Properties

Label 4016.2.a.m.1.10
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.452441 q^{3} +1.91039 q^{5} -1.96124 q^{7} -2.79530 q^{9} +O(q^{10})\) \(q-0.452441 q^{3} +1.91039 q^{5} -1.96124 q^{7} -2.79530 q^{9} -0.787387 q^{11} +5.79638 q^{13} -0.864341 q^{15} -3.13249 q^{17} -4.63676 q^{19} +0.887346 q^{21} -2.51256 q^{23} -1.35039 q^{25} +2.62203 q^{27} +3.62687 q^{29} +6.20008 q^{31} +0.356246 q^{33} -3.74674 q^{35} +9.71962 q^{37} -2.62252 q^{39} -0.892103 q^{41} +5.80229 q^{43} -5.34012 q^{45} -3.65849 q^{47} -3.15353 q^{49} +1.41727 q^{51} +12.6489 q^{53} -1.50422 q^{55} +2.09786 q^{57} -6.08621 q^{59} +6.47835 q^{61} +5.48225 q^{63} +11.0734 q^{65} +8.94464 q^{67} +1.13679 q^{69} -7.14955 q^{71} -11.3319 q^{73} +0.610974 q^{75} +1.54426 q^{77} +11.9354 q^{79} +7.19957 q^{81} -4.55162 q^{83} -5.98429 q^{85} -1.64095 q^{87} +1.55704 q^{89} -11.3681 q^{91} -2.80517 q^{93} -8.85805 q^{95} +5.55502 q^{97} +2.20098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −0.452441 −0.261217 −0.130609 0.991434i \(-0.541693\pi\)
−0.130609 + 0.991434i \(0.541693\pi\)
\(4\) 0 0
\(5\) 1.91039 0.854354 0.427177 0.904168i \(-0.359508\pi\)
0.427177 + 0.904168i \(0.359508\pi\)
\(6\) 0 0
\(7\) −1.96124 −0.741279 −0.370640 0.928777i \(-0.620862\pi\)
−0.370640 + 0.928777i \(0.620862\pi\)
\(8\) 0 0
\(9\) −2.79530 −0.931766
\(10\) 0 0
\(11\) −0.787387 −0.237406 −0.118703 0.992930i \(-0.537874\pi\)
−0.118703 + 0.992930i \(0.537874\pi\)
\(12\) 0 0
\(13\) 5.79638 1.60763 0.803814 0.594881i \(-0.202801\pi\)
0.803814 + 0.594881i \(0.202801\pi\)
\(14\) 0 0
\(15\) −0.864341 −0.223172
\(16\) 0 0
\(17\) −3.13249 −0.759740 −0.379870 0.925040i \(-0.624031\pi\)
−0.379870 + 0.925040i \(0.624031\pi\)
\(18\) 0 0
\(19\) −4.63676 −1.06375 −0.531873 0.846824i \(-0.678512\pi\)
−0.531873 + 0.846824i \(0.678512\pi\)
\(20\) 0 0
\(21\) 0.887346 0.193635
\(22\) 0 0
\(23\) −2.51256 −0.523906 −0.261953 0.965081i \(-0.584367\pi\)
−0.261953 + 0.965081i \(0.584367\pi\)
\(24\) 0 0
\(25\) −1.35039 −0.270079
\(26\) 0 0
\(27\) 2.62203 0.504610
\(28\) 0 0
\(29\) 3.62687 0.673493 0.336746 0.941595i \(-0.390674\pi\)
0.336746 + 0.941595i \(0.390674\pi\)
\(30\) 0 0
\(31\) 6.20008 1.11357 0.556783 0.830658i \(-0.312035\pi\)
0.556783 + 0.830658i \(0.312035\pi\)
\(32\) 0 0
\(33\) 0.356246 0.0620145
\(34\) 0 0
\(35\) −3.74674 −0.633315
\(36\) 0 0
\(37\) 9.71962 1.59790 0.798948 0.601400i \(-0.205390\pi\)
0.798948 + 0.601400i \(0.205390\pi\)
\(38\) 0 0
\(39\) −2.62252 −0.419940
\(40\) 0 0
\(41\) −0.892103 −0.139323 −0.0696615 0.997571i \(-0.522192\pi\)
−0.0696615 + 0.997571i \(0.522192\pi\)
\(42\) 0 0
\(43\) 5.80229 0.884840 0.442420 0.896808i \(-0.354120\pi\)
0.442420 + 0.896808i \(0.354120\pi\)
\(44\) 0 0
\(45\) −5.34012 −0.796058
\(46\) 0 0
\(47\) −3.65849 −0.533646 −0.266823 0.963746i \(-0.585974\pi\)
−0.266823 + 0.963746i \(0.585974\pi\)
\(48\) 0 0
\(49\) −3.15353 −0.450505
\(50\) 0 0
\(51\) 1.41727 0.198457
\(52\) 0 0
\(53\) 12.6489 1.73746 0.868729 0.495288i \(-0.164938\pi\)
0.868729 + 0.495288i \(0.164938\pi\)
\(54\) 0 0
\(55\) −1.50422 −0.202829
\(56\) 0 0
\(57\) 2.09786 0.277869
\(58\) 0 0
\(59\) −6.08621 −0.792357 −0.396178 0.918174i \(-0.629664\pi\)
−0.396178 + 0.918174i \(0.629664\pi\)
\(60\) 0 0
\(61\) 6.47835 0.829467 0.414734 0.909943i \(-0.363875\pi\)
0.414734 + 0.909943i \(0.363875\pi\)
\(62\) 0 0
\(63\) 5.48225 0.690699
\(64\) 0 0
\(65\) 11.0734 1.37348
\(66\) 0 0
\(67\) 8.94464 1.09276 0.546381 0.837537i \(-0.316005\pi\)
0.546381 + 0.837537i \(0.316005\pi\)
\(68\) 0 0
\(69\) 1.13679 0.136853
\(70\) 0 0
\(71\) −7.14955 −0.848496 −0.424248 0.905546i \(-0.639461\pi\)
−0.424248 + 0.905546i \(0.639461\pi\)
\(72\) 0 0
\(73\) −11.3319 −1.32629 −0.663147 0.748489i \(-0.730780\pi\)
−0.663147 + 0.748489i \(0.730780\pi\)
\(74\) 0 0
\(75\) 0.610974 0.0705492
\(76\) 0 0
\(77\) 1.54426 0.175984
\(78\) 0 0
\(79\) 11.9354 1.34283 0.671416 0.741080i \(-0.265686\pi\)
0.671416 + 0.741080i \(0.265686\pi\)
\(80\) 0 0
\(81\) 7.19957 0.799953
\(82\) 0 0
\(83\) −4.55162 −0.499606 −0.249803 0.968297i \(-0.580366\pi\)
−0.249803 + 0.968297i \(0.580366\pi\)
\(84\) 0 0
\(85\) −5.98429 −0.649087
\(86\) 0 0
\(87\) −1.64095 −0.175928
\(88\) 0 0
\(89\) 1.55704 0.165046 0.0825228 0.996589i \(-0.473702\pi\)
0.0825228 + 0.996589i \(0.473702\pi\)
\(90\) 0 0
\(91\) −11.3681 −1.19170
\(92\) 0 0
\(93\) −2.80517 −0.290883
\(94\) 0 0
\(95\) −8.85805 −0.908816
\(96\) 0 0
\(97\) 5.55502 0.564027 0.282013 0.959410i \(-0.408998\pi\)
0.282013 + 0.959410i \(0.408998\pi\)
\(98\) 0 0
\(99\) 2.20098 0.221207
\(100\) 0 0
\(101\) 2.50744 0.249500 0.124750 0.992188i \(-0.460187\pi\)
0.124750 + 0.992188i \(0.460187\pi\)
\(102\) 0 0
\(103\) 15.7471 1.55161 0.775805 0.630973i \(-0.217344\pi\)
0.775805 + 0.630973i \(0.217344\pi\)
\(104\) 0 0
\(105\) 1.69518 0.165433
\(106\) 0 0
\(107\) 14.5671 1.40826 0.704129 0.710072i \(-0.251338\pi\)
0.704129 + 0.710072i \(0.251338\pi\)
\(108\) 0 0
\(109\) 19.2481 1.84364 0.921818 0.387623i \(-0.126704\pi\)
0.921818 + 0.387623i \(0.126704\pi\)
\(110\) 0 0
\(111\) −4.39756 −0.417398
\(112\) 0 0
\(113\) 15.5531 1.46311 0.731555 0.681782i \(-0.238795\pi\)
0.731555 + 0.681782i \(0.238795\pi\)
\(114\) 0 0
\(115\) −4.79999 −0.447601
\(116\) 0 0
\(117\) −16.2026 −1.49793
\(118\) 0 0
\(119\) 6.14356 0.563179
\(120\) 0 0
\(121\) −10.3800 −0.943638
\(122\) 0 0
\(123\) 0.403624 0.0363936
\(124\) 0 0
\(125\) −12.1318 −1.08510
\(126\) 0 0
\(127\) −2.29660 −0.203790 −0.101895 0.994795i \(-0.532491\pi\)
−0.101895 + 0.994795i \(0.532491\pi\)
\(128\) 0 0
\(129\) −2.62519 −0.231135
\(130\) 0 0
\(131\) 11.3850 0.994711 0.497355 0.867547i \(-0.334305\pi\)
0.497355 + 0.867547i \(0.334305\pi\)
\(132\) 0 0
\(133\) 9.09381 0.788533
\(134\) 0 0
\(135\) 5.00912 0.431116
\(136\) 0 0
\(137\) −20.6460 −1.76390 −0.881951 0.471340i \(-0.843770\pi\)
−0.881951 + 0.471340i \(0.843770\pi\)
\(138\) 0 0
\(139\) −18.4827 −1.56769 −0.783843 0.620959i \(-0.786743\pi\)
−0.783843 + 0.620959i \(0.786743\pi\)
\(140\) 0 0
\(141\) 1.65525 0.139398
\(142\) 0 0
\(143\) −4.56400 −0.381661
\(144\) 0 0
\(145\) 6.92875 0.575401
\(146\) 0 0
\(147\) 1.42679 0.117680
\(148\) 0 0
\(149\) 5.25249 0.430301 0.215150 0.976581i \(-0.430976\pi\)
0.215150 + 0.976581i \(0.430976\pi\)
\(150\) 0 0
\(151\) −23.5014 −1.91252 −0.956258 0.292525i \(-0.905504\pi\)
−0.956258 + 0.292525i \(0.905504\pi\)
\(152\) 0 0
\(153\) 8.75623 0.707899
\(154\) 0 0
\(155\) 11.8446 0.951381
\(156\) 0 0
\(157\) −0.0874349 −0.00697807 −0.00348903 0.999994i \(-0.501111\pi\)
−0.00348903 + 0.999994i \(0.501111\pi\)
\(158\) 0 0
\(159\) −5.72288 −0.453854
\(160\) 0 0
\(161\) 4.92774 0.388361
\(162\) 0 0
\(163\) 19.1980 1.50371 0.751853 0.659331i \(-0.229160\pi\)
0.751853 + 0.659331i \(0.229160\pi\)
\(164\) 0 0
\(165\) 0.680571 0.0529824
\(166\) 0 0
\(167\) −1.82664 −0.141349 −0.0706747 0.997499i \(-0.522515\pi\)
−0.0706747 + 0.997499i \(0.522515\pi\)
\(168\) 0 0
\(169\) 20.5981 1.58447
\(170\) 0 0
\(171\) 12.9611 0.991162
\(172\) 0 0
\(173\) 21.4790 1.63302 0.816509 0.577333i \(-0.195906\pi\)
0.816509 + 0.577333i \(0.195906\pi\)
\(174\) 0 0
\(175\) 2.64845 0.200204
\(176\) 0 0
\(177\) 2.75365 0.206977
\(178\) 0 0
\(179\) −7.53705 −0.563346 −0.281673 0.959510i \(-0.590889\pi\)
−0.281673 + 0.959510i \(0.590889\pi\)
\(180\) 0 0
\(181\) 2.63731 0.196029 0.0980147 0.995185i \(-0.468751\pi\)
0.0980147 + 0.995185i \(0.468751\pi\)
\(182\) 0 0
\(183\) −2.93107 −0.216671
\(184\) 0 0
\(185\) 18.5683 1.36517
\(186\) 0 0
\(187\) 2.46648 0.180367
\(188\) 0 0
\(189\) −5.14244 −0.374057
\(190\) 0 0
\(191\) 5.11657 0.370222 0.185111 0.982718i \(-0.440736\pi\)
0.185111 + 0.982718i \(0.440736\pi\)
\(192\) 0 0
\(193\) −1.28124 −0.0922257 −0.0461128 0.998936i \(-0.514683\pi\)
−0.0461128 + 0.998936i \(0.514683\pi\)
\(194\) 0 0
\(195\) −5.01006 −0.358778
\(196\) 0 0
\(197\) 12.8801 0.917667 0.458833 0.888522i \(-0.348267\pi\)
0.458833 + 0.888522i \(0.348267\pi\)
\(198\) 0 0
\(199\) 24.0559 1.70528 0.852638 0.522503i \(-0.175001\pi\)
0.852638 + 0.522503i \(0.175001\pi\)
\(200\) 0 0
\(201\) −4.04693 −0.285448
\(202\) 0 0
\(203\) −7.11316 −0.499246
\(204\) 0 0
\(205\) −1.70427 −0.119031
\(206\) 0 0
\(207\) 7.02336 0.488157
\(208\) 0 0
\(209\) 3.65093 0.252540
\(210\) 0 0
\(211\) 10.7763 0.741874 0.370937 0.928658i \(-0.379037\pi\)
0.370937 + 0.928658i \(0.379037\pi\)
\(212\) 0 0
\(213\) 3.23475 0.221642
\(214\) 0 0
\(215\) 11.0847 0.755967
\(216\) 0 0
\(217\) −12.1598 −0.825464
\(218\) 0 0
\(219\) 5.12700 0.346451
\(220\) 0 0
\(221\) −18.1571 −1.22138
\(222\) 0 0
\(223\) −15.8073 −1.05854 −0.529268 0.848455i \(-0.677534\pi\)
−0.529268 + 0.848455i \(0.677534\pi\)
\(224\) 0 0
\(225\) 3.77475 0.251650
\(226\) 0 0
\(227\) −17.8386 −1.18399 −0.591995 0.805942i \(-0.701659\pi\)
−0.591995 + 0.805942i \(0.701659\pi\)
\(228\) 0 0
\(229\) −24.0567 −1.58971 −0.794856 0.606798i \(-0.792454\pi\)
−0.794856 + 0.606798i \(0.792454\pi\)
\(230\) 0 0
\(231\) −0.698685 −0.0459701
\(232\) 0 0
\(233\) 15.4663 1.01323 0.506616 0.862172i \(-0.330896\pi\)
0.506616 + 0.862172i \(0.330896\pi\)
\(234\) 0 0
\(235\) −6.98917 −0.455923
\(236\) 0 0
\(237\) −5.40005 −0.350771
\(238\) 0 0
\(239\) −4.57069 −0.295653 −0.147827 0.989013i \(-0.547228\pi\)
−0.147827 + 0.989013i \(0.547228\pi\)
\(240\) 0 0
\(241\) 15.9646 1.02837 0.514185 0.857679i \(-0.328095\pi\)
0.514185 + 0.857679i \(0.328095\pi\)
\(242\) 0 0
\(243\) −11.1235 −0.713572
\(244\) 0 0
\(245\) −6.02449 −0.384891
\(246\) 0 0
\(247\) −26.8765 −1.71011
\(248\) 0 0
\(249\) 2.05934 0.130506
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 1.97836 0.124378
\(254\) 0 0
\(255\) 2.70754 0.169553
\(256\) 0 0
\(257\) −8.72312 −0.544133 −0.272067 0.962278i \(-0.587707\pi\)
−0.272067 + 0.962278i \(0.587707\pi\)
\(258\) 0 0
\(259\) −19.0625 −1.18449
\(260\) 0 0
\(261\) −10.1382 −0.627537
\(262\) 0 0
\(263\) 23.8788 1.47243 0.736214 0.676749i \(-0.236612\pi\)
0.736214 + 0.676749i \(0.236612\pi\)
\(264\) 0 0
\(265\) 24.1643 1.48440
\(266\) 0 0
\(267\) −0.704468 −0.0431127
\(268\) 0 0
\(269\) 13.4422 0.819587 0.409794 0.912178i \(-0.365601\pi\)
0.409794 + 0.912178i \(0.365601\pi\)
\(270\) 0 0
\(271\) 11.5155 0.699518 0.349759 0.936840i \(-0.386263\pi\)
0.349759 + 0.936840i \(0.386263\pi\)
\(272\) 0 0
\(273\) 5.14340 0.311293
\(274\) 0 0
\(275\) 1.06328 0.0641183
\(276\) 0 0
\(277\) −7.37275 −0.442986 −0.221493 0.975162i \(-0.571093\pi\)
−0.221493 + 0.975162i \(0.571093\pi\)
\(278\) 0 0
\(279\) −17.3311 −1.03758
\(280\) 0 0
\(281\) −19.9735 −1.19152 −0.595758 0.803164i \(-0.703148\pi\)
−0.595758 + 0.803164i \(0.703148\pi\)
\(282\) 0 0
\(283\) 28.0411 1.66687 0.833434 0.552619i \(-0.186371\pi\)
0.833434 + 0.552619i \(0.186371\pi\)
\(284\) 0 0
\(285\) 4.00775 0.237398
\(286\) 0 0
\(287\) 1.74963 0.103277
\(288\) 0 0
\(289\) −7.18753 −0.422796
\(290\) 0 0
\(291\) −2.51332 −0.147333
\(292\) 0 0
\(293\) −24.2201 −1.41496 −0.707478 0.706735i \(-0.750167\pi\)
−0.707478 + 0.706735i \(0.750167\pi\)
\(294\) 0 0
\(295\) −11.6271 −0.676954
\(296\) 0 0
\(297\) −2.06455 −0.119798
\(298\) 0 0
\(299\) −14.5638 −0.842246
\(300\) 0 0
\(301\) −11.3797 −0.655914
\(302\) 0 0
\(303\) −1.13447 −0.0651737
\(304\) 0 0
\(305\) 12.3762 0.708659
\(306\) 0 0
\(307\) −14.9324 −0.852236 −0.426118 0.904667i \(-0.640119\pi\)
−0.426118 + 0.904667i \(0.640119\pi\)
\(308\) 0 0
\(309\) −7.12464 −0.405307
\(310\) 0 0
\(311\) 26.2949 1.49105 0.745524 0.666479i \(-0.232199\pi\)
0.745524 + 0.666479i \(0.232199\pi\)
\(312\) 0 0
\(313\) −3.51404 −0.198625 −0.0993127 0.995056i \(-0.531664\pi\)
−0.0993127 + 0.995056i \(0.531664\pi\)
\(314\) 0 0
\(315\) 10.4733 0.590101
\(316\) 0 0
\(317\) −15.1169 −0.849047 −0.424524 0.905417i \(-0.639558\pi\)
−0.424524 + 0.905417i \(0.639558\pi\)
\(318\) 0 0
\(319\) −2.85575 −0.159891
\(320\) 0 0
\(321\) −6.59077 −0.367861
\(322\) 0 0
\(323\) 14.5246 0.808170
\(324\) 0 0
\(325\) −7.82740 −0.434186
\(326\) 0 0
\(327\) −8.70865 −0.481589
\(328\) 0 0
\(329\) 7.17519 0.395581
\(330\) 0 0
\(331\) 34.0881 1.87365 0.936825 0.349799i \(-0.113750\pi\)
0.936825 + 0.349799i \(0.113750\pi\)
\(332\) 0 0
\(333\) −27.1692 −1.48886
\(334\) 0 0
\(335\) 17.0878 0.933606
\(336\) 0 0
\(337\) −2.67369 −0.145645 −0.0728227 0.997345i \(-0.523201\pi\)
−0.0728227 + 0.997345i \(0.523201\pi\)
\(338\) 0 0
\(339\) −7.03686 −0.382190
\(340\) 0 0
\(341\) −4.88186 −0.264368
\(342\) 0 0
\(343\) 19.9135 1.07523
\(344\) 0 0
\(345\) 2.17171 0.116921
\(346\) 0 0
\(347\) 24.8044 1.33157 0.665786 0.746143i \(-0.268096\pi\)
0.665786 + 0.746143i \(0.268096\pi\)
\(348\) 0 0
\(349\) −1.31555 −0.0704198 −0.0352099 0.999380i \(-0.511210\pi\)
−0.0352099 + 0.999380i \(0.511210\pi\)
\(350\) 0 0
\(351\) 15.1983 0.811226
\(352\) 0 0
\(353\) −17.7470 −0.944576 −0.472288 0.881444i \(-0.656572\pi\)
−0.472288 + 0.881444i \(0.656572\pi\)
\(354\) 0 0
\(355\) −13.6585 −0.724916
\(356\) 0 0
\(357\) −2.77960 −0.147112
\(358\) 0 0
\(359\) 14.9012 0.786457 0.393228 0.919441i \(-0.371358\pi\)
0.393228 + 0.919441i \(0.371358\pi\)
\(360\) 0 0
\(361\) 2.49957 0.131556
\(362\) 0 0
\(363\) 4.69635 0.246494
\(364\) 0 0
\(365\) −21.6483 −1.13313
\(366\) 0 0
\(367\) 26.1918 1.36720 0.683600 0.729857i \(-0.260413\pi\)
0.683600 + 0.729857i \(0.260413\pi\)
\(368\) 0 0
\(369\) 2.49369 0.129816
\(370\) 0 0
\(371\) −24.8075 −1.28794
\(372\) 0 0
\(373\) −1.81955 −0.0942130 −0.0471065 0.998890i \(-0.515000\pi\)
−0.0471065 + 0.998890i \(0.515000\pi\)
\(374\) 0 0
\(375\) 5.48891 0.283446
\(376\) 0 0
\(377\) 21.0227 1.08273
\(378\) 0 0
\(379\) −1.39119 −0.0714607 −0.0357304 0.999361i \(-0.511376\pi\)
−0.0357304 + 0.999361i \(0.511376\pi\)
\(380\) 0 0
\(381\) 1.03908 0.0532335
\(382\) 0 0
\(383\) −5.65910 −0.289167 −0.144583 0.989493i \(-0.546184\pi\)
−0.144583 + 0.989493i \(0.546184\pi\)
\(384\) 0 0
\(385\) 2.95014 0.150353
\(386\) 0 0
\(387\) −16.2191 −0.824464
\(388\) 0 0
\(389\) 33.3761 1.69224 0.846118 0.532996i \(-0.178934\pi\)
0.846118 + 0.532996i \(0.178934\pi\)
\(390\) 0 0
\(391\) 7.87057 0.398032
\(392\) 0 0
\(393\) −5.15104 −0.259835
\(394\) 0 0
\(395\) 22.8012 1.14726
\(396\) 0 0
\(397\) 2.80826 0.140943 0.0704713 0.997514i \(-0.477550\pi\)
0.0704713 + 0.997514i \(0.477550\pi\)
\(398\) 0 0
\(399\) −4.11442 −0.205978
\(400\) 0 0
\(401\) 20.0554 1.00152 0.500759 0.865587i \(-0.333054\pi\)
0.500759 + 0.865587i \(0.333054\pi\)
\(402\) 0 0
\(403\) 35.9380 1.79020
\(404\) 0 0
\(405\) 13.7540 0.683443
\(406\) 0 0
\(407\) −7.65310 −0.379350
\(408\) 0 0
\(409\) 5.60055 0.276929 0.138465 0.990367i \(-0.455783\pi\)
0.138465 + 0.990367i \(0.455783\pi\)
\(410\) 0 0
\(411\) 9.34108 0.460762
\(412\) 0 0
\(413\) 11.9365 0.587358
\(414\) 0 0
\(415\) −8.69540 −0.426840
\(416\) 0 0
\(417\) 8.36236 0.409506
\(418\) 0 0
\(419\) −11.6046 −0.566922 −0.283461 0.958984i \(-0.591483\pi\)
−0.283461 + 0.958984i \(0.591483\pi\)
\(420\) 0 0
\(421\) −32.0502 −1.56203 −0.781014 0.624513i \(-0.785298\pi\)
−0.781014 + 0.624513i \(0.785298\pi\)
\(422\) 0 0
\(423\) 10.2266 0.497233
\(424\) 0 0
\(425\) 4.23009 0.205189
\(426\) 0 0
\(427\) −12.7056 −0.614867
\(428\) 0 0
\(429\) 2.06494 0.0996963
\(430\) 0 0
\(431\) 33.0806 1.59344 0.796719 0.604349i \(-0.206567\pi\)
0.796719 + 0.604349i \(0.206567\pi\)
\(432\) 0 0
\(433\) 7.51349 0.361075 0.180538 0.983568i \(-0.442216\pi\)
0.180538 + 0.983568i \(0.442216\pi\)
\(434\) 0 0
\(435\) −3.13485 −0.150305
\(436\) 0 0
\(437\) 11.6502 0.557303
\(438\) 0 0
\(439\) 1.95743 0.0934231 0.0467116 0.998908i \(-0.485126\pi\)
0.0467116 + 0.998908i \(0.485126\pi\)
\(440\) 0 0
\(441\) 8.81506 0.419765
\(442\) 0 0
\(443\) −0.880392 −0.0418287 −0.0209143 0.999781i \(-0.506658\pi\)
−0.0209143 + 0.999781i \(0.506658\pi\)
\(444\) 0 0
\(445\) 2.97456 0.141007
\(446\) 0 0
\(447\) −2.37644 −0.112402
\(448\) 0 0
\(449\) −33.1514 −1.56451 −0.782255 0.622958i \(-0.785931\pi\)
−0.782255 + 0.622958i \(0.785931\pi\)
\(450\) 0 0
\(451\) 0.702430 0.0330761
\(452\) 0 0
\(453\) 10.6330 0.499582
\(454\) 0 0
\(455\) −21.7176 −1.01814
\(456\) 0 0
\(457\) 33.5917 1.57136 0.785678 0.618636i \(-0.212314\pi\)
0.785678 + 0.618636i \(0.212314\pi\)
\(458\) 0 0
\(459\) −8.21348 −0.383372
\(460\) 0 0
\(461\) −14.2767 −0.664930 −0.332465 0.943116i \(-0.607880\pi\)
−0.332465 + 0.943116i \(0.607880\pi\)
\(462\) 0 0
\(463\) 1.99819 0.0928636 0.0464318 0.998921i \(-0.485215\pi\)
0.0464318 + 0.998921i \(0.485215\pi\)
\(464\) 0 0
\(465\) −5.35898 −0.248517
\(466\) 0 0
\(467\) 22.7336 1.05199 0.525993 0.850489i \(-0.323694\pi\)
0.525993 + 0.850489i \(0.323694\pi\)
\(468\) 0 0
\(469\) −17.5426 −0.810042
\(470\) 0 0
\(471\) 0.0395592 0.00182279
\(472\) 0 0
\(473\) −4.56864 −0.210066
\(474\) 0 0
\(475\) 6.26145 0.287295
\(476\) 0 0
\(477\) −35.3574 −1.61890
\(478\) 0 0
\(479\) 8.15942 0.372813 0.186407 0.982473i \(-0.440316\pi\)
0.186407 + 0.982473i \(0.440316\pi\)
\(480\) 0 0
\(481\) 56.3387 2.56882
\(482\) 0 0
\(483\) −2.22951 −0.101446
\(484\) 0 0
\(485\) 10.6123 0.481879
\(486\) 0 0
\(487\) −2.44996 −0.111019 −0.0555093 0.998458i \(-0.517678\pi\)
−0.0555093 + 0.998458i \(0.517678\pi\)
\(488\) 0 0
\(489\) −8.68599 −0.392794
\(490\) 0 0
\(491\) −12.7893 −0.577171 −0.288586 0.957454i \(-0.593185\pi\)
−0.288586 + 0.957454i \(0.593185\pi\)
\(492\) 0 0
\(493\) −11.3611 −0.511679
\(494\) 0 0
\(495\) 4.20474 0.188989
\(496\) 0 0
\(497\) 14.0220 0.628972
\(498\) 0 0
\(499\) 0.938315 0.0420048 0.0210024 0.999779i \(-0.493314\pi\)
0.0210024 + 0.999779i \(0.493314\pi\)
\(500\) 0 0
\(501\) 0.826446 0.0369229
\(502\) 0 0
\(503\) −29.2146 −1.30262 −0.651308 0.758814i \(-0.725779\pi\)
−0.651308 + 0.758814i \(0.725779\pi\)
\(504\) 0 0
\(505\) 4.79021 0.213161
\(506\) 0 0
\(507\) −9.31942 −0.413890
\(508\) 0 0
\(509\) 40.9310 1.81423 0.907117 0.420879i \(-0.138278\pi\)
0.907117 + 0.420879i \(0.138278\pi\)
\(510\) 0 0
\(511\) 22.2245 0.983154
\(512\) 0 0
\(513\) −12.1577 −0.536777
\(514\) 0 0
\(515\) 30.0832 1.32562
\(516\) 0 0
\(517\) 2.88065 0.126691
\(518\) 0 0
\(519\) −9.71799 −0.426572
\(520\) 0 0
\(521\) 29.9804 1.31347 0.656733 0.754123i \(-0.271938\pi\)
0.656733 + 0.754123i \(0.271938\pi\)
\(522\) 0 0
\(523\) 26.2955 1.14982 0.574911 0.818216i \(-0.305037\pi\)
0.574911 + 0.818216i \(0.305037\pi\)
\(524\) 0 0
\(525\) −1.19827 −0.0522966
\(526\) 0 0
\(527\) −19.4217 −0.846021
\(528\) 0 0
\(529\) −16.6870 −0.725523
\(530\) 0 0
\(531\) 17.0128 0.738291
\(532\) 0 0
\(533\) −5.17097 −0.223980
\(534\) 0 0
\(535\) 27.8290 1.20315
\(536\) 0 0
\(537\) 3.41008 0.147156
\(538\) 0 0
\(539\) 2.48305 0.106953
\(540\) 0 0
\(541\) −22.9843 −0.988171 −0.494085 0.869413i \(-0.664497\pi\)
−0.494085 + 0.869413i \(0.664497\pi\)
\(542\) 0 0
\(543\) −1.19323 −0.0512063
\(544\) 0 0
\(545\) 36.7715 1.57512
\(546\) 0 0
\(547\) −7.79728 −0.333387 −0.166694 0.986009i \(-0.553309\pi\)
−0.166694 + 0.986009i \(0.553309\pi\)
\(548\) 0 0
\(549\) −18.1089 −0.772869
\(550\) 0 0
\(551\) −16.8169 −0.716425
\(552\) 0 0
\(553\) −23.4081 −0.995414
\(554\) 0 0
\(555\) −8.40107 −0.356606
\(556\) 0 0
\(557\) −26.6843 −1.13065 −0.565325 0.824868i \(-0.691249\pi\)
−0.565325 + 0.824868i \(0.691249\pi\)
\(558\) 0 0
\(559\) 33.6323 1.42249
\(560\) 0 0
\(561\) −1.11594 −0.0471149
\(562\) 0 0
\(563\) −15.3602 −0.647357 −0.323679 0.946167i \(-0.604920\pi\)
−0.323679 + 0.946167i \(0.604920\pi\)
\(564\) 0 0
\(565\) 29.7125 1.25001
\(566\) 0 0
\(567\) −14.1201 −0.592988
\(568\) 0 0
\(569\) 2.53660 0.106340 0.0531700 0.998585i \(-0.483067\pi\)
0.0531700 + 0.998585i \(0.483067\pi\)
\(570\) 0 0
\(571\) −24.5090 −1.02567 −0.512836 0.858487i \(-0.671405\pi\)
−0.512836 + 0.858487i \(0.671405\pi\)
\(572\) 0 0
\(573\) −2.31495 −0.0967083
\(574\) 0 0
\(575\) 3.39295 0.141496
\(576\) 0 0
\(577\) −37.4112 −1.55745 −0.778725 0.627366i \(-0.784133\pi\)
−0.778725 + 0.627366i \(0.784133\pi\)
\(578\) 0 0
\(579\) 0.579686 0.0240909
\(580\) 0 0
\(581\) 8.92683 0.370347
\(582\) 0 0
\(583\) −9.95956 −0.412483
\(584\) 0 0
\(585\) −30.9534 −1.27977
\(586\) 0 0
\(587\) −32.3390 −1.33477 −0.667387 0.744711i \(-0.732587\pi\)
−0.667387 + 0.744711i \(0.732587\pi\)
\(588\) 0 0
\(589\) −28.7483 −1.18455
\(590\) 0 0
\(591\) −5.82748 −0.239710
\(592\) 0 0
\(593\) −17.8932 −0.734785 −0.367392 0.930066i \(-0.619749\pi\)
−0.367392 + 0.930066i \(0.619749\pi\)
\(594\) 0 0
\(595\) 11.7366 0.481155
\(596\) 0 0
\(597\) −10.8839 −0.445447
\(598\) 0 0
\(599\) −19.3881 −0.792175 −0.396088 0.918213i \(-0.629632\pi\)
−0.396088 + 0.918213i \(0.629632\pi\)
\(600\) 0 0
\(601\) −11.0687 −0.451503 −0.225751 0.974185i \(-0.572484\pi\)
−0.225751 + 0.974185i \(0.572484\pi\)
\(602\) 0 0
\(603\) −25.0029 −1.01820
\(604\) 0 0
\(605\) −19.8299 −0.806202
\(606\) 0 0
\(607\) 30.8771 1.25326 0.626632 0.779316i \(-0.284433\pi\)
0.626632 + 0.779316i \(0.284433\pi\)
\(608\) 0 0
\(609\) 3.21829 0.130412
\(610\) 0 0
\(611\) −21.2060 −0.857905
\(612\) 0 0
\(613\) 9.94691 0.401752 0.200876 0.979617i \(-0.435621\pi\)
0.200876 + 0.979617i \(0.435621\pi\)
\(614\) 0 0
\(615\) 0.771081 0.0310930
\(616\) 0 0
\(617\) −28.8807 −1.16269 −0.581346 0.813656i \(-0.697474\pi\)
−0.581346 + 0.813656i \(0.697474\pi\)
\(618\) 0 0
\(619\) −9.25598 −0.372029 −0.186015 0.982547i \(-0.559557\pi\)
−0.186015 + 0.982547i \(0.559557\pi\)
\(620\) 0 0
\(621\) −6.58802 −0.264368
\(622\) 0 0
\(623\) −3.05373 −0.122345
\(624\) 0 0
\(625\) −16.4245 −0.656979
\(626\) 0 0
\(627\) −1.65183 −0.0659678
\(628\) 0 0
\(629\) −30.4466 −1.21398
\(630\) 0 0
\(631\) 7.76256 0.309023 0.154511 0.987991i \(-0.450620\pi\)
0.154511 + 0.987991i \(0.450620\pi\)
\(632\) 0 0
\(633\) −4.87566 −0.193790
\(634\) 0 0
\(635\) −4.38741 −0.174109
\(636\) 0 0
\(637\) −18.2791 −0.724244
\(638\) 0 0
\(639\) 19.9851 0.790599
\(640\) 0 0
\(641\) −39.4109 −1.55664 −0.778319 0.627869i \(-0.783927\pi\)
−0.778319 + 0.627869i \(0.783927\pi\)
\(642\) 0 0
\(643\) 36.5538 1.44154 0.720771 0.693174i \(-0.243788\pi\)
0.720771 + 0.693174i \(0.243788\pi\)
\(644\) 0 0
\(645\) −5.01516 −0.197472
\(646\) 0 0
\(647\) 8.94030 0.351479 0.175740 0.984437i \(-0.443768\pi\)
0.175740 + 0.984437i \(0.443768\pi\)
\(648\) 0 0
\(649\) 4.79220 0.188110
\(650\) 0 0
\(651\) 5.50162 0.215625
\(652\) 0 0
\(653\) −12.1726 −0.476352 −0.238176 0.971222i \(-0.576549\pi\)
−0.238176 + 0.971222i \(0.576549\pi\)
\(654\) 0 0
\(655\) 21.7498 0.849835
\(656\) 0 0
\(657\) 31.6759 1.23580
\(658\) 0 0
\(659\) −29.4761 −1.14823 −0.574114 0.818776i \(-0.694653\pi\)
−0.574114 + 0.818776i \(0.694653\pi\)
\(660\) 0 0
\(661\) −10.5472 −0.410239 −0.205120 0.978737i \(-0.565758\pi\)
−0.205120 + 0.978737i \(0.565758\pi\)
\(662\) 0 0
\(663\) 8.21502 0.319045
\(664\) 0 0
\(665\) 17.3728 0.673687
\(666\) 0 0
\(667\) −9.11274 −0.352847
\(668\) 0 0
\(669\) 7.15189 0.276508
\(670\) 0 0
\(671\) −5.10097 −0.196921
\(672\) 0 0
\(673\) −28.4861 −1.09806 −0.549029 0.835803i \(-0.685002\pi\)
−0.549029 + 0.835803i \(0.685002\pi\)
\(674\) 0 0
\(675\) −3.54077 −0.136284
\(676\) 0 0
\(677\) 3.92813 0.150970 0.0754851 0.997147i \(-0.475949\pi\)
0.0754851 + 0.997147i \(0.475949\pi\)
\(678\) 0 0
\(679\) −10.8947 −0.418101
\(680\) 0 0
\(681\) 8.07092 0.309278
\(682\) 0 0
\(683\) 42.9694 1.64418 0.822089 0.569359i \(-0.192808\pi\)
0.822089 + 0.569359i \(0.192808\pi\)
\(684\) 0 0
\(685\) −39.4419 −1.50700
\(686\) 0 0
\(687\) 10.8843 0.415260
\(688\) 0 0
\(689\) 73.3178 2.79318
\(690\) 0 0
\(691\) −13.4562 −0.511897 −0.255949 0.966690i \(-0.582388\pi\)
−0.255949 + 0.966690i \(0.582388\pi\)
\(692\) 0 0
\(693\) −4.31665 −0.163976
\(694\) 0 0
\(695\) −35.3093 −1.33936
\(696\) 0 0
\(697\) 2.79450 0.105849
\(698\) 0 0
\(699\) −6.99760 −0.264673
\(700\) 0 0
\(701\) 19.9131 0.752107 0.376054 0.926598i \(-0.377281\pi\)
0.376054 + 0.926598i \(0.377281\pi\)
\(702\) 0 0
\(703\) −45.0676 −1.69976
\(704\) 0 0
\(705\) 3.16219 0.119095
\(706\) 0 0
\(707\) −4.91770 −0.184949
\(708\) 0 0
\(709\) −12.1399 −0.455924 −0.227962 0.973670i \(-0.573206\pi\)
−0.227962 + 0.973670i \(0.573206\pi\)
\(710\) 0 0
\(711\) −33.3629 −1.25121
\(712\) 0 0
\(713\) −15.5781 −0.583404
\(714\) 0 0
\(715\) −8.71904 −0.326074
\(716\) 0 0
\(717\) 2.06797 0.0772297
\(718\) 0 0
\(719\) −28.7871 −1.07358 −0.536789 0.843716i \(-0.680363\pi\)
−0.536789 + 0.843716i \(0.680363\pi\)
\(720\) 0 0
\(721\) −30.8839 −1.15018
\(722\) 0 0
\(723\) −7.22304 −0.268628
\(724\) 0 0
\(725\) −4.89770 −0.181896
\(726\) 0 0
\(727\) −36.9370 −1.36992 −0.684960 0.728581i \(-0.740180\pi\)
−0.684960 + 0.728581i \(0.740180\pi\)
\(728\) 0 0
\(729\) −16.5660 −0.613556
\(730\) 0 0
\(731\) −18.1756 −0.672248
\(732\) 0 0
\(733\) −11.7116 −0.432579 −0.216289 0.976329i \(-0.569395\pi\)
−0.216289 + 0.976329i \(0.569395\pi\)
\(734\) 0 0
\(735\) 2.72573 0.100540
\(736\) 0 0
\(737\) −7.04289 −0.259428
\(738\) 0 0
\(739\) 28.6602 1.05428 0.527141 0.849778i \(-0.323264\pi\)
0.527141 + 0.849778i \(0.323264\pi\)
\(740\) 0 0
\(741\) 12.1600 0.446710
\(742\) 0 0
\(743\) −9.65811 −0.354322 −0.177161 0.984182i \(-0.556691\pi\)
−0.177161 + 0.984182i \(0.556691\pi\)
\(744\) 0 0
\(745\) 10.0343 0.367629
\(746\) 0 0
\(747\) 12.7231 0.465515
\(748\) 0 0
\(749\) −28.5696 −1.04391
\(750\) 0 0
\(751\) 25.1095 0.916260 0.458130 0.888885i \(-0.348519\pi\)
0.458130 + 0.888885i \(0.348519\pi\)
\(752\) 0 0
\(753\) −0.452441 −0.0164879
\(754\) 0 0
\(755\) −44.8969 −1.63397
\(756\) 0 0
\(757\) 5.68729 0.206708 0.103354 0.994645i \(-0.467043\pi\)
0.103354 + 0.994645i \(0.467043\pi\)
\(758\) 0 0
\(759\) −0.895092 −0.0324898
\(760\) 0 0
\(761\) 9.65366 0.349945 0.174972 0.984573i \(-0.444016\pi\)
0.174972 + 0.984573i \(0.444016\pi\)
\(762\) 0 0
\(763\) −37.7502 −1.36665
\(764\) 0 0
\(765\) 16.7279 0.604797
\(766\) 0 0
\(767\) −35.2780 −1.27382
\(768\) 0 0
\(769\) −6.79824 −0.245151 −0.122575 0.992459i \(-0.539115\pi\)
−0.122575 + 0.992459i \(0.539115\pi\)
\(770\) 0 0
\(771\) 3.94670 0.142137
\(772\) 0 0
\(773\) −51.3076 −1.84541 −0.922704 0.385510i \(-0.874025\pi\)
−0.922704 + 0.385510i \(0.874025\pi\)
\(774\) 0 0
\(775\) −8.37254 −0.300751
\(776\) 0 0
\(777\) 8.62467 0.309408
\(778\) 0 0
\(779\) 4.13647 0.148204
\(780\) 0 0
\(781\) 5.62947 0.201438
\(782\) 0 0
\(783\) 9.50976 0.339851
\(784\) 0 0
\(785\) −0.167035 −0.00596174
\(786\) 0 0
\(787\) −36.4549 −1.29948 −0.649738 0.760158i \(-0.725121\pi\)
−0.649738 + 0.760158i \(0.725121\pi\)
\(788\) 0 0
\(789\) −10.8037 −0.384623
\(790\) 0 0
\(791\) −30.5033 −1.08457
\(792\) 0 0
\(793\) 37.5510 1.33348
\(794\) 0 0
\(795\) −10.9330 −0.387752
\(796\) 0 0
\(797\) 49.1111 1.73961 0.869803 0.493399i \(-0.164246\pi\)
0.869803 + 0.493399i \(0.164246\pi\)
\(798\) 0 0
\(799\) 11.4602 0.405432
\(800\) 0 0
\(801\) −4.35238 −0.153784
\(802\) 0 0
\(803\) 8.92256 0.314870
\(804\) 0 0
\(805\) 9.41393 0.331798
\(806\) 0 0
\(807\) −6.08182 −0.214090
\(808\) 0 0
\(809\) −3.96420 −0.139374 −0.0696870 0.997569i \(-0.522200\pi\)
−0.0696870 + 0.997569i \(0.522200\pi\)
\(810\) 0 0
\(811\) −38.6956 −1.35879 −0.679393 0.733774i \(-0.737757\pi\)
−0.679393 + 0.733774i \(0.737757\pi\)
\(812\) 0 0
\(813\) −5.21010 −0.182726
\(814\) 0 0
\(815\) 36.6758 1.28470
\(816\) 0 0
\(817\) −26.9038 −0.941246
\(818\) 0 0
\(819\) 31.7772 1.11039
\(820\) 0 0
\(821\) −18.4011 −0.642202 −0.321101 0.947045i \(-0.604053\pi\)
−0.321101 + 0.947045i \(0.604053\pi\)
\(822\) 0 0
\(823\) −39.2854 −1.36940 −0.684701 0.728824i \(-0.740067\pi\)
−0.684701 + 0.728824i \(0.740067\pi\)
\(824\) 0 0
\(825\) −0.481073 −0.0167488
\(826\) 0 0
\(827\) −24.4883 −0.851541 −0.425771 0.904831i \(-0.639997\pi\)
−0.425771 + 0.904831i \(0.639997\pi\)
\(828\) 0 0
\(829\) 3.40002 0.118088 0.0590438 0.998255i \(-0.481195\pi\)
0.0590438 + 0.998255i \(0.481195\pi\)
\(830\) 0 0
\(831\) 3.33574 0.115715
\(832\) 0 0
\(833\) 9.87841 0.342266
\(834\) 0 0
\(835\) −3.48960 −0.120763
\(836\) 0 0
\(837\) 16.2568 0.561917
\(838\) 0 0
\(839\) −29.8387 −1.03015 −0.515074 0.857146i \(-0.672235\pi\)
−0.515074 + 0.857146i \(0.672235\pi\)
\(840\) 0 0
\(841\) −15.8458 −0.546408
\(842\) 0 0
\(843\) 9.03681 0.311244
\(844\) 0 0
\(845\) 39.3505 1.35370
\(846\) 0 0
\(847\) 20.3577 0.699500
\(848\) 0 0
\(849\) −12.6869 −0.435415
\(850\) 0 0
\(851\) −24.4212 −0.837147
\(852\) 0 0
\(853\) 2.73462 0.0936315 0.0468157 0.998904i \(-0.485093\pi\)
0.0468157 + 0.998904i \(0.485093\pi\)
\(854\) 0 0
\(855\) 24.7609 0.846804
\(856\) 0 0
\(857\) −16.3691 −0.559158 −0.279579 0.960123i \(-0.590195\pi\)
−0.279579 + 0.960123i \(0.590195\pi\)
\(858\) 0 0
\(859\) 3.18932 0.108818 0.0544092 0.998519i \(-0.482672\pi\)
0.0544092 + 0.998519i \(0.482672\pi\)
\(860\) 0 0
\(861\) −0.791604 −0.0269778
\(862\) 0 0
\(863\) 42.0992 1.43307 0.716537 0.697549i \(-0.245726\pi\)
0.716537 + 0.697549i \(0.245726\pi\)
\(864\) 0 0
\(865\) 41.0334 1.39518
\(866\) 0 0
\(867\) 3.25193 0.110441
\(868\) 0 0
\(869\) −9.39775 −0.318797
\(870\) 0 0
\(871\) 51.8466 1.75675
\(872\) 0 0
\(873\) −15.5279 −0.525541
\(874\) 0 0
\(875\) 23.7933 0.804360
\(876\) 0 0
\(877\) −9.14103 −0.308671 −0.154335 0.988019i \(-0.549324\pi\)
−0.154335 + 0.988019i \(0.549324\pi\)
\(878\) 0 0
\(879\) 10.9582 0.369611
\(880\) 0 0
\(881\) 3.14380 0.105917 0.0529586 0.998597i \(-0.483135\pi\)
0.0529586 + 0.998597i \(0.483135\pi\)
\(882\) 0 0
\(883\) 30.6344 1.03093 0.515464 0.856911i \(-0.327620\pi\)
0.515464 + 0.856911i \(0.327620\pi\)
\(884\) 0 0
\(885\) 5.26056 0.176832
\(886\) 0 0
\(887\) −17.3622 −0.582965 −0.291483 0.956576i \(-0.594149\pi\)
−0.291483 + 0.956576i \(0.594149\pi\)
\(888\) 0 0
\(889\) 4.50418 0.151065
\(890\) 0 0
\(891\) −5.66885 −0.189914
\(892\) 0 0
\(893\) 16.9636 0.567664
\(894\) 0 0
\(895\) −14.3987 −0.481297
\(896\) 0 0
\(897\) 6.58926 0.220009
\(898\) 0 0
\(899\) 22.4869 0.749979
\(900\) 0 0
\(901\) −39.6224 −1.32002
\(902\) 0 0
\(903\) 5.14864 0.171336
\(904\) 0 0
\(905\) 5.03830 0.167479
\(906\) 0 0
\(907\) −13.0635 −0.433767 −0.216883 0.976198i \(-0.569589\pi\)
−0.216883 + 0.976198i \(0.569589\pi\)
\(908\) 0 0
\(909\) −7.00905 −0.232475
\(910\) 0 0
\(911\) −23.2857 −0.771491 −0.385746 0.922605i \(-0.626056\pi\)
−0.385746 + 0.922605i \(0.626056\pi\)
\(912\) 0 0
\(913\) 3.58389 0.118609
\(914\) 0 0
\(915\) −5.59950 −0.185114
\(916\) 0 0
\(917\) −22.3287 −0.737358
\(918\) 0 0
\(919\) −49.1025 −1.61974 −0.809871 0.586608i \(-0.800463\pi\)
−0.809871 + 0.586608i \(0.800463\pi\)
\(920\) 0 0
\(921\) 6.75603 0.222619
\(922\) 0 0
\(923\) −41.4416 −1.36407
\(924\) 0 0
\(925\) −13.1253 −0.431557
\(926\) 0 0
\(927\) −44.0179 −1.44574
\(928\) 0 0
\(929\) 40.9252 1.34271 0.671356 0.741135i \(-0.265712\pi\)
0.671356 + 0.741135i \(0.265712\pi\)
\(930\) 0 0
\(931\) 14.6222 0.479223
\(932\) 0 0
\(933\) −11.8969 −0.389487
\(934\) 0 0
\(935\) 4.71195 0.154097
\(936\) 0 0
\(937\) 43.3581 1.41645 0.708224 0.705988i \(-0.249497\pi\)
0.708224 + 0.705988i \(0.249497\pi\)
\(938\) 0 0
\(939\) 1.58990 0.0518844
\(940\) 0 0
\(941\) 35.9586 1.17222 0.586108 0.810233i \(-0.300659\pi\)
0.586108 + 0.810233i \(0.300659\pi\)
\(942\) 0 0
\(943\) 2.24146 0.0729921
\(944\) 0 0
\(945\) −9.82408 −0.319577
\(946\) 0 0
\(947\) −40.6909 −1.32228 −0.661138 0.750265i \(-0.729926\pi\)
−0.661138 + 0.750265i \(0.729926\pi\)
\(948\) 0 0
\(949\) −65.6838 −2.13219
\(950\) 0 0
\(951\) 6.83949 0.221786
\(952\) 0 0
\(953\) 2.43322 0.0788199 0.0394099 0.999223i \(-0.487452\pi\)
0.0394099 + 0.999223i \(0.487452\pi\)
\(954\) 0 0
\(955\) 9.77467 0.316301
\(956\) 0 0
\(957\) 1.29206 0.0417663
\(958\) 0 0
\(959\) 40.4917 1.30754
\(960\) 0 0
\(961\) 7.44096 0.240031
\(962\) 0 0
\(963\) −40.7194 −1.31217
\(964\) 0 0
\(965\) −2.44767 −0.0787934
\(966\) 0 0
\(967\) −54.8236 −1.76301 −0.881504 0.472177i \(-0.843468\pi\)
−0.881504 + 0.472177i \(0.843468\pi\)
\(968\) 0 0
\(969\) −6.57153 −0.211108
\(970\) 0 0
\(971\) 9.42580 0.302488 0.151244 0.988496i \(-0.451672\pi\)
0.151244 + 0.988496i \(0.451672\pi\)
\(972\) 0 0
\(973\) 36.2491 1.16209
\(974\) 0 0
\(975\) 3.54144 0.113417
\(976\) 0 0
\(977\) 14.3979 0.460630 0.230315 0.973116i \(-0.426024\pi\)
0.230315 + 0.973116i \(0.426024\pi\)
\(978\) 0 0
\(979\) −1.22599 −0.0391828
\(980\) 0 0
\(981\) −53.8042 −1.71784
\(982\) 0 0
\(983\) −18.7587 −0.598311 −0.299156 0.954204i \(-0.596705\pi\)
−0.299156 + 0.954204i \(0.596705\pi\)
\(984\) 0 0
\(985\) 24.6060 0.784013
\(986\) 0 0
\(987\) −3.24635 −0.103333
\(988\) 0 0
\(989\) −14.5786 −0.463573
\(990\) 0 0
\(991\) 31.3172 0.994824 0.497412 0.867514i \(-0.334284\pi\)
0.497412 + 0.867514i \(0.334284\pi\)
\(992\) 0 0
\(993\) −15.4228 −0.489429
\(994\) 0 0
\(995\) 45.9562 1.45691
\(996\) 0 0
\(997\) 39.2848 1.24416 0.622082 0.782952i \(-0.286287\pi\)
0.622082 + 0.782952i \(0.286287\pi\)
\(998\) 0 0
\(999\) 25.4852 0.806315
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 4016.2.a.m.1.10 23
4.3 odd 2 2008.2.a.d.1.14 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.14 23 4.3 odd 2
4016.2.a.m.1.10 23 1.1 even 1 trivial