Properties

Label 6008.2.a.b.1.21
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 1.21
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.486347 q^{3} +3.55566 q^{5} +0.471175 q^{7} -2.76347 q^{9} +O(q^{10})\) \(q-0.486347 q^{3} +3.55566 q^{5} +0.471175 q^{7} -2.76347 q^{9} -0.531450 q^{11} +4.46716 q^{13} -1.72928 q^{15} -4.83915 q^{17} -7.53934 q^{19} -0.229155 q^{21} -6.36896 q^{23} +7.64269 q^{25} +2.80305 q^{27} -0.479671 q^{29} +2.79010 q^{31} +0.258469 q^{33} +1.67534 q^{35} +10.7314 q^{37} -2.17259 q^{39} -0.506440 q^{41} -10.2121 q^{43} -9.82593 q^{45} -0.860204 q^{47} -6.77799 q^{49} +2.35351 q^{51} -6.48986 q^{53} -1.88965 q^{55} +3.66674 q^{57} -3.90844 q^{59} -10.7206 q^{61} -1.30208 q^{63} +15.8837 q^{65} -9.72226 q^{67} +3.09753 q^{69} -7.91477 q^{71} +4.56729 q^{73} -3.71700 q^{75} -0.250406 q^{77} +2.55175 q^{79} +6.92714 q^{81} +15.8184 q^{83} -17.2064 q^{85} +0.233287 q^{87} -10.2860 q^{89} +2.10482 q^{91} -1.35696 q^{93} -26.8073 q^{95} -14.1804 q^{97} +1.46864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.486347 −0.280793 −0.140396 0.990095i \(-0.544838\pi\)
−0.140396 + 0.990095i \(0.544838\pi\)
\(4\) 0 0
\(5\) 3.55566 1.59014 0.795069 0.606519i \(-0.207435\pi\)
0.795069 + 0.606519i \(0.207435\pi\)
\(6\) 0 0
\(7\) 0.471175 0.178088 0.0890438 0.996028i \(-0.471619\pi\)
0.0890438 + 0.996028i \(0.471619\pi\)
\(8\) 0 0
\(9\) −2.76347 −0.921155
\(10\) 0 0
\(11\) −0.531450 −0.160238 −0.0801191 0.996785i \(-0.525530\pi\)
−0.0801191 + 0.996785i \(0.525530\pi\)
\(12\) 0 0
\(13\) 4.46716 1.23897 0.619484 0.785010i \(-0.287342\pi\)
0.619484 + 0.785010i \(0.287342\pi\)
\(14\) 0 0
\(15\) −1.72928 −0.446499
\(16\) 0 0
\(17\) −4.83915 −1.17367 −0.586834 0.809707i \(-0.699626\pi\)
−0.586834 + 0.809707i \(0.699626\pi\)
\(18\) 0 0
\(19\) −7.53934 −1.72964 −0.864822 0.502079i \(-0.832569\pi\)
−0.864822 + 0.502079i \(0.832569\pi\)
\(20\) 0 0
\(21\) −0.229155 −0.0500057
\(22\) 0 0
\(23\) −6.36896 −1.32802 −0.664010 0.747724i \(-0.731147\pi\)
−0.664010 + 0.747724i \(0.731147\pi\)
\(24\) 0 0
\(25\) 7.64269 1.52854
\(26\) 0 0
\(27\) 2.80305 0.539447
\(28\) 0 0
\(29\) −0.479671 −0.0890726 −0.0445363 0.999008i \(-0.514181\pi\)
−0.0445363 + 0.999008i \(0.514181\pi\)
\(30\) 0 0
\(31\) 2.79010 0.501117 0.250558 0.968102i \(-0.419386\pi\)
0.250558 + 0.968102i \(0.419386\pi\)
\(32\) 0 0
\(33\) 0.258469 0.0449938
\(34\) 0 0
\(35\) 1.67534 0.283184
\(36\) 0 0
\(37\) 10.7314 1.76422 0.882112 0.471040i \(-0.156121\pi\)
0.882112 + 0.471040i \(0.156121\pi\)
\(38\) 0 0
\(39\) −2.17259 −0.347893
\(40\) 0 0
\(41\) −0.506440 −0.0790926 −0.0395463 0.999218i \(-0.512591\pi\)
−0.0395463 + 0.999218i \(0.512591\pi\)
\(42\) 0 0
\(43\) −10.2121 −1.55734 −0.778668 0.627436i \(-0.784104\pi\)
−0.778668 + 0.627436i \(0.784104\pi\)
\(44\) 0 0
\(45\) −9.82593 −1.46476
\(46\) 0 0
\(47\) −0.860204 −0.125474 −0.0627368 0.998030i \(-0.519983\pi\)
−0.0627368 + 0.998030i \(0.519983\pi\)
\(48\) 0 0
\(49\) −6.77799 −0.968285
\(50\) 0 0
\(51\) 2.35351 0.329557
\(52\) 0 0
\(53\) −6.48986 −0.891451 −0.445726 0.895170i \(-0.647054\pi\)
−0.445726 + 0.895170i \(0.647054\pi\)
\(54\) 0 0
\(55\) −1.88965 −0.254801
\(56\) 0 0
\(57\) 3.66674 0.485671
\(58\) 0 0
\(59\) −3.90844 −0.508835 −0.254418 0.967094i \(-0.581884\pi\)
−0.254418 + 0.967094i \(0.581884\pi\)
\(60\) 0 0
\(61\) −10.7206 −1.37263 −0.686316 0.727303i \(-0.740773\pi\)
−0.686316 + 0.727303i \(0.740773\pi\)
\(62\) 0 0
\(63\) −1.30208 −0.164046
\(64\) 0 0
\(65\) 15.8837 1.97013
\(66\) 0 0
\(67\) −9.72226 −1.18776 −0.593881 0.804553i \(-0.702405\pi\)
−0.593881 + 0.804553i \(0.702405\pi\)
\(68\) 0 0
\(69\) 3.09753 0.372898
\(70\) 0 0
\(71\) −7.91477 −0.939311 −0.469655 0.882850i \(-0.655622\pi\)
−0.469655 + 0.882850i \(0.655622\pi\)
\(72\) 0 0
\(73\) 4.56729 0.534561 0.267280 0.963619i \(-0.413875\pi\)
0.267280 + 0.963619i \(0.413875\pi\)
\(74\) 0 0
\(75\) −3.71700 −0.429202
\(76\) 0 0
\(77\) −0.250406 −0.0285364
\(78\) 0 0
\(79\) 2.55175 0.287094 0.143547 0.989644i \(-0.454149\pi\)
0.143547 + 0.989644i \(0.454149\pi\)
\(80\) 0 0
\(81\) 6.92714 0.769683
\(82\) 0 0
\(83\) 15.8184 1.73629 0.868145 0.496310i \(-0.165312\pi\)
0.868145 + 0.496310i \(0.165312\pi\)
\(84\) 0 0
\(85\) −17.2064 −1.86629
\(86\) 0 0
\(87\) 0.233287 0.0250110
\(88\) 0 0
\(89\) −10.2860 −1.09031 −0.545154 0.838336i \(-0.683529\pi\)
−0.545154 + 0.838336i \(0.683529\pi\)
\(90\) 0 0
\(91\) 2.10482 0.220645
\(92\) 0 0
\(93\) −1.35696 −0.140710
\(94\) 0 0
\(95\) −26.8073 −2.75037
\(96\) 0 0
\(97\) −14.1804 −1.43981 −0.719903 0.694075i \(-0.755814\pi\)
−0.719903 + 0.694075i \(0.755814\pi\)
\(98\) 0 0
\(99\) 1.46864 0.147604
\(100\) 0 0
\(101\) 8.92361 0.887932 0.443966 0.896044i \(-0.353571\pi\)
0.443966 + 0.896044i \(0.353571\pi\)
\(102\) 0 0
\(103\) −4.44511 −0.437989 −0.218995 0.975726i \(-0.570278\pi\)
−0.218995 + 0.975726i \(0.570278\pi\)
\(104\) 0 0
\(105\) −0.814796 −0.0795160
\(106\) 0 0
\(107\) −1.57696 −0.152450 −0.0762251 0.997091i \(-0.524287\pi\)
−0.0762251 + 0.997091i \(0.524287\pi\)
\(108\) 0 0
\(109\) −14.6773 −1.40583 −0.702913 0.711276i \(-0.748118\pi\)
−0.702913 + 0.711276i \(0.748118\pi\)
\(110\) 0 0
\(111\) −5.21916 −0.495381
\(112\) 0 0
\(113\) 20.4523 1.92399 0.961995 0.273068i \(-0.0880385\pi\)
0.961995 + 0.273068i \(0.0880385\pi\)
\(114\) 0 0
\(115\) −22.6458 −2.11173
\(116\) 0 0
\(117\) −12.3448 −1.14128
\(118\) 0 0
\(119\) −2.28009 −0.209016
\(120\) 0 0
\(121\) −10.7176 −0.974324
\(122\) 0 0
\(123\) 0.246306 0.0222086
\(124\) 0 0
\(125\) 9.39648 0.840447
\(126\) 0 0
\(127\) 8.11004 0.719649 0.359825 0.933020i \(-0.382837\pi\)
0.359825 + 0.933020i \(0.382837\pi\)
\(128\) 0 0
\(129\) 4.96664 0.437289
\(130\) 0 0
\(131\) 7.89824 0.690072 0.345036 0.938589i \(-0.387867\pi\)
0.345036 + 0.938589i \(0.387867\pi\)
\(132\) 0 0
\(133\) −3.55235 −0.308028
\(134\) 0 0
\(135\) 9.96667 0.857794
\(136\) 0 0
\(137\) 6.31103 0.539188 0.269594 0.962974i \(-0.413111\pi\)
0.269594 + 0.962974i \(0.413111\pi\)
\(138\) 0 0
\(139\) 1.58288 0.134258 0.0671290 0.997744i \(-0.478616\pi\)
0.0671290 + 0.997744i \(0.478616\pi\)
\(140\) 0 0
\(141\) 0.418358 0.0352321
\(142\) 0 0
\(143\) −2.37407 −0.198530
\(144\) 0 0
\(145\) −1.70554 −0.141638
\(146\) 0 0
\(147\) 3.29646 0.271887
\(148\) 0 0
\(149\) −18.1857 −1.48983 −0.744915 0.667159i \(-0.767510\pi\)
−0.744915 + 0.667159i \(0.767510\pi\)
\(150\) 0 0
\(151\) −6.36421 −0.517912 −0.258956 0.965889i \(-0.583378\pi\)
−0.258956 + 0.965889i \(0.583378\pi\)
\(152\) 0 0
\(153\) 13.3728 1.08113
\(154\) 0 0
\(155\) 9.92063 0.796844
\(156\) 0 0
\(157\) −7.76662 −0.619844 −0.309922 0.950762i \(-0.600303\pi\)
−0.309922 + 0.950762i \(0.600303\pi\)
\(158\) 0 0
\(159\) 3.15633 0.250313
\(160\) 0 0
\(161\) −3.00090 −0.236504
\(162\) 0 0
\(163\) −15.3220 −1.20011 −0.600056 0.799958i \(-0.704855\pi\)
−0.600056 + 0.799958i \(0.704855\pi\)
\(164\) 0 0
\(165\) 0.919028 0.0715463
\(166\) 0 0
\(167\) −20.3910 −1.57790 −0.788950 0.614457i \(-0.789375\pi\)
−0.788950 + 0.614457i \(0.789375\pi\)
\(168\) 0 0
\(169\) 6.95552 0.535040
\(170\) 0 0
\(171\) 20.8347 1.59327
\(172\) 0 0
\(173\) 16.2476 1.23528 0.617640 0.786461i \(-0.288089\pi\)
0.617640 + 0.786461i \(0.288089\pi\)
\(174\) 0 0
\(175\) 3.60105 0.272213
\(176\) 0 0
\(177\) 1.90086 0.142877
\(178\) 0 0
\(179\) 12.1874 0.910930 0.455465 0.890254i \(-0.349473\pi\)
0.455465 + 0.890254i \(0.349473\pi\)
\(180\) 0 0
\(181\) 21.2565 1.57999 0.789993 0.613116i \(-0.210084\pi\)
0.789993 + 0.613116i \(0.210084\pi\)
\(182\) 0 0
\(183\) 5.21394 0.385425
\(184\) 0 0
\(185\) 38.1570 2.80536
\(186\) 0 0
\(187\) 2.57177 0.188066
\(188\) 0 0
\(189\) 1.32073 0.0960687
\(190\) 0 0
\(191\) 4.73713 0.342766 0.171383 0.985204i \(-0.445176\pi\)
0.171383 + 0.985204i \(0.445176\pi\)
\(192\) 0 0
\(193\) 14.7747 1.06351 0.531754 0.846899i \(-0.321533\pi\)
0.531754 + 0.846899i \(0.321533\pi\)
\(194\) 0 0
\(195\) −7.72499 −0.553198
\(196\) 0 0
\(197\) −9.59995 −0.683968 −0.341984 0.939706i \(-0.611099\pi\)
−0.341984 + 0.939706i \(0.611099\pi\)
\(198\) 0 0
\(199\) 27.3050 1.93560 0.967800 0.251719i \(-0.0809958\pi\)
0.967800 + 0.251719i \(0.0809958\pi\)
\(200\) 0 0
\(201\) 4.72839 0.333515
\(202\) 0 0
\(203\) −0.226009 −0.0158627
\(204\) 0 0
\(205\) −1.80072 −0.125768
\(206\) 0 0
\(207\) 17.6004 1.22331
\(208\) 0 0
\(209\) 4.00678 0.277155
\(210\) 0 0
\(211\) −18.6715 −1.28540 −0.642698 0.766120i \(-0.722185\pi\)
−0.642698 + 0.766120i \(0.722185\pi\)
\(212\) 0 0
\(213\) 3.84933 0.263752
\(214\) 0 0
\(215\) −36.3108 −2.47638
\(216\) 0 0
\(217\) 1.31463 0.0892426
\(218\) 0 0
\(219\) −2.22129 −0.150101
\(220\) 0 0
\(221\) −21.6173 −1.45414
\(222\) 0 0
\(223\) 20.7481 1.38940 0.694698 0.719302i \(-0.255538\pi\)
0.694698 + 0.719302i \(0.255538\pi\)
\(224\) 0 0
\(225\) −21.1203 −1.40802
\(226\) 0 0
\(227\) −28.9848 −1.92379 −0.961894 0.273422i \(-0.911845\pi\)
−0.961894 + 0.273422i \(0.911845\pi\)
\(228\) 0 0
\(229\) −22.2012 −1.46710 −0.733549 0.679636i \(-0.762138\pi\)
−0.733549 + 0.679636i \(0.762138\pi\)
\(230\) 0 0
\(231\) 0.121784 0.00801283
\(232\) 0 0
\(233\) 22.9873 1.50595 0.752973 0.658051i \(-0.228619\pi\)
0.752973 + 0.658051i \(0.228619\pi\)
\(234\) 0 0
\(235\) −3.05859 −0.199520
\(236\) 0 0
\(237\) −1.24103 −0.0806139
\(238\) 0 0
\(239\) −19.3670 −1.25275 −0.626374 0.779522i \(-0.715462\pi\)
−0.626374 + 0.779522i \(0.715462\pi\)
\(240\) 0 0
\(241\) 10.7978 0.695548 0.347774 0.937578i \(-0.386938\pi\)
0.347774 + 0.937578i \(0.386938\pi\)
\(242\) 0 0
\(243\) −11.7781 −0.755568
\(244\) 0 0
\(245\) −24.1002 −1.53971
\(246\) 0 0
\(247\) −33.6794 −2.14297
\(248\) 0 0
\(249\) −7.69322 −0.487538
\(250\) 0 0
\(251\) −24.4356 −1.54236 −0.771180 0.636618i \(-0.780333\pi\)
−0.771180 + 0.636618i \(0.780333\pi\)
\(252\) 0 0
\(253\) 3.38478 0.212799
\(254\) 0 0
\(255\) 8.36827 0.524042
\(256\) 0 0
\(257\) 28.3410 1.76786 0.883932 0.467616i \(-0.154887\pi\)
0.883932 + 0.467616i \(0.154887\pi\)
\(258\) 0 0
\(259\) 5.05635 0.314186
\(260\) 0 0
\(261\) 1.32555 0.0820497
\(262\) 0 0
\(263\) 10.2206 0.630228 0.315114 0.949054i \(-0.397957\pi\)
0.315114 + 0.949054i \(0.397957\pi\)
\(264\) 0 0
\(265\) −23.0757 −1.41753
\(266\) 0 0
\(267\) 5.00255 0.306151
\(268\) 0 0
\(269\) 14.5474 0.886970 0.443485 0.896282i \(-0.353742\pi\)
0.443485 + 0.896282i \(0.353742\pi\)
\(270\) 0 0
\(271\) −3.44221 −0.209099 −0.104550 0.994520i \(-0.533340\pi\)
−0.104550 + 0.994520i \(0.533340\pi\)
\(272\) 0 0
\(273\) −1.02367 −0.0619554
\(274\) 0 0
\(275\) −4.06171 −0.244930
\(276\) 0 0
\(277\) 1.89766 0.114019 0.0570096 0.998374i \(-0.481843\pi\)
0.0570096 + 0.998374i \(0.481843\pi\)
\(278\) 0 0
\(279\) −7.71034 −0.461606
\(280\) 0 0
\(281\) 19.5571 1.16668 0.583340 0.812228i \(-0.301746\pi\)
0.583340 + 0.812228i \(0.301746\pi\)
\(282\) 0 0
\(283\) 10.3015 0.612361 0.306181 0.951973i \(-0.400949\pi\)
0.306181 + 0.951973i \(0.400949\pi\)
\(284\) 0 0
\(285\) 13.0377 0.772284
\(286\) 0 0
\(287\) −0.238622 −0.0140854
\(288\) 0 0
\(289\) 6.41742 0.377495
\(290\) 0 0
\(291\) 6.89662 0.404287
\(292\) 0 0
\(293\) 6.85071 0.400223 0.200111 0.979773i \(-0.435870\pi\)
0.200111 + 0.979773i \(0.435870\pi\)
\(294\) 0 0
\(295\) −13.8971 −0.809118
\(296\) 0 0
\(297\) −1.48968 −0.0864400
\(298\) 0 0
\(299\) −28.4511 −1.64537
\(300\) 0 0
\(301\) −4.81171 −0.277342
\(302\) 0 0
\(303\) −4.33997 −0.249325
\(304\) 0 0
\(305\) −38.1188 −2.18267
\(306\) 0 0
\(307\) −3.62604 −0.206949 −0.103474 0.994632i \(-0.532996\pi\)
−0.103474 + 0.994632i \(0.532996\pi\)
\(308\) 0 0
\(309\) 2.16187 0.122984
\(310\) 0 0
\(311\) −30.9186 −1.75323 −0.876616 0.481190i \(-0.840205\pi\)
−0.876616 + 0.481190i \(0.840205\pi\)
\(312\) 0 0
\(313\) −12.7910 −0.722988 −0.361494 0.932374i \(-0.617733\pi\)
−0.361494 + 0.932374i \(0.617733\pi\)
\(314\) 0 0
\(315\) −4.62974 −0.260856
\(316\) 0 0
\(317\) −1.16410 −0.0653821 −0.0326911 0.999466i \(-0.510408\pi\)
−0.0326911 + 0.999466i \(0.510408\pi\)
\(318\) 0 0
\(319\) 0.254921 0.0142728
\(320\) 0 0
\(321\) 0.766949 0.0428069
\(322\) 0 0
\(323\) 36.4840 2.03003
\(324\) 0 0
\(325\) 34.1411 1.89381
\(326\) 0 0
\(327\) 7.13824 0.394746
\(328\) 0 0
\(329\) −0.405307 −0.0223453
\(330\) 0 0
\(331\) −9.17768 −0.504451 −0.252225 0.967668i \(-0.581162\pi\)
−0.252225 + 0.967668i \(0.581162\pi\)
\(332\) 0 0
\(333\) −29.6557 −1.62512
\(334\) 0 0
\(335\) −34.5690 −1.88871
\(336\) 0 0
\(337\) 15.6228 0.851026 0.425513 0.904952i \(-0.360094\pi\)
0.425513 + 0.904952i \(0.360094\pi\)
\(338\) 0 0
\(339\) −9.94692 −0.540242
\(340\) 0 0
\(341\) −1.48280 −0.0802981
\(342\) 0 0
\(343\) −6.49185 −0.350527
\(344\) 0 0
\(345\) 11.0137 0.592959
\(346\) 0 0
\(347\) −4.28442 −0.230000 −0.115000 0.993366i \(-0.536687\pi\)
−0.115000 + 0.993366i \(0.536687\pi\)
\(348\) 0 0
\(349\) −10.2557 −0.548976 −0.274488 0.961591i \(-0.588508\pi\)
−0.274488 + 0.961591i \(0.588508\pi\)
\(350\) 0 0
\(351\) 12.5217 0.668357
\(352\) 0 0
\(353\) −26.0089 −1.38432 −0.692158 0.721746i \(-0.743340\pi\)
−0.692158 + 0.721746i \(0.743340\pi\)
\(354\) 0 0
\(355\) −28.1422 −1.49363
\(356\) 0 0
\(357\) 1.10892 0.0586901
\(358\) 0 0
\(359\) 6.93158 0.365835 0.182917 0.983128i \(-0.441446\pi\)
0.182917 + 0.983128i \(0.441446\pi\)
\(360\) 0 0
\(361\) 37.8416 1.99167
\(362\) 0 0
\(363\) 5.21246 0.273583
\(364\) 0 0
\(365\) 16.2397 0.850025
\(366\) 0 0
\(367\) 5.61288 0.292990 0.146495 0.989211i \(-0.453201\pi\)
0.146495 + 0.989211i \(0.453201\pi\)
\(368\) 0 0
\(369\) 1.39953 0.0728566
\(370\) 0 0
\(371\) −3.05786 −0.158756
\(372\) 0 0
\(373\) 18.9073 0.978981 0.489490 0.872009i \(-0.337183\pi\)
0.489490 + 0.872009i \(0.337183\pi\)
\(374\) 0 0
\(375\) −4.56995 −0.235991
\(376\) 0 0
\(377\) −2.14277 −0.110358
\(378\) 0 0
\(379\) 24.0839 1.23711 0.618555 0.785742i \(-0.287719\pi\)
0.618555 + 0.785742i \(0.287719\pi\)
\(380\) 0 0
\(381\) −3.94429 −0.202072
\(382\) 0 0
\(383\) −23.2970 −1.19042 −0.595211 0.803569i \(-0.702932\pi\)
−0.595211 + 0.803569i \(0.702932\pi\)
\(384\) 0 0
\(385\) −0.890359 −0.0453769
\(386\) 0 0
\(387\) 28.2209 1.43455
\(388\) 0 0
\(389\) 4.68326 0.237451 0.118725 0.992927i \(-0.462119\pi\)
0.118725 + 0.992927i \(0.462119\pi\)
\(390\) 0 0
\(391\) 30.8204 1.55865
\(392\) 0 0
\(393\) −3.84129 −0.193767
\(394\) 0 0
\(395\) 9.07313 0.456519
\(396\) 0 0
\(397\) −30.5325 −1.53238 −0.766192 0.642612i \(-0.777851\pi\)
−0.766192 + 0.642612i \(0.777851\pi\)
\(398\) 0 0
\(399\) 1.72768 0.0864920
\(400\) 0 0
\(401\) −8.38688 −0.418821 −0.209410 0.977828i \(-0.567154\pi\)
−0.209410 + 0.977828i \(0.567154\pi\)
\(402\) 0 0
\(403\) 12.4638 0.620867
\(404\) 0 0
\(405\) 24.6305 1.22390
\(406\) 0 0
\(407\) −5.70318 −0.282696
\(408\) 0 0
\(409\) −34.5383 −1.70781 −0.853905 0.520430i \(-0.825772\pi\)
−0.853905 + 0.520430i \(0.825772\pi\)
\(410\) 0 0
\(411\) −3.06935 −0.151400
\(412\) 0 0
\(413\) −1.84156 −0.0906172
\(414\) 0 0
\(415\) 56.2446 2.76094
\(416\) 0 0
\(417\) −0.769829 −0.0376987
\(418\) 0 0
\(419\) 19.3497 0.945295 0.472647 0.881252i \(-0.343298\pi\)
0.472647 + 0.881252i \(0.343298\pi\)
\(420\) 0 0
\(421\) −27.7411 −1.35202 −0.676009 0.736893i \(-0.736292\pi\)
−0.676009 + 0.736893i \(0.736292\pi\)
\(422\) 0 0
\(423\) 2.37714 0.115581
\(424\) 0 0
\(425\) −36.9841 −1.79399
\(426\) 0 0
\(427\) −5.05129 −0.244449
\(428\) 0 0
\(429\) 1.15462 0.0557458
\(430\) 0 0
\(431\) 18.9533 0.912947 0.456474 0.889737i \(-0.349112\pi\)
0.456474 + 0.889737i \(0.349112\pi\)
\(432\) 0 0
\(433\) 11.9612 0.574821 0.287410 0.957808i \(-0.407206\pi\)
0.287410 + 0.957808i \(0.407206\pi\)
\(434\) 0 0
\(435\) 0.829487 0.0397709
\(436\) 0 0
\(437\) 48.0177 2.29700
\(438\) 0 0
\(439\) −41.3205 −1.97212 −0.986060 0.166391i \(-0.946789\pi\)
−0.986060 + 0.166391i \(0.946789\pi\)
\(440\) 0 0
\(441\) 18.7308 0.891941
\(442\) 0 0
\(443\) 16.9817 0.806827 0.403413 0.915018i \(-0.367824\pi\)
0.403413 + 0.915018i \(0.367824\pi\)
\(444\) 0 0
\(445\) −36.5733 −1.73374
\(446\) 0 0
\(447\) 8.84457 0.418334
\(448\) 0 0
\(449\) 15.7016 0.741005 0.370502 0.928832i \(-0.379186\pi\)
0.370502 + 0.928832i \(0.379186\pi\)
\(450\) 0 0
\(451\) 0.269147 0.0126737
\(452\) 0 0
\(453\) 3.09522 0.145426
\(454\) 0 0
\(455\) 7.48400 0.350855
\(456\) 0 0
\(457\) −1.80809 −0.0845789 −0.0422894 0.999105i \(-0.513465\pi\)
−0.0422894 + 0.999105i \(0.513465\pi\)
\(458\) 0 0
\(459\) −13.5644 −0.633131
\(460\) 0 0
\(461\) 12.7436 0.593530 0.296765 0.954951i \(-0.404092\pi\)
0.296765 + 0.954951i \(0.404092\pi\)
\(462\) 0 0
\(463\) −21.6426 −1.00582 −0.502908 0.864340i \(-0.667737\pi\)
−0.502908 + 0.864340i \(0.667737\pi\)
\(464\) 0 0
\(465\) −4.82487 −0.223748
\(466\) 0 0
\(467\) −33.0550 −1.52960 −0.764801 0.644266i \(-0.777163\pi\)
−0.764801 + 0.644266i \(0.777163\pi\)
\(468\) 0 0
\(469\) −4.58089 −0.211526
\(470\) 0 0
\(471\) 3.77728 0.174048
\(472\) 0 0
\(473\) 5.42724 0.249545
\(474\) 0 0
\(475\) −57.6208 −2.64382
\(476\) 0 0
\(477\) 17.9345 0.821165
\(478\) 0 0
\(479\) −4.21102 −0.192406 −0.0962032 0.995362i \(-0.530670\pi\)
−0.0962032 + 0.995362i \(0.530670\pi\)
\(480\) 0 0
\(481\) 47.9387 2.18582
\(482\) 0 0
\(483\) 1.45948 0.0664085
\(484\) 0 0
\(485\) −50.4208 −2.28949
\(486\) 0 0
\(487\) −15.7179 −0.712248 −0.356124 0.934439i \(-0.615902\pi\)
−0.356124 + 0.934439i \(0.615902\pi\)
\(488\) 0 0
\(489\) 7.45181 0.336983
\(490\) 0 0
\(491\) 12.7693 0.576270 0.288135 0.957590i \(-0.406965\pi\)
0.288135 + 0.957590i \(0.406965\pi\)
\(492\) 0 0
\(493\) 2.32120 0.104542
\(494\) 0 0
\(495\) 5.22199 0.234711
\(496\) 0 0
\(497\) −3.72925 −0.167280
\(498\) 0 0
\(499\) 35.9814 1.61075 0.805375 0.592766i \(-0.201964\pi\)
0.805375 + 0.592766i \(0.201964\pi\)
\(500\) 0 0
\(501\) 9.91709 0.443063
\(502\) 0 0
\(503\) −14.7280 −0.656687 −0.328343 0.944558i \(-0.606490\pi\)
−0.328343 + 0.944558i \(0.606490\pi\)
\(504\) 0 0
\(505\) 31.7293 1.41193
\(506\) 0 0
\(507\) −3.38280 −0.150235
\(508\) 0 0
\(509\) 9.10540 0.403590 0.201795 0.979428i \(-0.435323\pi\)
0.201795 + 0.979428i \(0.435323\pi\)
\(510\) 0 0
\(511\) 2.15199 0.0951986
\(512\) 0 0
\(513\) −21.1331 −0.933050
\(514\) 0 0
\(515\) −15.8053 −0.696463
\(516\) 0 0
\(517\) 0.457155 0.0201057
\(518\) 0 0
\(519\) −7.90197 −0.346858
\(520\) 0 0
\(521\) −23.0330 −1.00909 −0.504547 0.863384i \(-0.668340\pi\)
−0.504547 + 0.863384i \(0.668340\pi\)
\(522\) 0 0
\(523\) 4.19303 0.183349 0.0916743 0.995789i \(-0.470778\pi\)
0.0916743 + 0.995789i \(0.470778\pi\)
\(524\) 0 0
\(525\) −1.75136 −0.0764356
\(526\) 0 0
\(527\) −13.5017 −0.588144
\(528\) 0 0
\(529\) 17.5636 0.763635
\(530\) 0 0
\(531\) 10.8008 0.468716
\(532\) 0 0
\(533\) −2.26235 −0.0979931
\(534\) 0 0
\(535\) −5.60712 −0.242417
\(536\) 0 0
\(537\) −5.92731 −0.255782
\(538\) 0 0
\(539\) 3.60217 0.155156
\(540\) 0 0
\(541\) −21.4633 −0.922780 −0.461390 0.887197i \(-0.652649\pi\)
−0.461390 + 0.887197i \(0.652649\pi\)
\(542\) 0 0
\(543\) −10.3381 −0.443649
\(544\) 0 0
\(545\) −52.1873 −2.23546
\(546\) 0 0
\(547\) 18.9838 0.811688 0.405844 0.913942i \(-0.366978\pi\)
0.405844 + 0.913942i \(0.366978\pi\)
\(548\) 0 0
\(549\) 29.6260 1.26441
\(550\) 0 0
\(551\) 3.61640 0.154064
\(552\) 0 0
\(553\) 1.20232 0.0511278
\(554\) 0 0
\(555\) −18.5576 −0.787724
\(556\) 0 0
\(557\) 10.3668 0.439254 0.219627 0.975584i \(-0.429516\pi\)
0.219627 + 0.975584i \(0.429516\pi\)
\(558\) 0 0
\(559\) −45.6192 −1.92949
\(560\) 0 0
\(561\) −1.25077 −0.0528077
\(562\) 0 0
\(563\) 7.45466 0.314177 0.157088 0.987585i \(-0.449789\pi\)
0.157088 + 0.987585i \(0.449789\pi\)
\(564\) 0 0
\(565\) 72.7213 3.05941
\(566\) 0 0
\(567\) 3.26390 0.137071
\(568\) 0 0
\(569\) −19.0968 −0.800580 −0.400290 0.916388i \(-0.631091\pi\)
−0.400290 + 0.916388i \(0.631091\pi\)
\(570\) 0 0
\(571\) −11.9090 −0.498377 −0.249189 0.968455i \(-0.580164\pi\)
−0.249189 + 0.968455i \(0.580164\pi\)
\(572\) 0 0
\(573\) −2.30389 −0.0962464
\(574\) 0 0
\(575\) −48.6759 −2.02993
\(576\) 0 0
\(577\) −1.27577 −0.0531111 −0.0265556 0.999647i \(-0.508454\pi\)
−0.0265556 + 0.999647i \(0.508454\pi\)
\(578\) 0 0
\(579\) −7.18565 −0.298626
\(580\) 0 0
\(581\) 7.45322 0.309212
\(582\) 0 0
\(583\) 3.44904 0.142845
\(584\) 0 0
\(585\) −43.8940 −1.81479
\(586\) 0 0
\(587\) −13.9517 −0.575847 −0.287923 0.957653i \(-0.592965\pi\)
−0.287923 + 0.957653i \(0.592965\pi\)
\(588\) 0 0
\(589\) −21.0355 −0.866753
\(590\) 0 0
\(591\) 4.66891 0.192053
\(592\) 0 0
\(593\) 20.1128 0.825932 0.412966 0.910746i \(-0.364493\pi\)
0.412966 + 0.910746i \(0.364493\pi\)
\(594\) 0 0
\(595\) −8.10722 −0.332364
\(596\) 0 0
\(597\) −13.2797 −0.543503
\(598\) 0 0
\(599\) −32.0813 −1.31081 −0.655403 0.755279i \(-0.727501\pi\)
−0.655403 + 0.755279i \(0.727501\pi\)
\(600\) 0 0
\(601\) 3.35248 0.136751 0.0683753 0.997660i \(-0.478218\pi\)
0.0683753 + 0.997660i \(0.478218\pi\)
\(602\) 0 0
\(603\) 26.8671 1.09411
\(604\) 0 0
\(605\) −38.1080 −1.54931
\(606\) 0 0
\(607\) 27.5588 1.11858 0.559289 0.828973i \(-0.311074\pi\)
0.559289 + 0.828973i \(0.311074\pi\)
\(608\) 0 0
\(609\) 0.109919 0.00445414
\(610\) 0 0
\(611\) −3.84267 −0.155458
\(612\) 0 0
\(613\) −22.9924 −0.928655 −0.464328 0.885664i \(-0.653704\pi\)
−0.464328 + 0.885664i \(0.653704\pi\)
\(614\) 0 0
\(615\) 0.875778 0.0353148
\(616\) 0 0
\(617\) −42.9010 −1.72713 −0.863565 0.504237i \(-0.831774\pi\)
−0.863565 + 0.504237i \(0.831774\pi\)
\(618\) 0 0
\(619\) −4.27994 −0.172025 −0.0860126 0.996294i \(-0.527413\pi\)
−0.0860126 + 0.996294i \(0.527413\pi\)
\(620\) 0 0
\(621\) −17.8525 −0.716395
\(622\) 0 0
\(623\) −4.84649 −0.194170
\(624\) 0 0
\(625\) −4.80278 −0.192111
\(626\) 0 0
\(627\) −1.94869 −0.0778231
\(628\) 0 0
\(629\) −51.9307 −2.07061
\(630\) 0 0
\(631\) −14.8743 −0.592136 −0.296068 0.955167i \(-0.595675\pi\)
−0.296068 + 0.955167i \(0.595675\pi\)
\(632\) 0 0
\(633\) 9.08081 0.360930
\(634\) 0 0
\(635\) 28.8365 1.14434
\(636\) 0 0
\(637\) −30.2784 −1.19967
\(638\) 0 0
\(639\) 21.8722 0.865251
\(640\) 0 0
\(641\) 8.23306 0.325186 0.162593 0.986693i \(-0.448014\pi\)
0.162593 + 0.986693i \(0.448014\pi\)
\(642\) 0 0
\(643\) 8.38792 0.330787 0.165394 0.986228i \(-0.447111\pi\)
0.165394 + 0.986228i \(0.447111\pi\)
\(644\) 0 0
\(645\) 17.6597 0.695349
\(646\) 0 0
\(647\) 36.6037 1.43904 0.719520 0.694472i \(-0.244362\pi\)
0.719520 + 0.694472i \(0.244362\pi\)
\(648\) 0 0
\(649\) 2.07714 0.0815349
\(650\) 0 0
\(651\) −0.639365 −0.0250587
\(652\) 0 0
\(653\) −27.4024 −1.07234 −0.536170 0.844110i \(-0.680129\pi\)
−0.536170 + 0.844110i \(0.680129\pi\)
\(654\) 0 0
\(655\) 28.0834 1.09731
\(656\) 0 0
\(657\) −12.6215 −0.492413
\(658\) 0 0
\(659\) 23.7235 0.924138 0.462069 0.886844i \(-0.347107\pi\)
0.462069 + 0.886844i \(0.347107\pi\)
\(660\) 0 0
\(661\) 33.8612 1.31705 0.658524 0.752560i \(-0.271181\pi\)
0.658524 + 0.752560i \(0.271181\pi\)
\(662\) 0 0
\(663\) 10.5135 0.408311
\(664\) 0 0
\(665\) −12.6309 −0.489807
\(666\) 0 0
\(667\) 3.05500 0.118290
\(668\) 0 0
\(669\) −10.0908 −0.390132
\(670\) 0 0
\(671\) 5.69747 0.219948
\(672\) 0 0
\(673\) 20.5924 0.793780 0.396890 0.917866i \(-0.370089\pi\)
0.396890 + 0.917866i \(0.370089\pi\)
\(674\) 0 0
\(675\) 21.4228 0.824564
\(676\) 0 0
\(677\) 11.0601 0.425076 0.212538 0.977153i \(-0.431827\pi\)
0.212538 + 0.977153i \(0.431827\pi\)
\(678\) 0 0
\(679\) −6.68148 −0.256411
\(680\) 0 0
\(681\) 14.0967 0.540186
\(682\) 0 0
\(683\) −23.2209 −0.888523 −0.444261 0.895897i \(-0.646534\pi\)
−0.444261 + 0.895897i \(0.646534\pi\)
\(684\) 0 0
\(685\) 22.4399 0.857383
\(686\) 0 0
\(687\) 10.7975 0.411951
\(688\) 0 0
\(689\) −28.9913 −1.10448
\(690\) 0 0
\(691\) −0.393183 −0.0149574 −0.00747870 0.999972i \(-0.502381\pi\)
−0.00747870 + 0.999972i \(0.502381\pi\)
\(692\) 0 0
\(693\) 0.691989 0.0262865
\(694\) 0 0
\(695\) 5.62817 0.213489
\(696\) 0 0
\(697\) 2.45074 0.0928284
\(698\) 0 0
\(699\) −11.1798 −0.422859
\(700\) 0 0
\(701\) −39.8171 −1.50387 −0.751935 0.659237i \(-0.770879\pi\)
−0.751935 + 0.659237i \(0.770879\pi\)
\(702\) 0 0
\(703\) −80.9073 −3.05148
\(704\) 0 0
\(705\) 1.48754 0.0560238
\(706\) 0 0
\(707\) 4.20459 0.158130
\(708\) 0 0
\(709\) −43.4510 −1.63184 −0.815919 0.578166i \(-0.803769\pi\)
−0.815919 + 0.578166i \(0.803769\pi\)
\(710\) 0 0
\(711\) −7.05166 −0.264458
\(712\) 0 0
\(713\) −17.7700 −0.665492
\(714\) 0 0
\(715\) −8.44139 −0.315690
\(716\) 0 0
\(717\) 9.41910 0.351763
\(718\) 0 0
\(719\) 37.2523 1.38928 0.694639 0.719358i \(-0.255564\pi\)
0.694639 + 0.719358i \(0.255564\pi\)
\(720\) 0 0
\(721\) −2.09443 −0.0780005
\(722\) 0 0
\(723\) −5.25149 −0.195305
\(724\) 0 0
\(725\) −3.66597 −0.136151
\(726\) 0 0
\(727\) −4.33842 −0.160903 −0.0804515 0.996759i \(-0.525636\pi\)
−0.0804515 + 0.996759i \(0.525636\pi\)
\(728\) 0 0
\(729\) −15.0532 −0.557525
\(730\) 0 0
\(731\) 49.4181 1.82779
\(732\) 0 0
\(733\) 14.5444 0.537211 0.268605 0.963250i \(-0.413437\pi\)
0.268605 + 0.963250i \(0.413437\pi\)
\(734\) 0 0
\(735\) 11.7211 0.432338
\(736\) 0 0
\(737\) 5.16690 0.190325
\(738\) 0 0
\(739\) −45.4842 −1.67316 −0.836582 0.547841i \(-0.815450\pi\)
−0.836582 + 0.547841i \(0.815450\pi\)
\(740\) 0 0
\(741\) 16.3799 0.601731
\(742\) 0 0
\(743\) 24.4865 0.898324 0.449162 0.893450i \(-0.351723\pi\)
0.449162 + 0.893450i \(0.351723\pi\)
\(744\) 0 0
\(745\) −64.6621 −2.36903
\(746\) 0 0
\(747\) −43.7135 −1.59939
\(748\) 0 0
\(749\) −0.743024 −0.0271495
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 11.8842 0.433083
\(754\) 0 0
\(755\) −22.6289 −0.823551
\(756\) 0 0
\(757\) −2.30651 −0.0838317 −0.0419158 0.999121i \(-0.513346\pi\)
−0.0419158 + 0.999121i \(0.513346\pi\)
\(758\) 0 0
\(759\) −1.64618 −0.0597526
\(760\) 0 0
\(761\) 39.3856 1.42773 0.713863 0.700285i \(-0.246944\pi\)
0.713863 + 0.700285i \(0.246944\pi\)
\(762\) 0 0
\(763\) −6.91556 −0.250360
\(764\) 0 0
\(765\) 47.5492 1.71915
\(766\) 0 0
\(767\) −17.4596 −0.630430
\(768\) 0 0
\(769\) −32.1702 −1.16009 −0.580043 0.814586i \(-0.696964\pi\)
−0.580043 + 0.814586i \(0.696964\pi\)
\(770\) 0 0
\(771\) −13.7836 −0.496403
\(772\) 0 0
\(773\) −4.07712 −0.146644 −0.0733219 0.997308i \(-0.523360\pi\)
−0.0733219 + 0.997308i \(0.523360\pi\)
\(774\) 0 0
\(775\) 21.3239 0.765975
\(776\) 0 0
\(777\) −2.45914 −0.0882212
\(778\) 0 0
\(779\) 3.81822 0.136802
\(780\) 0 0
\(781\) 4.20631 0.150514
\(782\) 0 0
\(783\) −1.34454 −0.0480499
\(784\) 0 0
\(785\) −27.6154 −0.985637
\(786\) 0 0
\(787\) 50.7653 1.80959 0.904794 0.425850i \(-0.140025\pi\)
0.904794 + 0.425850i \(0.140025\pi\)
\(788\) 0 0
\(789\) −4.97075 −0.176963
\(790\) 0 0
\(791\) 9.63661 0.342639
\(792\) 0 0
\(793\) −47.8907 −1.70065
\(794\) 0 0
\(795\) 11.2228 0.398032
\(796\) 0 0
\(797\) 16.1180 0.570931 0.285465 0.958389i \(-0.407852\pi\)
0.285465 + 0.958389i \(0.407852\pi\)
\(798\) 0 0
\(799\) 4.16266 0.147264
\(800\) 0 0
\(801\) 28.4249 1.00434
\(802\) 0 0
\(803\) −2.42729 −0.0856571
\(804\) 0 0
\(805\) −10.6702 −0.376073
\(806\) 0 0
\(807\) −7.07509 −0.249055
\(808\) 0 0
\(809\) −33.7460 −1.18645 −0.593223 0.805038i \(-0.702145\pi\)
−0.593223 + 0.805038i \(0.702145\pi\)
\(810\) 0 0
\(811\) −47.8021 −1.67856 −0.839279 0.543701i \(-0.817023\pi\)
−0.839279 + 0.543701i \(0.817023\pi\)
\(812\) 0 0
\(813\) 1.67411 0.0587135
\(814\) 0 0
\(815\) −54.4797 −1.90834
\(816\) 0 0
\(817\) 76.9927 2.69364
\(818\) 0 0
\(819\) −5.81659 −0.203248
\(820\) 0 0
\(821\) −26.0626 −0.909593 −0.454796 0.890595i \(-0.650288\pi\)
−0.454796 + 0.890595i \(0.650288\pi\)
\(822\) 0 0
\(823\) −28.5055 −0.993638 −0.496819 0.867854i \(-0.665499\pi\)
−0.496819 + 0.867854i \(0.665499\pi\)
\(824\) 0 0
\(825\) 1.97540 0.0687746
\(826\) 0 0
\(827\) 22.7240 0.790191 0.395096 0.918640i \(-0.370711\pi\)
0.395096 + 0.918640i \(0.370711\pi\)
\(828\) 0 0
\(829\) 23.6283 0.820643 0.410322 0.911941i \(-0.365416\pi\)
0.410322 + 0.911941i \(0.365416\pi\)
\(830\) 0 0
\(831\) −0.922921 −0.0320158
\(832\) 0 0
\(833\) 32.7998 1.13644
\(834\) 0 0
\(835\) −72.5033 −2.50908
\(836\) 0 0
\(837\) 7.82078 0.270326
\(838\) 0 0
\(839\) 53.4577 1.84557 0.922783 0.385320i \(-0.125909\pi\)
0.922783 + 0.385320i \(0.125909\pi\)
\(840\) 0 0
\(841\) −28.7699 −0.992066
\(842\) 0 0
\(843\) −9.51155 −0.327595
\(844\) 0 0
\(845\) 24.7314 0.850787
\(846\) 0 0
\(847\) −5.04985 −0.173515
\(848\) 0 0
\(849\) −5.01011 −0.171947
\(850\) 0 0
\(851\) −68.3475 −2.34292
\(852\) 0 0
\(853\) −6.44369 −0.220628 −0.110314 0.993897i \(-0.535186\pi\)
−0.110314 + 0.993897i \(0.535186\pi\)
\(854\) 0 0
\(855\) 74.0811 2.53352
\(856\) 0 0
\(857\) 23.0826 0.788485 0.394243 0.919006i \(-0.371007\pi\)
0.394243 + 0.919006i \(0.371007\pi\)
\(858\) 0 0
\(859\) 18.3323 0.625491 0.312745 0.949837i \(-0.398751\pi\)
0.312745 + 0.949837i \(0.398751\pi\)
\(860\) 0 0
\(861\) 0.116053 0.00395508
\(862\) 0 0
\(863\) 19.4092 0.660695 0.330348 0.943859i \(-0.392834\pi\)
0.330348 + 0.943859i \(0.392834\pi\)
\(864\) 0 0
\(865\) 57.7708 1.96427
\(866\) 0 0
\(867\) −3.12110 −0.105998
\(868\) 0 0
\(869\) −1.35613 −0.0460034
\(870\) 0 0
\(871\) −43.4309 −1.47160
\(872\) 0 0
\(873\) 39.1872 1.32628
\(874\) 0 0
\(875\) 4.42739 0.149673
\(876\) 0 0
\(877\) 29.4784 0.995414 0.497707 0.867345i \(-0.334176\pi\)
0.497707 + 0.867345i \(0.334176\pi\)
\(878\) 0 0
\(879\) −3.33183 −0.112380
\(880\) 0 0
\(881\) 38.2282 1.28794 0.643971 0.765050i \(-0.277286\pi\)
0.643971 + 0.765050i \(0.277286\pi\)
\(882\) 0 0
\(883\) −16.4754 −0.554441 −0.277221 0.960806i \(-0.589413\pi\)
−0.277221 + 0.960806i \(0.589413\pi\)
\(884\) 0 0
\(885\) 6.75880 0.227194
\(886\) 0 0
\(887\) 46.1505 1.54958 0.774790 0.632218i \(-0.217855\pi\)
0.774790 + 0.632218i \(0.217855\pi\)
\(888\) 0 0
\(889\) 3.82125 0.128161
\(890\) 0 0
\(891\) −3.68143 −0.123333
\(892\) 0 0
\(893\) 6.48537 0.217025
\(894\) 0 0
\(895\) 43.3342 1.44850
\(896\) 0 0
\(897\) 13.8371 0.462009
\(898\) 0 0
\(899\) −1.33833 −0.0446358
\(900\) 0 0
\(901\) 31.4054 1.04627
\(902\) 0 0
\(903\) 2.34016 0.0778757
\(904\) 0 0
\(905\) 75.5809 2.51240
\(906\) 0 0
\(907\) 31.2290 1.03694 0.518471 0.855095i \(-0.326501\pi\)
0.518471 + 0.855095i \(0.326501\pi\)
\(908\) 0 0
\(909\) −24.6601 −0.817924
\(910\) 0 0
\(911\) 18.9325 0.627262 0.313631 0.949545i \(-0.398454\pi\)
0.313631 + 0.949545i \(0.398454\pi\)
\(912\) 0 0
\(913\) −8.40667 −0.278220
\(914\) 0 0
\(915\) 18.5390 0.612879
\(916\) 0 0
\(917\) 3.72146 0.122893
\(918\) 0 0
\(919\) −18.0737 −0.596198 −0.298099 0.954535i \(-0.596353\pi\)
−0.298099 + 0.954535i \(0.596353\pi\)
\(920\) 0 0
\(921\) 1.76351 0.0581098
\(922\) 0 0
\(923\) −35.3566 −1.16378
\(924\) 0 0
\(925\) 82.0164 2.69668
\(926\) 0 0
\(927\) 12.2839 0.403456
\(928\) 0 0
\(929\) −17.3500 −0.569236 −0.284618 0.958641i \(-0.591867\pi\)
−0.284618 + 0.958641i \(0.591867\pi\)
\(930\) 0 0
\(931\) 51.1016 1.67479
\(932\) 0 0
\(933\) 15.0372 0.492295
\(934\) 0 0
\(935\) 9.14433 0.299051
\(936\) 0 0
\(937\) 7.90880 0.258369 0.129185 0.991621i \(-0.458764\pi\)
0.129185 + 0.991621i \(0.458764\pi\)
\(938\) 0 0
\(939\) 6.22085 0.203010
\(940\) 0 0
\(941\) 34.7045 1.13134 0.565668 0.824633i \(-0.308618\pi\)
0.565668 + 0.824633i \(0.308618\pi\)
\(942\) 0 0
\(943\) 3.22549 0.105036
\(944\) 0 0
\(945\) 4.69605 0.152763
\(946\) 0 0
\(947\) −54.3618 −1.76652 −0.883260 0.468884i \(-0.844656\pi\)
−0.883260 + 0.468884i \(0.844656\pi\)
\(948\) 0 0
\(949\) 20.4028 0.662303
\(950\) 0 0
\(951\) 0.566155 0.0183588
\(952\) 0 0
\(953\) 9.89694 0.320593 0.160297 0.987069i \(-0.448755\pi\)
0.160297 + 0.987069i \(0.448755\pi\)
\(954\) 0 0
\(955\) 16.8436 0.545046
\(956\) 0 0
\(957\) −0.123980 −0.00400771
\(958\) 0 0
\(959\) 2.97360 0.0960227
\(960\) 0 0
\(961\) −23.2153 −0.748882
\(962\) 0 0
\(963\) 4.35787 0.140430
\(964\) 0 0
\(965\) 52.5339 1.69113
\(966\) 0 0
\(967\) 28.1171 0.904185 0.452092 0.891971i \(-0.350678\pi\)
0.452092 + 0.891971i \(0.350678\pi\)
\(968\) 0 0
\(969\) −17.7439 −0.570017
\(970\) 0 0
\(971\) 15.7537 0.505560 0.252780 0.967524i \(-0.418655\pi\)
0.252780 + 0.967524i \(0.418655\pi\)
\(972\) 0 0
\(973\) 0.745813 0.0239097
\(974\) 0 0
\(975\) −16.6044 −0.531768
\(976\) 0 0
\(977\) −49.1758 −1.57327 −0.786636 0.617417i \(-0.788179\pi\)
−0.786636 + 0.617417i \(0.788179\pi\)
\(978\) 0 0
\(979\) 5.46647 0.174709
\(980\) 0 0
\(981\) 40.5601 1.29498
\(982\) 0 0
\(983\) −44.6943 −1.42553 −0.712763 0.701405i \(-0.752556\pi\)
−0.712763 + 0.701405i \(0.752556\pi\)
\(984\) 0 0
\(985\) −34.1341 −1.08760
\(986\) 0 0
\(987\) 0.197120 0.00627440
\(988\) 0 0
\(989\) 65.0406 2.06817
\(990\) 0 0
\(991\) 29.5381 0.938307 0.469154 0.883117i \(-0.344559\pi\)
0.469154 + 0.883117i \(0.344559\pi\)
\(992\) 0 0
\(993\) 4.46354 0.141646
\(994\) 0 0
\(995\) 97.0872 3.07787
\(996\) 0 0
\(997\) 37.3118 1.18168 0.590838 0.806790i \(-0.298797\pi\)
0.590838 + 0.806790i \(0.298797\pi\)
\(998\) 0 0
\(999\) 30.0805 0.951704
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.1.21 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.21 44 1.1 even 1 trivial