20.6241 −0.821034 −0.410517 0.911853i \(-0.634652\pi\)
−0.410517 + 0.911853i \(0.634652\pi\)
\(632\) −1.85244 −0.0736862
\(633\) 0 0
\(634\) −9.78267 −0.388520
\(635\) 0 0
\(636\) 0 0
\(637\) 9.32662 0.369534
\(638\) 1.13659 0.0449980
\(639\) 0 0
\(640\) 0 0
\(641\) −27.1332 −1.07170 −0.535849 0.844314i \(-0.680008\pi\)
−0.535849 + 0.844314i \(0.680008\pi\)
\(642\) 0 0
\(643\) −35.0016 −1.38033 −0.690164 0.723653i \(-0.742461\pi\)
−0.690164 + 0.723653i \(0.742461\pi\)
\(644\) 9.04646 0.356481
\(645\) 0 0
\(646\) 4.94567 0.194585
\(647\) −5.77018 −0.226849 −0.113425 0.993547i \(-0.536182\pi\)
−0.113425 + 0.993547i \(0.536182\pi\)
\(648\) 0 0
\(649\) −3.46258 −0.135918
\(650\) 0 0
\(651\) 0 0
\(652\) −16.6944 −0.653802
\(653\) −41.6087 −1.62827 −0.814137 0.580673i \(-0.802790\pi\)
−0.814137 + 0.580673i \(0.802790\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −10.1993 −0.398214
\(657\) 0 0
\(658\) 35.6943 1.39151
\(659\) 6.16139 0.240014 0.120007 0.992773i \(-0.461708\pi\)
0.120007 + 0.992773i \(0.461708\pi\)
\(660\) 0 0
\(661\) 33.3091 1.29557 0.647787 0.761821i \(-0.275695\pi\)
0.647787 + 0.761821i \(0.275695\pi\)
\(662\) −12.4596 −0.484257
\(663\) 0 0
\(664\) 4.37737 0.169875
\(665\) 0 0
\(666\) 0 0
\(667\) −5.43643 −0.210499
\(668\) −19.7827 −0.765415
\(669\) 0 0
\(670\) 0 0
\(671\) −3.01138 −0.116253
\(672\) 0 0
\(673\) 20.7576 0.800146 0.400073 0.916483i \(-0.368985\pi\)
0.400073 + 0.916483i \(0.368985\pi\)
\(674\) −10.5522 −0.406454
\(675\) 0 0
\(676\) −12.0279 −0.462612
\(677\) −0.403781 −0.0155186 −0.00775928 0.999970i \(-0.502470\pi\)
−0.00775928 + 0.999970i \(0.502470\pi\)
\(678\) 0 0
\(679\) 26.8106 1.02890
\(680\) 0 0
\(681\) 0 0
\(682\) −0.333720 −0.0127788
\(683\) −29.8913 −1.14376 −0.571880 0.820337i \(-0.693786\pi\)
−0.571880 + 0.820337i \(0.693786\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −9.97884 −0.380994
\(687\) 0 0
\(688\) 0.466185 0.0177731
\(689\) 3.83662 0.146164
\(690\) 0 0
\(691\) 18.1336 0.689836 0.344918 0.938633i \(-0.387907\pi\)
0.344918 + 0.938633i \(0.387907\pi\)
\(692\) 12.3510 0.469513
\(693\) 0 0
\(694\) 19.8649 0.754062
\(695\) 0 0
\(696\) 0 0
\(697\) 50.4422 1.91063
\(698\) 32.3510 1.22450
\(699\) 0 0
\(700\) 0 0
\(701\) 27.1676 1.02611 0.513054 0.858357i \(-0.328514\pi\)
0.513054 + 0.858357i \(0.328514\pi\)
\(702\) 0 0
\(703\) −10.0324 −0.378379
\(704\) 0.466185 0.0175700
\(705\) 0 0
\(706\) −17.4053 −0.655057
\(707\) 22.8106 0.857881
\(708\) 0 0
\(709\) −16.1087 −0.604974 −0.302487 0.953154i \(-0.597817\pi\)
−0.302487 + 0.953154i \(0.597817\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.02892 −0.225944
\(713\) 1.59622 0.0597789
\(714\) 0 0
\(715\) 0 0
\(716\) −4.52323 −0.169041
\(717\) 0 0
\(718\) −32.5099 −1.21326
\(719\) 38.2113 1.42504 0.712521 0.701651i \(-0.247554\pi\)
0.712521 + 0.701651i \(0.247554\pi\)
\(720\) 0 0
\(721\) −76.8664 −2.86266
\(722\) −1.00000 −0.0372161
\(723\) 0 0
\(724\) 0.147558 0.00548396
\(725\) 0 0
\(726\) 0 0
\(727\) 26.3203 0.976166 0.488083 0.872797i \(-0.337696\pi\)
0.488083 + 0.872797i \(0.337696\pi\)
\(728\) −4.00000 −0.148250
\(729\) 0 0
\(730\) 0 0
\(731\) −2.30560 −0.0852756
\(732\) 0 0
\(733\) 31.1023 1.14879 0.574395 0.818578i \(-0.305237\pi\)
0.574395 + 0.818578i \(0.305237\pi\)
\(734\) −35.2473 −1.30100
\(735\) 0 0
\(736\) −2.22982 −0.0821921
\(737\) −6.49051 −0.239081
\(738\) 0 0
\(739\) −6.86341 −0.252475 −0.126237 0.992000i \(-0.540290\pi\)
−0.126237 + 0.992000i \(0.540290\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −15.7873 −0.579571
\(743\) −14.1865 −0.520450 −0.260225 0.965548i \(-0.583797\pi\)
−0.260225 + 0.965548i \(0.583797\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 16.0675 0.588272
\(747\) 0 0
\(748\) −2.30560 −0.0843010
\(749\) −32.4564 −1.18593
\(750\) 0 0
\(751\) −27.3091 −0.996524 −0.498262 0.867027i \(-0.666028\pi\)
−0.498262 + 0.867027i \(0.666028\pi\)
\(752\) −8.79811 −0.320834
\(753\) 0 0
\(754\) 2.40378 0.0875405
\(755\) 0 0
\(756\) 0 0
\(757\) −1.72612 −0.0627369 −0.0313685 0.999508i \(-0.509987\pi\)
−0.0313685 + 0.999508i \(0.509987\pi\)
\(758\) −8.24230 −0.299374
\(759\) 0 0
\(760\) 0 0
\(761\) 2.63932 0.0956752 0.0478376 0.998855i \(-0.484767\pi\)
0.0478376 + 0.998855i \(0.484767\pi\)
\(762\) 0 0
\(763\) 18.6916 0.676681
\(764\) 1.91831 0.0694020
\(765\) 0 0
\(766\) −12.9193 −0.466792
\(767\) −7.32304 −0.264420
\(768\) 0 0
\(769\) 26.6241 0.960091 0.480046 0.877244i \(-0.340620\pi\)
0.480046 + 0.877244i \(0.340620\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 26.6732 0.959990
\(773\) −10.1645 −0.365592 −0.182796 0.983151i \(-0.558515\pi\)
−0.182796 + 0.983151i \(0.558515\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −6.60840 −0.237228
\(777\) 0 0
\(778\) −22.7830 −0.816811
\(779\) −10.1993 −0.365427
\(780\) 0 0
\(781\) −2.86341 −0.102461
\(782\) 11.0279 0.394358
\(783\) 0 0
\(784\) 9.45963 0.337844
\(785\) 0 0
\(786\) 0 0
\(787\) −20.1719 −0.719052 −0.359526 0.933135i \(-0.617062\pi\)
−0.359526 + 0.933135i \(0.617062\pi\)
\(788\) 6.58078 0.234431
\(789\) 0 0
\(790\) 0 0
\(791\) −58.6634 −2.08583
\(792\) 0 0
\(793\) −6.36880 −0.226163
\(794\) −20.4177 −0.724597
\(795\) 0 0
\(796\) −12.4596 −0.441620
\(797\) 52.0808 1.84480 0.922399 0.386239i \(-0.126226\pi\)
0.922399 + 0.386239i \(0.126226\pi\)
\(798\) 0 0
\(799\) 43.5125 1.53936
\(800\) 0 0
\(801\) 0 0
\(802\) −21.8163 −0.770359
\(803\) 3.29807 0.116386
\(804\) 0 0
\(805\) 0 0
\(806\) −0.705787 −0.0248603
\(807\) 0 0
\(808\) −5.62246 −0.197798
\(809\) 11.4592 0.402884 0.201442 0.979500i \(-0.435437\pi\)
0.201442 + 0.979500i \(0.435437\pi\)
\(810\) 0 0
\(811\) 13.5962 0.477428 0.238714 0.971090i \(-0.423274\pi\)
0.238714 + 0.971090i \(0.423274\pi\)
\(812\) −9.89134 −0.347118
\(813\) 0 0
\(814\) 4.67696 0.163927
\(815\) 0 0
\(816\) 0 0
\(817\) 0.466185 0.0163098
\(818\) −19.3789 −0.677567
\(819\) 0 0
\(820\) 0 0
\(821\) −43.6731 −1.52420 −0.762100 0.647459i \(-0.775832\pi\)
−0.762100 + 0.647459i \(0.775832\pi\)
\(822\) 0 0
\(823\) 42.2148 1.47151 0.735757 0.677245i \(-0.236826\pi\)
0.735757 + 0.677245i \(0.236826\pi\)
\(824\) 18.9464 0.660029
\(825\) 0 0
\(826\) 30.1336 1.04848
\(827\) −53.8385 −1.87215 −0.936074 0.351802i \(-0.885569\pi\)
−0.936074 + 0.351802i \(0.885569\pi\)
\(828\) 0 0
\(829\) −55.1755 −1.91632 −0.958162 0.286227i \(-0.907599\pi\)
−0.958162 + 0.286227i \(0.907599\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.985939 0.0341813
\(833\) −46.7842 −1.62098
\(834\) 0 0
\(835\) 0 0
\(836\) 0.466185 0.0161234
\(837\) 0 0
\(838\) 28.7522 0.993229
\(839\) −17.0534 −0.588750 −0.294375 0.955690i \(-0.595111\pi\)
−0.294375 + 0.955690i \(0.595111\pi\)
\(840\) 0 0
\(841\) −23.0558 −0.795029
\(842\) 14.7159 0.507142
\(843\) 0 0
\(844\) 12.0000 0.413057
\(845\) 0 0
\(846\) 0 0
\(847\) −43.7458 −1.50312
\(848\) 3.89134 0.133629
\(849\) 0 0
\(850\) 0 0
\(851\) −22.3704 −0.766848
\(852\) 0 0
\(853\) 14.0106 0.479712 0.239856 0.970808i \(-0.422900\pi\)
0.239856 + 0.970808i \(0.422900\pi\)
\(854\) 26.2070 0.896786
\(855\) 0 0
\(856\) 8.00000 0.273434
\(857\) −48.5933 −1.65991 −0.829957 0.557827i \(-0.811635\pi\)
−0.829957 + 0.557827i \(0.811635\pi\)
\(858\) 0 0
\(859\) 57.5434 1.96336 0.981678 0.190548i \(-0.0610266\pi\)
0.981678 + 0.190548i \(0.0610266\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −18.2001 −0.619897
\(863\) −30.8634 −1.05060 −0.525301 0.850916i \(-0.676047\pi\)
−0.525301 + 0.850916i \(0.676047\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −2.77178 −0.0941890
\(867\) 0 0
\(868\) 2.90425 0.0985766
\(869\) 0.863581 0.0292950
\(870\) 0 0
\(871\) −13.7268 −0.465116
\(872\) −4.60719 −0.156019
\(873\) 0 0
\(874\) −2.22982 −0.0754246
\(875\) 0 0
\(876\) 0 0
\(877\) 42.4888 1.43474 0.717372 0.696690i \(-0.245345\pi\)
0.717372 + 0.696690i \(0.245345\pi\)
\(878\) 12.2034 0.411845
\(879\) 0 0
\(880\) 0 0
\(881\) 30.8182 1.03829 0.519146 0.854686i \(-0.326250\pi\)
0.519146 + 0.854686i \(0.326250\pi\)
\(882\) 0 0
\(883\) −39.8900 −1.34241 −0.671203 0.741274i \(-0.734222\pi\)
−0.671203 + 0.741274i \(0.734222\pi\)
\(884\) −4.87613 −0.164002
\(885\) 0 0
\(886\) −21.9736 −0.738217
\(887\) 39.1924 1.31595 0.657977 0.753038i \(-0.271413\pi\)
0.657977 + 0.753038i \(0.271413\pi\)
\(888\) 0 0
\(889\) −19.0279 −0.638176
\(890\) 0 0
\(891\) 0 0
\(892\) 3.75772 0.125818
\(893\) −8.79811 −0.294418
\(894\) 0 0
\(895\) 0 0
\(896\) −4.05705 −0.135536
\(897\) 0 0
\(898\) 23.1895 0.773843
\(899\) −1.74529 −0.0582088
\(900\) 0 0
\(901\) −19.2453 −0.641152
\(902\) 4.75475 0.158316
\(903\) 0 0
\(904\) 14.4596 0.480920
\(905\) 0 0
\(906\) 0 0
\(907\) −49.5098 −1.64395 −0.821973 0.569527i \(-0.807127\pi\)
−0.821973 + 0.569527i \(0.807127\pi\)
\(908\) −17.8913 −0.593745
\(909\) 0 0
\(910\) 0 0
\(911\) 14.3634 0.475882 0.237941 0.971280i \(-0.423527\pi\)
0.237941 + 0.971280i \(0.423527\pi\)
\(912\) 0 0
\(913\) −2.04067 −0.0675362
\(914\) 34.3211 1.13524
\(915\) 0 0
\(916\) −5.32304 −0.175878
\(917\) 39.0279 1.28882
\(918\) 0 0
\(919\) −54.1336 −1.78570 −0.892852 0.450350i \(-0.851299\pi\)
−0.892852 + 0.450350i \(0.851299\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 23.5959 0.777091
\(923\) −6.05585 −0.199331
\(924\) 0 0
\(925\) 0 0
\(926\) −3.94991 −0.129802
\(927\) 0 0
\(928\) 2.43806 0.0800333
\(929\) 30.2579 0.992730 0.496365 0.868114i \(-0.334668\pi\)
0.496365 + 0.868114i \(0.334668\pi\)
\(930\) 0 0
\(931\) 9.45963 0.310027
\(932\) 3.51396 0.115104
\(933\) 0 0
\(934\) 9.51396 0.311306
\(935\) 0 0
\(936\) 0 0
\(937\) −49.7747 −1.62607 −0.813035 0.582215i \(-0.802186\pi\)
−0.813035 + 0.582215i \(0.802186\pi\)
\(938\) 56.4846 1.84429
\(939\) 0 0
\(940\) 0 0
\(941\) 9.51265 0.310104 0.155052 0.987906i \(-0.450446\pi\)
0.155052 + 0.987906i \(0.450446\pi\)
\(942\) 0 0
\(943\) −22.7425 −0.740597
\(944\) −7.42748 −0.241744
\(945\) 0 0
\(946\) −0.217329 −0.00706597
\(947\) 2.26871 0.0737231 0.0368616 0.999320i \(-0.488264\pi\)
0.0368616 + 0.999320i \(0.488264\pi\)
\(948\) 0 0
\(949\) 6.97511 0.226422
\(950\) 0 0
\(951\) 0 0
\(952\) 20.0648 0.650304
\(953\) −1.75770 −0.0569374 −0.0284687 0.999595i \(-0.509063\pi\)
−0.0284687 + 0.999595i \(0.509063\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 29.4986 0.954052
\(957\) 0 0
\(958\) 28.4591 0.919470
\(959\) −76.4226 −2.46781
\(960\) 0 0
\(961\) −30.4876 −0.983470
\(962\) 9.89134 0.318909
\(963\) 0 0
\(964\) 29.2702 0.942731
\(965\) 0 0
\(966\) 0 0
\(967\) 9.60061 0.308735 0.154367 0.988014i \(-0.450666\pi\)
0.154367 + 0.988014i \(0.450666\pi\)
\(968\) 10.7827 0.346568
\(969\) 0 0
\(970\) 0 0
\(971\) 48.8232 1.56681 0.783405 0.621511i \(-0.213481\pi\)
0.783405 + 0.621511i \(0.213481\pi\)
\(972\) 0 0
\(973\) 58.2225 1.86653
\(974\) −21.5169 −0.689447
\(975\) 0 0
\(976\) −6.45963 −0.206768
\(977\) −25.1057 −0.803203 −0.401601 0.915815i \(-0.631546\pi\)
−0.401601 + 0.915815i \(0.631546\pi\)
\(978\) 0 0
\(979\) 2.81060 0.0898270
\(980\) 0 0
\(981\) 0 0
\(982\) 20.3044 0.647940
\(983\) 27.7827 0.886130 0.443065 0.896490i \(-0.353891\pi\)
0.443065 + 0.896490i \(0.353891\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −12.0578 −0.384000
\(987\) 0 0
\(988\) 0.985939 0.0313669
\(989\) 1.03951 0.0330544
\(990\) 0 0
\(991\) −51.0140 −1.62051 −0.810257 0.586075i \(-0.800672\pi\)
−0.810257 + 0.586075i \(0.800672\pi\)
\(992\) −0.715853 −0.0227283
\(993\) 0 0
\(994\) 24.9193 0.790391
\(995\) 0 0
\(996\) 0 0
\(997\) −14.2371 −0.450895 −0.225447 0.974255i \(-0.572384\pi\)
−0.225447 + 0.974255i \(0.572384\pi\)
\(998\) 12.9193 0.408952
\(999\) 0 0
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 8550.2.a.cw.1.6 6
3.2 odd 2 8550.2.a.cx.1.6 6
5.2 odd 4 1710.2.d.h.1369.3 12
5.3 odd 4 1710.2.d.h.1369.9 yes 12
5.4 even 2 8550.2.a.cx.1.1 6
15.2 even 4 1710.2.d.h.1369.10 yes 12
15.8 even 4 1710.2.d.h.1369.4 yes 12
15.14 odd 2 inner 8550.2.a.cw.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1710.2.d.h.1369.3 12 5.2 odd 4
1710.2.d.h.1369.4 yes 12 15.8 even 4
1710.2.d.h.1369.9 yes 12 5.3 odd 4
1710.2.d.h.1369.10 yes 12 15.2 even 4
8550.2.a.cw.1.1 6 15.14 odd 2 inner
8550.2.a.cw.1.6 6 1.1 even 1 trivial
8550.2.a.cx.1.1 6 5.4 even 2
8550.2.a.cx.1.6 6 3.2 odd 2