Properties

Label 6008.2.a.b.1.16
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 1.16
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.52846 q^{3} +0.276340 q^{5} +2.37933 q^{7} -0.663805 q^{9} +O(q^{10})\) \(q-1.52846 q^{3} +0.276340 q^{5} +2.37933 q^{7} -0.663805 q^{9} -0.982619 q^{11} -5.12922 q^{13} -0.422376 q^{15} +7.66490 q^{17} +4.67902 q^{19} -3.63671 q^{21} -7.09647 q^{23} -4.92364 q^{25} +5.59999 q^{27} +2.66042 q^{29} -5.74196 q^{31} +1.50189 q^{33} +0.657504 q^{35} -0.273473 q^{37} +7.83981 q^{39} -4.12965 q^{41} +7.07236 q^{43} -0.183436 q^{45} +12.1984 q^{47} -1.33880 q^{49} -11.7155 q^{51} -0.726931 q^{53} -0.271537 q^{55} -7.15171 q^{57} -6.80195 q^{59} +5.98444 q^{61} -1.57941 q^{63} -1.41741 q^{65} -10.6673 q^{67} +10.8467 q^{69} -8.23431 q^{71} +15.4776 q^{73} +7.52559 q^{75} -2.33797 q^{77} -12.1624 q^{79} -6.56795 q^{81} -8.56428 q^{83} +2.11812 q^{85} -4.06634 q^{87} -16.3251 q^{89} -12.2041 q^{91} +8.77637 q^{93} +1.29300 q^{95} +6.63657 q^{97} +0.652267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −1.52846 −0.882458 −0.441229 0.897395i \(-0.645457\pi\)
−0.441229 + 0.897395i \(0.645457\pi\)
\(4\) 0 0
\(5\) 0.276340 0.123583 0.0617916 0.998089i \(-0.480319\pi\)
0.0617916 + 0.998089i \(0.480319\pi\)
\(6\) 0 0
\(7\) 2.37933 0.899302 0.449651 0.893204i \(-0.351548\pi\)
0.449651 + 0.893204i \(0.351548\pi\)
\(8\) 0 0
\(9\) −0.663805 −0.221268
\(10\) 0 0
\(11\) −0.982619 −0.296271 −0.148135 0.988967i \(-0.547327\pi\)
−0.148135 + 0.988967i \(0.547327\pi\)
\(12\) 0 0
\(13\) −5.12922 −1.42259 −0.711295 0.702894i \(-0.751891\pi\)
−0.711295 + 0.702894i \(0.751891\pi\)
\(14\) 0 0
\(15\) −0.422376 −0.109057
\(16\) 0 0
\(17\) 7.66490 1.85901 0.929505 0.368808i \(-0.120234\pi\)
0.929505 + 0.368808i \(0.120234\pi\)
\(18\) 0 0
\(19\) 4.67902 1.07344 0.536721 0.843760i \(-0.319663\pi\)
0.536721 + 0.843760i \(0.319663\pi\)
\(20\) 0 0
\(21\) −3.63671 −0.793596
\(22\) 0 0
\(23\) −7.09647 −1.47972 −0.739858 0.672763i \(-0.765107\pi\)
−0.739858 + 0.672763i \(0.765107\pi\)
\(24\) 0 0
\(25\) −4.92364 −0.984727
\(26\) 0 0
\(27\) 5.59999 1.07772
\(28\) 0 0
\(29\) 2.66042 0.494027 0.247013 0.969012i \(-0.420551\pi\)
0.247013 + 0.969012i \(0.420551\pi\)
\(30\) 0 0
\(31\) −5.74196 −1.03129 −0.515644 0.856803i \(-0.672447\pi\)
−0.515644 + 0.856803i \(0.672447\pi\)
\(32\) 0 0
\(33\) 1.50189 0.261446
\(34\) 0 0
\(35\) 0.657504 0.111139
\(36\) 0 0
\(37\) −0.273473 −0.0449587 −0.0224793 0.999747i \(-0.507156\pi\)
−0.0224793 + 0.999747i \(0.507156\pi\)
\(38\) 0 0
\(39\) 7.83981 1.25538
\(40\) 0 0
\(41\) −4.12965 −0.644944 −0.322472 0.946579i \(-0.604514\pi\)
−0.322472 + 0.946579i \(0.604514\pi\)
\(42\) 0 0
\(43\) 7.07236 1.07852 0.539262 0.842138i \(-0.318703\pi\)
0.539262 + 0.842138i \(0.318703\pi\)
\(44\) 0 0
\(45\) −0.183436 −0.0273451
\(46\) 0 0
\(47\) 12.1984 1.77932 0.889659 0.456626i \(-0.150942\pi\)
0.889659 + 0.456626i \(0.150942\pi\)
\(48\) 0 0
\(49\) −1.33880 −0.191257
\(50\) 0 0
\(51\) −11.7155 −1.64050
\(52\) 0 0
\(53\) −0.726931 −0.0998516 −0.0499258 0.998753i \(-0.515898\pi\)
−0.0499258 + 0.998753i \(0.515898\pi\)
\(54\) 0 0
\(55\) −0.271537 −0.0366141
\(56\) 0 0
\(57\) −7.15171 −0.947267
\(58\) 0 0
\(59\) −6.80195 −0.885538 −0.442769 0.896636i \(-0.646004\pi\)
−0.442769 + 0.896636i \(0.646004\pi\)
\(60\) 0 0
\(61\) 5.98444 0.766229 0.383114 0.923701i \(-0.374851\pi\)
0.383114 + 0.923701i \(0.374851\pi\)
\(62\) 0 0
\(63\) −1.57941 −0.198987
\(64\) 0 0
\(65\) −1.41741 −0.175808
\(66\) 0 0
\(67\) −10.6673 −1.30322 −0.651611 0.758553i \(-0.725907\pi\)
−0.651611 + 0.758553i \(0.725907\pi\)
\(68\) 0 0
\(69\) 10.8467 1.30579
\(70\) 0 0
\(71\) −8.23431 −0.977232 −0.488616 0.872499i \(-0.662498\pi\)
−0.488616 + 0.872499i \(0.662498\pi\)
\(72\) 0 0
\(73\) 15.4776 1.81152 0.905758 0.423796i \(-0.139303\pi\)
0.905758 + 0.423796i \(0.139303\pi\)
\(74\) 0 0
\(75\) 7.52559 0.868980
\(76\) 0 0
\(77\) −2.33797 −0.266437
\(78\) 0 0
\(79\) −12.1624 −1.36837 −0.684187 0.729307i \(-0.739843\pi\)
−0.684187 + 0.729307i \(0.739843\pi\)
\(80\) 0 0
\(81\) −6.56795 −0.729772
\(82\) 0 0
\(83\) −8.56428 −0.940052 −0.470026 0.882653i \(-0.655755\pi\)
−0.470026 + 0.882653i \(0.655755\pi\)
\(84\) 0 0
\(85\) 2.11812 0.229742
\(86\) 0 0
\(87\) −4.06634 −0.435958
\(88\) 0 0
\(89\) −16.3251 −1.73046 −0.865230 0.501374i \(-0.832828\pi\)
−0.865230 + 0.501374i \(0.832828\pi\)
\(90\) 0 0
\(91\) −12.2041 −1.27934
\(92\) 0 0
\(93\) 8.77637 0.910067
\(94\) 0 0
\(95\) 1.29300 0.132659
\(96\) 0 0
\(97\) 6.63657 0.673841 0.336921 0.941533i \(-0.390615\pi\)
0.336921 + 0.941533i \(0.390615\pi\)
\(98\) 0 0
\(99\) 0.652267 0.0655553
\(100\) 0 0
\(101\) 10.3406 1.02893 0.514466 0.857511i \(-0.327990\pi\)
0.514466 + 0.857511i \(0.327990\pi\)
\(102\) 0 0
\(103\) 2.66191 0.262286 0.131143 0.991363i \(-0.458135\pi\)
0.131143 + 0.991363i \(0.458135\pi\)
\(104\) 0 0
\(105\) −1.00497 −0.0980750
\(106\) 0 0
\(107\) −9.29618 −0.898695 −0.449348 0.893357i \(-0.648344\pi\)
−0.449348 + 0.893357i \(0.648344\pi\)
\(108\) 0 0
\(109\) 11.0187 1.05540 0.527698 0.849432i \(-0.323055\pi\)
0.527698 + 0.849432i \(0.323055\pi\)
\(110\) 0 0
\(111\) 0.417993 0.0396741
\(112\) 0 0
\(113\) 1.38536 0.130324 0.0651621 0.997875i \(-0.479244\pi\)
0.0651621 + 0.997875i \(0.479244\pi\)
\(114\) 0 0
\(115\) −1.96104 −0.182868
\(116\) 0 0
\(117\) 3.40480 0.314774
\(118\) 0 0
\(119\) 18.2373 1.67181
\(120\) 0 0
\(121\) −10.0345 −0.912224
\(122\) 0 0
\(123\) 6.31202 0.569136
\(124\) 0 0
\(125\) −2.74230 −0.245279
\(126\) 0 0
\(127\) 1.69029 0.149989 0.0749945 0.997184i \(-0.476106\pi\)
0.0749945 + 0.997184i \(0.476106\pi\)
\(128\) 0 0
\(129\) −10.8098 −0.951752
\(130\) 0 0
\(131\) 11.3218 0.989186 0.494593 0.869125i \(-0.335317\pi\)
0.494593 + 0.869125i \(0.335317\pi\)
\(132\) 0 0
\(133\) 11.1329 0.965347
\(134\) 0 0
\(135\) 1.54750 0.133188
\(136\) 0 0
\(137\) −8.67204 −0.740902 −0.370451 0.928852i \(-0.620797\pi\)
−0.370451 + 0.928852i \(0.620797\pi\)
\(138\) 0 0
\(139\) 14.6663 1.24398 0.621988 0.783027i \(-0.286325\pi\)
0.621988 + 0.783027i \(0.286325\pi\)
\(140\) 0 0
\(141\) −18.6448 −1.57017
\(142\) 0 0
\(143\) 5.04007 0.421472
\(144\) 0 0
\(145\) 0.735180 0.0610534
\(146\) 0 0
\(147\) 2.04630 0.168776
\(148\) 0 0
\(149\) −11.9171 −0.976291 −0.488145 0.872762i \(-0.662326\pi\)
−0.488145 + 0.872762i \(0.662326\pi\)
\(150\) 0 0
\(151\) −7.77060 −0.632362 −0.316181 0.948699i \(-0.602401\pi\)
−0.316181 + 0.948699i \(0.602401\pi\)
\(152\) 0 0
\(153\) −5.08800 −0.411340
\(154\) 0 0
\(155\) −1.58674 −0.127450
\(156\) 0 0
\(157\) −14.9081 −1.18980 −0.594900 0.803800i \(-0.702808\pi\)
−0.594900 + 0.803800i \(0.702808\pi\)
\(158\) 0 0
\(159\) 1.11109 0.0881148
\(160\) 0 0
\(161\) −16.8848 −1.33071
\(162\) 0 0
\(163\) −16.2000 −1.26889 −0.634443 0.772970i \(-0.718770\pi\)
−0.634443 + 0.772970i \(0.718770\pi\)
\(164\) 0 0
\(165\) 0.415034 0.0323104
\(166\) 0 0
\(167\) 0.0637168 0.00493055 0.00246528 0.999997i \(-0.499215\pi\)
0.00246528 + 0.999997i \(0.499215\pi\)
\(168\) 0 0
\(169\) 13.3089 1.02376
\(170\) 0 0
\(171\) −3.10596 −0.237519
\(172\) 0 0
\(173\) 23.8595 1.81401 0.907003 0.421124i \(-0.138364\pi\)
0.907003 + 0.421124i \(0.138364\pi\)
\(174\) 0 0
\(175\) −11.7149 −0.885567
\(176\) 0 0
\(177\) 10.3965 0.781450
\(178\) 0 0
\(179\) −14.2960 −1.06853 −0.534267 0.845316i \(-0.679412\pi\)
−0.534267 + 0.845316i \(0.679412\pi\)
\(180\) 0 0
\(181\) 16.7621 1.24592 0.622960 0.782254i \(-0.285930\pi\)
0.622960 + 0.782254i \(0.285930\pi\)
\(182\) 0 0
\(183\) −9.14698 −0.676165
\(184\) 0 0
\(185\) −0.0755716 −0.00555614
\(186\) 0 0
\(187\) −7.53167 −0.550770
\(188\) 0 0
\(189\) 13.3242 0.969193
\(190\) 0 0
\(191\) −14.9060 −1.07856 −0.539279 0.842127i \(-0.681303\pi\)
−0.539279 + 0.842127i \(0.681303\pi\)
\(192\) 0 0
\(193\) −4.51590 −0.325062 −0.162531 0.986703i \(-0.551966\pi\)
−0.162531 + 0.986703i \(0.551966\pi\)
\(194\) 0 0
\(195\) 2.16646 0.155143
\(196\) 0 0
\(197\) 17.9542 1.27919 0.639593 0.768714i \(-0.279103\pi\)
0.639593 + 0.768714i \(0.279103\pi\)
\(198\) 0 0
\(199\) 12.5885 0.892378 0.446189 0.894939i \(-0.352781\pi\)
0.446189 + 0.894939i \(0.352781\pi\)
\(200\) 0 0
\(201\) 16.3046 1.15004
\(202\) 0 0
\(203\) 6.33000 0.444279
\(204\) 0 0
\(205\) −1.14119 −0.0797042
\(206\) 0 0
\(207\) 4.71068 0.327415
\(208\) 0 0
\(209\) −4.59769 −0.318029
\(210\) 0 0
\(211\) −1.10396 −0.0760001 −0.0380000 0.999278i \(-0.512099\pi\)
−0.0380000 + 0.999278i \(0.512099\pi\)
\(212\) 0 0
\(213\) 12.5858 0.862366
\(214\) 0 0
\(215\) 1.95438 0.133287
\(216\) 0 0
\(217\) −13.6620 −0.927438
\(218\) 0 0
\(219\) −23.6569 −1.59859
\(220\) 0 0
\(221\) −39.3149 −2.64461
\(222\) 0 0
\(223\) −27.8136 −1.86254 −0.931268 0.364335i \(-0.881296\pi\)
−0.931268 + 0.364335i \(0.881296\pi\)
\(224\) 0 0
\(225\) 3.26834 0.217889
\(226\) 0 0
\(227\) −15.4401 −1.02479 −0.512397 0.858749i \(-0.671242\pi\)
−0.512397 + 0.858749i \(0.671242\pi\)
\(228\) 0 0
\(229\) 9.73578 0.643359 0.321679 0.946849i \(-0.395753\pi\)
0.321679 + 0.946849i \(0.395753\pi\)
\(230\) 0 0
\(231\) 3.57350 0.235119
\(232\) 0 0
\(233\) −10.8528 −0.710988 −0.355494 0.934679i \(-0.615687\pi\)
−0.355494 + 0.934679i \(0.615687\pi\)
\(234\) 0 0
\(235\) 3.37091 0.219894
\(236\) 0 0
\(237\) 18.5897 1.20753
\(238\) 0 0
\(239\) −25.7278 −1.66419 −0.832095 0.554632i \(-0.812859\pi\)
−0.832095 + 0.554632i \(0.812859\pi\)
\(240\) 0 0
\(241\) −8.19705 −0.528018 −0.264009 0.964520i \(-0.585045\pi\)
−0.264009 + 0.964520i \(0.585045\pi\)
\(242\) 0 0
\(243\) −6.76110 −0.433725
\(244\) 0 0
\(245\) −0.369964 −0.0236361
\(246\) 0 0
\(247\) −23.9997 −1.52707
\(248\) 0 0
\(249\) 13.0902 0.829556
\(250\) 0 0
\(251\) 1.07869 0.0680862 0.0340431 0.999420i \(-0.489162\pi\)
0.0340431 + 0.999420i \(0.489162\pi\)
\(252\) 0 0
\(253\) 6.97312 0.438397
\(254\) 0 0
\(255\) −3.23747 −0.202738
\(256\) 0 0
\(257\) −25.7180 −1.60425 −0.802124 0.597158i \(-0.796297\pi\)
−0.802124 + 0.597158i \(0.796297\pi\)
\(258\) 0 0
\(259\) −0.650682 −0.0404314
\(260\) 0 0
\(261\) −1.76600 −0.109313
\(262\) 0 0
\(263\) 27.0811 1.66990 0.834948 0.550330i \(-0.185498\pi\)
0.834948 + 0.550330i \(0.185498\pi\)
\(264\) 0 0
\(265\) −0.200880 −0.0123400
\(266\) 0 0
\(267\) 24.9523 1.52706
\(268\) 0 0
\(269\) 18.3997 1.12185 0.560923 0.827868i \(-0.310446\pi\)
0.560923 + 0.827868i \(0.310446\pi\)
\(270\) 0 0
\(271\) −17.9111 −1.08802 −0.544010 0.839079i \(-0.683095\pi\)
−0.544010 + 0.839079i \(0.683095\pi\)
\(272\) 0 0
\(273\) 18.6535 1.12896
\(274\) 0 0
\(275\) 4.83806 0.291746
\(276\) 0 0
\(277\) −7.11279 −0.427366 −0.213683 0.976903i \(-0.568546\pi\)
−0.213683 + 0.976903i \(0.568546\pi\)
\(278\) 0 0
\(279\) 3.81155 0.228191
\(280\) 0 0
\(281\) −15.9208 −0.949758 −0.474879 0.880051i \(-0.657508\pi\)
−0.474879 + 0.880051i \(0.657508\pi\)
\(282\) 0 0
\(283\) −15.9716 −0.949415 −0.474708 0.880144i \(-0.657446\pi\)
−0.474708 + 0.880144i \(0.657446\pi\)
\(284\) 0 0
\(285\) −1.97630 −0.117066
\(286\) 0 0
\(287\) −9.82580 −0.579999
\(288\) 0 0
\(289\) 41.7507 2.45592
\(290\) 0 0
\(291\) −10.1437 −0.594636
\(292\) 0 0
\(293\) −12.1943 −0.712399 −0.356200 0.934410i \(-0.615928\pi\)
−0.356200 + 0.934410i \(0.615928\pi\)
\(294\) 0 0
\(295\) −1.87965 −0.109438
\(296\) 0 0
\(297\) −5.50265 −0.319296
\(298\) 0 0
\(299\) 36.3994 2.10503
\(300\) 0 0
\(301\) 16.8275 0.969919
\(302\) 0 0
\(303\) −15.8053 −0.907988
\(304\) 0 0
\(305\) 1.65374 0.0946930
\(306\) 0 0
\(307\) −25.9628 −1.48178 −0.740889 0.671628i \(-0.765595\pi\)
−0.740889 + 0.671628i \(0.765595\pi\)
\(308\) 0 0
\(309\) −4.06863 −0.231456
\(310\) 0 0
\(311\) −9.92858 −0.562998 −0.281499 0.959562i \(-0.590832\pi\)
−0.281499 + 0.959562i \(0.590832\pi\)
\(312\) 0 0
\(313\) 22.4924 1.27135 0.635673 0.771958i \(-0.280723\pi\)
0.635673 + 0.771958i \(0.280723\pi\)
\(314\) 0 0
\(315\) −0.436455 −0.0245914
\(316\) 0 0
\(317\) −6.16889 −0.346480 −0.173240 0.984880i \(-0.555424\pi\)
−0.173240 + 0.984880i \(0.555424\pi\)
\(318\) 0 0
\(319\) −2.61417 −0.146366
\(320\) 0 0
\(321\) 14.2088 0.793061
\(322\) 0 0
\(323\) 35.8642 1.99554
\(324\) 0 0
\(325\) 25.2544 1.40086
\(326\) 0 0
\(327\) −16.8416 −0.931343
\(328\) 0 0
\(329\) 29.0240 1.60014
\(330\) 0 0
\(331\) −24.3642 −1.33918 −0.669588 0.742733i \(-0.733529\pi\)
−0.669588 + 0.742733i \(0.733529\pi\)
\(332\) 0 0
\(333\) 0.181533 0.00994794
\(334\) 0 0
\(335\) −2.94782 −0.161056
\(336\) 0 0
\(337\) −27.5839 −1.50259 −0.751294 0.659967i \(-0.770570\pi\)
−0.751294 + 0.659967i \(0.770570\pi\)
\(338\) 0 0
\(339\) −2.11748 −0.115006
\(340\) 0 0
\(341\) 5.64216 0.305540
\(342\) 0 0
\(343\) −19.8407 −1.07130
\(344\) 0 0
\(345\) 2.99738 0.161373
\(346\) 0 0
\(347\) 16.1313 0.865972 0.432986 0.901401i \(-0.357460\pi\)
0.432986 + 0.901401i \(0.357460\pi\)
\(348\) 0 0
\(349\) −10.0145 −0.536064 −0.268032 0.963410i \(-0.586373\pi\)
−0.268032 + 0.963410i \(0.586373\pi\)
\(350\) 0 0
\(351\) −28.7236 −1.53315
\(352\) 0 0
\(353\) 18.2704 0.972437 0.486218 0.873837i \(-0.338376\pi\)
0.486218 + 0.873837i \(0.338376\pi\)
\(354\) 0 0
\(355\) −2.27547 −0.120769
\(356\) 0 0
\(357\) −27.8750 −1.47530
\(358\) 0 0
\(359\) 36.9280 1.94898 0.974492 0.224421i \(-0.0720491\pi\)
0.974492 + 0.224421i \(0.0720491\pi\)
\(360\) 0 0
\(361\) 2.89325 0.152276
\(362\) 0 0
\(363\) 15.3373 0.804999
\(364\) 0 0
\(365\) 4.27708 0.223873
\(366\) 0 0
\(367\) −13.0694 −0.682219 −0.341109 0.940024i \(-0.610803\pi\)
−0.341109 + 0.940024i \(0.610803\pi\)
\(368\) 0 0
\(369\) 2.74129 0.142706
\(370\) 0 0
\(371\) −1.72961 −0.0897967
\(372\) 0 0
\(373\) 22.5438 1.16728 0.583638 0.812014i \(-0.301629\pi\)
0.583638 + 0.812014i \(0.301629\pi\)
\(374\) 0 0
\(375\) 4.19150 0.216448
\(376\) 0 0
\(377\) −13.6459 −0.702797
\(378\) 0 0
\(379\) 8.21538 0.421996 0.210998 0.977487i \(-0.432329\pi\)
0.210998 + 0.977487i \(0.432329\pi\)
\(380\) 0 0
\(381\) −2.58354 −0.132359
\(382\) 0 0
\(383\) 18.7975 0.960508 0.480254 0.877129i \(-0.340544\pi\)
0.480254 + 0.877129i \(0.340544\pi\)
\(384\) 0 0
\(385\) −0.646076 −0.0329271
\(386\) 0 0
\(387\) −4.69467 −0.238643
\(388\) 0 0
\(389\) 6.78801 0.344166 0.172083 0.985082i \(-0.444950\pi\)
0.172083 + 0.985082i \(0.444950\pi\)
\(390\) 0 0
\(391\) −54.3937 −2.75081
\(392\) 0 0
\(393\) −17.3049 −0.872915
\(394\) 0 0
\(395\) −3.36095 −0.169108
\(396\) 0 0
\(397\) −6.42103 −0.322262 −0.161131 0.986933i \(-0.551514\pi\)
−0.161131 + 0.986933i \(0.551514\pi\)
\(398\) 0 0
\(399\) −17.0163 −0.851878
\(400\) 0 0
\(401\) −5.42818 −0.271070 −0.135535 0.990773i \(-0.543275\pi\)
−0.135535 + 0.990773i \(0.543275\pi\)
\(402\) 0 0
\(403\) 29.4518 1.46710
\(404\) 0 0
\(405\) −1.81499 −0.0901875
\(406\) 0 0
\(407\) 0.268720 0.0133199
\(408\) 0 0
\(409\) −31.8163 −1.57321 −0.786607 0.617453i \(-0.788164\pi\)
−0.786607 + 0.617453i \(0.788164\pi\)
\(410\) 0 0
\(411\) 13.2549 0.653815
\(412\) 0 0
\(413\) −16.1841 −0.796366
\(414\) 0 0
\(415\) −2.36666 −0.116175
\(416\) 0 0
\(417\) −22.4168 −1.09776
\(418\) 0 0
\(419\) −24.8898 −1.21594 −0.607972 0.793958i \(-0.708017\pi\)
−0.607972 + 0.793958i \(0.708017\pi\)
\(420\) 0 0
\(421\) −22.1147 −1.07780 −0.538902 0.842368i \(-0.681161\pi\)
−0.538902 + 0.842368i \(0.681161\pi\)
\(422\) 0 0
\(423\) −8.09736 −0.393707
\(424\) 0 0
\(425\) −37.7392 −1.83062
\(426\) 0 0
\(427\) 14.2389 0.689071
\(428\) 0 0
\(429\) −7.70355 −0.371931
\(430\) 0 0
\(431\) −30.2171 −1.45551 −0.727754 0.685839i \(-0.759436\pi\)
−0.727754 + 0.685839i \(0.759436\pi\)
\(432\) 0 0
\(433\) 6.28105 0.301848 0.150924 0.988545i \(-0.451775\pi\)
0.150924 + 0.988545i \(0.451775\pi\)
\(434\) 0 0
\(435\) −1.12369 −0.0538770
\(436\) 0 0
\(437\) −33.2045 −1.58839
\(438\) 0 0
\(439\) −37.6291 −1.79594 −0.897969 0.440058i \(-0.854958\pi\)
−0.897969 + 0.440058i \(0.854958\pi\)
\(440\) 0 0
\(441\) 0.888701 0.0423191
\(442\) 0 0
\(443\) −23.5280 −1.11785 −0.558925 0.829219i \(-0.688786\pi\)
−0.558925 + 0.829219i \(0.688786\pi\)
\(444\) 0 0
\(445\) −4.51129 −0.213856
\(446\) 0 0
\(447\) 18.2149 0.861535
\(448\) 0 0
\(449\) 6.42606 0.303264 0.151632 0.988437i \(-0.451547\pi\)
0.151632 + 0.988437i \(0.451547\pi\)
\(450\) 0 0
\(451\) 4.05787 0.191078
\(452\) 0 0
\(453\) 11.8771 0.558033
\(454\) 0 0
\(455\) −3.37248 −0.158104
\(456\) 0 0
\(457\) −34.7818 −1.62702 −0.813511 0.581549i \(-0.802447\pi\)
−0.813511 + 0.581549i \(0.802447\pi\)
\(458\) 0 0
\(459\) 42.9233 2.00349
\(460\) 0 0
\(461\) 16.7636 0.780761 0.390380 0.920654i \(-0.372343\pi\)
0.390380 + 0.920654i \(0.372343\pi\)
\(462\) 0 0
\(463\) −17.1355 −0.796356 −0.398178 0.917308i \(-0.630357\pi\)
−0.398178 + 0.917308i \(0.630357\pi\)
\(464\) 0 0
\(465\) 2.42527 0.112469
\(466\) 0 0
\(467\) −3.92161 −0.181470 −0.0907351 0.995875i \(-0.528922\pi\)
−0.0907351 + 0.995875i \(0.528922\pi\)
\(468\) 0 0
\(469\) −25.3811 −1.17199
\(470\) 0 0
\(471\) 22.7865 1.04995
\(472\) 0 0
\(473\) −6.94943 −0.319535
\(474\) 0 0
\(475\) −23.0378 −1.05705
\(476\) 0 0
\(477\) 0.482540 0.0220940
\(478\) 0 0
\(479\) −12.9032 −0.589560 −0.294780 0.955565i \(-0.595246\pi\)
−0.294780 + 0.955565i \(0.595246\pi\)
\(480\) 0 0
\(481\) 1.40270 0.0639578
\(482\) 0 0
\(483\) 25.8078 1.17430
\(484\) 0 0
\(485\) 1.83395 0.0832754
\(486\) 0 0
\(487\) −31.9698 −1.44869 −0.724345 0.689438i \(-0.757858\pi\)
−0.724345 + 0.689438i \(0.757858\pi\)
\(488\) 0 0
\(489\) 24.7611 1.11974
\(490\) 0 0
\(491\) −18.1637 −0.819716 −0.409858 0.912149i \(-0.634422\pi\)
−0.409858 + 0.912149i \(0.634422\pi\)
\(492\) 0 0
\(493\) 20.3918 0.918401
\(494\) 0 0
\(495\) 0.180248 0.00810154
\(496\) 0 0
\(497\) −19.5921 −0.878827
\(498\) 0 0
\(499\) −23.9820 −1.07358 −0.536791 0.843715i \(-0.680363\pi\)
−0.536791 + 0.843715i \(0.680363\pi\)
\(500\) 0 0
\(501\) −0.0973887 −0.00435100
\(502\) 0 0
\(503\) −29.0278 −1.29429 −0.647143 0.762368i \(-0.724037\pi\)
−0.647143 + 0.762368i \(0.724037\pi\)
\(504\) 0 0
\(505\) 2.85753 0.127159
\(506\) 0 0
\(507\) −20.3421 −0.903426
\(508\) 0 0
\(509\) 3.24316 0.143750 0.0718752 0.997414i \(-0.477102\pi\)
0.0718752 + 0.997414i \(0.477102\pi\)
\(510\) 0 0
\(511\) 36.8263 1.62910
\(512\) 0 0
\(513\) 26.2025 1.15687
\(514\) 0 0
\(515\) 0.735593 0.0324141
\(516\) 0 0
\(517\) −11.9864 −0.527160
\(518\) 0 0
\(519\) −36.4684 −1.60078
\(520\) 0 0
\(521\) 5.00903 0.219450 0.109725 0.993962i \(-0.465003\pi\)
0.109725 + 0.993962i \(0.465003\pi\)
\(522\) 0 0
\(523\) 10.7377 0.469525 0.234763 0.972053i \(-0.424569\pi\)
0.234763 + 0.972053i \(0.424569\pi\)
\(524\) 0 0
\(525\) 17.9058 0.781475
\(526\) 0 0
\(527\) −44.0116 −1.91717
\(528\) 0 0
\(529\) 27.3599 1.18956
\(530\) 0 0
\(531\) 4.51517 0.195942
\(532\) 0 0
\(533\) 21.1819 0.917490
\(534\) 0 0
\(535\) −2.56891 −0.111064
\(536\) 0 0
\(537\) 21.8509 0.942936
\(538\) 0 0
\(539\) 1.31553 0.0566638
\(540\) 0 0
\(541\) −16.9617 −0.729239 −0.364619 0.931157i \(-0.618801\pi\)
−0.364619 + 0.931157i \(0.618801\pi\)
\(542\) 0 0
\(543\) −25.6203 −1.09947
\(544\) 0 0
\(545\) 3.04490 0.130429
\(546\) 0 0
\(547\) −21.5194 −0.920105 −0.460052 0.887892i \(-0.652169\pi\)
−0.460052 + 0.887892i \(0.652169\pi\)
\(548\) 0 0
\(549\) −3.97250 −0.169542
\(550\) 0 0
\(551\) 12.4481 0.530309
\(552\) 0 0
\(553\) −28.9383 −1.23058
\(554\) 0 0
\(555\) 0.115508 0.00490306
\(556\) 0 0
\(557\) 13.5868 0.575689 0.287845 0.957677i \(-0.407061\pi\)
0.287845 + 0.957677i \(0.407061\pi\)
\(558\) 0 0
\(559\) −36.2757 −1.53430
\(560\) 0 0
\(561\) 11.5119 0.486032
\(562\) 0 0
\(563\) 14.9004 0.627978 0.313989 0.949427i \(-0.398335\pi\)
0.313989 + 0.949427i \(0.398335\pi\)
\(564\) 0 0
\(565\) 0.382832 0.0161059
\(566\) 0 0
\(567\) −15.6273 −0.656285
\(568\) 0 0
\(569\) 36.0502 1.51130 0.755651 0.654974i \(-0.227320\pi\)
0.755651 + 0.654974i \(0.227320\pi\)
\(570\) 0 0
\(571\) 40.6936 1.70298 0.851488 0.524375i \(-0.175701\pi\)
0.851488 + 0.524375i \(0.175701\pi\)
\(572\) 0 0
\(573\) 22.7832 0.951782
\(574\) 0 0
\(575\) 34.9404 1.45712
\(576\) 0 0
\(577\) −42.6151 −1.77409 −0.887046 0.461681i \(-0.847246\pi\)
−0.887046 + 0.461681i \(0.847246\pi\)
\(578\) 0 0
\(579\) 6.90238 0.286853
\(580\) 0 0
\(581\) −20.3772 −0.845390
\(582\) 0 0
\(583\) 0.714295 0.0295831
\(584\) 0 0
\(585\) 0.940884 0.0389008
\(586\) 0 0
\(587\) 25.7650 1.06343 0.531717 0.846922i \(-0.321547\pi\)
0.531717 + 0.846922i \(0.321547\pi\)
\(588\) 0 0
\(589\) −26.8668 −1.10703
\(590\) 0 0
\(591\) −27.4424 −1.12883
\(592\) 0 0
\(593\) −22.5745 −0.927025 −0.463513 0.886090i \(-0.653411\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(594\) 0 0
\(595\) 5.03970 0.206608
\(596\) 0 0
\(597\) −19.2411 −0.787486
\(598\) 0 0
\(599\) 8.92050 0.364482 0.182241 0.983254i \(-0.441665\pi\)
0.182241 + 0.983254i \(0.441665\pi\)
\(600\) 0 0
\(601\) 14.7007 0.599656 0.299828 0.953993i \(-0.403071\pi\)
0.299828 + 0.953993i \(0.403071\pi\)
\(602\) 0 0
\(603\) 7.08104 0.288362
\(604\) 0 0
\(605\) −2.77293 −0.112735
\(606\) 0 0
\(607\) −5.61731 −0.227999 −0.114000 0.993481i \(-0.536366\pi\)
−0.114000 + 0.993481i \(0.536366\pi\)
\(608\) 0 0
\(609\) −9.67516 −0.392057
\(610\) 0 0
\(611\) −62.5682 −2.53124
\(612\) 0 0
\(613\) −33.0260 −1.33391 −0.666953 0.745100i \(-0.732402\pi\)
−0.666953 + 0.745100i \(0.732402\pi\)
\(614\) 0 0
\(615\) 1.74427 0.0703356
\(616\) 0 0
\(617\) 38.6964 1.55786 0.778930 0.627111i \(-0.215763\pi\)
0.778930 + 0.627111i \(0.215763\pi\)
\(618\) 0 0
\(619\) 1.27152 0.0511065 0.0255533 0.999673i \(-0.491865\pi\)
0.0255533 + 0.999673i \(0.491865\pi\)
\(620\) 0 0
\(621\) −39.7401 −1.59472
\(622\) 0 0
\(623\) −38.8429 −1.55621
\(624\) 0 0
\(625\) 23.8604 0.954415
\(626\) 0 0
\(627\) 7.02740 0.280647
\(628\) 0 0
\(629\) −2.09614 −0.0835787
\(630\) 0 0
\(631\) −17.6529 −0.702750 −0.351375 0.936235i \(-0.614286\pi\)
−0.351375 + 0.936235i \(0.614286\pi\)
\(632\) 0 0
\(633\) 1.68737 0.0670668
\(634\) 0 0
\(635\) 0.467095 0.0185361
\(636\) 0 0
\(637\) 6.86699 0.272080
\(638\) 0 0
\(639\) 5.46598 0.216231
\(640\) 0 0
\(641\) −24.0368 −0.949395 −0.474697 0.880149i \(-0.657442\pi\)
−0.474697 + 0.880149i \(0.657442\pi\)
\(642\) 0 0
\(643\) 2.27807 0.0898382 0.0449191 0.998991i \(-0.485697\pi\)
0.0449191 + 0.998991i \(0.485697\pi\)
\(644\) 0 0
\(645\) −2.98719 −0.117621
\(646\) 0 0
\(647\) 14.6344 0.575337 0.287668 0.957730i \(-0.407120\pi\)
0.287668 + 0.957730i \(0.407120\pi\)
\(648\) 0 0
\(649\) 6.68372 0.262359
\(650\) 0 0
\(651\) 20.8819 0.818425
\(652\) 0 0
\(653\) −45.3939 −1.77640 −0.888200 0.459456i \(-0.848044\pi\)
−0.888200 + 0.459456i \(0.848044\pi\)
\(654\) 0 0
\(655\) 3.12866 0.122247
\(656\) 0 0
\(657\) −10.2741 −0.400831
\(658\) 0 0
\(659\) 16.7090 0.650891 0.325446 0.945561i \(-0.394486\pi\)
0.325446 + 0.945561i \(0.394486\pi\)
\(660\) 0 0
\(661\) −2.30234 −0.0895505 −0.0447752 0.998997i \(-0.514257\pi\)
−0.0447752 + 0.998997i \(0.514257\pi\)
\(662\) 0 0
\(663\) 60.0914 2.33376
\(664\) 0 0
\(665\) 3.07648 0.119301
\(666\) 0 0
\(667\) −18.8796 −0.731020
\(668\) 0 0
\(669\) 42.5120 1.64361
\(670\) 0 0
\(671\) −5.88042 −0.227011
\(672\) 0 0
\(673\) 16.7779 0.646739 0.323369 0.946273i \(-0.395184\pi\)
0.323369 + 0.946273i \(0.395184\pi\)
\(674\) 0 0
\(675\) −27.5723 −1.06126
\(676\) 0 0
\(677\) 30.0279 1.15407 0.577033 0.816721i \(-0.304210\pi\)
0.577033 + 0.816721i \(0.304210\pi\)
\(678\) 0 0
\(679\) 15.7906 0.605986
\(680\) 0 0
\(681\) 23.5996 0.904337
\(682\) 0 0
\(683\) 32.0981 1.22820 0.614099 0.789229i \(-0.289519\pi\)
0.614099 + 0.789229i \(0.289519\pi\)
\(684\) 0 0
\(685\) −2.39643 −0.0915631
\(686\) 0 0
\(687\) −14.8808 −0.567737
\(688\) 0 0
\(689\) 3.72859 0.142048
\(690\) 0 0
\(691\) −19.4004 −0.738027 −0.369014 0.929424i \(-0.620304\pi\)
−0.369014 + 0.929424i \(0.620304\pi\)
\(692\) 0 0
\(693\) 1.55196 0.0589540
\(694\) 0 0
\(695\) 4.05288 0.153734
\(696\) 0 0
\(697\) −31.6534 −1.19896
\(698\) 0 0
\(699\) 16.5880 0.627417
\(700\) 0 0
\(701\) −16.9642 −0.640730 −0.320365 0.947294i \(-0.603806\pi\)
−0.320365 + 0.947294i \(0.603806\pi\)
\(702\) 0 0
\(703\) −1.27959 −0.0482605
\(704\) 0 0
\(705\) −5.15230 −0.194047
\(706\) 0 0
\(707\) 24.6038 0.925319
\(708\) 0 0
\(709\) 13.7779 0.517440 0.258720 0.965952i \(-0.416699\pi\)
0.258720 + 0.965952i \(0.416699\pi\)
\(710\) 0 0
\(711\) 8.07345 0.302778
\(712\) 0 0
\(713\) 40.7477 1.52601
\(714\) 0 0
\(715\) 1.39277 0.0520868
\(716\) 0 0
\(717\) 39.3239 1.46858
\(718\) 0 0
\(719\) 33.1958 1.23800 0.618998 0.785393i \(-0.287539\pi\)
0.618998 + 0.785393i \(0.287539\pi\)
\(720\) 0 0
\(721\) 6.33356 0.235874
\(722\) 0 0
\(723\) 12.5289 0.465954
\(724\) 0 0
\(725\) −13.0989 −0.486482
\(726\) 0 0
\(727\) 12.4300 0.461004 0.230502 0.973072i \(-0.425963\pi\)
0.230502 + 0.973072i \(0.425963\pi\)
\(728\) 0 0
\(729\) 30.0379 1.11252
\(730\) 0 0
\(731\) 54.2089 2.00499
\(732\) 0 0
\(733\) 10.0371 0.370727 0.185363 0.982670i \(-0.440654\pi\)
0.185363 + 0.982670i \(0.440654\pi\)
\(734\) 0 0
\(735\) 0.565475 0.0208579
\(736\) 0 0
\(737\) 10.4819 0.386107
\(738\) 0 0
\(739\) 39.0083 1.43494 0.717471 0.696588i \(-0.245299\pi\)
0.717471 + 0.696588i \(0.245299\pi\)
\(740\) 0 0
\(741\) 36.6827 1.34757
\(742\) 0 0
\(743\) −27.3362 −1.00287 −0.501433 0.865196i \(-0.667194\pi\)
−0.501433 + 0.865196i \(0.667194\pi\)
\(744\) 0 0
\(745\) −3.29319 −0.120653
\(746\) 0 0
\(747\) 5.68502 0.208004
\(748\) 0 0
\(749\) −22.1187 −0.808198
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −1.64873 −0.0600832
\(754\) 0 0
\(755\) −2.14733 −0.0781493
\(756\) 0 0
\(757\) 23.9456 0.870317 0.435159 0.900354i \(-0.356692\pi\)
0.435159 + 0.900354i \(0.356692\pi\)
\(758\) 0 0
\(759\) −10.6582 −0.386866
\(760\) 0 0
\(761\) 32.7674 1.18782 0.593909 0.804533i \(-0.297584\pi\)
0.593909 + 0.804533i \(0.297584\pi\)
\(762\) 0 0
\(763\) 26.2170 0.949120
\(764\) 0 0
\(765\) −1.40602 −0.0508347
\(766\) 0 0
\(767\) 34.8887 1.25976
\(768\) 0 0
\(769\) −9.43022 −0.340063 −0.170031 0.985439i \(-0.554387\pi\)
−0.170031 + 0.985439i \(0.554387\pi\)
\(770\) 0 0
\(771\) 39.3090 1.41568
\(772\) 0 0
\(773\) −23.8115 −0.856442 −0.428221 0.903674i \(-0.640859\pi\)
−0.428221 + 0.903674i \(0.640859\pi\)
\(774\) 0 0
\(775\) 28.2713 1.01554
\(776\) 0 0
\(777\) 0.994542 0.0356790
\(778\) 0 0
\(779\) −19.3227 −0.692309
\(780\) 0 0
\(781\) 8.09118 0.289525
\(782\) 0 0
\(783\) 14.8983 0.532421
\(784\) 0 0
\(785\) −4.11972 −0.147039
\(786\) 0 0
\(787\) −23.1542 −0.825359 −0.412679 0.910876i \(-0.635407\pi\)
−0.412679 + 0.910876i \(0.635407\pi\)
\(788\) 0 0
\(789\) −41.3925 −1.47361
\(790\) 0 0
\(791\) 3.29624 0.117201
\(792\) 0 0
\(793\) −30.6955 −1.09003
\(794\) 0 0
\(795\) 0.307038 0.0108895
\(796\) 0 0
\(797\) 1.66856 0.0591035 0.0295517 0.999563i \(-0.490592\pi\)
0.0295517 + 0.999563i \(0.490592\pi\)
\(798\) 0 0
\(799\) 93.4994 3.30777
\(800\) 0 0
\(801\) 10.8367 0.382896
\(802\) 0 0
\(803\) −15.2086 −0.536699
\(804\) 0 0
\(805\) −4.66596 −0.164453
\(806\) 0 0
\(807\) −28.1232 −0.989982
\(808\) 0 0
\(809\) −9.91277 −0.348515 −0.174257 0.984700i \(-0.555752\pi\)
−0.174257 + 0.984700i \(0.555752\pi\)
\(810\) 0 0
\(811\) 41.7942 1.46759 0.733797 0.679369i \(-0.237747\pi\)
0.733797 + 0.679369i \(0.237747\pi\)
\(812\) 0 0
\(813\) 27.3764 0.960132
\(814\) 0 0
\(815\) −4.47673 −0.156813
\(816\) 0 0
\(817\) 33.0917 1.15773
\(818\) 0 0
\(819\) 8.10114 0.283077
\(820\) 0 0
\(821\) 46.0792 1.60818 0.804088 0.594511i \(-0.202654\pi\)
0.804088 + 0.594511i \(0.202654\pi\)
\(822\) 0 0
\(823\) 28.1828 0.982392 0.491196 0.871049i \(-0.336560\pi\)
0.491196 + 0.871049i \(0.336560\pi\)
\(824\) 0 0
\(825\) −7.39478 −0.257453
\(826\) 0 0
\(827\) 0.268104 0.00932290 0.00466145 0.999989i \(-0.498516\pi\)
0.00466145 + 0.999989i \(0.498516\pi\)
\(828\) 0 0
\(829\) −18.1618 −0.630787 −0.315393 0.948961i \(-0.602136\pi\)
−0.315393 + 0.948961i \(0.602136\pi\)
\(830\) 0 0
\(831\) 10.8716 0.377133
\(832\) 0 0
\(833\) −10.2617 −0.355548
\(834\) 0 0
\(835\) 0.0176075 0.000609333 0
\(836\) 0 0
\(837\) −32.1549 −1.11144
\(838\) 0 0
\(839\) 9.35795 0.323072 0.161536 0.986867i \(-0.448355\pi\)
0.161536 + 0.986867i \(0.448355\pi\)
\(840\) 0 0
\(841\) −21.9222 −0.755938
\(842\) 0 0
\(843\) 24.3344 0.838121
\(844\) 0 0
\(845\) 3.67778 0.126520
\(846\) 0 0
\(847\) −23.8753 −0.820364
\(848\) 0 0
\(849\) 24.4120 0.837819
\(850\) 0 0
\(851\) 1.94069 0.0665261
\(852\) 0 0
\(853\) −6.02773 −0.206386 −0.103193 0.994661i \(-0.532906\pi\)
−0.103193 + 0.994661i \(0.532906\pi\)
\(854\) 0 0
\(855\) −0.858302 −0.0293533
\(856\) 0 0
\(857\) 10.0052 0.341770 0.170885 0.985291i \(-0.445337\pi\)
0.170885 + 0.985291i \(0.445337\pi\)
\(858\) 0 0
\(859\) −51.9917 −1.77394 −0.886968 0.461832i \(-0.847192\pi\)
−0.886968 + 0.461832i \(0.847192\pi\)
\(860\) 0 0
\(861\) 15.0184 0.511824
\(862\) 0 0
\(863\) 19.4576 0.662344 0.331172 0.943570i \(-0.392556\pi\)
0.331172 + 0.943570i \(0.392556\pi\)
\(864\) 0 0
\(865\) 6.59335 0.224181
\(866\) 0 0
\(867\) −63.8143 −2.16725
\(868\) 0 0
\(869\) 11.9510 0.405409
\(870\) 0 0
\(871\) 54.7151 1.85395
\(872\) 0 0
\(873\) −4.40539 −0.149100
\(874\) 0 0
\(875\) −6.52483 −0.220580
\(876\) 0 0
\(877\) 38.0330 1.28428 0.642142 0.766586i \(-0.278046\pi\)
0.642142 + 0.766586i \(0.278046\pi\)
\(878\) 0 0
\(879\) 18.6385 0.628662
\(880\) 0 0
\(881\) 18.3218 0.617277 0.308638 0.951179i \(-0.400127\pi\)
0.308638 + 0.951179i \(0.400127\pi\)
\(882\) 0 0
\(883\) −44.2160 −1.48799 −0.743993 0.668187i \(-0.767071\pi\)
−0.743993 + 0.668187i \(0.767071\pi\)
\(884\) 0 0
\(885\) 2.87298 0.0965740
\(886\) 0 0
\(887\) 35.6691 1.19765 0.598825 0.800880i \(-0.295634\pi\)
0.598825 + 0.800880i \(0.295634\pi\)
\(888\) 0 0
\(889\) 4.02176 0.134885
\(890\) 0 0
\(891\) 6.45379 0.216210
\(892\) 0 0
\(893\) 57.0765 1.90999
\(894\) 0 0
\(895\) −3.95056 −0.132053
\(896\) 0 0
\(897\) −55.6350 −1.85760
\(898\) 0 0
\(899\) −15.2760 −0.509483
\(900\) 0 0
\(901\) −5.57185 −0.185625
\(902\) 0 0
\(903\) −25.7201 −0.855912
\(904\) 0 0
\(905\) 4.63205 0.153975
\(906\) 0 0
\(907\) −26.6991 −0.886530 −0.443265 0.896391i \(-0.646180\pi\)
−0.443265 + 0.896391i \(0.646180\pi\)
\(908\) 0 0
\(909\) −6.86417 −0.227670
\(910\) 0 0
\(911\) 52.9433 1.75409 0.877045 0.480408i \(-0.159511\pi\)
0.877045 + 0.480408i \(0.159511\pi\)
\(912\) 0 0
\(913\) 8.41542 0.278510
\(914\) 0 0
\(915\) −2.52768 −0.0835625
\(916\) 0 0
\(917\) 26.9382 0.889577
\(918\) 0 0
\(919\) 6.37609 0.210328 0.105164 0.994455i \(-0.466463\pi\)
0.105164 + 0.994455i \(0.466463\pi\)
\(920\) 0 0
\(921\) 39.6832 1.30761
\(922\) 0 0
\(923\) 42.2356 1.39020
\(924\) 0 0
\(925\) 1.34648 0.0442720
\(926\) 0 0
\(927\) −1.76699 −0.0580356
\(928\) 0 0
\(929\) 15.7445 0.516559 0.258279 0.966070i \(-0.416845\pi\)
0.258279 + 0.966070i \(0.416845\pi\)
\(930\) 0 0
\(931\) −6.26426 −0.205303
\(932\) 0 0
\(933\) 15.1754 0.496822
\(934\) 0 0
\(935\) −2.08130 −0.0680659
\(936\) 0 0
\(937\) −17.1060 −0.558827 −0.279414 0.960171i \(-0.590140\pi\)
−0.279414 + 0.960171i \(0.590140\pi\)
\(938\) 0 0
\(939\) −34.3788 −1.12191
\(940\) 0 0
\(941\) −2.71609 −0.0885421 −0.0442710 0.999020i \(-0.514097\pi\)
−0.0442710 + 0.999020i \(0.514097\pi\)
\(942\) 0 0
\(943\) 29.3060 0.954334
\(944\) 0 0
\(945\) 3.68201 0.119776
\(946\) 0 0
\(947\) −44.7796 −1.45514 −0.727571 0.686032i \(-0.759351\pi\)
−0.727571 + 0.686032i \(0.759351\pi\)
\(948\) 0 0
\(949\) −79.3880 −2.57704
\(950\) 0 0
\(951\) 9.42892 0.305754
\(952\) 0 0
\(953\) −10.3455 −0.335123 −0.167562 0.985862i \(-0.553589\pi\)
−0.167562 + 0.985862i \(0.553589\pi\)
\(954\) 0 0
\(955\) −4.11912 −0.133292
\(956\) 0 0
\(957\) 3.99566 0.129161
\(958\) 0 0
\(959\) −20.6336 −0.666295
\(960\) 0 0
\(961\) 1.97015 0.0635533
\(962\) 0 0
\(963\) 6.17085 0.198853
\(964\) 0 0
\(965\) −1.24793 −0.0401721
\(966\) 0 0
\(967\) 21.7745 0.700222 0.350111 0.936708i \(-0.386144\pi\)
0.350111 + 0.936708i \(0.386144\pi\)
\(968\) 0 0
\(969\) −54.8171 −1.76098
\(970\) 0 0
\(971\) −2.57418 −0.0826093 −0.0413046 0.999147i \(-0.513151\pi\)
−0.0413046 + 0.999147i \(0.513151\pi\)
\(972\) 0 0
\(973\) 34.8958 1.11871
\(974\) 0 0
\(975\) −38.6004 −1.23620
\(976\) 0 0
\(977\) −1.36961 −0.0438178 −0.0219089 0.999760i \(-0.506974\pi\)
−0.0219089 + 0.999760i \(0.506974\pi\)
\(978\) 0 0
\(979\) 16.0414 0.512685
\(980\) 0 0
\(981\) −7.31425 −0.233526
\(982\) 0 0
\(983\) 10.2147 0.325799 0.162899 0.986643i \(-0.447915\pi\)
0.162899 + 0.986643i \(0.447915\pi\)
\(984\) 0 0
\(985\) 4.96148 0.158086
\(986\) 0 0
\(987\) −44.3620 −1.41206
\(988\) 0 0
\(989\) −50.1888 −1.59591
\(990\) 0 0
\(991\) −18.2800 −0.580682 −0.290341 0.956923i \(-0.593769\pi\)
−0.290341 + 0.956923i \(0.593769\pi\)
\(992\) 0 0
\(993\) 37.2397 1.18177
\(994\) 0 0
\(995\) 3.47872 0.110283
\(996\) 0 0
\(997\) −13.3344 −0.422304 −0.211152 0.977453i \(-0.567721\pi\)
−0.211152 + 0.977453i \(0.567721\pi\)
\(998\) 0 0
\(999\) −1.53144 −0.0484528
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.1.16 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.16 44 1.1 even 1 trivial