Properties

Label 6003.2.a.t.1.21
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 1.21
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.31658 q^{2} +3.36653 q^{4} -2.07685 q^{5} +1.30399 q^{7} +3.16567 q^{8} +O(q^{10})\) \(q+2.31658 q^{2} +3.36653 q^{4} -2.07685 q^{5} +1.30399 q^{7} +3.16567 q^{8} -4.81118 q^{10} -0.169489 q^{11} +0.705806 q^{13} +3.02080 q^{14} +0.600462 q^{16} -2.81253 q^{17} -7.73667 q^{19} -6.99178 q^{20} -0.392634 q^{22} +1.00000 q^{23} -0.686694 q^{25} +1.63505 q^{26} +4.38993 q^{28} +1.00000 q^{29} -4.11205 q^{31} -4.94033 q^{32} -6.51545 q^{34} -2.70820 q^{35} +4.93337 q^{37} -17.9226 q^{38} -6.57462 q^{40} -2.38205 q^{41} -1.36487 q^{43} -0.570590 q^{44} +2.31658 q^{46} -8.06261 q^{47} -5.29960 q^{49} -1.59078 q^{50} +2.37612 q^{52} +10.8473 q^{53} +0.352003 q^{55} +4.12802 q^{56} +2.31658 q^{58} +5.91579 q^{59} -2.67059 q^{61} -9.52588 q^{62} -12.6456 q^{64} -1.46585 q^{65} -4.10168 q^{67} -9.46847 q^{68} -6.27375 q^{70} +2.86912 q^{71} -9.80599 q^{73} +11.4285 q^{74} -26.0457 q^{76} -0.221013 q^{77} -3.16854 q^{79} -1.24707 q^{80} -5.51821 q^{82} -4.01310 q^{83} +5.84121 q^{85} -3.16183 q^{86} -0.536547 q^{88} -10.7736 q^{89} +0.920367 q^{91} +3.36653 q^{92} -18.6777 q^{94} +16.0679 q^{95} -8.28631 q^{97} -12.2769 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31658 1.63807 0.819034 0.573745i \(-0.194510\pi\)
0.819034 + 0.573745i \(0.194510\pi\)
\(3\) 0 0
\(4\) 3.36653 1.68326
\(5\) −2.07685 −0.928796 −0.464398 0.885627i \(-0.653729\pi\)
−0.464398 + 0.885627i \(0.653729\pi\)
\(6\) 0 0
\(7\) 1.30399 0.492863 0.246432 0.969160i \(-0.420742\pi\)
0.246432 + 0.969160i \(0.420742\pi\)
\(8\) 3.16567 1.11923
\(9\) 0 0
\(10\) −4.81118 −1.52143
\(11\) −0.169489 −0.0511029 −0.0255514 0.999674i \(-0.508134\pi\)
−0.0255514 + 0.999674i \(0.508134\pi\)
\(12\) 0 0
\(13\) 0.705806 0.195755 0.0978777 0.995198i \(-0.468795\pi\)
0.0978777 + 0.995198i \(0.468795\pi\)
\(14\) 3.02080 0.807344
\(15\) 0 0
\(16\) 0.600462 0.150116
\(17\) −2.81253 −0.682139 −0.341070 0.940038i \(-0.610789\pi\)
−0.341070 + 0.940038i \(0.610789\pi\)
\(18\) 0 0
\(19\) −7.73667 −1.77491 −0.887457 0.460891i \(-0.847530\pi\)
−0.887457 + 0.460891i \(0.847530\pi\)
\(20\) −6.99178 −1.56341
\(21\) 0 0
\(22\) −0.392634 −0.0837100
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −0.686694 −0.137339
\(26\) 1.63505 0.320660
\(27\) 0 0
\(28\) 4.38993 0.829620
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −4.11205 −0.738546 −0.369273 0.929321i \(-0.620393\pi\)
−0.369273 + 0.929321i \(0.620393\pi\)
\(32\) −4.94033 −0.873334
\(33\) 0 0
\(34\) −6.51545 −1.11739
\(35\) −2.70820 −0.457769
\(36\) 0 0
\(37\) 4.93337 0.811041 0.405520 0.914086i \(-0.367090\pi\)
0.405520 + 0.914086i \(0.367090\pi\)
\(38\) −17.9226 −2.90743
\(39\) 0 0
\(40\) −6.57462 −1.03954
\(41\) −2.38205 −0.372014 −0.186007 0.982548i \(-0.559555\pi\)
−0.186007 + 0.982548i \(0.559555\pi\)
\(42\) 0 0
\(43\) −1.36487 −0.208141 −0.104070 0.994570i \(-0.533187\pi\)
−0.104070 + 0.994570i \(0.533187\pi\)
\(44\) −0.570590 −0.0860197
\(45\) 0 0
\(46\) 2.31658 0.341561
\(47\) −8.06261 −1.17605 −0.588026 0.808842i \(-0.700095\pi\)
−0.588026 + 0.808842i \(0.700095\pi\)
\(48\) 0 0
\(49\) −5.29960 −0.757086
\(50\) −1.59078 −0.224970
\(51\) 0 0
\(52\) 2.37612 0.329508
\(53\) 10.8473 1.49000 0.744998 0.667066i \(-0.232450\pi\)
0.744998 + 0.667066i \(0.232450\pi\)
\(54\) 0 0
\(55\) 0.352003 0.0474641
\(56\) 4.12802 0.551629
\(57\) 0 0
\(58\) 2.31658 0.304181
\(59\) 5.91579 0.770170 0.385085 0.922881i \(-0.374172\pi\)
0.385085 + 0.922881i \(0.374172\pi\)
\(60\) 0 0
\(61\) −2.67059 −0.341934 −0.170967 0.985277i \(-0.554689\pi\)
−0.170967 + 0.985277i \(0.554689\pi\)
\(62\) −9.52588 −1.20979
\(63\) 0 0
\(64\) −12.6456 −1.58070
\(65\) −1.46585 −0.181817
\(66\) 0 0
\(67\) −4.10168 −0.501100 −0.250550 0.968104i \(-0.580612\pi\)
−0.250550 + 0.968104i \(0.580612\pi\)
\(68\) −9.46847 −1.14822
\(69\) 0 0
\(70\) −6.27375 −0.749857
\(71\) 2.86912 0.340502 0.170251 0.985401i \(-0.445542\pi\)
0.170251 + 0.985401i \(0.445542\pi\)
\(72\) 0 0
\(73\) −9.80599 −1.14770 −0.573852 0.818959i \(-0.694552\pi\)
−0.573852 + 0.818959i \(0.694552\pi\)
\(74\) 11.4285 1.32854
\(75\) 0 0
\(76\) −26.0457 −2.98765
\(77\) −0.221013 −0.0251867
\(78\) 0 0
\(79\) −3.16854 −0.356489 −0.178245 0.983986i \(-0.557042\pi\)
−0.178245 + 0.983986i \(0.557042\pi\)
\(80\) −1.24707 −0.139427
\(81\) 0 0
\(82\) −5.51821 −0.609384
\(83\) −4.01310 −0.440495 −0.220247 0.975444i \(-0.570686\pi\)
−0.220247 + 0.975444i \(0.570686\pi\)
\(84\) 0 0
\(85\) 5.84121 0.633568
\(86\) −3.16183 −0.340948
\(87\) 0 0
\(88\) −0.536547 −0.0571961
\(89\) −10.7736 −1.14200 −0.570998 0.820951i \(-0.693444\pi\)
−0.570998 + 0.820951i \(0.693444\pi\)
\(90\) 0 0
\(91\) 0.920367 0.0964806
\(92\) 3.36653 0.350985
\(93\) 0 0
\(94\) −18.6777 −1.92645
\(95\) 16.0679 1.64853
\(96\) 0 0
\(97\) −8.28631 −0.841347 −0.420673 0.907212i \(-0.638206\pi\)
−0.420673 + 0.907212i \(0.638206\pi\)
\(98\) −12.2769 −1.24016
\(99\) 0 0
\(100\) −2.31177 −0.231177
\(101\) −10.1111 −1.00609 −0.503045 0.864260i \(-0.667787\pi\)
−0.503045 + 0.864260i \(0.667787\pi\)
\(102\) 0 0
\(103\) 17.7619 1.75013 0.875066 0.484004i \(-0.160818\pi\)
0.875066 + 0.484004i \(0.160818\pi\)
\(104\) 2.23435 0.219096
\(105\) 0 0
\(106\) 25.1287 2.44071
\(107\) 9.90380 0.957436 0.478718 0.877969i \(-0.341102\pi\)
0.478718 + 0.877969i \(0.341102\pi\)
\(108\) 0 0
\(109\) −17.3128 −1.65826 −0.829130 0.559055i \(-0.811164\pi\)
−0.829130 + 0.559055i \(0.811164\pi\)
\(110\) 0.815443 0.0777494
\(111\) 0 0
\(112\) 0.782999 0.0739864
\(113\) 16.8475 1.58487 0.792437 0.609953i \(-0.208812\pi\)
0.792437 + 0.609953i \(0.208812\pi\)
\(114\) 0 0
\(115\) −2.07685 −0.193667
\(116\) 3.36653 0.312574
\(117\) 0 0
\(118\) 13.7044 1.26159
\(119\) −3.66752 −0.336201
\(120\) 0 0
\(121\) −10.9713 −0.997388
\(122\) −6.18663 −0.560112
\(123\) 0 0
\(124\) −13.8433 −1.24317
\(125\) 11.8104 1.05636
\(126\) 0 0
\(127\) 13.2186 1.17296 0.586481 0.809963i \(-0.300513\pi\)
0.586481 + 0.809963i \(0.300513\pi\)
\(128\) −19.4138 −1.71595
\(129\) 0 0
\(130\) −3.39576 −0.297828
\(131\) −11.4306 −0.998695 −0.499347 0.866402i \(-0.666427\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(132\) 0 0
\(133\) −10.0886 −0.874790
\(134\) −9.50187 −0.820836
\(135\) 0 0
\(136\) −8.90355 −0.763473
\(137\) 8.68483 0.741995 0.370998 0.928634i \(-0.379016\pi\)
0.370998 + 0.928634i \(0.379016\pi\)
\(138\) 0 0
\(139\) −12.5103 −1.06111 −0.530553 0.847652i \(-0.678016\pi\)
−0.530553 + 0.847652i \(0.678016\pi\)
\(140\) −9.11724 −0.770547
\(141\) 0 0
\(142\) 6.64655 0.557766
\(143\) −0.119626 −0.0100037
\(144\) 0 0
\(145\) −2.07685 −0.172473
\(146\) −22.7163 −1.88002
\(147\) 0 0
\(148\) 16.6083 1.36520
\(149\) 15.1639 1.24228 0.621138 0.783701i \(-0.286670\pi\)
0.621138 + 0.783701i \(0.286670\pi\)
\(150\) 0 0
\(151\) −10.1266 −0.824091 −0.412045 0.911163i \(-0.635185\pi\)
−0.412045 + 0.911163i \(0.635185\pi\)
\(152\) −24.4918 −1.98654
\(153\) 0 0
\(154\) −0.511993 −0.0412576
\(155\) 8.54011 0.685958
\(156\) 0 0
\(157\) 0.740894 0.0591298 0.0295649 0.999563i \(-0.490588\pi\)
0.0295649 + 0.999563i \(0.490588\pi\)
\(158\) −7.34018 −0.583953
\(159\) 0 0
\(160\) 10.2603 0.811149
\(161\) 1.30399 0.102769
\(162\) 0 0
\(163\) 1.49045 0.116741 0.0583706 0.998295i \(-0.481409\pi\)
0.0583706 + 0.998295i \(0.481409\pi\)
\(164\) −8.01925 −0.626198
\(165\) 0 0
\(166\) −9.29665 −0.721560
\(167\) −10.1972 −0.789079 −0.394540 0.918879i \(-0.629096\pi\)
−0.394540 + 0.918879i \(0.629096\pi\)
\(168\) 0 0
\(169\) −12.5018 −0.961680
\(170\) 13.5316 1.03783
\(171\) 0 0
\(172\) −4.59487 −0.350356
\(173\) 14.4841 1.10121 0.550603 0.834767i \(-0.314398\pi\)
0.550603 + 0.834767i \(0.314398\pi\)
\(174\) 0 0
\(175\) −0.895444 −0.0676892
\(176\) −0.101772 −0.00767133
\(177\) 0 0
\(178\) −24.9578 −1.87067
\(179\) −15.8281 −1.18305 −0.591525 0.806287i \(-0.701474\pi\)
−0.591525 + 0.806287i \(0.701474\pi\)
\(180\) 0 0
\(181\) −10.5567 −0.784672 −0.392336 0.919822i \(-0.628333\pi\)
−0.392336 + 0.919822i \(0.628333\pi\)
\(182\) 2.13210 0.158042
\(183\) 0 0
\(184\) 3.16567 0.233376
\(185\) −10.2459 −0.753291
\(186\) 0 0
\(187\) 0.476693 0.0348593
\(188\) −27.1430 −1.97961
\(189\) 0 0
\(190\) 37.2225 2.70041
\(191\) 12.5067 0.904952 0.452476 0.891777i \(-0.350541\pi\)
0.452476 + 0.891777i \(0.350541\pi\)
\(192\) 0 0
\(193\) −16.2747 −1.17148 −0.585739 0.810500i \(-0.699196\pi\)
−0.585739 + 0.810500i \(0.699196\pi\)
\(194\) −19.1959 −1.37818
\(195\) 0 0
\(196\) −17.8413 −1.27438
\(197\) 17.8816 1.27401 0.637006 0.770859i \(-0.280173\pi\)
0.637006 + 0.770859i \(0.280173\pi\)
\(198\) 0 0
\(199\) 11.4755 0.813479 0.406739 0.913544i \(-0.366666\pi\)
0.406739 + 0.913544i \(0.366666\pi\)
\(200\) −2.17385 −0.153714
\(201\) 0 0
\(202\) −23.4231 −1.64804
\(203\) 1.30399 0.0915224
\(204\) 0 0
\(205\) 4.94717 0.345525
\(206\) 41.1468 2.86683
\(207\) 0 0
\(208\) 0.423810 0.0293859
\(209\) 1.31128 0.0907032
\(210\) 0 0
\(211\) −16.9126 −1.16431 −0.582154 0.813078i \(-0.697790\pi\)
−0.582154 + 0.813078i \(0.697790\pi\)
\(212\) 36.5179 2.50806
\(213\) 0 0
\(214\) 22.9429 1.56835
\(215\) 2.83463 0.193320
\(216\) 0 0
\(217\) −5.36209 −0.364002
\(218\) −40.1063 −2.71634
\(219\) 0 0
\(220\) 1.18503 0.0798947
\(221\) −1.98510 −0.133532
\(222\) 0 0
\(223\) 25.4479 1.70412 0.852058 0.523447i \(-0.175354\pi\)
0.852058 + 0.523447i \(0.175354\pi\)
\(224\) −6.44216 −0.430435
\(225\) 0 0
\(226\) 39.0284 2.59613
\(227\) −3.16010 −0.209743 −0.104871 0.994486i \(-0.533443\pi\)
−0.104871 + 0.994486i \(0.533443\pi\)
\(228\) 0 0
\(229\) 4.29359 0.283728 0.141864 0.989886i \(-0.454690\pi\)
0.141864 + 0.989886i \(0.454690\pi\)
\(230\) −4.81118 −0.317240
\(231\) 0 0
\(232\) 3.16567 0.207836
\(233\) −14.4837 −0.948859 −0.474430 0.880293i \(-0.657346\pi\)
−0.474430 + 0.880293i \(0.657346\pi\)
\(234\) 0 0
\(235\) 16.7448 1.09231
\(236\) 19.9157 1.29640
\(237\) 0 0
\(238\) −8.49610 −0.550721
\(239\) 25.3341 1.63873 0.819364 0.573273i \(-0.194327\pi\)
0.819364 + 0.573273i \(0.194327\pi\)
\(240\) 0 0
\(241\) 29.8407 1.92221 0.961105 0.276185i \(-0.0890701\pi\)
0.961105 + 0.276185i \(0.0890701\pi\)
\(242\) −25.4158 −1.63379
\(243\) 0 0
\(244\) −8.99063 −0.575566
\(245\) 11.0065 0.703178
\(246\) 0 0
\(247\) −5.46059 −0.347449
\(248\) −13.0174 −0.826606
\(249\) 0 0
\(250\) 27.3597 1.73038
\(251\) −13.9620 −0.881273 −0.440637 0.897686i \(-0.645247\pi\)
−0.440637 + 0.897686i \(0.645247\pi\)
\(252\) 0 0
\(253\) −0.169489 −0.0106557
\(254\) 30.6219 1.92139
\(255\) 0 0
\(256\) −19.6824 −1.23015
\(257\) 2.06288 0.128679 0.0643396 0.997928i \(-0.479506\pi\)
0.0643396 + 0.997928i \(0.479506\pi\)
\(258\) 0 0
\(259\) 6.43308 0.399732
\(260\) −4.93484 −0.306046
\(261\) 0 0
\(262\) −26.4798 −1.63593
\(263\) 6.51820 0.401929 0.200965 0.979599i \(-0.435592\pi\)
0.200965 + 0.979599i \(0.435592\pi\)
\(264\) 0 0
\(265\) −22.5283 −1.38390
\(266\) −23.3710 −1.43297
\(267\) 0 0
\(268\) −13.8084 −0.843485
\(269\) −22.3808 −1.36458 −0.682290 0.731082i \(-0.739016\pi\)
−0.682290 + 0.731082i \(0.739016\pi\)
\(270\) 0 0
\(271\) 13.7657 0.836208 0.418104 0.908399i \(-0.362695\pi\)
0.418104 + 0.908399i \(0.362695\pi\)
\(272\) −1.68882 −0.102400
\(273\) 0 0
\(274\) 20.1191 1.21544
\(275\) 0.116387 0.00701840
\(276\) 0 0
\(277\) 5.06087 0.304078 0.152039 0.988374i \(-0.451416\pi\)
0.152039 + 0.988374i \(0.451416\pi\)
\(278\) −28.9810 −1.73816
\(279\) 0 0
\(280\) −8.57327 −0.512351
\(281\) −24.2561 −1.44700 −0.723499 0.690326i \(-0.757467\pi\)
−0.723499 + 0.690326i \(0.757467\pi\)
\(282\) 0 0
\(283\) −5.35557 −0.318356 −0.159178 0.987250i \(-0.550884\pi\)
−0.159178 + 0.987250i \(0.550884\pi\)
\(284\) 9.65899 0.573156
\(285\) 0 0
\(286\) −0.277124 −0.0163867
\(287\) −3.10618 −0.183352
\(288\) 0 0
\(289\) −9.08967 −0.534686
\(290\) −4.81118 −0.282522
\(291\) 0 0
\(292\) −33.0121 −1.93189
\(293\) −6.01450 −0.351371 −0.175685 0.984446i \(-0.556214\pi\)
−0.175685 + 0.984446i \(0.556214\pi\)
\(294\) 0 0
\(295\) −12.2862 −0.715331
\(296\) 15.6174 0.907744
\(297\) 0 0
\(298\) 35.1284 2.03493
\(299\) 0.705806 0.0408178
\(300\) 0 0
\(301\) −1.77978 −0.102585
\(302\) −23.4590 −1.34992
\(303\) 0 0
\(304\) −4.64558 −0.266442
\(305\) 5.54642 0.317587
\(306\) 0 0
\(307\) 17.3807 0.991966 0.495983 0.868332i \(-0.334808\pi\)
0.495983 + 0.868332i \(0.334808\pi\)
\(308\) −0.744046 −0.0423959
\(309\) 0 0
\(310\) 19.7838 1.12365
\(311\) −28.2892 −1.60413 −0.802067 0.597234i \(-0.796266\pi\)
−0.802067 + 0.597234i \(0.796266\pi\)
\(312\) 0 0
\(313\) −9.92102 −0.560769 −0.280385 0.959888i \(-0.590462\pi\)
−0.280385 + 0.959888i \(0.590462\pi\)
\(314\) 1.71634 0.0968586
\(315\) 0 0
\(316\) −10.6670 −0.600066
\(317\) −20.6462 −1.15961 −0.579803 0.814756i \(-0.696871\pi\)
−0.579803 + 0.814756i \(0.696871\pi\)
\(318\) 0 0
\(319\) −0.169489 −0.00948957
\(320\) 26.2630 1.46814
\(321\) 0 0
\(322\) 3.02080 0.168343
\(323\) 21.7596 1.21074
\(324\) 0 0
\(325\) −0.484672 −0.0268848
\(326\) 3.45275 0.191230
\(327\) 0 0
\(328\) −7.54080 −0.416371
\(329\) −10.5136 −0.579633
\(330\) 0 0
\(331\) 4.94691 0.271907 0.135953 0.990715i \(-0.456590\pi\)
0.135953 + 0.990715i \(0.456590\pi\)
\(332\) −13.5102 −0.741469
\(333\) 0 0
\(334\) −23.6225 −1.29257
\(335\) 8.51858 0.465420
\(336\) 0 0
\(337\) −23.6415 −1.28784 −0.643918 0.765094i \(-0.722692\pi\)
−0.643918 + 0.765094i \(0.722692\pi\)
\(338\) −28.9615 −1.57530
\(339\) 0 0
\(340\) 19.6646 1.06646
\(341\) 0.696948 0.0377418
\(342\) 0 0
\(343\) −16.0386 −0.866003
\(344\) −4.32073 −0.232958
\(345\) 0 0
\(346\) 33.5536 1.80385
\(347\) −6.29098 −0.337717 −0.168859 0.985640i \(-0.554008\pi\)
−0.168859 + 0.985640i \(0.554008\pi\)
\(348\) 0 0
\(349\) 33.5081 1.79365 0.896823 0.442390i \(-0.145869\pi\)
0.896823 + 0.442390i \(0.145869\pi\)
\(350\) −2.07437 −0.110880
\(351\) 0 0
\(352\) 0.837331 0.0446299
\(353\) 28.8240 1.53415 0.767074 0.641559i \(-0.221712\pi\)
0.767074 + 0.641559i \(0.221712\pi\)
\(354\) 0 0
\(355\) −5.95874 −0.316257
\(356\) −36.2695 −1.92228
\(357\) 0 0
\(358\) −36.6671 −1.93791
\(359\) −30.9936 −1.63578 −0.817891 0.575373i \(-0.804857\pi\)
−0.817891 + 0.575373i \(0.804857\pi\)
\(360\) 0 0
\(361\) 40.8561 2.15032
\(362\) −24.4554 −1.28535
\(363\) 0 0
\(364\) 3.09844 0.162402
\(365\) 20.3656 1.06598
\(366\) 0 0
\(367\) 13.7921 0.719941 0.359971 0.932964i \(-0.382787\pi\)
0.359971 + 0.932964i \(0.382787\pi\)
\(368\) 0.600462 0.0313012
\(369\) 0 0
\(370\) −23.7353 −1.23394
\(371\) 14.1449 0.734365
\(372\) 0 0
\(373\) −1.58905 −0.0822781 −0.0411390 0.999153i \(-0.513099\pi\)
−0.0411390 + 0.999153i \(0.513099\pi\)
\(374\) 1.10430 0.0571018
\(375\) 0 0
\(376\) −25.5236 −1.31628
\(377\) 0.705806 0.0363509
\(378\) 0 0
\(379\) −11.7068 −0.601338 −0.300669 0.953729i \(-0.597210\pi\)
−0.300669 + 0.953729i \(0.597210\pi\)
\(380\) 54.0931 2.77492
\(381\) 0 0
\(382\) 28.9727 1.48237
\(383\) −5.46335 −0.279164 −0.139582 0.990211i \(-0.544576\pi\)
−0.139582 + 0.990211i \(0.544576\pi\)
\(384\) 0 0
\(385\) 0.459010 0.0233933
\(386\) −37.7016 −1.91896
\(387\) 0 0
\(388\) −27.8961 −1.41621
\(389\) 5.66382 0.287167 0.143584 0.989638i \(-0.454137\pi\)
0.143584 + 0.989638i \(0.454137\pi\)
\(390\) 0 0
\(391\) −2.81253 −0.142236
\(392\) −16.7768 −0.847356
\(393\) 0 0
\(394\) 41.4242 2.08692
\(395\) 6.58059 0.331106
\(396\) 0 0
\(397\) −24.5959 −1.23443 −0.617215 0.786794i \(-0.711739\pi\)
−0.617215 + 0.786794i \(0.711739\pi\)
\(398\) 26.5839 1.33253
\(399\) 0 0
\(400\) −0.412333 −0.0206167
\(401\) 23.2123 1.15916 0.579582 0.814914i \(-0.303216\pi\)
0.579582 + 0.814914i \(0.303216\pi\)
\(402\) 0 0
\(403\) −2.90231 −0.144574
\(404\) −34.0393 −1.69352
\(405\) 0 0
\(406\) 3.02080 0.149920
\(407\) −0.836152 −0.0414465
\(408\) 0 0
\(409\) −22.6437 −1.11966 −0.559829 0.828608i \(-0.689133\pi\)
−0.559829 + 0.828608i \(0.689133\pi\)
\(410\) 11.4605 0.565994
\(411\) 0 0
\(412\) 59.7959 2.94593
\(413\) 7.71416 0.379589
\(414\) 0 0
\(415\) 8.33460 0.409129
\(416\) −3.48691 −0.170960
\(417\) 0 0
\(418\) 3.03768 0.148578
\(419\) 19.3996 0.947732 0.473866 0.880597i \(-0.342858\pi\)
0.473866 + 0.880597i \(0.342858\pi\)
\(420\) 0 0
\(421\) −17.6305 −0.859259 −0.429630 0.903005i \(-0.641356\pi\)
−0.429630 + 0.903005i \(0.641356\pi\)
\(422\) −39.1792 −1.90722
\(423\) 0 0
\(424\) 34.3391 1.66765
\(425\) 1.93135 0.0936841
\(426\) 0 0
\(427\) −3.48244 −0.168527
\(428\) 33.3414 1.61162
\(429\) 0 0
\(430\) 6.56664 0.316671
\(431\) −3.82141 −0.184071 −0.0920355 0.995756i \(-0.529337\pi\)
−0.0920355 + 0.995756i \(0.529337\pi\)
\(432\) 0 0
\(433\) 34.6578 1.66555 0.832774 0.553613i \(-0.186751\pi\)
0.832774 + 0.553613i \(0.186751\pi\)
\(434\) −12.4217 −0.596261
\(435\) 0 0
\(436\) −58.2839 −2.79129
\(437\) −7.73667 −0.370095
\(438\) 0 0
\(439\) 18.4524 0.880686 0.440343 0.897830i \(-0.354857\pi\)
0.440343 + 0.897830i \(0.354857\pi\)
\(440\) 1.11433 0.0531234
\(441\) 0 0
\(442\) −4.59864 −0.218735
\(443\) 27.6628 1.31430 0.657150 0.753760i \(-0.271762\pi\)
0.657150 + 0.753760i \(0.271762\pi\)
\(444\) 0 0
\(445\) 22.3751 1.06068
\(446\) 58.9520 2.79146
\(447\) 0 0
\(448\) −16.4897 −0.779067
\(449\) 27.7271 1.30852 0.654262 0.756268i \(-0.272979\pi\)
0.654262 + 0.756268i \(0.272979\pi\)
\(450\) 0 0
\(451\) 0.403732 0.0190110
\(452\) 56.7174 2.66776
\(453\) 0 0
\(454\) −7.32061 −0.343573
\(455\) −1.91146 −0.0896108
\(456\) 0 0
\(457\) −4.85874 −0.227282 −0.113641 0.993522i \(-0.536251\pi\)
−0.113641 + 0.993522i \(0.536251\pi\)
\(458\) 9.94642 0.464766
\(459\) 0 0
\(460\) −6.99178 −0.325993
\(461\) 19.6497 0.915178 0.457589 0.889164i \(-0.348713\pi\)
0.457589 + 0.889164i \(0.348713\pi\)
\(462\) 0 0
\(463\) −31.9707 −1.48580 −0.742902 0.669401i \(-0.766551\pi\)
−0.742902 + 0.669401i \(0.766551\pi\)
\(464\) 0.600462 0.0278757
\(465\) 0 0
\(466\) −33.5526 −1.55430
\(467\) 7.06027 0.326710 0.163355 0.986567i \(-0.447768\pi\)
0.163355 + 0.986567i \(0.447768\pi\)
\(468\) 0 0
\(469\) −5.34857 −0.246974
\(470\) 38.7907 1.78928
\(471\) 0 0
\(472\) 18.7274 0.862001
\(473\) 0.231330 0.0106366
\(474\) 0 0
\(475\) 5.31272 0.243764
\(476\) −12.3468 −0.565916
\(477\) 0 0
\(478\) 58.6885 2.68435
\(479\) 3.49893 0.159870 0.0799350 0.996800i \(-0.474529\pi\)
0.0799350 + 0.996800i \(0.474529\pi\)
\(480\) 0 0
\(481\) 3.48200 0.158766
\(482\) 69.1283 3.14871
\(483\) 0 0
\(484\) −36.9351 −1.67887
\(485\) 17.2094 0.781439
\(486\) 0 0
\(487\) 21.6955 0.983118 0.491559 0.870844i \(-0.336427\pi\)
0.491559 + 0.870844i \(0.336427\pi\)
\(488\) −8.45422 −0.382704
\(489\) 0 0
\(490\) 25.4973 1.15185
\(491\) 1.99184 0.0898903 0.0449452 0.998989i \(-0.485689\pi\)
0.0449452 + 0.998989i \(0.485689\pi\)
\(492\) 0 0
\(493\) −2.81253 −0.126670
\(494\) −12.6499 −0.569145
\(495\) 0 0
\(496\) −2.46913 −0.110867
\(497\) 3.74132 0.167821
\(498\) 0 0
\(499\) −27.0930 −1.21285 −0.606424 0.795142i \(-0.707396\pi\)
−0.606424 + 0.795142i \(0.707396\pi\)
\(500\) 39.7601 1.77813
\(501\) 0 0
\(502\) −32.3440 −1.44358
\(503\) −12.4494 −0.555094 −0.277547 0.960712i \(-0.589521\pi\)
−0.277547 + 0.960712i \(0.589521\pi\)
\(504\) 0 0
\(505\) 20.9992 0.934452
\(506\) −0.392634 −0.0174547
\(507\) 0 0
\(508\) 44.5008 1.97441
\(509\) 0.109995 0.00487546 0.00243773 0.999997i \(-0.499224\pi\)
0.00243773 + 0.999997i \(0.499224\pi\)
\(510\) 0 0
\(511\) −12.7869 −0.565661
\(512\) −6.76821 −0.299115
\(513\) 0 0
\(514\) 4.77883 0.210785
\(515\) −36.8888 −1.62551
\(516\) 0 0
\(517\) 1.36652 0.0600997
\(518\) 14.9027 0.654788
\(519\) 0 0
\(520\) −4.64041 −0.203495
\(521\) 7.73135 0.338717 0.169358 0.985555i \(-0.445830\pi\)
0.169358 + 0.985555i \(0.445830\pi\)
\(522\) 0 0
\(523\) −3.75686 −0.164276 −0.0821381 0.996621i \(-0.526175\pi\)
−0.0821381 + 0.996621i \(0.526175\pi\)
\(524\) −38.4814 −1.68107
\(525\) 0 0
\(526\) 15.0999 0.658387
\(527\) 11.5653 0.503791
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −52.1885 −2.26693
\(531\) 0 0
\(532\) −33.9635 −1.47250
\(533\) −1.68127 −0.0728238
\(534\) 0 0
\(535\) −20.5687 −0.889263
\(536\) −12.9846 −0.560849
\(537\) 0 0
\(538\) −51.8468 −2.23527
\(539\) 0.898224 0.0386893
\(540\) 0 0
\(541\) 14.1131 0.606769 0.303385 0.952868i \(-0.401883\pi\)
0.303385 + 0.952868i \(0.401883\pi\)
\(542\) 31.8894 1.36977
\(543\) 0 0
\(544\) 13.8948 0.595735
\(545\) 35.9560 1.54019
\(546\) 0 0
\(547\) −5.60250 −0.239546 −0.119773 0.992801i \(-0.538217\pi\)
−0.119773 + 0.992801i \(0.538217\pi\)
\(548\) 29.2377 1.24897
\(549\) 0 0
\(550\) 0.269620 0.0114966
\(551\) −7.73667 −0.329593
\(552\) 0 0
\(553\) −4.13176 −0.175700
\(554\) 11.7239 0.498101
\(555\) 0 0
\(556\) −42.1162 −1.78612
\(557\) 38.1737 1.61747 0.808735 0.588173i \(-0.200153\pi\)
0.808735 + 0.588173i \(0.200153\pi\)
\(558\) 0 0
\(559\) −0.963333 −0.0407446
\(560\) −1.62617 −0.0687183
\(561\) 0 0
\(562\) −56.1911 −2.37028
\(563\) −19.9152 −0.839324 −0.419662 0.907680i \(-0.637851\pi\)
−0.419662 + 0.907680i \(0.637851\pi\)
\(564\) 0 0
\(565\) −34.9896 −1.47202
\(566\) −12.4066 −0.521488
\(567\) 0 0
\(568\) 9.08270 0.381102
\(569\) 24.1599 1.01283 0.506417 0.862288i \(-0.330970\pi\)
0.506417 + 0.862288i \(0.330970\pi\)
\(570\) 0 0
\(571\) 0.809648 0.0338827 0.0169414 0.999856i \(-0.494607\pi\)
0.0169414 + 0.999856i \(0.494607\pi\)
\(572\) −0.402726 −0.0168388
\(573\) 0 0
\(574\) −7.19571 −0.300343
\(575\) −0.686694 −0.0286371
\(576\) 0 0
\(577\) −7.99326 −0.332764 −0.166382 0.986061i \(-0.553208\pi\)
−0.166382 + 0.986061i \(0.553208\pi\)
\(578\) −21.0569 −0.875852
\(579\) 0 0
\(580\) −6.99178 −0.290318
\(581\) −5.23305 −0.217104
\(582\) 0 0
\(583\) −1.83851 −0.0761431
\(584\) −31.0425 −1.28455
\(585\) 0 0
\(586\) −13.9330 −0.575569
\(587\) 4.08246 0.168501 0.0842506 0.996445i \(-0.473150\pi\)
0.0842506 + 0.996445i \(0.473150\pi\)
\(588\) 0 0
\(589\) 31.8136 1.31086
\(590\) −28.4620 −1.17176
\(591\) 0 0
\(592\) 2.96230 0.121750
\(593\) 8.41250 0.345460 0.172730 0.984969i \(-0.444741\pi\)
0.172730 + 0.984969i \(0.444741\pi\)
\(594\) 0 0
\(595\) 7.61690 0.312262
\(596\) 51.0498 2.09108
\(597\) 0 0
\(598\) 1.63505 0.0668623
\(599\) −37.6547 −1.53853 −0.769265 0.638930i \(-0.779377\pi\)
−0.769265 + 0.638930i \(0.779377\pi\)
\(600\) 0 0
\(601\) 11.6127 0.473693 0.236846 0.971547i \(-0.423886\pi\)
0.236846 + 0.971547i \(0.423886\pi\)
\(602\) −4.12300 −0.168041
\(603\) 0 0
\(604\) −34.0915 −1.38716
\(605\) 22.7857 0.926370
\(606\) 0 0
\(607\) 35.6191 1.44573 0.722867 0.690987i \(-0.242824\pi\)
0.722867 + 0.690987i \(0.242824\pi\)
\(608\) 38.2217 1.55009
\(609\) 0 0
\(610\) 12.8487 0.520229
\(611\) −5.69064 −0.230219
\(612\) 0 0
\(613\) 36.4041 1.47035 0.735174 0.677878i \(-0.237100\pi\)
0.735174 + 0.677878i \(0.237100\pi\)
\(614\) 40.2636 1.62491
\(615\) 0 0
\(616\) −0.699654 −0.0281898
\(617\) 32.5101 1.30881 0.654404 0.756145i \(-0.272920\pi\)
0.654404 + 0.756145i \(0.272920\pi\)
\(618\) 0 0
\(619\) −3.18797 −0.128135 −0.0640677 0.997946i \(-0.520407\pi\)
−0.0640677 + 0.997946i \(0.520407\pi\)
\(620\) 28.7505 1.15465
\(621\) 0 0
\(622\) −65.5341 −2.62768
\(623\) −14.0487 −0.562848
\(624\) 0 0
\(625\) −21.0950 −0.843799
\(626\) −22.9828 −0.918578
\(627\) 0 0
\(628\) 2.49424 0.0995311
\(629\) −13.8753 −0.553242
\(630\) 0 0
\(631\) −18.6025 −0.740553 −0.370277 0.928922i \(-0.620737\pi\)
−0.370277 + 0.928922i \(0.620737\pi\)
\(632\) −10.0306 −0.398995
\(633\) 0 0
\(634\) −47.8285 −1.89951
\(635\) −27.4531 −1.08944
\(636\) 0 0
\(637\) −3.74049 −0.148204
\(638\) −0.392634 −0.0155445
\(639\) 0 0
\(640\) 40.3195 1.59377
\(641\) −47.2445 −1.86605 −0.933023 0.359817i \(-0.882839\pi\)
−0.933023 + 0.359817i \(0.882839\pi\)
\(642\) 0 0
\(643\) 26.7049 1.05314 0.526569 0.850133i \(-0.323478\pi\)
0.526569 + 0.850133i \(0.323478\pi\)
\(644\) 4.38993 0.172988
\(645\) 0 0
\(646\) 50.4078 1.98327
\(647\) 7.37359 0.289886 0.144943 0.989440i \(-0.453700\pi\)
0.144943 + 0.989440i \(0.453700\pi\)
\(648\) 0 0
\(649\) −1.00266 −0.0393579
\(650\) −1.12278 −0.0440391
\(651\) 0 0
\(652\) 5.01765 0.196506
\(653\) 25.1850 0.985567 0.492783 0.870152i \(-0.335979\pi\)
0.492783 + 0.870152i \(0.335979\pi\)
\(654\) 0 0
\(655\) 23.7396 0.927583
\(656\) −1.43033 −0.0558451
\(657\) 0 0
\(658\) −24.3556 −0.949479
\(659\) 34.1093 1.32871 0.664355 0.747417i \(-0.268706\pi\)
0.664355 + 0.747417i \(0.268706\pi\)
\(660\) 0 0
\(661\) −18.1675 −0.706635 −0.353318 0.935503i \(-0.614947\pi\)
−0.353318 + 0.935503i \(0.614947\pi\)
\(662\) 11.4599 0.445401
\(663\) 0 0
\(664\) −12.7041 −0.493016
\(665\) 20.9525 0.812501
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −34.3290 −1.32823
\(669\) 0 0
\(670\) 19.7340 0.762389
\(671\) 0.452636 0.0174738
\(672\) 0 0
\(673\) −14.2757 −0.550286 −0.275143 0.961403i \(-0.588725\pi\)
−0.275143 + 0.961403i \(0.588725\pi\)
\(674\) −54.7675 −2.10956
\(675\) 0 0
\(676\) −42.0878 −1.61876
\(677\) 47.2256 1.81503 0.907514 0.420021i \(-0.137977\pi\)
0.907514 + 0.420021i \(0.137977\pi\)
\(678\) 0 0
\(679\) −10.8053 −0.414669
\(680\) 18.4913 0.709110
\(681\) 0 0
\(682\) 1.61453 0.0618237
\(683\) 14.4612 0.553344 0.276672 0.960964i \(-0.410768\pi\)
0.276672 + 0.960964i \(0.410768\pi\)
\(684\) 0 0
\(685\) −18.0371 −0.689162
\(686\) −37.1547 −1.41857
\(687\) 0 0
\(688\) −0.819552 −0.0312451
\(689\) 7.65611 0.291675
\(690\) 0 0
\(691\) −43.7378 −1.66386 −0.831932 0.554878i \(-0.812765\pi\)
−0.831932 + 0.554878i \(0.812765\pi\)
\(692\) 48.7612 1.85362
\(693\) 0 0
\(694\) −14.5735 −0.553204
\(695\) 25.9819 0.985551
\(696\) 0 0
\(697\) 6.69960 0.253765
\(698\) 77.6240 2.93811
\(699\) 0 0
\(700\) −3.01454 −0.113939
\(701\) 16.5091 0.623540 0.311770 0.950158i \(-0.399078\pi\)
0.311770 + 0.950158i \(0.399078\pi\)
\(702\) 0 0
\(703\) −38.1678 −1.43953
\(704\) 2.14329 0.0807781
\(705\) 0 0
\(706\) 66.7731 2.51304
\(707\) −13.1848 −0.495865
\(708\) 0 0
\(709\) 44.8286 1.68357 0.841786 0.539811i \(-0.181504\pi\)
0.841786 + 0.539811i \(0.181504\pi\)
\(710\) −13.8039 −0.518050
\(711\) 0 0
\(712\) −34.1056 −1.27816
\(713\) −4.11205 −0.153998
\(714\) 0 0
\(715\) 0.248446 0.00929136
\(716\) −53.2858 −1.99139
\(717\) 0 0
\(718\) −71.7992 −2.67952
\(719\) 0.824697 0.0307560 0.0153780 0.999882i \(-0.495105\pi\)
0.0153780 + 0.999882i \(0.495105\pi\)
\(720\) 0 0
\(721\) 23.1614 0.862576
\(722\) 94.6462 3.52237
\(723\) 0 0
\(724\) −35.5394 −1.32081
\(725\) −0.686694 −0.0255032
\(726\) 0 0
\(727\) −46.9159 −1.74002 −0.870008 0.493038i \(-0.835886\pi\)
−0.870008 + 0.493038i \(0.835886\pi\)
\(728\) 2.91358 0.107984
\(729\) 0 0
\(730\) 47.1784 1.74615
\(731\) 3.83874 0.141981
\(732\) 0 0
\(733\) −34.3606 −1.26914 −0.634570 0.772866i \(-0.718823\pi\)
−0.634570 + 0.772866i \(0.718823\pi\)
\(734\) 31.9504 1.17931
\(735\) 0 0
\(736\) −4.94033 −0.182103
\(737\) 0.695191 0.0256077
\(738\) 0 0
\(739\) 6.08214 0.223735 0.111868 0.993723i \(-0.464317\pi\)
0.111868 + 0.993723i \(0.464317\pi\)
\(740\) −34.4930 −1.26799
\(741\) 0 0
\(742\) 32.7677 1.20294
\(743\) 10.0165 0.367471 0.183735 0.982976i \(-0.441181\pi\)
0.183735 + 0.982976i \(0.441181\pi\)
\(744\) 0 0
\(745\) −31.4932 −1.15382
\(746\) −3.68117 −0.134777
\(747\) 0 0
\(748\) 1.60480 0.0586774
\(749\) 12.9145 0.471885
\(750\) 0 0
\(751\) 13.3546 0.487318 0.243659 0.969861i \(-0.421652\pi\)
0.243659 + 0.969861i \(0.421652\pi\)
\(752\) −4.84129 −0.176544
\(753\) 0 0
\(754\) 1.63505 0.0595451
\(755\) 21.0314 0.765412
\(756\) 0 0
\(757\) 2.19148 0.0796508 0.0398254 0.999207i \(-0.487320\pi\)
0.0398254 + 0.999207i \(0.487320\pi\)
\(758\) −27.1197 −0.985032
\(759\) 0 0
\(760\) 50.8657 1.84509
\(761\) −5.49565 −0.199217 −0.0996085 0.995027i \(-0.531759\pi\)
−0.0996085 + 0.995027i \(0.531759\pi\)
\(762\) 0 0
\(763\) −22.5757 −0.817296
\(764\) 42.1041 1.52327
\(765\) 0 0
\(766\) −12.6563 −0.457289
\(767\) 4.17540 0.150765
\(768\) 0 0
\(769\) −38.1501 −1.37573 −0.687863 0.725841i \(-0.741451\pi\)
−0.687863 + 0.725841i \(0.741451\pi\)
\(770\) 1.06333 0.0383199
\(771\) 0 0
\(772\) −54.7892 −1.97191
\(773\) −33.6301 −1.20959 −0.604796 0.796381i \(-0.706745\pi\)
−0.604796 + 0.796381i \(0.706745\pi\)
\(774\) 0 0
\(775\) 2.82372 0.101431
\(776\) −26.2317 −0.941664
\(777\) 0 0
\(778\) 13.1207 0.470399
\(779\) 18.4292 0.660293
\(780\) 0 0
\(781\) −0.486285 −0.0174006
\(782\) −6.51545 −0.232992
\(783\) 0 0
\(784\) −3.18221 −0.113650
\(785\) −1.53873 −0.0549195
\(786\) 0 0
\(787\) 41.8793 1.49284 0.746418 0.665477i \(-0.231772\pi\)
0.746418 + 0.665477i \(0.231772\pi\)
\(788\) 60.1990 2.14450
\(789\) 0 0
\(790\) 15.2445 0.542373
\(791\) 21.9690 0.781127
\(792\) 0 0
\(793\) −1.88492 −0.0669355
\(794\) −56.9782 −2.02208
\(795\) 0 0
\(796\) 38.6327 1.36930
\(797\) −22.3903 −0.793104 −0.396552 0.918012i \(-0.629793\pi\)
−0.396552 + 0.918012i \(0.629793\pi\)
\(798\) 0 0
\(799\) 22.6763 0.802232
\(800\) 3.39249 0.119943
\(801\) 0 0
\(802\) 53.7730 1.89879
\(803\) 1.66201 0.0586510
\(804\) 0 0
\(805\) −2.70820 −0.0954515
\(806\) −6.72342 −0.236823
\(807\) 0 0
\(808\) −32.0084 −1.12605
\(809\) −18.9095 −0.664821 −0.332411 0.943135i \(-0.607862\pi\)
−0.332411 + 0.943135i \(0.607862\pi\)
\(810\) 0 0
\(811\) 19.8033 0.695387 0.347694 0.937608i \(-0.386965\pi\)
0.347694 + 0.937608i \(0.386965\pi\)
\(812\) 4.38993 0.154057
\(813\) 0 0
\(814\) −1.93701 −0.0678922
\(815\) −3.09545 −0.108429
\(816\) 0 0
\(817\) 10.5595 0.369432
\(818\) −52.4559 −1.83408
\(819\) 0 0
\(820\) 16.6548 0.581610
\(821\) −28.6472 −0.999794 −0.499897 0.866085i \(-0.666629\pi\)
−0.499897 + 0.866085i \(0.666629\pi\)
\(822\) 0 0
\(823\) 3.81800 0.133087 0.0665435 0.997784i \(-0.478803\pi\)
0.0665435 + 0.997784i \(0.478803\pi\)
\(824\) 56.2283 1.95881
\(825\) 0 0
\(826\) 17.8704 0.621792
\(827\) 2.25983 0.0785819 0.0392909 0.999228i \(-0.487490\pi\)
0.0392909 + 0.999228i \(0.487490\pi\)
\(828\) 0 0
\(829\) 33.7692 1.17285 0.586426 0.810002i \(-0.300534\pi\)
0.586426 + 0.810002i \(0.300534\pi\)
\(830\) 19.3077 0.670181
\(831\) 0 0
\(832\) −8.92532 −0.309430
\(833\) 14.9053 0.516438
\(834\) 0 0
\(835\) 21.1780 0.732894
\(836\) 4.41447 0.152677
\(837\) 0 0
\(838\) 44.9406 1.55245
\(839\) 39.6474 1.36878 0.684390 0.729116i \(-0.260068\pi\)
0.684390 + 0.729116i \(0.260068\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −40.8425 −1.40752
\(843\) 0 0
\(844\) −56.9366 −1.95984
\(845\) 25.9644 0.893204
\(846\) 0 0
\(847\) −14.3065 −0.491576
\(848\) 6.51341 0.223672
\(849\) 0 0
\(850\) 4.47411 0.153461
\(851\) 4.93337 0.169114
\(852\) 0 0
\(853\) −20.9935 −0.718805 −0.359402 0.933183i \(-0.617019\pi\)
−0.359402 + 0.933183i \(0.617019\pi\)
\(854\) −8.06733 −0.276059
\(855\) 0 0
\(856\) 31.3522 1.07160
\(857\) −11.0997 −0.379158 −0.189579 0.981865i \(-0.560712\pi\)
−0.189579 + 0.981865i \(0.560712\pi\)
\(858\) 0 0
\(859\) −8.62331 −0.294224 −0.147112 0.989120i \(-0.546998\pi\)
−0.147112 + 0.989120i \(0.546998\pi\)
\(860\) 9.54286 0.325409
\(861\) 0 0
\(862\) −8.85260 −0.301521
\(863\) 47.2590 1.60872 0.804358 0.594145i \(-0.202509\pi\)
0.804358 + 0.594145i \(0.202509\pi\)
\(864\) 0 0
\(865\) −30.0813 −1.02280
\(866\) 80.2875 2.72828
\(867\) 0 0
\(868\) −18.0516 −0.612712
\(869\) 0.537034 0.0182176
\(870\) 0 0
\(871\) −2.89499 −0.0980931
\(872\) −54.8065 −1.85598
\(873\) 0 0
\(874\) −17.9226 −0.606241
\(875\) 15.4007 0.520639
\(876\) 0 0
\(877\) 31.9405 1.07855 0.539277 0.842128i \(-0.318697\pi\)
0.539277 + 0.842128i \(0.318697\pi\)
\(878\) 42.7464 1.44262
\(879\) 0 0
\(880\) 0.211365 0.00712510
\(881\) 7.21420 0.243053 0.121526 0.992588i \(-0.461221\pi\)
0.121526 + 0.992588i \(0.461221\pi\)
\(882\) 0 0
\(883\) −47.6682 −1.60416 −0.802082 0.597215i \(-0.796274\pi\)
−0.802082 + 0.597215i \(0.796274\pi\)
\(884\) −6.68290 −0.224770
\(885\) 0 0
\(886\) 64.0830 2.15291
\(887\) 21.0745 0.707614 0.353807 0.935318i \(-0.384887\pi\)
0.353807 + 0.935318i \(0.384887\pi\)
\(888\) 0 0
\(889\) 17.2370 0.578110
\(890\) 51.8336 1.73747
\(891\) 0 0
\(892\) 85.6711 2.86848
\(893\) 62.3778 2.08739
\(894\) 0 0
\(895\) 32.8726 1.09881
\(896\) −25.3155 −0.845730
\(897\) 0 0
\(898\) 64.2320 2.14345
\(899\) −4.11205 −0.137145
\(900\) 0 0
\(901\) −30.5085 −1.01638
\(902\) 0.935276 0.0311413
\(903\) 0 0
\(904\) 53.3335 1.77385
\(905\) 21.9247 0.728800
\(906\) 0 0
\(907\) −57.2893 −1.90226 −0.951131 0.308788i \(-0.900077\pi\)
−0.951131 + 0.308788i \(0.900077\pi\)
\(908\) −10.6386 −0.353053
\(909\) 0 0
\(910\) −4.42805 −0.146789
\(911\) −9.02378 −0.298971 −0.149486 0.988764i \(-0.547762\pi\)
−0.149486 + 0.988764i \(0.547762\pi\)
\(912\) 0 0
\(913\) 0.680176 0.0225105
\(914\) −11.2556 −0.372304
\(915\) 0 0
\(916\) 14.4545 0.477590
\(917\) −14.9054 −0.492220
\(918\) 0 0
\(919\) −2.32312 −0.0766328 −0.0383164 0.999266i \(-0.512199\pi\)
−0.0383164 + 0.999266i \(0.512199\pi\)
\(920\) −6.57462 −0.216759
\(921\) 0 0
\(922\) 45.5200 1.49912
\(923\) 2.02504 0.0666551
\(924\) 0 0
\(925\) −3.38771 −0.111387
\(926\) −74.0625 −2.43385
\(927\) 0 0
\(928\) −4.94033 −0.162174
\(929\) −51.3272 −1.68399 −0.841995 0.539486i \(-0.818619\pi\)
−0.841995 + 0.539486i \(0.818619\pi\)
\(930\) 0 0
\(931\) 41.0013 1.34376
\(932\) −48.7598 −1.59718
\(933\) 0 0
\(934\) 16.3557 0.535174
\(935\) −0.990020 −0.0323771
\(936\) 0 0
\(937\) −22.1298 −0.722948 −0.361474 0.932382i \(-0.617726\pi\)
−0.361474 + 0.932382i \(0.617726\pi\)
\(938\) −12.3904 −0.404560
\(939\) 0 0
\(940\) 56.3720 1.83865
\(941\) −45.4073 −1.48024 −0.740118 0.672477i \(-0.765230\pi\)
−0.740118 + 0.672477i \(0.765230\pi\)
\(942\) 0 0
\(943\) −2.38205 −0.0775703
\(944\) 3.55221 0.115615
\(945\) 0 0
\(946\) 0.535895 0.0174234
\(947\) −1.93103 −0.0627502 −0.0313751 0.999508i \(-0.509989\pi\)
−0.0313751 + 0.999508i \(0.509989\pi\)
\(948\) 0 0
\(949\) −6.92112 −0.224669
\(950\) 12.3073 0.399302
\(951\) 0 0
\(952\) −11.6102 −0.376288
\(953\) −18.7399 −0.607046 −0.303523 0.952824i \(-0.598163\pi\)
−0.303523 + 0.952824i \(0.598163\pi\)
\(954\) 0 0
\(955\) −25.9745 −0.840516
\(956\) 85.2881 2.75841
\(957\) 0 0
\(958\) 8.10554 0.261878
\(959\) 11.3250 0.365702
\(960\) 0 0
\(961\) −14.0910 −0.454549
\(962\) 8.06632 0.260069
\(963\) 0 0
\(964\) 100.460 3.23559
\(965\) 33.8001 1.08806
\(966\) 0 0
\(967\) 8.69701 0.279677 0.139839 0.990174i \(-0.455342\pi\)
0.139839 + 0.990174i \(0.455342\pi\)
\(968\) −34.7314 −1.11631
\(969\) 0 0
\(970\) 39.8669 1.28005
\(971\) −48.9916 −1.57221 −0.786107 0.618090i \(-0.787907\pi\)
−0.786107 + 0.618090i \(0.787907\pi\)
\(972\) 0 0
\(973\) −16.3133 −0.522981
\(974\) 50.2594 1.61041
\(975\) 0 0
\(976\) −1.60359 −0.0513297
\(977\) 13.6751 0.437505 0.218753 0.975780i \(-0.429801\pi\)
0.218753 + 0.975780i \(0.429801\pi\)
\(978\) 0 0
\(979\) 1.82600 0.0583593
\(980\) 37.0536 1.18363
\(981\) 0 0
\(982\) 4.61424 0.147246
\(983\) 51.7903 1.65185 0.825927 0.563777i \(-0.190652\pi\)
0.825927 + 0.563777i \(0.190652\pi\)
\(984\) 0 0
\(985\) −37.1374 −1.18330
\(986\) −6.51545 −0.207494
\(987\) 0 0
\(988\) −18.3832 −0.584848
\(989\) −1.36487 −0.0434003
\(990\) 0 0
\(991\) −32.8944 −1.04492 −0.522462 0.852663i \(-0.674986\pi\)
−0.522462 + 0.852663i \(0.674986\pi\)
\(992\) 20.3149 0.644998
\(993\) 0 0
\(994\) 8.66706 0.274902
\(995\) −23.8329 −0.755555
\(996\) 0 0
\(997\) −46.7778 −1.48147 −0.740733 0.671799i \(-0.765522\pi\)
−0.740733 + 0.671799i \(0.765522\pi\)
\(998\) −62.7629 −1.98673
\(999\) 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 \(a_p\))