Properties

Label 6008.2.a.b.1.2
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.25541 q^{3} +3.98380 q^{5} -3.42108 q^{7} +7.59768 q^{9} +O(q^{10})\) \(q-3.25541 q^{3} +3.98380 q^{5} -3.42108 q^{7} +7.59768 q^{9} +3.25732 q^{11} -0.807608 q^{13} -12.9689 q^{15} -7.09260 q^{17} -1.26064 q^{19} +11.1370 q^{21} +4.19001 q^{23} +10.8706 q^{25} -14.9673 q^{27} +9.60617 q^{29} -3.56038 q^{31} -10.6039 q^{33} -13.6289 q^{35} -8.53329 q^{37} +2.62909 q^{39} +1.78776 q^{41} -3.07321 q^{43} +30.2676 q^{45} +1.74557 q^{47} +4.70377 q^{49} +23.0893 q^{51} -8.29290 q^{53} +12.9765 q^{55} +4.10389 q^{57} -8.47606 q^{59} -5.19121 q^{61} -25.9923 q^{63} -3.21735 q^{65} -4.78894 q^{67} -13.6402 q^{69} -3.44947 q^{71} +7.82156 q^{73} -35.3884 q^{75} -11.1435 q^{77} -10.4003 q^{79} +25.9317 q^{81} -6.41097 q^{83} -28.2555 q^{85} -31.2720 q^{87} -0.0939472 q^{89} +2.76289 q^{91} +11.5905 q^{93} -5.02213 q^{95} +7.80321 q^{97} +24.7481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −3.25541 −1.87951 −0.939755 0.341847i \(-0.888947\pi\)
−0.939755 + 0.341847i \(0.888947\pi\)
\(4\) 0 0
\(5\) 3.98380 1.78161 0.890804 0.454387i \(-0.150142\pi\)
0.890804 + 0.454387i \(0.150142\pi\)
\(6\) 0 0
\(7\) −3.42108 −1.29305 −0.646523 0.762895i \(-0.723777\pi\)
−0.646523 + 0.762895i \(0.723777\pi\)
\(8\) 0 0
\(9\) 7.59768 2.53256
\(10\) 0 0
\(11\) 3.25732 0.982120 0.491060 0.871126i \(-0.336610\pi\)
0.491060 + 0.871126i \(0.336610\pi\)
\(12\) 0 0
\(13\) −0.807608 −0.223990 −0.111995 0.993709i \(-0.535724\pi\)
−0.111995 + 0.993709i \(0.535724\pi\)
\(14\) 0 0
\(15\) −12.9689 −3.34855
\(16\) 0 0
\(17\) −7.09260 −1.72021 −0.860104 0.510118i \(-0.829602\pi\)
−0.860104 + 0.510118i \(0.829602\pi\)
\(18\) 0 0
\(19\) −1.26064 −0.289210 −0.144605 0.989489i \(-0.546191\pi\)
−0.144605 + 0.989489i \(0.546191\pi\)
\(20\) 0 0
\(21\) 11.1370 2.43029
\(22\) 0 0
\(23\) 4.19001 0.873678 0.436839 0.899540i \(-0.356098\pi\)
0.436839 + 0.899540i \(0.356098\pi\)
\(24\) 0 0
\(25\) 10.8706 2.17413
\(26\) 0 0
\(27\) −14.9673 −2.88047
\(28\) 0 0
\(29\) 9.60617 1.78382 0.891910 0.452212i \(-0.149365\pi\)
0.891910 + 0.452212i \(0.149365\pi\)
\(30\) 0 0
\(31\) −3.56038 −0.639463 −0.319731 0.947508i \(-0.603593\pi\)
−0.319731 + 0.947508i \(0.603593\pi\)
\(32\) 0 0
\(33\) −10.6039 −1.84590
\(34\) 0 0
\(35\) −13.6289 −2.30370
\(36\) 0 0
\(37\) −8.53329 −1.40286 −0.701432 0.712737i \(-0.747456\pi\)
−0.701432 + 0.712737i \(0.747456\pi\)
\(38\) 0 0
\(39\) 2.62909 0.420992
\(40\) 0 0
\(41\) 1.78776 0.279201 0.139601 0.990208i \(-0.455418\pi\)
0.139601 + 0.990208i \(0.455418\pi\)
\(42\) 0 0
\(43\) −3.07321 −0.468660 −0.234330 0.972157i \(-0.575290\pi\)
−0.234330 + 0.972157i \(0.575290\pi\)
\(44\) 0 0
\(45\) 30.2676 4.51203
\(46\) 0 0
\(47\) 1.74557 0.254617 0.127308 0.991863i \(-0.459366\pi\)
0.127308 + 0.991863i \(0.459366\pi\)
\(48\) 0 0
\(49\) 4.70377 0.671967
\(50\) 0 0
\(51\) 23.0893 3.23315
\(52\) 0 0
\(53\) −8.29290 −1.13912 −0.569559 0.821950i \(-0.692886\pi\)
−0.569559 + 0.821950i \(0.692886\pi\)
\(54\) 0 0
\(55\) 12.9765 1.74975
\(56\) 0 0
\(57\) 4.10389 0.543574
\(58\) 0 0
\(59\) −8.47606 −1.10349 −0.551745 0.834013i \(-0.686038\pi\)
−0.551745 + 0.834013i \(0.686038\pi\)
\(60\) 0 0
\(61\) −5.19121 −0.664666 −0.332333 0.943162i \(-0.607836\pi\)
−0.332333 + 0.943162i \(0.607836\pi\)
\(62\) 0 0
\(63\) −25.9923 −3.27472
\(64\) 0 0
\(65\) −3.21735 −0.399063
\(66\) 0 0
\(67\) −4.78894 −0.585062 −0.292531 0.956256i \(-0.594497\pi\)
−0.292531 + 0.956256i \(0.594497\pi\)
\(68\) 0 0
\(69\) −13.6402 −1.64209
\(70\) 0 0
\(71\) −3.44947 −0.409376 −0.204688 0.978827i \(-0.565618\pi\)
−0.204688 + 0.978827i \(0.565618\pi\)
\(72\) 0 0
\(73\) 7.82156 0.915445 0.457722 0.889095i \(-0.348665\pi\)
0.457722 + 0.889095i \(0.348665\pi\)
\(74\) 0 0
\(75\) −35.3884 −4.08630
\(76\) 0 0
\(77\) −11.1435 −1.26993
\(78\) 0 0
\(79\) −10.4003 −1.17012 −0.585062 0.810988i \(-0.698930\pi\)
−0.585062 + 0.810988i \(0.698930\pi\)
\(80\) 0 0
\(81\) 25.9317 2.88130
\(82\) 0 0
\(83\) −6.41097 −0.703695 −0.351848 0.936057i \(-0.614447\pi\)
−0.351848 + 0.936057i \(0.614447\pi\)
\(84\) 0 0
\(85\) −28.2555 −3.06474
\(86\) 0 0
\(87\) −31.2720 −3.35271
\(88\) 0 0
\(89\) −0.0939472 −0.00995838 −0.00497919 0.999988i \(-0.501585\pi\)
−0.00497919 + 0.999988i \(0.501585\pi\)
\(90\) 0 0
\(91\) 2.76289 0.289629
\(92\) 0 0
\(93\) 11.5905 1.20188
\(94\) 0 0
\(95\) −5.02213 −0.515260
\(96\) 0 0
\(97\) 7.80321 0.792295 0.396148 0.918187i \(-0.370347\pi\)
0.396148 + 0.918187i \(0.370347\pi\)
\(98\) 0 0
\(99\) 24.7481 2.48728
\(100\) 0 0
\(101\) 9.94811 0.989874 0.494937 0.868929i \(-0.335191\pi\)
0.494937 + 0.868929i \(0.335191\pi\)
\(102\) 0 0
\(103\) 14.3593 1.41486 0.707431 0.706782i \(-0.249854\pi\)
0.707431 + 0.706782i \(0.249854\pi\)
\(104\) 0 0
\(105\) 44.3676 4.32983
\(106\) 0 0
\(107\) 16.7197 1.61635 0.808177 0.588939i \(-0.200454\pi\)
0.808177 + 0.588939i \(0.200454\pi\)
\(108\) 0 0
\(109\) −10.7314 −1.02788 −0.513939 0.857827i \(-0.671814\pi\)
−0.513939 + 0.857827i \(0.671814\pi\)
\(110\) 0 0
\(111\) 27.7793 2.63670
\(112\) 0 0
\(113\) −16.2319 −1.52697 −0.763486 0.645824i \(-0.776514\pi\)
−0.763486 + 0.645824i \(0.776514\pi\)
\(114\) 0 0
\(115\) 16.6922 1.55655
\(116\) 0 0
\(117\) −6.13595 −0.567269
\(118\) 0 0
\(119\) 24.2643 2.22431
\(120\) 0 0
\(121\) −0.389852 −0.0354411
\(122\) 0 0
\(123\) −5.81989 −0.524762
\(124\) 0 0
\(125\) 23.3875 2.09184
\(126\) 0 0
\(127\) 8.83449 0.783934 0.391967 0.919979i \(-0.371795\pi\)
0.391967 + 0.919979i \(0.371795\pi\)
\(128\) 0 0
\(129\) 10.0045 0.880851
\(130\) 0 0
\(131\) 14.0418 1.22684 0.613418 0.789759i \(-0.289794\pi\)
0.613418 + 0.789759i \(0.289794\pi\)
\(132\) 0 0
\(133\) 4.31274 0.373962
\(134\) 0 0
\(135\) −59.6268 −5.13186
\(136\) 0 0
\(137\) 13.2854 1.13505 0.567526 0.823356i \(-0.307901\pi\)
0.567526 + 0.823356i \(0.307901\pi\)
\(138\) 0 0
\(139\) −7.12458 −0.604299 −0.302149 0.953261i \(-0.597704\pi\)
−0.302149 + 0.953261i \(0.597704\pi\)
\(140\) 0 0
\(141\) −5.68253 −0.478555
\(142\) 0 0
\(143\) −2.63064 −0.219985
\(144\) 0 0
\(145\) 38.2690 3.17807
\(146\) 0 0
\(147\) −15.3127 −1.26297
\(148\) 0 0
\(149\) 6.10732 0.500332 0.250166 0.968203i \(-0.419515\pi\)
0.250166 + 0.968203i \(0.419515\pi\)
\(150\) 0 0
\(151\) 4.91160 0.399700 0.199850 0.979827i \(-0.435955\pi\)
0.199850 + 0.979827i \(0.435955\pi\)
\(152\) 0 0
\(153\) −53.8873 −4.35653
\(154\) 0 0
\(155\) −14.1838 −1.13927
\(156\) 0 0
\(157\) −9.18561 −0.733092 −0.366546 0.930400i \(-0.619460\pi\)
−0.366546 + 0.930400i \(0.619460\pi\)
\(158\) 0 0
\(159\) 26.9968 2.14098
\(160\) 0 0
\(161\) −14.3343 −1.12970
\(162\) 0 0
\(163\) 11.3050 0.885476 0.442738 0.896651i \(-0.354007\pi\)
0.442738 + 0.896651i \(0.354007\pi\)
\(164\) 0 0
\(165\) −42.2439 −3.28868
\(166\) 0 0
\(167\) −24.2822 −1.87901 −0.939507 0.342529i \(-0.888716\pi\)
−0.939507 + 0.342529i \(0.888716\pi\)
\(168\) 0 0
\(169\) −12.3478 −0.949828
\(170\) 0 0
\(171\) −9.57794 −0.732443
\(172\) 0 0
\(173\) −9.43435 −0.717280 −0.358640 0.933476i \(-0.616759\pi\)
−0.358640 + 0.933476i \(0.616759\pi\)
\(174\) 0 0
\(175\) −37.1893 −2.81125
\(176\) 0 0
\(177\) 27.5930 2.07402
\(178\) 0 0
\(179\) −19.6876 −1.47152 −0.735760 0.677242i \(-0.763175\pi\)
−0.735760 + 0.677242i \(0.763175\pi\)
\(180\) 0 0
\(181\) 11.8912 0.883865 0.441933 0.897048i \(-0.354293\pi\)
0.441933 + 0.897048i \(0.354293\pi\)
\(182\) 0 0
\(183\) 16.8995 1.24925
\(184\) 0 0
\(185\) −33.9949 −2.49935
\(186\) 0 0
\(187\) −23.1029 −1.68945
\(188\) 0 0
\(189\) 51.2044 3.72457
\(190\) 0 0
\(191\) 21.5931 1.56242 0.781211 0.624267i \(-0.214602\pi\)
0.781211 + 0.624267i \(0.214602\pi\)
\(192\) 0 0
\(193\) 7.38434 0.531536 0.265768 0.964037i \(-0.414374\pi\)
0.265768 + 0.964037i \(0.414374\pi\)
\(194\) 0 0
\(195\) 10.4738 0.750043
\(196\) 0 0
\(197\) 3.94819 0.281297 0.140648 0.990060i \(-0.455081\pi\)
0.140648 + 0.990060i \(0.455081\pi\)
\(198\) 0 0
\(199\) 5.88359 0.417077 0.208538 0.978014i \(-0.433129\pi\)
0.208538 + 0.978014i \(0.433129\pi\)
\(200\) 0 0
\(201\) 15.5900 1.09963
\(202\) 0 0
\(203\) −32.8634 −2.30656
\(204\) 0 0
\(205\) 7.12207 0.497427
\(206\) 0 0
\(207\) 31.8344 2.21264
\(208\) 0 0
\(209\) −4.10631 −0.284039
\(210\) 0 0
\(211\) 11.8761 0.817585 0.408793 0.912627i \(-0.365950\pi\)
0.408793 + 0.912627i \(0.365950\pi\)
\(212\) 0 0
\(213\) 11.2294 0.769427
\(214\) 0 0
\(215\) −12.2430 −0.834969
\(216\) 0 0
\(217\) 12.1803 0.826854
\(218\) 0 0
\(219\) −25.4624 −1.72059
\(220\) 0 0
\(221\) 5.72804 0.385310
\(222\) 0 0
\(223\) −10.5414 −0.705904 −0.352952 0.935641i \(-0.614822\pi\)
−0.352952 + 0.935641i \(0.614822\pi\)
\(224\) 0 0
\(225\) 82.5917 5.50612
\(226\) 0 0
\(227\) −18.0890 −1.20061 −0.600304 0.799772i \(-0.704954\pi\)
−0.600304 + 0.799772i \(0.704954\pi\)
\(228\) 0 0
\(229\) −7.44054 −0.491685 −0.245842 0.969310i \(-0.579065\pi\)
−0.245842 + 0.969310i \(0.579065\pi\)
\(230\) 0 0
\(231\) 36.2768 2.38684
\(232\) 0 0
\(233\) −11.0306 −0.722641 −0.361321 0.932442i \(-0.617674\pi\)
−0.361321 + 0.932442i \(0.617674\pi\)
\(234\) 0 0
\(235\) 6.95398 0.453628
\(236\) 0 0
\(237\) 33.8572 2.19926
\(238\) 0 0
\(239\) −22.1481 −1.43264 −0.716321 0.697771i \(-0.754175\pi\)
−0.716321 + 0.697771i \(0.754175\pi\)
\(240\) 0 0
\(241\) −25.1368 −1.61921 −0.809603 0.586978i \(-0.800317\pi\)
−0.809603 + 0.586978i \(0.800317\pi\)
\(242\) 0 0
\(243\) −39.5164 −2.53498
\(244\) 0 0
\(245\) 18.7389 1.19718
\(246\) 0 0
\(247\) 1.01810 0.0647803
\(248\) 0 0
\(249\) 20.8703 1.32260
\(250\) 0 0
\(251\) −28.8358 −1.82010 −0.910050 0.414499i \(-0.863957\pi\)
−0.910050 + 0.414499i \(0.863957\pi\)
\(252\) 0 0
\(253\) 13.6482 0.858056
\(254\) 0 0
\(255\) 91.9832 5.76021
\(256\) 0 0
\(257\) −31.6103 −1.97180 −0.985898 0.167348i \(-0.946480\pi\)
−0.985898 + 0.167348i \(0.946480\pi\)
\(258\) 0 0
\(259\) 29.1930 1.81397
\(260\) 0 0
\(261\) 72.9846 4.51764
\(262\) 0 0
\(263\) −12.1291 −0.747910 −0.373955 0.927447i \(-0.621999\pi\)
−0.373955 + 0.927447i \(0.621999\pi\)
\(264\) 0 0
\(265\) −33.0373 −2.02946
\(266\) 0 0
\(267\) 0.305836 0.0187169
\(268\) 0 0
\(269\) 1.17950 0.0719153 0.0359577 0.999353i \(-0.488552\pi\)
0.0359577 + 0.999353i \(0.488552\pi\)
\(270\) 0 0
\(271\) −2.48302 −0.150833 −0.0754163 0.997152i \(-0.524029\pi\)
−0.0754163 + 0.997152i \(0.524029\pi\)
\(272\) 0 0
\(273\) −8.99433 −0.544362
\(274\) 0 0
\(275\) 35.4092 2.13526
\(276\) 0 0
\(277\) −15.2937 −0.918909 −0.459454 0.888201i \(-0.651955\pi\)
−0.459454 + 0.888201i \(0.651955\pi\)
\(278\) 0 0
\(279\) −27.0506 −1.61948
\(280\) 0 0
\(281\) 14.3825 0.857985 0.428993 0.903308i \(-0.358869\pi\)
0.428993 + 0.903308i \(0.358869\pi\)
\(282\) 0 0
\(283\) 26.7379 1.58941 0.794703 0.606999i \(-0.207627\pi\)
0.794703 + 0.606999i \(0.207627\pi\)
\(284\) 0 0
\(285\) 16.3491 0.968436
\(286\) 0 0
\(287\) −6.11606 −0.361020
\(288\) 0 0
\(289\) 33.3050 1.95912
\(290\) 0 0
\(291\) −25.4026 −1.48913
\(292\) 0 0
\(293\) 2.21933 0.129655 0.0648273 0.997896i \(-0.479350\pi\)
0.0648273 + 0.997896i \(0.479350\pi\)
\(294\) 0 0
\(295\) −33.7669 −1.96599
\(296\) 0 0
\(297\) −48.7534 −2.82896
\(298\) 0 0
\(299\) −3.38389 −0.195695
\(300\) 0 0
\(301\) 10.5137 0.605999
\(302\) 0 0
\(303\) −32.3852 −1.86048
\(304\) 0 0
\(305\) −20.6807 −1.18417
\(306\) 0 0
\(307\) −5.05256 −0.288365 −0.144182 0.989551i \(-0.546055\pi\)
−0.144182 + 0.989551i \(0.546055\pi\)
\(308\) 0 0
\(309\) −46.7453 −2.65925
\(310\) 0 0
\(311\) −27.1784 −1.54114 −0.770572 0.637353i \(-0.780029\pi\)
−0.770572 + 0.637353i \(0.780029\pi\)
\(312\) 0 0
\(313\) −2.21976 −0.125468 −0.0627342 0.998030i \(-0.519982\pi\)
−0.0627342 + 0.998030i \(0.519982\pi\)
\(314\) 0 0
\(315\) −103.548 −5.83426
\(316\) 0 0
\(317\) 22.1714 1.24527 0.622635 0.782513i \(-0.286062\pi\)
0.622635 + 0.782513i \(0.286062\pi\)
\(318\) 0 0
\(319\) 31.2904 1.75193
\(320\) 0 0
\(321\) −54.4295 −3.03796
\(322\) 0 0
\(323\) 8.94121 0.497502
\(324\) 0 0
\(325\) −8.77922 −0.486984
\(326\) 0 0
\(327\) 34.9350 1.93191
\(328\) 0 0
\(329\) −5.97171 −0.329231
\(330\) 0 0
\(331\) 34.0036 1.86901 0.934504 0.355952i \(-0.115843\pi\)
0.934504 + 0.355952i \(0.115843\pi\)
\(332\) 0 0
\(333\) −64.8332 −3.55284
\(334\) 0 0
\(335\) −19.0782 −1.04235
\(336\) 0 0
\(337\) −28.7726 −1.56734 −0.783672 0.621174i \(-0.786656\pi\)
−0.783672 + 0.621174i \(0.786656\pi\)
\(338\) 0 0
\(339\) 52.8416 2.86996
\(340\) 0 0
\(341\) −11.5973 −0.628029
\(342\) 0 0
\(343\) 7.85559 0.424162
\(344\) 0 0
\(345\) −54.3398 −2.92556
\(346\) 0 0
\(347\) 3.50293 0.188047 0.0940235 0.995570i \(-0.470027\pi\)
0.0940235 + 0.995570i \(0.470027\pi\)
\(348\) 0 0
\(349\) 6.78478 0.363181 0.181590 0.983374i \(-0.441876\pi\)
0.181590 + 0.983374i \(0.441876\pi\)
\(350\) 0 0
\(351\) 12.0877 0.645196
\(352\) 0 0
\(353\) −32.2304 −1.71545 −0.857726 0.514107i \(-0.828124\pi\)
−0.857726 + 0.514107i \(0.828124\pi\)
\(354\) 0 0
\(355\) −13.7420 −0.729348
\(356\) 0 0
\(357\) −78.9903 −4.18061
\(358\) 0 0
\(359\) −4.36621 −0.230440 −0.115220 0.993340i \(-0.536757\pi\)
−0.115220 + 0.993340i \(0.536757\pi\)
\(360\) 0 0
\(361\) −17.4108 −0.916357
\(362\) 0 0
\(363\) 1.26913 0.0666120
\(364\) 0 0
\(365\) 31.1595 1.63096
\(366\) 0 0
\(367\) 37.9134 1.97906 0.989532 0.144312i \(-0.0460969\pi\)
0.989532 + 0.144312i \(0.0460969\pi\)
\(368\) 0 0
\(369\) 13.5828 0.707094
\(370\) 0 0
\(371\) 28.3707 1.47293
\(372\) 0 0
\(373\) −8.56182 −0.443314 −0.221657 0.975125i \(-0.571147\pi\)
−0.221657 + 0.975125i \(0.571147\pi\)
\(374\) 0 0
\(375\) −76.1358 −3.93163
\(376\) 0 0
\(377\) −7.75802 −0.399558
\(378\) 0 0
\(379\) −24.8590 −1.27692 −0.638460 0.769655i \(-0.720428\pi\)
−0.638460 + 0.769655i \(0.720428\pi\)
\(380\) 0 0
\(381\) −28.7599 −1.47341
\(382\) 0 0
\(383\) −20.0236 −1.02316 −0.511579 0.859236i \(-0.670939\pi\)
−0.511579 + 0.859236i \(0.670939\pi\)
\(384\) 0 0
\(385\) −44.3937 −2.26251
\(386\) 0 0
\(387\) −23.3493 −1.18691
\(388\) 0 0
\(389\) −21.9099 −1.11088 −0.555438 0.831558i \(-0.687449\pi\)
−0.555438 + 0.831558i \(0.687449\pi\)
\(390\) 0 0
\(391\) −29.7181 −1.50291
\(392\) 0 0
\(393\) −45.7117 −2.30585
\(394\) 0 0
\(395\) −41.4327 −2.08470
\(396\) 0 0
\(397\) −30.2337 −1.51739 −0.758693 0.651449i \(-0.774162\pi\)
−0.758693 + 0.651449i \(0.774162\pi\)
\(398\) 0 0
\(399\) −14.0397 −0.702866
\(400\) 0 0
\(401\) 22.2039 1.10881 0.554404 0.832247i \(-0.312946\pi\)
0.554404 + 0.832247i \(0.312946\pi\)
\(402\) 0 0
\(403\) 2.87539 0.143233
\(404\) 0 0
\(405\) 103.307 5.13336
\(406\) 0 0
\(407\) −27.7957 −1.37778
\(408\) 0 0
\(409\) −5.76070 −0.284848 −0.142424 0.989806i \(-0.545490\pi\)
−0.142424 + 0.989806i \(0.545490\pi\)
\(410\) 0 0
\(411\) −43.2495 −2.13334
\(412\) 0 0
\(413\) 28.9973 1.42686
\(414\) 0 0
\(415\) −25.5400 −1.25371
\(416\) 0 0
\(417\) 23.1934 1.13579
\(418\) 0 0
\(419\) −6.67763 −0.326224 −0.163112 0.986608i \(-0.552153\pi\)
−0.163112 + 0.986608i \(0.552153\pi\)
\(420\) 0 0
\(421\) −35.5326 −1.73175 −0.865877 0.500257i \(-0.833239\pi\)
−0.865877 + 0.500257i \(0.833239\pi\)
\(422\) 0 0
\(423\) 13.2623 0.644833
\(424\) 0 0
\(425\) −77.1012 −3.73996
\(426\) 0 0
\(427\) 17.7595 0.859443
\(428\) 0 0
\(429\) 8.56380 0.413464
\(430\) 0 0
\(431\) 10.1940 0.491028 0.245514 0.969393i \(-0.421043\pi\)
0.245514 + 0.969393i \(0.421043\pi\)
\(432\) 0 0
\(433\) −2.87531 −0.138179 −0.0690893 0.997610i \(-0.522009\pi\)
−0.0690893 + 0.997610i \(0.522009\pi\)
\(434\) 0 0
\(435\) −124.581 −5.97322
\(436\) 0 0
\(437\) −5.28209 −0.252677
\(438\) 0 0
\(439\) 0.679234 0.0324181 0.0162090 0.999869i \(-0.494840\pi\)
0.0162090 + 0.999869i \(0.494840\pi\)
\(440\) 0 0
\(441\) 35.7377 1.70180
\(442\) 0 0
\(443\) −29.2162 −1.38810 −0.694052 0.719925i \(-0.744176\pi\)
−0.694052 + 0.719925i \(0.744176\pi\)
\(444\) 0 0
\(445\) −0.374267 −0.0177419
\(446\) 0 0
\(447\) −19.8818 −0.940379
\(448\) 0 0
\(449\) 20.9446 0.988438 0.494219 0.869337i \(-0.335454\pi\)
0.494219 + 0.869337i \(0.335454\pi\)
\(450\) 0 0
\(451\) 5.82331 0.274209
\(452\) 0 0
\(453\) −15.9893 −0.751241
\(454\) 0 0
\(455\) 11.0068 0.516006
\(456\) 0 0
\(457\) 29.9887 1.40281 0.701407 0.712761i \(-0.252556\pi\)
0.701407 + 0.712761i \(0.252556\pi\)
\(458\) 0 0
\(459\) 106.157 4.95500
\(460\) 0 0
\(461\) 1.16824 0.0544104 0.0272052 0.999630i \(-0.491339\pi\)
0.0272052 + 0.999630i \(0.491339\pi\)
\(462\) 0 0
\(463\) 23.1537 1.07604 0.538021 0.842931i \(-0.319172\pi\)
0.538021 + 0.842931i \(0.319172\pi\)
\(464\) 0 0
\(465\) 46.1741 2.14127
\(466\) 0 0
\(467\) 36.4043 1.68459 0.842295 0.539017i \(-0.181204\pi\)
0.842295 + 0.539017i \(0.181204\pi\)
\(468\) 0 0
\(469\) 16.3833 0.756512
\(470\) 0 0
\(471\) 29.9029 1.37785
\(472\) 0 0
\(473\) −10.0104 −0.460280
\(474\) 0 0
\(475\) −13.7040 −0.628781
\(476\) 0 0
\(477\) −63.0069 −2.88489
\(478\) 0 0
\(479\) 3.83238 0.175106 0.0875529 0.996160i \(-0.472095\pi\)
0.0875529 + 0.996160i \(0.472095\pi\)
\(480\) 0 0
\(481\) 6.89155 0.314228
\(482\) 0 0
\(483\) 46.6642 2.12329
\(484\) 0 0
\(485\) 31.0864 1.41156
\(486\) 0 0
\(487\) −19.7865 −0.896612 −0.448306 0.893880i \(-0.647973\pi\)
−0.448306 + 0.893880i \(0.647973\pi\)
\(488\) 0 0
\(489\) −36.8024 −1.66426
\(490\) 0 0
\(491\) 6.69904 0.302324 0.151162 0.988509i \(-0.451699\pi\)
0.151162 + 0.988509i \(0.451699\pi\)
\(492\) 0 0
\(493\) −68.1327 −3.06854
\(494\) 0 0
\(495\) 98.5914 4.43136
\(496\) 0 0
\(497\) 11.8009 0.529342
\(498\) 0 0
\(499\) −37.1137 −1.66144 −0.830720 0.556691i \(-0.812071\pi\)
−0.830720 + 0.556691i \(0.812071\pi\)
\(500\) 0 0
\(501\) 79.0485 3.53163
\(502\) 0 0
\(503\) −22.8289 −1.01789 −0.508946 0.860799i \(-0.669965\pi\)
−0.508946 + 0.860799i \(0.669965\pi\)
\(504\) 0 0
\(505\) 39.6313 1.76357
\(506\) 0 0
\(507\) 40.1970 1.78521
\(508\) 0 0
\(509\) −38.3428 −1.69951 −0.849757 0.527175i \(-0.823251\pi\)
−0.849757 + 0.527175i \(0.823251\pi\)
\(510\) 0 0
\(511\) −26.7582 −1.18371
\(512\) 0 0
\(513\) 18.8684 0.833061
\(514\) 0 0
\(515\) 57.2045 2.52073
\(516\) 0 0
\(517\) 5.68587 0.250064
\(518\) 0 0
\(519\) 30.7126 1.34814
\(520\) 0 0
\(521\) −28.4935 −1.24832 −0.624160 0.781296i \(-0.714559\pi\)
−0.624160 + 0.781296i \(0.714559\pi\)
\(522\) 0 0
\(523\) 21.3657 0.934255 0.467128 0.884190i \(-0.345289\pi\)
0.467128 + 0.884190i \(0.345289\pi\)
\(524\) 0 0
\(525\) 121.066 5.28377
\(526\) 0 0
\(527\) 25.2523 1.10001
\(528\) 0 0
\(529\) −5.44381 −0.236687
\(530\) 0 0
\(531\) −64.3984 −2.79465
\(532\) 0 0
\(533\) −1.44381 −0.0625383
\(534\) 0 0
\(535\) 66.6079 2.87971
\(536\) 0 0
\(537\) 64.0912 2.76574
\(538\) 0 0
\(539\) 15.3217 0.659952
\(540\) 0 0
\(541\) 8.11124 0.348730 0.174365 0.984681i \(-0.444213\pi\)
0.174365 + 0.984681i \(0.444213\pi\)
\(542\) 0 0
\(543\) −38.7107 −1.66123
\(544\) 0 0
\(545\) −42.7516 −1.83128
\(546\) 0 0
\(547\) 20.5632 0.879221 0.439610 0.898189i \(-0.355117\pi\)
0.439610 + 0.898189i \(0.355117\pi\)
\(548\) 0 0
\(549\) −39.4411 −1.68331
\(550\) 0 0
\(551\) −12.1099 −0.515900
\(552\) 0 0
\(553\) 35.5802 1.51302
\(554\) 0 0
\(555\) 110.667 4.69756
\(556\) 0 0
\(557\) −28.3552 −1.20145 −0.600724 0.799456i \(-0.705121\pi\)
−0.600724 + 0.799456i \(0.705121\pi\)
\(558\) 0 0
\(559\) 2.48195 0.104975
\(560\) 0 0
\(561\) 75.2093 3.17534
\(562\) 0 0
\(563\) 8.95165 0.377267 0.188633 0.982048i \(-0.439594\pi\)
0.188633 + 0.982048i \(0.439594\pi\)
\(564\) 0 0
\(565\) −64.6648 −2.72047
\(566\) 0 0
\(567\) −88.7145 −3.72566
\(568\) 0 0
\(569\) −1.24021 −0.0519923 −0.0259961 0.999662i \(-0.508276\pi\)
−0.0259961 + 0.999662i \(0.508276\pi\)
\(570\) 0 0
\(571\) 11.0486 0.462368 0.231184 0.972910i \(-0.425740\pi\)
0.231184 + 0.972910i \(0.425740\pi\)
\(572\) 0 0
\(573\) −70.2944 −2.93659
\(574\) 0 0
\(575\) 45.5481 1.89949
\(576\) 0 0
\(577\) −35.1213 −1.46212 −0.731060 0.682313i \(-0.760974\pi\)
−0.731060 + 0.682313i \(0.760974\pi\)
\(578\) 0 0
\(579\) −24.0390 −0.999028
\(580\) 0 0
\(581\) 21.9324 0.909910
\(582\) 0 0
\(583\) −27.0127 −1.11875
\(584\) 0 0
\(585\) −24.4444 −1.01065
\(586\) 0 0
\(587\) −12.1454 −0.501293 −0.250646 0.968079i \(-0.580643\pi\)
−0.250646 + 0.968079i \(0.580643\pi\)
\(588\) 0 0
\(589\) 4.48835 0.184939
\(590\) 0 0
\(591\) −12.8530 −0.528700
\(592\) 0 0
\(593\) −26.7848 −1.09992 −0.549961 0.835191i \(-0.685357\pi\)
−0.549961 + 0.835191i \(0.685357\pi\)
\(594\) 0 0
\(595\) 96.6642 3.96285
\(596\) 0 0
\(597\) −19.1535 −0.783901
\(598\) 0 0
\(599\) −4.85522 −0.198379 −0.0991895 0.995069i \(-0.531625\pi\)
−0.0991895 + 0.995069i \(0.531625\pi\)
\(600\) 0 0
\(601\) −39.2427 −1.60074 −0.800371 0.599505i \(-0.795364\pi\)
−0.800371 + 0.599505i \(0.795364\pi\)
\(602\) 0 0
\(603\) −36.3848 −1.48171
\(604\) 0 0
\(605\) −1.55309 −0.0631422
\(606\) 0 0
\(607\) −21.4714 −0.871495 −0.435748 0.900069i \(-0.643516\pi\)
−0.435748 + 0.900069i \(0.643516\pi\)
\(608\) 0 0
\(609\) 106.984 4.33521
\(610\) 0 0
\(611\) −1.40973 −0.0570317
\(612\) 0 0
\(613\) 7.89473 0.318865 0.159433 0.987209i \(-0.449034\pi\)
0.159433 + 0.987209i \(0.449034\pi\)
\(614\) 0 0
\(615\) −23.1853 −0.934920
\(616\) 0 0
\(617\) 6.97253 0.280704 0.140352 0.990102i \(-0.455177\pi\)
0.140352 + 0.990102i \(0.455177\pi\)
\(618\) 0 0
\(619\) 19.0118 0.764149 0.382075 0.924131i \(-0.375210\pi\)
0.382075 + 0.924131i \(0.375210\pi\)
\(620\) 0 0
\(621\) −62.7133 −2.51660
\(622\) 0 0
\(623\) 0.321401 0.0128766
\(624\) 0 0
\(625\) 38.8177 1.55271
\(626\) 0 0
\(627\) 13.3677 0.533855
\(628\) 0 0
\(629\) 60.5232 2.41322
\(630\) 0 0
\(631\) −16.2520 −0.646983 −0.323492 0.946231i \(-0.604857\pi\)
−0.323492 + 0.946231i \(0.604857\pi\)
\(632\) 0 0
\(633\) −38.6616 −1.53666
\(634\) 0 0
\(635\) 35.1948 1.39666
\(636\) 0 0
\(637\) −3.79880 −0.150514
\(638\) 0 0
\(639\) −26.2079 −1.03677
\(640\) 0 0
\(641\) −36.8993 −1.45744 −0.728718 0.684814i \(-0.759883\pi\)
−0.728718 + 0.684814i \(0.759883\pi\)
\(642\) 0 0
\(643\) 9.10483 0.359059 0.179530 0.983753i \(-0.442542\pi\)
0.179530 + 0.983753i \(0.442542\pi\)
\(644\) 0 0
\(645\) 39.8561 1.56933
\(646\) 0 0
\(647\) −45.4351 −1.78624 −0.893120 0.449819i \(-0.851488\pi\)
−0.893120 + 0.449819i \(0.851488\pi\)
\(648\) 0 0
\(649\) −27.6093 −1.08376
\(650\) 0 0
\(651\) −39.6519 −1.55408
\(652\) 0 0
\(653\) −37.4827 −1.46681 −0.733405 0.679792i \(-0.762070\pi\)
−0.733405 + 0.679792i \(0.762070\pi\)
\(654\) 0 0
\(655\) 55.9396 2.18574
\(656\) 0 0
\(657\) 59.4258 2.31842
\(658\) 0 0
\(659\) −5.97908 −0.232912 −0.116456 0.993196i \(-0.537153\pi\)
−0.116456 + 0.993196i \(0.537153\pi\)
\(660\) 0 0
\(661\) 49.2370 1.91510 0.957548 0.288272i \(-0.0930808\pi\)
0.957548 + 0.288272i \(0.0930808\pi\)
\(662\) 0 0
\(663\) −18.6471 −0.724194
\(664\) 0 0
\(665\) 17.1811 0.666254
\(666\) 0 0
\(667\) 40.2499 1.55848
\(668\) 0 0
\(669\) 34.3166 1.32675
\(670\) 0 0
\(671\) −16.9094 −0.652781
\(672\) 0 0
\(673\) −51.1888 −1.97318 −0.986592 0.163206i \(-0.947816\pi\)
−0.986592 + 0.163206i \(0.947816\pi\)
\(674\) 0 0
\(675\) −162.705 −6.26250
\(676\) 0 0
\(677\) −5.66213 −0.217613 −0.108807 0.994063i \(-0.534703\pi\)
−0.108807 + 0.994063i \(0.534703\pi\)
\(678\) 0 0
\(679\) −26.6954 −1.02447
\(680\) 0 0
\(681\) 58.8870 2.25656
\(682\) 0 0
\(683\) 44.1051 1.68764 0.843818 0.536630i \(-0.180303\pi\)
0.843818 + 0.536630i \(0.180303\pi\)
\(684\) 0 0
\(685\) 52.9265 2.02222
\(686\) 0 0
\(687\) 24.2220 0.924127
\(688\) 0 0
\(689\) 6.69741 0.255151
\(690\) 0 0
\(691\) −7.24429 −0.275586 −0.137793 0.990461i \(-0.544001\pi\)
−0.137793 + 0.990461i \(0.544001\pi\)
\(692\) 0 0
\(693\) −84.6652 −3.21616
\(694\) 0 0
\(695\) −28.3829 −1.07662
\(696\) 0 0
\(697\) −12.6799 −0.480284
\(698\) 0 0
\(699\) 35.9092 1.35821
\(700\) 0 0
\(701\) 9.55968 0.361064 0.180532 0.983569i \(-0.442218\pi\)
0.180532 + 0.983569i \(0.442218\pi\)
\(702\) 0 0
\(703\) 10.7574 0.405723
\(704\) 0 0
\(705\) −22.6380 −0.852598
\(706\) 0 0
\(707\) −34.0333 −1.27995
\(708\) 0 0
\(709\) −21.4083 −0.804004 −0.402002 0.915639i \(-0.631686\pi\)
−0.402002 + 0.915639i \(0.631686\pi\)
\(710\) 0 0
\(711\) −79.0181 −2.96341
\(712\) 0 0
\(713\) −14.9180 −0.558684
\(714\) 0 0
\(715\) −10.4799 −0.391927
\(716\) 0 0
\(717\) 72.1012 2.69267
\(718\) 0 0
\(719\) −4.49117 −0.167492 −0.0837461 0.996487i \(-0.526688\pi\)
−0.0837461 + 0.996487i \(0.526688\pi\)
\(720\) 0 0
\(721\) −49.1242 −1.82948
\(722\) 0 0
\(723\) 81.8306 3.04331
\(724\) 0 0
\(725\) 104.425 3.87826
\(726\) 0 0
\(727\) 8.41611 0.312136 0.156068 0.987746i \(-0.450118\pi\)
0.156068 + 0.987746i \(0.450118\pi\)
\(728\) 0 0
\(729\) 50.8468 1.88321
\(730\) 0 0
\(731\) 21.7970 0.806193
\(732\) 0 0
\(733\) 46.4050 1.71401 0.857003 0.515311i \(-0.172324\pi\)
0.857003 + 0.515311i \(0.172324\pi\)
\(734\) 0 0
\(735\) −61.0026 −2.25012
\(736\) 0 0
\(737\) −15.5991 −0.574601
\(738\) 0 0
\(739\) 6.26522 0.230470 0.115235 0.993338i \(-0.463238\pi\)
0.115235 + 0.993338i \(0.463238\pi\)
\(740\) 0 0
\(741\) −3.31434 −0.121755
\(742\) 0 0
\(743\) −15.7833 −0.579034 −0.289517 0.957173i \(-0.593495\pi\)
−0.289517 + 0.957173i \(0.593495\pi\)
\(744\) 0 0
\(745\) 24.3303 0.891395
\(746\) 0 0
\(747\) −48.7085 −1.78215
\(748\) 0 0
\(749\) −57.1994 −2.09002
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 93.8723 3.42090
\(754\) 0 0
\(755\) 19.5668 0.712109
\(756\) 0 0
\(757\) 21.3890 0.777396 0.388698 0.921365i \(-0.372925\pi\)
0.388698 + 0.921365i \(0.372925\pi\)
\(758\) 0 0
\(759\) −44.4305 −1.61273
\(760\) 0 0
\(761\) −20.1231 −0.729462 −0.364731 0.931113i \(-0.618839\pi\)
−0.364731 + 0.931113i \(0.618839\pi\)
\(762\) 0 0
\(763\) 36.7128 1.32909
\(764\) 0 0
\(765\) −214.676 −7.76164
\(766\) 0 0
\(767\) 6.84533 0.247171
\(768\) 0 0
\(769\) 46.8679 1.69010 0.845050 0.534687i \(-0.179571\pi\)
0.845050 + 0.534687i \(0.179571\pi\)
\(770\) 0 0
\(771\) 102.904 3.70601
\(772\) 0 0
\(773\) −32.4710 −1.16790 −0.583951 0.811789i \(-0.698494\pi\)
−0.583951 + 0.811789i \(0.698494\pi\)
\(774\) 0 0
\(775\) −38.7036 −1.39027
\(776\) 0 0
\(777\) −95.0352 −3.40937
\(778\) 0 0
\(779\) −2.25372 −0.0807479
\(780\) 0 0
\(781\) −11.2360 −0.402056
\(782\) 0 0
\(783\) −143.779 −5.13823
\(784\) 0 0
\(785\) −36.5936 −1.30608
\(786\) 0 0
\(787\) 31.3602 1.11787 0.558936 0.829211i \(-0.311210\pi\)
0.558936 + 0.829211i \(0.311210\pi\)
\(788\) 0 0
\(789\) 39.4851 1.40571
\(790\) 0 0
\(791\) 55.5307 1.97444
\(792\) 0 0
\(793\) 4.19246 0.148879
\(794\) 0 0
\(795\) 107.550 3.81440
\(796\) 0 0
\(797\) −3.28579 −0.116388 −0.0581942 0.998305i \(-0.518534\pi\)
−0.0581942 + 0.998305i \(0.518534\pi\)
\(798\) 0 0
\(799\) −12.3806 −0.437994
\(800\) 0 0
\(801\) −0.713781 −0.0252202
\(802\) 0 0
\(803\) 25.4774 0.899076
\(804\) 0 0
\(805\) −57.1051 −2.01269
\(806\) 0 0
\(807\) −3.83975 −0.135166
\(808\) 0 0
\(809\) 27.9216 0.981672 0.490836 0.871252i \(-0.336691\pi\)
0.490836 + 0.871252i \(0.336691\pi\)
\(810\) 0 0
\(811\) 2.37264 0.0833145 0.0416573 0.999132i \(-0.486736\pi\)
0.0416573 + 0.999132i \(0.486736\pi\)
\(812\) 0 0
\(813\) 8.08323 0.283491
\(814\) 0 0
\(815\) 45.0369 1.57757
\(816\) 0 0
\(817\) 3.87421 0.135541
\(818\) 0 0
\(819\) 20.9916 0.733504
\(820\) 0 0
\(821\) 27.0229 0.943105 0.471553 0.881838i \(-0.343694\pi\)
0.471553 + 0.881838i \(0.343694\pi\)
\(822\) 0 0
\(823\) 13.1553 0.458566 0.229283 0.973360i \(-0.426362\pi\)
0.229283 + 0.973360i \(0.426362\pi\)
\(824\) 0 0
\(825\) −115.271 −4.01324
\(826\) 0 0
\(827\) −1.32207 −0.0459730 −0.0229865 0.999736i \(-0.507317\pi\)
−0.0229865 + 0.999736i \(0.507317\pi\)
\(828\) 0 0
\(829\) 35.1684 1.22145 0.610725 0.791843i \(-0.290878\pi\)
0.610725 + 0.791843i \(0.290878\pi\)
\(830\) 0 0
\(831\) 49.7872 1.72710
\(832\) 0 0
\(833\) −33.3619 −1.15592
\(834\) 0 0
\(835\) −96.7354 −3.34767
\(836\) 0 0
\(837\) 53.2894 1.84195
\(838\) 0 0
\(839\) −50.9475 −1.75890 −0.879451 0.475989i \(-0.842090\pi\)
−0.879451 + 0.475989i \(0.842090\pi\)
\(840\) 0 0
\(841\) 63.2785 2.18202
\(842\) 0 0
\(843\) −46.8208 −1.61259
\(844\) 0 0
\(845\) −49.1910 −1.69222
\(846\) 0 0
\(847\) 1.33371 0.0458270
\(848\) 0 0
\(849\) −87.0429 −2.98730
\(850\) 0 0
\(851\) −35.7546 −1.22565
\(852\) 0 0
\(853\) −56.3181 −1.92829 −0.964147 0.265370i \(-0.914506\pi\)
−0.964147 + 0.265370i \(0.914506\pi\)
\(854\) 0 0
\(855\) −38.1566 −1.30493
\(856\) 0 0
\(857\) 50.7152 1.73240 0.866199 0.499700i \(-0.166556\pi\)
0.866199 + 0.499700i \(0.166556\pi\)
\(858\) 0 0
\(859\) −49.1843 −1.67815 −0.839073 0.544018i \(-0.816902\pi\)
−0.839073 + 0.544018i \(0.816902\pi\)
\(860\) 0 0
\(861\) 19.9103 0.678541
\(862\) 0 0
\(863\) 33.3076 1.13380 0.566902 0.823786i \(-0.308142\pi\)
0.566902 + 0.823786i \(0.308142\pi\)
\(864\) 0 0
\(865\) −37.5845 −1.27791
\(866\) 0 0
\(867\) −108.421 −3.68218
\(868\) 0 0
\(869\) −33.8771 −1.14920
\(870\) 0 0
\(871\) 3.86759 0.131048
\(872\) 0 0
\(873\) 59.2863 2.00654
\(874\) 0 0
\(875\) −80.0103 −2.70484
\(876\) 0 0
\(877\) 32.6366 1.10206 0.551030 0.834486i \(-0.314235\pi\)
0.551030 + 0.834486i \(0.314235\pi\)
\(878\) 0 0
\(879\) −7.22482 −0.243687
\(880\) 0 0
\(881\) −8.33467 −0.280802 −0.140401 0.990095i \(-0.544839\pi\)
−0.140401 + 0.990095i \(0.544839\pi\)
\(882\) 0 0
\(883\) 44.1851 1.48695 0.743474 0.668765i \(-0.233177\pi\)
0.743474 + 0.668765i \(0.233177\pi\)
\(884\) 0 0
\(885\) 109.925 3.69509
\(886\) 0 0
\(887\) −24.0589 −0.807820 −0.403910 0.914799i \(-0.632349\pi\)
−0.403910 + 0.914799i \(0.632349\pi\)
\(888\) 0 0
\(889\) −30.2235 −1.01366
\(890\) 0 0
\(891\) 84.4680 2.82979
\(892\) 0 0
\(893\) −2.20053 −0.0736378
\(894\) 0 0
\(895\) −78.4314 −2.62167
\(896\) 0 0
\(897\) 11.0159 0.367811
\(898\) 0 0
\(899\) −34.2016 −1.14069
\(900\) 0 0
\(901\) 58.8183 1.95952
\(902\) 0 0
\(903\) −34.2263 −1.13898
\(904\) 0 0
\(905\) 47.3721 1.57470
\(906\) 0 0
\(907\) −30.5796 −1.01538 −0.507690 0.861540i \(-0.669500\pi\)
−0.507690 + 0.861540i \(0.669500\pi\)
\(908\) 0 0
\(909\) 75.5826 2.50692
\(910\) 0 0
\(911\) 31.0213 1.02778 0.513891 0.857855i \(-0.328203\pi\)
0.513891 + 0.857855i \(0.328203\pi\)
\(912\) 0 0
\(913\) −20.8826 −0.691113
\(914\) 0 0
\(915\) 67.3242 2.22567
\(916\) 0 0
\(917\) −48.0380 −1.58635
\(918\) 0 0
\(919\) −26.8679 −0.886289 −0.443144 0.896450i \(-0.646137\pi\)
−0.443144 + 0.896450i \(0.646137\pi\)
\(920\) 0 0
\(921\) 16.4481 0.541984
\(922\) 0 0
\(923\) 2.78582 0.0916962
\(924\) 0 0
\(925\) −92.7624 −3.05001
\(926\) 0 0
\(927\) 109.097 3.58323
\(928\) 0 0
\(929\) 9.41665 0.308950 0.154475 0.987997i \(-0.450631\pi\)
0.154475 + 0.987997i \(0.450631\pi\)
\(930\) 0 0
\(931\) −5.92975 −0.194340
\(932\) 0 0
\(933\) 88.4767 2.89660
\(934\) 0 0
\(935\) −92.0372 −3.00994
\(936\) 0 0
\(937\) −0.902024 −0.0294678 −0.0147339 0.999891i \(-0.504690\pi\)
−0.0147339 + 0.999891i \(0.504690\pi\)
\(938\) 0 0
\(939\) 7.22623 0.235819
\(940\) 0 0
\(941\) 16.2562 0.529938 0.264969 0.964257i \(-0.414638\pi\)
0.264969 + 0.964257i \(0.414638\pi\)
\(942\) 0 0
\(943\) 7.49073 0.243932
\(944\) 0 0
\(945\) 203.988 6.63573
\(946\) 0 0
\(947\) 5.47695 0.177977 0.0889885 0.996033i \(-0.471637\pi\)
0.0889885 + 0.996033i \(0.471637\pi\)
\(948\) 0 0
\(949\) −6.31676 −0.205051
\(950\) 0 0
\(951\) −72.1769 −2.34050
\(952\) 0 0
\(953\) 50.4670 1.63479 0.817393 0.576081i \(-0.195419\pi\)
0.817393 + 0.576081i \(0.195419\pi\)
\(954\) 0 0
\(955\) 86.0226 2.78362
\(956\) 0 0
\(957\) −101.863 −3.29276
\(958\) 0 0
\(959\) −45.4505 −1.46767
\(960\) 0 0
\(961\) −18.3237 −0.591088
\(962\) 0 0
\(963\) 127.031 4.09352
\(964\) 0 0
\(965\) 29.4177 0.946989
\(966\) 0 0
\(967\) −1.56488 −0.0503231 −0.0251616 0.999683i \(-0.508010\pi\)
−0.0251616 + 0.999683i \(0.508010\pi\)
\(968\) 0 0
\(969\) −29.1073 −0.935061
\(970\) 0 0
\(971\) 17.5450 0.563046 0.281523 0.959554i \(-0.409160\pi\)
0.281523 + 0.959554i \(0.409160\pi\)
\(972\) 0 0
\(973\) 24.3737 0.781386
\(974\) 0 0
\(975\) 28.5799 0.915291
\(976\) 0 0
\(977\) −5.09155 −0.162893 −0.0814466 0.996678i \(-0.525954\pi\)
−0.0814466 + 0.996678i \(0.525954\pi\)
\(978\) 0 0
\(979\) −0.306016 −0.00978032
\(980\) 0 0
\(981\) −81.5335 −2.60316
\(982\) 0 0
\(983\) 26.2053 0.835820 0.417910 0.908489i \(-0.362763\pi\)
0.417910 + 0.908489i \(0.362763\pi\)
\(984\) 0 0
\(985\) 15.7288 0.501160
\(986\) 0 0
\(987\) 19.4404 0.618794
\(988\) 0 0
\(989\) −12.8768 −0.409458
\(990\) 0 0
\(991\) −26.8396 −0.852588 −0.426294 0.904585i \(-0.640181\pi\)
−0.426294 + 0.904585i \(0.640181\pi\)
\(992\) 0 0
\(993\) −110.696 −3.51282
\(994\) 0 0
\(995\) 23.4391 0.743068
\(996\) 0 0
\(997\) 25.5246 0.808373 0.404187 0.914676i \(-0.367555\pi\)
0.404187 + 0.914676i \(0.367555\pi\)
\(998\) 0 0
\(999\) 127.721 4.04090
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 6008.2.a.b.1.2 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.2 44 1.1 even 1 trivial