Properties

Label 8008.2.a.j.1.4
Level 8008
Weight 2
Character 8008.1
Self dual yes
Analytic conductor 63.944
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.668973.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.553533\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.18752 q^{3} -2.05962 q^{5} +1.00000 q^{7} +1.78523 q^{9} +O(q^{10})\) \(q+2.18752 q^{3} -2.05962 q^{5} +1.00000 q^{7} +1.78523 q^{9} -1.00000 q^{11} -1.00000 q^{13} -4.50545 q^{15} +1.94038 q^{17} +2.63335 q^{19} +2.18752 q^{21} -2.37755 q^{23} -0.757976 q^{25} -2.65733 q^{27} +8.17116 q^{29} +0.915644 q^{31} -2.18752 q^{33} -2.05962 q^{35} +0.853512 q^{37} -2.18752 q^{39} +6.33422 q^{41} -8.24965 q^{43} -3.67689 q^{45} -4.20381 q^{47} +1.00000 q^{49} +4.24462 q^{51} +6.84485 q^{53} +2.05962 q^{55} +5.76049 q^{57} +12.3639 q^{59} +3.68207 q^{61} +1.78523 q^{63} +2.05962 q^{65} +13.4099 q^{67} -5.20093 q^{69} -2.58135 q^{71} -9.32883 q^{73} -1.65809 q^{75} -1.00000 q^{77} +11.9316 q^{79} -11.1686 q^{81} +3.62756 q^{83} -3.99645 q^{85} +17.8745 q^{87} -7.74169 q^{89} -1.00000 q^{91} +2.00299 q^{93} -5.42369 q^{95} +4.78272 q^{97} -1.78523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} - 5q^{11} - 5q^{13} - 5q^{15} + 19q^{17} - 5q^{19} + q^{21} + 5q^{23} + 12q^{25} - 11q^{27} - 17q^{29} + 4q^{31} - q^{33} - q^{35} + 10q^{37} - q^{39} + 10q^{41} - 25q^{43} + q^{45} + 3q^{47} + 5q^{49} - q^{51} + 22q^{53} + q^{55} + 16q^{57} + 21q^{59} + 26q^{61} + 6q^{63} + q^{65} + 28q^{67} + 16q^{69} + 28q^{71} - 4q^{73} - 5q^{77} - 11q^{79} + 5q^{81} + 33q^{85} + 31q^{87} - 37q^{89} - 5q^{91} - 49q^{93} + 29q^{95} + 18q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 2.18752 1.26296 0.631482 0.775391i \(-0.282447\pi\)
0.631482 + 0.775391i \(0.282447\pi\)
\(4\) 0 0
\(5\) −2.05962 −0.921089 −0.460544 0.887637i \(-0.652346\pi\)
−0.460544 + 0.887637i \(0.652346\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 1.78523 0.595077
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −4.50545 −1.16330
\(16\) 0 0
\(17\) 1.94038 0.470612 0.235306 0.971921i \(-0.424391\pi\)
0.235306 + 0.971921i \(0.424391\pi\)
\(18\) 0 0
\(19\) 2.63335 0.604131 0.302066 0.953287i \(-0.402324\pi\)
0.302066 + 0.953287i \(0.402324\pi\)
\(20\) 0 0
\(21\) 2.18752 0.477355
\(22\) 0 0
\(23\) −2.37755 −0.495753 −0.247877 0.968792i \(-0.579733\pi\)
−0.247877 + 0.968792i \(0.579733\pi\)
\(24\) 0 0
\(25\) −0.757976 −0.151595
\(26\) 0 0
\(27\) −2.65733 −0.511403
\(28\) 0 0
\(29\) 8.17116 1.51735 0.758673 0.651472i \(-0.225848\pi\)
0.758673 + 0.651472i \(0.225848\pi\)
\(30\) 0 0
\(31\) 0.915644 0.164454 0.0822272 0.996614i \(-0.473797\pi\)
0.0822272 + 0.996614i \(0.473797\pi\)
\(32\) 0 0
\(33\) −2.18752 −0.380798
\(34\) 0 0
\(35\) −2.05962 −0.348139
\(36\) 0 0
\(37\) 0.853512 0.140316 0.0701582 0.997536i \(-0.477650\pi\)
0.0701582 + 0.997536i \(0.477650\pi\)
\(38\) 0 0
\(39\) −2.18752 −0.350283
\(40\) 0 0
\(41\) 6.33422 0.989239 0.494620 0.869110i \(-0.335307\pi\)
0.494620 + 0.869110i \(0.335307\pi\)
\(42\) 0 0
\(43\) −8.24965 −1.25806 −0.629030 0.777381i \(-0.716548\pi\)
−0.629030 + 0.777381i \(0.716548\pi\)
\(44\) 0 0
\(45\) −3.67689 −0.548118
\(46\) 0 0
\(47\) −4.20381 −0.613188 −0.306594 0.951840i \(-0.599189\pi\)
−0.306594 + 0.951840i \(0.599189\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.24462 0.594366
\(52\) 0 0
\(53\) 6.84485 0.940212 0.470106 0.882610i \(-0.344216\pi\)
0.470106 + 0.882610i \(0.344216\pi\)
\(54\) 0 0
\(55\) 2.05962 0.277719
\(56\) 0 0
\(57\) 5.76049 0.762996
\(58\) 0 0
\(59\) 12.3639 1.60964 0.804818 0.593521i \(-0.202263\pi\)
0.804818 + 0.593521i \(0.202263\pi\)
\(60\) 0 0
\(61\) 3.68207 0.471441 0.235720 0.971821i \(-0.424255\pi\)
0.235720 + 0.971821i \(0.424255\pi\)
\(62\) 0 0
\(63\) 1.78523 0.224918
\(64\) 0 0
\(65\) 2.05962 0.255464
\(66\) 0 0
\(67\) 13.4099 1.63828 0.819141 0.573593i \(-0.194451\pi\)
0.819141 + 0.573593i \(0.194451\pi\)
\(68\) 0 0
\(69\) −5.20093 −0.626118
\(70\) 0 0
\(71\) −2.58135 −0.306350 −0.153175 0.988199i \(-0.548950\pi\)
−0.153175 + 0.988199i \(0.548950\pi\)
\(72\) 0 0
\(73\) −9.32883 −1.09186 −0.545928 0.837832i \(-0.683823\pi\)
−0.545928 + 0.837832i \(0.683823\pi\)
\(74\) 0 0
\(75\) −1.65809 −0.191459
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 11.9316 1.34242 0.671208 0.741269i \(-0.265776\pi\)
0.671208 + 0.741269i \(0.265776\pi\)
\(80\) 0 0
\(81\) −11.1686 −1.24096
\(82\) 0 0
\(83\) 3.62756 0.398177 0.199088 0.979982i \(-0.436202\pi\)
0.199088 + 0.979982i \(0.436202\pi\)
\(84\) 0 0
\(85\) −3.99645 −0.433475
\(86\) 0 0
\(87\) 17.8745 1.91635
\(88\) 0 0
\(89\) −7.74169 −0.820617 −0.410309 0.911947i \(-0.634579\pi\)
−0.410309 + 0.911947i \(0.634579\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 2.00299 0.207700
\(94\) 0 0
\(95\) −5.42369 −0.556459
\(96\) 0 0
\(97\) 4.78272 0.485611 0.242806 0.970075i \(-0.421932\pi\)
0.242806 + 0.970075i \(0.421932\pi\)
\(98\) 0 0
\(99\) −1.78523 −0.179422
\(100\) 0 0
\(101\) 9.95966 0.991023 0.495512 0.868601i \(-0.334981\pi\)
0.495512 + 0.868601i \(0.334981\pi\)
\(102\) 0 0
\(103\) 6.10036 0.601087 0.300543 0.953768i \(-0.402832\pi\)
0.300543 + 0.953768i \(0.402832\pi\)
\(104\) 0 0
\(105\) −4.50545 −0.439687
\(106\) 0 0
\(107\) −12.7093 −1.22865 −0.614325 0.789053i \(-0.710572\pi\)
−0.614325 + 0.789053i \(0.710572\pi\)
\(108\) 0 0
\(109\) 8.17731 0.783244 0.391622 0.920126i \(-0.371914\pi\)
0.391622 + 0.920126i \(0.371914\pi\)
\(110\) 0 0
\(111\) 1.86707 0.177215
\(112\) 0 0
\(113\) 4.02747 0.378872 0.189436 0.981893i \(-0.439334\pi\)
0.189436 + 0.981893i \(0.439334\pi\)
\(114\) 0 0
\(115\) 4.89684 0.456633
\(116\) 0 0
\(117\) −1.78523 −0.165045
\(118\) 0 0
\(119\) 1.94038 0.177875
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 13.8562 1.24937
\(124\) 0 0
\(125\) 11.8592 1.06072
\(126\) 0 0
\(127\) 18.6388 1.65393 0.826965 0.562253i \(-0.190065\pi\)
0.826965 + 0.562253i \(0.190065\pi\)
\(128\) 0 0
\(129\) −18.0462 −1.58888
\(130\) 0 0
\(131\) 5.34512 0.467005 0.233502 0.972356i \(-0.424981\pi\)
0.233502 + 0.972356i \(0.424981\pi\)
\(132\) 0 0
\(133\) 2.63335 0.228340
\(134\) 0 0
\(135\) 5.47308 0.471048
\(136\) 0 0
\(137\) −21.5592 −1.84193 −0.920964 0.389648i \(-0.872597\pi\)
−0.920964 + 0.389648i \(0.872597\pi\)
\(138\) 0 0
\(139\) −21.3696 −1.81254 −0.906272 0.422696i \(-0.861084\pi\)
−0.906272 + 0.422696i \(0.861084\pi\)
\(140\) 0 0
\(141\) −9.19590 −0.774434
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −16.8295 −1.39761
\(146\) 0 0
\(147\) 2.18752 0.180423
\(148\) 0 0
\(149\) 17.1326 1.40356 0.701780 0.712393i \(-0.252389\pi\)
0.701780 + 0.712393i \(0.252389\pi\)
\(150\) 0 0
\(151\) 18.4106 1.49823 0.749117 0.662438i \(-0.230478\pi\)
0.749117 + 0.662438i \(0.230478\pi\)
\(152\) 0 0
\(153\) 3.46403 0.280050
\(154\) 0 0
\(155\) −1.88588 −0.151477
\(156\) 0 0
\(157\) −1.70141 −0.135788 −0.0678938 0.997693i \(-0.521628\pi\)
−0.0678938 + 0.997693i \(0.521628\pi\)
\(158\) 0 0
\(159\) 14.9732 1.18745
\(160\) 0 0
\(161\) −2.37755 −0.187377
\(162\) 0 0
\(163\) 0.673620 0.0527620 0.0263810 0.999652i \(-0.491602\pi\)
0.0263810 + 0.999652i \(0.491602\pi\)
\(164\) 0 0
\(165\) 4.50545 0.350749
\(166\) 0 0
\(167\) 9.53270 0.737663 0.368831 0.929496i \(-0.379758\pi\)
0.368831 + 0.929496i \(0.379758\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 4.70113 0.359504
\(172\) 0 0
\(173\) 3.73651 0.284081 0.142041 0.989861i \(-0.454634\pi\)
0.142041 + 0.989861i \(0.454634\pi\)
\(174\) 0 0
\(175\) −0.757976 −0.0572976
\(176\) 0 0
\(177\) 27.0461 2.03291
\(178\) 0 0
\(179\) −13.2525 −0.990535 −0.495268 0.868740i \(-0.664930\pi\)
−0.495268 + 0.868740i \(0.664930\pi\)
\(180\) 0 0
\(181\) −0.353565 −0.0262803 −0.0131401 0.999914i \(-0.504183\pi\)
−0.0131401 + 0.999914i \(0.504183\pi\)
\(182\) 0 0
\(183\) 8.05459 0.595412
\(184\) 0 0
\(185\) −1.75791 −0.129244
\(186\) 0 0
\(187\) −1.94038 −0.141895
\(188\) 0 0
\(189\) −2.65733 −0.193292
\(190\) 0 0
\(191\) −8.22049 −0.594814 −0.297407 0.954751i \(-0.596122\pi\)
−0.297407 + 0.954751i \(0.596122\pi\)
\(192\) 0 0
\(193\) 26.7045 1.92224 0.961118 0.276139i \(-0.0890551\pi\)
0.961118 + 0.276139i \(0.0890551\pi\)
\(194\) 0 0
\(195\) 4.50545 0.322642
\(196\) 0 0
\(197\) 5.17655 0.368814 0.184407 0.982850i \(-0.440964\pi\)
0.184407 + 0.982850i \(0.440964\pi\)
\(198\) 0 0
\(199\) −3.62238 −0.256784 −0.128392 0.991724i \(-0.540982\pi\)
−0.128392 + 0.991724i \(0.540982\pi\)
\(200\) 0 0
\(201\) 29.3344 2.06909
\(202\) 0 0
\(203\) 8.17116 0.573503
\(204\) 0 0
\(205\) −13.0461 −0.911177
\(206\) 0 0
\(207\) −4.24447 −0.295011
\(208\) 0 0
\(209\) −2.63335 −0.182152
\(210\) 0 0
\(211\) −0.926323 −0.0637707 −0.0318854 0.999492i \(-0.510151\pi\)
−0.0318854 + 0.999492i \(0.510151\pi\)
\(212\) 0 0
\(213\) −5.64676 −0.386909
\(214\) 0 0
\(215\) 16.9911 1.15878
\(216\) 0 0
\(217\) 0.915644 0.0621579
\(218\) 0 0
\(219\) −20.4070 −1.37897
\(220\) 0 0
\(221\) −1.94038 −0.130524
\(222\) 0 0
\(223\) 23.1088 1.54748 0.773740 0.633503i \(-0.218384\pi\)
0.773740 + 0.633503i \(0.218384\pi\)
\(224\) 0 0
\(225\) −1.35316 −0.0902108
\(226\) 0 0
\(227\) 26.8203 1.78013 0.890063 0.455838i \(-0.150660\pi\)
0.890063 + 0.455838i \(0.150660\pi\)
\(228\) 0 0
\(229\) −29.0541 −1.91995 −0.959974 0.280089i \(-0.909636\pi\)
−0.959974 + 0.280089i \(0.909636\pi\)
\(230\) 0 0
\(231\) −2.18752 −0.143928
\(232\) 0 0
\(233\) 26.0397 1.70592 0.852959 0.521978i \(-0.174806\pi\)
0.852959 + 0.521978i \(0.174806\pi\)
\(234\) 0 0
\(235\) 8.65823 0.564801
\(236\) 0 0
\(237\) 26.1007 1.69542
\(238\) 0 0
\(239\) −11.9480 −0.772852 −0.386426 0.922320i \(-0.626291\pi\)
−0.386426 + 0.922320i \(0.626291\pi\)
\(240\) 0 0
\(241\) 12.8182 0.825693 0.412846 0.910801i \(-0.364535\pi\)
0.412846 + 0.910801i \(0.364535\pi\)
\(242\) 0 0
\(243\) −16.4596 −1.05588
\(244\) 0 0
\(245\) −2.05962 −0.131584
\(246\) 0 0
\(247\) −2.63335 −0.167556
\(248\) 0 0
\(249\) 7.93535 0.502883
\(250\) 0 0
\(251\) 28.3473 1.78927 0.894634 0.446799i \(-0.147436\pi\)
0.894634 + 0.446799i \(0.147436\pi\)
\(252\) 0 0
\(253\) 2.37755 0.149475
\(254\) 0 0
\(255\) −8.74229 −0.547464
\(256\) 0 0
\(257\) −14.1222 −0.880916 −0.440458 0.897773i \(-0.645184\pi\)
−0.440458 + 0.897773i \(0.645184\pi\)
\(258\) 0 0
\(259\) 0.853512 0.0530346
\(260\) 0 0
\(261\) 14.5874 0.902937
\(262\) 0 0
\(263\) −17.2667 −1.06471 −0.532355 0.846521i \(-0.678693\pi\)
−0.532355 + 0.846521i \(0.678693\pi\)
\(264\) 0 0
\(265\) −14.0978 −0.866019
\(266\) 0 0
\(267\) −16.9351 −1.03641
\(268\) 0 0
\(269\) 4.71695 0.287597 0.143799 0.989607i \(-0.454068\pi\)
0.143799 + 0.989607i \(0.454068\pi\)
\(270\) 0 0
\(271\) −28.2552 −1.71638 −0.858189 0.513333i \(-0.828411\pi\)
−0.858189 + 0.513333i \(0.828411\pi\)
\(272\) 0 0
\(273\) −2.18752 −0.132395
\(274\) 0 0
\(275\) 0.757976 0.0457077
\(276\) 0 0
\(277\) 5.00578 0.300768 0.150384 0.988628i \(-0.451949\pi\)
0.150384 + 0.988628i \(0.451949\pi\)
\(278\) 0 0
\(279\) 1.63463 0.0978630
\(280\) 0 0
\(281\) −17.2182 −1.02715 −0.513575 0.858044i \(-0.671679\pi\)
−0.513575 + 0.858044i \(0.671679\pi\)
\(282\) 0 0
\(283\) −9.84309 −0.585111 −0.292555 0.956249i \(-0.594506\pi\)
−0.292555 + 0.956249i \(0.594506\pi\)
\(284\) 0 0
\(285\) −11.8644 −0.702787
\(286\) 0 0
\(287\) 6.33422 0.373897
\(288\) 0 0
\(289\) −13.2349 −0.778524
\(290\) 0 0
\(291\) 10.4623 0.613309
\(292\) 0 0
\(293\) −18.3613 −1.07268 −0.536338 0.844003i \(-0.680193\pi\)
−0.536338 + 0.844003i \(0.680193\pi\)
\(294\) 0 0
\(295\) −25.4648 −1.48262
\(296\) 0 0
\(297\) 2.65733 0.154194
\(298\) 0 0
\(299\) 2.37755 0.137497
\(300\) 0 0
\(301\) −8.24965 −0.475502
\(302\) 0 0
\(303\) 21.7869 1.25163
\(304\) 0 0
\(305\) −7.58365 −0.434239
\(306\) 0 0
\(307\) 13.4378 0.766934 0.383467 0.923555i \(-0.374730\pi\)
0.383467 + 0.923555i \(0.374730\pi\)
\(308\) 0 0
\(309\) 13.3446 0.759150
\(310\) 0 0
\(311\) 28.0625 1.59128 0.795640 0.605770i \(-0.207135\pi\)
0.795640 + 0.605770i \(0.207135\pi\)
\(312\) 0 0
\(313\) −14.4622 −0.817452 −0.408726 0.912657i \(-0.634027\pi\)
−0.408726 + 0.912657i \(0.634027\pi\)
\(314\) 0 0
\(315\) −3.67689 −0.207169
\(316\) 0 0
\(317\) 18.2981 1.02772 0.513861 0.857873i \(-0.328215\pi\)
0.513861 + 0.857873i \(0.328215\pi\)
\(318\) 0 0
\(319\) −8.17116 −0.457497
\(320\) 0 0
\(321\) −27.8017 −1.55174
\(322\) 0 0
\(323\) 5.10970 0.284311
\(324\) 0 0
\(325\) 0.757976 0.0420450
\(326\) 0 0
\(327\) 17.8880 0.989209
\(328\) 0 0
\(329\) −4.20381 −0.231763
\(330\) 0 0
\(331\) 9.35127 0.513992 0.256996 0.966412i \(-0.417267\pi\)
0.256996 + 0.966412i \(0.417267\pi\)
\(332\) 0 0
\(333\) 1.52371 0.0834991
\(334\) 0 0
\(335\) −27.6193 −1.50900
\(336\) 0 0
\(337\) 11.6926 0.636937 0.318469 0.947933i \(-0.396831\pi\)
0.318469 + 0.947933i \(0.396831\pi\)
\(338\) 0 0
\(339\) 8.81016 0.478502
\(340\) 0 0
\(341\) −0.915644 −0.0495849
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 10.7119 0.576710
\(346\) 0 0
\(347\) 5.72583 0.307379 0.153689 0.988119i \(-0.450885\pi\)
0.153689 + 0.988119i \(0.450885\pi\)
\(348\) 0 0
\(349\) −36.9425 −1.97749 −0.988743 0.149626i \(-0.952193\pi\)
−0.988743 + 0.149626i \(0.952193\pi\)
\(350\) 0 0
\(351\) 2.65733 0.141838
\(352\) 0 0
\(353\) 1.74420 0.0928345 0.0464172 0.998922i \(-0.485220\pi\)
0.0464172 + 0.998922i \(0.485220\pi\)
\(354\) 0 0
\(355\) 5.31660 0.282176
\(356\) 0 0
\(357\) 4.24462 0.224649
\(358\) 0 0
\(359\) 36.3846 1.92031 0.960153 0.279475i \(-0.0901604\pi\)
0.960153 + 0.279475i \(0.0901604\pi\)
\(360\) 0 0
\(361\) −12.0655 −0.635025
\(362\) 0 0
\(363\) 2.18752 0.114815
\(364\) 0 0
\(365\) 19.2138 1.00570
\(366\) 0 0
\(367\) 20.0647 1.04737 0.523683 0.851913i \(-0.324558\pi\)
0.523683 + 0.851913i \(0.324558\pi\)
\(368\) 0 0
\(369\) 11.3080 0.588673
\(370\) 0 0
\(371\) 6.84485 0.355367
\(372\) 0 0
\(373\) −25.5948 −1.32525 −0.662625 0.748951i \(-0.730558\pi\)
−0.662625 + 0.748951i \(0.730558\pi\)
\(374\) 0 0
\(375\) 25.9423 1.33965
\(376\) 0 0
\(377\) −8.17116 −0.420836
\(378\) 0 0
\(379\) 11.2631 0.578544 0.289272 0.957247i \(-0.406587\pi\)
0.289272 + 0.957247i \(0.406587\pi\)
\(380\) 0 0
\(381\) 40.7728 2.08885
\(382\) 0 0
\(383\) 11.8962 0.607866 0.303933 0.952693i \(-0.401700\pi\)
0.303933 + 0.952693i \(0.401700\pi\)
\(384\) 0 0
\(385\) 2.05962 0.104968
\(386\) 0 0
\(387\) −14.7275 −0.748642
\(388\) 0 0
\(389\) 14.2863 0.724342 0.362171 0.932112i \(-0.382036\pi\)
0.362171 + 0.932112i \(0.382036\pi\)
\(390\) 0 0
\(391\) −4.61335 −0.233307
\(392\) 0 0
\(393\) 11.6925 0.589810
\(394\) 0 0
\(395\) −24.5746 −1.23648
\(396\) 0 0
\(397\) 14.6623 0.735879 0.367940 0.929850i \(-0.380063\pi\)
0.367940 + 0.929850i \(0.380063\pi\)
\(398\) 0 0
\(399\) 5.76049 0.288385
\(400\) 0 0
\(401\) 12.1559 0.607037 0.303519 0.952826i \(-0.401839\pi\)
0.303519 + 0.952826i \(0.401839\pi\)
\(402\) 0 0
\(403\) −0.915644 −0.0456115
\(404\) 0 0
\(405\) 23.0031 1.14303
\(406\) 0 0
\(407\) −0.853512 −0.0423070
\(408\) 0 0
\(409\) 12.3792 0.612111 0.306055 0.952014i \(-0.400991\pi\)
0.306055 + 0.952014i \(0.400991\pi\)
\(410\) 0 0
\(411\) −47.1611 −2.32629
\(412\) 0 0
\(413\) 12.3639 0.608385
\(414\) 0 0
\(415\) −7.47139 −0.366756
\(416\) 0 0
\(417\) −46.7463 −2.28918
\(418\) 0 0
\(419\) −21.6126 −1.05584 −0.527921 0.849293i \(-0.677028\pi\)
−0.527921 + 0.849293i \(0.677028\pi\)
\(420\) 0 0
\(421\) −28.3147 −1.37997 −0.689987 0.723822i \(-0.742384\pi\)
−0.689987 + 0.723822i \(0.742384\pi\)
\(422\) 0 0
\(423\) −7.50476 −0.364894
\(424\) 0 0
\(425\) −1.47076 −0.0713425
\(426\) 0 0
\(427\) 3.68207 0.178188
\(428\) 0 0
\(429\) 2.18752 0.105614
\(430\) 0 0
\(431\) 22.0242 1.06087 0.530435 0.847726i \(-0.322029\pi\)
0.530435 + 0.847726i \(0.322029\pi\)
\(432\) 0 0
\(433\) 32.5563 1.56455 0.782277 0.622931i \(-0.214058\pi\)
0.782277 + 0.622931i \(0.214058\pi\)
\(434\) 0 0
\(435\) −36.8147 −1.76513
\(436\) 0 0
\(437\) −6.26091 −0.299500
\(438\) 0 0
\(439\) −37.2907 −1.77979 −0.889894 0.456168i \(-0.849222\pi\)
−0.889894 + 0.456168i \(0.849222\pi\)
\(440\) 0 0
\(441\) 1.78523 0.0850109
\(442\) 0 0
\(443\) 12.6741 0.602164 0.301082 0.953598i \(-0.402652\pi\)
0.301082 + 0.953598i \(0.402652\pi\)
\(444\) 0 0
\(445\) 15.9449 0.755861
\(446\) 0 0
\(447\) 37.4779 1.77265
\(448\) 0 0
\(449\) 31.2717 1.47580 0.737902 0.674908i \(-0.235817\pi\)
0.737902 + 0.674908i \(0.235817\pi\)
\(450\) 0 0
\(451\) −6.33422 −0.298267
\(452\) 0 0
\(453\) 40.2735 1.89221
\(454\) 0 0
\(455\) 2.05962 0.0965564
\(456\) 0 0
\(457\) 18.8173 0.880237 0.440118 0.897940i \(-0.354937\pi\)
0.440118 + 0.897940i \(0.354937\pi\)
\(458\) 0 0
\(459\) −5.15624 −0.240673
\(460\) 0 0
\(461\) 28.0432 1.30610 0.653050 0.757314i \(-0.273489\pi\)
0.653050 + 0.757314i \(0.273489\pi\)
\(462\) 0 0
\(463\) −7.45939 −0.346667 −0.173334 0.984863i \(-0.555454\pi\)
−0.173334 + 0.984863i \(0.555454\pi\)
\(464\) 0 0
\(465\) −4.12538 −0.191310
\(466\) 0 0
\(467\) 12.4758 0.577312 0.288656 0.957433i \(-0.406792\pi\)
0.288656 + 0.957433i \(0.406792\pi\)
\(468\) 0 0
\(469\) 13.4099 0.619212
\(470\) 0 0
\(471\) −3.72187 −0.171495
\(472\) 0 0
\(473\) 8.24965 0.379319
\(474\) 0 0
\(475\) −1.99601 −0.0915834
\(476\) 0 0
\(477\) 12.2196 0.559498
\(478\) 0 0
\(479\) 11.9292 0.545059 0.272530 0.962147i \(-0.412140\pi\)
0.272530 + 0.962147i \(0.412140\pi\)
\(480\) 0 0
\(481\) −0.853512 −0.0389168
\(482\) 0 0
\(483\) −5.20093 −0.236650
\(484\) 0 0
\(485\) −9.85056 −0.447291
\(486\) 0 0
\(487\) 5.15523 0.233606 0.116803 0.993155i \(-0.462735\pi\)
0.116803 + 0.993155i \(0.462735\pi\)
\(488\) 0 0
\(489\) 1.47356 0.0666365
\(490\) 0 0
\(491\) −39.8312 −1.79756 −0.898778 0.438404i \(-0.855544\pi\)
−0.898778 + 0.438404i \(0.855544\pi\)
\(492\) 0 0
\(493\) 15.8552 0.714081
\(494\) 0 0
\(495\) 3.67689 0.165264
\(496\) 0 0
\(497\) −2.58135 −0.115790
\(498\) 0 0
\(499\) −41.6137 −1.86289 −0.931443 0.363887i \(-0.881450\pi\)
−0.931443 + 0.363887i \(0.881450\pi\)
\(500\) 0 0
\(501\) 20.8529 0.931641
\(502\) 0 0
\(503\) 28.6242 1.27629 0.638146 0.769916i \(-0.279702\pi\)
0.638146 + 0.769916i \(0.279702\pi\)
\(504\) 0 0
\(505\) −20.5131 −0.912820
\(506\) 0 0
\(507\) 2.18752 0.0971510
\(508\) 0 0
\(509\) −12.5655 −0.556954 −0.278477 0.960443i \(-0.589830\pi\)
−0.278477 + 0.960443i \(0.589830\pi\)
\(510\) 0 0
\(511\) −9.32883 −0.412683
\(512\) 0 0
\(513\) −6.99767 −0.308955
\(514\) 0 0
\(515\) −12.5644 −0.553654
\(516\) 0 0
\(517\) 4.20381 0.184883
\(518\) 0 0
\(519\) 8.17367 0.358784
\(520\) 0 0
\(521\) −4.96660 −0.217591 −0.108795 0.994064i \(-0.534699\pi\)
−0.108795 + 0.994064i \(0.534699\pi\)
\(522\) 0 0
\(523\) −43.5177 −1.90290 −0.951449 0.307806i \(-0.900405\pi\)
−0.951449 + 0.307806i \(0.900405\pi\)
\(524\) 0 0
\(525\) −1.65809 −0.0723648
\(526\) 0 0
\(527\) 1.77670 0.0773942
\(528\) 0 0
\(529\) −17.3473 −0.754229
\(530\) 0 0
\(531\) 22.0723 0.957857
\(532\) 0 0
\(533\) −6.33422 −0.274366
\(534\) 0 0
\(535\) 26.1762 1.13170
\(536\) 0 0
\(537\) −28.9900 −1.25101
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −10.2877 −0.442304 −0.221152 0.975239i \(-0.570982\pi\)
−0.221152 + 0.975239i \(0.570982\pi\)
\(542\) 0 0
\(543\) −0.773429 −0.0331910
\(544\) 0 0
\(545\) −16.8421 −0.721437
\(546\) 0 0
\(547\) −22.0693 −0.943613 −0.471807 0.881702i \(-0.656398\pi\)
−0.471807 + 0.881702i \(0.656398\pi\)
\(548\) 0 0
\(549\) 6.57334 0.280543
\(550\) 0 0
\(551\) 21.5175 0.916676
\(552\) 0 0
\(553\) 11.9316 0.507385
\(554\) 0 0
\(555\) −3.84545 −0.163230
\(556\) 0 0
\(557\) −19.7691 −0.837643 −0.418822 0.908069i \(-0.637557\pi\)
−0.418822 + 0.908069i \(0.637557\pi\)
\(558\) 0 0
\(559\) 8.24965 0.348923
\(560\) 0 0
\(561\) −4.24462 −0.179208
\(562\) 0 0
\(563\) −9.17954 −0.386871 −0.193436 0.981113i \(-0.561963\pi\)
−0.193436 + 0.981113i \(0.561963\pi\)
\(564\) 0 0
\(565\) −8.29505 −0.348975
\(566\) 0 0
\(567\) −11.1686 −0.469039
\(568\) 0 0
\(569\) 40.4185 1.69443 0.847217 0.531247i \(-0.178276\pi\)
0.847217 + 0.531247i \(0.178276\pi\)
\(570\) 0 0
\(571\) −33.9688 −1.42155 −0.710776 0.703419i \(-0.751656\pi\)
−0.710776 + 0.703419i \(0.751656\pi\)
\(572\) 0 0
\(573\) −17.9825 −0.751228
\(574\) 0 0
\(575\) 1.80213 0.0751538
\(576\) 0 0
\(577\) 43.4229 1.80772 0.903860 0.427829i \(-0.140722\pi\)
0.903860 + 0.427829i \(0.140722\pi\)
\(578\) 0 0
\(579\) 58.4166 2.42771
\(580\) 0 0
\(581\) 3.62756 0.150497
\(582\) 0 0
\(583\) −6.84485 −0.283485
\(584\) 0 0
\(585\) 3.67689 0.152021
\(586\) 0 0
\(587\) −41.6860 −1.72056 −0.860282 0.509819i \(-0.829712\pi\)
−0.860282 + 0.509819i \(0.829712\pi\)
\(588\) 0 0
\(589\) 2.41121 0.0993521
\(590\) 0 0
\(591\) 11.3238 0.465799
\(592\) 0 0
\(593\) 16.8018 0.689969 0.344984 0.938608i \(-0.387884\pi\)
0.344984 + 0.938608i \(0.387884\pi\)
\(594\) 0 0
\(595\) −3.99645 −0.163838
\(596\) 0 0
\(597\) −7.92402 −0.324309
\(598\) 0 0
\(599\) −37.6019 −1.53637 −0.768186 0.640227i \(-0.778840\pi\)
−0.768186 + 0.640227i \(0.778840\pi\)
\(600\) 0 0
\(601\) −40.0375 −1.63316 −0.816582 0.577229i \(-0.804134\pi\)
−0.816582 + 0.577229i \(0.804134\pi\)
\(602\) 0 0
\(603\) 23.9398 0.974903
\(604\) 0 0
\(605\) −2.05962 −0.0837354
\(606\) 0 0
\(607\) 38.6907 1.57041 0.785204 0.619238i \(-0.212558\pi\)
0.785204 + 0.619238i \(0.212558\pi\)
\(608\) 0 0
\(609\) 17.8745 0.724313
\(610\) 0 0
\(611\) 4.20381 0.170068
\(612\) 0 0
\(613\) −43.6420 −1.76269 −0.881343 0.472477i \(-0.843360\pi\)
−0.881343 + 0.472477i \(0.843360\pi\)
\(614\) 0 0
\(615\) −28.5385 −1.15078
\(616\) 0 0
\(617\) 14.4978 0.583660 0.291830 0.956470i \(-0.405736\pi\)
0.291830 + 0.956470i \(0.405736\pi\)
\(618\) 0 0
\(619\) 27.1430 1.09097 0.545485 0.838121i \(-0.316346\pi\)
0.545485 + 0.838121i \(0.316346\pi\)
\(620\) 0 0
\(621\) 6.31793 0.253530
\(622\) 0 0
\(623\) −7.74169 −0.310164
\(624\) 0 0
\(625\) −20.6356 −0.825424
\(626\) 0 0
\(627\) −5.76049 −0.230052
\(628\) 0 0
\(629\) 1.65614 0.0660346
\(630\) 0 0
\(631\) −8.83123 −0.351566 −0.175783 0.984429i \(-0.556246\pi\)
−0.175783 + 0.984429i \(0.556246\pi\)
\(632\) 0 0
\(633\) −2.02635 −0.0805401
\(634\) 0 0
\(635\) −38.3889 −1.52342
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −4.60831 −0.182302
\(640\) 0 0
\(641\) 6.93557 0.273939 0.136969 0.990575i \(-0.456264\pi\)
0.136969 + 0.990575i \(0.456264\pi\)
\(642\) 0 0
\(643\) −3.44674 −0.135926 −0.0679630 0.997688i \(-0.521650\pi\)
−0.0679630 + 0.997688i \(0.521650\pi\)
\(644\) 0 0
\(645\) 37.1684 1.46350
\(646\) 0 0
\(647\) −1.99442 −0.0784087 −0.0392043 0.999231i \(-0.512482\pi\)
−0.0392043 + 0.999231i \(0.512482\pi\)
\(648\) 0 0
\(649\) −12.3639 −0.485324
\(650\) 0 0
\(651\) 2.00299 0.0785032
\(652\) 0 0
\(653\) 41.2655 1.61484 0.807422 0.589974i \(-0.200862\pi\)
0.807422 + 0.589974i \(0.200862\pi\)
\(654\) 0 0
\(655\) −11.0089 −0.430153
\(656\) 0 0
\(657\) −16.6541 −0.649738
\(658\) 0 0
\(659\) −15.4748 −0.602812 −0.301406 0.953496i \(-0.597456\pi\)
−0.301406 + 0.953496i \(0.597456\pi\)
\(660\) 0 0
\(661\) 8.07135 0.313939 0.156970 0.987603i \(-0.449828\pi\)
0.156970 + 0.987603i \(0.449828\pi\)
\(662\) 0 0
\(663\) −4.24462 −0.164847
\(664\) 0 0
\(665\) −5.42369 −0.210322
\(666\) 0 0
\(667\) −19.4273 −0.752229
\(668\) 0 0
\(669\) 50.5509 1.95441
\(670\) 0 0
\(671\) −3.68207 −0.142145
\(672\) 0 0
\(673\) −26.7774 −1.03219 −0.516097 0.856530i \(-0.672616\pi\)
−0.516097 + 0.856530i \(0.672616\pi\)
\(674\) 0 0
\(675\) 2.01419 0.0775263
\(676\) 0 0
\(677\) 46.3091 1.77980 0.889902 0.456151i \(-0.150772\pi\)
0.889902 + 0.456151i \(0.150772\pi\)
\(678\) 0 0
\(679\) 4.78272 0.183544
\(680\) 0 0
\(681\) 58.6698 2.24823
\(682\) 0 0
\(683\) 8.40909 0.321765 0.160882 0.986974i \(-0.448566\pi\)
0.160882 + 0.986974i \(0.448566\pi\)
\(684\) 0 0
\(685\) 44.4037 1.69658
\(686\) 0 0
\(687\) −63.5563 −2.42482
\(688\) 0 0
\(689\) −6.84485 −0.260768
\(690\) 0 0
\(691\) 37.1060 1.41158 0.705789 0.708422i \(-0.250593\pi\)
0.705789 + 0.708422i \(0.250593\pi\)
\(692\) 0 0
\(693\) −1.78523 −0.0678153
\(694\) 0 0
\(695\) 44.0131 1.66951
\(696\) 0 0
\(697\) 12.2908 0.465548
\(698\) 0 0
\(699\) 56.9623 2.15451
\(700\) 0 0
\(701\) −49.9600 −1.88696 −0.943481 0.331425i \(-0.892470\pi\)
−0.943481 + 0.331425i \(0.892470\pi\)
\(702\) 0 0
\(703\) 2.24759 0.0847696
\(704\) 0 0
\(705\) 18.9400 0.713323
\(706\) 0 0
\(707\) 9.95966 0.374572
\(708\) 0 0
\(709\) 42.5349 1.59743 0.798717 0.601707i \(-0.205513\pi\)
0.798717 + 0.601707i \(0.205513\pi\)
\(710\) 0 0
\(711\) 21.3007 0.798840
\(712\) 0 0
\(713\) −2.17699 −0.0815288
\(714\) 0 0
\(715\) −2.05962 −0.0770253
\(716\) 0 0
\(717\) −26.1365 −0.976084
\(718\) 0 0
\(719\) −29.5845 −1.10332 −0.551658 0.834070i \(-0.686005\pi\)
−0.551658 + 0.834070i \(0.686005\pi\)
\(720\) 0 0
\(721\) 6.10036 0.227189
\(722\) 0 0
\(723\) 28.0400 1.04282
\(724\) 0 0
\(725\) −6.19354 −0.230022
\(726\) 0 0
\(727\) −43.6553 −1.61908 −0.809542 0.587061i \(-0.800285\pi\)
−0.809542 + 0.587061i \(0.800285\pi\)
\(728\) 0 0
\(729\) −2.49973 −0.0925826
\(730\) 0 0
\(731\) −16.0075 −0.592058
\(732\) 0 0
\(733\) 19.5254 0.721187 0.360594 0.932723i \(-0.382574\pi\)
0.360594 + 0.932723i \(0.382574\pi\)
\(734\) 0 0
\(735\) −4.50545 −0.166186
\(736\) 0 0
\(737\) −13.4099 −0.493960
\(738\) 0 0
\(739\) −45.1902 −1.66235 −0.831175 0.556012i \(-0.812331\pi\)
−0.831175 + 0.556012i \(0.812331\pi\)
\(740\) 0 0
\(741\) −5.76049 −0.211617
\(742\) 0 0
\(743\) −2.25278 −0.0826467 −0.0413233 0.999146i \(-0.513157\pi\)
−0.0413233 + 0.999146i \(0.513157\pi\)
\(744\) 0 0
\(745\) −35.2867 −1.29280
\(746\) 0 0
\(747\) 6.47603 0.236946
\(748\) 0 0
\(749\) −12.7093 −0.464386
\(750\) 0 0
\(751\) −16.2216 −0.591935 −0.295968 0.955198i \(-0.595642\pi\)
−0.295968 + 0.955198i \(0.595642\pi\)
\(752\) 0 0
\(753\) 62.0103 2.25978
\(754\) 0 0
\(755\) −37.9188 −1.38001
\(756\) 0 0
\(757\) −12.1966 −0.443292 −0.221646 0.975127i \(-0.571143\pi\)
−0.221646 + 0.975127i \(0.571143\pi\)
\(758\) 0 0
\(759\) 5.20093 0.188782
\(760\) 0 0
\(761\) −34.7661 −1.26027 −0.630136 0.776485i \(-0.717001\pi\)
−0.630136 + 0.776485i \(0.717001\pi\)
\(762\) 0 0
\(763\) 8.17731 0.296038
\(764\) 0 0
\(765\) −7.13457 −0.257951
\(766\) 0 0
\(767\) −12.3639 −0.446433
\(768\) 0 0
\(769\) 12.1295 0.437402 0.218701 0.975792i \(-0.429818\pi\)
0.218701 + 0.975792i \(0.429818\pi\)
\(770\) 0 0
\(771\) −30.8924 −1.11256
\(772\) 0 0
\(773\) 21.5202 0.774026 0.387013 0.922074i \(-0.373507\pi\)
0.387013 + 0.922074i \(0.373507\pi\)
\(774\) 0 0
\(775\) −0.694036 −0.0249305
\(776\) 0 0
\(777\) 1.86707 0.0669808
\(778\) 0 0
\(779\) 16.6802 0.597630
\(780\) 0 0
\(781\) 2.58135 0.0923681
\(782\) 0 0
\(783\) −21.7135 −0.775976
\(784\) 0 0
\(785\) 3.50426 0.125072
\(786\) 0 0
\(787\) −39.4297 −1.40552 −0.702759 0.711428i \(-0.748049\pi\)
−0.702759 + 0.711428i \(0.748049\pi\)
\(788\) 0 0
\(789\) −37.7712 −1.34469
\(790\) 0 0
\(791\) 4.02747 0.143200
\(792\) 0 0
\(793\) −3.68207 −0.130754
\(794\) 0 0
\(795\) −30.8391 −1.09375
\(796\) 0 0
\(797\) 4.27518 0.151435 0.0757174 0.997129i \(-0.475875\pi\)
0.0757174 + 0.997129i \(0.475875\pi\)
\(798\) 0 0
\(799\) −8.15699 −0.288574
\(800\) 0 0
\(801\) −13.8207 −0.488330
\(802\) 0 0
\(803\) 9.32883 0.329207
\(804\) 0 0
\(805\) 4.89684 0.172591
\(806\) 0 0
\(807\) 10.3184 0.363225
\(808\) 0 0
\(809\) 20.2794 0.712984 0.356492 0.934298i \(-0.383973\pi\)
0.356492 + 0.934298i \(0.383973\pi\)
\(810\) 0 0
\(811\) −35.4650 −1.24535 −0.622673 0.782482i \(-0.713953\pi\)
−0.622673 + 0.782482i \(0.713953\pi\)
\(812\) 0 0
\(813\) −61.8086 −2.16772
\(814\) 0 0
\(815\) −1.38740 −0.0485985
\(816\) 0 0
\(817\) −21.7242 −0.760033
\(818\) 0 0
\(819\) −1.78523 −0.0623810
\(820\) 0 0
\(821\) −19.6107 −0.684417 −0.342208 0.939624i \(-0.611175\pi\)
−0.342208 + 0.939624i \(0.611175\pi\)
\(822\) 0 0
\(823\) 18.5669 0.647202 0.323601 0.946194i \(-0.395106\pi\)
0.323601 + 0.946194i \(0.395106\pi\)
\(824\) 0 0
\(825\) 1.65809 0.0577271
\(826\) 0 0
\(827\) −50.4514 −1.75437 −0.877184 0.480155i \(-0.840580\pi\)
−0.877184 + 0.480155i \(0.840580\pi\)
\(828\) 0 0
\(829\) 4.12771 0.143361 0.0716806 0.997428i \(-0.477164\pi\)
0.0716806 + 0.997428i \(0.477164\pi\)
\(830\) 0 0
\(831\) 10.9502 0.379860
\(832\) 0 0
\(833\) 1.94038 0.0672303
\(834\) 0 0
\(835\) −19.6337 −0.679453
\(836\) 0 0
\(837\) −2.43317 −0.0841026
\(838\) 0 0
\(839\) −25.7910 −0.890403 −0.445201 0.895430i \(-0.646868\pi\)
−0.445201 + 0.895430i \(0.646868\pi\)
\(840\) 0 0
\(841\) 37.7678 1.30234
\(842\) 0 0
\(843\) −37.6651 −1.29725
\(844\) 0 0
\(845\) −2.05962 −0.0708530
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −21.5319 −0.738974
\(850\) 0 0
\(851\) −2.02927 −0.0695623
\(852\) 0 0
\(853\) 28.4982 0.975761 0.487881 0.872910i \(-0.337770\pi\)
0.487881 + 0.872910i \(0.337770\pi\)
\(854\) 0 0
\(855\) −9.68253 −0.331135
\(856\) 0 0
\(857\) −1.38098 −0.0471734 −0.0235867 0.999722i \(-0.507509\pi\)
−0.0235867 + 0.999722i \(0.507509\pi\)
\(858\) 0 0
\(859\) −29.0451 −0.991006 −0.495503 0.868606i \(-0.665016\pi\)
−0.495503 + 0.868606i \(0.665016\pi\)
\(860\) 0 0
\(861\) 13.8562 0.472219
\(862\) 0 0
\(863\) 12.5657 0.427742 0.213871 0.976862i \(-0.431393\pi\)
0.213871 + 0.976862i \(0.431393\pi\)
\(864\) 0 0
\(865\) −7.69578 −0.261664
\(866\) 0 0
\(867\) −28.9516 −0.983248
\(868\) 0 0
\(869\) −11.9316 −0.404753
\(870\) 0 0
\(871\) −13.4099 −0.454378
\(872\) 0 0
\(873\) 8.53825 0.288976
\(874\) 0 0
\(875\) 11.8592 0.400915
\(876\) 0 0
\(877\) 33.8689 1.14367 0.571837 0.820368i \(-0.306231\pi\)
0.571837 + 0.820368i \(0.306231\pi\)
\(878\) 0 0
\(879\) −40.1656 −1.35475
\(880\) 0 0
\(881\) 4.45741 0.150174 0.0750870 0.997177i \(-0.476077\pi\)
0.0750870 + 0.997177i \(0.476077\pi\)
\(882\) 0 0
\(883\) −22.2039 −0.747220 −0.373610 0.927586i \(-0.621880\pi\)
−0.373610 + 0.927586i \(0.621880\pi\)
\(884\) 0 0
\(885\) −55.7047 −1.87249
\(886\) 0 0
\(887\) 42.9156 1.44096 0.720482 0.693474i \(-0.243921\pi\)
0.720482 + 0.693474i \(0.243921\pi\)
\(888\) 0 0
\(889\) 18.6388 0.625127
\(890\) 0 0
\(891\) 11.1686 0.374164
\(892\) 0 0
\(893\) −11.0701 −0.370446
\(894\) 0 0
\(895\) 27.2950 0.912371
\(896\) 0 0
\(897\) 5.20093 0.173654
\(898\) 0 0
\(899\) 7.48187 0.249534
\(900\) 0 0
\(901\) 13.2816 0.442475
\(902\) 0 0
\(903\) −18.0462 −0.600541
\(904\) 0 0
\(905\) 0.728208 0.0242065
\(906\) 0 0
\(907\) −8.18957 −0.271930 −0.135965 0.990714i \(-0.543414\pi\)
−0.135965 + 0.990714i \(0.543414\pi\)
\(908\) 0 0
\(909\) 17.7803 0.589735
\(910\) 0 0
\(911\) 32.1220 1.06425 0.532125 0.846666i \(-0.321394\pi\)
0.532125 + 0.846666i \(0.321394\pi\)
\(912\) 0 0
\(913\) −3.62756 −0.120055
\(914\) 0 0
\(915\) −16.5894 −0.548428
\(916\) 0 0
\(917\) 5.34512 0.176511
\(918\) 0 0
\(919\) −39.4195 −1.30033 −0.650165 0.759793i \(-0.725300\pi\)
−0.650165 + 0.759793i \(0.725300\pi\)
\(920\) 0 0
\(921\) 29.3954 0.968610
\(922\) 0 0
\(923\) 2.58135 0.0849663
\(924\) 0 0
\(925\) −0.646942 −0.0212713
\(926\) 0 0
\(927\) 10.8905 0.357693
\(928\) 0 0
\(929\) −21.8852 −0.718029 −0.359014 0.933332i \(-0.616887\pi\)
−0.359014 + 0.933332i \(0.616887\pi\)
\(930\) 0 0
\(931\) 2.63335 0.0863045
\(932\) 0 0
\(933\) 61.3873 2.00973
\(934\) 0 0
\(935\) 3.99645 0.130698
\(936\) 0 0
\(937\) 18.6548 0.609426 0.304713 0.952444i \(-0.401439\pi\)
0.304713 + 0.952444i \(0.401439\pi\)
\(938\) 0 0
\(939\) −31.6363 −1.03241
\(940\) 0 0
\(941\) −2.91191 −0.0949255 −0.0474627 0.998873i \(-0.515114\pi\)
−0.0474627 + 0.998873i \(0.515114\pi\)
\(942\) 0 0
\(943\) −15.0599 −0.490418
\(944\) 0 0
\(945\) 5.47308 0.178039
\(946\) 0 0
\(947\) 44.8350 1.45694 0.728470 0.685077i \(-0.240232\pi\)
0.728470 + 0.685077i \(0.240232\pi\)
\(948\) 0 0
\(949\) 9.32883 0.302827
\(950\) 0 0
\(951\) 40.0274 1.29798
\(952\) 0 0
\(953\) −48.0339 −1.55597 −0.777986 0.628282i \(-0.783758\pi\)
−0.777986 + 0.628282i \(0.783758\pi\)
\(954\) 0 0
\(955\) 16.9311 0.547876
\(956\) 0 0
\(957\) −17.8745 −0.577802
\(958\) 0 0
\(959\) −21.5592 −0.696183
\(960\) 0 0
\(961\) −30.1616 −0.972955
\(962\) 0 0
\(963\) −22.6889 −0.731141
\(964\) 0 0
\(965\) −55.0011 −1.77055
\(966\) 0 0
\(967\) −19.8944 −0.639760 −0.319880 0.947458i \(-0.603643\pi\)
−0.319880 + 0.947458i \(0.603643\pi\)
\(968\) 0 0
\(969\) 11.1776 0.359075
\(970\) 0 0
\(971\) −31.9804 −1.02630 −0.513150 0.858299i \(-0.671522\pi\)
−0.513150 + 0.858299i \(0.671522\pi\)
\(972\) 0 0
\(973\) −21.3696 −0.685077
\(974\) 0 0
\(975\) 1.65809 0.0531012
\(976\) 0 0
\(977\) 19.4945 0.623684 0.311842 0.950134i \(-0.399054\pi\)
0.311842 + 0.950134i \(0.399054\pi\)
\(978\) 0 0
\(979\) 7.74169 0.247425
\(980\) 0 0
\(981\) 14.5984 0.466090
\(982\) 0 0
\(983\) 4.21514 0.134442 0.0672210 0.997738i \(-0.478587\pi\)
0.0672210 + 0.997738i \(0.478587\pi\)
\(984\) 0 0
\(985\) −10.6617 −0.339711
\(986\) 0 0
\(987\) −9.19590 −0.292709
\(988\) 0 0
\(989\) 19.6139 0.623687
\(990\) 0 0
\(991\) 35.9947 1.14341 0.571704 0.820460i \(-0.306282\pi\)
0.571704 + 0.820460i \(0.306282\pi\)
\(992\) 0 0
\(993\) 20.4561 0.649153
\(994\) 0 0
\(995\) 7.46072 0.236521
\(996\) 0 0
\(997\) −56.2334 −1.78093 −0.890464 0.455053i \(-0.849620\pi\)
−0.890464 + 0.455053i \(0.849620\pi\)
\(998\) 0 0
\(999\) −2.26806 −0.0717583
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 8008.2.a.j.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8008.2.a.j.1.4 5 1.1 even 1 trivial