Properties

Label 6008.2.a.b.1.4
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 1.4
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.18197 q^{3} -2.41204 q^{5} +2.14400 q^{7} +7.12495 q^{9} +O(q^{10})\) \(q-3.18197 q^{3} -2.41204 q^{5} +2.14400 q^{7} +7.12495 q^{9} +4.27932 q^{11} +6.04339 q^{13} +7.67503 q^{15} -4.10147 q^{17} -5.68811 q^{19} -6.82215 q^{21} -7.79317 q^{23} +0.817913 q^{25} -13.1255 q^{27} +4.70794 q^{29} +2.59911 q^{31} -13.6167 q^{33} -5.17141 q^{35} -9.09774 q^{37} -19.2299 q^{39} +0.788241 q^{41} +8.65874 q^{43} -17.1856 q^{45} -3.21353 q^{47} -2.40326 q^{49} +13.0508 q^{51} +14.2957 q^{53} -10.3219 q^{55} +18.0994 q^{57} +1.45990 q^{59} -3.31142 q^{61} +15.2759 q^{63} -14.5769 q^{65} -8.27604 q^{67} +24.7976 q^{69} +6.59994 q^{71} -8.46722 q^{73} -2.60258 q^{75} +9.17487 q^{77} -5.68149 q^{79} +20.3900 q^{81} -2.17621 q^{83} +9.89289 q^{85} -14.9805 q^{87} -3.16790 q^{89} +12.9570 q^{91} -8.27031 q^{93} +13.7199 q^{95} +13.7492 q^{97} +30.4899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −3.18197 −1.83711 −0.918556 0.395290i \(-0.870644\pi\)
−0.918556 + 0.395290i \(0.870644\pi\)
\(4\) 0 0
\(5\) −2.41204 −1.07869 −0.539347 0.842083i \(-0.681329\pi\)
−0.539347 + 0.842083i \(0.681329\pi\)
\(6\) 0 0
\(7\) 2.14400 0.810356 0.405178 0.914238i \(-0.367209\pi\)
0.405178 + 0.914238i \(0.367209\pi\)
\(8\) 0 0
\(9\) 7.12495 2.37498
\(10\) 0 0
\(11\) 4.27932 1.29026 0.645132 0.764071i \(-0.276802\pi\)
0.645132 + 0.764071i \(0.276802\pi\)
\(12\) 0 0
\(13\) 6.04339 1.67613 0.838067 0.545567i \(-0.183686\pi\)
0.838067 + 0.545567i \(0.183686\pi\)
\(14\) 0 0
\(15\) 7.67503 1.98168
\(16\) 0 0
\(17\) −4.10147 −0.994753 −0.497376 0.867535i \(-0.665703\pi\)
−0.497376 + 0.867535i \(0.665703\pi\)
\(18\) 0 0
\(19\) −5.68811 −1.30494 −0.652471 0.757814i \(-0.726268\pi\)
−0.652471 + 0.757814i \(0.726268\pi\)
\(20\) 0 0
\(21\) −6.82215 −1.48872
\(22\) 0 0
\(23\) −7.79317 −1.62499 −0.812494 0.582969i \(-0.801891\pi\)
−0.812494 + 0.582969i \(0.801891\pi\)
\(24\) 0 0
\(25\) 0.817913 0.163583
\(26\) 0 0
\(27\) −13.1255 −2.52600
\(28\) 0 0
\(29\) 4.70794 0.874243 0.437121 0.899402i \(-0.355998\pi\)
0.437121 + 0.899402i \(0.355998\pi\)
\(30\) 0 0
\(31\) 2.59911 0.466815 0.233407 0.972379i \(-0.425012\pi\)
0.233407 + 0.972379i \(0.425012\pi\)
\(32\) 0 0
\(33\) −13.6167 −2.37036
\(34\) 0 0
\(35\) −5.17141 −0.874127
\(36\) 0 0
\(37\) −9.09774 −1.49566 −0.747829 0.663891i \(-0.768904\pi\)
−0.747829 + 0.663891i \(0.768904\pi\)
\(38\) 0 0
\(39\) −19.2299 −3.07925
\(40\) 0 0
\(41\) 0.788241 0.123103 0.0615513 0.998104i \(-0.480395\pi\)
0.0615513 + 0.998104i \(0.480395\pi\)
\(42\) 0 0
\(43\) 8.65874 1.32045 0.660223 0.751070i \(-0.270462\pi\)
0.660223 + 0.751070i \(0.270462\pi\)
\(44\) 0 0
\(45\) −17.1856 −2.56188
\(46\) 0 0
\(47\) −3.21353 −0.468741 −0.234371 0.972147i \(-0.575303\pi\)
−0.234371 + 0.972147i \(0.575303\pi\)
\(48\) 0 0
\(49\) −2.40326 −0.343322
\(50\) 0 0
\(51\) 13.0508 1.82747
\(52\) 0 0
\(53\) 14.2957 1.96367 0.981836 0.189732i \(-0.0607619\pi\)
0.981836 + 0.189732i \(0.0607619\pi\)
\(54\) 0 0
\(55\) −10.3219 −1.39180
\(56\) 0 0
\(57\) 18.0994 2.39733
\(58\) 0 0
\(59\) 1.45990 0.190062 0.0950312 0.995474i \(-0.469705\pi\)
0.0950312 + 0.995474i \(0.469705\pi\)
\(60\) 0 0
\(61\) −3.31142 −0.423984 −0.211992 0.977271i \(-0.567995\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(62\) 0 0
\(63\) 15.2759 1.92458
\(64\) 0 0
\(65\) −14.5769 −1.80804
\(66\) 0 0
\(67\) −8.27604 −1.01108 −0.505540 0.862803i \(-0.668707\pi\)
−0.505540 + 0.862803i \(0.668707\pi\)
\(68\) 0 0
\(69\) 24.7976 2.98529
\(70\) 0 0
\(71\) 6.59994 0.783268 0.391634 0.920121i \(-0.371910\pi\)
0.391634 + 0.920121i \(0.371910\pi\)
\(72\) 0 0
\(73\) −8.46722 −0.991013 −0.495507 0.868604i \(-0.665018\pi\)
−0.495507 + 0.868604i \(0.665018\pi\)
\(74\) 0 0
\(75\) −2.60258 −0.300520
\(76\) 0 0
\(77\) 9.17487 1.04557
\(78\) 0 0
\(79\) −5.68149 −0.639218 −0.319609 0.947550i \(-0.603552\pi\)
−0.319609 + 0.947550i \(0.603552\pi\)
\(80\) 0 0
\(81\) 20.3900 2.26556
\(82\) 0 0
\(83\) −2.17621 −0.238870 −0.119435 0.992842i \(-0.538108\pi\)
−0.119435 + 0.992842i \(0.538108\pi\)
\(84\) 0 0
\(85\) 9.89289 1.07303
\(86\) 0 0
\(87\) −14.9805 −1.60608
\(88\) 0 0
\(89\) −3.16790 −0.335797 −0.167898 0.985804i \(-0.553698\pi\)
−0.167898 + 0.985804i \(0.553698\pi\)
\(90\) 0 0
\(91\) 12.9570 1.35827
\(92\) 0 0
\(93\) −8.27031 −0.857591
\(94\) 0 0
\(95\) 13.7199 1.40763
\(96\) 0 0
\(97\) 13.7492 1.39602 0.698011 0.716087i \(-0.254069\pi\)
0.698011 + 0.716087i \(0.254069\pi\)
\(98\) 0 0
\(99\) 30.4899 3.06435
\(100\) 0 0
\(101\) 7.96474 0.792522 0.396261 0.918138i \(-0.370308\pi\)
0.396261 + 0.918138i \(0.370308\pi\)
\(102\) 0 0
\(103\) −16.7528 −1.65070 −0.825352 0.564619i \(-0.809023\pi\)
−0.825352 + 0.564619i \(0.809023\pi\)
\(104\) 0 0
\(105\) 16.4553 1.60587
\(106\) 0 0
\(107\) 5.45238 0.527102 0.263551 0.964645i \(-0.415106\pi\)
0.263551 + 0.964645i \(0.415106\pi\)
\(108\) 0 0
\(109\) −0.704006 −0.0674315 −0.0337157 0.999431i \(-0.510734\pi\)
−0.0337157 + 0.999431i \(0.510734\pi\)
\(110\) 0 0
\(111\) 28.9487 2.74769
\(112\) 0 0
\(113\) 9.31870 0.876630 0.438315 0.898821i \(-0.355575\pi\)
0.438315 + 0.898821i \(0.355575\pi\)
\(114\) 0 0
\(115\) 18.7974 1.75287
\(116\) 0 0
\(117\) 43.0588 3.98079
\(118\) 0 0
\(119\) −8.79356 −0.806104
\(120\) 0 0
\(121\) 7.31260 0.664782
\(122\) 0 0
\(123\) −2.50816 −0.226153
\(124\) 0 0
\(125\) 10.0873 0.902239
\(126\) 0 0
\(127\) −21.0967 −1.87203 −0.936014 0.351963i \(-0.885514\pi\)
−0.936014 + 0.351963i \(0.885514\pi\)
\(128\) 0 0
\(129\) −27.5519 −2.42581
\(130\) 0 0
\(131\) 3.12482 0.273017 0.136508 0.990639i \(-0.456412\pi\)
0.136508 + 0.990639i \(0.456412\pi\)
\(132\) 0 0
\(133\) −12.1953 −1.05747
\(134\) 0 0
\(135\) 31.6591 2.72478
\(136\) 0 0
\(137\) −1.15467 −0.0986504 −0.0493252 0.998783i \(-0.515707\pi\)
−0.0493252 + 0.998783i \(0.515707\pi\)
\(138\) 0 0
\(139\) 2.06879 0.175472 0.0877362 0.996144i \(-0.472037\pi\)
0.0877362 + 0.996144i \(0.472037\pi\)
\(140\) 0 0
\(141\) 10.2254 0.861130
\(142\) 0 0
\(143\) 25.8616 2.16266
\(144\) 0 0
\(145\) −11.3557 −0.943041
\(146\) 0 0
\(147\) 7.64710 0.630722
\(148\) 0 0
\(149\) −3.45818 −0.283305 −0.141653 0.989916i \(-0.545242\pi\)
−0.141653 + 0.989916i \(0.545242\pi\)
\(150\) 0 0
\(151\) 0.585657 0.0476601 0.0238301 0.999716i \(-0.492414\pi\)
0.0238301 + 0.999716i \(0.492414\pi\)
\(152\) 0 0
\(153\) −29.2228 −2.36252
\(154\) 0 0
\(155\) −6.26916 −0.503551
\(156\) 0 0
\(157\) −18.9851 −1.51518 −0.757588 0.652733i \(-0.773623\pi\)
−0.757588 + 0.652733i \(0.773623\pi\)
\(158\) 0 0
\(159\) −45.4887 −3.60749
\(160\) 0 0
\(161\) −16.7086 −1.31682
\(162\) 0 0
\(163\) −12.1185 −0.949191 −0.474595 0.880204i \(-0.657406\pi\)
−0.474595 + 0.880204i \(0.657406\pi\)
\(164\) 0 0
\(165\) 32.8439 2.55690
\(166\) 0 0
\(167\) −25.0534 −1.93869 −0.969346 0.245701i \(-0.920982\pi\)
−0.969346 + 0.245701i \(0.920982\pi\)
\(168\) 0 0
\(169\) 23.5226 1.80943
\(170\) 0 0
\(171\) −40.5275 −3.09921
\(172\) 0 0
\(173\) 19.1817 1.45836 0.729179 0.684323i \(-0.239902\pi\)
0.729179 + 0.684323i \(0.239902\pi\)
\(174\) 0 0
\(175\) 1.75361 0.132560
\(176\) 0 0
\(177\) −4.64535 −0.349166
\(178\) 0 0
\(179\) 14.2807 1.06739 0.533694 0.845677i \(-0.320803\pi\)
0.533694 + 0.845677i \(0.320803\pi\)
\(180\) 0 0
\(181\) −14.6368 −1.08795 −0.543973 0.839103i \(-0.683081\pi\)
−0.543973 + 0.839103i \(0.683081\pi\)
\(182\) 0 0
\(183\) 10.5368 0.778906
\(184\) 0 0
\(185\) 21.9441 1.61336
\(186\) 0 0
\(187\) −17.5515 −1.28349
\(188\) 0 0
\(189\) −28.1410 −2.04696
\(190\) 0 0
\(191\) −4.68767 −0.339188 −0.169594 0.985514i \(-0.554246\pi\)
−0.169594 + 0.985514i \(0.554246\pi\)
\(192\) 0 0
\(193\) 14.2675 1.02700 0.513500 0.858090i \(-0.328349\pi\)
0.513500 + 0.858090i \(0.328349\pi\)
\(194\) 0 0
\(195\) 46.3832 3.32157
\(196\) 0 0
\(197\) 23.5457 1.67756 0.838780 0.544470i \(-0.183269\pi\)
0.838780 + 0.544470i \(0.183269\pi\)
\(198\) 0 0
\(199\) 0.553056 0.0392051 0.0196026 0.999808i \(-0.493760\pi\)
0.0196026 + 0.999808i \(0.493760\pi\)
\(200\) 0 0
\(201\) 26.3341 1.85747
\(202\) 0 0
\(203\) 10.0938 0.708448
\(204\) 0 0
\(205\) −1.90127 −0.132790
\(206\) 0 0
\(207\) −55.5259 −3.85932
\(208\) 0 0
\(209\) −24.3413 −1.68372
\(210\) 0 0
\(211\) 8.30437 0.571696 0.285848 0.958275i \(-0.407725\pi\)
0.285848 + 0.958275i \(0.407725\pi\)
\(212\) 0 0
\(213\) −21.0008 −1.43895
\(214\) 0 0
\(215\) −20.8852 −1.42436
\(216\) 0 0
\(217\) 5.57251 0.378286
\(218\) 0 0
\(219\) 26.9425 1.82060
\(220\) 0 0
\(221\) −24.7868 −1.66734
\(222\) 0 0
\(223\) −24.7570 −1.65785 −0.828927 0.559357i \(-0.811048\pi\)
−0.828927 + 0.559357i \(0.811048\pi\)
\(224\) 0 0
\(225\) 5.82759 0.388506
\(226\) 0 0
\(227\) −17.3506 −1.15160 −0.575801 0.817590i \(-0.695310\pi\)
−0.575801 + 0.817590i \(0.695310\pi\)
\(228\) 0 0
\(229\) 6.99497 0.462241 0.231120 0.972925i \(-0.425761\pi\)
0.231120 + 0.972925i \(0.425761\pi\)
\(230\) 0 0
\(231\) −29.1942 −1.92084
\(232\) 0 0
\(233\) 13.2735 0.869574 0.434787 0.900533i \(-0.356824\pi\)
0.434787 + 0.900533i \(0.356824\pi\)
\(234\) 0 0
\(235\) 7.75114 0.505629
\(236\) 0 0
\(237\) 18.0784 1.17432
\(238\) 0 0
\(239\) 1.51469 0.0979772 0.0489886 0.998799i \(-0.484400\pi\)
0.0489886 + 0.998799i \(0.484400\pi\)
\(240\) 0 0
\(241\) −12.7844 −0.823517 −0.411758 0.911293i \(-0.635085\pi\)
−0.411758 + 0.911293i \(0.635085\pi\)
\(242\) 0 0
\(243\) −25.5041 −1.63609
\(244\) 0 0
\(245\) 5.79674 0.370340
\(246\) 0 0
\(247\) −34.3755 −2.18726
\(248\) 0 0
\(249\) 6.92463 0.438831
\(250\) 0 0
\(251\) −5.90243 −0.372558 −0.186279 0.982497i \(-0.559643\pi\)
−0.186279 + 0.982497i \(0.559643\pi\)
\(252\) 0 0
\(253\) −33.3495 −2.09666
\(254\) 0 0
\(255\) −31.4789 −1.97129
\(256\) 0 0
\(257\) 8.31994 0.518984 0.259492 0.965745i \(-0.416445\pi\)
0.259492 + 0.965745i \(0.416445\pi\)
\(258\) 0 0
\(259\) −19.5056 −1.21202
\(260\) 0 0
\(261\) 33.5438 2.07631
\(262\) 0 0
\(263\) 3.88818 0.239755 0.119878 0.992789i \(-0.461750\pi\)
0.119878 + 0.992789i \(0.461750\pi\)
\(264\) 0 0
\(265\) −34.4818 −2.11820
\(266\) 0 0
\(267\) 10.0802 0.616896
\(268\) 0 0
\(269\) 20.6433 1.25864 0.629322 0.777145i \(-0.283333\pi\)
0.629322 + 0.777145i \(0.283333\pi\)
\(270\) 0 0
\(271\) 12.4758 0.757850 0.378925 0.925427i \(-0.376294\pi\)
0.378925 + 0.925427i \(0.376294\pi\)
\(272\) 0 0
\(273\) −41.2289 −2.49529
\(274\) 0 0
\(275\) 3.50011 0.211065
\(276\) 0 0
\(277\) −11.8192 −0.710148 −0.355074 0.934838i \(-0.615544\pi\)
−0.355074 + 0.934838i \(0.615544\pi\)
\(278\) 0 0
\(279\) 18.5186 1.10868
\(280\) 0 0
\(281\) −10.9486 −0.653140 −0.326570 0.945173i \(-0.605893\pi\)
−0.326570 + 0.945173i \(0.605893\pi\)
\(282\) 0 0
\(283\) −24.5751 −1.46084 −0.730420 0.682999i \(-0.760676\pi\)
−0.730420 + 0.682999i \(0.760676\pi\)
\(284\) 0 0
\(285\) −43.6564 −2.58598
\(286\) 0 0
\(287\) 1.68999 0.0997570
\(288\) 0 0
\(289\) −0.177939 −0.0104670
\(290\) 0 0
\(291\) −43.7496 −2.56465
\(292\) 0 0
\(293\) 4.22642 0.246910 0.123455 0.992350i \(-0.460603\pi\)
0.123455 + 0.992350i \(0.460603\pi\)
\(294\) 0 0
\(295\) −3.52132 −0.205019
\(296\) 0 0
\(297\) −56.1681 −3.25920
\(298\) 0 0
\(299\) −47.0972 −2.72370
\(300\) 0 0
\(301\) 18.5644 1.07003
\(302\) 0 0
\(303\) −25.3436 −1.45595
\(304\) 0 0
\(305\) 7.98726 0.457349
\(306\) 0 0
\(307\) 28.4382 1.62305 0.811527 0.584315i \(-0.198637\pi\)
0.811527 + 0.584315i \(0.198637\pi\)
\(308\) 0 0
\(309\) 53.3070 3.03253
\(310\) 0 0
\(311\) −24.2743 −1.37647 −0.688236 0.725487i \(-0.741615\pi\)
−0.688236 + 0.725487i \(0.741615\pi\)
\(312\) 0 0
\(313\) −13.1400 −0.742717 −0.371359 0.928490i \(-0.621108\pi\)
−0.371359 + 0.928490i \(0.621108\pi\)
\(314\) 0 0
\(315\) −36.8460 −2.07604
\(316\) 0 0
\(317\) −27.3949 −1.53865 −0.769324 0.638859i \(-0.779407\pi\)
−0.769324 + 0.638859i \(0.779407\pi\)
\(318\) 0 0
\(319\) 20.1468 1.12800
\(320\) 0 0
\(321\) −17.3493 −0.968345
\(322\) 0 0
\(323\) 23.3296 1.29809
\(324\) 0 0
\(325\) 4.94297 0.274187
\(326\) 0 0
\(327\) 2.24013 0.123879
\(328\) 0 0
\(329\) −6.88981 −0.379847
\(330\) 0 0
\(331\) −10.0742 −0.553727 −0.276864 0.960909i \(-0.589295\pi\)
−0.276864 + 0.960909i \(0.589295\pi\)
\(332\) 0 0
\(333\) −64.8209 −3.55216
\(334\) 0 0
\(335\) 19.9621 1.09065
\(336\) 0 0
\(337\) 34.3371 1.87046 0.935230 0.354041i \(-0.115193\pi\)
0.935230 + 0.354041i \(0.115193\pi\)
\(338\) 0 0
\(339\) −29.6519 −1.61047
\(340\) 0 0
\(341\) 11.1225 0.602314
\(342\) 0 0
\(343\) −20.1606 −1.08857
\(344\) 0 0
\(345\) −59.8128 −3.22021
\(346\) 0 0
\(347\) −29.6494 −1.59166 −0.795832 0.605517i \(-0.792966\pi\)
−0.795832 + 0.605517i \(0.792966\pi\)
\(348\) 0 0
\(349\) −8.29858 −0.444213 −0.222106 0.975022i \(-0.571293\pi\)
−0.222106 + 0.975022i \(0.571293\pi\)
\(350\) 0 0
\(351\) −79.3223 −4.23391
\(352\) 0 0
\(353\) −9.16523 −0.487816 −0.243908 0.969798i \(-0.578430\pi\)
−0.243908 + 0.969798i \(0.578430\pi\)
\(354\) 0 0
\(355\) −15.9193 −0.844907
\(356\) 0 0
\(357\) 27.9809 1.48090
\(358\) 0 0
\(359\) 28.6357 1.51134 0.755668 0.654954i \(-0.227312\pi\)
0.755668 + 0.654954i \(0.227312\pi\)
\(360\) 0 0
\(361\) 13.3546 0.702874
\(362\) 0 0
\(363\) −23.2685 −1.22128
\(364\) 0 0
\(365\) 20.4232 1.06900
\(366\) 0 0
\(367\) 6.08254 0.317506 0.158753 0.987318i \(-0.449253\pi\)
0.158753 + 0.987318i \(0.449253\pi\)
\(368\) 0 0
\(369\) 5.61618 0.292367
\(370\) 0 0
\(371\) 30.6501 1.59127
\(372\) 0 0
\(373\) −8.63400 −0.447052 −0.223526 0.974698i \(-0.571757\pi\)
−0.223526 + 0.974698i \(0.571757\pi\)
\(374\) 0 0
\(375\) −32.0976 −1.65751
\(376\) 0 0
\(377\) 28.4519 1.46535
\(378\) 0 0
\(379\) −6.95523 −0.357266 −0.178633 0.983916i \(-0.557167\pi\)
−0.178633 + 0.983916i \(0.557167\pi\)
\(380\) 0 0
\(381\) 67.1291 3.43913
\(382\) 0 0
\(383\) 35.4097 1.80935 0.904676 0.426100i \(-0.140113\pi\)
0.904676 + 0.426100i \(0.140113\pi\)
\(384\) 0 0
\(385\) −22.1301 −1.12786
\(386\) 0 0
\(387\) 61.6931 3.13604
\(388\) 0 0
\(389\) −3.62879 −0.183987 −0.0919934 0.995760i \(-0.529324\pi\)
−0.0919934 + 0.995760i \(0.529324\pi\)
\(390\) 0 0
\(391\) 31.9635 1.61646
\(392\) 0 0
\(393\) −9.94309 −0.501563
\(394\) 0 0
\(395\) 13.7040 0.689521
\(396\) 0 0
\(397\) 8.06758 0.404900 0.202450 0.979293i \(-0.435110\pi\)
0.202450 + 0.979293i \(0.435110\pi\)
\(398\) 0 0
\(399\) 38.8052 1.94269
\(400\) 0 0
\(401\) −21.9377 −1.09551 −0.547757 0.836637i \(-0.684518\pi\)
−0.547757 + 0.836637i \(0.684518\pi\)
\(402\) 0 0
\(403\) 15.7075 0.782445
\(404\) 0 0
\(405\) −49.1815 −2.44385
\(406\) 0 0
\(407\) −38.9321 −1.92979
\(408\) 0 0
\(409\) −28.2850 −1.39860 −0.699301 0.714827i \(-0.746505\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(410\) 0 0
\(411\) 3.67414 0.181232
\(412\) 0 0
\(413\) 3.13002 0.154018
\(414\) 0 0
\(415\) 5.24909 0.257668
\(416\) 0 0
\(417\) −6.58283 −0.322363
\(418\) 0 0
\(419\) −19.3503 −0.945323 −0.472661 0.881244i \(-0.656707\pi\)
−0.472661 + 0.881244i \(0.656707\pi\)
\(420\) 0 0
\(421\) 3.28476 0.160089 0.0800447 0.996791i \(-0.474494\pi\)
0.0800447 + 0.996791i \(0.474494\pi\)
\(422\) 0 0
\(423\) −22.8962 −1.11325
\(424\) 0 0
\(425\) −3.35465 −0.162724
\(426\) 0 0
\(427\) −7.09969 −0.343578
\(428\) 0 0
\(429\) −82.2909 −3.97304
\(430\) 0 0
\(431\) −30.8826 −1.48756 −0.743780 0.668424i \(-0.766969\pi\)
−0.743780 + 0.668424i \(0.766969\pi\)
\(432\) 0 0
\(433\) 5.34217 0.256728 0.128364 0.991727i \(-0.459027\pi\)
0.128364 + 0.991727i \(0.459027\pi\)
\(434\) 0 0
\(435\) 36.1336 1.73247
\(436\) 0 0
\(437\) 44.3284 2.12052
\(438\) 0 0
\(439\) 26.9492 1.28621 0.643107 0.765776i \(-0.277645\pi\)
0.643107 + 0.765776i \(0.277645\pi\)
\(440\) 0 0
\(441\) −17.1231 −0.815385
\(442\) 0 0
\(443\) −18.0731 −0.858677 −0.429339 0.903144i \(-0.641253\pi\)
−0.429339 + 0.903144i \(0.641253\pi\)
\(444\) 0 0
\(445\) 7.64108 0.362222
\(446\) 0 0
\(447\) 11.0038 0.520464
\(448\) 0 0
\(449\) 17.7406 0.837230 0.418615 0.908164i \(-0.362516\pi\)
0.418615 + 0.908164i \(0.362516\pi\)
\(450\) 0 0
\(451\) 3.37314 0.158835
\(452\) 0 0
\(453\) −1.86354 −0.0875570
\(454\) 0 0
\(455\) −31.2528 −1.46516
\(456\) 0 0
\(457\) −10.5462 −0.493331 −0.246665 0.969101i \(-0.579335\pi\)
−0.246665 + 0.969101i \(0.579335\pi\)
\(458\) 0 0
\(459\) 53.8337 2.51274
\(460\) 0 0
\(461\) 33.2430 1.54828 0.774140 0.633015i \(-0.218183\pi\)
0.774140 + 0.633015i \(0.218183\pi\)
\(462\) 0 0
\(463\) 9.43193 0.438339 0.219169 0.975687i \(-0.429665\pi\)
0.219169 + 0.975687i \(0.429665\pi\)
\(464\) 0 0
\(465\) 19.9483 0.925079
\(466\) 0 0
\(467\) 19.8667 0.919320 0.459660 0.888095i \(-0.347971\pi\)
0.459660 + 0.888095i \(0.347971\pi\)
\(468\) 0 0
\(469\) −17.7438 −0.819335
\(470\) 0 0
\(471\) 60.4101 2.78355
\(472\) 0 0
\(473\) 37.0535 1.70372
\(474\) 0 0
\(475\) −4.65238 −0.213466
\(476\) 0 0
\(477\) 101.856 4.66369
\(478\) 0 0
\(479\) −13.7806 −0.629653 −0.314826 0.949149i \(-0.601946\pi\)
−0.314826 + 0.949149i \(0.601946\pi\)
\(480\) 0 0
\(481\) −54.9812 −2.50693
\(482\) 0 0
\(483\) 53.1662 2.41915
\(484\) 0 0
\(485\) −33.1636 −1.50588
\(486\) 0 0
\(487\) 0.762405 0.0345479 0.0172739 0.999851i \(-0.494501\pi\)
0.0172739 + 0.999851i \(0.494501\pi\)
\(488\) 0 0
\(489\) 38.5606 1.74377
\(490\) 0 0
\(491\) −29.4198 −1.32770 −0.663849 0.747867i \(-0.731078\pi\)
−0.663849 + 0.747867i \(0.731078\pi\)
\(492\) 0 0
\(493\) −19.3095 −0.869656
\(494\) 0 0
\(495\) −73.5428 −3.30550
\(496\) 0 0
\(497\) 14.1503 0.634726
\(498\) 0 0
\(499\) 15.4130 0.689980 0.344990 0.938606i \(-0.387882\pi\)
0.344990 + 0.938606i \(0.387882\pi\)
\(500\) 0 0
\(501\) 79.7193 3.56159
\(502\) 0 0
\(503\) 1.92155 0.0856775 0.0428387 0.999082i \(-0.486360\pi\)
0.0428387 + 0.999082i \(0.486360\pi\)
\(504\) 0 0
\(505\) −19.2112 −0.854889
\(506\) 0 0
\(507\) −74.8481 −3.32412
\(508\) 0 0
\(509\) −34.0545 −1.50944 −0.754719 0.656048i \(-0.772227\pi\)
−0.754719 + 0.656048i \(0.772227\pi\)
\(510\) 0 0
\(511\) −18.1537 −0.803074
\(512\) 0 0
\(513\) 74.6591 3.29628
\(514\) 0 0
\(515\) 40.4084 1.78061
\(516\) 0 0
\(517\) −13.7517 −0.604800
\(518\) 0 0
\(519\) −61.0357 −2.67917
\(520\) 0 0
\(521\) 14.3394 0.628222 0.314111 0.949386i \(-0.398294\pi\)
0.314111 + 0.949386i \(0.398294\pi\)
\(522\) 0 0
\(523\) 24.7546 1.08244 0.541221 0.840880i \(-0.317962\pi\)
0.541221 + 0.840880i \(0.317962\pi\)
\(524\) 0 0
\(525\) −5.57993 −0.243528
\(526\) 0 0
\(527\) −10.6602 −0.464365
\(528\) 0 0
\(529\) 37.7335 1.64059
\(530\) 0 0
\(531\) 10.4017 0.451395
\(532\) 0 0
\(533\) 4.76365 0.206337
\(534\) 0 0
\(535\) −13.1513 −0.568582
\(536\) 0 0
\(537\) −45.4408 −1.96091
\(538\) 0 0
\(539\) −10.2843 −0.442977
\(540\) 0 0
\(541\) 10.9539 0.470945 0.235472 0.971881i \(-0.424336\pi\)
0.235472 + 0.971881i \(0.424336\pi\)
\(542\) 0 0
\(543\) 46.5739 1.99868
\(544\) 0 0
\(545\) 1.69809 0.0727380
\(546\) 0 0
\(547\) −14.1730 −0.605992 −0.302996 0.952992i \(-0.597987\pi\)
−0.302996 + 0.952992i \(0.597987\pi\)
\(548\) 0 0
\(549\) −23.5937 −1.00695
\(550\) 0 0
\(551\) −26.7793 −1.14084
\(552\) 0 0
\(553\) −12.1811 −0.517994
\(554\) 0 0
\(555\) −69.8254 −2.96392
\(556\) 0 0
\(557\) −7.48107 −0.316983 −0.158492 0.987360i \(-0.550663\pi\)
−0.158492 + 0.987360i \(0.550663\pi\)
\(558\) 0 0
\(559\) 52.3282 2.21325
\(560\) 0 0
\(561\) 55.8484 2.35792
\(562\) 0 0
\(563\) −24.3726 −1.02718 −0.513592 0.858035i \(-0.671685\pi\)
−0.513592 + 0.858035i \(0.671685\pi\)
\(564\) 0 0
\(565\) −22.4770 −0.945616
\(566\) 0 0
\(567\) 43.7162 1.83591
\(568\) 0 0
\(569\) 22.5084 0.943603 0.471802 0.881705i \(-0.343604\pi\)
0.471802 + 0.881705i \(0.343604\pi\)
\(570\) 0 0
\(571\) −32.8894 −1.37638 −0.688190 0.725531i \(-0.741594\pi\)
−0.688190 + 0.725531i \(0.741594\pi\)
\(572\) 0 0
\(573\) 14.9160 0.623126
\(574\) 0 0
\(575\) −6.37414 −0.265820
\(576\) 0 0
\(577\) 6.95324 0.289467 0.144733 0.989471i \(-0.453768\pi\)
0.144733 + 0.989471i \(0.453768\pi\)
\(578\) 0 0
\(579\) −45.3989 −1.88671
\(580\) 0 0
\(581\) −4.66579 −0.193570
\(582\) 0 0
\(583\) 61.1761 2.53366
\(584\) 0 0
\(585\) −103.859 −4.29406
\(586\) 0 0
\(587\) −28.0595 −1.15814 −0.579070 0.815278i \(-0.696584\pi\)
−0.579070 + 0.815278i \(0.696584\pi\)
\(588\) 0 0
\(589\) −14.7841 −0.609166
\(590\) 0 0
\(591\) −74.9217 −3.08187
\(592\) 0 0
\(593\) −22.8304 −0.937532 −0.468766 0.883322i \(-0.655301\pi\)
−0.468766 + 0.883322i \(0.655301\pi\)
\(594\) 0 0
\(595\) 21.2104 0.869541
\(596\) 0 0
\(597\) −1.75981 −0.0720242
\(598\) 0 0
\(599\) 26.5132 1.08330 0.541649 0.840605i \(-0.317800\pi\)
0.541649 + 0.840605i \(0.317800\pi\)
\(600\) 0 0
\(601\) −9.27038 −0.378147 −0.189073 0.981963i \(-0.560548\pi\)
−0.189073 + 0.981963i \(0.560548\pi\)
\(602\) 0 0
\(603\) −58.9664 −2.40130
\(604\) 0 0
\(605\) −17.6382 −0.717096
\(606\) 0 0
\(607\) −37.1211 −1.50670 −0.753349 0.657621i \(-0.771563\pi\)
−0.753349 + 0.657621i \(0.771563\pi\)
\(608\) 0 0
\(609\) −32.1183 −1.30150
\(610\) 0 0
\(611\) −19.4206 −0.785673
\(612\) 0 0
\(613\) −15.4695 −0.624806 −0.312403 0.949950i \(-0.601134\pi\)
−0.312403 + 0.949950i \(0.601134\pi\)
\(614\) 0 0
\(615\) 6.04978 0.243951
\(616\) 0 0
\(617\) −35.2283 −1.41824 −0.709120 0.705088i \(-0.750908\pi\)
−0.709120 + 0.705088i \(0.750908\pi\)
\(618\) 0 0
\(619\) 24.2717 0.975561 0.487781 0.872966i \(-0.337807\pi\)
0.487781 + 0.872966i \(0.337807\pi\)
\(620\) 0 0
\(621\) 102.289 4.10472
\(622\) 0 0
\(623\) −6.79198 −0.272115
\(624\) 0 0
\(625\) −28.4206 −1.13682
\(626\) 0 0
\(627\) 77.4532 3.09318
\(628\) 0 0
\(629\) 37.3141 1.48781
\(630\) 0 0
\(631\) 19.0657 0.758994 0.379497 0.925193i \(-0.376097\pi\)
0.379497 + 0.925193i \(0.376097\pi\)
\(632\) 0 0
\(633\) −26.4243 −1.05027
\(634\) 0 0
\(635\) 50.8859 2.01935
\(636\) 0 0
\(637\) −14.5238 −0.575455
\(638\) 0 0
\(639\) 47.0242 1.86025
\(640\) 0 0
\(641\) −29.2188 −1.15407 −0.577037 0.816718i \(-0.695791\pi\)
−0.577037 + 0.816718i \(0.695791\pi\)
\(642\) 0 0
\(643\) −3.60188 −0.142044 −0.0710221 0.997475i \(-0.522626\pi\)
−0.0710221 + 0.997475i \(0.522626\pi\)
\(644\) 0 0
\(645\) 66.4561 2.61671
\(646\) 0 0
\(647\) −25.8057 −1.01453 −0.507263 0.861791i \(-0.669343\pi\)
−0.507263 + 0.861791i \(0.669343\pi\)
\(648\) 0 0
\(649\) 6.24737 0.245231
\(650\) 0 0
\(651\) −17.7316 −0.694955
\(652\) 0 0
\(653\) −24.0728 −0.942041 −0.471021 0.882122i \(-0.656114\pi\)
−0.471021 + 0.882122i \(0.656114\pi\)
\(654\) 0 0
\(655\) −7.53718 −0.294502
\(656\) 0 0
\(657\) −60.3285 −2.35364
\(658\) 0 0
\(659\) 35.3043 1.37526 0.687630 0.726061i \(-0.258651\pi\)
0.687630 + 0.726061i \(0.258651\pi\)
\(660\) 0 0
\(661\) 4.58117 0.178187 0.0890935 0.996023i \(-0.471603\pi\)
0.0890935 + 0.996023i \(0.471603\pi\)
\(662\) 0 0
\(663\) 78.8709 3.06309
\(664\) 0 0
\(665\) 29.4155 1.14069
\(666\) 0 0
\(667\) −36.6898 −1.42063
\(668\) 0 0
\(669\) 78.7762 3.04566
\(670\) 0 0
\(671\) −14.1706 −0.547051
\(672\) 0 0
\(673\) 22.7644 0.877503 0.438751 0.898609i \(-0.355421\pi\)
0.438751 + 0.898609i \(0.355421\pi\)
\(674\) 0 0
\(675\) −10.7355 −0.413209
\(676\) 0 0
\(677\) −32.4053 −1.24544 −0.622718 0.782446i \(-0.713972\pi\)
−0.622718 + 0.782446i \(0.713972\pi\)
\(678\) 0 0
\(679\) 29.4783 1.13128
\(680\) 0 0
\(681\) 55.2092 2.11562
\(682\) 0 0
\(683\) −42.4112 −1.62282 −0.811409 0.584478i \(-0.801299\pi\)
−0.811409 + 0.584478i \(0.801299\pi\)
\(684\) 0 0
\(685\) 2.78511 0.106414
\(686\) 0 0
\(687\) −22.2578 −0.849188
\(688\) 0 0
\(689\) 86.3948 3.29138
\(690\) 0 0
\(691\) −37.5434 −1.42822 −0.714109 0.700035i \(-0.753168\pi\)
−0.714109 + 0.700035i \(0.753168\pi\)
\(692\) 0 0
\(693\) 65.3705 2.48322
\(694\) 0 0
\(695\) −4.98999 −0.189281
\(696\) 0 0
\(697\) −3.23295 −0.122457
\(698\) 0 0
\(699\) −42.2358 −1.59751
\(700\) 0 0
\(701\) 33.8929 1.28012 0.640059 0.768325i \(-0.278910\pi\)
0.640059 + 0.768325i \(0.278910\pi\)
\(702\) 0 0
\(703\) 51.7489 1.95175
\(704\) 0 0
\(705\) −24.6639 −0.928897
\(706\) 0 0
\(707\) 17.0764 0.642225
\(708\) 0 0
\(709\) −1.98557 −0.0745696 −0.0372848 0.999305i \(-0.511871\pi\)
−0.0372848 + 0.999305i \(0.511871\pi\)
\(710\) 0 0
\(711\) −40.4803 −1.51813
\(712\) 0 0
\(713\) −20.2553 −0.758569
\(714\) 0 0
\(715\) −62.3791 −2.33285
\(716\) 0 0
\(717\) −4.81970 −0.179995
\(718\) 0 0
\(719\) −29.4203 −1.09719 −0.548596 0.836088i \(-0.684838\pi\)
−0.548596 + 0.836088i \(0.684838\pi\)
\(720\) 0 0
\(721\) −35.9180 −1.33766
\(722\) 0 0
\(723\) 40.6797 1.51289
\(724\) 0 0
\(725\) 3.85069 0.143011
\(726\) 0 0
\(727\) −49.4355 −1.83346 −0.916731 0.399505i \(-0.869182\pi\)
−0.916731 + 0.399505i \(0.869182\pi\)
\(728\) 0 0
\(729\) 19.9832 0.740120
\(730\) 0 0
\(731\) −35.5136 −1.31352
\(732\) 0 0
\(733\) −8.18741 −0.302409 −0.151205 0.988503i \(-0.548315\pi\)
−0.151205 + 0.988503i \(0.548315\pi\)
\(734\) 0 0
\(735\) −18.4451 −0.680357
\(736\) 0 0
\(737\) −35.4158 −1.30456
\(738\) 0 0
\(739\) −28.3164 −1.04163 −0.520817 0.853668i \(-0.674373\pi\)
−0.520817 + 0.853668i \(0.674373\pi\)
\(740\) 0 0
\(741\) 109.382 4.01824
\(742\) 0 0
\(743\) −19.6007 −0.719078 −0.359539 0.933130i \(-0.617066\pi\)
−0.359539 + 0.933130i \(0.617066\pi\)
\(744\) 0 0
\(745\) 8.34126 0.305600
\(746\) 0 0
\(747\) −15.5054 −0.567311
\(748\) 0 0
\(749\) 11.6899 0.427140
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 18.7814 0.684431
\(754\) 0 0
\(755\) −1.41263 −0.0514107
\(756\) 0 0
\(757\) −30.8106 −1.11983 −0.559914 0.828551i \(-0.689166\pi\)
−0.559914 + 0.828551i \(0.689166\pi\)
\(758\) 0 0
\(759\) 106.117 3.85181
\(760\) 0 0
\(761\) −11.0937 −0.402145 −0.201073 0.979576i \(-0.564443\pi\)
−0.201073 + 0.979576i \(0.564443\pi\)
\(762\) 0 0
\(763\) −1.50939 −0.0546435
\(764\) 0 0
\(765\) 70.4863 2.54844
\(766\) 0 0
\(767\) 8.82273 0.318570
\(768\) 0 0
\(769\) −35.9512 −1.29643 −0.648216 0.761457i \(-0.724485\pi\)
−0.648216 + 0.761457i \(0.724485\pi\)
\(770\) 0 0
\(771\) −26.4738 −0.953431
\(772\) 0 0
\(773\) 23.3605 0.840219 0.420110 0.907473i \(-0.361992\pi\)
0.420110 + 0.907473i \(0.361992\pi\)
\(774\) 0 0
\(775\) 2.12585 0.0763628
\(776\) 0 0
\(777\) 62.0662 2.22661
\(778\) 0 0
\(779\) −4.48361 −0.160642
\(780\) 0 0
\(781\) 28.2432 1.01062
\(782\) 0 0
\(783\) −61.7939 −2.20834
\(784\) 0 0
\(785\) 45.7928 1.63441
\(786\) 0 0
\(787\) 23.5839 0.840676 0.420338 0.907368i \(-0.361912\pi\)
0.420338 + 0.907368i \(0.361912\pi\)
\(788\) 0 0
\(789\) −12.3721 −0.440458
\(790\) 0 0
\(791\) 19.9793 0.710383
\(792\) 0 0
\(793\) −20.0122 −0.710654
\(794\) 0 0
\(795\) 109.720 3.89138
\(796\) 0 0
\(797\) 18.5554 0.657266 0.328633 0.944458i \(-0.393412\pi\)
0.328633 + 0.944458i \(0.393412\pi\)
\(798\) 0 0
\(799\) 13.1802 0.466282
\(800\) 0 0
\(801\) −22.5711 −0.797511
\(802\) 0 0
\(803\) −36.2340 −1.27867
\(804\) 0 0
\(805\) 40.3016 1.42045
\(806\) 0 0
\(807\) −65.6864 −2.31227
\(808\) 0 0
\(809\) 33.5383 1.17914 0.589572 0.807716i \(-0.299296\pi\)
0.589572 + 0.807716i \(0.299296\pi\)
\(810\) 0 0
\(811\) −2.34171 −0.0822286 −0.0411143 0.999154i \(-0.513091\pi\)
−0.0411143 + 0.999154i \(0.513091\pi\)
\(812\) 0 0
\(813\) −39.6976 −1.39226
\(814\) 0 0
\(815\) 29.2301 1.02389
\(816\) 0 0
\(817\) −49.2519 −1.72311
\(818\) 0 0
\(819\) 92.3182 3.22586
\(820\) 0 0
\(821\) −11.1611 −0.389527 −0.194763 0.980850i \(-0.562394\pi\)
−0.194763 + 0.980850i \(0.562394\pi\)
\(822\) 0 0
\(823\) −26.3292 −0.917779 −0.458889 0.888493i \(-0.651753\pi\)
−0.458889 + 0.888493i \(0.651753\pi\)
\(824\) 0 0
\(825\) −11.1373 −0.387750
\(826\) 0 0
\(827\) 17.7898 0.618612 0.309306 0.950963i \(-0.399903\pi\)
0.309306 + 0.950963i \(0.399903\pi\)
\(828\) 0 0
\(829\) −49.6223 −1.72345 −0.861727 0.507371i \(-0.830617\pi\)
−0.861727 + 0.507371i \(0.830617\pi\)
\(830\) 0 0
\(831\) 37.6084 1.30462
\(832\) 0 0
\(833\) 9.85689 0.341521
\(834\) 0 0
\(835\) 60.4297 2.09126
\(836\) 0 0
\(837\) −34.1146 −1.17917
\(838\) 0 0
\(839\) −43.3742 −1.49744 −0.748721 0.662885i \(-0.769332\pi\)
−0.748721 + 0.662885i \(0.769332\pi\)
\(840\) 0 0
\(841\) −6.83528 −0.235699
\(842\) 0 0
\(843\) 34.8382 1.19989
\(844\) 0 0
\(845\) −56.7372 −1.95182
\(846\) 0 0
\(847\) 15.6782 0.538710
\(848\) 0 0
\(849\) 78.1974 2.68373
\(850\) 0 0
\(851\) 70.9002 2.43043
\(852\) 0 0
\(853\) −52.0354 −1.78166 −0.890829 0.454339i \(-0.849876\pi\)
−0.890829 + 0.454339i \(0.849876\pi\)
\(854\) 0 0
\(855\) 97.7537 3.34311
\(856\) 0 0
\(857\) −34.9752 −1.19473 −0.597365 0.801969i \(-0.703786\pi\)
−0.597365 + 0.801969i \(0.703786\pi\)
\(858\) 0 0
\(859\) 46.2471 1.57793 0.788965 0.614438i \(-0.210617\pi\)
0.788965 + 0.614438i \(0.210617\pi\)
\(860\) 0 0
\(861\) −5.37750 −0.183265
\(862\) 0 0
\(863\) 25.4230 0.865408 0.432704 0.901536i \(-0.357559\pi\)
0.432704 + 0.901536i \(0.357559\pi\)
\(864\) 0 0
\(865\) −46.2669 −1.57312
\(866\) 0 0
\(867\) 0.566196 0.0192290
\(868\) 0 0
\(869\) −24.3129 −0.824760
\(870\) 0 0
\(871\) −50.0153 −1.69471
\(872\) 0 0
\(873\) 97.9625 3.31553
\(874\) 0 0
\(875\) 21.6273 0.731135
\(876\) 0 0
\(877\) −42.9765 −1.45121 −0.725606 0.688110i \(-0.758440\pi\)
−0.725606 + 0.688110i \(0.758440\pi\)
\(878\) 0 0
\(879\) −13.4484 −0.453602
\(880\) 0 0
\(881\) −22.8167 −0.768713 −0.384356 0.923185i \(-0.625577\pi\)
−0.384356 + 0.923185i \(0.625577\pi\)
\(882\) 0 0
\(883\) 2.86518 0.0964211 0.0482105 0.998837i \(-0.484648\pi\)
0.0482105 + 0.998837i \(0.484648\pi\)
\(884\) 0 0
\(885\) 11.2048 0.376644
\(886\) 0 0
\(887\) −33.4635 −1.12360 −0.561798 0.827275i \(-0.689890\pi\)
−0.561798 + 0.827275i \(0.689890\pi\)
\(888\) 0 0
\(889\) −45.2313 −1.51701
\(890\) 0 0
\(891\) 87.2555 2.92317
\(892\) 0 0
\(893\) 18.2789 0.611680
\(894\) 0 0
\(895\) −34.4455 −1.15139
\(896\) 0 0
\(897\) 149.862 5.00374
\(898\) 0 0
\(899\) 12.2365 0.408110
\(900\) 0 0
\(901\) −58.6336 −1.95337
\(902\) 0 0
\(903\) −59.0713 −1.96577
\(904\) 0 0
\(905\) 35.3045 1.17356
\(906\) 0 0
\(907\) 34.5940 1.14867 0.574337 0.818619i \(-0.305260\pi\)
0.574337 + 0.818619i \(0.305260\pi\)
\(908\) 0 0
\(909\) 56.7484 1.88222
\(910\) 0 0
\(911\) −16.1897 −0.536388 −0.268194 0.963365i \(-0.586427\pi\)
−0.268194 + 0.963365i \(0.586427\pi\)
\(912\) 0 0
\(913\) −9.31269 −0.308205
\(914\) 0 0
\(915\) −25.4152 −0.840202
\(916\) 0 0
\(917\) 6.69962 0.221241
\(918\) 0 0
\(919\) 59.5114 1.96310 0.981549 0.191209i \(-0.0612407\pi\)
0.981549 + 0.191209i \(0.0612407\pi\)
\(920\) 0 0
\(921\) −90.4896 −2.98173
\(922\) 0 0
\(923\) 39.8860 1.31286
\(924\) 0 0
\(925\) −7.44116 −0.244664
\(926\) 0 0
\(927\) −119.363 −3.92039
\(928\) 0 0
\(929\) −39.2807 −1.28876 −0.644379 0.764706i \(-0.722884\pi\)
−0.644379 + 0.764706i \(0.722884\pi\)
\(930\) 0 0
\(931\) 13.6700 0.448016
\(932\) 0 0
\(933\) 77.2403 2.52873
\(934\) 0 0
\(935\) 42.3349 1.38450
\(936\) 0 0
\(937\) −4.87273 −0.159185 −0.0795925 0.996827i \(-0.525362\pi\)
−0.0795925 + 0.996827i \(0.525362\pi\)
\(938\) 0 0
\(939\) 41.8111 1.36445
\(940\) 0 0
\(941\) 14.3248 0.466975 0.233487 0.972360i \(-0.424986\pi\)
0.233487 + 0.972360i \(0.424986\pi\)
\(942\) 0 0
\(943\) −6.14290 −0.200040
\(944\) 0 0
\(945\) 67.8771 2.20804
\(946\) 0 0
\(947\) 12.8887 0.418826 0.209413 0.977827i \(-0.432845\pi\)
0.209413 + 0.977827i \(0.432845\pi\)
\(948\) 0 0
\(949\) −51.1707 −1.66107
\(950\) 0 0
\(951\) 87.1697 2.82667
\(952\) 0 0
\(953\) −42.1470 −1.36528 −0.682638 0.730757i \(-0.739167\pi\)
−0.682638 + 0.730757i \(0.739167\pi\)
\(954\) 0 0
\(955\) 11.3068 0.365880
\(956\) 0 0
\(957\) −64.1066 −2.07227
\(958\) 0 0
\(959\) −2.47562 −0.0799420
\(960\) 0 0
\(961\) −24.2446 −0.782084
\(962\) 0 0
\(963\) 38.8479 1.25186
\(964\) 0 0
\(965\) −34.4138 −1.10782
\(966\) 0 0
\(967\) −18.4349 −0.592828 −0.296414 0.955060i \(-0.595791\pi\)
−0.296414 + 0.955060i \(0.595791\pi\)
\(968\) 0 0
\(969\) −74.2342 −2.38475
\(970\) 0 0
\(971\) 61.1213 1.96147 0.980737 0.195330i \(-0.0625779\pi\)
0.980737 + 0.195330i \(0.0625779\pi\)
\(972\) 0 0
\(973\) 4.43549 0.142195
\(974\) 0 0
\(975\) −15.7284 −0.503711
\(976\) 0 0
\(977\) 5.52698 0.176824 0.0884118 0.996084i \(-0.471821\pi\)
0.0884118 + 0.996084i \(0.471821\pi\)
\(978\) 0 0
\(979\) −13.5565 −0.433266
\(980\) 0 0
\(981\) −5.01600 −0.160149
\(982\) 0 0
\(983\) −36.1706 −1.15366 −0.576831 0.816864i \(-0.695711\pi\)
−0.576831 + 0.816864i \(0.695711\pi\)
\(984\) 0 0
\(985\) −56.7930 −1.80958
\(986\) 0 0
\(987\) 21.9232 0.697823
\(988\) 0 0
\(989\) −67.4790 −2.14571
\(990\) 0 0
\(991\) 32.1201 1.02033 0.510164 0.860077i \(-0.329585\pi\)
0.510164 + 0.860077i \(0.329585\pi\)
\(992\) 0 0
\(993\) 32.0558 1.01726
\(994\) 0 0
\(995\) −1.33399 −0.0422904
\(996\) 0 0
\(997\) 59.5135 1.88481 0.942406 0.334472i \(-0.108558\pi\)
0.942406 + 0.334472i \(0.108558\pi\)
\(998\) 0 0
\(999\) 119.412 3.77803
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.1.4 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.4 44 1.1 even 1 trivial