Properties

Label 6008.2.a.b.1.37
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 1.37
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.77382 q^{3} -3.34355 q^{5} +0.838649 q^{7} +0.146429 q^{9} +O(q^{10})\) \(q+1.77382 q^{3} -3.34355 q^{5} +0.838649 q^{7} +0.146429 q^{9} -0.297273 q^{11} -1.29535 q^{13} -5.93085 q^{15} +2.69073 q^{17} -2.59218 q^{19} +1.48761 q^{21} +5.00797 q^{23} +6.17933 q^{25} -5.06171 q^{27} +4.26847 q^{29} -1.16112 q^{31} -0.527309 q^{33} -2.80407 q^{35} +6.31269 q^{37} -2.29772 q^{39} +0.0977895 q^{41} +7.74167 q^{43} -0.489594 q^{45} -4.23944 q^{47} -6.29667 q^{49} +4.77286 q^{51} -3.41633 q^{53} +0.993949 q^{55} -4.59806 q^{57} +5.04471 q^{59} -11.7533 q^{61} +0.122803 q^{63} +4.33108 q^{65} -4.02906 q^{67} +8.88323 q^{69} -2.77177 q^{71} -12.8527 q^{73} +10.9610 q^{75} -0.249308 q^{77} +9.39050 q^{79} -9.41785 q^{81} -15.8476 q^{83} -8.99658 q^{85} +7.57148 q^{87} -11.7826 q^{89} -1.08635 q^{91} -2.05962 q^{93} +8.66710 q^{95} -8.20439 q^{97} -0.0435295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.77382 1.02411 0.512057 0.858951i \(-0.328884\pi\)
0.512057 + 0.858951i \(0.328884\pi\)
\(4\) 0 0
\(5\) −3.34355 −1.49528 −0.747641 0.664103i \(-0.768813\pi\)
−0.747641 + 0.664103i \(0.768813\pi\)
\(6\) 0 0
\(7\) 0.838649 0.316980 0.158490 0.987361i \(-0.449338\pi\)
0.158490 + 0.987361i \(0.449338\pi\)
\(8\) 0 0
\(9\) 0.146429 0.0488097
\(10\) 0 0
\(11\) −0.297273 −0.0896313 −0.0448157 0.998995i \(-0.514270\pi\)
−0.0448157 + 0.998995i \(0.514270\pi\)
\(12\) 0 0
\(13\) −1.29535 −0.359267 −0.179633 0.983734i \(-0.557491\pi\)
−0.179633 + 0.983734i \(0.557491\pi\)
\(14\) 0 0
\(15\) −5.93085 −1.53134
\(16\) 0 0
\(17\) 2.69073 0.652597 0.326299 0.945267i \(-0.394199\pi\)
0.326299 + 0.945267i \(0.394199\pi\)
\(18\) 0 0
\(19\) −2.59218 −0.594688 −0.297344 0.954770i \(-0.596101\pi\)
−0.297344 + 0.954770i \(0.596101\pi\)
\(20\) 0 0
\(21\) 1.48761 0.324623
\(22\) 0 0
\(23\) 5.00797 1.04423 0.522117 0.852874i \(-0.325142\pi\)
0.522117 + 0.852874i \(0.325142\pi\)
\(24\) 0 0
\(25\) 6.17933 1.23587
\(26\) 0 0
\(27\) −5.06171 −0.974127
\(28\) 0 0
\(29\) 4.26847 0.792635 0.396317 0.918114i \(-0.370288\pi\)
0.396317 + 0.918114i \(0.370288\pi\)
\(30\) 0 0
\(31\) −1.16112 −0.208544 −0.104272 0.994549i \(-0.533251\pi\)
−0.104272 + 0.994549i \(0.533251\pi\)
\(32\) 0 0
\(33\) −0.527309 −0.0917927
\(34\) 0 0
\(35\) −2.80407 −0.473974
\(36\) 0 0
\(37\) 6.31269 1.03780 0.518900 0.854835i \(-0.326342\pi\)
0.518900 + 0.854835i \(0.326342\pi\)
\(38\) 0 0
\(39\) −2.29772 −0.367930
\(40\) 0 0
\(41\) 0.0977895 0.0152722 0.00763608 0.999971i \(-0.497569\pi\)
0.00763608 + 0.999971i \(0.497569\pi\)
\(42\) 0 0
\(43\) 7.74167 1.18059 0.590297 0.807186i \(-0.299011\pi\)
0.590297 + 0.807186i \(0.299011\pi\)
\(44\) 0 0
\(45\) −0.489594 −0.0729843
\(46\) 0 0
\(47\) −4.23944 −0.618385 −0.309193 0.950999i \(-0.600059\pi\)
−0.309193 + 0.950999i \(0.600059\pi\)
\(48\) 0 0
\(49\) −6.29667 −0.899524
\(50\) 0 0
\(51\) 4.77286 0.668334
\(52\) 0 0
\(53\) −3.41633 −0.469269 −0.234634 0.972084i \(-0.575389\pi\)
−0.234634 + 0.972084i \(0.575389\pi\)
\(54\) 0 0
\(55\) 0.993949 0.134024
\(56\) 0 0
\(57\) −4.59806 −0.609028
\(58\) 0 0
\(59\) 5.04471 0.656765 0.328382 0.944545i \(-0.393497\pi\)
0.328382 + 0.944545i \(0.393497\pi\)
\(60\) 0 0
\(61\) −11.7533 −1.50485 −0.752426 0.658677i \(-0.771117\pi\)
−0.752426 + 0.658677i \(0.771117\pi\)
\(62\) 0 0
\(63\) 0.122803 0.0154717
\(64\) 0 0
\(65\) 4.33108 0.537205
\(66\) 0 0
\(67\) −4.02906 −0.492228 −0.246114 0.969241i \(-0.579154\pi\)
−0.246114 + 0.969241i \(0.579154\pi\)
\(68\) 0 0
\(69\) 8.88323 1.06942
\(70\) 0 0
\(71\) −2.77177 −0.328949 −0.164475 0.986381i \(-0.552593\pi\)
−0.164475 + 0.986381i \(0.552593\pi\)
\(72\) 0 0
\(73\) −12.8527 −1.50429 −0.752146 0.658997i \(-0.770981\pi\)
−0.752146 + 0.658997i \(0.770981\pi\)
\(74\) 0 0
\(75\) 10.9610 1.26567
\(76\) 0 0
\(77\) −0.249308 −0.0284113
\(78\) 0 0
\(79\) 9.39050 1.05651 0.528257 0.849085i \(-0.322846\pi\)
0.528257 + 0.849085i \(0.322846\pi\)
\(80\) 0 0
\(81\) −9.41785 −1.04643
\(82\) 0 0
\(83\) −15.8476 −1.73950 −0.869750 0.493493i \(-0.835720\pi\)
−0.869750 + 0.493493i \(0.835720\pi\)
\(84\) 0 0
\(85\) −8.99658 −0.975816
\(86\) 0 0
\(87\) 7.57148 0.811748
\(88\) 0 0
\(89\) −11.7826 −1.24895 −0.624477 0.781043i \(-0.714688\pi\)
−0.624477 + 0.781043i \(0.714688\pi\)
\(90\) 0 0
\(91\) −1.08635 −0.113880
\(92\) 0 0
\(93\) −2.05962 −0.213573
\(94\) 0 0
\(95\) 8.66710 0.889225
\(96\) 0 0
\(97\) −8.20439 −0.833029 −0.416515 0.909129i \(-0.636749\pi\)
−0.416515 + 0.909129i \(0.636749\pi\)
\(98\) 0 0
\(99\) −0.0435295 −0.00437488
\(100\) 0 0
\(101\) −4.74409 −0.472054 −0.236027 0.971746i \(-0.575845\pi\)
−0.236027 + 0.971746i \(0.575845\pi\)
\(102\) 0 0
\(103\) −1.44010 −0.141898 −0.0709488 0.997480i \(-0.522603\pi\)
−0.0709488 + 0.997480i \(0.522603\pi\)
\(104\) 0 0
\(105\) −4.97390 −0.485403
\(106\) 0 0
\(107\) −5.75172 −0.556039 −0.278020 0.960575i \(-0.589678\pi\)
−0.278020 + 0.960575i \(0.589678\pi\)
\(108\) 0 0
\(109\) 6.93535 0.664287 0.332143 0.943229i \(-0.392228\pi\)
0.332143 + 0.943229i \(0.392228\pi\)
\(110\) 0 0
\(111\) 11.1976 1.06283
\(112\) 0 0
\(113\) −18.6893 −1.75814 −0.879071 0.476691i \(-0.841836\pi\)
−0.879071 + 0.476691i \(0.841836\pi\)
\(114\) 0 0
\(115\) −16.7444 −1.56142
\(116\) 0 0
\(117\) −0.189678 −0.0175357
\(118\) 0 0
\(119\) 2.25658 0.206860
\(120\) 0 0
\(121\) −10.9116 −0.991966
\(122\) 0 0
\(123\) 0.173461 0.0156404
\(124\) 0 0
\(125\) −3.94316 −0.352687
\(126\) 0 0
\(127\) −10.9674 −0.973196 −0.486598 0.873626i \(-0.661762\pi\)
−0.486598 + 0.873626i \(0.661762\pi\)
\(128\) 0 0
\(129\) 13.7323 1.20906
\(130\) 0 0
\(131\) 18.3875 1.60653 0.803263 0.595625i \(-0.203096\pi\)
0.803263 + 0.595625i \(0.203096\pi\)
\(132\) 0 0
\(133\) −2.17393 −0.188504
\(134\) 0 0
\(135\) 16.9241 1.45659
\(136\) 0 0
\(137\) −13.2031 −1.12801 −0.564007 0.825770i \(-0.690741\pi\)
−0.564007 + 0.825770i \(0.690741\pi\)
\(138\) 0 0
\(139\) −17.2135 −1.46003 −0.730014 0.683432i \(-0.760487\pi\)
−0.730014 + 0.683432i \(0.760487\pi\)
\(140\) 0 0
\(141\) −7.51999 −0.633297
\(142\) 0 0
\(143\) 0.385075 0.0322016
\(144\) 0 0
\(145\) −14.2718 −1.18521
\(146\) 0 0
\(147\) −11.1691 −0.921215
\(148\) 0 0
\(149\) −1.64240 −0.134551 −0.0672753 0.997734i \(-0.521431\pi\)
−0.0672753 + 0.997734i \(0.521431\pi\)
\(150\) 0 0
\(151\) −16.4309 −1.33713 −0.668564 0.743655i \(-0.733091\pi\)
−0.668564 + 0.743655i \(0.733091\pi\)
\(152\) 0 0
\(153\) 0.394001 0.0318531
\(154\) 0 0
\(155\) 3.88228 0.311832
\(156\) 0 0
\(157\) 18.2844 1.45925 0.729627 0.683845i \(-0.239694\pi\)
0.729627 + 0.683845i \(0.239694\pi\)
\(158\) 0 0
\(159\) −6.05994 −0.480585
\(160\) 0 0
\(161\) 4.19993 0.331001
\(162\) 0 0
\(163\) 10.1749 0.796960 0.398480 0.917177i \(-0.369538\pi\)
0.398480 + 0.917177i \(0.369538\pi\)
\(164\) 0 0
\(165\) 1.76308 0.137256
\(166\) 0 0
\(167\) −3.99023 −0.308773 −0.154387 0.988010i \(-0.549340\pi\)
−0.154387 + 0.988010i \(0.549340\pi\)
\(168\) 0 0
\(169\) −11.3221 −0.870927
\(170\) 0 0
\(171\) −0.379571 −0.0290266
\(172\) 0 0
\(173\) −11.6567 −0.886241 −0.443121 0.896462i \(-0.646129\pi\)
−0.443121 + 0.896462i \(0.646129\pi\)
\(174\) 0 0
\(175\) 5.18229 0.391744
\(176\) 0 0
\(177\) 8.94839 0.672602
\(178\) 0 0
\(179\) 12.1000 0.904399 0.452199 0.891917i \(-0.350640\pi\)
0.452199 + 0.891917i \(0.350640\pi\)
\(180\) 0 0
\(181\) −5.13687 −0.381820 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(182\) 0 0
\(183\) −20.8482 −1.54114
\(184\) 0 0
\(185\) −21.1068 −1.55180
\(186\) 0 0
\(187\) −0.799881 −0.0584931
\(188\) 0 0
\(189\) −4.24500 −0.308779
\(190\) 0 0
\(191\) 13.2013 0.955213 0.477607 0.878574i \(-0.341504\pi\)
0.477607 + 0.878574i \(0.341504\pi\)
\(192\) 0 0
\(193\) 15.0529 1.08353 0.541765 0.840530i \(-0.317756\pi\)
0.541765 + 0.840530i \(0.317756\pi\)
\(194\) 0 0
\(195\) 7.68256 0.550159
\(196\) 0 0
\(197\) 27.6452 1.96964 0.984821 0.173572i \(-0.0555310\pi\)
0.984821 + 0.173572i \(0.0555310\pi\)
\(198\) 0 0
\(199\) −4.08758 −0.289761 −0.144880 0.989449i \(-0.546280\pi\)
−0.144880 + 0.989449i \(0.546280\pi\)
\(200\) 0 0
\(201\) −7.14681 −0.504097
\(202\) 0 0
\(203\) 3.57975 0.251249
\(204\) 0 0
\(205\) −0.326964 −0.0228362
\(206\) 0 0
\(207\) 0.733314 0.0509688
\(208\) 0 0
\(209\) 0.770587 0.0533026
\(210\) 0 0
\(211\) 8.92644 0.614522 0.307261 0.951625i \(-0.400588\pi\)
0.307261 + 0.951625i \(0.400588\pi\)
\(212\) 0 0
\(213\) −4.91662 −0.336881
\(214\) 0 0
\(215\) −25.8847 −1.76532
\(216\) 0 0
\(217\) −0.973777 −0.0661043
\(218\) 0 0
\(219\) −22.7983 −1.54057
\(220\) 0 0
\(221\) −3.48545 −0.234456
\(222\) 0 0
\(223\) 8.07168 0.540519 0.270260 0.962787i \(-0.412890\pi\)
0.270260 + 0.962787i \(0.412890\pi\)
\(224\) 0 0
\(225\) 0.904835 0.0603223
\(226\) 0 0
\(227\) −10.8324 −0.718970 −0.359485 0.933151i \(-0.617048\pi\)
−0.359485 + 0.933151i \(0.617048\pi\)
\(228\) 0 0
\(229\) −4.06858 −0.268860 −0.134430 0.990923i \(-0.542920\pi\)
−0.134430 + 0.990923i \(0.542920\pi\)
\(230\) 0 0
\(231\) −0.442227 −0.0290964
\(232\) 0 0
\(233\) 4.37960 0.286917 0.143459 0.989656i \(-0.454178\pi\)
0.143459 + 0.989656i \(0.454178\pi\)
\(234\) 0 0
\(235\) 14.1748 0.924660
\(236\) 0 0
\(237\) 16.6570 1.08199
\(238\) 0 0
\(239\) −22.4530 −1.45236 −0.726182 0.687502i \(-0.758707\pi\)
−0.726182 + 0.687502i \(0.758707\pi\)
\(240\) 0 0
\(241\) −1.50796 −0.0971362 −0.0485681 0.998820i \(-0.515466\pi\)
−0.0485681 + 0.998820i \(0.515466\pi\)
\(242\) 0 0
\(243\) −1.52040 −0.0975337
\(244\) 0 0
\(245\) 21.0532 1.34504
\(246\) 0 0
\(247\) 3.35780 0.213652
\(248\) 0 0
\(249\) −28.1108 −1.78145
\(250\) 0 0
\(251\) −10.5663 −0.666939 −0.333469 0.942761i \(-0.608219\pi\)
−0.333469 + 0.942761i \(0.608219\pi\)
\(252\) 0 0
\(253\) −1.48874 −0.0935961
\(254\) 0 0
\(255\) −15.9583 −0.999347
\(256\) 0 0
\(257\) −6.34538 −0.395814 −0.197907 0.980221i \(-0.563414\pi\)
−0.197907 + 0.980221i \(0.563414\pi\)
\(258\) 0 0
\(259\) 5.29413 0.328961
\(260\) 0 0
\(261\) 0.625029 0.0386883
\(262\) 0 0
\(263\) 25.1599 1.55142 0.775711 0.631088i \(-0.217391\pi\)
0.775711 + 0.631088i \(0.217391\pi\)
\(264\) 0 0
\(265\) 11.4227 0.701689
\(266\) 0 0
\(267\) −20.9002 −1.27907
\(268\) 0 0
\(269\) 16.8199 1.02553 0.512765 0.858529i \(-0.328621\pi\)
0.512765 + 0.858529i \(0.328621\pi\)
\(270\) 0 0
\(271\) −14.7714 −0.897298 −0.448649 0.893708i \(-0.648095\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(272\) 0 0
\(273\) −1.92698 −0.116626
\(274\) 0 0
\(275\) −1.83695 −0.110772
\(276\) 0 0
\(277\) −16.3951 −0.985086 −0.492543 0.870288i \(-0.663933\pi\)
−0.492543 + 0.870288i \(0.663933\pi\)
\(278\) 0 0
\(279\) −0.170023 −0.0101790
\(280\) 0 0
\(281\) 2.11245 0.126018 0.0630092 0.998013i \(-0.479930\pi\)
0.0630092 + 0.998013i \(0.479930\pi\)
\(282\) 0 0
\(283\) 22.9049 1.36156 0.680778 0.732490i \(-0.261642\pi\)
0.680778 + 0.732490i \(0.261642\pi\)
\(284\) 0 0
\(285\) 15.3738 0.910668
\(286\) 0 0
\(287\) 0.0820111 0.00484096
\(288\) 0 0
\(289\) −9.75999 −0.574117
\(290\) 0 0
\(291\) −14.5531 −0.853117
\(292\) 0 0
\(293\) −29.4136 −1.71836 −0.859181 0.511672i \(-0.829026\pi\)
−0.859181 + 0.511672i \(0.829026\pi\)
\(294\) 0 0
\(295\) −16.8672 −0.982048
\(296\) 0 0
\(297\) 1.50471 0.0873123
\(298\) 0 0
\(299\) −6.48710 −0.375159
\(300\) 0 0
\(301\) 6.49255 0.374224
\(302\) 0 0
\(303\) −8.41514 −0.483437
\(304\) 0 0
\(305\) 39.2977 2.25018
\(306\) 0 0
\(307\) 8.96347 0.511572 0.255786 0.966733i \(-0.417666\pi\)
0.255786 + 0.966733i \(0.417666\pi\)
\(308\) 0 0
\(309\) −2.55448 −0.145319
\(310\) 0 0
\(311\) −4.27774 −0.242568 −0.121284 0.992618i \(-0.538701\pi\)
−0.121284 + 0.992618i \(0.538701\pi\)
\(312\) 0 0
\(313\) 1.98402 0.112143 0.0560716 0.998427i \(-0.482142\pi\)
0.0560716 + 0.998427i \(0.482142\pi\)
\(314\) 0 0
\(315\) −0.410597 −0.0231345
\(316\) 0 0
\(317\) 21.1918 1.19025 0.595126 0.803632i \(-0.297102\pi\)
0.595126 + 0.803632i \(0.297102\pi\)
\(318\) 0 0
\(319\) −1.26890 −0.0710449
\(320\) 0 0
\(321\) −10.2025 −0.569448
\(322\) 0 0
\(323\) −6.97486 −0.388091
\(324\) 0 0
\(325\) −8.00443 −0.444006
\(326\) 0 0
\(327\) 12.3021 0.680305
\(328\) 0 0
\(329\) −3.55540 −0.196015
\(330\) 0 0
\(331\) −23.2369 −1.27721 −0.638607 0.769533i \(-0.720489\pi\)
−0.638607 + 0.769533i \(0.720489\pi\)
\(332\) 0 0
\(333\) 0.924363 0.0506548
\(334\) 0 0
\(335\) 13.4714 0.736019
\(336\) 0 0
\(337\) −21.4801 −1.17010 −0.585049 0.810998i \(-0.698925\pi\)
−0.585049 + 0.810998i \(0.698925\pi\)
\(338\) 0 0
\(339\) −33.1514 −1.80054
\(340\) 0 0
\(341\) 0.345172 0.0186921
\(342\) 0 0
\(343\) −11.1512 −0.602110
\(344\) 0 0
\(345\) −29.7015 −1.59908
\(346\) 0 0
\(347\) 32.3974 1.73919 0.869593 0.493770i \(-0.164381\pi\)
0.869593 + 0.493770i \(0.164381\pi\)
\(348\) 0 0
\(349\) −8.97027 −0.480167 −0.240084 0.970752i \(-0.577175\pi\)
−0.240084 + 0.970752i \(0.577175\pi\)
\(350\) 0 0
\(351\) 6.55672 0.349972
\(352\) 0 0
\(353\) 5.98482 0.318540 0.159270 0.987235i \(-0.449086\pi\)
0.159270 + 0.987235i \(0.449086\pi\)
\(354\) 0 0
\(355\) 9.26757 0.491872
\(356\) 0 0
\(357\) 4.00275 0.211848
\(358\) 0 0
\(359\) 1.69118 0.0892571 0.0446285 0.999004i \(-0.485790\pi\)
0.0446285 + 0.999004i \(0.485790\pi\)
\(360\) 0 0
\(361\) −12.2806 −0.646347
\(362\) 0 0
\(363\) −19.3552 −1.01589
\(364\) 0 0
\(365\) 42.9736 2.24934
\(366\) 0 0
\(367\) 15.1243 0.789481 0.394741 0.918793i \(-0.370834\pi\)
0.394741 + 0.918793i \(0.370834\pi\)
\(368\) 0 0
\(369\) 0.0143192 0.000745430 0
\(370\) 0 0
\(371\) −2.86510 −0.148749
\(372\) 0 0
\(373\) 1.18552 0.0613839 0.0306919 0.999529i \(-0.490229\pi\)
0.0306919 + 0.999529i \(0.490229\pi\)
\(374\) 0 0
\(375\) −6.99445 −0.361192
\(376\) 0 0
\(377\) −5.52918 −0.284767
\(378\) 0 0
\(379\) −28.7848 −1.47857 −0.739287 0.673390i \(-0.764837\pi\)
−0.739287 + 0.673390i \(0.764837\pi\)
\(380\) 0 0
\(381\) −19.4541 −0.996664
\(382\) 0 0
\(383\) −26.3351 −1.34566 −0.672829 0.739798i \(-0.734921\pi\)
−0.672829 + 0.739798i \(0.734921\pi\)
\(384\) 0 0
\(385\) 0.833574 0.0424829
\(386\) 0 0
\(387\) 1.13361 0.0576245
\(388\) 0 0
\(389\) −1.72684 −0.0875544 −0.0437772 0.999041i \(-0.513939\pi\)
−0.0437772 + 0.999041i \(0.513939\pi\)
\(390\) 0 0
\(391\) 13.4751 0.681465
\(392\) 0 0
\(393\) 32.6161 1.64527
\(394\) 0 0
\(395\) −31.3976 −1.57978
\(396\) 0 0
\(397\) −16.7181 −0.839057 −0.419528 0.907742i \(-0.637804\pi\)
−0.419528 + 0.907742i \(0.637804\pi\)
\(398\) 0 0
\(399\) −3.85616 −0.193049
\(400\) 0 0
\(401\) 22.2971 1.11346 0.556731 0.830693i \(-0.312055\pi\)
0.556731 + 0.830693i \(0.312055\pi\)
\(402\) 0 0
\(403\) 1.50407 0.0749230
\(404\) 0 0
\(405\) 31.4890 1.56470
\(406\) 0 0
\(407\) −1.87659 −0.0930194
\(408\) 0 0
\(409\) −37.7115 −1.86471 −0.932356 0.361541i \(-0.882251\pi\)
−0.932356 + 0.361541i \(0.882251\pi\)
\(410\) 0 0
\(411\) −23.4198 −1.15521
\(412\) 0 0
\(413\) 4.23074 0.208181
\(414\) 0 0
\(415\) 52.9873 2.60104
\(416\) 0 0
\(417\) −30.5336 −1.49524
\(418\) 0 0
\(419\) −35.6033 −1.73934 −0.869668 0.493638i \(-0.835667\pi\)
−0.869668 + 0.493638i \(0.835667\pi\)
\(420\) 0 0
\(421\) 18.4505 0.899223 0.449611 0.893224i \(-0.351562\pi\)
0.449611 + 0.893224i \(0.351562\pi\)
\(422\) 0 0
\(423\) −0.620777 −0.0301832
\(424\) 0 0
\(425\) 16.6269 0.806523
\(426\) 0 0
\(427\) −9.85687 −0.477008
\(428\) 0 0
\(429\) 0.683052 0.0329781
\(430\) 0 0
\(431\) −15.3236 −0.738114 −0.369057 0.929407i \(-0.620319\pi\)
−0.369057 + 0.929407i \(0.620319\pi\)
\(432\) 0 0
\(433\) −25.2338 −1.21266 −0.606329 0.795214i \(-0.707359\pi\)
−0.606329 + 0.795214i \(0.707359\pi\)
\(434\) 0 0
\(435\) −25.3156 −1.21379
\(436\) 0 0
\(437\) −12.9816 −0.620994
\(438\) 0 0
\(439\) −10.0447 −0.479406 −0.239703 0.970846i \(-0.577050\pi\)
−0.239703 + 0.970846i \(0.577050\pi\)
\(440\) 0 0
\(441\) −0.922016 −0.0439055
\(442\) 0 0
\(443\) 26.8947 1.27780 0.638902 0.769288i \(-0.279389\pi\)
0.638902 + 0.769288i \(0.279389\pi\)
\(444\) 0 0
\(445\) 39.3957 1.86754
\(446\) 0 0
\(447\) −2.91332 −0.137795
\(448\) 0 0
\(449\) 27.2235 1.28476 0.642379 0.766387i \(-0.277948\pi\)
0.642379 + 0.766387i \(0.277948\pi\)
\(450\) 0 0
\(451\) −0.0290702 −0.00136886
\(452\) 0 0
\(453\) −29.1454 −1.36937
\(454\) 0 0
\(455\) 3.63226 0.170283
\(456\) 0 0
\(457\) −15.9248 −0.744929 −0.372465 0.928046i \(-0.621487\pi\)
−0.372465 + 0.928046i \(0.621487\pi\)
\(458\) 0 0
\(459\) −13.6197 −0.635713
\(460\) 0 0
\(461\) 30.5077 1.42088 0.710442 0.703756i \(-0.248495\pi\)
0.710442 + 0.703756i \(0.248495\pi\)
\(462\) 0 0
\(463\) −6.96729 −0.323797 −0.161899 0.986807i \(-0.551762\pi\)
−0.161899 + 0.986807i \(0.551762\pi\)
\(464\) 0 0
\(465\) 6.88646 0.319352
\(466\) 0 0
\(467\) −14.5795 −0.674660 −0.337330 0.941386i \(-0.609524\pi\)
−0.337330 + 0.941386i \(0.609524\pi\)
\(468\) 0 0
\(469\) −3.37897 −0.156026
\(470\) 0 0
\(471\) 32.4332 1.49444
\(472\) 0 0
\(473\) −2.30139 −0.105818
\(474\) 0 0
\(475\) −16.0180 −0.734955
\(476\) 0 0
\(477\) −0.500250 −0.0229049
\(478\) 0 0
\(479\) −11.8995 −0.543702 −0.271851 0.962339i \(-0.587636\pi\)
−0.271851 + 0.962339i \(0.587636\pi\)
\(480\) 0 0
\(481\) −8.17717 −0.372847
\(482\) 0 0
\(483\) 7.44992 0.338983
\(484\) 0 0
\(485\) 27.4318 1.24561
\(486\) 0 0
\(487\) 18.1105 0.820663 0.410331 0.911936i \(-0.365413\pi\)
0.410331 + 0.911936i \(0.365413\pi\)
\(488\) 0 0
\(489\) 18.0484 0.816178
\(490\) 0 0
\(491\) 1.41825 0.0640049 0.0320024 0.999488i \(-0.489812\pi\)
0.0320024 + 0.999488i \(0.489812\pi\)
\(492\) 0 0
\(493\) 11.4853 0.517271
\(494\) 0 0
\(495\) 0.145543 0.00654168
\(496\) 0 0
\(497\) −2.32455 −0.104270
\(498\) 0 0
\(499\) −15.0810 −0.675118 −0.337559 0.941304i \(-0.609601\pi\)
−0.337559 + 0.941304i \(0.609601\pi\)
\(500\) 0 0
\(501\) −7.07795 −0.316219
\(502\) 0 0
\(503\) 28.6085 1.27559 0.637794 0.770207i \(-0.279847\pi\)
0.637794 + 0.770207i \(0.279847\pi\)
\(504\) 0 0
\(505\) 15.8621 0.705854
\(506\) 0 0
\(507\) −20.0833 −0.891929
\(508\) 0 0
\(509\) 21.5883 0.956887 0.478443 0.878118i \(-0.341201\pi\)
0.478443 + 0.878118i \(0.341201\pi\)
\(510\) 0 0
\(511\) −10.7789 −0.476830
\(512\) 0 0
\(513\) 13.1209 0.579301
\(514\) 0 0
\(515\) 4.81506 0.212177
\(516\) 0 0
\(517\) 1.26027 0.0554267
\(518\) 0 0
\(519\) −20.6768 −0.907612
\(520\) 0 0
\(521\) 29.3717 1.28680 0.643398 0.765532i \(-0.277524\pi\)
0.643398 + 0.765532i \(0.277524\pi\)
\(522\) 0 0
\(523\) 5.73648 0.250839 0.125419 0.992104i \(-0.459972\pi\)
0.125419 + 0.992104i \(0.459972\pi\)
\(524\) 0 0
\(525\) 9.19244 0.401191
\(526\) 0 0
\(527\) −3.12427 −0.136095
\(528\) 0 0
\(529\) 2.07981 0.0904264
\(530\) 0 0
\(531\) 0.738693 0.0320565
\(532\) 0 0
\(533\) −0.126672 −0.00548678
\(534\) 0 0
\(535\) 19.2312 0.831435
\(536\) 0 0
\(537\) 21.4633 0.926208
\(538\) 0 0
\(539\) 1.87183 0.0806255
\(540\) 0 0
\(541\) 35.9411 1.54523 0.772614 0.634876i \(-0.218949\pi\)
0.772614 + 0.634876i \(0.218949\pi\)
\(542\) 0 0
\(543\) −9.11187 −0.391028
\(544\) 0 0
\(545\) −23.1887 −0.993295
\(546\) 0 0
\(547\) 11.0642 0.473073 0.236536 0.971623i \(-0.423988\pi\)
0.236536 + 0.971623i \(0.423988\pi\)
\(548\) 0 0
\(549\) −1.72102 −0.0734515
\(550\) 0 0
\(551\) −11.0647 −0.471370
\(552\) 0 0
\(553\) 7.87533 0.334893
\(554\) 0 0
\(555\) −37.4396 −1.58922
\(556\) 0 0
\(557\) 25.5527 1.08270 0.541352 0.840796i \(-0.317913\pi\)
0.541352 + 0.840796i \(0.317913\pi\)
\(558\) 0 0
\(559\) −10.0282 −0.424148
\(560\) 0 0
\(561\) −1.41884 −0.0599036
\(562\) 0 0
\(563\) −33.0701 −1.39374 −0.696869 0.717198i \(-0.745424\pi\)
−0.696869 + 0.717198i \(0.745424\pi\)
\(564\) 0 0
\(565\) 62.4887 2.62892
\(566\) 0 0
\(567\) −7.89827 −0.331696
\(568\) 0 0
\(569\) 32.7223 1.37179 0.685895 0.727701i \(-0.259411\pi\)
0.685895 + 0.727701i \(0.259411\pi\)
\(570\) 0 0
\(571\) 22.8069 0.954437 0.477219 0.878785i \(-0.341645\pi\)
0.477219 + 0.878785i \(0.341645\pi\)
\(572\) 0 0
\(573\) 23.4167 0.978247
\(574\) 0 0
\(575\) 30.9459 1.29053
\(576\) 0 0
\(577\) 19.2941 0.803226 0.401613 0.915810i \(-0.368450\pi\)
0.401613 + 0.915810i \(0.368450\pi\)
\(578\) 0 0
\(579\) 26.7011 1.10966
\(580\) 0 0
\(581\) −13.2906 −0.551386
\(582\) 0 0
\(583\) 1.01558 0.0420612
\(584\) 0 0
\(585\) 0.634198 0.0262208
\(586\) 0 0
\(587\) 3.86822 0.159658 0.0798292 0.996809i \(-0.474563\pi\)
0.0798292 + 0.996809i \(0.474563\pi\)
\(588\) 0 0
\(589\) 3.00985 0.124019
\(590\) 0 0
\(591\) 49.0376 2.01714
\(592\) 0 0
\(593\) 17.8742 0.734007 0.367004 0.930219i \(-0.380384\pi\)
0.367004 + 0.930219i \(0.380384\pi\)
\(594\) 0 0
\(595\) −7.54498 −0.309314
\(596\) 0 0
\(597\) −7.25062 −0.296748
\(598\) 0 0
\(599\) −10.5041 −0.429184 −0.214592 0.976704i \(-0.568842\pi\)
−0.214592 + 0.976704i \(0.568842\pi\)
\(600\) 0 0
\(601\) −16.9813 −0.692682 −0.346341 0.938109i \(-0.612576\pi\)
−0.346341 + 0.938109i \(0.612576\pi\)
\(602\) 0 0
\(603\) −0.589972 −0.0240255
\(604\) 0 0
\(605\) 36.4836 1.48327
\(606\) 0 0
\(607\) −14.0223 −0.569149 −0.284574 0.958654i \(-0.591852\pi\)
−0.284574 + 0.958654i \(0.591852\pi\)
\(608\) 0 0
\(609\) 6.34982 0.257308
\(610\) 0 0
\(611\) 5.49157 0.222165
\(612\) 0 0
\(613\) −31.9887 −1.29201 −0.646005 0.763333i \(-0.723561\pi\)
−0.646005 + 0.763333i \(0.723561\pi\)
\(614\) 0 0
\(615\) −0.579975 −0.0233868
\(616\) 0 0
\(617\) 22.4234 0.902734 0.451367 0.892338i \(-0.350937\pi\)
0.451367 + 0.892338i \(0.350937\pi\)
\(618\) 0 0
\(619\) −25.9749 −1.04402 −0.522009 0.852940i \(-0.674817\pi\)
−0.522009 + 0.852940i \(0.674817\pi\)
\(620\) 0 0
\(621\) −25.3489 −1.01722
\(622\) 0 0
\(623\) −9.88147 −0.395893
\(624\) 0 0
\(625\) −17.7125 −0.708500
\(626\) 0 0
\(627\) 1.36688 0.0545880
\(628\) 0 0
\(629\) 16.9857 0.677265
\(630\) 0 0
\(631\) 1.28039 0.0509713 0.0254857 0.999675i \(-0.491887\pi\)
0.0254857 + 0.999675i \(0.491887\pi\)
\(632\) 0 0
\(633\) 15.8339 0.629340
\(634\) 0 0
\(635\) 36.6699 1.45520
\(636\) 0 0
\(637\) 8.15642 0.323169
\(638\) 0 0
\(639\) −0.405869 −0.0160559
\(640\) 0 0
\(641\) 1.02127 0.0403378 0.0201689 0.999797i \(-0.493580\pi\)
0.0201689 + 0.999797i \(0.493580\pi\)
\(642\) 0 0
\(643\) 33.3204 1.31403 0.657014 0.753878i \(-0.271819\pi\)
0.657014 + 0.753878i \(0.271819\pi\)
\(644\) 0 0
\(645\) −45.9147 −1.80789
\(646\) 0 0
\(647\) 8.19602 0.322219 0.161109 0.986937i \(-0.448493\pi\)
0.161109 + 0.986937i \(0.448493\pi\)
\(648\) 0 0
\(649\) −1.49966 −0.0588667
\(650\) 0 0
\(651\) −1.72730 −0.0676983
\(652\) 0 0
\(653\) −15.4705 −0.605408 −0.302704 0.953085i \(-0.597889\pi\)
−0.302704 + 0.953085i \(0.597889\pi\)
\(654\) 0 0
\(655\) −61.4796 −2.40221
\(656\) 0 0
\(657\) −1.88201 −0.0734241
\(658\) 0 0
\(659\) 25.9045 1.00909 0.504547 0.863384i \(-0.331659\pi\)
0.504547 + 0.863384i \(0.331659\pi\)
\(660\) 0 0
\(661\) −30.8453 −1.19974 −0.599872 0.800096i \(-0.704782\pi\)
−0.599872 + 0.800096i \(0.704782\pi\)
\(662\) 0 0
\(663\) −6.18255 −0.240110
\(664\) 0 0
\(665\) 7.26865 0.281866
\(666\) 0 0
\(667\) 21.3764 0.827697
\(668\) 0 0
\(669\) 14.3177 0.553554
\(670\) 0 0
\(671\) 3.49394 0.134882
\(672\) 0 0
\(673\) −6.75901 −0.260541 −0.130270 0.991479i \(-0.541585\pi\)
−0.130270 + 0.991479i \(0.541585\pi\)
\(674\) 0 0
\(675\) −31.2780 −1.20389
\(676\) 0 0
\(677\) −19.4418 −0.747208 −0.373604 0.927588i \(-0.621878\pi\)
−0.373604 + 0.927588i \(0.621878\pi\)
\(678\) 0 0
\(679\) −6.88060 −0.264053
\(680\) 0 0
\(681\) −19.2147 −0.736307
\(682\) 0 0
\(683\) 2.82651 0.108153 0.0540767 0.998537i \(-0.482778\pi\)
0.0540767 + 0.998537i \(0.482778\pi\)
\(684\) 0 0
\(685\) 44.1451 1.68670
\(686\) 0 0
\(687\) −7.21693 −0.275343
\(688\) 0 0
\(689\) 4.42536 0.168593
\(690\) 0 0
\(691\) −13.0757 −0.497421 −0.248711 0.968578i \(-0.580007\pi\)
−0.248711 + 0.968578i \(0.580007\pi\)
\(692\) 0 0
\(693\) −0.0365060 −0.00138675
\(694\) 0 0
\(695\) 57.5542 2.18315
\(696\) 0 0
\(697\) 0.263125 0.00996656
\(698\) 0 0
\(699\) 7.76861 0.293836
\(700\) 0 0
\(701\) 26.0613 0.984321 0.492160 0.870505i \(-0.336207\pi\)
0.492160 + 0.870505i \(0.336207\pi\)
\(702\) 0 0
\(703\) −16.3637 −0.617167
\(704\) 0 0
\(705\) 25.1435 0.946957
\(706\) 0 0
\(707\) −3.97862 −0.149632
\(708\) 0 0
\(709\) −1.89091 −0.0710144 −0.0355072 0.999369i \(-0.511305\pi\)
−0.0355072 + 0.999369i \(0.511305\pi\)
\(710\) 0 0
\(711\) 1.37504 0.0515681
\(712\) 0 0
\(713\) −5.81488 −0.217769
\(714\) 0 0
\(715\) −1.28752 −0.0481504
\(716\) 0 0
\(717\) −39.8276 −1.48739
\(718\) 0 0
\(719\) 32.8096 1.22359 0.611796 0.791016i \(-0.290448\pi\)
0.611796 + 0.791016i \(0.290448\pi\)
\(720\) 0 0
\(721\) −1.20774 −0.0449786
\(722\) 0 0
\(723\) −2.67485 −0.0994786
\(724\) 0 0
\(725\) 26.3763 0.979591
\(726\) 0 0
\(727\) −47.1519 −1.74877 −0.874384 0.485235i \(-0.838734\pi\)
−0.874384 + 0.485235i \(0.838734\pi\)
\(728\) 0 0
\(729\) 25.5566 0.946542
\(730\) 0 0
\(731\) 20.8307 0.770452
\(732\) 0 0
\(733\) 9.47504 0.349968 0.174984 0.984571i \(-0.444013\pi\)
0.174984 + 0.984571i \(0.444013\pi\)
\(734\) 0 0
\(735\) 37.3446 1.37748
\(736\) 0 0
\(737\) 1.19773 0.0441190
\(738\) 0 0
\(739\) −21.5448 −0.792540 −0.396270 0.918134i \(-0.629695\pi\)
−0.396270 + 0.918134i \(0.629695\pi\)
\(740\) 0 0
\(741\) 5.95612 0.218804
\(742\) 0 0
\(743\) 25.8284 0.947550 0.473775 0.880646i \(-0.342891\pi\)
0.473775 + 0.880646i \(0.342891\pi\)
\(744\) 0 0
\(745\) 5.49144 0.201191
\(746\) 0 0
\(747\) −2.32055 −0.0849046
\(748\) 0 0
\(749\) −4.82367 −0.176253
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −18.7427 −0.683021
\(754\) 0 0
\(755\) 54.9375 1.99938
\(756\) 0 0
\(757\) 0.222073 0.00807139 0.00403570 0.999992i \(-0.498715\pi\)
0.00403570 + 0.999992i \(0.498715\pi\)
\(758\) 0 0
\(759\) −2.64075 −0.0958531
\(760\) 0 0
\(761\) −45.5022 −1.64945 −0.824726 0.565532i \(-0.808671\pi\)
−0.824726 + 0.565532i \(0.808671\pi\)
\(762\) 0 0
\(763\) 5.81633 0.210565
\(764\) 0 0
\(765\) −1.31736 −0.0476293
\(766\) 0 0
\(767\) −6.53469 −0.235954
\(768\) 0 0
\(769\) 27.1900 0.980496 0.490248 0.871583i \(-0.336906\pi\)
0.490248 + 0.871583i \(0.336906\pi\)
\(770\) 0 0
\(771\) −11.2555 −0.405359
\(772\) 0 0
\(773\) 35.8941 1.29102 0.645511 0.763751i \(-0.276645\pi\)
0.645511 + 0.763751i \(0.276645\pi\)
\(774\) 0 0
\(775\) −7.17498 −0.257733
\(776\) 0 0
\(777\) 9.39083 0.336894
\(778\) 0 0
\(779\) −0.253488 −0.00908216
\(780\) 0 0
\(781\) 0.823975 0.0294841
\(782\) 0 0
\(783\) −21.6058 −0.772127
\(784\) 0 0
\(785\) −61.1348 −2.18200
\(786\) 0 0
\(787\) −41.3722 −1.47476 −0.737380 0.675478i \(-0.763937\pi\)
−0.737380 + 0.675478i \(0.763937\pi\)
\(788\) 0 0
\(789\) 44.6290 1.58883
\(790\) 0 0
\(791\) −15.6738 −0.557295
\(792\) 0 0
\(793\) 15.2247 0.540644
\(794\) 0 0
\(795\) 20.2617 0.718610
\(796\) 0 0
\(797\) 31.9129 1.13041 0.565207 0.824949i \(-0.308796\pi\)
0.565207 + 0.824949i \(0.308796\pi\)
\(798\) 0 0
\(799\) −11.4072 −0.403556
\(800\) 0 0
\(801\) −1.72532 −0.0609611
\(802\) 0 0
\(803\) 3.82076 0.134832
\(804\) 0 0
\(805\) −14.0427 −0.494940
\(806\) 0 0
\(807\) 29.8355 1.05026
\(808\) 0 0
\(809\) −10.8494 −0.381445 −0.190723 0.981644i \(-0.561083\pi\)
−0.190723 + 0.981644i \(0.561083\pi\)
\(810\) 0 0
\(811\) −19.3176 −0.678331 −0.339166 0.940727i \(-0.610145\pi\)
−0.339166 + 0.940727i \(0.610145\pi\)
\(812\) 0 0
\(813\) −26.2017 −0.918935
\(814\) 0 0
\(815\) −34.0203 −1.19168
\(816\) 0 0
\(817\) −20.0678 −0.702085
\(818\) 0 0
\(819\) −0.159073 −0.00555847
\(820\) 0 0
\(821\) 0.499718 0.0174403 0.00872013 0.999962i \(-0.497224\pi\)
0.00872013 + 0.999962i \(0.497224\pi\)
\(822\) 0 0
\(823\) −13.3239 −0.464440 −0.232220 0.972663i \(-0.574599\pi\)
−0.232220 + 0.972663i \(0.574599\pi\)
\(824\) 0 0
\(825\) −3.25842 −0.113444
\(826\) 0 0
\(827\) −50.7089 −1.76332 −0.881661 0.471883i \(-0.843574\pi\)
−0.881661 + 0.471883i \(0.843574\pi\)
\(828\) 0 0
\(829\) −50.2587 −1.74556 −0.872778 0.488117i \(-0.837684\pi\)
−0.872778 + 0.488117i \(0.837684\pi\)
\(830\) 0 0
\(831\) −29.0819 −1.00884
\(832\) 0 0
\(833\) −16.9426 −0.587027
\(834\) 0 0
\(835\) 13.3415 0.461703
\(836\) 0 0
\(837\) 5.87728 0.203149
\(838\) 0 0
\(839\) −8.50592 −0.293657 −0.146828 0.989162i \(-0.546907\pi\)
−0.146828 + 0.989162i \(0.546907\pi\)
\(840\) 0 0
\(841\) −10.7802 −0.371730
\(842\) 0 0
\(843\) 3.74711 0.129057
\(844\) 0 0
\(845\) 37.8559 1.30228
\(846\) 0 0
\(847\) −9.15103 −0.314433
\(848\) 0 0
\(849\) 40.6291 1.39439
\(850\) 0 0
\(851\) 31.6138 1.08371
\(852\) 0 0
\(853\) −11.0777 −0.379295 −0.189647 0.981852i \(-0.560734\pi\)
−0.189647 + 0.981852i \(0.560734\pi\)
\(854\) 0 0
\(855\) 1.26912 0.0434029
\(856\) 0 0
\(857\) 9.07021 0.309832 0.154916 0.987928i \(-0.450489\pi\)
0.154916 + 0.987928i \(0.450489\pi\)
\(858\) 0 0
\(859\) −40.8995 −1.39547 −0.697737 0.716354i \(-0.745810\pi\)
−0.697737 + 0.716354i \(0.745810\pi\)
\(860\) 0 0
\(861\) 0.145473 0.00495770
\(862\) 0 0
\(863\) −14.0328 −0.477682 −0.238841 0.971059i \(-0.576767\pi\)
−0.238841 + 0.971059i \(0.576767\pi\)
\(864\) 0 0
\(865\) 38.9747 1.32518
\(866\) 0 0
\(867\) −17.3124 −0.587961
\(868\) 0 0
\(869\) −2.79154 −0.0946967
\(870\) 0 0
\(871\) 5.21906 0.176841
\(872\) 0 0
\(873\) −1.20136 −0.0406600
\(874\) 0 0
\(875\) −3.30693 −0.111795
\(876\) 0 0
\(877\) −24.8320 −0.838518 −0.419259 0.907867i \(-0.637710\pi\)
−0.419259 + 0.907867i \(0.637710\pi\)
\(878\) 0 0
\(879\) −52.1744 −1.75980
\(880\) 0 0
\(881\) 3.31728 0.111762 0.0558811 0.998437i \(-0.482203\pi\)
0.0558811 + 0.998437i \(0.482203\pi\)
\(882\) 0 0
\(883\) −5.25743 −0.176927 −0.0884633 0.996079i \(-0.528196\pi\)
−0.0884633 + 0.996079i \(0.528196\pi\)
\(884\) 0 0
\(885\) −29.9194 −1.00573
\(886\) 0 0
\(887\) −7.16812 −0.240682 −0.120341 0.992733i \(-0.538399\pi\)
−0.120341 + 0.992733i \(0.538399\pi\)
\(888\) 0 0
\(889\) −9.19777 −0.308483
\(890\) 0 0
\(891\) 2.79968 0.0937926
\(892\) 0 0
\(893\) 10.9894 0.367746
\(894\) 0 0
\(895\) −40.4571 −1.35233
\(896\) 0 0
\(897\) −11.5069 −0.384206
\(898\) 0 0
\(899\) −4.95623 −0.165299
\(900\) 0 0
\(901\) −9.19241 −0.306243
\(902\) 0 0
\(903\) 11.5166 0.383248
\(904\) 0 0
\(905\) 17.1754 0.570929
\(906\) 0 0
\(907\) 41.8851 1.39077 0.695386 0.718636i \(-0.255233\pi\)
0.695386 + 0.718636i \(0.255233\pi\)
\(908\) 0 0
\(909\) −0.694673 −0.0230408
\(910\) 0 0
\(911\) 47.7780 1.58296 0.791478 0.611197i \(-0.209312\pi\)
0.791478 + 0.611197i \(0.209312\pi\)
\(912\) 0 0
\(913\) 4.71107 0.155914
\(914\) 0 0
\(915\) 69.7069 2.30444
\(916\) 0 0
\(917\) 15.4207 0.509236
\(918\) 0 0
\(919\) 47.4339 1.56470 0.782350 0.622840i \(-0.214021\pi\)
0.782350 + 0.622840i \(0.214021\pi\)
\(920\) 0 0
\(921\) 15.8996 0.523909
\(922\) 0 0
\(923\) 3.59043 0.118181
\(924\) 0 0
\(925\) 39.0082 1.28258
\(926\) 0 0
\(927\) −0.210873 −0.00692598
\(928\) 0 0
\(929\) 16.0929 0.527991 0.263996 0.964524i \(-0.414960\pi\)
0.263996 + 0.964524i \(0.414960\pi\)
\(930\) 0 0
\(931\) 16.3221 0.534936
\(932\) 0 0
\(933\) −7.58793 −0.248418
\(934\) 0 0
\(935\) 2.67444 0.0874637
\(936\) 0 0
\(937\) 50.8755 1.66203 0.831015 0.556251i \(-0.187761\pi\)
0.831015 + 0.556251i \(0.187761\pi\)
\(938\) 0 0
\(939\) 3.51929 0.114848
\(940\) 0 0
\(941\) 40.6160 1.32404 0.662021 0.749485i \(-0.269699\pi\)
0.662021 + 0.749485i \(0.269699\pi\)
\(942\) 0 0
\(943\) 0.489727 0.0159477
\(944\) 0 0
\(945\) 14.1934 0.461711
\(946\) 0 0
\(947\) 54.3798 1.76711 0.883553 0.468332i \(-0.155145\pi\)
0.883553 + 0.468332i \(0.155145\pi\)
\(948\) 0 0
\(949\) 16.6488 0.540442
\(950\) 0 0
\(951\) 37.5905 1.21895
\(952\) 0 0
\(953\) −40.3359 −1.30661 −0.653304 0.757096i \(-0.726618\pi\)
−0.653304 + 0.757096i \(0.726618\pi\)
\(954\) 0 0
\(955\) −44.1392 −1.42831
\(956\) 0 0
\(957\) −2.25080 −0.0727581
\(958\) 0 0
\(959\) −11.0727 −0.357557
\(960\) 0 0
\(961\) −29.6518 −0.956509
\(962\) 0 0
\(963\) −0.842219 −0.0271401
\(964\) 0 0
\(965\) −50.3301 −1.62018
\(966\) 0 0
\(967\) −39.8958 −1.28296 −0.641481 0.767139i \(-0.721680\pi\)
−0.641481 + 0.767139i \(0.721680\pi\)
\(968\) 0 0
\(969\) −12.3721 −0.397450
\(970\) 0 0
\(971\) −35.8777 −1.15137 −0.575684 0.817672i \(-0.695264\pi\)
−0.575684 + 0.817672i \(0.695264\pi\)
\(972\) 0 0
\(973\) −14.4361 −0.462799
\(974\) 0 0
\(975\) −14.1984 −0.454713
\(976\) 0 0
\(977\) −10.6239 −0.339890 −0.169945 0.985454i \(-0.554359\pi\)
−0.169945 + 0.985454i \(0.554359\pi\)
\(978\) 0 0
\(979\) 3.50265 0.111945
\(980\) 0 0
\(981\) 1.01554 0.0324237
\(982\) 0 0
\(983\) 41.7017 1.33008 0.665039 0.746809i \(-0.268415\pi\)
0.665039 + 0.746809i \(0.268415\pi\)
\(984\) 0 0
\(985\) −92.4333 −2.94517
\(986\) 0 0
\(987\) −6.30663 −0.200742
\(988\) 0 0
\(989\) 38.7701 1.23282
\(990\) 0 0
\(991\) −43.2323 −1.37332 −0.686660 0.726979i \(-0.740924\pi\)
−0.686660 + 0.726979i \(0.740924\pi\)
\(992\) 0 0
\(993\) −41.2180 −1.30801
\(994\) 0 0
\(995\) 13.6670 0.433274
\(996\) 0 0
\(997\) 23.4982 0.744195 0.372098 0.928194i \(-0.378639\pi\)
0.372098 + 0.928194i \(0.378639\pi\)
\(998\) 0 0
\(999\) −31.9530 −1.01095
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.1.37 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.37 44 1.1 even 1 trivial