Properties

Label 4016.2.a.m.1.15
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 1.15
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.15579 q^{3} -4.09592 q^{5} +0.621313 q^{7} -1.66414 q^{9} +O(q^{10})\) \(q+1.15579 q^{3} -4.09592 q^{5} +0.621313 q^{7} -1.66414 q^{9} -0.176674 q^{11} -6.62113 q^{13} -4.73404 q^{15} -4.87879 q^{17} +6.67634 q^{19} +0.718109 q^{21} -1.95079 q^{23} +11.7766 q^{25} -5.39078 q^{27} -4.79872 q^{29} +3.71027 q^{31} -0.204199 q^{33} -2.54485 q^{35} +6.22498 q^{37} -7.65265 q^{39} +1.84850 q^{41} +6.89738 q^{43} +6.81620 q^{45} +0.545127 q^{47} -6.61397 q^{49} -5.63887 q^{51} -4.30758 q^{53} +0.723644 q^{55} +7.71646 q^{57} -11.0491 q^{59} -3.06372 q^{61} -1.03395 q^{63} +27.1196 q^{65} +9.29195 q^{67} -2.25471 q^{69} +6.86513 q^{71} +5.09365 q^{73} +13.6113 q^{75} -0.109770 q^{77} +7.28093 q^{79} -1.23820 q^{81} +18.1951 q^{83} +19.9832 q^{85} -5.54633 q^{87} +15.4585 q^{89} -4.11379 q^{91} +4.28831 q^{93} -27.3458 q^{95} +8.30697 q^{97} +0.294011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) 1.15579 0.667297 0.333649 0.942697i \(-0.391720\pi\)
0.333649 + 0.942697i \(0.391720\pi\)
\(4\) 0 0
\(5\) −4.09592 −1.83175 −0.915876 0.401460i \(-0.868503\pi\)
−0.915876 + 0.401460i \(0.868503\pi\)
\(6\) 0 0
\(7\) 0.621313 0.234834 0.117417 0.993083i \(-0.462539\pi\)
0.117417 + 0.993083i \(0.462539\pi\)
\(8\) 0 0
\(9\) −1.66414 −0.554714
\(10\) 0 0
\(11\) −0.176674 −0.0532693 −0.0266346 0.999645i \(-0.508479\pi\)
−0.0266346 + 0.999645i \(0.508479\pi\)
\(12\) 0 0
\(13\) −6.62113 −1.83637 −0.918185 0.396152i \(-0.870345\pi\)
−0.918185 + 0.396152i \(0.870345\pi\)
\(14\) 0 0
\(15\) −4.73404 −1.22232
\(16\) 0 0
\(17\) −4.87879 −1.18328 −0.591640 0.806202i \(-0.701519\pi\)
−0.591640 + 0.806202i \(0.701519\pi\)
\(18\) 0 0
\(19\) 6.67634 1.53166 0.765828 0.643045i \(-0.222329\pi\)
0.765828 + 0.643045i \(0.222329\pi\)
\(20\) 0 0
\(21\) 0.718109 0.156704
\(22\) 0 0
\(23\) −1.95079 −0.406769 −0.203384 0.979099i \(-0.565194\pi\)
−0.203384 + 0.979099i \(0.565194\pi\)
\(24\) 0 0
\(25\) 11.7766 2.35532
\(26\) 0 0
\(27\) −5.39078 −1.03746
\(28\) 0 0
\(29\) −4.79872 −0.891100 −0.445550 0.895257i \(-0.646992\pi\)
−0.445550 + 0.895257i \(0.646992\pi\)
\(30\) 0 0
\(31\) 3.71027 0.666385 0.333192 0.942859i \(-0.391874\pi\)
0.333192 + 0.942859i \(0.391874\pi\)
\(32\) 0 0
\(33\) −0.204199 −0.0355464
\(34\) 0 0
\(35\) −2.54485 −0.430158
\(36\) 0 0
\(37\) 6.22498 1.02338 0.511690 0.859170i \(-0.329020\pi\)
0.511690 + 0.859170i \(0.329020\pi\)
\(38\) 0 0
\(39\) −7.65265 −1.22541
\(40\) 0 0
\(41\) 1.84850 0.288688 0.144344 0.989528i \(-0.453893\pi\)
0.144344 + 0.989528i \(0.453893\pi\)
\(42\) 0 0
\(43\) 6.89738 1.05184 0.525920 0.850534i \(-0.323721\pi\)
0.525920 + 0.850534i \(0.323721\pi\)
\(44\) 0 0
\(45\) 6.81620 1.01610
\(46\) 0 0
\(47\) 0.545127 0.0795150 0.0397575 0.999209i \(-0.487341\pi\)
0.0397575 + 0.999209i \(0.487341\pi\)
\(48\) 0 0
\(49\) −6.61397 −0.944853
\(50\) 0 0
\(51\) −5.63887 −0.789600
\(52\) 0 0
\(53\) −4.30758 −0.591692 −0.295846 0.955236i \(-0.595602\pi\)
−0.295846 + 0.955236i \(0.595602\pi\)
\(54\) 0 0
\(55\) 0.723644 0.0975761
\(56\) 0 0
\(57\) 7.71646 1.02207
\(58\) 0 0
\(59\) −11.0491 −1.43847 −0.719237 0.694765i \(-0.755508\pi\)
−0.719237 + 0.694765i \(0.755508\pi\)
\(60\) 0 0
\(61\) −3.06372 −0.392269 −0.196135 0.980577i \(-0.562839\pi\)
−0.196135 + 0.980577i \(0.562839\pi\)
\(62\) 0 0
\(63\) −1.03395 −0.130266
\(64\) 0 0
\(65\) 27.1196 3.36378
\(66\) 0 0
\(67\) 9.29195 1.13519 0.567596 0.823307i \(-0.307873\pi\)
0.567596 + 0.823307i \(0.307873\pi\)
\(68\) 0 0
\(69\) −2.25471 −0.271436
\(70\) 0 0
\(71\) 6.86513 0.814741 0.407370 0.913263i \(-0.366446\pi\)
0.407370 + 0.913263i \(0.366446\pi\)
\(72\) 0 0
\(73\) 5.09365 0.596167 0.298083 0.954540i \(-0.403653\pi\)
0.298083 + 0.954540i \(0.403653\pi\)
\(74\) 0 0
\(75\) 13.6113 1.57170
\(76\) 0 0
\(77\) −0.109770 −0.0125095
\(78\) 0 0
\(79\) 7.28093 0.819169 0.409584 0.912272i \(-0.365674\pi\)
0.409584 + 0.912272i \(0.365674\pi\)
\(80\) 0 0
\(81\) −1.23820 −0.137578
\(82\) 0 0
\(83\) 18.1951 1.99717 0.998586 0.0531544i \(-0.0169276\pi\)
0.998586 + 0.0531544i \(0.0169276\pi\)
\(84\) 0 0
\(85\) 19.9832 2.16748
\(86\) 0 0
\(87\) −5.54633 −0.594629
\(88\) 0 0
\(89\) 15.4585 1.63860 0.819298 0.573368i \(-0.194363\pi\)
0.819298 + 0.573368i \(0.194363\pi\)
\(90\) 0 0
\(91\) −4.11379 −0.431243
\(92\) 0 0
\(93\) 4.28831 0.444677
\(94\) 0 0
\(95\) −27.3458 −2.80562
\(96\) 0 0
\(97\) 8.30697 0.843445 0.421722 0.906725i \(-0.361426\pi\)
0.421722 + 0.906725i \(0.361426\pi\)
\(98\) 0 0
\(99\) 0.294011 0.0295492
\(100\) 0 0
\(101\) −9.59493 −0.954731 −0.477365 0.878705i \(-0.658408\pi\)
−0.477365 + 0.878705i \(0.658408\pi\)
\(102\) 0 0
\(103\) −5.65954 −0.557651 −0.278825 0.960342i \(-0.589945\pi\)
−0.278825 + 0.960342i \(0.589945\pi\)
\(104\) 0 0
\(105\) −2.94132 −0.287044
\(106\) 0 0
\(107\) −15.7163 −1.51935 −0.759674 0.650304i \(-0.774641\pi\)
−0.759674 + 0.650304i \(0.774641\pi\)
\(108\) 0 0
\(109\) 13.9298 1.33424 0.667118 0.744952i \(-0.267528\pi\)
0.667118 + 0.744952i \(0.267528\pi\)
\(110\) 0 0
\(111\) 7.19479 0.682899
\(112\) 0 0
\(113\) 11.6659 1.09743 0.548717 0.836008i \(-0.315117\pi\)
0.548717 + 0.836008i \(0.315117\pi\)
\(114\) 0 0
\(115\) 7.99030 0.745099
\(116\) 0 0
\(117\) 11.0185 1.01866
\(118\) 0 0
\(119\) −3.03126 −0.277875
\(120\) 0 0
\(121\) −10.9688 −0.997162
\(122\) 0 0
\(123\) 2.13649 0.192641
\(124\) 0 0
\(125\) −27.7564 −2.48261
\(126\) 0 0
\(127\) −17.4141 −1.54525 −0.772624 0.634864i \(-0.781056\pi\)
−0.772624 + 0.634864i \(0.781056\pi\)
\(128\) 0 0
\(129\) 7.97194 0.701890
\(130\) 0 0
\(131\) −13.4754 −1.17735 −0.588675 0.808370i \(-0.700350\pi\)
−0.588675 + 0.808370i \(0.700350\pi\)
\(132\) 0 0
\(133\) 4.14810 0.359686
\(134\) 0 0
\(135\) 22.0802 1.90036
\(136\) 0 0
\(137\) 7.07181 0.604186 0.302093 0.953279i \(-0.402315\pi\)
0.302093 + 0.953279i \(0.402315\pi\)
\(138\) 0 0
\(139\) 9.12679 0.774124 0.387062 0.922054i \(-0.373490\pi\)
0.387062 + 0.922054i \(0.373490\pi\)
\(140\) 0 0
\(141\) 0.630054 0.0530601
\(142\) 0 0
\(143\) 1.16978 0.0978221
\(144\) 0 0
\(145\) 19.6552 1.63227
\(146\) 0 0
\(147\) −7.64438 −0.630498
\(148\) 0 0
\(149\) 4.03604 0.330645 0.165322 0.986240i \(-0.447134\pi\)
0.165322 + 0.986240i \(0.447134\pi\)
\(150\) 0 0
\(151\) 17.1672 1.39705 0.698525 0.715585i \(-0.253840\pi\)
0.698525 + 0.715585i \(0.253840\pi\)
\(152\) 0 0
\(153\) 8.11901 0.656383
\(154\) 0 0
\(155\) −15.1970 −1.22065
\(156\) 0 0
\(157\) −12.9500 −1.03352 −0.516760 0.856130i \(-0.672862\pi\)
−0.516760 + 0.856130i \(0.672862\pi\)
\(158\) 0 0
\(159\) −4.97867 −0.394834
\(160\) 0 0
\(161\) −1.21205 −0.0955232
\(162\) 0 0
\(163\) −1.48780 −0.116533 −0.0582666 0.998301i \(-0.518557\pi\)
−0.0582666 + 0.998301i \(0.518557\pi\)
\(164\) 0 0
\(165\) 0.836382 0.0651123
\(166\) 0 0
\(167\) 18.1588 1.40517 0.702584 0.711600i \(-0.252029\pi\)
0.702584 + 0.711600i \(0.252029\pi\)
\(168\) 0 0
\(169\) 30.8393 2.37226
\(170\) 0 0
\(171\) −11.1104 −0.849632
\(172\) 0 0
\(173\) 1.60318 0.121888 0.0609439 0.998141i \(-0.480589\pi\)
0.0609439 + 0.998141i \(0.480589\pi\)
\(174\) 0 0
\(175\) 7.31695 0.553110
\(176\) 0 0
\(177\) −12.7705 −0.959890
\(178\) 0 0
\(179\) 6.35905 0.475298 0.237649 0.971351i \(-0.423623\pi\)
0.237649 + 0.971351i \(0.423623\pi\)
\(180\) 0 0
\(181\) −14.2799 −1.06142 −0.530709 0.847554i \(-0.678074\pi\)
−0.530709 + 0.847554i \(0.678074\pi\)
\(182\) 0 0
\(183\) −3.54103 −0.261760
\(184\) 0 0
\(185\) −25.4970 −1.87458
\(186\) 0 0
\(187\) 0.861956 0.0630325
\(188\) 0 0
\(189\) −3.34936 −0.243630
\(190\) 0 0
\(191\) 9.85686 0.713217 0.356609 0.934254i \(-0.383933\pi\)
0.356609 + 0.934254i \(0.383933\pi\)
\(192\) 0 0
\(193\) −24.8826 −1.79109 −0.895545 0.444971i \(-0.853214\pi\)
−0.895545 + 0.444971i \(0.853214\pi\)
\(194\) 0 0
\(195\) 31.3447 2.24464
\(196\) 0 0
\(197\) −2.59600 −0.184957 −0.0924787 0.995715i \(-0.529479\pi\)
−0.0924787 + 0.995715i \(0.529479\pi\)
\(198\) 0 0
\(199\) 14.1845 1.00551 0.502755 0.864429i \(-0.332320\pi\)
0.502755 + 0.864429i \(0.332320\pi\)
\(200\) 0 0
\(201\) 10.7396 0.757511
\(202\) 0 0
\(203\) −2.98151 −0.209261
\(204\) 0 0
\(205\) −7.57133 −0.528805
\(206\) 0 0
\(207\) 3.24640 0.225640
\(208\) 0 0
\(209\) −1.17954 −0.0815902
\(210\) 0 0
\(211\) −7.99464 −0.550374 −0.275187 0.961391i \(-0.588740\pi\)
−0.275187 + 0.961391i \(0.588740\pi\)
\(212\) 0 0
\(213\) 7.93467 0.543674
\(214\) 0 0
\(215\) −28.2511 −1.92671
\(216\) 0 0
\(217\) 2.30524 0.156490
\(218\) 0 0
\(219\) 5.88721 0.397821
\(220\) 0 0
\(221\) 32.3031 2.17294
\(222\) 0 0
\(223\) 0.532491 0.0356583 0.0178291 0.999841i \(-0.494325\pi\)
0.0178291 + 0.999841i \(0.494325\pi\)
\(224\) 0 0
\(225\) −19.5979 −1.30653
\(226\) 0 0
\(227\) −2.38209 −0.158105 −0.0790525 0.996870i \(-0.525189\pi\)
−0.0790525 + 0.996870i \(0.525189\pi\)
\(228\) 0 0
\(229\) −22.8726 −1.51146 −0.755732 0.654882i \(-0.772719\pi\)
−0.755732 + 0.654882i \(0.772719\pi\)
\(230\) 0 0
\(231\) −0.126871 −0.00834752
\(232\) 0 0
\(233\) 17.8670 1.17051 0.585253 0.810850i \(-0.300995\pi\)
0.585253 + 0.810850i \(0.300995\pi\)
\(234\) 0 0
\(235\) −2.23280 −0.145652
\(236\) 0 0
\(237\) 8.41525 0.546629
\(238\) 0 0
\(239\) 15.6266 1.01080 0.505401 0.862884i \(-0.331344\pi\)
0.505401 + 0.862884i \(0.331344\pi\)
\(240\) 0 0
\(241\) −5.48709 −0.353455 −0.176727 0.984260i \(-0.556551\pi\)
−0.176727 + 0.984260i \(0.556551\pi\)
\(242\) 0 0
\(243\) 14.7412 0.945651
\(244\) 0 0
\(245\) 27.0903 1.73074
\(246\) 0 0
\(247\) −44.2049 −2.81269
\(248\) 0 0
\(249\) 21.0298 1.33271
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 0.344655 0.0216683
\(254\) 0 0
\(255\) 23.0964 1.44635
\(256\) 0 0
\(257\) 8.10440 0.505538 0.252769 0.967527i \(-0.418659\pi\)
0.252769 + 0.967527i \(0.418659\pi\)
\(258\) 0 0
\(259\) 3.86766 0.240325
\(260\) 0 0
\(261\) 7.98575 0.494306
\(262\) 0 0
\(263\) 9.89980 0.610448 0.305224 0.952281i \(-0.401269\pi\)
0.305224 + 0.952281i \(0.401269\pi\)
\(264\) 0 0
\(265\) 17.6435 1.08383
\(266\) 0 0
\(267\) 17.8668 1.09343
\(268\) 0 0
\(269\) 11.7770 0.718054 0.359027 0.933327i \(-0.383109\pi\)
0.359027 + 0.933327i \(0.383109\pi\)
\(270\) 0 0
\(271\) 30.1836 1.83353 0.916763 0.399432i \(-0.130793\pi\)
0.916763 + 0.399432i \(0.130793\pi\)
\(272\) 0 0
\(273\) −4.75469 −0.287767
\(274\) 0 0
\(275\) −2.08062 −0.125466
\(276\) 0 0
\(277\) −30.7074 −1.84503 −0.922516 0.385960i \(-0.873870\pi\)
−0.922516 + 0.385960i \(0.873870\pi\)
\(278\) 0 0
\(279\) −6.17442 −0.369653
\(280\) 0 0
\(281\) 3.98785 0.237895 0.118948 0.992901i \(-0.462048\pi\)
0.118948 + 0.992901i \(0.462048\pi\)
\(282\) 0 0
\(283\) 26.9321 1.60095 0.800474 0.599368i \(-0.204581\pi\)
0.800474 + 0.599368i \(0.204581\pi\)
\(284\) 0 0
\(285\) −31.6060 −1.87218
\(286\) 0 0
\(287\) 1.14850 0.0677938
\(288\) 0 0
\(289\) 6.80261 0.400153
\(290\) 0 0
\(291\) 9.60113 0.562828
\(292\) 0 0
\(293\) 0.717962 0.0419438 0.0209719 0.999780i \(-0.493324\pi\)
0.0209719 + 0.999780i \(0.493324\pi\)
\(294\) 0 0
\(295\) 45.2564 2.63493
\(296\) 0 0
\(297\) 0.952412 0.0552646
\(298\) 0 0
\(299\) 12.9165 0.746978
\(300\) 0 0
\(301\) 4.28543 0.247008
\(302\) 0 0
\(303\) −11.0897 −0.637089
\(304\) 0 0
\(305\) 12.5488 0.718540
\(306\) 0 0
\(307\) −25.8617 −1.47600 −0.738001 0.674799i \(-0.764230\pi\)
−0.738001 + 0.674799i \(0.764230\pi\)
\(308\) 0 0
\(309\) −6.54125 −0.372119
\(310\) 0 0
\(311\) −8.54054 −0.484290 −0.242145 0.970240i \(-0.577851\pi\)
−0.242145 + 0.970240i \(0.577851\pi\)
\(312\) 0 0
\(313\) −5.77877 −0.326635 −0.163318 0.986574i \(-0.552220\pi\)
−0.163318 + 0.986574i \(0.552220\pi\)
\(314\) 0 0
\(315\) 4.23500 0.238615
\(316\) 0 0
\(317\) 15.7025 0.881941 0.440970 0.897522i \(-0.354634\pi\)
0.440970 + 0.897522i \(0.354634\pi\)
\(318\) 0 0
\(319\) 0.847810 0.0474682
\(320\) 0 0
\(321\) −18.1647 −1.01386
\(322\) 0 0
\(323\) −32.5724 −1.81238
\(324\) 0 0
\(325\) −77.9743 −4.32524
\(326\) 0 0
\(327\) 16.1000 0.890332
\(328\) 0 0
\(329\) 0.338695 0.0186728
\(330\) 0 0
\(331\) 31.5004 1.73142 0.865709 0.500548i \(-0.166868\pi\)
0.865709 + 0.500548i \(0.166868\pi\)
\(332\) 0 0
\(333\) −10.3593 −0.567684
\(334\) 0 0
\(335\) −38.0591 −2.07939
\(336\) 0 0
\(337\) 28.5754 1.55660 0.778300 0.627893i \(-0.216082\pi\)
0.778300 + 0.627893i \(0.216082\pi\)
\(338\) 0 0
\(339\) 13.4833 0.732315
\(340\) 0 0
\(341\) −0.655509 −0.0354978
\(342\) 0 0
\(343\) −8.45854 −0.456718
\(344\) 0 0
\(345\) 9.23513 0.497203
\(346\) 0 0
\(347\) 9.66818 0.519015 0.259507 0.965741i \(-0.416440\pi\)
0.259507 + 0.965741i \(0.416440\pi\)
\(348\) 0 0
\(349\) −20.4603 −1.09522 −0.547608 0.836735i \(-0.684462\pi\)
−0.547608 + 0.836735i \(0.684462\pi\)
\(350\) 0 0
\(351\) 35.6931 1.90515
\(352\) 0 0
\(353\) −28.3991 −1.51153 −0.755767 0.654841i \(-0.772736\pi\)
−0.755767 + 0.654841i \(0.772736\pi\)
\(354\) 0 0
\(355\) −28.1190 −1.49240
\(356\) 0 0
\(357\) −3.50351 −0.185425
\(358\) 0 0
\(359\) −13.2598 −0.699827 −0.349914 0.936782i \(-0.613789\pi\)
−0.349914 + 0.936782i \(0.613789\pi\)
\(360\) 0 0
\(361\) 25.5735 1.34597
\(362\) 0 0
\(363\) −12.6776 −0.665404
\(364\) 0 0
\(365\) −20.8632 −1.09203
\(366\) 0 0
\(367\) 8.13315 0.424547 0.212273 0.977210i \(-0.431913\pi\)
0.212273 + 0.977210i \(0.431913\pi\)
\(368\) 0 0
\(369\) −3.07617 −0.160139
\(370\) 0 0
\(371\) −2.67636 −0.138950
\(372\) 0 0
\(373\) 4.63673 0.240081 0.120040 0.992769i \(-0.461698\pi\)
0.120040 + 0.992769i \(0.461698\pi\)
\(374\) 0 0
\(375\) −32.0806 −1.65664
\(376\) 0 0
\(377\) 31.7729 1.63639
\(378\) 0 0
\(379\) 4.92306 0.252881 0.126440 0.991974i \(-0.459645\pi\)
0.126440 + 0.991974i \(0.459645\pi\)
\(380\) 0 0
\(381\) −20.1271 −1.03114
\(382\) 0 0
\(383\) −30.8916 −1.57849 −0.789244 0.614080i \(-0.789527\pi\)
−0.789244 + 0.614080i \(0.789527\pi\)
\(384\) 0 0
\(385\) 0.449610 0.0229142
\(386\) 0 0
\(387\) −11.4782 −0.583471
\(388\) 0 0
\(389\) 28.8261 1.46154 0.730770 0.682624i \(-0.239161\pi\)
0.730770 + 0.682624i \(0.239161\pi\)
\(390\) 0 0
\(391\) 9.51751 0.481321
\(392\) 0 0
\(393\) −15.5748 −0.785642
\(394\) 0 0
\(395\) −29.8221 −1.50051
\(396\) 0 0
\(397\) −13.2631 −0.665654 −0.332827 0.942988i \(-0.608003\pi\)
−0.332827 + 0.942988i \(0.608003\pi\)
\(398\) 0 0
\(399\) 4.79434 0.240017
\(400\) 0 0
\(401\) −10.2827 −0.513495 −0.256748 0.966478i \(-0.582651\pi\)
−0.256748 + 0.966478i \(0.582651\pi\)
\(402\) 0 0
\(403\) −24.5662 −1.22373
\(404\) 0 0
\(405\) 5.07158 0.252009
\(406\) 0 0
\(407\) −1.09979 −0.0545147
\(408\) 0 0
\(409\) −2.97111 −0.146912 −0.0734559 0.997298i \(-0.523403\pi\)
−0.0734559 + 0.997298i \(0.523403\pi\)
\(410\) 0 0
\(411\) 8.17355 0.403172
\(412\) 0 0
\(413\) −6.86497 −0.337803
\(414\) 0 0
\(415\) −74.5258 −3.65833
\(416\) 0 0
\(417\) 10.5487 0.516571
\(418\) 0 0
\(419\) 0.443124 0.0216480 0.0108240 0.999941i \(-0.496555\pi\)
0.0108240 + 0.999941i \(0.496555\pi\)
\(420\) 0 0
\(421\) 14.7536 0.719045 0.359522 0.933136i \(-0.382940\pi\)
0.359522 + 0.933136i \(0.382940\pi\)
\(422\) 0 0
\(423\) −0.907170 −0.0441081
\(424\) 0 0
\(425\) −57.4555 −2.78700
\(426\) 0 0
\(427\) −1.90353 −0.0921183
\(428\) 0 0
\(429\) 1.35203 0.0652764
\(430\) 0 0
\(431\) 15.6553 0.754091 0.377045 0.926195i \(-0.376940\pi\)
0.377045 + 0.926195i \(0.376940\pi\)
\(432\) 0 0
\(433\) 35.6406 1.71278 0.856388 0.516332i \(-0.172703\pi\)
0.856388 + 0.516332i \(0.172703\pi\)
\(434\) 0 0
\(435\) 22.7173 1.08921
\(436\) 0 0
\(437\) −13.0242 −0.623030
\(438\) 0 0
\(439\) −8.10726 −0.386938 −0.193469 0.981106i \(-0.561974\pi\)
−0.193469 + 0.981106i \(0.561974\pi\)
\(440\) 0 0
\(441\) 11.0066 0.524123
\(442\) 0 0
\(443\) −22.3263 −1.06076 −0.530378 0.847761i \(-0.677950\pi\)
−0.530378 + 0.847761i \(0.677950\pi\)
\(444\) 0 0
\(445\) −63.3168 −3.00150
\(446\) 0 0
\(447\) 4.66482 0.220639
\(448\) 0 0
\(449\) −10.9038 −0.514582 −0.257291 0.966334i \(-0.582830\pi\)
−0.257291 + 0.966334i \(0.582830\pi\)
\(450\) 0 0
\(451\) −0.326583 −0.0153782
\(452\) 0 0
\(453\) 19.8418 0.932248
\(454\) 0 0
\(455\) 16.8498 0.789930
\(456\) 0 0
\(457\) −17.4789 −0.817629 −0.408814 0.912618i \(-0.634058\pi\)
−0.408814 + 0.912618i \(0.634058\pi\)
\(458\) 0 0
\(459\) 26.3005 1.22760
\(460\) 0 0
\(461\) −6.16799 −0.287272 −0.143636 0.989631i \(-0.545879\pi\)
−0.143636 + 0.989631i \(0.545879\pi\)
\(462\) 0 0
\(463\) 12.6042 0.585768 0.292884 0.956148i \(-0.405385\pi\)
0.292884 + 0.956148i \(0.405385\pi\)
\(464\) 0 0
\(465\) −17.5646 −0.814538
\(466\) 0 0
\(467\) −33.8888 −1.56819 −0.784093 0.620643i \(-0.786871\pi\)
−0.784093 + 0.620643i \(0.786871\pi\)
\(468\) 0 0
\(469\) 5.77321 0.266582
\(470\) 0 0
\(471\) −14.9675 −0.689665
\(472\) 0 0
\(473\) −1.21859 −0.0560307
\(474\) 0 0
\(475\) 78.6245 3.60754
\(476\) 0 0
\(477\) 7.16843 0.328220
\(478\) 0 0
\(479\) 41.2752 1.88591 0.942956 0.332917i \(-0.108033\pi\)
0.942956 + 0.332917i \(0.108033\pi\)
\(480\) 0 0
\(481\) −41.2164 −1.87931
\(482\) 0 0
\(483\) −1.40088 −0.0637424
\(484\) 0 0
\(485\) −34.0247 −1.54498
\(486\) 0 0
\(487\) −26.0800 −1.18180 −0.590898 0.806746i \(-0.701227\pi\)
−0.590898 + 0.806746i \(0.701227\pi\)
\(488\) 0 0
\(489\) −1.71958 −0.0777623
\(490\) 0 0
\(491\) −8.95179 −0.403989 −0.201994 0.979387i \(-0.564742\pi\)
−0.201994 + 0.979387i \(0.564742\pi\)
\(492\) 0 0
\(493\) 23.4120 1.05442
\(494\) 0 0
\(495\) −1.20425 −0.0541269
\(496\) 0 0
\(497\) 4.26539 0.191329
\(498\) 0 0
\(499\) 2.94870 0.132002 0.0660010 0.997820i \(-0.478976\pi\)
0.0660010 + 0.997820i \(0.478976\pi\)
\(500\) 0 0
\(501\) 20.9878 0.937666
\(502\) 0 0
\(503\) −4.04092 −0.180176 −0.0900878 0.995934i \(-0.528715\pi\)
−0.0900878 + 0.995934i \(0.528715\pi\)
\(504\) 0 0
\(505\) 39.3001 1.74883
\(506\) 0 0
\(507\) 35.6439 1.58300
\(508\) 0 0
\(509\) −10.0547 −0.445667 −0.222834 0.974856i \(-0.571531\pi\)
−0.222834 + 0.974856i \(0.571531\pi\)
\(510\) 0 0
\(511\) 3.16475 0.140000
\(512\) 0 0
\(513\) −35.9907 −1.58903
\(514\) 0 0
\(515\) 23.1810 1.02148
\(516\) 0 0
\(517\) −0.0963099 −0.00423570
\(518\) 0 0
\(519\) 1.85295 0.0813354
\(520\) 0 0
\(521\) −14.1483 −0.619850 −0.309925 0.950761i \(-0.600304\pi\)
−0.309925 + 0.950761i \(0.600304\pi\)
\(522\) 0 0
\(523\) 44.6455 1.95221 0.976106 0.217295i \(-0.0697234\pi\)
0.976106 + 0.217295i \(0.0697234\pi\)
\(524\) 0 0
\(525\) 8.45688 0.369089
\(526\) 0 0
\(527\) −18.1016 −0.788520
\(528\) 0 0
\(529\) −19.1944 −0.834539
\(530\) 0 0
\(531\) 18.3873 0.797942
\(532\) 0 0
\(533\) −12.2392 −0.530138
\(534\) 0 0
\(535\) 64.3726 2.78307
\(536\) 0 0
\(537\) 7.34975 0.317165
\(538\) 0 0
\(539\) 1.16852 0.0503316
\(540\) 0 0
\(541\) 42.6957 1.83563 0.917816 0.397005i \(-0.129951\pi\)
0.917816 + 0.397005i \(0.129951\pi\)
\(542\) 0 0
\(543\) −16.5046 −0.708281
\(544\) 0 0
\(545\) −57.0555 −2.44399
\(546\) 0 0
\(547\) −37.3069 −1.59513 −0.797563 0.603235i \(-0.793878\pi\)
−0.797563 + 0.603235i \(0.793878\pi\)
\(548\) 0 0
\(549\) 5.09847 0.217597
\(550\) 0 0
\(551\) −32.0379 −1.36486
\(552\) 0 0
\(553\) 4.52374 0.192369
\(554\) 0 0
\(555\) −29.4693 −1.25090
\(556\) 0 0
\(557\) −6.47875 −0.274514 −0.137257 0.990536i \(-0.543829\pi\)
−0.137257 + 0.990536i \(0.543829\pi\)
\(558\) 0 0
\(559\) −45.6684 −1.93157
\(560\) 0 0
\(561\) 0.996243 0.0420614
\(562\) 0 0
\(563\) −1.47270 −0.0620671 −0.0310335 0.999518i \(-0.509880\pi\)
−0.0310335 + 0.999518i \(0.509880\pi\)
\(564\) 0 0
\(565\) −47.7826 −2.01023
\(566\) 0 0
\(567\) −0.769311 −0.0323080
\(568\) 0 0
\(569\) −30.0094 −1.25806 −0.629030 0.777381i \(-0.716548\pi\)
−0.629030 + 0.777381i \(0.716548\pi\)
\(570\) 0 0
\(571\) 33.9014 1.41873 0.709366 0.704841i \(-0.248981\pi\)
0.709366 + 0.704841i \(0.248981\pi\)
\(572\) 0 0
\(573\) 11.3925 0.475928
\(574\) 0 0
\(575\) −22.9737 −0.958069
\(576\) 0 0
\(577\) 26.4242 1.10005 0.550027 0.835147i \(-0.314618\pi\)
0.550027 + 0.835147i \(0.314618\pi\)
\(578\) 0 0
\(579\) −28.7592 −1.19519
\(580\) 0 0
\(581\) 11.3049 0.469005
\(582\) 0 0
\(583\) 0.761038 0.0315190
\(584\) 0 0
\(585\) −45.1309 −1.86593
\(586\) 0 0
\(587\) 31.1846 1.28713 0.643563 0.765393i \(-0.277455\pi\)
0.643563 + 0.765393i \(0.277455\pi\)
\(588\) 0 0
\(589\) 24.7710 1.02067
\(590\) 0 0
\(591\) −3.00044 −0.123422
\(592\) 0 0
\(593\) 10.9552 0.449875 0.224938 0.974373i \(-0.427782\pi\)
0.224938 + 0.974373i \(0.427782\pi\)
\(594\) 0 0
\(595\) 12.4158 0.508998
\(596\) 0 0
\(597\) 16.3943 0.670974
\(598\) 0 0
\(599\) −34.2254 −1.39841 −0.699206 0.714920i \(-0.746463\pi\)
−0.699206 + 0.714920i \(0.746463\pi\)
\(600\) 0 0
\(601\) 13.0090 0.530647 0.265323 0.964159i \(-0.414521\pi\)
0.265323 + 0.964159i \(0.414521\pi\)
\(602\) 0 0
\(603\) −15.4631 −0.629708
\(604\) 0 0
\(605\) 44.9273 1.82655
\(606\) 0 0
\(607\) 0.895769 0.0363581 0.0181791 0.999835i \(-0.494213\pi\)
0.0181791 + 0.999835i \(0.494213\pi\)
\(608\) 0 0
\(609\) −3.44601 −0.139639
\(610\) 0 0
\(611\) −3.60936 −0.146019
\(612\) 0 0
\(613\) 16.1728 0.653212 0.326606 0.945161i \(-0.394095\pi\)
0.326606 + 0.945161i \(0.394095\pi\)
\(614\) 0 0
\(615\) −8.75089 −0.352870
\(616\) 0 0
\(617\) 13.5442 0.545267 0.272633 0.962118i \(-0.412105\pi\)
0.272633 + 0.962118i \(0.412105\pi\)
\(618\) 0 0
\(619\) 7.95361 0.319683 0.159841 0.987143i \(-0.448902\pi\)
0.159841 + 0.987143i \(0.448902\pi\)
\(620\) 0 0
\(621\) 10.5163 0.422005
\(622\) 0 0
\(623\) 9.60456 0.384799
\(624\) 0 0
\(625\) 54.8051 2.19220
\(626\) 0 0
\(627\) −1.36330 −0.0544449
\(628\) 0 0
\(629\) −30.3704 −1.21095
\(630\) 0 0
\(631\) 28.8274 1.14760 0.573800 0.818995i \(-0.305469\pi\)
0.573800 + 0.818995i \(0.305469\pi\)
\(632\) 0 0
\(633\) −9.24015 −0.367263
\(634\) 0 0
\(635\) 71.3267 2.83051
\(636\) 0 0
\(637\) 43.7919 1.73510
\(638\) 0 0
\(639\) −11.4246 −0.451948
\(640\) 0 0
\(641\) 39.1175 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(642\) 0 0
\(643\) 6.17610 0.243562 0.121781 0.992557i \(-0.461139\pi\)
0.121781 + 0.992557i \(0.461139\pi\)
\(644\) 0 0
\(645\) −32.6525 −1.28569
\(646\) 0 0
\(647\) 4.77971 0.187910 0.0939548 0.995576i \(-0.470049\pi\)
0.0939548 + 0.995576i \(0.470049\pi\)
\(648\) 0 0
\(649\) 1.95210 0.0766265
\(650\) 0 0
\(651\) 2.66438 0.104425
\(652\) 0 0
\(653\) −12.9339 −0.506144 −0.253072 0.967447i \(-0.581441\pi\)
−0.253072 + 0.967447i \(0.581441\pi\)
\(654\) 0 0
\(655\) 55.1941 2.15661
\(656\) 0 0
\(657\) −8.47657 −0.330702
\(658\) 0 0
\(659\) 29.6390 1.15457 0.577285 0.816543i \(-0.304112\pi\)
0.577285 + 0.816543i \(0.304112\pi\)
\(660\) 0 0
\(661\) 36.1729 1.40696 0.703481 0.710714i \(-0.251628\pi\)
0.703481 + 0.710714i \(0.251628\pi\)
\(662\) 0 0
\(663\) 37.3357 1.45000
\(664\) 0 0
\(665\) −16.9903 −0.658855
\(666\) 0 0
\(667\) 9.36131 0.362471
\(668\) 0 0
\(669\) 0.615450 0.0237947
\(670\) 0 0
\(671\) 0.541280 0.0208959
\(672\) 0 0
\(673\) −7.81880 −0.301393 −0.150696 0.988580i \(-0.548152\pi\)
−0.150696 + 0.988580i \(0.548152\pi\)
\(674\) 0 0
\(675\) −63.4850 −2.44354
\(676\) 0 0
\(677\) −3.61795 −0.139049 −0.0695245 0.997580i \(-0.522148\pi\)
−0.0695245 + 0.997580i \(0.522148\pi\)
\(678\) 0 0
\(679\) 5.16123 0.198070
\(680\) 0 0
\(681\) −2.75321 −0.105503
\(682\) 0 0
\(683\) 1.68227 0.0643704 0.0321852 0.999482i \(-0.489753\pi\)
0.0321852 + 0.999482i \(0.489753\pi\)
\(684\) 0 0
\(685\) −28.9656 −1.10672
\(686\) 0 0
\(687\) −26.4360 −1.00860
\(688\) 0 0
\(689\) 28.5210 1.08657
\(690\) 0 0
\(691\) −39.8337 −1.51534 −0.757672 0.652635i \(-0.773663\pi\)
−0.757672 + 0.652635i \(0.773663\pi\)
\(692\) 0 0
\(693\) 0.182673 0.00693917
\(694\) 0 0
\(695\) −37.3826 −1.41800
\(696\) 0 0
\(697\) −9.01846 −0.341599
\(698\) 0 0
\(699\) 20.6506 0.781076
\(700\) 0 0
\(701\) −1.65966 −0.0626845 −0.0313423 0.999509i \(-0.509978\pi\)
−0.0313423 + 0.999509i \(0.509978\pi\)
\(702\) 0 0
\(703\) 41.5601 1.56747
\(704\) 0 0
\(705\) −2.58065 −0.0971931
\(706\) 0 0
\(707\) −5.96145 −0.224204
\(708\) 0 0
\(709\) 19.3607 0.727105 0.363552 0.931574i \(-0.381564\pi\)
0.363552 + 0.931574i \(0.381564\pi\)
\(710\) 0 0
\(711\) −12.1165 −0.454405
\(712\) 0 0
\(713\) −7.23798 −0.271064
\(714\) 0 0
\(715\) −4.79134 −0.179186
\(716\) 0 0
\(717\) 18.0612 0.674506
\(718\) 0 0
\(719\) −17.7607 −0.662363 −0.331181 0.943567i \(-0.607447\pi\)
−0.331181 + 0.943567i \(0.607447\pi\)
\(720\) 0 0
\(721\) −3.51635 −0.130956
\(722\) 0 0
\(723\) −6.34194 −0.235859
\(724\) 0 0
\(725\) −56.5126 −2.09882
\(726\) 0 0
\(727\) −29.3612 −1.08895 −0.544473 0.838779i \(-0.683270\pi\)
−0.544473 + 0.838779i \(0.683270\pi\)
\(728\) 0 0
\(729\) 20.7524 0.768609
\(730\) 0 0
\(731\) −33.6509 −1.24462
\(732\) 0 0
\(733\) −27.9740 −1.03324 −0.516622 0.856214i \(-0.672811\pi\)
−0.516622 + 0.856214i \(0.672811\pi\)
\(734\) 0 0
\(735\) 31.3108 1.15492
\(736\) 0 0
\(737\) −1.64165 −0.0604709
\(738\) 0 0
\(739\) −3.94807 −0.145232 −0.0726160 0.997360i \(-0.523135\pi\)
−0.0726160 + 0.997360i \(0.523135\pi\)
\(740\) 0 0
\(741\) −51.0917 −1.87690
\(742\) 0 0
\(743\) −12.8304 −0.470701 −0.235351 0.971911i \(-0.575624\pi\)
−0.235351 + 0.971911i \(0.575624\pi\)
\(744\) 0 0
\(745\) −16.5313 −0.605660
\(746\) 0 0
\(747\) −30.2793 −1.10786
\(748\) 0 0
\(749\) −9.76472 −0.356795
\(750\) 0 0
\(751\) 10.6222 0.387611 0.193805 0.981040i \(-0.437917\pi\)
0.193805 + 0.981040i \(0.437917\pi\)
\(752\) 0 0
\(753\) 1.15579 0.0421194
\(754\) 0 0
\(755\) −70.3157 −2.55905
\(756\) 0 0
\(757\) 2.07752 0.0755086 0.0377543 0.999287i \(-0.487980\pi\)
0.0377543 + 0.999287i \(0.487980\pi\)
\(758\) 0 0
\(759\) 0.398350 0.0144592
\(760\) 0 0
\(761\) 0.610314 0.0221239 0.0110619 0.999939i \(-0.496479\pi\)
0.0110619 + 0.999939i \(0.496479\pi\)
\(762\) 0 0
\(763\) 8.65479 0.313324
\(764\) 0 0
\(765\) −33.2548 −1.20233
\(766\) 0 0
\(767\) 73.1577 2.64157
\(768\) 0 0
\(769\) 42.9945 1.55042 0.775210 0.631704i \(-0.217644\pi\)
0.775210 + 0.631704i \(0.217644\pi\)
\(770\) 0 0
\(771\) 9.36701 0.337344
\(772\) 0 0
\(773\) 28.3483 1.01962 0.509809 0.860288i \(-0.329716\pi\)
0.509809 + 0.860288i \(0.329716\pi\)
\(774\) 0 0
\(775\) 43.6944 1.56955
\(776\) 0 0
\(777\) 4.47022 0.160368
\(778\) 0 0
\(779\) 12.3412 0.442170
\(780\) 0 0
\(781\) −1.21289 −0.0434006
\(782\) 0 0
\(783\) 25.8689 0.924478
\(784\) 0 0
\(785\) 53.0421 1.89315
\(786\) 0 0
\(787\) −38.3435 −1.36680 −0.683399 0.730045i \(-0.739499\pi\)
−0.683399 + 0.730045i \(0.739499\pi\)
\(788\) 0 0
\(789\) 11.4421 0.407350
\(790\) 0 0
\(791\) 7.24817 0.257715
\(792\) 0 0
\(793\) 20.2853 0.720351
\(794\) 0 0
\(795\) 20.3923 0.723239
\(796\) 0 0
\(797\) 7.48153 0.265010 0.132505 0.991182i \(-0.457698\pi\)
0.132505 + 0.991182i \(0.457698\pi\)
\(798\) 0 0
\(799\) −2.65956 −0.0940886
\(800\) 0 0
\(801\) −25.7251 −0.908953
\(802\) 0 0
\(803\) −0.899917 −0.0317574
\(804\) 0 0
\(805\) 4.96448 0.174975
\(806\) 0 0
\(807\) 13.6117 0.479156
\(808\) 0 0
\(809\) 34.6803 1.21929 0.609646 0.792674i \(-0.291311\pi\)
0.609646 + 0.792674i \(0.291311\pi\)
\(810\) 0 0
\(811\) −39.0793 −1.37226 −0.686130 0.727479i \(-0.740692\pi\)
−0.686130 + 0.727479i \(0.740692\pi\)
\(812\) 0 0
\(813\) 34.8860 1.22351
\(814\) 0 0
\(815\) 6.09390 0.213460
\(816\) 0 0
\(817\) 46.0492 1.61106
\(818\) 0 0
\(819\) 6.84594 0.239217
\(820\) 0 0
\(821\) −22.7662 −0.794545 −0.397273 0.917701i \(-0.630043\pi\)
−0.397273 + 0.917701i \(0.630043\pi\)
\(822\) 0 0
\(823\) −20.9505 −0.730289 −0.365145 0.930951i \(-0.618980\pi\)
−0.365145 + 0.930951i \(0.618980\pi\)
\(824\) 0 0
\(825\) −2.40476 −0.0837232
\(826\) 0 0
\(827\) −7.80711 −0.271480 −0.135740 0.990744i \(-0.543341\pi\)
−0.135740 + 0.990744i \(0.543341\pi\)
\(828\) 0 0
\(829\) −35.4966 −1.23285 −0.616423 0.787415i \(-0.711419\pi\)
−0.616423 + 0.787415i \(0.711419\pi\)
\(830\) 0 0
\(831\) −35.4914 −1.23118
\(832\) 0 0
\(833\) 32.2682 1.11803
\(834\) 0 0
\(835\) −74.3770 −2.57392
\(836\) 0 0
\(837\) −20.0013 −0.691345
\(838\) 0 0
\(839\) 28.3734 0.979559 0.489780 0.871846i \(-0.337077\pi\)
0.489780 + 0.871846i \(0.337077\pi\)
\(840\) 0 0
\(841\) −5.97228 −0.205941
\(842\) 0 0
\(843\) 4.60913 0.158747
\(844\) 0 0
\(845\) −126.316 −4.34539
\(846\) 0 0
\(847\) −6.81505 −0.234168
\(848\) 0 0
\(849\) 31.1279 1.06831
\(850\) 0 0
\(851\) −12.1437 −0.416279
\(852\) 0 0
\(853\) 49.0270 1.67865 0.839326 0.543628i \(-0.182950\pi\)
0.839326 + 0.543628i \(0.182950\pi\)
\(854\) 0 0
\(855\) 45.5072 1.55632
\(856\) 0 0
\(857\) −32.1040 −1.09665 −0.548325 0.836265i \(-0.684734\pi\)
−0.548325 + 0.836265i \(0.684734\pi\)
\(858\) 0 0
\(859\) −8.31632 −0.283749 −0.141875 0.989885i \(-0.545313\pi\)
−0.141875 + 0.989885i \(0.545313\pi\)
\(860\) 0 0
\(861\) 1.32743 0.0452386
\(862\) 0 0
\(863\) −46.7903 −1.59276 −0.796380 0.604796i \(-0.793255\pi\)
−0.796380 + 0.604796i \(0.793255\pi\)
\(864\) 0 0
\(865\) −6.56652 −0.223268
\(866\) 0 0
\(867\) 7.86240 0.267021
\(868\) 0 0
\(869\) −1.28635 −0.0436365
\(870\) 0 0
\(871\) −61.5232 −2.08463
\(872\) 0 0
\(873\) −13.8240 −0.467871
\(874\) 0 0
\(875\) −17.2454 −0.583001
\(876\) 0 0
\(877\) 17.5910 0.594007 0.297004 0.954876i \(-0.404013\pi\)
0.297004 + 0.954876i \(0.404013\pi\)
\(878\) 0 0
\(879\) 0.829815 0.0279890
\(880\) 0 0
\(881\) −42.9312 −1.44639 −0.723195 0.690644i \(-0.757327\pi\)
−0.723195 + 0.690644i \(0.757327\pi\)
\(882\) 0 0
\(883\) 16.2432 0.546628 0.273314 0.961925i \(-0.411880\pi\)
0.273314 + 0.961925i \(0.411880\pi\)
\(884\) 0 0
\(885\) 52.3070 1.75828
\(886\) 0 0
\(887\) 27.1735 0.912398 0.456199 0.889878i \(-0.349210\pi\)
0.456199 + 0.889878i \(0.349210\pi\)
\(888\) 0 0
\(889\) −10.8196 −0.362877
\(890\) 0 0
\(891\) 0.218758 0.00732867
\(892\) 0 0
\(893\) 3.63945 0.121790
\(894\) 0 0
\(895\) −26.0462 −0.870628
\(896\) 0 0
\(897\) 14.9287 0.498456
\(898\) 0 0
\(899\) −17.8046 −0.593815
\(900\) 0 0
\(901\) 21.0158 0.700138
\(902\) 0 0
\(903\) 4.95307 0.164828
\(904\) 0 0
\(905\) 58.4894 1.94425
\(906\) 0 0
\(907\) 32.4060 1.07602 0.538011 0.842938i \(-0.319176\pi\)
0.538011 + 0.842938i \(0.319176\pi\)
\(908\) 0 0
\(909\) 15.9673 0.529603
\(910\) 0 0
\(911\) −22.2655 −0.737688 −0.368844 0.929491i \(-0.620246\pi\)
−0.368844 + 0.929491i \(0.620246\pi\)
\(912\) 0 0
\(913\) −3.21461 −0.106388
\(914\) 0 0
\(915\) 14.5038 0.479480
\(916\) 0 0
\(917\) −8.37244 −0.276482
\(918\) 0 0
\(919\) 53.9357 1.77918 0.889588 0.456764i \(-0.150992\pi\)
0.889588 + 0.456764i \(0.150992\pi\)
\(920\) 0 0
\(921\) −29.8907 −0.984933
\(922\) 0 0
\(923\) −45.4549 −1.49617
\(924\) 0 0
\(925\) 73.3090 2.41039
\(926\) 0 0
\(927\) 9.41828 0.309337
\(928\) 0 0
\(929\) 30.0362 0.985456 0.492728 0.870183i \(-0.336000\pi\)
0.492728 + 0.870183i \(0.336000\pi\)
\(930\) 0 0
\(931\) −44.1571 −1.44719
\(932\) 0 0
\(933\) −9.87110 −0.323165
\(934\) 0 0
\(935\) −3.53051 −0.115460
\(936\) 0 0
\(937\) 4.90313 0.160178 0.0800892 0.996788i \(-0.474479\pi\)
0.0800892 + 0.996788i \(0.474479\pi\)
\(938\) 0 0
\(939\) −6.67906 −0.217963
\(940\) 0 0
\(941\) −34.8436 −1.13587 −0.567934 0.823074i \(-0.692257\pi\)
−0.567934 + 0.823074i \(0.692257\pi\)
\(942\) 0 0
\(943\) −3.60605 −0.117429
\(944\) 0 0
\(945\) 13.7187 0.446271
\(946\) 0 0
\(947\) −53.9666 −1.75368 −0.876840 0.480782i \(-0.840353\pi\)
−0.876840 + 0.480782i \(0.840353\pi\)
\(948\) 0 0
\(949\) −33.7257 −1.09478
\(950\) 0 0
\(951\) 18.1489 0.588517
\(952\) 0 0
\(953\) 17.8743 0.579005 0.289502 0.957177i \(-0.406510\pi\)
0.289502 + 0.957177i \(0.406510\pi\)
\(954\) 0 0
\(955\) −40.3729 −1.30644
\(956\) 0 0
\(957\) 0.979893 0.0316754
\(958\) 0 0
\(959\) 4.39381 0.141884
\(960\) 0 0
\(961\) −17.2339 −0.555931
\(962\) 0 0
\(963\) 26.1541 0.842804
\(964\) 0 0
\(965\) 101.917 3.28083
\(966\) 0 0
\(967\) 28.2898 0.909739 0.454869 0.890558i \(-0.349686\pi\)
0.454869 + 0.890558i \(0.349686\pi\)
\(968\) 0 0
\(969\) −37.6470 −1.20940
\(970\) 0 0
\(971\) 11.5535 0.370770 0.185385 0.982666i \(-0.440647\pi\)
0.185385 + 0.982666i \(0.440647\pi\)
\(972\) 0 0
\(973\) 5.67060 0.181791
\(974\) 0 0
\(975\) −90.1221 −2.88622
\(976\) 0 0
\(977\) −27.3097 −0.873714 −0.436857 0.899531i \(-0.643908\pi\)
−0.436857 + 0.899531i \(0.643908\pi\)
\(978\) 0 0
\(979\) −2.73112 −0.0872868
\(980\) 0 0
\(981\) −23.1812 −0.740119
\(982\) 0 0
\(983\) −5.50331 −0.175528 −0.0877641 0.996141i \(-0.527972\pi\)
−0.0877641 + 0.996141i \(0.527972\pi\)
\(984\) 0 0
\(985\) 10.6330 0.338796
\(986\) 0 0
\(987\) 0.391461 0.0124603
\(988\) 0 0
\(989\) −13.4554 −0.427855
\(990\) 0 0
\(991\) 22.3080 0.708636 0.354318 0.935125i \(-0.384713\pi\)
0.354318 + 0.935125i \(0.384713\pi\)
\(992\) 0 0
\(993\) 36.4079 1.15537
\(994\) 0 0
\(995\) −58.0985 −1.84184
\(996\) 0 0
\(997\) −1.01117 −0.0320240 −0.0160120 0.999872i \(-0.505097\pi\)
−0.0160120 + 0.999872i \(0.505097\pi\)
\(998\) 0 0
\(999\) −33.5575 −1.06171
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.1.15 23
4.3 odd 2 2008.2.a.d.1.9 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.9 23 4.3 odd 2
4016.2.a.m.1.15 23 1.1 even 1 trivial