Properties

Label 6008.2.a.b.1.43
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 1.43
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.95352 q^{3} -2.20957 q^{5} +2.79098 q^{7} +5.72330 q^{9} +O(q^{10})\) \(q+2.95352 q^{3} -2.20957 q^{5} +2.79098 q^{7} +5.72330 q^{9} -1.59219 q^{11} -3.09648 q^{13} -6.52601 q^{15} -6.40426 q^{17} -3.68929 q^{19} +8.24322 q^{21} +3.82834 q^{23} -0.117811 q^{25} +8.04333 q^{27} +1.84859 q^{29} -9.59961 q^{31} -4.70258 q^{33} -6.16685 q^{35} -9.44224 q^{37} -9.14553 q^{39} -9.33089 q^{41} -2.49925 q^{43} -12.6460 q^{45} -2.81656 q^{47} +0.789558 q^{49} -18.9151 q^{51} +1.77002 q^{53} +3.51806 q^{55} -10.8964 q^{57} +5.74373 q^{59} +2.55137 q^{61} +15.9736 q^{63} +6.84188 q^{65} +7.92611 q^{67} +11.3071 q^{69} +0.0832947 q^{71} -2.15722 q^{73} -0.347957 q^{75} -4.44377 q^{77} +3.81067 q^{79} +6.58627 q^{81} -2.22034 q^{83} +14.1506 q^{85} +5.45984 q^{87} +7.81827 q^{89} -8.64221 q^{91} -28.3527 q^{93} +8.15173 q^{95} -9.44586 q^{97} -9.11259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 2.95352 1.70522 0.852609 0.522550i \(-0.175019\pi\)
0.852609 + 0.522550i \(0.175019\pi\)
\(4\) 0 0
\(5\) −2.20957 −0.988149 −0.494074 0.869420i \(-0.664493\pi\)
−0.494074 + 0.869420i \(0.664493\pi\)
\(6\) 0 0
\(7\) 2.79098 1.05489 0.527445 0.849589i \(-0.323150\pi\)
0.527445 + 0.849589i \(0.323150\pi\)
\(8\) 0 0
\(9\) 5.72330 1.90777
\(10\) 0 0
\(11\) −1.59219 −0.480064 −0.240032 0.970765i \(-0.577158\pi\)
−0.240032 + 0.970765i \(0.577158\pi\)
\(12\) 0 0
\(13\) −3.09648 −0.858809 −0.429405 0.903112i \(-0.641277\pi\)
−0.429405 + 0.903112i \(0.641277\pi\)
\(14\) 0 0
\(15\) −6.52601 −1.68501
\(16\) 0 0
\(17\) −6.40426 −1.55326 −0.776630 0.629957i \(-0.783073\pi\)
−0.776630 + 0.629957i \(0.783073\pi\)
\(18\) 0 0
\(19\) −3.68929 −0.846381 −0.423190 0.906041i \(-0.639090\pi\)
−0.423190 + 0.906041i \(0.639090\pi\)
\(20\) 0 0
\(21\) 8.24322 1.79882
\(22\) 0 0
\(23\) 3.82834 0.798263 0.399132 0.916894i \(-0.369312\pi\)
0.399132 + 0.916894i \(0.369312\pi\)
\(24\) 0 0
\(25\) −0.117811 −0.0235621
\(26\) 0 0
\(27\) 8.04333 1.54794
\(28\) 0 0
\(29\) 1.84859 0.343274 0.171637 0.985160i \(-0.445094\pi\)
0.171637 + 0.985160i \(0.445094\pi\)
\(30\) 0 0
\(31\) −9.59961 −1.72414 −0.862071 0.506788i \(-0.830833\pi\)
−0.862071 + 0.506788i \(0.830833\pi\)
\(32\) 0 0
\(33\) −4.70258 −0.818613
\(34\) 0 0
\(35\) −6.16685 −1.04239
\(36\) 0 0
\(37\) −9.44224 −1.55230 −0.776148 0.630551i \(-0.782829\pi\)
−0.776148 + 0.630551i \(0.782829\pi\)
\(38\) 0 0
\(39\) −9.14553 −1.46446
\(40\) 0 0
\(41\) −9.33089 −1.45724 −0.728620 0.684918i \(-0.759838\pi\)
−0.728620 + 0.684918i \(0.759838\pi\)
\(42\) 0 0
\(43\) −2.49925 −0.381132 −0.190566 0.981674i \(-0.561032\pi\)
−0.190566 + 0.981674i \(0.561032\pi\)
\(44\) 0 0
\(45\) −12.6460 −1.88516
\(46\) 0 0
\(47\) −2.81656 −0.410838 −0.205419 0.978674i \(-0.565856\pi\)
−0.205419 + 0.978674i \(0.565856\pi\)
\(48\) 0 0
\(49\) 0.789558 0.112794
\(50\) 0 0
\(51\) −18.9151 −2.64865
\(52\) 0 0
\(53\) 1.77002 0.243131 0.121565 0.992583i \(-0.461209\pi\)
0.121565 + 0.992583i \(0.461209\pi\)
\(54\) 0 0
\(55\) 3.51806 0.474375
\(56\) 0 0
\(57\) −10.8964 −1.44326
\(58\) 0 0
\(59\) 5.74373 0.747770 0.373885 0.927475i \(-0.378025\pi\)
0.373885 + 0.927475i \(0.378025\pi\)
\(60\) 0 0
\(61\) 2.55137 0.326669 0.163334 0.986571i \(-0.447775\pi\)
0.163334 + 0.986571i \(0.447775\pi\)
\(62\) 0 0
\(63\) 15.9736 2.01249
\(64\) 0 0
\(65\) 6.84188 0.848631
\(66\) 0 0
\(67\) 7.92611 0.968329 0.484164 0.874977i \(-0.339124\pi\)
0.484164 + 0.874977i \(0.339124\pi\)
\(68\) 0 0
\(69\) 11.3071 1.36121
\(70\) 0 0
\(71\) 0.0832947 0.00988526 0.00494263 0.999988i \(-0.498427\pi\)
0.00494263 + 0.999988i \(0.498427\pi\)
\(72\) 0 0
\(73\) −2.15722 −0.252484 −0.126242 0.991999i \(-0.540292\pi\)
−0.126242 + 0.991999i \(0.540292\pi\)
\(74\) 0 0
\(75\) −0.347957 −0.0401786
\(76\) 0 0
\(77\) −4.44377 −0.506415
\(78\) 0 0
\(79\) 3.81067 0.428734 0.214367 0.976753i \(-0.431231\pi\)
0.214367 + 0.976753i \(0.431231\pi\)
\(80\) 0 0
\(81\) 6.58627 0.731808
\(82\) 0 0
\(83\) −2.22034 −0.243714 −0.121857 0.992548i \(-0.538885\pi\)
−0.121857 + 0.992548i \(0.538885\pi\)
\(84\) 0 0
\(85\) 14.1506 1.53485
\(86\) 0 0
\(87\) 5.45984 0.585356
\(88\) 0 0
\(89\) 7.81827 0.828735 0.414367 0.910110i \(-0.364003\pi\)
0.414367 + 0.910110i \(0.364003\pi\)
\(90\) 0 0
\(91\) −8.64221 −0.905950
\(92\) 0 0
\(93\) −28.3527 −2.94004
\(94\) 0 0
\(95\) 8.15173 0.836350
\(96\) 0 0
\(97\) −9.44586 −0.959081 −0.479541 0.877520i \(-0.659197\pi\)
−0.479541 + 0.877520i \(0.659197\pi\)
\(98\) 0 0
\(99\) −9.11259 −0.915850
\(100\) 0 0
\(101\) −5.00534 −0.498050 −0.249025 0.968497i \(-0.580110\pi\)
−0.249025 + 0.968497i \(0.580110\pi\)
\(102\) 0 0
\(103\) 5.08879 0.501413 0.250707 0.968063i \(-0.419337\pi\)
0.250707 + 0.968063i \(0.419337\pi\)
\(104\) 0 0
\(105\) −18.2140 −1.77750
\(106\) 0 0
\(107\) 13.0939 1.26584 0.632918 0.774219i \(-0.281857\pi\)
0.632918 + 0.774219i \(0.281857\pi\)
\(108\) 0 0
\(109\) −12.5138 −1.19860 −0.599301 0.800523i \(-0.704555\pi\)
−0.599301 + 0.800523i \(0.704555\pi\)
\(110\) 0 0
\(111\) −27.8879 −2.64700
\(112\) 0 0
\(113\) 9.39986 0.884265 0.442132 0.896950i \(-0.354222\pi\)
0.442132 + 0.896950i \(0.354222\pi\)
\(114\) 0 0
\(115\) −8.45897 −0.788803
\(116\) 0 0
\(117\) −17.7221 −1.63841
\(118\) 0 0
\(119\) −17.8741 −1.63852
\(120\) 0 0
\(121\) −8.46493 −0.769539
\(122\) 0 0
\(123\) −27.5590 −2.48491
\(124\) 0 0
\(125\) 11.3081 1.01143
\(126\) 0 0
\(127\) 21.3179 1.89166 0.945830 0.324661i \(-0.105250\pi\)
0.945830 + 0.324661i \(0.105250\pi\)
\(128\) 0 0
\(129\) −7.38160 −0.649913
\(130\) 0 0
\(131\) −3.57963 −0.312754 −0.156377 0.987697i \(-0.549982\pi\)
−0.156377 + 0.987697i \(0.549982\pi\)
\(132\) 0 0
\(133\) −10.2967 −0.892839
\(134\) 0 0
\(135\) −17.7723 −1.52959
\(136\) 0 0
\(137\) −22.0256 −1.88177 −0.940886 0.338723i \(-0.890005\pi\)
−0.940886 + 0.338723i \(0.890005\pi\)
\(138\) 0 0
\(139\) 13.3419 1.13164 0.565822 0.824527i \(-0.308559\pi\)
0.565822 + 0.824527i \(0.308559\pi\)
\(140\) 0 0
\(141\) −8.31879 −0.700568
\(142\) 0 0
\(143\) 4.93019 0.412283
\(144\) 0 0
\(145\) −4.08458 −0.339206
\(146\) 0 0
\(147\) 2.33198 0.192338
\(148\) 0 0
\(149\) −10.8924 −0.892339 −0.446169 0.894949i \(-0.647212\pi\)
−0.446169 + 0.894949i \(0.647212\pi\)
\(150\) 0 0
\(151\) 20.3935 1.65960 0.829800 0.558061i \(-0.188455\pi\)
0.829800 + 0.558061i \(0.188455\pi\)
\(152\) 0 0
\(153\) −36.6535 −2.96326
\(154\) 0 0
\(155\) 21.2110 1.70371
\(156\) 0 0
\(157\) 20.7969 1.65978 0.829888 0.557929i \(-0.188404\pi\)
0.829888 + 0.557929i \(0.188404\pi\)
\(158\) 0 0
\(159\) 5.22779 0.414591
\(160\) 0 0
\(161\) 10.6848 0.842081
\(162\) 0 0
\(163\) −6.50279 −0.509338 −0.254669 0.967028i \(-0.581966\pi\)
−0.254669 + 0.967028i \(0.581966\pi\)
\(164\) 0 0
\(165\) 10.3907 0.808912
\(166\) 0 0
\(167\) 2.59953 0.201158 0.100579 0.994929i \(-0.467931\pi\)
0.100579 + 0.994929i \(0.467931\pi\)
\(168\) 0 0
\(169\) −3.41181 −0.262447
\(170\) 0 0
\(171\) −21.1149 −1.61470
\(172\) 0 0
\(173\) −2.08423 −0.158461 −0.0792306 0.996856i \(-0.525246\pi\)
−0.0792306 + 0.996856i \(0.525246\pi\)
\(174\) 0 0
\(175\) −0.328807 −0.0248555
\(176\) 0 0
\(177\) 16.9642 1.27511
\(178\) 0 0
\(179\) −4.99236 −0.373147 −0.186573 0.982441i \(-0.559738\pi\)
−0.186573 + 0.982441i \(0.559738\pi\)
\(180\) 0 0
\(181\) −6.41894 −0.477116 −0.238558 0.971128i \(-0.576675\pi\)
−0.238558 + 0.971128i \(0.576675\pi\)
\(182\) 0 0
\(183\) 7.53552 0.557042
\(184\) 0 0
\(185\) 20.8633 1.53390
\(186\) 0 0
\(187\) 10.1968 0.745664
\(188\) 0 0
\(189\) 22.4488 1.63291
\(190\) 0 0
\(191\) 7.14655 0.517107 0.258553 0.965997i \(-0.416754\pi\)
0.258553 + 0.965997i \(0.416754\pi\)
\(192\) 0 0
\(193\) −10.7630 −0.774738 −0.387369 0.921925i \(-0.626616\pi\)
−0.387369 + 0.921925i \(0.626616\pi\)
\(194\) 0 0
\(195\) 20.2077 1.44710
\(196\) 0 0
\(197\) 5.15452 0.367244 0.183622 0.982997i \(-0.441218\pi\)
0.183622 + 0.982997i \(0.441218\pi\)
\(198\) 0 0
\(199\) −9.68144 −0.686299 −0.343150 0.939281i \(-0.611494\pi\)
−0.343150 + 0.939281i \(0.611494\pi\)
\(200\) 0 0
\(201\) 23.4100 1.65121
\(202\) 0 0
\(203\) 5.15936 0.362116
\(204\) 0 0
\(205\) 20.6172 1.43997
\(206\) 0 0
\(207\) 21.9107 1.52290
\(208\) 0 0
\(209\) 5.87405 0.406317
\(210\) 0 0
\(211\) −5.36365 −0.369249 −0.184624 0.982809i \(-0.559107\pi\)
−0.184624 + 0.982809i \(0.559107\pi\)
\(212\) 0 0
\(213\) 0.246013 0.0168565
\(214\) 0 0
\(215\) 5.52226 0.376615
\(216\) 0 0
\(217\) −26.7923 −1.81878
\(218\) 0 0
\(219\) −6.37141 −0.430540
\(220\) 0 0
\(221\) 19.8307 1.33395
\(222\) 0 0
\(223\) 9.71908 0.650838 0.325419 0.945570i \(-0.394495\pi\)
0.325419 + 0.945570i \(0.394495\pi\)
\(224\) 0 0
\(225\) −0.674266 −0.0449511
\(226\) 0 0
\(227\) 4.18543 0.277797 0.138898 0.990307i \(-0.455644\pi\)
0.138898 + 0.990307i \(0.455644\pi\)
\(228\) 0 0
\(229\) −16.3864 −1.08285 −0.541423 0.840750i \(-0.682114\pi\)
−0.541423 + 0.840750i \(0.682114\pi\)
\(230\) 0 0
\(231\) −13.1248 −0.863547
\(232\) 0 0
\(233\) −9.39839 −0.615709 −0.307855 0.951433i \(-0.599611\pi\)
−0.307855 + 0.951433i \(0.599611\pi\)
\(234\) 0 0
\(235\) 6.22339 0.405969
\(236\) 0 0
\(237\) 11.2549 0.731085
\(238\) 0 0
\(239\) 23.1810 1.49946 0.749728 0.661746i \(-0.230184\pi\)
0.749728 + 0.661746i \(0.230184\pi\)
\(240\) 0 0
\(241\) −16.6968 −1.07554 −0.537768 0.843093i \(-0.680732\pi\)
−0.537768 + 0.843093i \(0.680732\pi\)
\(242\) 0 0
\(243\) −4.67730 −0.300049
\(244\) 0 0
\(245\) −1.74458 −0.111457
\(246\) 0 0
\(247\) 11.4238 0.726880
\(248\) 0 0
\(249\) −6.55782 −0.415585
\(250\) 0 0
\(251\) 19.8438 1.25253 0.626265 0.779610i \(-0.284583\pi\)
0.626265 + 0.779610i \(0.284583\pi\)
\(252\) 0 0
\(253\) −6.09545 −0.383217
\(254\) 0 0
\(255\) 41.7942 2.61726
\(256\) 0 0
\(257\) −6.77049 −0.422332 −0.211166 0.977450i \(-0.567726\pi\)
−0.211166 + 0.977450i \(0.567726\pi\)
\(258\) 0 0
\(259\) −26.3531 −1.63750
\(260\) 0 0
\(261\) 10.5800 0.654886
\(262\) 0 0
\(263\) −2.61357 −0.161160 −0.0805798 0.996748i \(-0.525677\pi\)
−0.0805798 + 0.996748i \(0.525677\pi\)
\(264\) 0 0
\(265\) −3.91098 −0.240249
\(266\) 0 0
\(267\) 23.0914 1.41317
\(268\) 0 0
\(269\) 6.39158 0.389701 0.194851 0.980833i \(-0.437578\pi\)
0.194851 + 0.980833i \(0.437578\pi\)
\(270\) 0 0
\(271\) 6.56193 0.398609 0.199305 0.979938i \(-0.436132\pi\)
0.199305 + 0.979938i \(0.436132\pi\)
\(272\) 0 0
\(273\) −25.5250 −1.54484
\(274\) 0 0
\(275\) 0.187577 0.0113113
\(276\) 0 0
\(277\) −5.47130 −0.328739 −0.164369 0.986399i \(-0.552559\pi\)
−0.164369 + 0.986399i \(0.552559\pi\)
\(278\) 0 0
\(279\) −54.9415 −3.28926
\(280\) 0 0
\(281\) −20.7471 −1.23767 −0.618833 0.785523i \(-0.712394\pi\)
−0.618833 + 0.785523i \(0.712394\pi\)
\(282\) 0 0
\(283\) −6.53526 −0.388481 −0.194240 0.980954i \(-0.562224\pi\)
−0.194240 + 0.980954i \(0.562224\pi\)
\(284\) 0 0
\(285\) 24.0763 1.42616
\(286\) 0 0
\(287\) −26.0423 −1.53723
\(288\) 0 0
\(289\) 24.0145 1.41262
\(290\) 0 0
\(291\) −27.8986 −1.63544
\(292\) 0 0
\(293\) 20.0638 1.17214 0.586071 0.810260i \(-0.300674\pi\)
0.586071 + 0.810260i \(0.300674\pi\)
\(294\) 0 0
\(295\) −12.6912 −0.738908
\(296\) 0 0
\(297\) −12.8065 −0.743110
\(298\) 0 0
\(299\) −11.8544 −0.685556
\(300\) 0 0
\(301\) −6.97535 −0.402053
\(302\) 0 0
\(303\) −14.7834 −0.849283
\(304\) 0 0
\(305\) −5.63742 −0.322797
\(306\) 0 0
\(307\) 13.2533 0.756405 0.378202 0.925723i \(-0.376542\pi\)
0.378202 + 0.925723i \(0.376542\pi\)
\(308\) 0 0
\(309\) 15.0299 0.855018
\(310\) 0 0
\(311\) −20.7386 −1.17598 −0.587990 0.808869i \(-0.700080\pi\)
−0.587990 + 0.808869i \(0.700080\pi\)
\(312\) 0 0
\(313\) −12.4283 −0.702489 −0.351244 0.936284i \(-0.614241\pi\)
−0.351244 + 0.936284i \(0.614241\pi\)
\(314\) 0 0
\(315\) −35.2948 −1.98863
\(316\) 0 0
\(317\) −7.73239 −0.434295 −0.217147 0.976139i \(-0.569675\pi\)
−0.217147 + 0.976139i \(0.569675\pi\)
\(318\) 0 0
\(319\) −2.94330 −0.164793
\(320\) 0 0
\(321\) 38.6732 2.15853
\(322\) 0 0
\(323\) 23.6271 1.31465
\(324\) 0 0
\(325\) 0.364798 0.0202354
\(326\) 0 0
\(327\) −36.9597 −2.04388
\(328\) 0 0
\(329\) −7.86097 −0.433389
\(330\) 0 0
\(331\) −0.796235 −0.0437650 −0.0218825 0.999761i \(-0.506966\pi\)
−0.0218825 + 0.999761i \(0.506966\pi\)
\(332\) 0 0
\(333\) −54.0408 −2.96142
\(334\) 0 0
\(335\) −17.5133 −0.956853
\(336\) 0 0
\(337\) −25.3093 −1.37868 −0.689342 0.724437i \(-0.742100\pi\)
−0.689342 + 0.724437i \(0.742100\pi\)
\(338\) 0 0
\(339\) 27.7627 1.50786
\(340\) 0 0
\(341\) 15.2844 0.827698
\(342\) 0 0
\(343\) −17.3332 −0.935905
\(344\) 0 0
\(345\) −24.9838 −1.34508
\(346\) 0 0
\(347\) −2.11729 −0.113662 −0.0568310 0.998384i \(-0.518100\pi\)
−0.0568310 + 0.998384i \(0.518100\pi\)
\(348\) 0 0
\(349\) 7.59151 0.406364 0.203182 0.979141i \(-0.434872\pi\)
0.203182 + 0.979141i \(0.434872\pi\)
\(350\) 0 0
\(351\) −24.9060 −1.32939
\(352\) 0 0
\(353\) 5.83946 0.310803 0.155401 0.987851i \(-0.450333\pi\)
0.155401 + 0.987851i \(0.450333\pi\)
\(354\) 0 0
\(355\) −0.184045 −0.00976811
\(356\) 0 0
\(357\) −52.7917 −2.79403
\(358\) 0 0
\(359\) 25.8687 1.36530 0.682649 0.730746i \(-0.260828\pi\)
0.682649 + 0.730746i \(0.260828\pi\)
\(360\) 0 0
\(361\) −5.38915 −0.283639
\(362\) 0 0
\(363\) −25.0014 −1.31223
\(364\) 0 0
\(365\) 4.76653 0.249492
\(366\) 0 0
\(367\) −2.50518 −0.130769 −0.0653846 0.997860i \(-0.520827\pi\)
−0.0653846 + 0.997860i \(0.520827\pi\)
\(368\) 0 0
\(369\) −53.4035 −2.78007
\(370\) 0 0
\(371\) 4.94008 0.256476
\(372\) 0 0
\(373\) 25.7541 1.33350 0.666748 0.745283i \(-0.267686\pi\)
0.666748 + 0.745283i \(0.267686\pi\)
\(374\) 0 0
\(375\) 33.3989 1.72471
\(376\) 0 0
\(377\) −5.72411 −0.294807
\(378\) 0 0
\(379\) 5.75495 0.295612 0.147806 0.989016i \(-0.452779\pi\)
0.147806 + 0.989016i \(0.452779\pi\)
\(380\) 0 0
\(381\) 62.9630 3.22569
\(382\) 0 0
\(383\) 15.4505 0.789483 0.394741 0.918792i \(-0.370834\pi\)
0.394741 + 0.918792i \(0.370834\pi\)
\(384\) 0 0
\(385\) 9.81882 0.500413
\(386\) 0 0
\(387\) −14.3040 −0.727111
\(388\) 0 0
\(389\) 32.6086 1.65332 0.826662 0.562699i \(-0.190237\pi\)
0.826662 + 0.562699i \(0.190237\pi\)
\(390\) 0 0
\(391\) −24.5177 −1.23991
\(392\) 0 0
\(393\) −10.5725 −0.533314
\(394\) 0 0
\(395\) −8.41994 −0.423653
\(396\) 0 0
\(397\) −19.5235 −0.979858 −0.489929 0.871762i \(-0.662977\pi\)
−0.489929 + 0.871762i \(0.662977\pi\)
\(398\) 0 0
\(399\) −30.4116 −1.52249
\(400\) 0 0
\(401\) −36.1517 −1.80533 −0.902666 0.430342i \(-0.858393\pi\)
−0.902666 + 0.430342i \(0.858393\pi\)
\(402\) 0 0
\(403\) 29.7250 1.48071
\(404\) 0 0
\(405\) −14.5528 −0.723135
\(406\) 0 0
\(407\) 15.0339 0.745201
\(408\) 0 0
\(409\) −20.8489 −1.03091 −0.515456 0.856916i \(-0.672377\pi\)
−0.515456 + 0.856916i \(0.672377\pi\)
\(410\) 0 0
\(411\) −65.0531 −3.20883
\(412\) 0 0
\(413\) 16.0306 0.788816
\(414\) 0 0
\(415\) 4.90599 0.240825
\(416\) 0 0
\(417\) 39.4056 1.92970
\(418\) 0 0
\(419\) −19.6753 −0.961200 −0.480600 0.876940i \(-0.659581\pi\)
−0.480600 + 0.876940i \(0.659581\pi\)
\(420\) 0 0
\(421\) −35.1107 −1.71119 −0.855594 0.517647i \(-0.826808\pi\)
−0.855594 + 0.517647i \(0.826808\pi\)
\(422\) 0 0
\(423\) −16.1200 −0.783783
\(424\) 0 0
\(425\) 0.754490 0.0365981
\(426\) 0 0
\(427\) 7.12081 0.344600
\(428\) 0 0
\(429\) 14.5614 0.703033
\(430\) 0 0
\(431\) −6.91371 −0.333022 −0.166511 0.986040i \(-0.553250\pi\)
−0.166511 + 0.986040i \(0.553250\pi\)
\(432\) 0 0
\(433\) 2.01226 0.0967030 0.0483515 0.998830i \(-0.484603\pi\)
0.0483515 + 0.998830i \(0.484603\pi\)
\(434\) 0 0
\(435\) −12.0639 −0.578419
\(436\) 0 0
\(437\) −14.1238 −0.675635
\(438\) 0 0
\(439\) −39.9694 −1.90763 −0.953817 0.300387i \(-0.902884\pi\)
−0.953817 + 0.300387i \(0.902884\pi\)
\(440\) 0 0
\(441\) 4.51888 0.215185
\(442\) 0 0
\(443\) 18.6185 0.884590 0.442295 0.896870i \(-0.354164\pi\)
0.442295 + 0.896870i \(0.354164\pi\)
\(444\) 0 0
\(445\) −17.2750 −0.818913
\(446\) 0 0
\(447\) −32.1709 −1.52163
\(448\) 0 0
\(449\) −3.16958 −0.149582 −0.0747909 0.997199i \(-0.523829\pi\)
−0.0747909 + 0.997199i \(0.523829\pi\)
\(450\) 0 0
\(451\) 14.8566 0.699568
\(452\) 0 0
\(453\) 60.2327 2.82998
\(454\) 0 0
\(455\) 19.0955 0.895213
\(456\) 0 0
\(457\) 4.36090 0.203994 0.101997 0.994785i \(-0.467477\pi\)
0.101997 + 0.994785i \(0.467477\pi\)
\(458\) 0 0
\(459\) −51.5116 −2.40435
\(460\) 0 0
\(461\) 16.1343 0.751451 0.375725 0.926731i \(-0.377394\pi\)
0.375725 + 0.926731i \(0.377394\pi\)
\(462\) 0 0
\(463\) −0.0431464 −0.00200518 −0.00100259 0.999999i \(-0.500319\pi\)
−0.00100259 + 0.999999i \(0.500319\pi\)
\(464\) 0 0
\(465\) 62.6472 2.90519
\(466\) 0 0
\(467\) 12.9118 0.597485 0.298743 0.954334i \(-0.403433\pi\)
0.298743 + 0.954334i \(0.403433\pi\)
\(468\) 0 0
\(469\) 22.1216 1.02148
\(470\) 0 0
\(471\) 61.4243 2.83028
\(472\) 0 0
\(473\) 3.97929 0.182968
\(474\) 0 0
\(475\) 0.434637 0.0199425
\(476\) 0 0
\(477\) 10.1304 0.463837
\(478\) 0 0
\(479\) 21.4679 0.980893 0.490447 0.871471i \(-0.336834\pi\)
0.490447 + 0.871471i \(0.336834\pi\)
\(480\) 0 0
\(481\) 29.2377 1.33313
\(482\) 0 0
\(483\) 31.5578 1.43593
\(484\) 0 0
\(485\) 20.8713 0.947715
\(486\) 0 0
\(487\) −38.2038 −1.73118 −0.865590 0.500754i \(-0.833056\pi\)
−0.865590 + 0.500754i \(0.833056\pi\)
\(488\) 0 0
\(489\) −19.2061 −0.868532
\(490\) 0 0
\(491\) −39.1385 −1.76630 −0.883148 0.469094i \(-0.844580\pi\)
−0.883148 + 0.469094i \(0.844580\pi\)
\(492\) 0 0
\(493\) −11.8388 −0.533193
\(494\) 0 0
\(495\) 20.1349 0.904996
\(496\) 0 0
\(497\) 0.232474 0.0104279
\(498\) 0 0
\(499\) −7.40982 −0.331709 −0.165854 0.986150i \(-0.553038\pi\)
−0.165854 + 0.986150i \(0.553038\pi\)
\(500\) 0 0
\(501\) 7.67778 0.343018
\(502\) 0 0
\(503\) −7.40546 −0.330193 −0.165096 0.986277i \(-0.552794\pi\)
−0.165096 + 0.986277i \(0.552794\pi\)
\(504\) 0 0
\(505\) 11.0596 0.492147
\(506\) 0 0
\(507\) −10.0769 −0.447529
\(508\) 0 0
\(509\) 41.1793 1.82524 0.912620 0.408809i \(-0.134056\pi\)
0.912620 + 0.408809i \(0.134056\pi\)
\(510\) 0 0
\(511\) −6.02076 −0.266343
\(512\) 0 0
\(513\) −29.6742 −1.31015
\(514\) 0 0
\(515\) −11.2440 −0.495471
\(516\) 0 0
\(517\) 4.48451 0.197229
\(518\) 0 0
\(519\) −6.15582 −0.270211
\(520\) 0 0
\(521\) 14.3037 0.626657 0.313329 0.949645i \(-0.398556\pi\)
0.313329 + 0.949645i \(0.398556\pi\)
\(522\) 0 0
\(523\) −36.1029 −1.57867 −0.789336 0.613962i \(-0.789575\pi\)
−0.789336 + 0.613962i \(0.789575\pi\)
\(524\) 0 0
\(525\) −0.971139 −0.0423840
\(526\) 0 0
\(527\) 61.4784 2.67804
\(528\) 0 0
\(529\) −8.34383 −0.362775
\(530\) 0 0
\(531\) 32.8731 1.42657
\(532\) 0 0
\(533\) 28.8929 1.25149
\(534\) 0 0
\(535\) −28.9319 −1.25083
\(536\) 0 0
\(537\) −14.7451 −0.636296
\(538\) 0 0
\(539\) −1.25713 −0.0541484
\(540\) 0 0
\(541\) 28.7919 1.23786 0.618930 0.785446i \(-0.287567\pi\)
0.618930 + 0.785446i \(0.287567\pi\)
\(542\) 0 0
\(543\) −18.9585 −0.813586
\(544\) 0 0
\(545\) 27.6500 1.18440
\(546\) 0 0
\(547\) 9.12238 0.390045 0.195022 0.980799i \(-0.437522\pi\)
0.195022 + 0.980799i \(0.437522\pi\)
\(548\) 0 0
\(549\) 14.6022 0.623208
\(550\) 0 0
\(551\) −6.81997 −0.290540
\(552\) 0 0
\(553\) 10.6355 0.452267
\(554\) 0 0
\(555\) 61.6202 2.61563
\(556\) 0 0
\(557\) 37.1915 1.57585 0.787927 0.615769i \(-0.211155\pi\)
0.787927 + 0.615769i \(0.211155\pi\)
\(558\) 0 0
\(559\) 7.73888 0.327320
\(560\) 0 0
\(561\) 30.1165 1.27152
\(562\) 0 0
\(563\) 38.4653 1.62112 0.810559 0.585657i \(-0.199164\pi\)
0.810559 + 0.585657i \(0.199164\pi\)
\(564\) 0 0
\(565\) −20.7696 −0.873785
\(566\) 0 0
\(567\) 18.3821 0.771977
\(568\) 0 0
\(569\) 15.1036 0.633178 0.316589 0.948563i \(-0.397462\pi\)
0.316589 + 0.948563i \(0.397462\pi\)
\(570\) 0 0
\(571\) −35.5136 −1.48620 −0.743100 0.669181i \(-0.766645\pi\)
−0.743100 + 0.669181i \(0.766645\pi\)
\(572\) 0 0
\(573\) 21.1075 0.881779
\(574\) 0 0
\(575\) −0.451019 −0.0188088
\(576\) 0 0
\(577\) −8.28053 −0.344723 −0.172362 0.985034i \(-0.555140\pi\)
−0.172362 + 0.985034i \(0.555140\pi\)
\(578\) 0 0
\(579\) −31.7888 −1.32110
\(580\) 0 0
\(581\) −6.19691 −0.257091
\(582\) 0 0
\(583\) −2.81821 −0.116718
\(584\) 0 0
\(585\) 39.1582 1.61899
\(586\) 0 0
\(587\) −8.17101 −0.337254 −0.168627 0.985680i \(-0.553933\pi\)
−0.168627 + 0.985680i \(0.553933\pi\)
\(588\) 0 0
\(589\) 35.4157 1.45928
\(590\) 0 0
\(591\) 15.2240 0.626231
\(592\) 0 0
\(593\) −9.96319 −0.409139 −0.204570 0.978852i \(-0.565579\pi\)
−0.204570 + 0.978852i \(0.565579\pi\)
\(594\) 0 0
\(595\) 39.4941 1.61910
\(596\) 0 0
\(597\) −28.5944 −1.17029
\(598\) 0 0
\(599\) 19.8594 0.811433 0.405717 0.913999i \(-0.367022\pi\)
0.405717 + 0.913999i \(0.367022\pi\)
\(600\) 0 0
\(601\) 21.1165 0.861361 0.430680 0.902504i \(-0.358274\pi\)
0.430680 + 0.902504i \(0.358274\pi\)
\(602\) 0 0
\(603\) 45.3635 1.84735
\(604\) 0 0
\(605\) 18.7038 0.760419
\(606\) 0 0
\(607\) −23.1420 −0.939305 −0.469653 0.882851i \(-0.655621\pi\)
−0.469653 + 0.882851i \(0.655621\pi\)
\(608\) 0 0
\(609\) 15.2383 0.617487
\(610\) 0 0
\(611\) 8.72144 0.352832
\(612\) 0 0
\(613\) −31.0338 −1.25344 −0.626721 0.779244i \(-0.715603\pi\)
−0.626721 + 0.779244i \(0.715603\pi\)
\(614\) 0 0
\(615\) 60.8935 2.45546
\(616\) 0 0
\(617\) −21.7744 −0.876606 −0.438303 0.898827i \(-0.644420\pi\)
−0.438303 + 0.898827i \(0.644420\pi\)
\(618\) 0 0
\(619\) 30.3890 1.22144 0.610719 0.791848i \(-0.290881\pi\)
0.610719 + 0.791848i \(0.290881\pi\)
\(620\) 0 0
\(621\) 30.7926 1.23566
\(622\) 0 0
\(623\) 21.8206 0.874225
\(624\) 0 0
\(625\) −24.3971 −0.975883
\(626\) 0 0
\(627\) 17.3492 0.692859
\(628\) 0 0
\(629\) 60.4705 2.41112
\(630\) 0 0
\(631\) 22.5313 0.896958 0.448479 0.893793i \(-0.351966\pi\)
0.448479 + 0.893793i \(0.351966\pi\)
\(632\) 0 0
\(633\) −15.8417 −0.629649
\(634\) 0 0
\(635\) −47.1034 −1.86924
\(636\) 0 0
\(637\) −2.44485 −0.0968686
\(638\) 0 0
\(639\) 0.476721 0.0188588
\(640\) 0 0
\(641\) −14.4396 −0.570331 −0.285165 0.958478i \(-0.592048\pi\)
−0.285165 + 0.958478i \(0.592048\pi\)
\(642\) 0 0
\(643\) −25.9112 −1.02184 −0.510920 0.859629i \(-0.670695\pi\)
−0.510920 + 0.859629i \(0.670695\pi\)
\(644\) 0 0
\(645\) 16.3101 0.642211
\(646\) 0 0
\(647\) −27.6243 −1.08602 −0.543012 0.839725i \(-0.682716\pi\)
−0.543012 + 0.839725i \(0.682716\pi\)
\(648\) 0 0
\(649\) −9.14512 −0.358977
\(650\) 0 0
\(651\) −79.1317 −3.10142
\(652\) 0 0
\(653\) −21.3271 −0.834595 −0.417297 0.908770i \(-0.637023\pi\)
−0.417297 + 0.908770i \(0.637023\pi\)
\(654\) 0 0
\(655\) 7.90945 0.309048
\(656\) 0 0
\(657\) −12.3464 −0.481681
\(658\) 0 0
\(659\) 23.0886 0.899406 0.449703 0.893178i \(-0.351530\pi\)
0.449703 + 0.893178i \(0.351530\pi\)
\(660\) 0 0
\(661\) −35.1231 −1.36613 −0.683066 0.730357i \(-0.739354\pi\)
−0.683066 + 0.730357i \(0.739354\pi\)
\(662\) 0 0
\(663\) 58.5703 2.27468
\(664\) 0 0
\(665\) 22.7513 0.882258
\(666\) 0 0
\(667\) 7.07701 0.274023
\(668\) 0 0
\(669\) 28.7055 1.10982
\(670\) 0 0
\(671\) −4.06226 −0.156822
\(672\) 0 0
\(673\) 0.258351 0.00995868 0.00497934 0.999988i \(-0.498415\pi\)
0.00497934 + 0.999988i \(0.498415\pi\)
\(674\) 0 0
\(675\) −0.947590 −0.0364728
\(676\) 0 0
\(677\) 11.2964 0.434155 0.217077 0.976154i \(-0.430348\pi\)
0.217077 + 0.976154i \(0.430348\pi\)
\(678\) 0 0
\(679\) −26.3632 −1.01173
\(680\) 0 0
\(681\) 12.3618 0.473704
\(682\) 0 0
\(683\) −29.0402 −1.11119 −0.555597 0.831452i \(-0.687510\pi\)
−0.555597 + 0.831452i \(0.687510\pi\)
\(684\) 0 0
\(685\) 48.6670 1.85947
\(686\) 0 0
\(687\) −48.3977 −1.84649
\(688\) 0 0
\(689\) −5.48083 −0.208803
\(690\) 0 0
\(691\) −37.4622 −1.42513 −0.712565 0.701606i \(-0.752467\pi\)
−0.712565 + 0.701606i \(0.752467\pi\)
\(692\) 0 0
\(693\) −25.4330 −0.966121
\(694\) 0 0
\(695\) −29.4798 −1.11823
\(696\) 0 0
\(697\) 59.7574 2.26347
\(698\) 0 0
\(699\) −27.7584 −1.04992
\(700\) 0 0
\(701\) 13.3760 0.505204 0.252602 0.967570i \(-0.418714\pi\)
0.252602 + 0.967570i \(0.418714\pi\)
\(702\) 0 0
\(703\) 34.8352 1.31383
\(704\) 0 0
\(705\) 18.3809 0.692266
\(706\) 0 0
\(707\) −13.9698 −0.525388
\(708\) 0 0
\(709\) −22.4683 −0.843815 −0.421907 0.906639i \(-0.638639\pi\)
−0.421907 + 0.906639i \(0.638639\pi\)
\(710\) 0 0
\(711\) 21.8096 0.817925
\(712\) 0 0
\(713\) −36.7506 −1.37632
\(714\) 0 0
\(715\) −10.8936 −0.407397
\(716\) 0 0
\(717\) 68.4658 2.55690
\(718\) 0 0
\(719\) −23.2297 −0.866320 −0.433160 0.901317i \(-0.642601\pi\)
−0.433160 + 0.901317i \(0.642601\pi\)
\(720\) 0 0
\(721\) 14.2027 0.528936
\(722\) 0 0
\(723\) −49.3144 −1.83402
\(724\) 0 0
\(725\) −0.217783 −0.00808826
\(726\) 0 0
\(727\) −24.2597 −0.899742 −0.449871 0.893094i \(-0.648530\pi\)
−0.449871 + 0.893094i \(0.648530\pi\)
\(728\) 0 0
\(729\) −33.5733 −1.24346
\(730\) 0 0
\(731\) 16.0058 0.591997
\(732\) 0 0
\(733\) 8.52348 0.314822 0.157411 0.987533i \(-0.449685\pi\)
0.157411 + 0.987533i \(0.449685\pi\)
\(734\) 0 0
\(735\) −5.15267 −0.190059
\(736\) 0 0
\(737\) −12.6199 −0.464860
\(738\) 0 0
\(739\) −19.3144 −0.710493 −0.355246 0.934773i \(-0.615603\pi\)
−0.355246 + 0.934773i \(0.615603\pi\)
\(740\) 0 0
\(741\) 33.7405 1.23949
\(742\) 0 0
\(743\) −19.5656 −0.717793 −0.358897 0.933377i \(-0.616847\pi\)
−0.358897 + 0.933377i \(0.616847\pi\)
\(744\) 0 0
\(745\) 24.0675 0.881763
\(746\) 0 0
\(747\) −12.7077 −0.464949
\(748\) 0 0
\(749\) 36.5448 1.33532
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 58.6092 2.13584
\(754\) 0 0
\(755\) −45.0608 −1.63993
\(756\) 0 0
\(757\) 34.8637 1.26714 0.633572 0.773684i \(-0.281588\pi\)
0.633572 + 0.773684i \(0.281588\pi\)
\(758\) 0 0
\(759\) −18.0030 −0.653469
\(760\) 0 0
\(761\) −48.0128 −1.74046 −0.870231 0.492644i \(-0.836030\pi\)
−0.870231 + 0.492644i \(0.836030\pi\)
\(762\) 0 0
\(763\) −34.9257 −1.26439
\(764\) 0 0
\(765\) 80.9884 2.92814
\(766\) 0 0
\(767\) −17.7854 −0.642192
\(768\) 0 0
\(769\) −9.08806 −0.327724 −0.163862 0.986483i \(-0.552395\pi\)
−0.163862 + 0.986483i \(0.552395\pi\)
\(770\) 0 0
\(771\) −19.9968 −0.720167
\(772\) 0 0
\(773\) −11.8463 −0.426082 −0.213041 0.977043i \(-0.568337\pi\)
−0.213041 + 0.977043i \(0.568337\pi\)
\(774\) 0 0
\(775\) 1.13094 0.0406244
\(776\) 0 0
\(777\) −77.8345 −2.79230
\(778\) 0 0
\(779\) 34.4243 1.23338
\(780\) 0 0
\(781\) −0.132621 −0.00474556
\(782\) 0 0
\(783\) 14.8688 0.531367
\(784\) 0 0
\(785\) −45.9523 −1.64011
\(786\) 0 0
\(787\) 39.0222 1.39099 0.695496 0.718530i \(-0.255185\pi\)
0.695496 + 0.718530i \(0.255185\pi\)
\(788\) 0 0
\(789\) −7.71924 −0.274812
\(790\) 0 0
\(791\) 26.2348 0.932802
\(792\) 0 0
\(793\) −7.90026 −0.280546
\(794\) 0 0
\(795\) −11.5512 −0.409677
\(796\) 0 0
\(797\) −25.5010 −0.903292 −0.451646 0.892197i \(-0.649163\pi\)
−0.451646 + 0.892197i \(0.649163\pi\)
\(798\) 0 0
\(799\) 18.0380 0.638138
\(800\) 0 0
\(801\) 44.7463 1.58103
\(802\) 0 0
\(803\) 3.43471 0.121208
\(804\) 0 0
\(805\) −23.6088 −0.832101
\(806\) 0 0
\(807\) 18.8777 0.664526
\(808\) 0 0
\(809\) 48.1735 1.69369 0.846844 0.531841i \(-0.178500\pi\)
0.846844 + 0.531841i \(0.178500\pi\)
\(810\) 0 0
\(811\) 36.9614 1.29789 0.648945 0.760835i \(-0.275211\pi\)
0.648945 + 0.760835i \(0.275211\pi\)
\(812\) 0 0
\(813\) 19.3808 0.679715
\(814\) 0 0
\(815\) 14.3684 0.503301
\(816\) 0 0
\(817\) 9.22046 0.322583
\(818\) 0 0
\(819\) −49.4620 −1.72834
\(820\) 0 0
\(821\) 29.5519 1.03137 0.515684 0.856779i \(-0.327538\pi\)
0.515684 + 0.856779i \(0.327538\pi\)
\(822\) 0 0
\(823\) 28.1257 0.980401 0.490201 0.871610i \(-0.336923\pi\)
0.490201 + 0.871610i \(0.336923\pi\)
\(824\) 0 0
\(825\) 0.554013 0.0192883
\(826\) 0 0
\(827\) −18.4000 −0.639832 −0.319916 0.947446i \(-0.603655\pi\)
−0.319916 + 0.947446i \(0.603655\pi\)
\(828\) 0 0
\(829\) 10.5514 0.366465 0.183233 0.983070i \(-0.441344\pi\)
0.183233 + 0.983070i \(0.441344\pi\)
\(830\) 0 0
\(831\) −16.1596 −0.560571
\(832\) 0 0
\(833\) −5.05653 −0.175199
\(834\) 0 0
\(835\) −5.74384 −0.198774
\(836\) 0 0
\(837\) −77.2129 −2.66887
\(838\) 0 0
\(839\) −16.9931 −0.586668 −0.293334 0.956010i \(-0.594765\pi\)
−0.293334 + 0.956010i \(0.594765\pi\)
\(840\) 0 0
\(841\) −25.5827 −0.882163
\(842\) 0 0
\(843\) −61.2769 −2.11049
\(844\) 0 0
\(845\) 7.53862 0.259336
\(846\) 0 0
\(847\) −23.6254 −0.811779
\(848\) 0 0
\(849\) −19.3020 −0.662444
\(850\) 0 0
\(851\) −36.1481 −1.23914
\(852\) 0 0
\(853\) −32.2185 −1.10314 −0.551569 0.834129i \(-0.685971\pi\)
−0.551569 + 0.834129i \(0.685971\pi\)
\(854\) 0 0
\(855\) 46.6548 1.59556
\(856\) 0 0
\(857\) 27.1617 0.927825 0.463912 0.885881i \(-0.346445\pi\)
0.463912 + 0.885881i \(0.346445\pi\)
\(858\) 0 0
\(859\) 24.0978 0.822207 0.411103 0.911589i \(-0.365144\pi\)
0.411103 + 0.911589i \(0.365144\pi\)
\(860\) 0 0
\(861\) −76.9165 −2.62131
\(862\) 0 0
\(863\) 39.0759 1.33016 0.665079 0.746773i \(-0.268398\pi\)
0.665079 + 0.746773i \(0.268398\pi\)
\(864\) 0 0
\(865\) 4.60525 0.156583
\(866\) 0 0
\(867\) 70.9274 2.40882
\(868\) 0 0
\(869\) −6.06732 −0.205820
\(870\) 0 0
\(871\) −24.5431 −0.831610
\(872\) 0 0
\(873\) −54.0615 −1.82970
\(874\) 0 0
\(875\) 31.5608 1.06695
\(876\) 0 0
\(877\) 44.5102 1.50300 0.751501 0.659732i \(-0.229330\pi\)
0.751501 + 0.659732i \(0.229330\pi\)
\(878\) 0 0
\(879\) 59.2590 1.99876
\(880\) 0 0
\(881\) 54.5078 1.83641 0.918206 0.396102i \(-0.129637\pi\)
0.918206 + 0.396102i \(0.129637\pi\)
\(882\) 0 0
\(883\) 13.4818 0.453699 0.226849 0.973930i \(-0.427158\pi\)
0.226849 + 0.973930i \(0.427158\pi\)
\(884\) 0 0
\(885\) −37.4837 −1.26000
\(886\) 0 0
\(887\) −16.3814 −0.550034 −0.275017 0.961439i \(-0.588684\pi\)
−0.275017 + 0.961439i \(0.588684\pi\)
\(888\) 0 0
\(889\) 59.4979 1.99550
\(890\) 0 0
\(891\) −10.4866 −0.351314
\(892\) 0 0
\(893\) 10.3911 0.347725
\(894\) 0 0
\(895\) 11.0310 0.368725
\(896\) 0 0
\(897\) −35.0122 −1.16902
\(898\) 0 0
\(899\) −17.7457 −0.591852
\(900\) 0 0
\(901\) −11.3357 −0.377645
\(902\) 0 0
\(903\) −20.6019 −0.685587
\(904\) 0 0
\(905\) 14.1831 0.471461
\(906\) 0 0
\(907\) −19.3793 −0.643479 −0.321739 0.946828i \(-0.604268\pi\)
−0.321739 + 0.946828i \(0.604268\pi\)
\(908\) 0 0
\(909\) −28.6470 −0.950162
\(910\) 0 0
\(911\) 52.5920 1.74245 0.871225 0.490883i \(-0.163326\pi\)
0.871225 + 0.490883i \(0.163326\pi\)
\(912\) 0 0
\(913\) 3.53520 0.116998
\(914\) 0 0
\(915\) −16.6502 −0.550440
\(916\) 0 0
\(917\) −9.99068 −0.329921
\(918\) 0 0
\(919\) 5.06710 0.167148 0.0835741 0.996502i \(-0.473366\pi\)
0.0835741 + 0.996502i \(0.473366\pi\)
\(920\) 0 0
\(921\) 39.1439 1.28983
\(922\) 0 0
\(923\) −0.257920 −0.00848956
\(924\) 0 0
\(925\) 1.11240 0.0365754
\(926\) 0 0
\(927\) 29.1247 0.956579
\(928\) 0 0
\(929\) −22.4490 −0.736528 −0.368264 0.929721i \(-0.620048\pi\)
−0.368264 + 0.929721i \(0.620048\pi\)
\(930\) 0 0
\(931\) −2.91291 −0.0954667
\(932\) 0 0
\(933\) −61.2520 −2.00530
\(934\) 0 0
\(935\) −22.5305 −0.736827
\(936\) 0 0
\(937\) −25.9615 −0.848124 −0.424062 0.905633i \(-0.639396\pi\)
−0.424062 + 0.905633i \(0.639396\pi\)
\(938\) 0 0
\(939\) −36.7073 −1.19790
\(940\) 0 0
\(941\) −31.7081 −1.03365 −0.516827 0.856090i \(-0.672887\pi\)
−0.516827 + 0.856090i \(0.672887\pi\)
\(942\) 0 0
\(943\) −35.7218 −1.16326
\(944\) 0 0
\(945\) −49.6021 −1.61356
\(946\) 0 0
\(947\) −3.16446 −0.102831 −0.0514155 0.998677i \(-0.516373\pi\)
−0.0514155 + 0.998677i \(0.516373\pi\)
\(948\) 0 0
\(949\) 6.67980 0.216836
\(950\) 0 0
\(951\) −22.8378 −0.740567
\(952\) 0 0
\(953\) 27.6308 0.895049 0.447525 0.894272i \(-0.352306\pi\)
0.447525 + 0.894272i \(0.352306\pi\)
\(954\) 0 0
\(955\) −15.7908 −0.510978
\(956\) 0 0
\(957\) −8.69311 −0.281008
\(958\) 0 0
\(959\) −61.4729 −1.98506
\(960\) 0 0
\(961\) 61.1525 1.97266
\(962\) 0 0
\(963\) 74.9404 2.41492
\(964\) 0 0
\(965\) 23.7816 0.765556
\(966\) 0 0
\(967\) −43.9255 −1.41255 −0.706275 0.707938i \(-0.749626\pi\)
−0.706275 + 0.707938i \(0.749626\pi\)
\(968\) 0 0
\(969\) 69.7833 2.24176
\(970\) 0 0
\(971\) 21.8322 0.700630 0.350315 0.936632i \(-0.386075\pi\)
0.350315 + 0.936632i \(0.386075\pi\)
\(972\) 0 0
\(973\) 37.2369 1.19376
\(974\) 0 0
\(975\) 1.07744 0.0345057
\(976\) 0 0
\(977\) 0.468434 0.0149865 0.00749326 0.999972i \(-0.497615\pi\)
0.00749326 + 0.999972i \(0.497615\pi\)
\(978\) 0 0
\(979\) −12.4482 −0.397846
\(980\) 0 0
\(981\) −71.6201 −2.28665
\(982\) 0 0
\(983\) −22.1145 −0.705342 −0.352671 0.935747i \(-0.614727\pi\)
−0.352671 + 0.935747i \(0.614727\pi\)
\(984\) 0 0
\(985\) −11.3893 −0.362892
\(986\) 0 0
\(987\) −23.2176 −0.739023
\(988\) 0 0
\(989\) −9.56798 −0.304244
\(990\) 0 0
\(991\) 58.1206 1.84626 0.923130 0.384488i \(-0.125622\pi\)
0.923130 + 0.384488i \(0.125622\pi\)
\(992\) 0 0
\(993\) −2.35170 −0.0746289
\(994\) 0 0
\(995\) 21.3918 0.678166
\(996\) 0 0
\(997\) −10.2231 −0.323769 −0.161885 0.986810i \(-0.551757\pi\)
−0.161885 + 0.986810i \(0.551757\pi\)
\(998\) 0 0
\(999\) −75.9471 −2.40286
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.1.43 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.43 44 1.1 even 1 trivial