Properties

Label 6008.2.a.b.1.34
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 1.34
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.63667 q^{3} +2.82337 q^{5} +2.24738 q^{7} -0.321314 q^{9} +O(q^{10})\) \(q+1.63667 q^{3} +2.82337 q^{5} +2.24738 q^{7} -0.321314 q^{9} -3.70116 q^{11} -6.16300 q^{13} +4.62093 q^{15} -5.15994 q^{17} -0.846675 q^{19} +3.67821 q^{21} -4.10789 q^{23} +2.97143 q^{25} -5.43589 q^{27} -1.81243 q^{29} -4.67573 q^{31} -6.05758 q^{33} +6.34518 q^{35} -2.39820 q^{37} -10.0868 q^{39} +2.12496 q^{41} +3.93377 q^{43} -0.907189 q^{45} +10.7385 q^{47} -1.94930 q^{49} -8.44512 q^{51} +6.85969 q^{53} -10.4498 q^{55} -1.38573 q^{57} -12.6324 q^{59} -11.6644 q^{61} -0.722113 q^{63} -17.4004 q^{65} +13.2410 q^{67} -6.72326 q^{69} -5.49181 q^{71} +9.21478 q^{73} +4.86325 q^{75} -8.31791 q^{77} -1.24182 q^{79} -7.93282 q^{81} -8.53084 q^{83} -14.5684 q^{85} -2.96636 q^{87} -5.06679 q^{89} -13.8506 q^{91} -7.65263 q^{93} -2.39048 q^{95} +3.83936 q^{97} +1.18924 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.63667 0.944931 0.472466 0.881349i \(-0.343364\pi\)
0.472466 + 0.881349i \(0.343364\pi\)
\(4\) 0 0
\(5\) 2.82337 1.26265 0.631325 0.775518i \(-0.282511\pi\)
0.631325 + 0.775518i \(0.282511\pi\)
\(6\) 0 0
\(7\) 2.24738 0.849428 0.424714 0.905328i \(-0.360375\pi\)
0.424714 + 0.905328i \(0.360375\pi\)
\(8\) 0 0
\(9\) −0.321314 −0.107105
\(10\) 0 0
\(11\) −3.70116 −1.11594 −0.557971 0.829860i \(-0.688420\pi\)
−0.557971 + 0.829860i \(0.688420\pi\)
\(12\) 0 0
\(13\) −6.16300 −1.70931 −0.854654 0.519197i \(-0.826231\pi\)
−0.854654 + 0.519197i \(0.826231\pi\)
\(14\) 0 0
\(15\) 4.62093 1.19312
\(16\) 0 0
\(17\) −5.15994 −1.25147 −0.625735 0.780036i \(-0.715201\pi\)
−0.625735 + 0.780036i \(0.715201\pi\)
\(18\) 0 0
\(19\) −0.846675 −0.194241 −0.0971203 0.995273i \(-0.530963\pi\)
−0.0971203 + 0.995273i \(0.530963\pi\)
\(20\) 0 0
\(21\) 3.67821 0.802651
\(22\) 0 0
\(23\) −4.10789 −0.856554 −0.428277 0.903647i \(-0.640879\pi\)
−0.428277 + 0.903647i \(0.640879\pi\)
\(24\) 0 0
\(25\) 2.97143 0.594286
\(26\) 0 0
\(27\) −5.43589 −1.04614
\(28\) 0 0
\(29\) −1.81243 −0.336561 −0.168280 0.985739i \(-0.553821\pi\)
−0.168280 + 0.985739i \(0.553821\pi\)
\(30\) 0 0
\(31\) −4.67573 −0.839787 −0.419893 0.907573i \(-0.637933\pi\)
−0.419893 + 0.907573i \(0.637933\pi\)
\(32\) 0 0
\(33\) −6.05758 −1.05449
\(34\) 0 0
\(35\) 6.34518 1.07253
\(36\) 0 0
\(37\) −2.39820 −0.394262 −0.197131 0.980377i \(-0.563162\pi\)
−0.197131 + 0.980377i \(0.563162\pi\)
\(38\) 0 0
\(39\) −10.0868 −1.61518
\(40\) 0 0
\(41\) 2.12496 0.331864 0.165932 0.986137i \(-0.446937\pi\)
0.165932 + 0.986137i \(0.446937\pi\)
\(42\) 0 0
\(43\) 3.93377 0.599894 0.299947 0.953956i \(-0.403031\pi\)
0.299947 + 0.953956i \(0.403031\pi\)
\(44\) 0 0
\(45\) −0.907189 −0.135236
\(46\) 0 0
\(47\) 10.7385 1.56637 0.783187 0.621786i \(-0.213592\pi\)
0.783187 + 0.621786i \(0.213592\pi\)
\(48\) 0 0
\(49\) −1.94930 −0.278472
\(50\) 0 0
\(51\) −8.44512 −1.18255
\(52\) 0 0
\(53\) 6.85969 0.942251 0.471126 0.882066i \(-0.343848\pi\)
0.471126 + 0.882066i \(0.343848\pi\)
\(54\) 0 0
\(55\) −10.4498 −1.40905
\(56\) 0 0
\(57\) −1.38573 −0.183544
\(58\) 0 0
\(59\) −12.6324 −1.64460 −0.822302 0.569051i \(-0.807311\pi\)
−0.822302 + 0.569051i \(0.807311\pi\)
\(60\) 0 0
\(61\) −11.6644 −1.49347 −0.746736 0.665121i \(-0.768380\pi\)
−0.746736 + 0.665121i \(0.768380\pi\)
\(62\) 0 0
\(63\) −0.722113 −0.0909777
\(64\) 0 0
\(65\) −17.4004 −2.15826
\(66\) 0 0
\(67\) 13.2410 1.61765 0.808824 0.588051i \(-0.200104\pi\)
0.808824 + 0.588051i \(0.200104\pi\)
\(68\) 0 0
\(69\) −6.72326 −0.809385
\(70\) 0 0
\(71\) −5.49181 −0.651758 −0.325879 0.945412i \(-0.605660\pi\)
−0.325879 + 0.945412i \(0.605660\pi\)
\(72\) 0 0
\(73\) 9.21478 1.07851 0.539254 0.842143i \(-0.318706\pi\)
0.539254 + 0.842143i \(0.318706\pi\)
\(74\) 0 0
\(75\) 4.86325 0.561560
\(76\) 0 0
\(77\) −8.31791 −0.947913
\(78\) 0 0
\(79\) −1.24182 −0.139716 −0.0698581 0.997557i \(-0.522255\pi\)
−0.0698581 + 0.997557i \(0.522255\pi\)
\(80\) 0 0
\(81\) −7.93282 −0.881424
\(82\) 0 0
\(83\) −8.53084 −0.936381 −0.468191 0.883627i \(-0.655094\pi\)
−0.468191 + 0.883627i \(0.655094\pi\)
\(84\) 0 0
\(85\) −14.5684 −1.58017
\(86\) 0 0
\(87\) −2.96636 −0.318027
\(88\) 0 0
\(89\) −5.06679 −0.537079 −0.268539 0.963269i \(-0.586541\pi\)
−0.268539 + 0.963269i \(0.586541\pi\)
\(90\) 0 0
\(91\) −13.8506 −1.45194
\(92\) 0 0
\(93\) −7.65263 −0.793541
\(94\) 0 0
\(95\) −2.39048 −0.245258
\(96\) 0 0
\(97\) 3.83936 0.389828 0.194914 0.980820i \(-0.437557\pi\)
0.194914 + 0.980820i \(0.437557\pi\)
\(98\) 0 0
\(99\) 1.18924 0.119523
\(100\) 0 0
\(101\) 2.79839 0.278450 0.139225 0.990261i \(-0.455539\pi\)
0.139225 + 0.990261i \(0.455539\pi\)
\(102\) 0 0
\(103\) 6.60990 0.651293 0.325646 0.945492i \(-0.394418\pi\)
0.325646 + 0.945492i \(0.394418\pi\)
\(104\) 0 0
\(105\) 10.3850 1.01347
\(106\) 0 0
\(107\) 17.5247 1.69418 0.847091 0.531448i \(-0.178352\pi\)
0.847091 + 0.531448i \(0.178352\pi\)
\(108\) 0 0
\(109\) 0.585236 0.0560554 0.0280277 0.999607i \(-0.491077\pi\)
0.0280277 + 0.999607i \(0.491077\pi\)
\(110\) 0 0
\(111\) −3.92506 −0.372550
\(112\) 0 0
\(113\) −4.42019 −0.415817 −0.207908 0.978148i \(-0.566666\pi\)
−0.207908 + 0.978148i \(0.566666\pi\)
\(114\) 0 0
\(115\) −11.5981 −1.08153
\(116\) 0 0
\(117\) 1.98026 0.183075
\(118\) 0 0
\(119\) −11.5963 −1.06303
\(120\) 0 0
\(121\) 2.69861 0.245328
\(122\) 0 0
\(123\) 3.47786 0.313588
\(124\) 0 0
\(125\) −5.72741 −0.512275
\(126\) 0 0
\(127\) −11.5338 −1.02346 −0.511729 0.859147i \(-0.670995\pi\)
−0.511729 + 0.859147i \(0.670995\pi\)
\(128\) 0 0
\(129\) 6.43828 0.566859
\(130\) 0 0
\(131\) 3.20736 0.280228 0.140114 0.990135i \(-0.455253\pi\)
0.140114 + 0.990135i \(0.455253\pi\)
\(132\) 0 0
\(133\) −1.90280 −0.164993
\(134\) 0 0
\(135\) −15.3475 −1.32091
\(136\) 0 0
\(137\) −3.04503 −0.260155 −0.130077 0.991504i \(-0.541523\pi\)
−0.130077 + 0.991504i \(0.541523\pi\)
\(138\) 0 0
\(139\) −15.8028 −1.34037 −0.670186 0.742193i \(-0.733786\pi\)
−0.670186 + 0.742193i \(0.733786\pi\)
\(140\) 0 0
\(141\) 17.5754 1.48012
\(142\) 0 0
\(143\) 22.8103 1.90749
\(144\) 0 0
\(145\) −5.11718 −0.424958
\(146\) 0 0
\(147\) −3.19036 −0.263137
\(148\) 0 0
\(149\) 16.0924 1.31834 0.659170 0.751994i \(-0.270908\pi\)
0.659170 + 0.751994i \(0.270908\pi\)
\(150\) 0 0
\(151\) −7.50521 −0.610765 −0.305383 0.952230i \(-0.598784\pi\)
−0.305383 + 0.952230i \(0.598784\pi\)
\(152\) 0 0
\(153\) 1.65796 0.134038
\(154\) 0 0
\(155\) −13.2013 −1.06036
\(156\) 0 0
\(157\) −10.9383 −0.872967 −0.436484 0.899712i \(-0.643776\pi\)
−0.436484 + 0.899712i \(0.643776\pi\)
\(158\) 0 0
\(159\) 11.2270 0.890363
\(160\) 0 0
\(161\) −9.23197 −0.727581
\(162\) 0 0
\(163\) 8.47019 0.663437 0.331718 0.943378i \(-0.392372\pi\)
0.331718 + 0.943378i \(0.392372\pi\)
\(164\) 0 0
\(165\) −17.1028 −1.33145
\(166\) 0 0
\(167\) −21.2987 −1.64815 −0.824073 0.566484i \(-0.808303\pi\)
−0.824073 + 0.566484i \(0.808303\pi\)
\(168\) 0 0
\(169\) 24.9826 1.92174
\(170\) 0 0
\(171\) 0.272048 0.0208041
\(172\) 0 0
\(173\) 20.8485 1.58508 0.792542 0.609817i \(-0.208757\pi\)
0.792542 + 0.609817i \(0.208757\pi\)
\(174\) 0 0
\(175\) 6.67792 0.504803
\(176\) 0 0
\(177\) −20.6751 −1.55404
\(178\) 0 0
\(179\) 11.1161 0.830859 0.415430 0.909625i \(-0.363631\pi\)
0.415430 + 0.909625i \(0.363631\pi\)
\(180\) 0 0
\(181\) −2.05779 −0.152955 −0.0764773 0.997071i \(-0.524367\pi\)
−0.0764773 + 0.997071i \(0.524367\pi\)
\(182\) 0 0
\(183\) −19.0907 −1.41123
\(184\) 0 0
\(185\) −6.77101 −0.497815
\(186\) 0 0
\(187\) 19.0978 1.39657
\(188\) 0 0
\(189\) −12.2165 −0.888619
\(190\) 0 0
\(191\) −14.9637 −1.08274 −0.541368 0.840786i \(-0.682093\pi\)
−0.541368 + 0.840786i \(0.682093\pi\)
\(192\) 0 0
\(193\) 23.4561 1.68841 0.844204 0.536022i \(-0.180074\pi\)
0.844204 + 0.536022i \(0.180074\pi\)
\(194\) 0 0
\(195\) −28.4788 −2.03941
\(196\) 0 0
\(197\) −2.89264 −0.206092 −0.103046 0.994677i \(-0.532859\pi\)
−0.103046 + 0.994677i \(0.532859\pi\)
\(198\) 0 0
\(199\) −24.8205 −1.75948 −0.879739 0.475458i \(-0.842282\pi\)
−0.879739 + 0.475458i \(0.842282\pi\)
\(200\) 0 0
\(201\) 21.6712 1.52857
\(202\) 0 0
\(203\) −4.07322 −0.285884
\(204\) 0 0
\(205\) 5.99956 0.419028
\(206\) 0 0
\(207\) 1.31992 0.0917409
\(208\) 0 0
\(209\) 3.13368 0.216761
\(210\) 0 0
\(211\) −10.9749 −0.755543 −0.377772 0.925899i \(-0.623310\pi\)
−0.377772 + 0.925899i \(0.623310\pi\)
\(212\) 0 0
\(213\) −8.98827 −0.615866
\(214\) 0 0
\(215\) 11.1065 0.757456
\(216\) 0 0
\(217\) −10.5081 −0.713339
\(218\) 0 0
\(219\) 15.0816 1.01912
\(220\) 0 0
\(221\) 31.8007 2.13915
\(222\) 0 0
\(223\) 22.7524 1.52361 0.761807 0.647804i \(-0.224312\pi\)
0.761807 + 0.647804i \(0.224312\pi\)
\(224\) 0 0
\(225\) −0.954762 −0.0636508
\(226\) 0 0
\(227\) 15.2523 1.01233 0.506165 0.862437i \(-0.331063\pi\)
0.506165 + 0.862437i \(0.331063\pi\)
\(228\) 0 0
\(229\) −4.67557 −0.308971 −0.154485 0.987995i \(-0.549372\pi\)
−0.154485 + 0.987995i \(0.549372\pi\)
\(230\) 0 0
\(231\) −13.6137 −0.895713
\(232\) 0 0
\(233\) −2.21870 −0.145352 −0.0726760 0.997356i \(-0.523154\pi\)
−0.0726760 + 0.997356i \(0.523154\pi\)
\(234\) 0 0
\(235\) 30.3189 1.97778
\(236\) 0 0
\(237\) −2.03246 −0.132022
\(238\) 0 0
\(239\) 6.75297 0.436813 0.218407 0.975858i \(-0.429914\pi\)
0.218407 + 0.975858i \(0.429914\pi\)
\(240\) 0 0
\(241\) 8.00501 0.515648 0.257824 0.966192i \(-0.416995\pi\)
0.257824 + 0.966192i \(0.416995\pi\)
\(242\) 0 0
\(243\) 3.32428 0.213253
\(244\) 0 0
\(245\) −5.50360 −0.351612
\(246\) 0 0
\(247\) 5.21806 0.332017
\(248\) 0 0
\(249\) −13.9622 −0.884816
\(250\) 0 0
\(251\) 3.48447 0.219938 0.109969 0.993935i \(-0.464925\pi\)
0.109969 + 0.993935i \(0.464925\pi\)
\(252\) 0 0
\(253\) 15.2040 0.955865
\(254\) 0 0
\(255\) −23.8437 −1.49315
\(256\) 0 0
\(257\) −7.75768 −0.483911 −0.241955 0.970287i \(-0.577789\pi\)
−0.241955 + 0.970287i \(0.577789\pi\)
\(258\) 0 0
\(259\) −5.38966 −0.334897
\(260\) 0 0
\(261\) 0.582360 0.0360472
\(262\) 0 0
\(263\) 13.5499 0.835521 0.417760 0.908557i \(-0.362815\pi\)
0.417760 + 0.908557i \(0.362815\pi\)
\(264\) 0 0
\(265\) 19.3675 1.18973
\(266\) 0 0
\(267\) −8.29266 −0.507503
\(268\) 0 0
\(269\) 7.18871 0.438303 0.219152 0.975691i \(-0.429671\pi\)
0.219152 + 0.975691i \(0.429671\pi\)
\(270\) 0 0
\(271\) −9.70848 −0.589748 −0.294874 0.955536i \(-0.595278\pi\)
−0.294874 + 0.955536i \(0.595278\pi\)
\(272\) 0 0
\(273\) −22.6688 −1.37198
\(274\) 0 0
\(275\) −10.9977 −0.663189
\(276\) 0 0
\(277\) 25.3127 1.52089 0.760446 0.649401i \(-0.224980\pi\)
0.760446 + 0.649401i \(0.224980\pi\)
\(278\) 0 0
\(279\) 1.50238 0.0899450
\(280\) 0 0
\(281\) 13.7441 0.819902 0.409951 0.912107i \(-0.365546\pi\)
0.409951 + 0.912107i \(0.365546\pi\)
\(282\) 0 0
\(283\) −7.60434 −0.452031 −0.226016 0.974124i \(-0.572570\pi\)
−0.226016 + 0.974124i \(0.572570\pi\)
\(284\) 0 0
\(285\) −3.91242 −0.231752
\(286\) 0 0
\(287\) 4.77559 0.281894
\(288\) 0 0
\(289\) 9.62503 0.566178
\(290\) 0 0
\(291\) 6.28377 0.368361
\(292\) 0 0
\(293\) 22.1781 1.29566 0.647828 0.761787i \(-0.275678\pi\)
0.647828 + 0.761787i \(0.275678\pi\)
\(294\) 0 0
\(295\) −35.6661 −2.07656
\(296\) 0 0
\(297\) 20.1191 1.16743
\(298\) 0 0
\(299\) 25.3169 1.46412
\(300\) 0 0
\(301\) 8.84065 0.509567
\(302\) 0 0
\(303\) 4.58003 0.263116
\(304\) 0 0
\(305\) −32.9329 −1.88573
\(306\) 0 0
\(307\) −4.69321 −0.267856 −0.133928 0.990991i \(-0.542759\pi\)
−0.133928 + 0.990991i \(0.542759\pi\)
\(308\) 0 0
\(309\) 10.8182 0.615427
\(310\) 0 0
\(311\) 9.00452 0.510599 0.255300 0.966862i \(-0.417826\pi\)
0.255300 + 0.966862i \(0.417826\pi\)
\(312\) 0 0
\(313\) 2.12786 0.120274 0.0601368 0.998190i \(-0.480846\pi\)
0.0601368 + 0.998190i \(0.480846\pi\)
\(314\) 0 0
\(315\) −2.03879 −0.114873
\(316\) 0 0
\(317\) −5.97888 −0.335807 −0.167904 0.985803i \(-0.553700\pi\)
−0.167904 + 0.985803i \(0.553700\pi\)
\(318\) 0 0
\(319\) 6.70812 0.375582
\(320\) 0 0
\(321\) 28.6822 1.60089
\(322\) 0 0
\(323\) 4.36879 0.243086
\(324\) 0 0
\(325\) −18.3129 −1.01582
\(326\) 0 0
\(327\) 0.957837 0.0529685
\(328\) 0 0
\(329\) 24.1335 1.33052
\(330\) 0 0
\(331\) 7.61128 0.418354 0.209177 0.977878i \(-0.432922\pi\)
0.209177 + 0.977878i \(0.432922\pi\)
\(332\) 0 0
\(333\) 0.770575 0.0422272
\(334\) 0 0
\(335\) 37.3843 2.04252
\(336\) 0 0
\(337\) 26.8154 1.46073 0.730365 0.683057i \(-0.239350\pi\)
0.730365 + 0.683057i \(0.239350\pi\)
\(338\) 0 0
\(339\) −7.23439 −0.392918
\(340\) 0 0
\(341\) 17.3057 0.937154
\(342\) 0 0
\(343\) −20.1124 −1.08597
\(344\) 0 0
\(345\) −18.9823 −1.02197
\(346\) 0 0
\(347\) −16.5979 −0.891021 −0.445511 0.895277i \(-0.646978\pi\)
−0.445511 + 0.895277i \(0.646978\pi\)
\(348\) 0 0
\(349\) −1.73924 −0.0930993 −0.0465497 0.998916i \(-0.514823\pi\)
−0.0465497 + 0.998916i \(0.514823\pi\)
\(350\) 0 0
\(351\) 33.5014 1.78817
\(352\) 0 0
\(353\) −16.3115 −0.868176 −0.434088 0.900871i \(-0.642929\pi\)
−0.434088 + 0.900871i \(0.642929\pi\)
\(354\) 0 0
\(355\) −15.5054 −0.822942
\(356\) 0 0
\(357\) −18.9794 −1.00449
\(358\) 0 0
\(359\) −3.90195 −0.205937 −0.102968 0.994685i \(-0.532834\pi\)
−0.102968 + 0.994685i \(0.532834\pi\)
\(360\) 0 0
\(361\) −18.2831 −0.962271
\(362\) 0 0
\(363\) 4.41673 0.231818
\(364\) 0 0
\(365\) 26.0168 1.36178
\(366\) 0 0
\(367\) −20.4779 −1.06894 −0.534468 0.845189i \(-0.679488\pi\)
−0.534468 + 0.845189i \(0.679488\pi\)
\(368\) 0 0
\(369\) −0.682780 −0.0355441
\(370\) 0 0
\(371\) 15.4163 0.800375
\(372\) 0 0
\(373\) −16.7146 −0.865450 −0.432725 0.901526i \(-0.642448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(374\) 0 0
\(375\) −9.37387 −0.484065
\(376\) 0 0
\(377\) 11.1700 0.575286
\(378\) 0 0
\(379\) −10.8625 −0.557968 −0.278984 0.960296i \(-0.589998\pi\)
−0.278984 + 0.960296i \(0.589998\pi\)
\(380\) 0 0
\(381\) −18.8770 −0.967097
\(382\) 0 0
\(383\) −29.8421 −1.52486 −0.762430 0.647071i \(-0.775994\pi\)
−0.762430 + 0.647071i \(0.775994\pi\)
\(384\) 0 0
\(385\) −23.4845 −1.19688
\(386\) 0 0
\(387\) −1.26397 −0.0642514
\(388\) 0 0
\(389\) −0.257173 −0.0130392 −0.00651960 0.999979i \(-0.502075\pi\)
−0.00651960 + 0.999979i \(0.502075\pi\)
\(390\) 0 0
\(391\) 21.1965 1.07195
\(392\) 0 0
\(393\) 5.24939 0.264797
\(394\) 0 0
\(395\) −3.50613 −0.176413
\(396\) 0 0
\(397\) −20.5449 −1.03112 −0.515559 0.856854i \(-0.672416\pi\)
−0.515559 + 0.856854i \(0.672416\pi\)
\(398\) 0 0
\(399\) −3.11425 −0.155907
\(400\) 0 0
\(401\) −14.9742 −0.747775 −0.373888 0.927474i \(-0.621975\pi\)
−0.373888 + 0.927474i \(0.621975\pi\)
\(402\) 0 0
\(403\) 28.8166 1.43545
\(404\) 0 0
\(405\) −22.3973 −1.11293
\(406\) 0 0
\(407\) 8.87613 0.439973
\(408\) 0 0
\(409\) −38.6274 −1.91000 −0.955001 0.296602i \(-0.904147\pi\)
−0.955001 + 0.296602i \(0.904147\pi\)
\(410\) 0 0
\(411\) −4.98371 −0.245828
\(412\) 0 0
\(413\) −28.3899 −1.39697
\(414\) 0 0
\(415\) −24.0857 −1.18232
\(416\) 0 0
\(417\) −25.8639 −1.26656
\(418\) 0 0
\(419\) −7.25831 −0.354591 −0.177296 0.984158i \(-0.556735\pi\)
−0.177296 + 0.984158i \(0.556735\pi\)
\(420\) 0 0
\(421\) 21.1192 1.02929 0.514643 0.857405i \(-0.327925\pi\)
0.514643 + 0.857405i \(0.327925\pi\)
\(422\) 0 0
\(423\) −3.45044 −0.167766
\(424\) 0 0
\(425\) −15.3324 −0.743731
\(426\) 0 0
\(427\) −26.2143 −1.26860
\(428\) 0 0
\(429\) 37.3329 1.80245
\(430\) 0 0
\(431\) 4.86169 0.234179 0.117090 0.993121i \(-0.462643\pi\)
0.117090 + 0.993121i \(0.462643\pi\)
\(432\) 0 0
\(433\) −7.17595 −0.344854 −0.172427 0.985022i \(-0.555161\pi\)
−0.172427 + 0.985022i \(0.555161\pi\)
\(434\) 0 0
\(435\) −8.37513 −0.401557
\(436\) 0 0
\(437\) 3.47805 0.166378
\(438\) 0 0
\(439\) −27.2703 −1.30154 −0.650770 0.759275i \(-0.725554\pi\)
−0.650770 + 0.759275i \(0.725554\pi\)
\(440\) 0 0
\(441\) 0.626337 0.0298256
\(442\) 0 0
\(443\) −0.147529 −0.00700931 −0.00350466 0.999994i \(-0.501116\pi\)
−0.00350466 + 0.999994i \(0.501116\pi\)
\(444\) 0 0
\(445\) −14.3054 −0.678143
\(446\) 0 0
\(447\) 26.3379 1.24574
\(448\) 0 0
\(449\) 19.1787 0.905096 0.452548 0.891740i \(-0.350515\pi\)
0.452548 + 0.891740i \(0.350515\pi\)
\(450\) 0 0
\(451\) −7.86484 −0.370341
\(452\) 0 0
\(453\) −12.2835 −0.577131
\(454\) 0 0
\(455\) −39.1053 −1.83329
\(456\) 0 0
\(457\) 21.4999 1.00572 0.502861 0.864367i \(-0.332281\pi\)
0.502861 + 0.864367i \(0.332281\pi\)
\(458\) 0 0
\(459\) 28.0489 1.30921
\(460\) 0 0
\(461\) −34.9411 −1.62737 −0.813685 0.581306i \(-0.802542\pi\)
−0.813685 + 0.581306i \(0.802542\pi\)
\(462\) 0 0
\(463\) −3.18896 −0.148204 −0.0741018 0.997251i \(-0.523609\pi\)
−0.0741018 + 0.997251i \(0.523609\pi\)
\(464\) 0 0
\(465\) −21.6062 −1.00196
\(466\) 0 0
\(467\) −20.0791 −0.929149 −0.464575 0.885534i \(-0.653793\pi\)
−0.464575 + 0.885534i \(0.653793\pi\)
\(468\) 0 0
\(469\) 29.7576 1.37408
\(470\) 0 0
\(471\) −17.9023 −0.824894
\(472\) 0 0
\(473\) −14.5595 −0.669447
\(474\) 0 0
\(475\) −2.51583 −0.115434
\(476\) 0 0
\(477\) −2.20411 −0.100919
\(478\) 0 0
\(479\) 7.78398 0.355659 0.177830 0.984061i \(-0.443092\pi\)
0.177830 + 0.984061i \(0.443092\pi\)
\(480\) 0 0
\(481\) 14.7801 0.673915
\(482\) 0 0
\(483\) −15.1097 −0.687514
\(484\) 0 0
\(485\) 10.8400 0.492217
\(486\) 0 0
\(487\) 33.3208 1.50991 0.754955 0.655776i \(-0.227659\pi\)
0.754955 + 0.655776i \(0.227659\pi\)
\(488\) 0 0
\(489\) 13.8629 0.626902
\(490\) 0 0
\(491\) 16.4851 0.743962 0.371981 0.928240i \(-0.378679\pi\)
0.371981 + 0.928240i \(0.378679\pi\)
\(492\) 0 0
\(493\) 9.35206 0.421196
\(494\) 0 0
\(495\) 3.35765 0.150915
\(496\) 0 0
\(497\) −12.3422 −0.553621
\(498\) 0 0
\(499\) −2.06220 −0.0923167 −0.0461584 0.998934i \(-0.514698\pi\)
−0.0461584 + 0.998934i \(0.514698\pi\)
\(500\) 0 0
\(501\) −34.8590 −1.55738
\(502\) 0 0
\(503\) 22.6791 1.01121 0.505604 0.862765i \(-0.331270\pi\)
0.505604 + 0.862765i \(0.331270\pi\)
\(504\) 0 0
\(505\) 7.90089 0.351585
\(506\) 0 0
\(507\) 40.8882 1.81591
\(508\) 0 0
\(509\) −5.17625 −0.229433 −0.114717 0.993398i \(-0.536596\pi\)
−0.114717 + 0.993398i \(0.536596\pi\)
\(510\) 0 0
\(511\) 20.7091 0.916116
\(512\) 0 0
\(513\) 4.60243 0.203202
\(514\) 0 0
\(515\) 18.6622 0.822355
\(516\) 0 0
\(517\) −39.7450 −1.74798
\(518\) 0 0
\(519\) 34.1222 1.49780
\(520\) 0 0
\(521\) 8.89698 0.389784 0.194892 0.980825i \(-0.437564\pi\)
0.194892 + 0.980825i \(0.437564\pi\)
\(522\) 0 0
\(523\) −23.2575 −1.01698 −0.508489 0.861068i \(-0.669796\pi\)
−0.508489 + 0.861068i \(0.669796\pi\)
\(524\) 0 0
\(525\) 10.9295 0.477005
\(526\) 0 0
\(527\) 24.1265 1.05097
\(528\) 0 0
\(529\) −6.12525 −0.266315
\(530\) 0 0
\(531\) 4.05898 0.176145
\(532\) 0 0
\(533\) −13.0962 −0.567257
\(534\) 0 0
\(535\) 49.4789 2.13916
\(536\) 0 0
\(537\) 18.1934 0.785105
\(538\) 0 0
\(539\) 7.21468 0.310758
\(540\) 0 0
\(541\) −4.51972 −0.194318 −0.0971590 0.995269i \(-0.530976\pi\)
−0.0971590 + 0.995269i \(0.530976\pi\)
\(542\) 0 0
\(543\) −3.36793 −0.144532
\(544\) 0 0
\(545\) 1.65234 0.0707784
\(546\) 0 0
\(547\) −2.81470 −0.120348 −0.0601739 0.998188i \(-0.519166\pi\)
−0.0601739 + 0.998188i \(0.519166\pi\)
\(548\) 0 0
\(549\) 3.74793 0.159958
\(550\) 0 0
\(551\) 1.53454 0.0653737
\(552\) 0 0
\(553\) −2.79085 −0.118679
\(554\) 0 0
\(555\) −11.0819 −0.470401
\(556\) 0 0
\(557\) −16.5865 −0.702794 −0.351397 0.936227i \(-0.614293\pi\)
−0.351397 + 0.936227i \(0.614293\pi\)
\(558\) 0 0
\(559\) −24.2438 −1.02540
\(560\) 0 0
\(561\) 31.2568 1.31966
\(562\) 0 0
\(563\) −37.4842 −1.57977 −0.789885 0.613255i \(-0.789860\pi\)
−0.789885 + 0.613255i \(0.789860\pi\)
\(564\) 0 0
\(565\) −12.4798 −0.525031
\(566\) 0 0
\(567\) −17.8280 −0.748706
\(568\) 0 0
\(569\) −12.5148 −0.524649 −0.262324 0.964980i \(-0.584489\pi\)
−0.262324 + 0.964980i \(0.584489\pi\)
\(570\) 0 0
\(571\) 15.6114 0.653319 0.326659 0.945142i \(-0.394077\pi\)
0.326659 + 0.945142i \(0.394077\pi\)
\(572\) 0 0
\(573\) −24.4906 −1.02311
\(574\) 0 0
\(575\) −12.2063 −0.509038
\(576\) 0 0
\(577\) 17.9380 0.746769 0.373385 0.927677i \(-0.378197\pi\)
0.373385 + 0.927677i \(0.378197\pi\)
\(578\) 0 0
\(579\) 38.3899 1.59543
\(580\) 0 0
\(581\) −19.1720 −0.795389
\(582\) 0 0
\(583\) −25.3888 −1.05150
\(584\) 0 0
\(585\) 5.59100 0.231160
\(586\) 0 0
\(587\) −27.1614 −1.12107 −0.560536 0.828130i \(-0.689405\pi\)
−0.560536 + 0.828130i \(0.689405\pi\)
\(588\) 0 0
\(589\) 3.95883 0.163121
\(590\) 0 0
\(591\) −4.73430 −0.194743
\(592\) 0 0
\(593\) 13.3843 0.549627 0.274813 0.961498i \(-0.411384\pi\)
0.274813 + 0.961498i \(0.411384\pi\)
\(594\) 0 0
\(595\) −32.7408 −1.34224
\(596\) 0 0
\(597\) −40.6229 −1.66259
\(598\) 0 0
\(599\) −44.4158 −1.81478 −0.907391 0.420288i \(-0.861929\pi\)
−0.907391 + 0.420288i \(0.861929\pi\)
\(600\) 0 0
\(601\) 19.7666 0.806296 0.403148 0.915135i \(-0.367916\pi\)
0.403148 + 0.915135i \(0.367916\pi\)
\(602\) 0 0
\(603\) −4.25452 −0.173258
\(604\) 0 0
\(605\) 7.61918 0.309764
\(606\) 0 0
\(607\) −29.6081 −1.20176 −0.600878 0.799341i \(-0.705182\pi\)
−0.600878 + 0.799341i \(0.705182\pi\)
\(608\) 0 0
\(609\) −6.66652 −0.270141
\(610\) 0 0
\(611\) −66.1815 −2.67742
\(612\) 0 0
\(613\) 41.6235 1.68116 0.840579 0.541689i \(-0.182215\pi\)
0.840579 + 0.541689i \(0.182215\pi\)
\(614\) 0 0
\(615\) 9.81930 0.395953
\(616\) 0 0
\(617\) −35.2189 −1.41786 −0.708929 0.705280i \(-0.750821\pi\)
−0.708929 + 0.705280i \(0.750821\pi\)
\(618\) 0 0
\(619\) −30.3909 −1.22152 −0.610758 0.791818i \(-0.709135\pi\)
−0.610758 + 0.791818i \(0.709135\pi\)
\(620\) 0 0
\(621\) 22.3300 0.896074
\(622\) 0 0
\(623\) −11.3870 −0.456210
\(624\) 0 0
\(625\) −31.0278 −1.24111
\(626\) 0 0
\(627\) 5.12880 0.204825
\(628\) 0 0
\(629\) 12.3746 0.493407
\(630\) 0 0
\(631\) 9.64462 0.383946 0.191973 0.981400i \(-0.438511\pi\)
0.191973 + 0.981400i \(0.438511\pi\)
\(632\) 0 0
\(633\) −17.9623 −0.713937
\(634\) 0 0
\(635\) −32.5641 −1.29227
\(636\) 0 0
\(637\) 12.0135 0.475994
\(638\) 0 0
\(639\) 1.76459 0.0698062
\(640\) 0 0
\(641\) 28.4017 1.12180 0.560900 0.827884i \(-0.310455\pi\)
0.560900 + 0.827884i \(0.310455\pi\)
\(642\) 0 0
\(643\) −29.8111 −1.17564 −0.587818 0.808993i \(-0.700013\pi\)
−0.587818 + 0.808993i \(0.700013\pi\)
\(644\) 0 0
\(645\) 18.1776 0.715744
\(646\) 0 0
\(647\) 13.4399 0.528377 0.264188 0.964471i \(-0.414896\pi\)
0.264188 + 0.964471i \(0.414896\pi\)
\(648\) 0 0
\(649\) 46.7548 1.83528
\(650\) 0 0
\(651\) −17.1983 −0.674056
\(652\) 0 0
\(653\) 28.0259 1.09674 0.548368 0.836237i \(-0.315249\pi\)
0.548368 + 0.836237i \(0.315249\pi\)
\(654\) 0 0
\(655\) 9.05557 0.353831
\(656\) 0 0
\(657\) −2.96084 −0.115513
\(658\) 0 0
\(659\) −22.3742 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(660\) 0 0
\(661\) 38.4604 1.49593 0.747967 0.663736i \(-0.231030\pi\)
0.747967 + 0.663736i \(0.231030\pi\)
\(662\) 0 0
\(663\) 52.0473 2.02135
\(664\) 0 0
\(665\) −5.37230 −0.208329
\(666\) 0 0
\(667\) 7.44528 0.288282
\(668\) 0 0
\(669\) 37.2382 1.43971
\(670\) 0 0
\(671\) 43.1718 1.66663
\(672\) 0 0
\(673\) −31.1617 −1.20119 −0.600597 0.799552i \(-0.705070\pi\)
−0.600597 + 0.799552i \(0.705070\pi\)
\(674\) 0 0
\(675\) −16.1524 −0.621705
\(676\) 0 0
\(677\) 18.6610 0.717201 0.358601 0.933491i \(-0.383254\pi\)
0.358601 + 0.933491i \(0.383254\pi\)
\(678\) 0 0
\(679\) 8.62849 0.331131
\(680\) 0 0
\(681\) 24.9629 0.956582
\(682\) 0 0
\(683\) −27.0059 −1.03335 −0.516676 0.856181i \(-0.672831\pi\)
−0.516676 + 0.856181i \(0.672831\pi\)
\(684\) 0 0
\(685\) −8.59726 −0.328484
\(686\) 0 0
\(687\) −7.65237 −0.291956
\(688\) 0 0
\(689\) −42.2763 −1.61060
\(690\) 0 0
\(691\) 13.4701 0.512425 0.256213 0.966620i \(-0.417525\pi\)
0.256213 + 0.966620i \(0.417525\pi\)
\(692\) 0 0
\(693\) 2.67266 0.101526
\(694\) 0 0
\(695\) −44.6171 −1.69242
\(696\) 0 0
\(697\) −10.9647 −0.415318
\(698\) 0 0
\(699\) −3.63128 −0.137348
\(700\) 0 0
\(701\) 9.02012 0.340685 0.170343 0.985385i \(-0.445513\pi\)
0.170343 + 0.985385i \(0.445513\pi\)
\(702\) 0 0
\(703\) 2.03050 0.0765816
\(704\) 0 0
\(705\) 49.6219 1.86887
\(706\) 0 0
\(707\) 6.28903 0.236523
\(708\) 0 0
\(709\) 30.9131 1.16097 0.580483 0.814272i \(-0.302864\pi\)
0.580483 + 0.814272i \(0.302864\pi\)
\(710\) 0 0
\(711\) 0.399015 0.0149642
\(712\) 0 0
\(713\) 19.2074 0.719323
\(714\) 0 0
\(715\) 64.4019 2.40849
\(716\) 0 0
\(717\) 11.0524 0.412759
\(718\) 0 0
\(719\) −2.57102 −0.0958828 −0.0479414 0.998850i \(-0.515266\pi\)
−0.0479414 + 0.998850i \(0.515266\pi\)
\(720\) 0 0
\(721\) 14.8549 0.553227
\(722\) 0 0
\(723\) 13.1015 0.487252
\(724\) 0 0
\(725\) −5.38552 −0.200013
\(726\) 0 0
\(727\) −37.0959 −1.37581 −0.687906 0.725800i \(-0.741470\pi\)
−0.687906 + 0.725800i \(0.741470\pi\)
\(728\) 0 0
\(729\) 29.2392 1.08293
\(730\) 0 0
\(731\) −20.2980 −0.750749
\(732\) 0 0
\(733\) 19.1665 0.707929 0.353965 0.935259i \(-0.384833\pi\)
0.353965 + 0.935259i \(0.384833\pi\)
\(734\) 0 0
\(735\) −9.00758 −0.332249
\(736\) 0 0
\(737\) −49.0072 −1.80520
\(738\) 0 0
\(739\) −37.6726 −1.38581 −0.692904 0.721029i \(-0.743669\pi\)
−0.692904 + 0.721029i \(0.743669\pi\)
\(740\) 0 0
\(741\) 8.54023 0.313733
\(742\) 0 0
\(743\) 2.92293 0.107232 0.0536159 0.998562i \(-0.482925\pi\)
0.0536159 + 0.998562i \(0.482925\pi\)
\(744\) 0 0
\(745\) 45.4348 1.66460
\(746\) 0 0
\(747\) 2.74108 0.100291
\(748\) 0 0
\(749\) 39.3847 1.43909
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 5.70293 0.207826
\(754\) 0 0
\(755\) −21.1900 −0.771183
\(756\) 0 0
\(757\) −2.76853 −0.100624 −0.0503119 0.998734i \(-0.516022\pi\)
−0.0503119 + 0.998734i \(0.516022\pi\)
\(758\) 0 0
\(759\) 24.8839 0.903227
\(760\) 0 0
\(761\) −34.7780 −1.26070 −0.630350 0.776311i \(-0.717089\pi\)
−0.630350 + 0.776311i \(0.717089\pi\)
\(762\) 0 0
\(763\) 1.31524 0.0476151
\(764\) 0 0
\(765\) 4.68104 0.169243
\(766\) 0 0
\(767\) 77.8538 2.81114
\(768\) 0 0
\(769\) 22.4400 0.809208 0.404604 0.914492i \(-0.367409\pi\)
0.404604 + 0.914492i \(0.367409\pi\)
\(770\) 0 0
\(771\) −12.6968 −0.457263
\(772\) 0 0
\(773\) −3.47901 −0.125131 −0.0625656 0.998041i \(-0.519928\pi\)
−0.0625656 + 0.998041i \(0.519928\pi\)
\(774\) 0 0
\(775\) −13.8936 −0.499074
\(776\) 0 0
\(777\) −8.82108 −0.316455
\(778\) 0 0
\(779\) −1.79915 −0.0644614
\(780\) 0 0
\(781\) 20.3261 0.727324
\(782\) 0 0
\(783\) 9.85220 0.352089
\(784\) 0 0
\(785\) −30.8828 −1.10225
\(786\) 0 0
\(787\) −25.7043 −0.916259 −0.458129 0.888886i \(-0.651480\pi\)
−0.458129 + 0.888886i \(0.651480\pi\)
\(788\) 0 0
\(789\) 22.1767 0.789510
\(790\) 0 0
\(791\) −9.93383 −0.353206
\(792\) 0 0
\(793\) 71.8876 2.55280
\(794\) 0 0
\(795\) 31.6981 1.12422
\(796\) 0 0
\(797\) −42.2691 −1.49725 −0.748624 0.662995i \(-0.769285\pi\)
−0.748624 + 0.662995i \(0.769285\pi\)
\(798\) 0 0
\(799\) −55.4102 −1.96027
\(800\) 0 0
\(801\) 1.62803 0.0575236
\(802\) 0 0
\(803\) −34.1054 −1.20355
\(804\) 0 0
\(805\) −26.0653 −0.918681
\(806\) 0 0
\(807\) 11.7655 0.414167
\(808\) 0 0
\(809\) 28.2635 0.993691 0.496846 0.867839i \(-0.334492\pi\)
0.496846 + 0.867839i \(0.334492\pi\)
\(810\) 0 0
\(811\) −40.9201 −1.43690 −0.718450 0.695579i \(-0.755148\pi\)
−0.718450 + 0.695579i \(0.755148\pi\)
\(812\) 0 0
\(813\) −15.8896 −0.557271
\(814\) 0 0
\(815\) 23.9145 0.837689
\(816\) 0 0
\(817\) −3.33062 −0.116524
\(818\) 0 0
\(819\) 4.45038 0.155509
\(820\) 0 0
\(821\) −46.4399 −1.62076 −0.810381 0.585903i \(-0.800740\pi\)
−0.810381 + 0.585903i \(0.800740\pi\)
\(822\) 0 0
\(823\) 16.4470 0.573306 0.286653 0.958034i \(-0.407457\pi\)
0.286653 + 0.958034i \(0.407457\pi\)
\(824\) 0 0
\(825\) −17.9997 −0.626668
\(826\) 0 0
\(827\) 9.70175 0.337363 0.168681 0.985671i \(-0.446049\pi\)
0.168681 + 0.985671i \(0.446049\pi\)
\(828\) 0 0
\(829\) 19.7687 0.686595 0.343298 0.939227i \(-0.388456\pi\)
0.343298 + 0.939227i \(0.388456\pi\)
\(830\) 0 0
\(831\) 41.4285 1.43714
\(832\) 0 0
\(833\) 10.0583 0.348499
\(834\) 0 0
\(835\) −60.1343 −2.08103
\(836\) 0 0
\(837\) 25.4168 0.878533
\(838\) 0 0
\(839\) −6.93077 −0.239277 −0.119638 0.992818i \(-0.538174\pi\)
−0.119638 + 0.992818i \(0.538174\pi\)
\(840\) 0 0
\(841\) −25.7151 −0.886727
\(842\) 0 0
\(843\) 22.4945 0.774751
\(844\) 0 0
\(845\) 70.5351 2.42648
\(846\) 0 0
\(847\) 6.06479 0.208389
\(848\) 0 0
\(849\) −12.4458 −0.427138
\(850\) 0 0
\(851\) 9.85154 0.337706
\(852\) 0 0
\(853\) 44.4234 1.52103 0.760513 0.649322i \(-0.224947\pi\)
0.760513 + 0.649322i \(0.224947\pi\)
\(854\) 0 0
\(855\) 0.768094 0.0262683
\(856\) 0 0
\(857\) −41.8400 −1.42923 −0.714614 0.699519i \(-0.753398\pi\)
−0.714614 + 0.699519i \(0.753398\pi\)
\(858\) 0 0
\(859\) −56.2569 −1.91946 −0.959731 0.280922i \(-0.909360\pi\)
−0.959731 + 0.280922i \(0.909360\pi\)
\(860\) 0 0
\(861\) 7.81607 0.266371
\(862\) 0 0
\(863\) 23.1473 0.787942 0.393971 0.919123i \(-0.371101\pi\)
0.393971 + 0.919123i \(0.371101\pi\)
\(864\) 0 0
\(865\) 58.8632 2.00141
\(866\) 0 0
\(867\) 15.7530 0.534999
\(868\) 0 0
\(869\) 4.59620 0.155915
\(870\) 0 0
\(871\) −81.6044 −2.76506
\(872\) 0 0
\(873\) −1.23364 −0.0417524
\(874\) 0 0
\(875\) −12.8716 −0.435141
\(876\) 0 0
\(877\) 26.5396 0.896179 0.448089 0.893989i \(-0.352105\pi\)
0.448089 + 0.893989i \(0.352105\pi\)
\(878\) 0 0
\(879\) 36.2982 1.22431
\(880\) 0 0
\(881\) −37.0510 −1.24828 −0.624141 0.781312i \(-0.714551\pi\)
−0.624141 + 0.781312i \(0.714551\pi\)
\(882\) 0 0
\(883\) −5.17449 −0.174135 −0.0870677 0.996202i \(-0.527750\pi\)
−0.0870677 + 0.996202i \(0.527750\pi\)
\(884\) 0 0
\(885\) −58.3736 −1.96221
\(886\) 0 0
\(887\) 33.5647 1.12699 0.563496 0.826119i \(-0.309456\pi\)
0.563496 + 0.826119i \(0.309456\pi\)
\(888\) 0 0
\(889\) −25.9207 −0.869353
\(890\) 0 0
\(891\) 29.3606 0.983619
\(892\) 0 0
\(893\) −9.09204 −0.304253
\(894\) 0 0
\(895\) 31.3850 1.04908
\(896\) 0 0
\(897\) 41.4354 1.38349
\(898\) 0 0
\(899\) 8.47446 0.282639
\(900\) 0 0
\(901\) −35.3956 −1.17920
\(902\) 0 0
\(903\) 14.4692 0.481506
\(904\) 0 0
\(905\) −5.80992 −0.193128
\(906\) 0 0
\(907\) 0.229378 0.00761639 0.00380819 0.999993i \(-0.498788\pi\)
0.00380819 + 0.999993i \(0.498788\pi\)
\(908\) 0 0
\(909\) −0.899161 −0.0298233
\(910\) 0 0
\(911\) −26.1240 −0.865525 −0.432763 0.901508i \(-0.642461\pi\)
−0.432763 + 0.901508i \(0.642461\pi\)
\(912\) 0 0
\(913\) 31.5740 1.04495
\(914\) 0 0
\(915\) −53.9003 −1.78189
\(916\) 0 0
\(917\) 7.20815 0.238034
\(918\) 0 0
\(919\) 19.4548 0.641756 0.320878 0.947121i \(-0.396022\pi\)
0.320878 + 0.947121i \(0.396022\pi\)
\(920\) 0 0
\(921\) −7.68124 −0.253105
\(922\) 0 0
\(923\) 33.8460 1.11405
\(924\) 0 0
\(925\) −7.12608 −0.234304
\(926\) 0 0
\(927\) −2.12385 −0.0697565
\(928\) 0 0
\(929\) 21.7263 0.712818 0.356409 0.934330i \(-0.384001\pi\)
0.356409 + 0.934330i \(0.384001\pi\)
\(930\) 0 0
\(931\) 1.65042 0.0540905
\(932\) 0 0
\(933\) 14.7374 0.482481
\(934\) 0 0
\(935\) 53.9202 1.76338
\(936\) 0 0
\(937\) −32.2210 −1.05261 −0.526306 0.850295i \(-0.676423\pi\)
−0.526306 + 0.850295i \(0.676423\pi\)
\(938\) 0 0
\(939\) 3.48260 0.113650
\(940\) 0 0
\(941\) 14.6698 0.478223 0.239111 0.970992i \(-0.423144\pi\)
0.239111 + 0.970992i \(0.423144\pi\)
\(942\) 0 0
\(943\) −8.72912 −0.284259
\(944\) 0 0
\(945\) −34.4917 −1.12202
\(946\) 0 0
\(947\) 22.0982 0.718094 0.359047 0.933319i \(-0.383102\pi\)
0.359047 + 0.933319i \(0.383102\pi\)
\(948\) 0 0
\(949\) −56.7907 −1.84350
\(950\) 0 0
\(951\) −9.78545 −0.317315
\(952\) 0 0
\(953\) −2.69782 −0.0873911 −0.0436955 0.999045i \(-0.513913\pi\)
−0.0436955 + 0.999045i \(0.513913\pi\)
\(954\) 0 0
\(955\) −42.2481 −1.36712
\(956\) 0 0
\(957\) 10.9790 0.354900
\(958\) 0 0
\(959\) −6.84333 −0.220983
\(960\) 0 0
\(961\) −9.13751 −0.294758
\(962\) 0 0
\(963\) −5.63094 −0.181455
\(964\) 0 0
\(965\) 66.2253 2.13187
\(966\) 0 0
\(967\) 5.16391 0.166060 0.0830301 0.996547i \(-0.473540\pi\)
0.0830301 + 0.996547i \(0.473540\pi\)
\(968\) 0 0
\(969\) 7.15027 0.229700
\(970\) 0 0
\(971\) −3.22182 −0.103393 −0.0516965 0.998663i \(-0.516463\pi\)
−0.0516965 + 0.998663i \(0.516463\pi\)
\(972\) 0 0
\(973\) −35.5147 −1.13855
\(974\) 0 0
\(975\) −29.9722 −0.959879
\(976\) 0 0
\(977\) 44.4817 1.42310 0.711549 0.702637i \(-0.247994\pi\)
0.711549 + 0.702637i \(0.247994\pi\)
\(978\) 0 0
\(979\) 18.7530 0.599349
\(980\) 0 0
\(981\) −0.188044 −0.00600379
\(982\) 0 0
\(983\) 29.2976 0.934448 0.467224 0.884139i \(-0.345254\pi\)
0.467224 + 0.884139i \(0.345254\pi\)
\(984\) 0 0
\(985\) −8.16701 −0.260223
\(986\) 0 0
\(987\) 39.4986 1.25725
\(988\) 0 0
\(989\) −16.1595 −0.513841
\(990\) 0 0
\(991\) 21.0261 0.667915 0.333958 0.942588i \(-0.391616\pi\)
0.333958 + 0.942588i \(0.391616\pi\)
\(992\) 0 0
\(993\) 12.4571 0.395316
\(994\) 0 0
\(995\) −70.0774 −2.22160
\(996\) 0 0
\(997\) −44.8922 −1.42175 −0.710876 0.703317i \(-0.751701\pi\)
−0.710876 + 0.703317i \(0.751701\pi\)
\(998\) 0 0
\(999\) 13.0364 0.412452
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.1.34 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.34 44 1.1 even 1 trivial