Properties

Label 6008.2.a.b.1.24
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 1.24
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.252021 q^{3} -1.14323 q^{5} -2.95394 q^{7} -2.93649 q^{9} +O(q^{10})\) \(q-0.252021 q^{3} -1.14323 q^{5} -2.95394 q^{7} -2.93649 q^{9} +4.60695 q^{11} -2.71345 q^{13} +0.288117 q^{15} +6.70585 q^{17} -3.81186 q^{19} +0.744454 q^{21} +8.43814 q^{23} -3.69304 q^{25} +1.49612 q^{27} -8.76408 q^{29} +5.25299 q^{31} -1.16105 q^{33} +3.37702 q^{35} +5.29340 q^{37} +0.683845 q^{39} -7.12412 q^{41} +10.1901 q^{43} +3.35707 q^{45} -4.85654 q^{47} +1.72574 q^{49} -1.69001 q^{51} +9.41547 q^{53} -5.26679 q^{55} +0.960668 q^{57} -12.5427 q^{59} +12.5093 q^{61} +8.67419 q^{63} +3.10208 q^{65} +0.810453 q^{67} -2.12659 q^{69} -9.99792 q^{71} -3.66059 q^{73} +0.930722 q^{75} -13.6086 q^{77} -5.78439 q^{79} +8.43240 q^{81} -2.78063 q^{83} -7.66630 q^{85} +2.20873 q^{87} +5.17695 q^{89} +8.01535 q^{91} -1.32386 q^{93} +4.35782 q^{95} +0.683095 q^{97} -13.5282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.252021 −0.145504 −0.0727522 0.997350i \(-0.523178\pi\)
−0.0727522 + 0.997350i \(0.523178\pi\)
\(4\) 0 0
\(5\) −1.14323 −0.511266 −0.255633 0.966774i \(-0.582284\pi\)
−0.255633 + 0.966774i \(0.582284\pi\)
\(6\) 0 0
\(7\) −2.95394 −1.11648 −0.558242 0.829678i \(-0.688524\pi\)
−0.558242 + 0.829678i \(0.688524\pi\)
\(8\) 0 0
\(9\) −2.93649 −0.978828
\(10\) 0 0
\(11\) 4.60695 1.38905 0.694524 0.719469i \(-0.255615\pi\)
0.694524 + 0.719469i \(0.255615\pi\)
\(12\) 0 0
\(13\) −2.71345 −0.752575 −0.376287 0.926503i \(-0.622799\pi\)
−0.376287 + 0.926503i \(0.622799\pi\)
\(14\) 0 0
\(15\) 0.288117 0.0743914
\(16\) 0 0
\(17\) 6.70585 1.62641 0.813204 0.581979i \(-0.197721\pi\)
0.813204 + 0.581979i \(0.197721\pi\)
\(18\) 0 0
\(19\) −3.81186 −0.874501 −0.437250 0.899340i \(-0.644048\pi\)
−0.437250 + 0.899340i \(0.644048\pi\)
\(20\) 0 0
\(21\) 0.744454 0.162453
\(22\) 0 0
\(23\) 8.43814 1.75947 0.879737 0.475460i \(-0.157718\pi\)
0.879737 + 0.475460i \(0.157718\pi\)
\(24\) 0 0
\(25\) −3.69304 −0.738607
\(26\) 0 0
\(27\) 1.49612 0.287928
\(28\) 0 0
\(29\) −8.76408 −1.62745 −0.813725 0.581251i \(-0.802564\pi\)
−0.813725 + 0.581251i \(0.802564\pi\)
\(30\) 0 0
\(31\) 5.25299 0.943464 0.471732 0.881742i \(-0.343629\pi\)
0.471732 + 0.881742i \(0.343629\pi\)
\(32\) 0 0
\(33\) −1.16105 −0.202113
\(34\) 0 0
\(35\) 3.37702 0.570820
\(36\) 0 0
\(37\) 5.29340 0.870230 0.435115 0.900375i \(-0.356708\pi\)
0.435115 + 0.900375i \(0.356708\pi\)
\(38\) 0 0
\(39\) 0.683845 0.109503
\(40\) 0 0
\(41\) −7.12412 −1.11260 −0.556301 0.830981i \(-0.687780\pi\)
−0.556301 + 0.830981i \(0.687780\pi\)
\(42\) 0 0
\(43\) 10.1901 1.55397 0.776987 0.629517i \(-0.216747\pi\)
0.776987 + 0.629517i \(0.216747\pi\)
\(44\) 0 0
\(45\) 3.35707 0.500442
\(46\) 0 0
\(47\) −4.85654 −0.708399 −0.354199 0.935170i \(-0.615247\pi\)
−0.354199 + 0.935170i \(0.615247\pi\)
\(48\) 0 0
\(49\) 1.72574 0.246535
\(50\) 0 0
\(51\) −1.69001 −0.236649
\(52\) 0 0
\(53\) 9.41547 1.29331 0.646657 0.762781i \(-0.276167\pi\)
0.646657 + 0.762781i \(0.276167\pi\)
\(54\) 0 0
\(55\) −5.26679 −0.710173
\(56\) 0 0
\(57\) 0.960668 0.127244
\(58\) 0 0
\(59\) −12.5427 −1.63291 −0.816457 0.577406i \(-0.804065\pi\)
−0.816457 + 0.577406i \(0.804065\pi\)
\(60\) 0 0
\(61\) 12.5093 1.60165 0.800823 0.598901i \(-0.204396\pi\)
0.800823 + 0.598901i \(0.204396\pi\)
\(62\) 0 0
\(63\) 8.67419 1.09285
\(64\) 0 0
\(65\) 3.10208 0.384766
\(66\) 0 0
\(67\) 0.810453 0.0990126 0.0495063 0.998774i \(-0.484235\pi\)
0.0495063 + 0.998774i \(0.484235\pi\)
\(68\) 0 0
\(69\) −2.12659 −0.256011
\(70\) 0 0
\(71\) −9.99792 −1.18654 −0.593268 0.805005i \(-0.702162\pi\)
−0.593268 + 0.805005i \(0.702162\pi\)
\(72\) 0 0
\(73\) −3.66059 −0.428439 −0.214220 0.976786i \(-0.568721\pi\)
−0.214220 + 0.976786i \(0.568721\pi\)
\(74\) 0 0
\(75\) 0.930722 0.107471
\(76\) 0 0
\(77\) −13.6086 −1.55085
\(78\) 0 0
\(79\) −5.78439 −0.650794 −0.325397 0.945577i \(-0.605498\pi\)
−0.325397 + 0.945577i \(0.605498\pi\)
\(80\) 0 0
\(81\) 8.43240 0.936934
\(82\) 0 0
\(83\) −2.78063 −0.305214 −0.152607 0.988287i \(-0.548767\pi\)
−0.152607 + 0.988287i \(0.548767\pi\)
\(84\) 0 0
\(85\) −7.66630 −0.831527
\(86\) 0 0
\(87\) 2.20873 0.236801
\(88\) 0 0
\(89\) 5.17695 0.548756 0.274378 0.961622i \(-0.411528\pi\)
0.274378 + 0.961622i \(0.411528\pi\)
\(90\) 0 0
\(91\) 8.01535 0.840237
\(92\) 0 0
\(93\) −1.32386 −0.137278
\(94\) 0 0
\(95\) 4.35782 0.447102
\(96\) 0 0
\(97\) 0.683095 0.0693578 0.0346789 0.999399i \(-0.488959\pi\)
0.0346789 + 0.999399i \(0.488959\pi\)
\(98\) 0 0
\(99\) −13.5282 −1.35964
\(100\) 0 0
\(101\) 17.7475 1.76594 0.882969 0.469431i \(-0.155541\pi\)
0.882969 + 0.469431i \(0.155541\pi\)
\(102\) 0 0
\(103\) 11.1758 1.10119 0.550595 0.834773i \(-0.314401\pi\)
0.550595 + 0.834773i \(0.314401\pi\)
\(104\) 0 0
\(105\) −0.851079 −0.0830568
\(106\) 0 0
\(107\) −4.88596 −0.472343 −0.236172 0.971711i \(-0.575893\pi\)
−0.236172 + 0.971711i \(0.575893\pi\)
\(108\) 0 0
\(109\) −8.12888 −0.778606 −0.389303 0.921110i \(-0.627284\pi\)
−0.389303 + 0.921110i \(0.627284\pi\)
\(110\) 0 0
\(111\) −1.33405 −0.126622
\(112\) 0 0
\(113\) −17.7705 −1.67170 −0.835852 0.548955i \(-0.815026\pi\)
−0.835852 + 0.548955i \(0.815026\pi\)
\(114\) 0 0
\(115\) −9.64670 −0.899560
\(116\) 0 0
\(117\) 7.96800 0.736642
\(118\) 0 0
\(119\) −19.8087 −1.81586
\(120\) 0 0
\(121\) 10.2240 0.929455
\(122\) 0 0
\(123\) 1.79543 0.161888
\(124\) 0 0
\(125\) 9.93810 0.888891
\(126\) 0 0
\(127\) −2.12777 −0.188809 −0.0944046 0.995534i \(-0.530095\pi\)
−0.0944046 + 0.995534i \(0.530095\pi\)
\(128\) 0 0
\(129\) −2.56811 −0.226110
\(130\) 0 0
\(131\) −2.22280 −0.194207 −0.0971036 0.995274i \(-0.530958\pi\)
−0.0971036 + 0.995274i \(0.530958\pi\)
\(132\) 0 0
\(133\) 11.2600 0.976365
\(134\) 0 0
\(135\) −1.71040 −0.147208
\(136\) 0 0
\(137\) 4.00853 0.342472 0.171236 0.985230i \(-0.445224\pi\)
0.171236 + 0.985230i \(0.445224\pi\)
\(138\) 0 0
\(139\) −18.0644 −1.53220 −0.766102 0.642719i \(-0.777806\pi\)
−0.766102 + 0.642719i \(0.777806\pi\)
\(140\) 0 0
\(141\) 1.22395 0.103075
\(142\) 0 0
\(143\) −12.5007 −1.04536
\(144\) 0 0
\(145\) 10.0193 0.832060
\(146\) 0 0
\(147\) −0.434923 −0.0358719
\(148\) 0 0
\(149\) −0.282976 −0.0231823 −0.0115911 0.999933i \(-0.503690\pi\)
−0.0115911 + 0.999933i \(0.503690\pi\)
\(150\) 0 0
\(151\) 17.5934 1.43173 0.715865 0.698238i \(-0.246032\pi\)
0.715865 + 0.698238i \(0.246032\pi\)
\(152\) 0 0
\(153\) −19.6916 −1.59197
\(154\) 0 0
\(155\) −6.00535 −0.482361
\(156\) 0 0
\(157\) −3.06030 −0.244239 −0.122119 0.992515i \(-0.538969\pi\)
−0.122119 + 0.992515i \(0.538969\pi\)
\(158\) 0 0
\(159\) −2.37289 −0.188183
\(160\) 0 0
\(161\) −24.9257 −1.96442
\(162\) 0 0
\(163\) −22.2746 −1.74468 −0.872340 0.488899i \(-0.837399\pi\)
−0.872340 + 0.488899i \(0.837399\pi\)
\(164\) 0 0
\(165\) 1.32734 0.103333
\(166\) 0 0
\(167\) −13.4126 −1.03790 −0.518949 0.854805i \(-0.673677\pi\)
−0.518949 + 0.854805i \(0.673677\pi\)
\(168\) 0 0
\(169\) −5.63721 −0.433631
\(170\) 0 0
\(171\) 11.1935 0.855986
\(172\) 0 0
\(173\) −6.74954 −0.513158 −0.256579 0.966523i \(-0.582595\pi\)
−0.256579 + 0.966523i \(0.582595\pi\)
\(174\) 0 0
\(175\) 10.9090 0.824642
\(176\) 0 0
\(177\) 3.16101 0.237596
\(178\) 0 0
\(179\) −15.9034 −1.18868 −0.594339 0.804215i \(-0.702586\pi\)
−0.594339 + 0.804215i \(0.702586\pi\)
\(180\) 0 0
\(181\) −20.1609 −1.49855 −0.749273 0.662262i \(-0.769597\pi\)
−0.749273 + 0.662262i \(0.769597\pi\)
\(182\) 0 0
\(183\) −3.15259 −0.233046
\(184\) 0 0
\(185\) −6.05155 −0.444919
\(186\) 0 0
\(187\) 30.8935 2.25916
\(188\) 0 0
\(189\) −4.41944 −0.321467
\(190\) 0 0
\(191\) −5.46129 −0.395165 −0.197583 0.980286i \(-0.563309\pi\)
−0.197583 + 0.980286i \(0.563309\pi\)
\(192\) 0 0
\(193\) −13.9352 −1.00307 −0.501537 0.865136i \(-0.667232\pi\)
−0.501537 + 0.865136i \(0.667232\pi\)
\(194\) 0 0
\(195\) −0.781789 −0.0559851
\(196\) 0 0
\(197\) −20.1623 −1.43650 −0.718252 0.695783i \(-0.755058\pi\)
−0.718252 + 0.695783i \(0.755058\pi\)
\(198\) 0 0
\(199\) 13.4525 0.953626 0.476813 0.879005i \(-0.341792\pi\)
0.476813 + 0.879005i \(0.341792\pi\)
\(200\) 0 0
\(201\) −0.204251 −0.0144068
\(202\) 0 0
\(203\) 25.8885 1.81702
\(204\) 0 0
\(205\) 8.14448 0.568835
\(206\) 0 0
\(207\) −24.7785 −1.72222
\(208\) 0 0
\(209\) −17.5611 −1.21472
\(210\) 0 0
\(211\) −2.99575 −0.206236 −0.103118 0.994669i \(-0.532882\pi\)
−0.103118 + 0.994669i \(0.532882\pi\)
\(212\) 0 0
\(213\) 2.51969 0.172646
\(214\) 0 0
\(215\) −11.6496 −0.794494
\(216\) 0 0
\(217\) −15.5170 −1.05336
\(218\) 0 0
\(219\) 0.922544 0.0623397
\(220\) 0 0
\(221\) −18.1960 −1.22399
\(222\) 0 0
\(223\) −0.957053 −0.0640890 −0.0320445 0.999486i \(-0.510202\pi\)
−0.0320445 + 0.999486i \(0.510202\pi\)
\(224\) 0 0
\(225\) 10.8445 0.722970
\(226\) 0 0
\(227\) −23.6386 −1.56895 −0.784474 0.620162i \(-0.787067\pi\)
−0.784474 + 0.620162i \(0.787067\pi\)
\(228\) 0 0
\(229\) −8.56225 −0.565809 −0.282905 0.959148i \(-0.591298\pi\)
−0.282905 + 0.959148i \(0.591298\pi\)
\(230\) 0 0
\(231\) 3.42966 0.225655
\(232\) 0 0
\(233\) 28.5277 1.86891 0.934456 0.356078i \(-0.115886\pi\)
0.934456 + 0.356078i \(0.115886\pi\)
\(234\) 0 0
\(235\) 5.55212 0.362180
\(236\) 0 0
\(237\) 1.45779 0.0946934
\(238\) 0 0
\(239\) −13.7041 −0.886443 −0.443222 0.896412i \(-0.646165\pi\)
−0.443222 + 0.896412i \(0.646165\pi\)
\(240\) 0 0
\(241\) −22.3406 −1.43908 −0.719541 0.694450i \(-0.755648\pi\)
−0.719541 + 0.694450i \(0.755648\pi\)
\(242\) 0 0
\(243\) −6.61350 −0.424256
\(244\) 0 0
\(245\) −1.97291 −0.126045
\(246\) 0 0
\(247\) 10.3433 0.658127
\(248\) 0 0
\(249\) 0.700777 0.0444099
\(250\) 0 0
\(251\) −18.8213 −1.18799 −0.593994 0.804470i \(-0.702450\pi\)
−0.593994 + 0.804470i \(0.702450\pi\)
\(252\) 0 0
\(253\) 38.8741 2.44400
\(254\) 0 0
\(255\) 1.93207 0.120991
\(256\) 0 0
\(257\) 3.75055 0.233953 0.116976 0.993135i \(-0.462680\pi\)
0.116976 + 0.993135i \(0.462680\pi\)
\(258\) 0 0
\(259\) −15.6364 −0.971597
\(260\) 0 0
\(261\) 25.7356 1.59299
\(262\) 0 0
\(263\) −2.37751 −0.146604 −0.0733018 0.997310i \(-0.523354\pi\)
−0.0733018 + 0.997310i \(0.523354\pi\)
\(264\) 0 0
\(265\) −10.7640 −0.661228
\(266\) 0 0
\(267\) −1.30470 −0.0798463
\(268\) 0 0
\(269\) 14.5047 0.884369 0.442185 0.896924i \(-0.354204\pi\)
0.442185 + 0.896924i \(0.354204\pi\)
\(270\) 0 0
\(271\) −8.82781 −0.536251 −0.268126 0.963384i \(-0.586404\pi\)
−0.268126 + 0.963384i \(0.586404\pi\)
\(272\) 0 0
\(273\) −2.02004 −0.122258
\(274\) 0 0
\(275\) −17.0136 −1.02596
\(276\) 0 0
\(277\) 24.3478 1.46292 0.731458 0.681887i \(-0.238840\pi\)
0.731458 + 0.681887i \(0.238840\pi\)
\(278\) 0 0
\(279\) −15.4253 −0.923490
\(280\) 0 0
\(281\) −16.4674 −0.982365 −0.491182 0.871057i \(-0.663435\pi\)
−0.491182 + 0.871057i \(0.663435\pi\)
\(282\) 0 0
\(283\) 1.07647 0.0639897 0.0319949 0.999488i \(-0.489814\pi\)
0.0319949 + 0.999488i \(0.489814\pi\)
\(284\) 0 0
\(285\) −1.09826 −0.0650553
\(286\) 0 0
\(287\) 21.0442 1.24220
\(288\) 0 0
\(289\) 27.9685 1.64520
\(290\) 0 0
\(291\) −0.172154 −0.0100919
\(292\) 0 0
\(293\) 8.83987 0.516430 0.258215 0.966087i \(-0.416866\pi\)
0.258215 + 0.966087i \(0.416866\pi\)
\(294\) 0 0
\(295\) 14.3391 0.834854
\(296\) 0 0
\(297\) 6.89254 0.399946
\(298\) 0 0
\(299\) −22.8965 −1.32414
\(300\) 0 0
\(301\) −30.1009 −1.73499
\(302\) 0 0
\(303\) −4.47273 −0.256952
\(304\) 0 0
\(305\) −14.3009 −0.818867
\(306\) 0 0
\(307\) −1.14588 −0.0653987 −0.0326993 0.999465i \(-0.510410\pi\)
−0.0326993 + 0.999465i \(0.510410\pi\)
\(308\) 0 0
\(309\) −2.81655 −0.160228
\(310\) 0 0
\(311\) −0.980364 −0.0555914 −0.0277957 0.999614i \(-0.508849\pi\)
−0.0277957 + 0.999614i \(0.508849\pi\)
\(312\) 0 0
\(313\) −26.6505 −1.50637 −0.753186 0.657807i \(-0.771484\pi\)
−0.753186 + 0.657807i \(0.771484\pi\)
\(314\) 0 0
\(315\) −9.91656 −0.558735
\(316\) 0 0
\(317\) 4.87754 0.273950 0.136975 0.990575i \(-0.456262\pi\)
0.136975 + 0.990575i \(0.456262\pi\)
\(318\) 0 0
\(319\) −40.3757 −2.26061
\(320\) 0 0
\(321\) 1.23136 0.0687280
\(322\) 0 0
\(323\) −25.5618 −1.42229
\(324\) 0 0
\(325\) 10.0209 0.555857
\(326\) 0 0
\(327\) 2.04865 0.113291
\(328\) 0 0
\(329\) 14.3459 0.790915
\(330\) 0 0
\(331\) 0.797406 0.0438294 0.0219147 0.999760i \(-0.493024\pi\)
0.0219147 + 0.999760i \(0.493024\pi\)
\(332\) 0 0
\(333\) −15.5440 −0.851806
\(334\) 0 0
\(335\) −0.926531 −0.0506218
\(336\) 0 0
\(337\) 28.4113 1.54766 0.773832 0.633391i \(-0.218338\pi\)
0.773832 + 0.633391i \(0.218338\pi\)
\(338\) 0 0
\(339\) 4.47853 0.243240
\(340\) 0 0
\(341\) 24.2003 1.31052
\(342\) 0 0
\(343\) 15.5798 0.841231
\(344\) 0 0
\(345\) 2.43117 0.130890
\(346\) 0 0
\(347\) −13.6649 −0.733569 −0.366784 0.930306i \(-0.619541\pi\)
−0.366784 + 0.930306i \(0.619541\pi\)
\(348\) 0 0
\(349\) 27.6224 1.47859 0.739296 0.673380i \(-0.235158\pi\)
0.739296 + 0.673380i \(0.235158\pi\)
\(350\) 0 0
\(351\) −4.05964 −0.216687
\(352\) 0 0
\(353\) −9.72895 −0.517820 −0.258910 0.965902i \(-0.583363\pi\)
−0.258910 + 0.965902i \(0.583363\pi\)
\(354\) 0 0
\(355\) 11.4299 0.606635
\(356\) 0 0
\(357\) 4.99220 0.264215
\(358\) 0 0
\(359\) −32.0359 −1.69079 −0.845396 0.534140i \(-0.820636\pi\)
−0.845396 + 0.534140i \(0.820636\pi\)
\(360\) 0 0
\(361\) −4.46973 −0.235249
\(362\) 0 0
\(363\) −2.57666 −0.135240
\(364\) 0 0
\(365\) 4.18488 0.219046
\(366\) 0 0
\(367\) 5.86530 0.306166 0.153083 0.988213i \(-0.451080\pi\)
0.153083 + 0.988213i \(0.451080\pi\)
\(368\) 0 0
\(369\) 20.9199 1.08905
\(370\) 0 0
\(371\) −27.8127 −1.44396
\(372\) 0 0
\(373\) 15.7819 0.817154 0.408577 0.912724i \(-0.366025\pi\)
0.408577 + 0.912724i \(0.366025\pi\)
\(374\) 0 0
\(375\) −2.50461 −0.129337
\(376\) 0 0
\(377\) 23.7809 1.22478
\(378\) 0 0
\(379\) 16.2902 0.836771 0.418385 0.908270i \(-0.362596\pi\)
0.418385 + 0.908270i \(0.362596\pi\)
\(380\) 0 0
\(381\) 0.536243 0.0274725
\(382\) 0 0
\(383\) 7.61829 0.389277 0.194638 0.980875i \(-0.437647\pi\)
0.194638 + 0.980875i \(0.437647\pi\)
\(384\) 0 0
\(385\) 15.5578 0.792896
\(386\) 0 0
\(387\) −29.9230 −1.52107
\(388\) 0 0
\(389\) 6.91050 0.350376 0.175188 0.984535i \(-0.443947\pi\)
0.175188 + 0.984535i \(0.443947\pi\)
\(390\) 0 0
\(391\) 56.5849 2.86162
\(392\) 0 0
\(393\) 0.560193 0.0282580
\(394\) 0 0
\(395\) 6.61286 0.332729
\(396\) 0 0
\(397\) −18.3598 −0.921453 −0.460726 0.887542i \(-0.652411\pi\)
−0.460726 + 0.887542i \(0.652411\pi\)
\(398\) 0 0
\(399\) −2.83775 −0.142065
\(400\) 0 0
\(401\) 4.42851 0.221149 0.110575 0.993868i \(-0.464731\pi\)
0.110575 + 0.993868i \(0.464731\pi\)
\(402\) 0 0
\(403\) −14.2537 −0.710027
\(404\) 0 0
\(405\) −9.64014 −0.479022
\(406\) 0 0
\(407\) 24.3864 1.20879
\(408\) 0 0
\(409\) −36.0535 −1.78273 −0.891367 0.453283i \(-0.850253\pi\)
−0.891367 + 0.453283i \(0.850253\pi\)
\(410\) 0 0
\(411\) −1.01023 −0.0498312
\(412\) 0 0
\(413\) 37.0502 1.82312
\(414\) 0 0
\(415\) 3.17889 0.156045
\(416\) 0 0
\(417\) 4.55261 0.222942
\(418\) 0 0
\(419\) 14.1124 0.689434 0.344717 0.938707i \(-0.387975\pi\)
0.344717 + 0.938707i \(0.387975\pi\)
\(420\) 0 0
\(421\) 8.08360 0.393970 0.196985 0.980406i \(-0.436885\pi\)
0.196985 + 0.980406i \(0.436885\pi\)
\(422\) 0 0
\(423\) 14.2611 0.693401
\(424\) 0 0
\(425\) −24.7649 −1.20128
\(426\) 0 0
\(427\) −36.9516 −1.78821
\(428\) 0 0
\(429\) 3.15044 0.152105
\(430\) 0 0
\(431\) 31.8067 1.53208 0.766038 0.642796i \(-0.222226\pi\)
0.766038 + 0.642796i \(0.222226\pi\)
\(432\) 0 0
\(433\) −31.0657 −1.49292 −0.746461 0.665430i \(-0.768248\pi\)
−0.746461 + 0.665430i \(0.768248\pi\)
\(434\) 0 0
\(435\) −2.52508 −0.121068
\(436\) 0 0
\(437\) −32.1650 −1.53866
\(438\) 0 0
\(439\) −29.0275 −1.38541 −0.692704 0.721222i \(-0.743581\pi\)
−0.692704 + 0.721222i \(0.743581\pi\)
\(440\) 0 0
\(441\) −5.06762 −0.241315
\(442\) 0 0
\(443\) 19.3683 0.920217 0.460109 0.887863i \(-0.347810\pi\)
0.460109 + 0.887863i \(0.347810\pi\)
\(444\) 0 0
\(445\) −5.91842 −0.280560
\(446\) 0 0
\(447\) 0.0713158 0.00337312
\(448\) 0 0
\(449\) 18.0937 0.853895 0.426947 0.904276i \(-0.359589\pi\)
0.426947 + 0.904276i \(0.359589\pi\)
\(450\) 0 0
\(451\) −32.8205 −1.54546
\(452\) 0 0
\(453\) −4.43390 −0.208323
\(454\) 0 0
\(455\) −9.16335 −0.429585
\(456\) 0 0
\(457\) 4.21494 0.197167 0.0985834 0.995129i \(-0.468569\pi\)
0.0985834 + 0.995129i \(0.468569\pi\)
\(458\) 0 0
\(459\) 10.0327 0.468289
\(460\) 0 0
\(461\) 20.0523 0.933927 0.466963 0.884277i \(-0.345348\pi\)
0.466963 + 0.884277i \(0.345348\pi\)
\(462\) 0 0
\(463\) −40.6145 −1.88752 −0.943759 0.330634i \(-0.892737\pi\)
−0.943759 + 0.330634i \(0.892737\pi\)
\(464\) 0 0
\(465\) 1.51347 0.0701856
\(466\) 0 0
\(467\) −33.2401 −1.53817 −0.769084 0.639148i \(-0.779287\pi\)
−0.769084 + 0.639148i \(0.779287\pi\)
\(468\) 0 0
\(469\) −2.39403 −0.110546
\(470\) 0 0
\(471\) 0.771260 0.0355378
\(472\) 0 0
\(473\) 46.9452 2.15854
\(474\) 0 0
\(475\) 14.0773 0.645912
\(476\) 0 0
\(477\) −27.6484 −1.26593
\(478\) 0 0
\(479\) −17.2081 −0.786260 −0.393130 0.919483i \(-0.628608\pi\)
−0.393130 + 0.919483i \(0.628608\pi\)
\(480\) 0 0
\(481\) −14.3634 −0.654913
\(482\) 0 0
\(483\) 6.28181 0.285832
\(484\) 0 0
\(485\) −0.780932 −0.0354603
\(486\) 0 0
\(487\) −25.4301 −1.15235 −0.576175 0.817327i \(-0.695455\pi\)
−0.576175 + 0.817327i \(0.695455\pi\)
\(488\) 0 0
\(489\) 5.61366 0.253859
\(490\) 0 0
\(491\) −2.16525 −0.0977164 −0.0488582 0.998806i \(-0.515558\pi\)
−0.0488582 + 0.998806i \(0.515558\pi\)
\(492\) 0 0
\(493\) −58.7706 −2.64690
\(494\) 0 0
\(495\) 15.4658 0.695138
\(496\) 0 0
\(497\) 29.5332 1.32475
\(498\) 0 0
\(499\) 22.0046 0.985063 0.492532 0.870295i \(-0.336072\pi\)
0.492532 + 0.870295i \(0.336072\pi\)
\(500\) 0 0
\(501\) 3.38025 0.151019
\(502\) 0 0
\(503\) 33.9725 1.51476 0.757379 0.652976i \(-0.226480\pi\)
0.757379 + 0.652976i \(0.226480\pi\)
\(504\) 0 0
\(505\) −20.2894 −0.902864
\(506\) 0 0
\(507\) 1.42069 0.0630952
\(508\) 0 0
\(509\) −28.1600 −1.24817 −0.624085 0.781356i \(-0.714528\pi\)
−0.624085 + 0.781356i \(0.714528\pi\)
\(510\) 0 0
\(511\) 10.8131 0.478345
\(512\) 0 0
\(513\) −5.70299 −0.251793
\(514\) 0 0
\(515\) −12.7765 −0.563001
\(516\) 0 0
\(517\) −22.3738 −0.984000
\(518\) 0 0
\(519\) 1.70102 0.0746667
\(520\) 0 0
\(521\) −5.99942 −0.262839 −0.131420 0.991327i \(-0.541954\pi\)
−0.131420 + 0.991327i \(0.541954\pi\)
\(522\) 0 0
\(523\) 2.86485 0.125271 0.0626355 0.998036i \(-0.480049\pi\)
0.0626355 + 0.998036i \(0.480049\pi\)
\(524\) 0 0
\(525\) −2.74929 −0.119989
\(526\) 0 0
\(527\) 35.2257 1.53446
\(528\) 0 0
\(529\) 48.2023 2.09575
\(530\) 0 0
\(531\) 36.8313 1.59834
\(532\) 0 0
\(533\) 19.3309 0.837316
\(534\) 0 0
\(535\) 5.58575 0.241493
\(536\) 0 0
\(537\) 4.00800 0.172958
\(538\) 0 0
\(539\) 7.95041 0.342449
\(540\) 0 0
\(541\) 20.9419 0.900362 0.450181 0.892937i \(-0.351360\pi\)
0.450181 + 0.892937i \(0.351360\pi\)
\(542\) 0 0
\(543\) 5.08096 0.218045
\(544\) 0 0
\(545\) 9.29315 0.398075
\(546\) 0 0
\(547\) −17.3985 −0.743908 −0.371954 0.928251i \(-0.621312\pi\)
−0.371954 + 0.928251i \(0.621312\pi\)
\(548\) 0 0
\(549\) −36.7333 −1.56774
\(550\) 0 0
\(551\) 33.4075 1.42321
\(552\) 0 0
\(553\) 17.0867 0.726601
\(554\) 0 0
\(555\) 1.52512 0.0647376
\(556\) 0 0
\(557\) −10.5066 −0.445180 −0.222590 0.974912i \(-0.571451\pi\)
−0.222590 + 0.974912i \(0.571451\pi\)
\(558\) 0 0
\(559\) −27.6503 −1.16948
\(560\) 0 0
\(561\) −7.78582 −0.328717
\(562\) 0 0
\(563\) 22.3769 0.943074 0.471537 0.881846i \(-0.343699\pi\)
0.471537 + 0.881846i \(0.343699\pi\)
\(564\) 0 0
\(565\) 20.3156 0.854685
\(566\) 0 0
\(567\) −24.9088 −1.04607
\(568\) 0 0
\(569\) −10.6913 −0.448201 −0.224100 0.974566i \(-0.571944\pi\)
−0.224100 + 0.974566i \(0.571944\pi\)
\(570\) 0 0
\(571\) 3.53095 0.147766 0.0738829 0.997267i \(-0.476461\pi\)
0.0738829 + 0.997267i \(0.476461\pi\)
\(572\) 0 0
\(573\) 1.37636 0.0574982
\(574\) 0 0
\(575\) −31.1624 −1.29956
\(576\) 0 0
\(577\) −1.96274 −0.0817098 −0.0408549 0.999165i \(-0.513008\pi\)
−0.0408549 + 0.999165i \(0.513008\pi\)
\(578\) 0 0
\(579\) 3.51195 0.145952
\(580\) 0 0
\(581\) 8.21381 0.340766
\(582\) 0 0
\(583\) 43.3766 1.79648
\(584\) 0 0
\(585\) −9.10922 −0.376620
\(586\) 0 0
\(587\) −40.0967 −1.65497 −0.827484 0.561489i \(-0.810229\pi\)
−0.827484 + 0.561489i \(0.810229\pi\)
\(588\) 0 0
\(589\) −20.0236 −0.825060
\(590\) 0 0
\(591\) 5.08132 0.209018
\(592\) 0 0
\(593\) 38.0326 1.56181 0.780905 0.624650i \(-0.214758\pi\)
0.780905 + 0.624650i \(0.214758\pi\)
\(594\) 0 0
\(595\) 22.6458 0.928386
\(596\) 0 0
\(597\) −3.39032 −0.138757
\(598\) 0 0
\(599\) 39.7839 1.62552 0.812762 0.582595i \(-0.197963\pi\)
0.812762 + 0.582595i \(0.197963\pi\)
\(600\) 0 0
\(601\) 3.28308 0.133920 0.0669598 0.997756i \(-0.478670\pi\)
0.0669598 + 0.997756i \(0.478670\pi\)
\(602\) 0 0
\(603\) −2.37988 −0.0969163
\(604\) 0 0
\(605\) −11.6883 −0.475199
\(606\) 0 0
\(607\) −24.1249 −0.979198 −0.489599 0.871948i \(-0.662857\pi\)
−0.489599 + 0.871948i \(0.662857\pi\)
\(608\) 0 0
\(609\) −6.52445 −0.264384
\(610\) 0 0
\(611\) 13.1780 0.533123
\(612\) 0 0
\(613\) −11.7593 −0.474955 −0.237478 0.971393i \(-0.576321\pi\)
−0.237478 + 0.971393i \(0.576321\pi\)
\(614\) 0 0
\(615\) −2.05258 −0.0827680
\(616\) 0 0
\(617\) 10.0660 0.405243 0.202621 0.979257i \(-0.435054\pi\)
0.202621 + 0.979257i \(0.435054\pi\)
\(618\) 0 0
\(619\) 32.5890 1.30986 0.654931 0.755689i \(-0.272698\pi\)
0.654931 + 0.755689i \(0.272698\pi\)
\(620\) 0 0
\(621\) 12.6245 0.506602
\(622\) 0 0
\(623\) −15.2924 −0.612677
\(624\) 0 0
\(625\) 7.10368 0.284147
\(626\) 0 0
\(627\) 4.42575 0.176748
\(628\) 0 0
\(629\) 35.4968 1.41535
\(630\) 0 0
\(631\) −13.6390 −0.542959 −0.271479 0.962444i \(-0.587513\pi\)
−0.271479 + 0.962444i \(0.587513\pi\)
\(632\) 0 0
\(633\) 0.754993 0.0300083
\(634\) 0 0
\(635\) 2.43252 0.0965317
\(636\) 0 0
\(637\) −4.68271 −0.185536
\(638\) 0 0
\(639\) 29.3588 1.16141
\(640\) 0 0
\(641\) 48.3226 1.90863 0.954314 0.298805i \(-0.0965881\pi\)
0.954314 + 0.298805i \(0.0965881\pi\)
\(642\) 0 0
\(643\) −8.93728 −0.352452 −0.176226 0.984350i \(-0.556389\pi\)
−0.176226 + 0.984350i \(0.556389\pi\)
\(644\) 0 0
\(645\) 2.93593 0.115602
\(646\) 0 0
\(647\) −39.7198 −1.56155 −0.780773 0.624814i \(-0.785175\pi\)
−0.780773 + 0.624814i \(0.785175\pi\)
\(648\) 0 0
\(649\) −57.7834 −2.26820
\(650\) 0 0
\(651\) 3.91061 0.153269
\(652\) 0 0
\(653\) −17.4501 −0.682874 −0.341437 0.939905i \(-0.610914\pi\)
−0.341437 + 0.939905i \(0.610914\pi\)
\(654\) 0 0
\(655\) 2.54117 0.0992916
\(656\) 0 0
\(657\) 10.7493 0.419368
\(658\) 0 0
\(659\) 34.8645 1.35813 0.679063 0.734080i \(-0.262386\pi\)
0.679063 + 0.734080i \(0.262386\pi\)
\(660\) 0 0
\(661\) −35.2295 −1.37027 −0.685134 0.728417i \(-0.740256\pi\)
−0.685134 + 0.728417i \(0.740256\pi\)
\(662\) 0 0
\(663\) 4.58576 0.178096
\(664\) 0 0
\(665\) −12.8727 −0.499182
\(666\) 0 0
\(667\) −73.9526 −2.86346
\(668\) 0 0
\(669\) 0.241197 0.00932523
\(670\) 0 0
\(671\) 57.6295 2.22476
\(672\) 0 0
\(673\) −7.35195 −0.283397 −0.141698 0.989910i \(-0.545256\pi\)
−0.141698 + 0.989910i \(0.545256\pi\)
\(674\) 0 0
\(675\) −5.52522 −0.212666
\(676\) 0 0
\(677\) −9.50512 −0.365311 −0.182656 0.983177i \(-0.558469\pi\)
−0.182656 + 0.983177i \(0.558469\pi\)
\(678\) 0 0
\(679\) −2.01782 −0.0774368
\(680\) 0 0
\(681\) 5.95742 0.228289
\(682\) 0 0
\(683\) −23.3338 −0.892842 −0.446421 0.894823i \(-0.647302\pi\)
−0.446421 + 0.894823i \(0.647302\pi\)
\(684\) 0 0
\(685\) −4.58266 −0.175094
\(686\) 0 0
\(687\) 2.15787 0.0823277
\(688\) 0 0
\(689\) −25.5484 −0.973315
\(690\) 0 0
\(691\) −26.0906 −0.992534 −0.496267 0.868170i \(-0.665296\pi\)
−0.496267 + 0.868170i \(0.665296\pi\)
\(692\) 0 0
\(693\) 39.9616 1.51802
\(694\) 0 0
\(695\) 20.6517 0.783364
\(696\) 0 0
\(697\) −47.7733 −1.80954
\(698\) 0 0
\(699\) −7.18958 −0.271935
\(700\) 0 0
\(701\) −35.5202 −1.34158 −0.670791 0.741647i \(-0.734045\pi\)
−0.670791 + 0.741647i \(0.734045\pi\)
\(702\) 0 0
\(703\) −20.1777 −0.761017
\(704\) 0 0
\(705\) −1.39925 −0.0526988
\(706\) 0 0
\(707\) −52.4249 −1.97164
\(708\) 0 0
\(709\) 47.0545 1.76717 0.883584 0.468273i \(-0.155124\pi\)
0.883584 + 0.468273i \(0.155124\pi\)
\(710\) 0 0
\(711\) 16.9858 0.637016
\(712\) 0 0
\(713\) 44.3255 1.66000
\(714\) 0 0
\(715\) 14.2911 0.534458
\(716\) 0 0
\(717\) 3.45371 0.128981
\(718\) 0 0
\(719\) −6.33724 −0.236339 −0.118170 0.992993i \(-0.537703\pi\)
−0.118170 + 0.992993i \(0.537703\pi\)
\(720\) 0 0
\(721\) −33.0128 −1.22946
\(722\) 0 0
\(723\) 5.63029 0.209393
\(724\) 0 0
\(725\) 32.3661 1.20205
\(726\) 0 0
\(727\) −10.6592 −0.395328 −0.197664 0.980270i \(-0.563335\pi\)
−0.197664 + 0.980270i \(0.563335\pi\)
\(728\) 0 0
\(729\) −23.6305 −0.875203
\(730\) 0 0
\(731\) 68.3332 2.52739
\(732\) 0 0
\(733\) 40.8304 1.50810 0.754052 0.656814i \(-0.228096\pi\)
0.754052 + 0.656814i \(0.228096\pi\)
\(734\) 0 0
\(735\) 0.497215 0.0183401
\(736\) 0 0
\(737\) 3.73372 0.137533
\(738\) 0 0
\(739\) −13.1822 −0.484917 −0.242458 0.970162i \(-0.577954\pi\)
−0.242458 + 0.970162i \(0.577954\pi\)
\(740\) 0 0
\(741\) −2.60672 −0.0957603
\(742\) 0 0
\(743\) −30.1895 −1.10754 −0.553772 0.832668i \(-0.686812\pi\)
−0.553772 + 0.832668i \(0.686812\pi\)
\(744\) 0 0
\(745\) 0.323505 0.0118523
\(746\) 0 0
\(747\) 8.16528 0.298752
\(748\) 0 0
\(749\) 14.4328 0.527363
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 4.74335 0.172857
\(754\) 0 0
\(755\) −20.1132 −0.731995
\(756\) 0 0
\(757\) 7.94987 0.288943 0.144471 0.989509i \(-0.453852\pi\)
0.144471 + 0.989509i \(0.453852\pi\)
\(758\) 0 0
\(759\) −9.79709 −0.355612
\(760\) 0 0
\(761\) −22.0572 −0.799571 −0.399786 0.916609i \(-0.630915\pi\)
−0.399786 + 0.916609i \(0.630915\pi\)
\(762\) 0 0
\(763\) 24.0122 0.869300
\(764\) 0 0
\(765\) 22.5120 0.813923
\(766\) 0 0
\(767\) 34.0338 1.22889
\(768\) 0 0
\(769\) −40.1229 −1.44687 −0.723435 0.690393i \(-0.757438\pi\)
−0.723435 + 0.690393i \(0.757438\pi\)
\(770\) 0 0
\(771\) −0.945217 −0.0340412
\(772\) 0 0
\(773\) −28.5766 −1.02783 −0.513915 0.857841i \(-0.671805\pi\)
−0.513915 + 0.857841i \(0.671805\pi\)
\(774\) 0 0
\(775\) −19.3995 −0.696849
\(776\) 0 0
\(777\) 3.94069 0.141372
\(778\) 0 0
\(779\) 27.1562 0.972970
\(780\) 0 0
\(781\) −46.0599 −1.64815
\(782\) 0 0
\(783\) −13.1121 −0.468588
\(784\) 0 0
\(785\) 3.49862 0.124871
\(786\) 0 0
\(787\) −3.05876 −0.109033 −0.0545164 0.998513i \(-0.517362\pi\)
−0.0545164 + 0.998513i \(0.517362\pi\)
\(788\) 0 0
\(789\) 0.599182 0.0213314
\(790\) 0 0
\(791\) 52.4928 1.86643
\(792\) 0 0
\(793\) −33.9432 −1.20536
\(794\) 0 0
\(795\) 2.71275 0.0962115
\(796\) 0 0
\(797\) 29.5429 1.04646 0.523232 0.852191i \(-0.324726\pi\)
0.523232 + 0.852191i \(0.324726\pi\)
\(798\) 0 0
\(799\) −32.5672 −1.15215
\(800\) 0 0
\(801\) −15.2020 −0.537138
\(802\) 0 0
\(803\) −16.8641 −0.595123
\(804\) 0 0
\(805\) 28.4958 1.00434
\(806\) 0 0
\(807\) −3.65550 −0.128680
\(808\) 0 0
\(809\) 18.4865 0.649950 0.324975 0.945723i \(-0.394644\pi\)
0.324975 + 0.945723i \(0.394644\pi\)
\(810\) 0 0
\(811\) −14.3391 −0.503516 −0.251758 0.967790i \(-0.581009\pi\)
−0.251758 + 0.967790i \(0.581009\pi\)
\(812\) 0 0
\(813\) 2.22479 0.0780269
\(814\) 0 0
\(815\) 25.4649 0.891996
\(816\) 0 0
\(817\) −38.8432 −1.35895
\(818\) 0 0
\(819\) −23.5370 −0.822448
\(820\) 0 0
\(821\) −7.24580 −0.252880 −0.126440 0.991974i \(-0.540355\pi\)
−0.126440 + 0.991974i \(0.540355\pi\)
\(822\) 0 0
\(823\) −25.0662 −0.873751 −0.436876 0.899522i \(-0.643915\pi\)
−0.436876 + 0.899522i \(0.643915\pi\)
\(824\) 0 0
\(825\) 4.28779 0.149282
\(826\) 0 0
\(827\) 23.7084 0.824423 0.412211 0.911088i \(-0.364757\pi\)
0.412211 + 0.911088i \(0.364757\pi\)
\(828\) 0 0
\(829\) 4.17291 0.144931 0.0724656 0.997371i \(-0.476913\pi\)
0.0724656 + 0.997371i \(0.476913\pi\)
\(830\) 0 0
\(831\) −6.13615 −0.212861
\(832\) 0 0
\(833\) 11.5726 0.400966
\(834\) 0 0
\(835\) 15.3336 0.530642
\(836\) 0 0
\(837\) 7.85909 0.271650
\(838\) 0 0
\(839\) −36.3469 −1.25483 −0.627417 0.778684i \(-0.715888\pi\)
−0.627417 + 0.778684i \(0.715888\pi\)
\(840\) 0 0
\(841\) 47.8091 1.64859
\(842\) 0 0
\(843\) 4.15014 0.142938
\(844\) 0 0
\(845\) 6.44460 0.221701
\(846\) 0 0
\(847\) −30.2011 −1.03772
\(848\) 0 0
\(849\) −0.271294 −0.00931078
\(850\) 0 0
\(851\) 44.6665 1.53115
\(852\) 0 0
\(853\) −2.60157 −0.0890759 −0.0445380 0.999008i \(-0.514182\pi\)
−0.0445380 + 0.999008i \(0.514182\pi\)
\(854\) 0 0
\(855\) −12.7967 −0.437637
\(856\) 0 0
\(857\) 2.25317 0.0769670 0.0384835 0.999259i \(-0.487747\pi\)
0.0384835 + 0.999259i \(0.487747\pi\)
\(858\) 0 0
\(859\) 17.7809 0.606678 0.303339 0.952883i \(-0.401899\pi\)
0.303339 + 0.952883i \(0.401899\pi\)
\(860\) 0 0
\(861\) −5.30358 −0.180746
\(862\) 0 0
\(863\) −49.5856 −1.68791 −0.843957 0.536411i \(-0.819780\pi\)
−0.843957 + 0.536411i \(0.819780\pi\)
\(864\) 0 0
\(865\) 7.71624 0.262360
\(866\) 0 0
\(867\) −7.04863 −0.239384
\(868\) 0 0
\(869\) −26.6484 −0.903985
\(870\) 0 0
\(871\) −2.19912 −0.0745144
\(872\) 0 0
\(873\) −2.00590 −0.0678894
\(874\) 0 0
\(875\) −29.3565 −0.992432
\(876\) 0 0
\(877\) 36.8074 1.24290 0.621448 0.783455i \(-0.286545\pi\)
0.621448 + 0.783455i \(0.286545\pi\)
\(878\) 0 0
\(879\) −2.22783 −0.0751429
\(880\) 0 0
\(881\) −20.5873 −0.693604 −0.346802 0.937938i \(-0.612732\pi\)
−0.346802 + 0.937938i \(0.612732\pi\)
\(882\) 0 0
\(883\) 42.5771 1.43283 0.716417 0.697673i \(-0.245781\pi\)
0.716417 + 0.697673i \(0.245781\pi\)
\(884\) 0 0
\(885\) −3.61375 −0.121475
\(886\) 0 0
\(887\) 3.91496 0.131452 0.0657258 0.997838i \(-0.479064\pi\)
0.0657258 + 0.997838i \(0.479064\pi\)
\(888\) 0 0
\(889\) 6.28530 0.210802
\(890\) 0 0
\(891\) 38.8477 1.30145
\(892\) 0 0
\(893\) 18.5124 0.619495
\(894\) 0 0
\(895\) 18.1812 0.607731
\(896\) 0 0
\(897\) 5.77038 0.192668
\(898\) 0 0
\(899\) −46.0376 −1.53544
\(900\) 0 0
\(901\) 63.1387 2.10346
\(902\) 0 0
\(903\) 7.58605 0.252448
\(904\) 0 0
\(905\) 23.0484 0.766155
\(906\) 0 0
\(907\) −9.46207 −0.314183 −0.157091 0.987584i \(-0.550212\pi\)
−0.157091 + 0.987584i \(0.550212\pi\)
\(908\) 0 0
\(909\) −52.1152 −1.72855
\(910\) 0 0
\(911\) −9.48825 −0.314360 −0.157180 0.987570i \(-0.550240\pi\)
−0.157180 + 0.987570i \(0.550240\pi\)
\(912\) 0 0
\(913\) −12.8102 −0.423957
\(914\) 0 0
\(915\) 3.60413 0.119149
\(916\) 0 0
\(917\) 6.56602 0.216829
\(918\) 0 0
\(919\) −30.8507 −1.01767 −0.508835 0.860864i \(-0.669924\pi\)
−0.508835 + 0.860864i \(0.669924\pi\)
\(920\) 0 0
\(921\) 0.288785 0.00951579
\(922\) 0 0
\(923\) 27.1288 0.892956
\(924\) 0 0
\(925\) −19.5487 −0.642758
\(926\) 0 0
\(927\) −32.8177 −1.07788
\(928\) 0 0
\(929\) 38.1553 1.25184 0.625918 0.779889i \(-0.284725\pi\)
0.625918 + 0.779889i \(0.284725\pi\)
\(930\) 0 0
\(931\) −6.57829 −0.215595
\(932\) 0 0
\(933\) 0.247072 0.00808878
\(934\) 0 0
\(935\) −35.3183 −1.15503
\(936\) 0 0
\(937\) −32.8566 −1.07338 −0.536689 0.843780i \(-0.680325\pi\)
−0.536689 + 0.843780i \(0.680325\pi\)
\(938\) 0 0
\(939\) 6.71647 0.219184
\(940\) 0 0
\(941\) 31.3849 1.02312 0.511559 0.859248i \(-0.329068\pi\)
0.511559 + 0.859248i \(0.329068\pi\)
\(942\) 0 0
\(943\) −60.1144 −1.95759
\(944\) 0 0
\(945\) 5.05242 0.164355
\(946\) 0 0
\(947\) 2.54658 0.0827527 0.0413763 0.999144i \(-0.486826\pi\)
0.0413763 + 0.999144i \(0.486826\pi\)
\(948\) 0 0
\(949\) 9.93280 0.322432
\(950\) 0 0
\(951\) −1.22924 −0.0398609
\(952\) 0 0
\(953\) −37.8956 −1.22756 −0.613780 0.789477i \(-0.710352\pi\)
−0.613780 + 0.789477i \(0.710352\pi\)
\(954\) 0 0
\(955\) 6.24349 0.202035
\(956\) 0 0
\(957\) 10.1755 0.328928
\(958\) 0 0
\(959\) −11.8410 −0.382364
\(960\) 0 0
\(961\) −3.40614 −0.109875
\(962\) 0 0
\(963\) 14.3475 0.462343
\(964\) 0 0
\(965\) 15.9310 0.512838
\(966\) 0 0
\(967\) 7.21263 0.231943 0.115971 0.993253i \(-0.463002\pi\)
0.115971 + 0.993253i \(0.463002\pi\)
\(968\) 0 0
\(969\) 6.44210 0.206950
\(970\) 0 0
\(971\) 34.8698 1.11903 0.559513 0.828821i \(-0.310988\pi\)
0.559513 + 0.828821i \(0.310988\pi\)
\(972\) 0 0
\(973\) 53.3611 1.71068
\(974\) 0 0
\(975\) −2.52546 −0.0808796
\(976\) 0 0
\(977\) 8.00216 0.256012 0.128006 0.991773i \(-0.459142\pi\)
0.128006 + 0.991773i \(0.459142\pi\)
\(978\) 0 0
\(979\) 23.8500 0.762248
\(980\) 0 0
\(981\) 23.8703 0.762122
\(982\) 0 0
\(983\) −26.1736 −0.834808 −0.417404 0.908721i \(-0.637060\pi\)
−0.417404 + 0.908721i \(0.637060\pi\)
\(984\) 0 0
\(985\) 23.0501 0.734436
\(986\) 0 0
\(987\) −3.61547 −0.115082
\(988\) 0 0
\(989\) 85.9854 2.73418
\(990\) 0 0
\(991\) −39.1644 −1.24410 −0.622050 0.782978i \(-0.713700\pi\)
−0.622050 + 0.782978i \(0.713700\pi\)
\(992\) 0 0
\(993\) −0.200963 −0.00637736
\(994\) 0 0
\(995\) −15.3793 −0.487557
\(996\) 0 0
\(997\) 55.9094 1.77067 0.885334 0.464955i \(-0.153929\pi\)
0.885334 + 0.464955i \(0.153929\pi\)
\(998\) 0 0
\(999\) 7.91956 0.250564
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.1.24 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.24 44 1.1 even 1 trivial