Properties

Label 6003.2.a.t.1.22
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.60337 q^{2} +4.77753 q^{4} -2.74879 q^{5} -2.14366 q^{7} +7.23092 q^{8} +O(q^{10})\) \(q+2.60337 q^{2} +4.77753 q^{4} -2.74879 q^{5} -2.14366 q^{7} +7.23092 q^{8} -7.15611 q^{10} +0.935134 q^{11} -3.80816 q^{13} -5.58073 q^{14} +9.26970 q^{16} +0.395185 q^{17} +3.48996 q^{19} -13.1324 q^{20} +2.43450 q^{22} +1.00000 q^{23} +2.55585 q^{25} -9.91405 q^{26} -10.2414 q^{28} +1.00000 q^{29} -6.61322 q^{31} +9.67060 q^{32} +1.02881 q^{34} +5.89247 q^{35} -9.78131 q^{37} +9.08566 q^{38} -19.8763 q^{40} -9.64119 q^{41} +7.07145 q^{43} +4.46762 q^{44} +2.60337 q^{46} -6.39436 q^{47} -2.40473 q^{49} +6.65382 q^{50} -18.1936 q^{52} -11.1647 q^{53} -2.57049 q^{55} -15.5006 q^{56} +2.60337 q^{58} -12.9239 q^{59} +9.19445 q^{61} -17.2166 q^{62} +6.63673 q^{64} +10.4678 q^{65} -0.642802 q^{67} +1.88800 q^{68} +15.3403 q^{70} +10.7985 q^{71} -1.05682 q^{73} -25.4643 q^{74} +16.6734 q^{76} -2.00461 q^{77} +3.20278 q^{79} -25.4805 q^{80} -25.0996 q^{82} -0.860006 q^{83} -1.08628 q^{85} +18.4096 q^{86} +6.76188 q^{88} +2.79612 q^{89} +8.16340 q^{91} +4.77753 q^{92} -16.6469 q^{94} -9.59318 q^{95} +11.7179 q^{97} -6.26039 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60337 1.84086 0.920430 0.390908i \(-0.127839\pi\)
0.920430 + 0.390908i \(0.127839\pi\)
\(3\) 0 0
\(4\) 4.77753 2.38876
\(5\) −2.74879 −1.22930 −0.614648 0.788801i \(-0.710702\pi\)
−0.614648 + 0.788801i \(0.710702\pi\)
\(6\) 0 0
\(7\) −2.14366 −0.810227 −0.405113 0.914266i \(-0.632768\pi\)
−0.405113 + 0.914266i \(0.632768\pi\)
\(8\) 7.23092 2.55652
\(9\) 0 0
\(10\) −7.15611 −2.26296
\(11\) 0.935134 0.281953 0.140977 0.990013i \(-0.454976\pi\)
0.140977 + 0.990013i \(0.454976\pi\)
\(12\) 0 0
\(13\) −3.80816 −1.05619 −0.528097 0.849184i \(-0.677094\pi\)
−0.528097 + 0.849184i \(0.677094\pi\)
\(14\) −5.58073 −1.49151
\(15\) 0 0
\(16\) 9.26970 2.31743
\(17\) 0.395185 0.0958463 0.0479232 0.998851i \(-0.484740\pi\)
0.0479232 + 0.998851i \(0.484740\pi\)
\(18\) 0 0
\(19\) 3.48996 0.800653 0.400326 0.916373i \(-0.368897\pi\)
0.400326 + 0.916373i \(0.368897\pi\)
\(20\) −13.1324 −2.93650
\(21\) 0 0
\(22\) 2.43450 0.519036
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 2.55585 0.511170
\(26\) −9.91405 −1.94430
\(27\) 0 0
\(28\) −10.2414 −1.93544
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −6.61322 −1.18777 −0.593885 0.804550i \(-0.702406\pi\)
−0.593885 + 0.804550i \(0.702406\pi\)
\(32\) 9.67060 1.70954
\(33\) 0 0
\(34\) 1.02881 0.176440
\(35\) 5.89247 0.996009
\(36\) 0 0
\(37\) −9.78131 −1.60804 −0.804018 0.594604i \(-0.797309\pi\)
−0.804018 + 0.594604i \(0.797309\pi\)
\(38\) 9.08566 1.47389
\(39\) 0 0
\(40\) −19.8763 −3.14272
\(41\) −9.64119 −1.50570 −0.752851 0.658191i \(-0.771322\pi\)
−0.752851 + 0.658191i \(0.771322\pi\)
\(42\) 0 0
\(43\) 7.07145 1.07839 0.539193 0.842182i \(-0.318729\pi\)
0.539193 + 0.842182i \(0.318729\pi\)
\(44\) 4.46762 0.673520
\(45\) 0 0
\(46\) 2.60337 0.383846
\(47\) −6.39436 −0.932713 −0.466356 0.884597i \(-0.654434\pi\)
−0.466356 + 0.884597i \(0.654434\pi\)
\(48\) 0 0
\(49\) −2.40473 −0.343532
\(50\) 6.65382 0.940992
\(51\) 0 0
\(52\) −18.1936 −2.52300
\(53\) −11.1647 −1.53359 −0.766797 0.641889i \(-0.778151\pi\)
−0.766797 + 0.641889i \(0.778151\pi\)
\(54\) 0 0
\(55\) −2.57049 −0.346604
\(56\) −15.5006 −2.07136
\(57\) 0 0
\(58\) 2.60337 0.341839
\(59\) −12.9239 −1.68255 −0.841277 0.540604i \(-0.818196\pi\)
−0.841277 + 0.540604i \(0.818196\pi\)
\(60\) 0 0
\(61\) 9.19445 1.17723 0.588614 0.808414i \(-0.299674\pi\)
0.588614 + 0.808414i \(0.299674\pi\)
\(62\) −17.2166 −2.18652
\(63\) 0 0
\(64\) 6.63673 0.829591
\(65\) 10.4678 1.29838
\(66\) 0 0
\(67\) −0.642802 −0.0785307 −0.0392654 0.999229i \(-0.512502\pi\)
−0.0392654 + 0.999229i \(0.512502\pi\)
\(68\) 1.88800 0.228954
\(69\) 0 0
\(70\) 15.3403 1.83351
\(71\) 10.7985 1.28154 0.640772 0.767731i \(-0.278614\pi\)
0.640772 + 0.767731i \(0.278614\pi\)
\(72\) 0 0
\(73\) −1.05682 −0.123692 −0.0618458 0.998086i \(-0.519699\pi\)
−0.0618458 + 0.998086i \(0.519699\pi\)
\(74\) −25.4643 −2.96017
\(75\) 0 0
\(76\) 16.6734 1.91257
\(77\) −2.00461 −0.228446
\(78\) 0 0
\(79\) 3.20278 0.360341 0.180170 0.983635i \(-0.442335\pi\)
0.180170 + 0.983635i \(0.442335\pi\)
\(80\) −25.4805 −2.84880
\(81\) 0 0
\(82\) −25.0996 −2.77178
\(83\) −0.860006 −0.0943979 −0.0471990 0.998886i \(-0.515029\pi\)
−0.0471990 + 0.998886i \(0.515029\pi\)
\(84\) 0 0
\(85\) −1.08628 −0.117824
\(86\) 18.4096 1.98516
\(87\) 0 0
\(88\) 6.76188 0.720819
\(89\) 2.79612 0.296388 0.148194 0.988958i \(-0.452654\pi\)
0.148194 + 0.988958i \(0.452654\pi\)
\(90\) 0 0
\(91\) 8.16340 0.855757
\(92\) 4.77753 0.498091
\(93\) 0 0
\(94\) −16.6469 −1.71699
\(95\) −9.59318 −0.984240
\(96\) 0 0
\(97\) 11.7179 1.18977 0.594886 0.803810i \(-0.297197\pi\)
0.594886 + 0.803810i \(0.297197\pi\)
\(98\) −6.26039 −0.632395
\(99\) 0 0
\(100\) 12.2106 1.22106
\(101\) −0.878967 −0.0874605 −0.0437303 0.999043i \(-0.513924\pi\)
−0.0437303 + 0.999043i \(0.513924\pi\)
\(102\) 0 0
\(103\) −13.6962 −1.34953 −0.674763 0.738035i \(-0.735754\pi\)
−0.674763 + 0.738035i \(0.735754\pi\)
\(104\) −27.5365 −2.70018
\(105\) 0 0
\(106\) −29.0659 −2.82313
\(107\) −11.9809 −1.15824 −0.579120 0.815242i \(-0.696604\pi\)
−0.579120 + 0.815242i \(0.696604\pi\)
\(108\) 0 0
\(109\) 3.15475 0.302171 0.151085 0.988521i \(-0.451723\pi\)
0.151085 + 0.988521i \(0.451723\pi\)
\(110\) −6.69192 −0.638050
\(111\) 0 0
\(112\) −19.8711 −1.87764
\(113\) 12.5297 1.17870 0.589350 0.807878i \(-0.299384\pi\)
0.589350 + 0.807878i \(0.299384\pi\)
\(114\) 0 0
\(115\) −2.74879 −0.256326
\(116\) 4.77753 0.443582
\(117\) 0 0
\(118\) −33.6458 −3.09734
\(119\) −0.847141 −0.0776573
\(120\) 0 0
\(121\) −10.1255 −0.920502
\(122\) 23.9365 2.16711
\(123\) 0 0
\(124\) −31.5948 −2.83730
\(125\) 6.71846 0.600917
\(126\) 0 0
\(127\) −18.8886 −1.67609 −0.838044 0.545602i \(-0.816301\pi\)
−0.838044 + 0.545602i \(0.816301\pi\)
\(128\) −2.06335 −0.182376
\(129\) 0 0
\(130\) 27.2516 2.39013
\(131\) −9.90165 −0.865111 −0.432556 0.901607i \(-0.642388\pi\)
−0.432556 + 0.901607i \(0.642388\pi\)
\(132\) 0 0
\(133\) −7.48129 −0.648710
\(134\) −1.67345 −0.144564
\(135\) 0 0
\(136\) 2.85755 0.245033
\(137\) 13.8131 1.18013 0.590066 0.807355i \(-0.299102\pi\)
0.590066 + 0.807355i \(0.299102\pi\)
\(138\) 0 0
\(139\) −11.2141 −0.951171 −0.475586 0.879669i \(-0.657764\pi\)
−0.475586 + 0.879669i \(0.657764\pi\)
\(140\) 28.1514 2.37923
\(141\) 0 0
\(142\) 28.1124 2.35914
\(143\) −3.56114 −0.297797
\(144\) 0 0
\(145\) −2.74879 −0.228275
\(146\) −2.75130 −0.227699
\(147\) 0 0
\(148\) −46.7304 −3.84122
\(149\) 13.0421 1.06845 0.534226 0.845342i \(-0.320603\pi\)
0.534226 + 0.845342i \(0.320603\pi\)
\(150\) 0 0
\(151\) −0.0305867 −0.00248911 −0.00124456 0.999999i \(-0.500396\pi\)
−0.00124456 + 0.999999i \(0.500396\pi\)
\(152\) 25.2357 2.04688
\(153\) 0 0
\(154\) −5.21873 −0.420537
\(155\) 18.1784 1.46012
\(156\) 0 0
\(157\) −23.8854 −1.90626 −0.953130 0.302562i \(-0.902158\pi\)
−0.953130 + 0.302562i \(0.902158\pi\)
\(158\) 8.33801 0.663336
\(159\) 0 0
\(160\) −26.5825 −2.10153
\(161\) −2.14366 −0.168944
\(162\) 0 0
\(163\) −15.5516 −1.21809 −0.609047 0.793134i \(-0.708448\pi\)
−0.609047 + 0.793134i \(0.708448\pi\)
\(164\) −46.0610 −3.59676
\(165\) 0 0
\(166\) −2.23891 −0.173773
\(167\) 6.50316 0.503229 0.251615 0.967827i \(-0.419038\pi\)
0.251615 + 0.967827i \(0.419038\pi\)
\(168\) 0 0
\(169\) 1.50209 0.115546
\(170\) −2.82799 −0.216897
\(171\) 0 0
\(172\) 33.7840 2.57601
\(173\) 6.05728 0.460527 0.230263 0.973128i \(-0.426041\pi\)
0.230263 + 0.973128i \(0.426041\pi\)
\(174\) 0 0
\(175\) −5.47887 −0.414164
\(176\) 8.66841 0.653406
\(177\) 0 0
\(178\) 7.27933 0.545609
\(179\) 6.92430 0.517546 0.258773 0.965938i \(-0.416682\pi\)
0.258773 + 0.965938i \(0.416682\pi\)
\(180\) 0 0
\(181\) 8.90515 0.661914 0.330957 0.943646i \(-0.392628\pi\)
0.330957 + 0.943646i \(0.392628\pi\)
\(182\) 21.2523 1.57533
\(183\) 0 0
\(184\) 7.23092 0.533071
\(185\) 26.8868 1.97675
\(186\) 0 0
\(187\) 0.369550 0.0270242
\(188\) −30.5492 −2.22803
\(189\) 0 0
\(190\) −24.9746 −1.81185
\(191\) −5.21206 −0.377132 −0.188566 0.982061i \(-0.560384\pi\)
−0.188566 + 0.982061i \(0.560384\pi\)
\(192\) 0 0
\(193\) −11.3259 −0.815258 −0.407629 0.913148i \(-0.633644\pi\)
−0.407629 + 0.913148i \(0.633644\pi\)
\(194\) 30.5060 2.19020
\(195\) 0 0
\(196\) −11.4886 −0.820618
\(197\) 16.8530 1.20073 0.600364 0.799727i \(-0.295022\pi\)
0.600364 + 0.799727i \(0.295022\pi\)
\(198\) 0 0
\(199\) −1.64734 −0.116777 −0.0583885 0.998294i \(-0.518596\pi\)
−0.0583885 + 0.998294i \(0.518596\pi\)
\(200\) 18.4812 1.30682
\(201\) 0 0
\(202\) −2.28828 −0.161002
\(203\) −2.14366 −0.150455
\(204\) 0 0
\(205\) 26.5016 1.85095
\(206\) −35.6562 −2.48429
\(207\) 0 0
\(208\) −35.3005 −2.44765
\(209\) 3.26358 0.225747
\(210\) 0 0
\(211\) 28.6574 1.97286 0.986428 0.164192i \(-0.0525017\pi\)
0.986428 + 0.164192i \(0.0525017\pi\)
\(212\) −53.3398 −3.66339
\(213\) 0 0
\(214\) −31.1908 −2.13216
\(215\) −19.4379 −1.32566
\(216\) 0 0
\(217\) 14.1765 0.962363
\(218\) 8.21299 0.556254
\(219\) 0 0
\(220\) −12.2806 −0.827956
\(221\) −1.50493 −0.101232
\(222\) 0 0
\(223\) −12.4082 −0.830916 −0.415458 0.909612i \(-0.636379\pi\)
−0.415458 + 0.909612i \(0.636379\pi\)
\(224\) −20.7305 −1.38511
\(225\) 0 0
\(226\) 32.6195 2.16982
\(227\) −15.3135 −1.01639 −0.508197 0.861241i \(-0.669688\pi\)
−0.508197 + 0.861241i \(0.669688\pi\)
\(228\) 0 0
\(229\) 15.4958 1.02399 0.511995 0.858989i \(-0.328907\pi\)
0.511995 + 0.858989i \(0.328907\pi\)
\(230\) −7.15611 −0.471860
\(231\) 0 0
\(232\) 7.23092 0.474733
\(233\) 5.64312 0.369693 0.184847 0.982767i \(-0.440821\pi\)
0.184847 + 0.982767i \(0.440821\pi\)
\(234\) 0 0
\(235\) 17.5768 1.14658
\(236\) −61.7445 −4.01922
\(237\) 0 0
\(238\) −2.20542 −0.142956
\(239\) 6.58266 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(240\) 0 0
\(241\) −6.01793 −0.387649 −0.193825 0.981036i \(-0.562089\pi\)
−0.193825 + 0.981036i \(0.562089\pi\)
\(242\) −26.3605 −1.69452
\(243\) 0 0
\(244\) 43.9267 2.81212
\(245\) 6.61009 0.422303
\(246\) 0 0
\(247\) −13.2903 −0.845644
\(248\) −47.8197 −3.03655
\(249\) 0 0
\(250\) 17.4906 1.10620
\(251\) 16.8183 1.06156 0.530779 0.847510i \(-0.321899\pi\)
0.530779 + 0.847510i \(0.321899\pi\)
\(252\) 0 0
\(253\) 0.935134 0.0587913
\(254\) −49.1739 −3.08544
\(255\) 0 0
\(256\) −18.6451 −1.16532
\(257\) 16.3640 1.02076 0.510378 0.859950i \(-0.329505\pi\)
0.510378 + 0.859950i \(0.329505\pi\)
\(258\) 0 0
\(259\) 20.9678 1.30287
\(260\) 50.0104 3.10151
\(261\) 0 0
\(262\) −25.7776 −1.59255
\(263\) 26.9113 1.65942 0.829711 0.558193i \(-0.188505\pi\)
0.829711 + 0.558193i \(0.188505\pi\)
\(264\) 0 0
\(265\) 30.6895 1.88524
\(266\) −19.4766 −1.19418
\(267\) 0 0
\(268\) −3.07100 −0.187591
\(269\) −3.47264 −0.211730 −0.105865 0.994380i \(-0.533761\pi\)
−0.105865 + 0.994380i \(0.533761\pi\)
\(270\) 0 0
\(271\) 2.00248 0.121642 0.0608211 0.998149i \(-0.480628\pi\)
0.0608211 + 0.998149i \(0.480628\pi\)
\(272\) 3.66324 0.222117
\(273\) 0 0
\(274\) 35.9606 2.17246
\(275\) 2.39006 0.144126
\(276\) 0 0
\(277\) −10.2554 −0.616187 −0.308093 0.951356i \(-0.599691\pi\)
−0.308093 + 0.951356i \(0.599691\pi\)
\(278\) −29.1945 −1.75097
\(279\) 0 0
\(280\) 42.6080 2.54631
\(281\) 14.4436 0.861632 0.430816 0.902440i \(-0.358226\pi\)
0.430816 + 0.902440i \(0.358226\pi\)
\(282\) 0 0
\(283\) −16.6941 −0.992364 −0.496182 0.868219i \(-0.665265\pi\)
−0.496182 + 0.868219i \(0.665265\pi\)
\(284\) 51.5900 3.06130
\(285\) 0 0
\(286\) −9.27096 −0.548203
\(287\) 20.6674 1.21996
\(288\) 0 0
\(289\) −16.8438 −0.990813
\(290\) −7.15611 −0.420222
\(291\) 0 0
\(292\) −5.04899 −0.295470
\(293\) −10.2934 −0.601346 −0.300673 0.953727i \(-0.597211\pi\)
−0.300673 + 0.953727i \(0.597211\pi\)
\(294\) 0 0
\(295\) 35.5252 2.06836
\(296\) −70.7279 −4.11097
\(297\) 0 0
\(298\) 33.9534 1.96687
\(299\) −3.80816 −0.220232
\(300\) 0 0
\(301\) −15.1588 −0.873737
\(302\) −0.0796286 −0.00458211
\(303\) 0 0
\(304\) 32.3509 1.85545
\(305\) −25.2736 −1.44716
\(306\) 0 0
\(307\) 11.9005 0.679199 0.339600 0.940570i \(-0.389708\pi\)
0.339600 + 0.940570i \(0.389708\pi\)
\(308\) −9.57706 −0.545704
\(309\) 0 0
\(310\) 47.3250 2.68788
\(311\) 28.7455 1.63001 0.815003 0.579457i \(-0.196735\pi\)
0.815003 + 0.579457i \(0.196735\pi\)
\(312\) 0 0
\(313\) 21.6771 1.22526 0.612631 0.790369i \(-0.290111\pi\)
0.612631 + 0.790369i \(0.290111\pi\)
\(314\) −62.1824 −3.50916
\(315\) 0 0
\(316\) 15.3013 0.860768
\(317\) 13.0706 0.734117 0.367058 0.930198i \(-0.380365\pi\)
0.367058 + 0.930198i \(0.380365\pi\)
\(318\) 0 0
\(319\) 0.935134 0.0523574
\(320\) −18.2430 −1.01981
\(321\) 0 0
\(322\) −5.58073 −0.311002
\(323\) 1.37918 0.0767396
\(324\) 0 0
\(325\) −9.73309 −0.539895
\(326\) −40.4865 −2.24234
\(327\) 0 0
\(328\) −69.7147 −3.84935
\(329\) 13.7073 0.755709
\(330\) 0 0
\(331\) 21.4831 1.18082 0.590409 0.807104i \(-0.298967\pi\)
0.590409 + 0.807104i \(0.298967\pi\)
\(332\) −4.10870 −0.225494
\(333\) 0 0
\(334\) 16.9301 0.926375
\(335\) 1.76693 0.0965376
\(336\) 0 0
\(337\) −8.82458 −0.480706 −0.240353 0.970686i \(-0.577263\pi\)
−0.240353 + 0.970686i \(0.577263\pi\)
\(338\) 3.91050 0.212703
\(339\) 0 0
\(340\) −5.18973 −0.281453
\(341\) −6.18424 −0.334896
\(342\) 0 0
\(343\) 20.1605 1.08857
\(344\) 51.1331 2.75691
\(345\) 0 0
\(346\) 15.7693 0.847764
\(347\) 25.1783 1.35164 0.675820 0.737067i \(-0.263790\pi\)
0.675820 + 0.737067i \(0.263790\pi\)
\(348\) 0 0
\(349\) −12.0798 −0.646619 −0.323310 0.946293i \(-0.604795\pi\)
−0.323310 + 0.946293i \(0.604795\pi\)
\(350\) −14.2635 −0.762417
\(351\) 0 0
\(352\) 9.04330 0.482010
\(353\) 7.37130 0.392335 0.196167 0.980570i \(-0.437150\pi\)
0.196167 + 0.980570i \(0.437150\pi\)
\(354\) 0 0
\(355\) −29.6828 −1.57540
\(356\) 13.3585 0.708001
\(357\) 0 0
\(358\) 18.0265 0.952730
\(359\) −15.0167 −0.792549 −0.396275 0.918132i \(-0.629697\pi\)
−0.396275 + 0.918132i \(0.629697\pi\)
\(360\) 0 0
\(361\) −6.82015 −0.358955
\(362\) 23.1834 1.21849
\(363\) 0 0
\(364\) 39.0008 2.04420
\(365\) 2.90498 0.152054
\(366\) 0 0
\(367\) −35.0361 −1.82887 −0.914435 0.404733i \(-0.867365\pi\)
−0.914435 + 0.404733i \(0.867365\pi\)
\(368\) 9.26970 0.483217
\(369\) 0 0
\(370\) 69.9961 3.63893
\(371\) 23.9334 1.24256
\(372\) 0 0
\(373\) −14.3222 −0.741576 −0.370788 0.928718i \(-0.620912\pi\)
−0.370788 + 0.928718i \(0.620912\pi\)
\(374\) 0.962076 0.0497477
\(375\) 0 0
\(376\) −46.2371 −2.38450
\(377\) −3.80816 −0.196130
\(378\) 0 0
\(379\) 24.7951 1.27364 0.636818 0.771014i \(-0.280250\pi\)
0.636818 + 0.771014i \(0.280250\pi\)
\(380\) −45.8317 −2.35111
\(381\) 0 0
\(382\) −13.5689 −0.694246
\(383\) 5.09661 0.260425 0.130212 0.991486i \(-0.458434\pi\)
0.130212 + 0.991486i \(0.458434\pi\)
\(384\) 0 0
\(385\) 5.51025 0.280828
\(386\) −29.4856 −1.50078
\(387\) 0 0
\(388\) 55.9826 2.84208
\(389\) 1.25884 0.0638256 0.0319128 0.999491i \(-0.489840\pi\)
0.0319128 + 0.999491i \(0.489840\pi\)
\(390\) 0 0
\(391\) 0.395185 0.0199853
\(392\) −17.3884 −0.878247
\(393\) 0 0
\(394\) 43.8746 2.21037
\(395\) −8.80376 −0.442965
\(396\) 0 0
\(397\) 22.5810 1.13331 0.566653 0.823956i \(-0.308238\pi\)
0.566653 + 0.823956i \(0.308238\pi\)
\(398\) −4.28864 −0.214970
\(399\) 0 0
\(400\) 23.6920 1.18460
\(401\) 35.3959 1.76759 0.883793 0.467879i \(-0.154982\pi\)
0.883793 + 0.467879i \(0.154982\pi\)
\(402\) 0 0
\(403\) 25.1842 1.25451
\(404\) −4.19929 −0.208922
\(405\) 0 0
\(406\) −5.58073 −0.276967
\(407\) −9.14683 −0.453391
\(408\) 0 0
\(409\) 27.7789 1.37358 0.686789 0.726857i \(-0.259020\pi\)
0.686789 + 0.726857i \(0.259020\pi\)
\(410\) 68.9935 3.40734
\(411\) 0 0
\(412\) −65.4339 −3.22370
\(413\) 27.7045 1.36325
\(414\) 0 0
\(415\) 2.36398 0.116043
\(416\) −36.8272 −1.80560
\(417\) 0 0
\(418\) 8.49631 0.415568
\(419\) −18.8066 −0.918762 −0.459381 0.888239i \(-0.651929\pi\)
−0.459381 + 0.888239i \(0.651929\pi\)
\(420\) 0 0
\(421\) −28.2932 −1.37893 −0.689464 0.724320i \(-0.742154\pi\)
−0.689464 + 0.724320i \(0.742154\pi\)
\(422\) 74.6058 3.63175
\(423\) 0 0
\(424\) −80.7314 −3.92066
\(425\) 1.01003 0.0489938
\(426\) 0 0
\(427\) −19.7098 −0.953822
\(428\) −57.2392 −2.76676
\(429\) 0 0
\(430\) −50.6041 −2.44035
\(431\) −2.26835 −0.109262 −0.0546312 0.998507i \(-0.517398\pi\)
−0.0546312 + 0.998507i \(0.517398\pi\)
\(432\) 0 0
\(433\) 19.6124 0.942511 0.471255 0.881997i \(-0.343801\pi\)
0.471255 + 0.881997i \(0.343801\pi\)
\(434\) 36.9066 1.77157
\(435\) 0 0
\(436\) 15.0719 0.721814
\(437\) 3.48996 0.166948
\(438\) 0 0
\(439\) −10.4449 −0.498508 −0.249254 0.968438i \(-0.580185\pi\)
−0.249254 + 0.968438i \(0.580185\pi\)
\(440\) −18.5870 −0.886100
\(441\) 0 0
\(442\) −3.91788 −0.186354
\(443\) −12.0910 −0.574462 −0.287231 0.957861i \(-0.592735\pi\)
−0.287231 + 0.957861i \(0.592735\pi\)
\(444\) 0 0
\(445\) −7.68595 −0.364349
\(446\) −32.3032 −1.52960
\(447\) 0 0
\(448\) −14.2269 −0.672157
\(449\) −29.3970 −1.38733 −0.693664 0.720298i \(-0.744005\pi\)
−0.693664 + 0.720298i \(0.744005\pi\)
\(450\) 0 0
\(451\) −9.01580 −0.424538
\(452\) 59.8612 2.81563
\(453\) 0 0
\(454\) −39.8667 −1.87104
\(455\) −22.4395 −1.05198
\(456\) 0 0
\(457\) −30.2374 −1.41445 −0.707223 0.706990i \(-0.750052\pi\)
−0.707223 + 0.706990i \(0.750052\pi\)
\(458\) 40.3412 1.88502
\(459\) 0 0
\(460\) −13.1324 −0.612302
\(461\) −27.6595 −1.28823 −0.644115 0.764929i \(-0.722774\pi\)
−0.644115 + 0.764929i \(0.722774\pi\)
\(462\) 0 0
\(463\) −1.90846 −0.0886937 −0.0443468 0.999016i \(-0.514121\pi\)
−0.0443468 + 0.999016i \(0.514121\pi\)
\(464\) 9.26970 0.430335
\(465\) 0 0
\(466\) 14.6911 0.680553
\(467\) −11.9120 −0.551221 −0.275610 0.961269i \(-0.588880\pi\)
−0.275610 + 0.961269i \(0.588880\pi\)
\(468\) 0 0
\(469\) 1.37795 0.0636277
\(470\) 45.7588 2.11069
\(471\) 0 0
\(472\) −93.4520 −4.30148
\(473\) 6.61275 0.304054
\(474\) 0 0
\(475\) 8.91983 0.409270
\(476\) −4.04724 −0.185505
\(477\) 0 0
\(478\) 17.1371 0.783832
\(479\) −7.24640 −0.331097 −0.165548 0.986202i \(-0.552939\pi\)
−0.165548 + 0.986202i \(0.552939\pi\)
\(480\) 0 0
\(481\) 37.2488 1.69840
\(482\) −15.6669 −0.713607
\(483\) 0 0
\(484\) −48.3750 −2.19886
\(485\) −32.2101 −1.46258
\(486\) 0 0
\(487\) 1.55045 0.0702577 0.0351289 0.999383i \(-0.488816\pi\)
0.0351289 + 0.999383i \(0.488816\pi\)
\(488\) 66.4844 3.00961
\(489\) 0 0
\(490\) 17.2085 0.777401
\(491\) 16.6954 0.753454 0.376727 0.926324i \(-0.377050\pi\)
0.376727 + 0.926324i \(0.377050\pi\)
\(492\) 0 0
\(493\) 0.395185 0.0177982
\(494\) −34.5997 −1.55671
\(495\) 0 0
\(496\) −61.3026 −2.75257
\(497\) −23.1483 −1.03834
\(498\) 0 0
\(499\) 6.18980 0.277093 0.138547 0.990356i \(-0.455757\pi\)
0.138547 + 0.990356i \(0.455757\pi\)
\(500\) 32.0976 1.43545
\(501\) 0 0
\(502\) 43.7841 1.95418
\(503\) −21.5398 −0.960413 −0.480206 0.877156i \(-0.659438\pi\)
−0.480206 + 0.877156i \(0.659438\pi\)
\(504\) 0 0
\(505\) 2.41610 0.107515
\(506\) 2.43450 0.108227
\(507\) 0 0
\(508\) −90.2406 −4.00378
\(509\) 9.20262 0.407899 0.203949 0.978981i \(-0.434622\pi\)
0.203949 + 0.978981i \(0.434622\pi\)
\(510\) 0 0
\(511\) 2.26547 0.100218
\(512\) −44.4134 −1.96281
\(513\) 0 0
\(514\) 42.6014 1.87907
\(515\) 37.6480 1.65897
\(516\) 0 0
\(517\) −5.97958 −0.262982
\(518\) 54.5869 2.39841
\(519\) 0 0
\(520\) 75.6921 3.31932
\(521\) 1.02791 0.0450336 0.0225168 0.999746i \(-0.492832\pi\)
0.0225168 + 0.999746i \(0.492832\pi\)
\(522\) 0 0
\(523\) 17.8505 0.780546 0.390273 0.920699i \(-0.372381\pi\)
0.390273 + 0.920699i \(0.372381\pi\)
\(524\) −47.3054 −2.06655
\(525\) 0 0
\(526\) 70.0600 3.05476
\(527\) −2.61344 −0.113843
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 79.8962 3.47047
\(531\) 0 0
\(532\) −35.7421 −1.54961
\(533\) 36.7152 1.59031
\(534\) 0 0
\(535\) 32.9331 1.42382
\(536\) −4.64805 −0.200765
\(537\) 0 0
\(538\) −9.04055 −0.389766
\(539\) −2.24874 −0.0968601
\(540\) 0 0
\(541\) −12.6863 −0.545427 −0.272714 0.962095i \(-0.587921\pi\)
−0.272714 + 0.962095i \(0.587921\pi\)
\(542\) 5.21320 0.223926
\(543\) 0 0
\(544\) 3.82167 0.163853
\(545\) −8.67176 −0.371457
\(546\) 0 0
\(547\) 14.2782 0.610493 0.305247 0.952273i \(-0.401261\pi\)
0.305247 + 0.952273i \(0.401261\pi\)
\(548\) 65.9924 2.81906
\(549\) 0 0
\(550\) 6.22221 0.265316
\(551\) 3.48996 0.148677
\(552\) 0 0
\(553\) −6.86566 −0.291958
\(554\) −26.6986 −1.13431
\(555\) 0 0
\(556\) −53.5759 −2.27212
\(557\) 9.77754 0.414288 0.207144 0.978310i \(-0.433583\pi\)
0.207144 + 0.978310i \(0.433583\pi\)
\(558\) 0 0
\(559\) −26.9292 −1.13898
\(560\) 54.6214 2.30818
\(561\) 0 0
\(562\) 37.6019 1.58614
\(563\) −22.0378 −0.928782 −0.464391 0.885630i \(-0.653727\pi\)
−0.464391 + 0.885630i \(0.653727\pi\)
\(564\) 0 0
\(565\) −34.4417 −1.44897
\(566\) −43.4610 −1.82680
\(567\) 0 0
\(568\) 78.0830 3.27629
\(569\) 9.95929 0.417515 0.208758 0.977967i \(-0.433058\pi\)
0.208758 + 0.977967i \(0.433058\pi\)
\(570\) 0 0
\(571\) −19.3496 −0.809755 −0.404877 0.914371i \(-0.632686\pi\)
−0.404877 + 0.914371i \(0.632686\pi\)
\(572\) −17.0134 −0.711368
\(573\) 0 0
\(574\) 53.8049 2.24577
\(575\) 2.55585 0.106586
\(576\) 0 0
\(577\) −21.7692 −0.906262 −0.453131 0.891444i \(-0.649693\pi\)
−0.453131 + 0.891444i \(0.649693\pi\)
\(578\) −43.8507 −1.82395
\(579\) 0 0
\(580\) −13.1324 −0.545294
\(581\) 1.84356 0.0764837
\(582\) 0 0
\(583\) −10.4405 −0.432402
\(584\) −7.64180 −0.316220
\(585\) 0 0
\(586\) −26.7975 −1.10699
\(587\) −3.87620 −0.159988 −0.0799939 0.996795i \(-0.525490\pi\)
−0.0799939 + 0.996795i \(0.525490\pi\)
\(588\) 0 0
\(589\) −23.0799 −0.950991
\(590\) 92.4852 3.80756
\(591\) 0 0
\(592\) −90.6698 −3.72650
\(593\) −18.8991 −0.776092 −0.388046 0.921640i \(-0.626850\pi\)
−0.388046 + 0.921640i \(0.626850\pi\)
\(594\) 0 0
\(595\) 2.32861 0.0954638
\(596\) 62.3091 2.55228
\(597\) 0 0
\(598\) −9.91405 −0.405416
\(599\) −12.2026 −0.498584 −0.249292 0.968428i \(-0.580198\pi\)
−0.249292 + 0.968428i \(0.580198\pi\)
\(600\) 0 0
\(601\) −23.5426 −0.960322 −0.480161 0.877180i \(-0.659422\pi\)
−0.480161 + 0.877180i \(0.659422\pi\)
\(602\) −39.4638 −1.60843
\(603\) 0 0
\(604\) −0.146129 −0.00594590
\(605\) 27.8330 1.13157
\(606\) 0 0
\(607\) −16.5073 −0.670011 −0.335006 0.942216i \(-0.608738\pi\)
−0.335006 + 0.942216i \(0.608738\pi\)
\(608\) 33.7500 1.36875
\(609\) 0 0
\(610\) −65.7965 −2.66402
\(611\) 24.3507 0.985126
\(612\) 0 0
\(613\) −1.67276 −0.0675620 −0.0337810 0.999429i \(-0.510755\pi\)
−0.0337810 + 0.999429i \(0.510755\pi\)
\(614\) 30.9815 1.25031
\(615\) 0 0
\(616\) −14.4952 −0.584027
\(617\) 43.7944 1.76310 0.881549 0.472093i \(-0.156501\pi\)
0.881549 + 0.472093i \(0.156501\pi\)
\(618\) 0 0
\(619\) 8.92052 0.358546 0.179273 0.983799i \(-0.442625\pi\)
0.179273 + 0.983799i \(0.442625\pi\)
\(620\) 86.8476 3.48788
\(621\) 0 0
\(622\) 74.8350 3.00061
\(623\) −5.99392 −0.240142
\(624\) 0 0
\(625\) −31.2469 −1.24988
\(626\) 56.4335 2.25553
\(627\) 0 0
\(628\) −114.113 −4.55360
\(629\) −3.86542 −0.154124
\(630\) 0 0
\(631\) −36.7446 −1.46278 −0.731390 0.681959i \(-0.761128\pi\)
−0.731390 + 0.681959i \(0.761128\pi\)
\(632\) 23.1590 0.921217
\(633\) 0 0
\(634\) 34.0275 1.35141
\(635\) 51.9207 2.06041
\(636\) 0 0
\(637\) 9.15759 0.362837
\(638\) 2.43450 0.0963827
\(639\) 0 0
\(640\) 5.67171 0.224194
\(641\) −39.8607 −1.57440 −0.787202 0.616695i \(-0.788471\pi\)
−0.787202 + 0.616695i \(0.788471\pi\)
\(642\) 0 0
\(643\) 13.9526 0.550236 0.275118 0.961411i \(-0.411283\pi\)
0.275118 + 0.961411i \(0.411283\pi\)
\(644\) −10.2414 −0.403567
\(645\) 0 0
\(646\) 3.59051 0.141267
\(647\) 6.07851 0.238971 0.119485 0.992836i \(-0.461876\pi\)
0.119485 + 0.992836i \(0.461876\pi\)
\(648\) 0 0
\(649\) −12.0856 −0.474402
\(650\) −25.3388 −0.993870
\(651\) 0 0
\(652\) −74.2981 −2.90974
\(653\) 22.3745 0.875582 0.437791 0.899077i \(-0.355761\pi\)
0.437791 + 0.899077i \(0.355761\pi\)
\(654\) 0 0
\(655\) 27.2176 1.06348
\(656\) −89.3710 −3.48935
\(657\) 0 0
\(658\) 35.6852 1.39115
\(659\) −38.1027 −1.48427 −0.742136 0.670250i \(-0.766187\pi\)
−0.742136 + 0.670250i \(0.766187\pi\)
\(660\) 0 0
\(661\) −6.48996 −0.252430 −0.126215 0.992003i \(-0.540283\pi\)
−0.126215 + 0.992003i \(0.540283\pi\)
\(662\) 55.9284 2.17372
\(663\) 0 0
\(664\) −6.21864 −0.241330
\(665\) 20.5645 0.797457
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 31.0690 1.20210
\(669\) 0 0
\(670\) 4.59996 0.177712
\(671\) 8.59804 0.331924
\(672\) 0 0
\(673\) 30.5785 1.17872 0.589358 0.807872i \(-0.299381\pi\)
0.589358 + 0.807872i \(0.299381\pi\)
\(674\) −22.9736 −0.884912
\(675\) 0 0
\(676\) 7.17630 0.276011
\(677\) −50.5208 −1.94167 −0.970836 0.239743i \(-0.922937\pi\)
−0.970836 + 0.239743i \(0.922937\pi\)
\(678\) 0 0
\(679\) −25.1192 −0.963986
\(680\) −7.85480 −0.301218
\(681\) 0 0
\(682\) −16.0999 −0.616496
\(683\) 4.47893 0.171382 0.0856908 0.996322i \(-0.472690\pi\)
0.0856908 + 0.996322i \(0.472690\pi\)
\(684\) 0 0
\(685\) −37.9693 −1.45073
\(686\) 52.4853 2.00390
\(687\) 0 0
\(688\) 65.5502 2.49908
\(689\) 42.5171 1.61977
\(690\) 0 0
\(691\) −17.9551 −0.683044 −0.341522 0.939874i \(-0.610942\pi\)
−0.341522 + 0.939874i \(0.610942\pi\)
\(692\) 28.9388 1.10009
\(693\) 0 0
\(694\) 65.5483 2.48818
\(695\) 30.8253 1.16927
\(696\) 0 0
\(697\) −3.81005 −0.144316
\(698\) −31.4483 −1.19033
\(699\) 0 0
\(700\) −26.1755 −0.989339
\(701\) −12.6626 −0.478261 −0.239131 0.970987i \(-0.576862\pi\)
−0.239131 + 0.970987i \(0.576862\pi\)
\(702\) 0 0
\(703\) −34.1364 −1.28748
\(704\) 6.20623 0.233906
\(705\) 0 0
\(706\) 19.1902 0.722233
\(707\) 1.88421 0.0708629
\(708\) 0 0
\(709\) −20.5699 −0.772520 −0.386260 0.922390i \(-0.626233\pi\)
−0.386260 + 0.922390i \(0.626233\pi\)
\(710\) −77.2751 −2.90008
\(711\) 0 0
\(712\) 20.2185 0.757721
\(713\) −6.61322 −0.247667
\(714\) 0 0
\(715\) 9.78883 0.366081
\(716\) 33.0810 1.23630
\(717\) 0 0
\(718\) −39.0939 −1.45897
\(719\) 42.7421 1.59401 0.797005 0.603972i \(-0.206416\pi\)
0.797005 + 0.603972i \(0.206416\pi\)
\(720\) 0 0
\(721\) 29.3600 1.09342
\(722\) −17.7554 −0.660786
\(723\) 0 0
\(724\) 42.5446 1.58116
\(725\) 2.55585 0.0949219
\(726\) 0 0
\(727\) 26.8622 0.996266 0.498133 0.867101i \(-0.334019\pi\)
0.498133 + 0.867101i \(0.334019\pi\)
\(728\) 59.0289 2.18776
\(729\) 0 0
\(730\) 7.56274 0.279909
\(731\) 2.79453 0.103359
\(732\) 0 0
\(733\) −17.0946 −0.631403 −0.315701 0.948859i \(-0.602240\pi\)
−0.315701 + 0.948859i \(0.602240\pi\)
\(734\) −91.2119 −3.36669
\(735\) 0 0
\(736\) 9.67060 0.356463
\(737\) −0.601105 −0.0221420
\(738\) 0 0
\(739\) 28.4610 1.04695 0.523477 0.852040i \(-0.324635\pi\)
0.523477 + 0.852040i \(0.324635\pi\)
\(740\) 128.452 4.72200
\(741\) 0 0
\(742\) 62.3074 2.28738
\(743\) 26.8306 0.984319 0.492160 0.870505i \(-0.336208\pi\)
0.492160 + 0.870505i \(0.336208\pi\)
\(744\) 0 0
\(745\) −35.8501 −1.31344
\(746\) −37.2860 −1.36514
\(747\) 0 0
\(748\) 1.76554 0.0645544
\(749\) 25.6830 0.938438
\(750\) 0 0
\(751\) 49.3690 1.80150 0.900750 0.434337i \(-0.143017\pi\)
0.900750 + 0.434337i \(0.143017\pi\)
\(752\) −59.2738 −2.16149
\(753\) 0 0
\(754\) −9.91405 −0.361048
\(755\) 0.0840766 0.00305986
\(756\) 0 0
\(757\) −48.2396 −1.75330 −0.876648 0.481131i \(-0.840226\pi\)
−0.876648 + 0.481131i \(0.840226\pi\)
\(758\) 64.5507 2.34459
\(759\) 0 0
\(760\) −69.3675 −2.51623
\(761\) 15.3989 0.558209 0.279104 0.960261i \(-0.409962\pi\)
0.279104 + 0.960261i \(0.409962\pi\)
\(762\) 0 0
\(763\) −6.76272 −0.244827
\(764\) −24.9008 −0.900878
\(765\) 0 0
\(766\) 13.2684 0.479405
\(767\) 49.2165 1.77710
\(768\) 0 0
\(769\) 14.9576 0.539385 0.269692 0.962947i \(-0.413078\pi\)
0.269692 + 0.962947i \(0.413078\pi\)
\(770\) 14.3452 0.516965
\(771\) 0 0
\(772\) −54.1099 −1.94746
\(773\) −31.0305 −1.11609 −0.558044 0.829811i \(-0.688448\pi\)
−0.558044 + 0.829811i \(0.688448\pi\)
\(774\) 0 0
\(775\) −16.9024 −0.607152
\(776\) 84.7312 3.04167
\(777\) 0 0
\(778\) 3.27722 0.117494
\(779\) −33.6474 −1.20554
\(780\) 0 0
\(781\) 10.0980 0.361336
\(782\) 1.02881 0.0367902
\(783\) 0 0
\(784\) −22.2911 −0.796111
\(785\) 65.6559 2.34336
\(786\) 0 0
\(787\) 0.943923 0.0336472 0.0168236 0.999858i \(-0.494645\pi\)
0.0168236 + 0.999858i \(0.494645\pi\)
\(788\) 80.5157 2.86825
\(789\) 0 0
\(790\) −22.9194 −0.815437
\(791\) −26.8595 −0.955014
\(792\) 0 0
\(793\) −35.0140 −1.24338
\(794\) 58.7866 2.08626
\(795\) 0 0
\(796\) −7.87022 −0.278952
\(797\) 13.6806 0.484593 0.242297 0.970202i \(-0.422099\pi\)
0.242297 + 0.970202i \(0.422099\pi\)
\(798\) 0 0
\(799\) −2.52695 −0.0893971
\(800\) 24.7166 0.873864
\(801\) 0 0
\(802\) 92.1485 3.25388
\(803\) −0.988270 −0.0348753
\(804\) 0 0
\(805\) 5.89247 0.207682
\(806\) 65.5638 2.30939
\(807\) 0 0
\(808\) −6.35574 −0.223594
\(809\) 38.3214 1.34731 0.673654 0.739047i \(-0.264724\pi\)
0.673654 + 0.739047i \(0.264724\pi\)
\(810\) 0 0
\(811\) −7.33098 −0.257426 −0.128713 0.991682i \(-0.541085\pi\)
−0.128713 + 0.991682i \(0.541085\pi\)
\(812\) −10.2414 −0.359402
\(813\) 0 0
\(814\) −23.8126 −0.834630
\(815\) 42.7480 1.49740
\(816\) 0 0
\(817\) 24.6791 0.863412
\(818\) 72.3186 2.52856
\(819\) 0 0
\(820\) 126.612 4.42149
\(821\) 50.3587 1.75753 0.878765 0.477254i \(-0.158368\pi\)
0.878765 + 0.477254i \(0.158368\pi\)
\(822\) 0 0
\(823\) −46.2199 −1.61112 −0.805562 0.592512i \(-0.798136\pi\)
−0.805562 + 0.592512i \(0.798136\pi\)
\(824\) −99.0361 −3.45009
\(825\) 0 0
\(826\) 72.1251 2.50955
\(827\) 43.3628 1.50787 0.753936 0.656948i \(-0.228153\pi\)
0.753936 + 0.656948i \(0.228153\pi\)
\(828\) 0 0
\(829\) −15.9732 −0.554773 −0.277387 0.960758i \(-0.589468\pi\)
−0.277387 + 0.960758i \(0.589468\pi\)
\(830\) 6.15430 0.213619
\(831\) 0 0
\(832\) −25.2737 −0.876209
\(833\) −0.950311 −0.0329263
\(834\) 0 0
\(835\) −17.8758 −0.618618
\(836\) 15.5918 0.539255
\(837\) 0 0
\(838\) −48.9605 −1.69131
\(839\) 5.52503 0.190745 0.0953726 0.995442i \(-0.469596\pi\)
0.0953726 + 0.995442i \(0.469596\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −73.6577 −2.53841
\(843\) 0 0
\(844\) 136.911 4.71269
\(845\) −4.12894 −0.142040
\(846\) 0 0
\(847\) 21.7057 0.745816
\(848\) −103.494 −3.55399
\(849\) 0 0
\(850\) 2.62949 0.0901907
\(851\) −9.78131 −0.335299
\(852\) 0 0
\(853\) 24.5699 0.841259 0.420629 0.907233i \(-0.361809\pi\)
0.420629 + 0.907233i \(0.361809\pi\)
\(854\) −51.3118 −1.75585
\(855\) 0 0
\(856\) −86.6332 −2.96106
\(857\) 12.3705 0.422568 0.211284 0.977425i \(-0.432235\pi\)
0.211284 + 0.977425i \(0.432235\pi\)
\(858\) 0 0
\(859\) −7.88043 −0.268877 −0.134438 0.990922i \(-0.542923\pi\)
−0.134438 + 0.990922i \(0.542923\pi\)
\(860\) −92.8652 −3.16668
\(861\) 0 0
\(862\) −5.90534 −0.201137
\(863\) −51.0535 −1.73788 −0.868941 0.494916i \(-0.835199\pi\)
−0.868941 + 0.494916i \(0.835199\pi\)
\(864\) 0 0
\(865\) −16.6502 −0.566124
\(866\) 51.0583 1.73503
\(867\) 0 0
\(868\) 67.7285 2.29886
\(869\) 2.99502 0.101599
\(870\) 0 0
\(871\) 2.44789 0.0829437
\(872\) 22.8118 0.772504
\(873\) 0 0
\(874\) 9.08566 0.307327
\(875\) −14.4021 −0.486879
\(876\) 0 0
\(877\) 10.6497 0.359614 0.179807 0.983702i \(-0.442453\pi\)
0.179807 + 0.983702i \(0.442453\pi\)
\(878\) −27.1919 −0.917683
\(879\) 0 0
\(880\) −23.8276 −0.803230
\(881\) −0.762404 −0.0256861 −0.0128430 0.999918i \(-0.504088\pi\)
−0.0128430 + 0.999918i \(0.504088\pi\)
\(882\) 0 0
\(883\) 9.03933 0.304198 0.152099 0.988365i \(-0.451397\pi\)
0.152099 + 0.988365i \(0.451397\pi\)
\(884\) −7.18983 −0.241820
\(885\) 0 0
\(886\) −31.4774 −1.05750
\(887\) −43.6806 −1.46665 −0.733325 0.679878i \(-0.762033\pi\)
−0.733325 + 0.679878i \(0.762033\pi\)
\(888\) 0 0
\(889\) 40.4906 1.35801
\(890\) −20.0093 −0.670715
\(891\) 0 0
\(892\) −59.2806 −1.98486
\(893\) −22.3161 −0.746779
\(894\) 0 0
\(895\) −19.0334 −0.636218
\(896\) 4.42311 0.147766
\(897\) 0 0
\(898\) −76.5311 −2.55388
\(899\) −6.61322 −0.220563
\(900\) 0 0
\(901\) −4.41213 −0.146989
\(902\) −23.4715 −0.781514
\(903\) 0 0
\(904\) 90.6016 3.01337
\(905\) −24.4784 −0.813689
\(906\) 0 0
\(907\) 11.0837 0.368028 0.184014 0.982924i \(-0.441091\pi\)
0.184014 + 0.982924i \(0.441091\pi\)
\(908\) −73.1607 −2.42792
\(909\) 0 0
\(910\) −58.4182 −1.93655
\(911\) 7.53101 0.249514 0.124757 0.992187i \(-0.460185\pi\)
0.124757 + 0.992187i \(0.460185\pi\)
\(912\) 0 0
\(913\) −0.804221 −0.0266158
\(914\) −78.7191 −2.60380
\(915\) 0 0
\(916\) 74.0315 2.44607
\(917\) 21.2258 0.700936
\(918\) 0 0
\(919\) −23.3625 −0.770659 −0.385329 0.922779i \(-0.625912\pi\)
−0.385329 + 0.922779i \(0.625912\pi\)
\(920\) −19.8763 −0.655302
\(921\) 0 0
\(922\) −72.0078 −2.37145
\(923\) −41.1224 −1.35356
\(924\) 0 0
\(925\) −24.9996 −0.821980
\(926\) −4.96842 −0.163273
\(927\) 0 0
\(928\) 9.67060 0.317453
\(929\) −39.3399 −1.29070 −0.645351 0.763886i \(-0.723289\pi\)
−0.645351 + 0.763886i \(0.723289\pi\)
\(930\) 0 0
\(931\) −8.39241 −0.275050
\(932\) 26.9602 0.883109
\(933\) 0 0
\(934\) −31.0113 −1.01472
\(935\) −1.01582 −0.0332208
\(936\) 0 0
\(937\) 24.0288 0.784985 0.392493 0.919755i \(-0.371613\pi\)
0.392493 + 0.919755i \(0.371613\pi\)
\(938\) 3.58730 0.117130
\(939\) 0 0
\(940\) 83.9734 2.73891
\(941\) −3.74465 −0.122072 −0.0610361 0.998136i \(-0.519440\pi\)
−0.0610361 + 0.998136i \(0.519440\pi\)
\(942\) 0 0
\(943\) −9.64119 −0.313960
\(944\) −119.801 −3.89919
\(945\) 0 0
\(946\) 17.2154 0.559721
\(947\) −38.4273 −1.24872 −0.624360 0.781136i \(-0.714640\pi\)
−0.624360 + 0.781136i \(0.714640\pi\)
\(948\) 0 0
\(949\) 4.02455 0.130642
\(950\) 23.2216 0.753408
\(951\) 0 0
\(952\) −6.12561 −0.198532
\(953\) 21.0295 0.681211 0.340606 0.940206i \(-0.389368\pi\)
0.340606 + 0.940206i \(0.389368\pi\)
\(954\) 0 0
\(955\) 14.3269 0.463607
\(956\) 31.4488 1.01713
\(957\) 0 0
\(958\) −18.8651 −0.609502
\(959\) −29.6106 −0.956175
\(960\) 0 0
\(961\) 12.7347 0.410796
\(962\) 96.9723 3.12651
\(963\) 0 0
\(964\) −28.7508 −0.926002
\(965\) 31.1326 1.00219
\(966\) 0 0
\(967\) −36.3360 −1.16849 −0.584244 0.811578i \(-0.698609\pi\)
−0.584244 + 0.811578i \(0.698609\pi\)
\(968\) −73.2169 −2.35328
\(969\) 0 0
\(970\) −83.8546 −2.69241
\(971\) 35.6304 1.14343 0.571716 0.820451i \(-0.306278\pi\)
0.571716 + 0.820451i \(0.306278\pi\)
\(972\) 0 0
\(973\) 24.0393 0.770664
\(974\) 4.03640 0.129335
\(975\) 0 0
\(976\) 85.2298 2.72814
\(977\) −40.0091 −1.28001 −0.640003 0.768373i \(-0.721067\pi\)
−0.640003 + 0.768373i \(0.721067\pi\)
\(978\) 0 0
\(979\) 2.61474 0.0835676
\(980\) 31.5799 1.00878
\(981\) 0 0
\(982\) 43.4643 1.38700
\(983\) −36.9133 −1.17735 −0.588676 0.808369i \(-0.700351\pi\)
−0.588676 + 0.808369i \(0.700351\pi\)
\(984\) 0 0
\(985\) −46.3254 −1.47605
\(986\) 1.02881 0.0327640
\(987\) 0 0
\(988\) −63.4950 −2.02004
\(989\) 7.07145 0.224859
\(990\) 0 0
\(991\) 33.1415 1.05277 0.526387 0.850245i \(-0.323546\pi\)
0.526387 + 0.850245i \(0.323546\pi\)
\(992\) −63.9538 −2.03054
\(993\) 0 0
\(994\) −60.2634 −1.91144
\(995\) 4.52820 0.143554
\(996\) 0 0
\(997\) 39.3035 1.24475 0.622377 0.782717i \(-0.286167\pi\)
0.622377 + 0.782717i \(0.286167\pi\)
\(998\) 16.1143 0.510090
\(999\) 0 0
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 \(a_p\))