Properties

Label 6008.2.a.b.1.36
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 1.36
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.67289 q^{3} +3.24936 q^{5} -2.55182 q^{7} -0.201452 q^{9} +O(q^{10})\) \(q+1.67289 q^{3} +3.24936 q^{5} -2.55182 q^{7} -0.201452 q^{9} -3.86634 q^{11} +4.77285 q^{13} +5.43581 q^{15} -7.34637 q^{17} +5.13856 q^{19} -4.26891 q^{21} -4.94464 q^{23} +5.55832 q^{25} -5.35566 q^{27} -0.579676 q^{29} -6.31968 q^{31} -6.46794 q^{33} -8.29178 q^{35} -7.52260 q^{37} +7.98443 q^{39} -7.67286 q^{41} -6.46398 q^{43} -0.654589 q^{45} -12.1946 q^{47} -0.488212 q^{49} -12.2896 q^{51} -2.15145 q^{53} -12.5631 q^{55} +8.59623 q^{57} +5.57924 q^{59} +2.81215 q^{61} +0.514069 q^{63} +15.5087 q^{65} +15.2590 q^{67} -8.27182 q^{69} +12.4025 q^{71} -1.40887 q^{73} +9.29844 q^{75} +9.86619 q^{77} -12.3648 q^{79} -8.35506 q^{81} +1.68284 q^{83} -23.8710 q^{85} -0.969732 q^{87} +15.0207 q^{89} -12.1794 q^{91} -10.5721 q^{93} +16.6970 q^{95} +5.00023 q^{97} +0.778880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.67289 0.965841 0.482921 0.875664i \(-0.339576\pi\)
0.482921 + 0.875664i \(0.339576\pi\)
\(4\) 0 0
\(5\) 3.24936 1.45316 0.726578 0.687084i \(-0.241109\pi\)
0.726578 + 0.687084i \(0.241109\pi\)
\(6\) 0 0
\(7\) −2.55182 −0.964497 −0.482249 0.876034i \(-0.660180\pi\)
−0.482249 + 0.876034i \(0.660180\pi\)
\(8\) 0 0
\(9\) −0.201452 −0.0671506
\(10\) 0 0
\(11\) −3.86634 −1.16574 −0.582872 0.812564i \(-0.698071\pi\)
−0.582872 + 0.812564i \(0.698071\pi\)
\(12\) 0 0
\(13\) 4.77285 1.32375 0.661875 0.749614i \(-0.269761\pi\)
0.661875 + 0.749614i \(0.269761\pi\)
\(14\) 0 0
\(15\) 5.43581 1.40352
\(16\) 0 0
\(17\) −7.34637 −1.78176 −0.890878 0.454243i \(-0.849910\pi\)
−0.890878 + 0.454243i \(0.849910\pi\)
\(18\) 0 0
\(19\) 5.13856 1.17887 0.589433 0.807817i \(-0.299351\pi\)
0.589433 + 0.807817i \(0.299351\pi\)
\(20\) 0 0
\(21\) −4.26891 −0.931551
\(22\) 0 0
\(23\) −4.94464 −1.03103 −0.515514 0.856881i \(-0.672399\pi\)
−0.515514 + 0.856881i \(0.672399\pi\)
\(24\) 0 0
\(25\) 5.55832 1.11166
\(26\) 0 0
\(27\) −5.35566 −1.03070
\(28\) 0 0
\(29\) −0.579676 −0.107643 −0.0538216 0.998551i \(-0.517140\pi\)
−0.0538216 + 0.998551i \(0.517140\pi\)
\(30\) 0 0
\(31\) −6.31968 −1.13505 −0.567524 0.823357i \(-0.692099\pi\)
−0.567524 + 0.823357i \(0.692099\pi\)
\(32\) 0 0
\(33\) −6.46794 −1.12592
\(34\) 0 0
\(35\) −8.29178 −1.40157
\(36\) 0 0
\(37\) −7.52260 −1.23671 −0.618354 0.785900i \(-0.712200\pi\)
−0.618354 + 0.785900i \(0.712200\pi\)
\(38\) 0 0
\(39\) 7.98443 1.27853
\(40\) 0 0
\(41\) −7.67286 −1.19830 −0.599150 0.800637i \(-0.704495\pi\)
−0.599150 + 0.800637i \(0.704495\pi\)
\(42\) 0 0
\(43\) −6.46398 −0.985747 −0.492874 0.870101i \(-0.664054\pi\)
−0.492874 + 0.870101i \(0.664054\pi\)
\(44\) 0 0
\(45\) −0.654589 −0.0975804
\(46\) 0 0
\(47\) −12.1946 −1.77876 −0.889380 0.457169i \(-0.848863\pi\)
−0.889380 + 0.457169i \(0.848863\pi\)
\(48\) 0 0
\(49\) −0.488212 −0.0697446
\(50\) 0 0
\(51\) −12.2896 −1.72089
\(52\) 0 0
\(53\) −2.15145 −0.295524 −0.147762 0.989023i \(-0.547207\pi\)
−0.147762 + 0.989023i \(0.547207\pi\)
\(54\) 0 0
\(55\) −12.5631 −1.69401
\(56\) 0 0
\(57\) 8.59623 1.13860
\(58\) 0 0
\(59\) 5.57924 0.726356 0.363178 0.931720i \(-0.381692\pi\)
0.363178 + 0.931720i \(0.381692\pi\)
\(60\) 0 0
\(61\) 2.81215 0.360058 0.180029 0.983661i \(-0.442381\pi\)
0.180029 + 0.983661i \(0.442381\pi\)
\(62\) 0 0
\(63\) 0.514069 0.0647666
\(64\) 0 0
\(65\) 15.5087 1.92362
\(66\) 0 0
\(67\) 15.2590 1.86419 0.932094 0.362215i \(-0.117980\pi\)
0.932094 + 0.362215i \(0.117980\pi\)
\(68\) 0 0
\(69\) −8.27182 −0.995810
\(70\) 0 0
\(71\) 12.4025 1.47191 0.735953 0.677033i \(-0.236735\pi\)
0.735953 + 0.677033i \(0.236735\pi\)
\(72\) 0 0
\(73\) −1.40887 −0.164895 −0.0824477 0.996595i \(-0.526274\pi\)
−0.0824477 + 0.996595i \(0.526274\pi\)
\(74\) 0 0
\(75\) 9.29844 1.07369
\(76\) 0 0
\(77\) 9.86619 1.12436
\(78\) 0 0
\(79\) −12.3648 −1.39115 −0.695574 0.718455i \(-0.744850\pi\)
−0.695574 + 0.718455i \(0.744850\pi\)
\(80\) 0 0
\(81\) −8.35506 −0.928340
\(82\) 0 0
\(83\) 1.68284 0.184716 0.0923579 0.995726i \(-0.470560\pi\)
0.0923579 + 0.995726i \(0.470560\pi\)
\(84\) 0 0
\(85\) −23.8710 −2.58917
\(86\) 0 0
\(87\) −0.969732 −0.103966
\(88\) 0 0
\(89\) 15.0207 1.59219 0.796095 0.605172i \(-0.206896\pi\)
0.796095 + 0.605172i \(0.206896\pi\)
\(90\) 0 0
\(91\) −12.1794 −1.27675
\(92\) 0 0
\(93\) −10.5721 −1.09628
\(94\) 0 0
\(95\) 16.6970 1.71308
\(96\) 0 0
\(97\) 5.00023 0.507697 0.253848 0.967244i \(-0.418304\pi\)
0.253848 + 0.967244i \(0.418304\pi\)
\(98\) 0 0
\(99\) 0.778880 0.0782804
\(100\) 0 0
\(101\) 16.4546 1.63730 0.818649 0.574295i \(-0.194724\pi\)
0.818649 + 0.574295i \(0.194724\pi\)
\(102\) 0 0
\(103\) −14.7144 −1.44985 −0.724926 0.688827i \(-0.758126\pi\)
−0.724926 + 0.688827i \(0.758126\pi\)
\(104\) 0 0
\(105\) −13.8712 −1.35369
\(106\) 0 0
\(107\) −16.9464 −1.63827 −0.819136 0.573600i \(-0.805547\pi\)
−0.819136 + 0.573600i \(0.805547\pi\)
\(108\) 0 0
\(109\) 11.9858 1.14803 0.574015 0.818845i \(-0.305385\pi\)
0.574015 + 0.818845i \(0.305385\pi\)
\(110\) 0 0
\(111\) −12.5845 −1.19446
\(112\) 0 0
\(113\) 12.1742 1.14525 0.572625 0.819817i \(-0.305925\pi\)
0.572625 + 0.819817i \(0.305925\pi\)
\(114\) 0 0
\(115\) −16.0669 −1.49825
\(116\) 0 0
\(117\) −0.961499 −0.0888906
\(118\) 0 0
\(119\) 18.7466 1.71850
\(120\) 0 0
\(121\) 3.94855 0.358959
\(122\) 0 0
\(123\) −12.8358 −1.15737
\(124\) 0 0
\(125\) 1.81419 0.162266
\(126\) 0 0
\(127\) 2.93088 0.260073 0.130037 0.991509i \(-0.458490\pi\)
0.130037 + 0.991509i \(0.458490\pi\)
\(128\) 0 0
\(129\) −10.8135 −0.952076
\(130\) 0 0
\(131\) 8.44438 0.737789 0.368895 0.929471i \(-0.379736\pi\)
0.368895 + 0.929471i \(0.379736\pi\)
\(132\) 0 0
\(133\) −13.1127 −1.13701
\(134\) 0 0
\(135\) −17.4025 −1.49777
\(136\) 0 0
\(137\) 7.31259 0.624756 0.312378 0.949958i \(-0.398874\pi\)
0.312378 + 0.949958i \(0.398874\pi\)
\(138\) 0 0
\(139\) −19.1762 −1.62650 −0.813251 0.581913i \(-0.802305\pi\)
−0.813251 + 0.581913i \(0.802305\pi\)
\(140\) 0 0
\(141\) −20.4001 −1.71800
\(142\) 0 0
\(143\) −18.4534 −1.54315
\(144\) 0 0
\(145\) −1.88357 −0.156422
\(146\) 0 0
\(147\) −0.816723 −0.0673622
\(148\) 0 0
\(149\) 17.5058 1.43413 0.717067 0.697004i \(-0.245484\pi\)
0.717067 + 0.697004i \(0.245484\pi\)
\(150\) 0 0
\(151\) −15.4411 −1.25658 −0.628291 0.777979i \(-0.716245\pi\)
−0.628291 + 0.777979i \(0.716245\pi\)
\(152\) 0 0
\(153\) 1.47994 0.119646
\(154\) 0 0
\(155\) −20.5349 −1.64940
\(156\) 0 0
\(157\) −6.55771 −0.523362 −0.261681 0.965154i \(-0.584277\pi\)
−0.261681 + 0.965154i \(0.584277\pi\)
\(158\) 0 0
\(159\) −3.59913 −0.285429
\(160\) 0 0
\(161\) 12.6178 0.994425
\(162\) 0 0
\(163\) −9.81113 −0.768467 −0.384234 0.923236i \(-0.625534\pi\)
−0.384234 + 0.923236i \(0.625534\pi\)
\(164\) 0 0
\(165\) −21.0166 −1.63614
\(166\) 0 0
\(167\) 2.47178 0.191272 0.0956359 0.995416i \(-0.469512\pi\)
0.0956359 + 0.995416i \(0.469512\pi\)
\(168\) 0 0
\(169\) 9.78007 0.752313
\(170\) 0 0
\(171\) −1.03517 −0.0791616
\(172\) 0 0
\(173\) 0.144954 0.0110206 0.00551031 0.999985i \(-0.498246\pi\)
0.00551031 + 0.999985i \(0.498246\pi\)
\(174\) 0 0
\(175\) −14.1838 −1.07220
\(176\) 0 0
\(177\) 9.33344 0.701544
\(178\) 0 0
\(179\) 0.265766 0.0198643 0.00993214 0.999951i \(-0.496838\pi\)
0.00993214 + 0.999951i \(0.496838\pi\)
\(180\) 0 0
\(181\) −16.2296 −1.20634 −0.603169 0.797613i \(-0.706096\pi\)
−0.603169 + 0.797613i \(0.706096\pi\)
\(182\) 0 0
\(183\) 4.70440 0.347759
\(184\) 0 0
\(185\) −24.4436 −1.79713
\(186\) 0 0
\(187\) 28.4035 2.07707
\(188\) 0 0
\(189\) 13.6667 0.994106
\(190\) 0 0
\(191\) 16.1429 1.16806 0.584030 0.811732i \(-0.301475\pi\)
0.584030 + 0.811732i \(0.301475\pi\)
\(192\) 0 0
\(193\) 5.60406 0.403389 0.201694 0.979448i \(-0.435355\pi\)
0.201694 + 0.979448i \(0.435355\pi\)
\(194\) 0 0
\(195\) 25.9443 1.85791
\(196\) 0 0
\(197\) 18.7095 1.33300 0.666498 0.745507i \(-0.267793\pi\)
0.666498 + 0.745507i \(0.267793\pi\)
\(198\) 0 0
\(199\) 8.35159 0.592029 0.296014 0.955183i \(-0.404342\pi\)
0.296014 + 0.955183i \(0.404342\pi\)
\(200\) 0 0
\(201\) 25.5266 1.80051
\(202\) 0 0
\(203\) 1.47923 0.103822
\(204\) 0 0
\(205\) −24.9319 −1.74132
\(206\) 0 0
\(207\) 0.996107 0.0692342
\(208\) 0 0
\(209\) −19.8674 −1.37426
\(210\) 0 0
\(211\) 25.7042 1.76955 0.884777 0.466015i \(-0.154311\pi\)
0.884777 + 0.466015i \(0.154311\pi\)
\(212\) 0 0
\(213\) 20.7480 1.42163
\(214\) 0 0
\(215\) −21.0038 −1.43245
\(216\) 0 0
\(217\) 16.1267 1.09475
\(218\) 0 0
\(219\) −2.35687 −0.159263
\(220\) 0 0
\(221\) −35.0631 −2.35860
\(222\) 0 0
\(223\) −24.7287 −1.65596 −0.827979 0.560759i \(-0.810509\pi\)
−0.827979 + 0.560759i \(0.810509\pi\)
\(224\) 0 0
\(225\) −1.11973 −0.0746490
\(226\) 0 0
\(227\) −11.8321 −0.785326 −0.392663 0.919682i \(-0.628446\pi\)
−0.392663 + 0.919682i \(0.628446\pi\)
\(228\) 0 0
\(229\) −5.19219 −0.343110 −0.171555 0.985175i \(-0.554879\pi\)
−0.171555 + 0.985175i \(0.554879\pi\)
\(230\) 0 0
\(231\) 16.5050 1.08595
\(232\) 0 0
\(233\) 2.17352 0.142392 0.0711959 0.997462i \(-0.477318\pi\)
0.0711959 + 0.997462i \(0.477318\pi\)
\(234\) 0 0
\(235\) −39.6245 −2.58482
\(236\) 0 0
\(237\) −20.6849 −1.34363
\(238\) 0 0
\(239\) 12.0873 0.781860 0.390930 0.920420i \(-0.372153\pi\)
0.390930 + 0.920420i \(0.372153\pi\)
\(240\) 0 0
\(241\) −11.0591 −0.712378 −0.356189 0.934414i \(-0.615924\pi\)
−0.356189 + 0.934414i \(0.615924\pi\)
\(242\) 0 0
\(243\) 2.08993 0.134069
\(244\) 0 0
\(245\) −1.58638 −0.101350
\(246\) 0 0
\(247\) 24.5256 1.56052
\(248\) 0 0
\(249\) 2.81520 0.178406
\(250\) 0 0
\(251\) 14.2693 0.900669 0.450335 0.892860i \(-0.351305\pi\)
0.450335 + 0.892860i \(0.351305\pi\)
\(252\) 0 0
\(253\) 19.1176 1.20192
\(254\) 0 0
\(255\) −39.9334 −2.50073
\(256\) 0 0
\(257\) −7.83668 −0.488839 −0.244419 0.969670i \(-0.578597\pi\)
−0.244419 + 0.969670i \(0.578597\pi\)
\(258\) 0 0
\(259\) 19.1963 1.19280
\(260\) 0 0
\(261\) 0.116777 0.00722830
\(262\) 0 0
\(263\) −18.3948 −1.13427 −0.567135 0.823625i \(-0.691948\pi\)
−0.567135 + 0.823625i \(0.691948\pi\)
\(264\) 0 0
\(265\) −6.99082 −0.429443
\(266\) 0 0
\(267\) 25.1279 1.53780
\(268\) 0 0
\(269\) −5.11081 −0.311612 −0.155806 0.987788i \(-0.549797\pi\)
−0.155806 + 0.987788i \(0.549797\pi\)
\(270\) 0 0
\(271\) 19.2724 1.17072 0.585358 0.810775i \(-0.300954\pi\)
0.585358 + 0.810775i \(0.300954\pi\)
\(272\) 0 0
\(273\) −20.3748 −1.23314
\(274\) 0 0
\(275\) −21.4903 −1.29592
\(276\) 0 0
\(277\) −32.5523 −1.95588 −0.977939 0.208890i \(-0.933015\pi\)
−0.977939 + 0.208890i \(0.933015\pi\)
\(278\) 0 0
\(279\) 1.27311 0.0762192
\(280\) 0 0
\(281\) −10.5395 −0.628737 −0.314368 0.949301i \(-0.601793\pi\)
−0.314368 + 0.949301i \(0.601793\pi\)
\(282\) 0 0
\(283\) −18.0435 −1.07257 −0.536287 0.844036i \(-0.680173\pi\)
−0.536287 + 0.844036i \(0.680173\pi\)
\(284\) 0 0
\(285\) 27.9322 1.65456
\(286\) 0 0
\(287\) 19.5798 1.15576
\(288\) 0 0
\(289\) 36.9691 2.17465
\(290\) 0 0
\(291\) 8.36482 0.490354
\(292\) 0 0
\(293\) −29.1173 −1.70105 −0.850524 0.525936i \(-0.823715\pi\)
−0.850524 + 0.525936i \(0.823715\pi\)
\(294\) 0 0
\(295\) 18.1290 1.05551
\(296\) 0 0
\(297\) 20.7068 1.20153
\(298\) 0 0
\(299\) −23.6000 −1.36482
\(300\) 0 0
\(301\) 16.4949 0.950751
\(302\) 0 0
\(303\) 27.5267 1.58137
\(304\) 0 0
\(305\) 9.13767 0.523221
\(306\) 0 0
\(307\) −1.88567 −0.107621 −0.0538105 0.998551i \(-0.517137\pi\)
−0.0538105 + 0.998551i \(0.517137\pi\)
\(308\) 0 0
\(309\) −24.6155 −1.40033
\(310\) 0 0
\(311\) −26.4793 −1.50150 −0.750750 0.660586i \(-0.770308\pi\)
−0.750750 + 0.660586i \(0.770308\pi\)
\(312\) 0 0
\(313\) −17.9790 −1.01623 −0.508116 0.861289i \(-0.669658\pi\)
−0.508116 + 0.861289i \(0.669658\pi\)
\(314\) 0 0
\(315\) 1.67039 0.0941160
\(316\) 0 0
\(317\) 17.4857 0.982094 0.491047 0.871133i \(-0.336614\pi\)
0.491047 + 0.871133i \(0.336614\pi\)
\(318\) 0 0
\(319\) 2.24122 0.125484
\(320\) 0 0
\(321\) −28.3494 −1.58231
\(322\) 0 0
\(323\) −37.7498 −2.10045
\(324\) 0 0
\(325\) 26.5290 1.47157
\(326\) 0 0
\(327\) 20.0509 1.10881
\(328\) 0 0
\(329\) 31.1183 1.71561
\(330\) 0 0
\(331\) −22.1630 −1.21819 −0.609093 0.793099i \(-0.708466\pi\)
−0.609093 + 0.793099i \(0.708466\pi\)
\(332\) 0 0
\(333\) 1.51544 0.0830457
\(334\) 0 0
\(335\) 49.5821 2.70896
\(336\) 0 0
\(337\) 13.2710 0.722917 0.361459 0.932388i \(-0.382279\pi\)
0.361459 + 0.932388i \(0.382279\pi\)
\(338\) 0 0
\(339\) 20.3660 1.10613
\(340\) 0 0
\(341\) 24.4340 1.32318
\(342\) 0 0
\(343\) 19.1086 1.03177
\(344\) 0 0
\(345\) −26.8781 −1.44707
\(346\) 0 0
\(347\) 5.00182 0.268512 0.134256 0.990947i \(-0.457136\pi\)
0.134256 + 0.990947i \(0.457136\pi\)
\(348\) 0 0
\(349\) −13.6624 −0.731334 −0.365667 0.930746i \(-0.619159\pi\)
−0.365667 + 0.930746i \(0.619159\pi\)
\(350\) 0 0
\(351\) −25.5618 −1.36439
\(352\) 0 0
\(353\) 0.383286 0.0204002 0.0102001 0.999948i \(-0.496753\pi\)
0.0102001 + 0.999948i \(0.496753\pi\)
\(354\) 0 0
\(355\) 40.3001 2.13891
\(356\) 0 0
\(357\) 31.3609 1.65980
\(358\) 0 0
\(359\) −2.89299 −0.152686 −0.0763430 0.997082i \(-0.524324\pi\)
−0.0763430 + 0.997082i \(0.524324\pi\)
\(360\) 0 0
\(361\) 7.40480 0.389726
\(362\) 0 0
\(363\) 6.60547 0.346698
\(364\) 0 0
\(365\) −4.57791 −0.239619
\(366\) 0 0
\(367\) 3.36998 0.175912 0.0879558 0.996124i \(-0.471967\pi\)
0.0879558 + 0.996124i \(0.471967\pi\)
\(368\) 0 0
\(369\) 1.54571 0.0804666
\(370\) 0 0
\(371\) 5.49011 0.285032
\(372\) 0 0
\(373\) −7.43334 −0.384884 −0.192442 0.981308i \(-0.561641\pi\)
−0.192442 + 0.981308i \(0.561641\pi\)
\(374\) 0 0
\(375\) 3.03494 0.156724
\(376\) 0 0
\(377\) −2.76671 −0.142493
\(378\) 0 0
\(379\) −3.45621 −0.177534 −0.0887669 0.996052i \(-0.528293\pi\)
−0.0887669 + 0.996052i \(0.528293\pi\)
\(380\) 0 0
\(381\) 4.90303 0.251190
\(382\) 0 0
\(383\) 17.0652 0.871990 0.435995 0.899949i \(-0.356397\pi\)
0.435995 + 0.899949i \(0.356397\pi\)
\(384\) 0 0
\(385\) 32.0588 1.63387
\(386\) 0 0
\(387\) 1.30218 0.0661935
\(388\) 0 0
\(389\) 26.2792 1.33241 0.666204 0.745769i \(-0.267918\pi\)
0.666204 + 0.745769i \(0.267918\pi\)
\(390\) 0 0
\(391\) 36.3251 1.83704
\(392\) 0 0
\(393\) 14.1265 0.712587
\(394\) 0 0
\(395\) −40.1776 −2.02156
\(396\) 0 0
\(397\) −2.25105 −0.112977 −0.0564884 0.998403i \(-0.517990\pi\)
−0.0564884 + 0.998403i \(0.517990\pi\)
\(398\) 0 0
\(399\) −21.9360 −1.09817
\(400\) 0 0
\(401\) −2.97404 −0.148517 −0.0742583 0.997239i \(-0.523659\pi\)
−0.0742583 + 0.997239i \(0.523659\pi\)
\(402\) 0 0
\(403\) −30.1629 −1.50252
\(404\) 0 0
\(405\) −27.1486 −1.34902
\(406\) 0 0
\(407\) 29.0849 1.44168
\(408\) 0 0
\(409\) 17.3041 0.855631 0.427816 0.903866i \(-0.359283\pi\)
0.427816 + 0.903866i \(0.359283\pi\)
\(410\) 0 0
\(411\) 12.2331 0.603415
\(412\) 0 0
\(413\) −14.2372 −0.700568
\(414\) 0 0
\(415\) 5.46815 0.268421
\(416\) 0 0
\(417\) −32.0796 −1.57094
\(418\) 0 0
\(419\) −25.2643 −1.23424 −0.617120 0.786869i \(-0.711701\pi\)
−0.617120 + 0.786869i \(0.711701\pi\)
\(420\) 0 0
\(421\) 29.5621 1.44077 0.720385 0.693574i \(-0.243965\pi\)
0.720385 + 0.693574i \(0.243965\pi\)
\(422\) 0 0
\(423\) 2.45662 0.119445
\(424\) 0 0
\(425\) −40.8335 −1.98072
\(426\) 0 0
\(427\) −7.17609 −0.347275
\(428\) 0 0
\(429\) −30.8705 −1.49044
\(430\) 0 0
\(431\) 41.0232 1.97602 0.988009 0.154399i \(-0.0493440\pi\)
0.988009 + 0.154399i \(0.0493440\pi\)
\(432\) 0 0
\(433\) −37.3663 −1.79571 −0.897855 0.440291i \(-0.854875\pi\)
−0.897855 + 0.440291i \(0.854875\pi\)
\(434\) 0 0
\(435\) −3.15101 −0.151079
\(436\) 0 0
\(437\) −25.4083 −1.21545
\(438\) 0 0
\(439\) −13.7981 −0.658547 −0.329273 0.944235i \(-0.606804\pi\)
−0.329273 + 0.944235i \(0.606804\pi\)
\(440\) 0 0
\(441\) 0.0983512 0.00468339
\(442\) 0 0
\(443\) −6.29465 −0.299068 −0.149534 0.988757i \(-0.547777\pi\)
−0.149534 + 0.988757i \(0.547777\pi\)
\(444\) 0 0
\(445\) 48.8076 2.31370
\(446\) 0 0
\(447\) 29.2853 1.38515
\(448\) 0 0
\(449\) 13.6628 0.644786 0.322393 0.946606i \(-0.395513\pi\)
0.322393 + 0.946606i \(0.395513\pi\)
\(450\) 0 0
\(451\) 29.6659 1.39691
\(452\) 0 0
\(453\) −25.8313 −1.21366
\(454\) 0 0
\(455\) −39.5754 −1.85532
\(456\) 0 0
\(457\) −11.2587 −0.526661 −0.263330 0.964706i \(-0.584821\pi\)
−0.263330 + 0.964706i \(0.584821\pi\)
\(458\) 0 0
\(459\) 39.3447 1.83645
\(460\) 0 0
\(461\) −27.9452 −1.30154 −0.650769 0.759276i \(-0.725553\pi\)
−0.650769 + 0.759276i \(0.725553\pi\)
\(462\) 0 0
\(463\) 19.8264 0.921413 0.460707 0.887552i \(-0.347596\pi\)
0.460707 + 0.887552i \(0.347596\pi\)
\(464\) 0 0
\(465\) −34.3526 −1.59306
\(466\) 0 0
\(467\) 13.6220 0.630352 0.315176 0.949033i \(-0.397936\pi\)
0.315176 + 0.949033i \(0.397936\pi\)
\(468\) 0 0
\(469\) −38.9383 −1.79801
\(470\) 0 0
\(471\) −10.9703 −0.505485
\(472\) 0 0
\(473\) 24.9919 1.14913
\(474\) 0 0
\(475\) 28.5618 1.31050
\(476\) 0 0
\(477\) 0.433413 0.0198446
\(478\) 0 0
\(479\) −5.39842 −0.246660 −0.123330 0.992366i \(-0.539357\pi\)
−0.123330 + 0.992366i \(0.539357\pi\)
\(480\) 0 0
\(481\) −35.9042 −1.63709
\(482\) 0 0
\(483\) 21.1082 0.960456
\(484\) 0 0
\(485\) 16.2475 0.737763
\(486\) 0 0
\(487\) −5.54090 −0.251082 −0.125541 0.992088i \(-0.540067\pi\)
−0.125541 + 0.992088i \(0.540067\pi\)
\(488\) 0 0
\(489\) −16.4129 −0.742217
\(490\) 0 0
\(491\) −14.4848 −0.653691 −0.326846 0.945078i \(-0.605986\pi\)
−0.326846 + 0.945078i \(0.605986\pi\)
\(492\) 0 0
\(493\) 4.25851 0.191794
\(494\) 0 0
\(495\) 2.53086 0.113754
\(496\) 0 0
\(497\) −31.6489 −1.41965
\(498\) 0 0
\(499\) 23.7664 1.06393 0.531964 0.846767i \(-0.321454\pi\)
0.531964 + 0.846767i \(0.321454\pi\)
\(500\) 0 0
\(501\) 4.13500 0.184738
\(502\) 0 0
\(503\) 7.53623 0.336024 0.168012 0.985785i \(-0.446265\pi\)
0.168012 + 0.985785i \(0.446265\pi\)
\(504\) 0 0
\(505\) 53.4670 2.37925
\(506\) 0 0
\(507\) 16.3609 0.726615
\(508\) 0 0
\(509\) 28.0122 1.24162 0.620810 0.783961i \(-0.286804\pi\)
0.620810 + 0.783961i \(0.286804\pi\)
\(510\) 0 0
\(511\) 3.59518 0.159041
\(512\) 0 0
\(513\) −27.5204 −1.21506
\(514\) 0 0
\(515\) −47.8123 −2.10686
\(516\) 0 0
\(517\) 47.1483 2.07358
\(518\) 0 0
\(519\) 0.242491 0.0106442
\(520\) 0 0
\(521\) 27.2359 1.19322 0.596612 0.802530i \(-0.296513\pi\)
0.596612 + 0.802530i \(0.296513\pi\)
\(522\) 0 0
\(523\) −40.5393 −1.77266 −0.886329 0.463056i \(-0.846753\pi\)
−0.886329 + 0.463056i \(0.846753\pi\)
\(524\) 0 0
\(525\) −23.7280 −1.03557
\(526\) 0 0
\(527\) 46.4267 2.02238
\(528\) 0 0
\(529\) 1.44947 0.0630202
\(530\) 0 0
\(531\) −1.12395 −0.0487752
\(532\) 0 0
\(533\) −36.6214 −1.58625
\(534\) 0 0
\(535\) −55.0650 −2.38067
\(536\) 0 0
\(537\) 0.444596 0.0191857
\(538\) 0 0
\(539\) 1.88759 0.0813043
\(540\) 0 0
\(541\) −8.28092 −0.356025 −0.178012 0.984028i \(-0.556967\pi\)
−0.178012 + 0.984028i \(0.556967\pi\)
\(542\) 0 0
\(543\) −27.1503 −1.16513
\(544\) 0 0
\(545\) 38.9461 1.66827
\(546\) 0 0
\(547\) −24.4071 −1.04357 −0.521787 0.853076i \(-0.674734\pi\)
−0.521787 + 0.853076i \(0.674734\pi\)
\(548\) 0 0
\(549\) −0.566512 −0.0241781
\(550\) 0 0
\(551\) −2.97870 −0.126897
\(552\) 0 0
\(553\) 31.5527 1.34176
\(554\) 0 0
\(555\) −40.8914 −1.73574
\(556\) 0 0
\(557\) 16.8420 0.713620 0.356810 0.934177i \(-0.383864\pi\)
0.356810 + 0.934177i \(0.383864\pi\)
\(558\) 0 0
\(559\) −30.8516 −1.30488
\(560\) 0 0
\(561\) 47.5159 2.00612
\(562\) 0 0
\(563\) −22.0365 −0.928727 −0.464364 0.885645i \(-0.653717\pi\)
−0.464364 + 0.885645i \(0.653717\pi\)
\(564\) 0 0
\(565\) 39.5582 1.66423
\(566\) 0 0
\(567\) 21.3206 0.895382
\(568\) 0 0
\(569\) −2.60335 −0.109138 −0.0545690 0.998510i \(-0.517378\pi\)
−0.0545690 + 0.998510i \(0.517378\pi\)
\(570\) 0 0
\(571\) 12.5814 0.526514 0.263257 0.964726i \(-0.415203\pi\)
0.263257 + 0.964726i \(0.415203\pi\)
\(572\) 0 0
\(573\) 27.0053 1.12816
\(574\) 0 0
\(575\) −27.4839 −1.14616
\(576\) 0 0
\(577\) 23.4115 0.974632 0.487316 0.873226i \(-0.337976\pi\)
0.487316 + 0.873226i \(0.337976\pi\)
\(578\) 0 0
\(579\) 9.37495 0.389610
\(580\) 0 0
\(581\) −4.29431 −0.178158
\(582\) 0 0
\(583\) 8.31822 0.344505
\(584\) 0 0
\(585\) −3.12425 −0.129172
\(586\) 0 0
\(587\) −7.26892 −0.300020 −0.150010 0.988684i \(-0.547931\pi\)
−0.150010 + 0.988684i \(0.547931\pi\)
\(588\) 0 0
\(589\) −32.4741 −1.33807
\(590\) 0 0
\(591\) 31.2988 1.28746
\(592\) 0 0
\(593\) −10.6941 −0.439154 −0.219577 0.975595i \(-0.570468\pi\)
−0.219577 + 0.975595i \(0.570468\pi\)
\(594\) 0 0
\(595\) 60.9144 2.49725
\(596\) 0 0
\(597\) 13.9713 0.571806
\(598\) 0 0
\(599\) 7.20414 0.294353 0.147177 0.989110i \(-0.452981\pi\)
0.147177 + 0.989110i \(0.452981\pi\)
\(600\) 0 0
\(601\) −4.23602 −0.172791 −0.0863954 0.996261i \(-0.527535\pi\)
−0.0863954 + 0.996261i \(0.527535\pi\)
\(602\) 0 0
\(603\) −3.07396 −0.125181
\(604\) 0 0
\(605\) 12.8303 0.521624
\(606\) 0 0
\(607\) −9.40480 −0.381729 −0.190865 0.981616i \(-0.561129\pi\)
−0.190865 + 0.981616i \(0.561129\pi\)
\(608\) 0 0
\(609\) 2.47458 0.100275
\(610\) 0 0
\(611\) −58.2028 −2.35463
\(612\) 0 0
\(613\) 14.1068 0.569768 0.284884 0.958562i \(-0.408045\pi\)
0.284884 + 0.958562i \(0.408045\pi\)
\(614\) 0 0
\(615\) −41.7082 −1.68184
\(616\) 0 0
\(617\) 24.4239 0.983271 0.491635 0.870801i \(-0.336399\pi\)
0.491635 + 0.870801i \(0.336399\pi\)
\(618\) 0 0
\(619\) −18.6508 −0.749640 −0.374820 0.927098i \(-0.622295\pi\)
−0.374820 + 0.927098i \(0.622295\pi\)
\(620\) 0 0
\(621\) 26.4818 1.06268
\(622\) 0 0
\(623\) −38.3301 −1.53566
\(624\) 0 0
\(625\) −21.8967 −0.875866
\(626\) 0 0
\(627\) −33.2359 −1.32731
\(628\) 0 0
\(629\) 55.2638 2.20351
\(630\) 0 0
\(631\) −45.6512 −1.81735 −0.908674 0.417507i \(-0.862904\pi\)
−0.908674 + 0.417507i \(0.862904\pi\)
\(632\) 0 0
\(633\) 43.0003 1.70911
\(634\) 0 0
\(635\) 9.52347 0.377927
\(636\) 0 0
\(637\) −2.33016 −0.0923244
\(638\) 0 0
\(639\) −2.49850 −0.0988393
\(640\) 0 0
\(641\) −3.68608 −0.145592 −0.0727958 0.997347i \(-0.523192\pi\)
−0.0727958 + 0.997347i \(0.523192\pi\)
\(642\) 0 0
\(643\) −37.6364 −1.48423 −0.742117 0.670270i \(-0.766178\pi\)
−0.742117 + 0.670270i \(0.766178\pi\)
\(644\) 0 0
\(645\) −35.1369 −1.38352
\(646\) 0 0
\(647\) −49.2705 −1.93702 −0.968511 0.248971i \(-0.919908\pi\)
−0.968511 + 0.248971i \(0.919908\pi\)
\(648\) 0 0
\(649\) −21.5712 −0.846745
\(650\) 0 0
\(651\) 26.9781 1.05736
\(652\) 0 0
\(653\) 9.86159 0.385914 0.192957 0.981207i \(-0.438192\pi\)
0.192957 + 0.981207i \(0.438192\pi\)
\(654\) 0 0
\(655\) 27.4388 1.07212
\(656\) 0 0
\(657\) 0.283819 0.0110728
\(658\) 0 0
\(659\) 31.9293 1.24379 0.621895 0.783101i \(-0.286363\pi\)
0.621895 + 0.783101i \(0.286363\pi\)
\(660\) 0 0
\(661\) −18.6107 −0.723874 −0.361937 0.932203i \(-0.617884\pi\)
−0.361937 + 0.932203i \(0.617884\pi\)
\(662\) 0 0
\(663\) −58.6566 −2.27803
\(664\) 0 0
\(665\) −42.6078 −1.65226
\(666\) 0 0
\(667\) 2.86629 0.110983
\(668\) 0 0
\(669\) −41.3683 −1.59939
\(670\) 0 0
\(671\) −10.8727 −0.419736
\(672\) 0 0
\(673\) −13.4646 −0.519021 −0.259510 0.965740i \(-0.583561\pi\)
−0.259510 + 0.965740i \(0.583561\pi\)
\(674\) 0 0
\(675\) −29.7685 −1.14579
\(676\) 0 0
\(677\) −29.3630 −1.12851 −0.564257 0.825599i \(-0.690837\pi\)
−0.564257 + 0.825599i \(0.690837\pi\)
\(678\) 0 0
\(679\) −12.7597 −0.489672
\(680\) 0 0
\(681\) −19.7938 −0.758500
\(682\) 0 0
\(683\) −2.74895 −0.105186 −0.0525929 0.998616i \(-0.516749\pi\)
−0.0525929 + 0.998616i \(0.516749\pi\)
\(684\) 0 0
\(685\) 23.7612 0.907869
\(686\) 0 0
\(687\) −8.68595 −0.331390
\(688\) 0 0
\(689\) −10.2685 −0.391200
\(690\) 0 0
\(691\) −34.0741 −1.29624 −0.648119 0.761539i \(-0.724444\pi\)
−0.648119 + 0.761539i \(0.724444\pi\)
\(692\) 0 0
\(693\) −1.98756 −0.0755013
\(694\) 0 0
\(695\) −62.3103 −2.36356
\(696\) 0 0
\(697\) 56.3677 2.13508
\(698\) 0 0
\(699\) 3.63605 0.137528
\(700\) 0 0
\(701\) 11.0186 0.416165 0.208083 0.978111i \(-0.433278\pi\)
0.208083 + 0.978111i \(0.433278\pi\)
\(702\) 0 0
\(703\) −38.6553 −1.45791
\(704\) 0 0
\(705\) −66.2873 −2.49652
\(706\) 0 0
\(707\) −41.9893 −1.57917
\(708\) 0 0
\(709\) −47.9570 −1.80106 −0.900531 0.434791i \(-0.856822\pi\)
−0.900531 + 0.434791i \(0.856822\pi\)
\(710\) 0 0
\(711\) 2.49091 0.0934164
\(712\) 0 0
\(713\) 31.2485 1.17027
\(714\) 0 0
\(715\) −59.9618 −2.24244
\(716\) 0 0
\(717\) 20.2206 0.755153
\(718\) 0 0
\(719\) −11.2994 −0.421397 −0.210698 0.977551i \(-0.567574\pi\)
−0.210698 + 0.977551i \(0.567574\pi\)
\(720\) 0 0
\(721\) 37.5485 1.39838
\(722\) 0 0
\(723\) −18.5006 −0.688044
\(724\) 0 0
\(725\) −3.22203 −0.119663
\(726\) 0 0
\(727\) 52.6897 1.95415 0.977076 0.212890i \(-0.0682875\pi\)
0.977076 + 0.212890i \(0.0682875\pi\)
\(728\) 0 0
\(729\) 28.5614 1.05783
\(730\) 0 0
\(731\) 47.4868 1.75636
\(732\) 0 0
\(733\) 49.9995 1.84677 0.923386 0.383873i \(-0.125410\pi\)
0.923386 + 0.383873i \(0.125410\pi\)
\(734\) 0 0
\(735\) −2.65383 −0.0978879
\(736\) 0 0
\(737\) −58.9966 −2.17317
\(738\) 0 0
\(739\) 38.6115 1.42035 0.710174 0.704026i \(-0.248616\pi\)
0.710174 + 0.704026i \(0.248616\pi\)
\(740\) 0 0
\(741\) 41.0285 1.50722
\(742\) 0 0
\(743\) 53.0323 1.94557 0.972784 0.231716i \(-0.0744340\pi\)
0.972784 + 0.231716i \(0.0744340\pi\)
\(744\) 0 0
\(745\) 56.8827 2.08402
\(746\) 0 0
\(747\) −0.339011 −0.0124038
\(748\) 0 0
\(749\) 43.2442 1.58011
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 23.8709 0.869903
\(754\) 0 0
\(755\) −50.1738 −1.82601
\(756\) 0 0
\(757\) 23.0149 0.836489 0.418245 0.908334i \(-0.362646\pi\)
0.418245 + 0.908334i \(0.362646\pi\)
\(758\) 0 0
\(759\) 31.9816 1.16086
\(760\) 0 0
\(761\) 17.1684 0.622355 0.311178 0.950352i \(-0.399277\pi\)
0.311178 + 0.950352i \(0.399277\pi\)
\(762\) 0 0
\(763\) −30.5856 −1.10727
\(764\) 0 0
\(765\) 4.80885 0.173864
\(766\) 0 0
\(767\) 26.6289 0.961513
\(768\) 0 0
\(769\) −28.0034 −1.00983 −0.504915 0.863169i \(-0.668476\pi\)
−0.504915 + 0.863169i \(0.668476\pi\)
\(770\) 0 0
\(771\) −13.1099 −0.472141
\(772\) 0 0
\(773\) −21.2341 −0.763737 −0.381869 0.924217i \(-0.624719\pi\)
−0.381869 + 0.924217i \(0.624719\pi\)
\(774\) 0 0
\(775\) −35.1268 −1.26179
\(776\) 0 0
\(777\) 32.1133 1.15206
\(778\) 0 0
\(779\) −39.4275 −1.41264
\(780\) 0 0
\(781\) −47.9522 −1.71586
\(782\) 0 0
\(783\) 3.10455 0.110948
\(784\) 0 0
\(785\) −21.3083 −0.760527
\(786\) 0 0
\(787\) 4.04884 0.144326 0.0721628 0.997393i \(-0.477010\pi\)
0.0721628 + 0.997393i \(0.477010\pi\)
\(788\) 0 0
\(789\) −30.7724 −1.09553
\(790\) 0 0
\(791\) −31.0663 −1.10459
\(792\) 0 0
\(793\) 13.4219 0.476627
\(794\) 0 0
\(795\) −11.6949 −0.414774
\(796\) 0 0
\(797\) −21.0550 −0.745807 −0.372903 0.927870i \(-0.621638\pi\)
−0.372903 + 0.927870i \(0.621638\pi\)
\(798\) 0 0
\(799\) 89.5857 3.16932
\(800\) 0 0
\(801\) −3.02594 −0.106916
\(802\) 0 0
\(803\) 5.44715 0.192226
\(804\) 0 0
\(805\) 40.9999 1.44505
\(806\) 0 0
\(807\) −8.54981 −0.300968
\(808\) 0 0
\(809\) 40.9035 1.43809 0.719045 0.694964i \(-0.244580\pi\)
0.719045 + 0.694964i \(0.244580\pi\)
\(810\) 0 0
\(811\) 15.6356 0.549041 0.274521 0.961581i \(-0.411481\pi\)
0.274521 + 0.961581i \(0.411481\pi\)
\(812\) 0 0
\(813\) 32.2406 1.13073
\(814\) 0 0
\(815\) −31.8799 −1.11670
\(816\) 0 0
\(817\) −33.2155 −1.16206
\(818\) 0 0
\(819\) 2.45357 0.0857347
\(820\) 0 0
\(821\) 13.7400 0.479529 0.239764 0.970831i \(-0.422930\pi\)
0.239764 + 0.970831i \(0.422930\pi\)
\(822\) 0 0
\(823\) 9.88944 0.344724 0.172362 0.985034i \(-0.444860\pi\)
0.172362 + 0.985034i \(0.444860\pi\)
\(824\) 0 0
\(825\) −35.9509 −1.25165
\(826\) 0 0
\(827\) 30.2012 1.05020 0.525099 0.851041i \(-0.324028\pi\)
0.525099 + 0.851041i \(0.324028\pi\)
\(828\) 0 0
\(829\) −37.6915 −1.30908 −0.654539 0.756028i \(-0.727137\pi\)
−0.654539 + 0.756028i \(0.727137\pi\)
\(830\) 0 0
\(831\) −54.4563 −1.88907
\(832\) 0 0
\(833\) 3.58659 0.124268
\(834\) 0 0
\(835\) 8.03169 0.277948
\(836\) 0 0
\(837\) 33.8461 1.16989
\(838\) 0 0
\(839\) −14.4155 −0.497677 −0.248839 0.968545i \(-0.580049\pi\)
−0.248839 + 0.968545i \(0.580049\pi\)
\(840\) 0 0
\(841\) −28.6640 −0.988413
\(842\) 0 0
\(843\) −17.6315 −0.607260
\(844\) 0 0
\(845\) 31.7789 1.09323
\(846\) 0 0
\(847\) −10.0760 −0.346215
\(848\) 0 0
\(849\) −30.1847 −1.03594
\(850\) 0 0
\(851\) 37.1966 1.27508
\(852\) 0 0
\(853\) 52.6060 1.80119 0.900597 0.434654i \(-0.143129\pi\)
0.900597 + 0.434654i \(0.143129\pi\)
\(854\) 0 0
\(855\) −3.36364 −0.115034
\(856\) 0 0
\(857\) 0.511833 0.0174839 0.00874195 0.999962i \(-0.497217\pi\)
0.00874195 + 0.999962i \(0.497217\pi\)
\(858\) 0 0
\(859\) −25.0052 −0.853168 −0.426584 0.904448i \(-0.640283\pi\)
−0.426584 + 0.904448i \(0.640283\pi\)
\(860\) 0 0
\(861\) 32.7547 1.11628
\(862\) 0 0
\(863\) 31.1650 1.06087 0.530434 0.847726i \(-0.322029\pi\)
0.530434 + 0.847726i \(0.322029\pi\)
\(864\) 0 0
\(865\) 0.471006 0.0160147
\(866\) 0 0
\(867\) 61.8451 2.10037
\(868\) 0 0
\(869\) 47.8064 1.62172
\(870\) 0 0
\(871\) 72.8291 2.46772
\(872\) 0 0
\(873\) −1.00731 −0.0340921
\(874\) 0 0
\(875\) −4.62950 −0.156506
\(876\) 0 0
\(877\) 12.2573 0.413900 0.206950 0.978352i \(-0.433646\pi\)
0.206950 + 0.978352i \(0.433646\pi\)
\(878\) 0 0
\(879\) −48.7099 −1.64294
\(880\) 0 0
\(881\) −20.3024 −0.684004 −0.342002 0.939699i \(-0.611105\pi\)
−0.342002 + 0.939699i \(0.611105\pi\)
\(882\) 0 0
\(883\) −18.8329 −0.633777 −0.316889 0.948463i \(-0.602638\pi\)
−0.316889 + 0.948463i \(0.602638\pi\)
\(884\) 0 0
\(885\) 30.3277 1.01945
\(886\) 0 0
\(887\) −3.70961 −0.124557 −0.0622783 0.998059i \(-0.519837\pi\)
−0.0622783 + 0.998059i \(0.519837\pi\)
\(888\) 0 0
\(889\) −7.47908 −0.250840
\(890\) 0 0
\(891\) 32.3035 1.08221
\(892\) 0 0
\(893\) −62.6625 −2.09692
\(894\) 0 0
\(895\) 0.863569 0.0288659
\(896\) 0 0
\(897\) −39.4801 −1.31820
\(898\) 0 0
\(899\) 3.66337 0.122180
\(900\) 0 0
\(901\) 15.8053 0.526552
\(902\) 0 0
\(903\) 27.5941 0.918275
\(904\) 0 0
\(905\) −52.7358 −1.75300
\(906\) 0 0
\(907\) −11.0725 −0.367656 −0.183828 0.982958i \(-0.558849\pi\)
−0.183828 + 0.982958i \(0.558849\pi\)
\(908\) 0 0
\(909\) −3.31482 −0.109945
\(910\) 0 0
\(911\) 19.7890 0.655639 0.327820 0.944740i \(-0.393686\pi\)
0.327820 + 0.944740i \(0.393686\pi\)
\(912\) 0 0
\(913\) −6.50643 −0.215331
\(914\) 0 0
\(915\) 15.2863 0.505349
\(916\) 0 0
\(917\) −21.5486 −0.711596
\(918\) 0 0
\(919\) 7.50904 0.247700 0.123850 0.992301i \(-0.460476\pi\)
0.123850 + 0.992301i \(0.460476\pi\)
\(920\) 0 0
\(921\) −3.15452 −0.103945
\(922\) 0 0
\(923\) 59.1952 1.94843
\(924\) 0 0
\(925\) −41.8130 −1.37480
\(926\) 0 0
\(927\) 2.96424 0.0973584
\(928\) 0 0
\(929\) −40.9324 −1.34295 −0.671474 0.741028i \(-0.734338\pi\)
−0.671474 + 0.741028i \(0.734338\pi\)
\(930\) 0 0
\(931\) −2.50871 −0.0822196
\(932\) 0 0
\(933\) −44.2968 −1.45021
\(934\) 0 0
\(935\) 92.2932 3.01831
\(936\) 0 0
\(937\) 48.8681 1.59645 0.798226 0.602358i \(-0.205772\pi\)
0.798226 + 0.602358i \(0.205772\pi\)
\(938\) 0 0
\(939\) −30.0768 −0.981519
\(940\) 0 0
\(941\) 37.7805 1.23161 0.615805 0.787899i \(-0.288831\pi\)
0.615805 + 0.787899i \(0.288831\pi\)
\(942\) 0 0
\(943\) 37.9396 1.23548
\(944\) 0 0
\(945\) 44.4080 1.44459
\(946\) 0 0
\(947\) −36.1188 −1.17370 −0.586852 0.809694i \(-0.699633\pi\)
−0.586852 + 0.809694i \(0.699633\pi\)
\(948\) 0 0
\(949\) −6.72431 −0.218280
\(950\) 0 0
\(951\) 29.2516 0.948547
\(952\) 0 0
\(953\) −48.0232 −1.55562 −0.777811 0.628498i \(-0.783670\pi\)
−0.777811 + 0.628498i \(0.783670\pi\)
\(954\) 0 0
\(955\) 52.4541 1.69737
\(956\) 0 0
\(957\) 3.74931 0.121198
\(958\) 0 0
\(959\) −18.6604 −0.602576
\(960\) 0 0
\(961\) 8.93836 0.288334
\(962\) 0 0
\(963\) 3.41389 0.110011
\(964\) 0 0
\(965\) 18.2096 0.586187
\(966\) 0 0
\(967\) 50.3577 1.61940 0.809698 0.586847i \(-0.199631\pi\)
0.809698 + 0.586847i \(0.199631\pi\)
\(968\) 0 0
\(969\) −63.1510 −2.02870
\(970\) 0 0
\(971\) −11.3491 −0.364210 −0.182105 0.983279i \(-0.558291\pi\)
−0.182105 + 0.983279i \(0.558291\pi\)
\(972\) 0 0
\(973\) 48.9342 1.56876
\(974\) 0 0
\(975\) 44.3800 1.42130
\(976\) 0 0
\(977\) −18.5837 −0.594546 −0.297273 0.954792i \(-0.596077\pi\)
−0.297273 + 0.954792i \(0.596077\pi\)
\(978\) 0 0
\(979\) −58.0750 −1.85609
\(980\) 0 0
\(981\) −2.41456 −0.0770909
\(982\) 0 0
\(983\) 35.6133 1.13589 0.567944 0.823067i \(-0.307739\pi\)
0.567944 + 0.823067i \(0.307739\pi\)
\(984\) 0 0
\(985\) 60.7938 1.93705
\(986\) 0 0
\(987\) 52.0574 1.65701
\(988\) 0 0
\(989\) 31.9620 1.01633
\(990\) 0 0
\(991\) −5.59651 −0.177779 −0.0888895 0.996041i \(-0.528332\pi\)
−0.0888895 + 0.996041i \(0.528332\pi\)
\(992\) 0 0
\(993\) −37.0761 −1.17657
\(994\) 0 0
\(995\) 27.1373 0.860311
\(996\) 0 0
\(997\) 34.7689 1.10114 0.550572 0.834788i \(-0.314410\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(998\) 0 0
\(999\) 40.2885 1.27467
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.1.36 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.36 44 1.1 even 1 trivial