Properties

Label 6010.2.a.c.1.15
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(2.75851\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +1.00000 q^{10} -1.05946 q^{11} +1.75851 q^{12} -5.92506 q^{13} -0.115571 q^{14} +1.75851 q^{15} +1.00000 q^{16} -7.65454 q^{17} +0.0923708 q^{18} -6.01137 q^{19} +1.00000 q^{20} -0.203233 q^{21} -1.05946 q^{22} -0.155960 q^{23} +1.75851 q^{24} +1.00000 q^{25} -5.92506 q^{26} -5.11311 q^{27} -0.115571 q^{28} +3.22489 q^{29} +1.75851 q^{30} -3.14463 q^{31} +1.00000 q^{32} -1.86308 q^{33} -7.65454 q^{34} -0.115571 q^{35} +0.0923708 q^{36} +6.44860 q^{37} -6.01137 q^{38} -10.4193 q^{39} +1.00000 q^{40} -0.499853 q^{41} -0.203233 q^{42} -3.20309 q^{43} -1.05946 q^{44} +0.0923708 q^{45} -0.155960 q^{46} +5.42049 q^{47} +1.75851 q^{48} -6.98664 q^{49} +1.00000 q^{50} -13.4606 q^{51} -5.92506 q^{52} +4.44313 q^{53} -5.11311 q^{54} -1.05946 q^{55} -0.115571 q^{56} -10.5711 q^{57} +3.22489 q^{58} +2.13926 q^{59} +1.75851 q^{60} +5.01100 q^{61} -3.14463 q^{62} -0.0106754 q^{63} +1.00000 q^{64} -5.92506 q^{65} -1.86308 q^{66} -15.5059 q^{67} -7.65454 q^{68} -0.274258 q^{69} -0.115571 q^{70} +8.80287 q^{71} +0.0923708 q^{72} -11.1478 q^{73} +6.44860 q^{74} +1.75851 q^{75} -6.01137 q^{76} +0.122443 q^{77} -10.4193 q^{78} -2.78887 q^{79} +1.00000 q^{80} -9.26858 q^{81} -0.499853 q^{82} +5.34566 q^{83} -0.203233 q^{84} -7.65454 q^{85} -3.20309 q^{86} +5.67101 q^{87} -1.05946 q^{88} -3.18269 q^{89} +0.0923708 q^{90} +0.684765 q^{91} -0.155960 q^{92} -5.52987 q^{93} +5.42049 q^{94} -6.01137 q^{95} +1.75851 q^{96} -7.38623 q^{97} -6.98664 q^{98} -0.0978633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.75851 1.01528 0.507639 0.861570i \(-0.330518\pi\)
0.507639 + 0.861570i \(0.330518\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.75851 0.717910
\(7\) −0.115571 −0.0436818 −0.0218409 0.999761i \(-0.506953\pi\)
−0.0218409 + 0.999761i \(0.506953\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.0923708 0.0307903
\(10\) 1.00000 0.316228
\(11\) −1.05946 −0.319440 −0.159720 0.987162i \(-0.551059\pi\)
−0.159720 + 0.987162i \(0.551059\pi\)
\(12\) 1.75851 0.507639
\(13\) −5.92506 −1.64332 −0.821658 0.569981i \(-0.806950\pi\)
−0.821658 + 0.569981i \(0.806950\pi\)
\(14\) −0.115571 −0.0308877
\(15\) 1.75851 0.454046
\(16\) 1.00000 0.250000
\(17\) −7.65454 −1.85650 −0.928249 0.371960i \(-0.878686\pi\)
−0.928249 + 0.371960i \(0.878686\pi\)
\(18\) 0.0923708 0.0217720
\(19\) −6.01137 −1.37910 −0.689551 0.724237i \(-0.742192\pi\)
−0.689551 + 0.724237i \(0.742192\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.203233 −0.0443491
\(22\) −1.05946 −0.225878
\(23\) −0.155960 −0.0325199 −0.0162600 0.999868i \(-0.505176\pi\)
−0.0162600 + 0.999868i \(0.505176\pi\)
\(24\) 1.75851 0.358955
\(25\) 1.00000 0.200000
\(26\) −5.92506 −1.16200
\(27\) −5.11311 −0.984018
\(28\) −0.115571 −0.0218409
\(29\) 3.22489 0.598847 0.299423 0.954120i \(-0.403206\pi\)
0.299423 + 0.954120i \(0.403206\pi\)
\(30\) 1.75851 0.321059
\(31\) −3.14463 −0.564791 −0.282396 0.959298i \(-0.591129\pi\)
−0.282396 + 0.959298i \(0.591129\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.86308 −0.324320
\(34\) −7.65454 −1.31274
\(35\) −0.115571 −0.0195351
\(36\) 0.0923708 0.0153951
\(37\) 6.44860 1.06014 0.530072 0.847953i \(-0.322165\pi\)
0.530072 + 0.847953i \(0.322165\pi\)
\(38\) −6.01137 −0.975173
\(39\) −10.4193 −1.66842
\(40\) 1.00000 0.158114
\(41\) −0.499853 −0.0780639 −0.0390319 0.999238i \(-0.512427\pi\)
−0.0390319 + 0.999238i \(0.512427\pi\)
\(42\) −0.203233 −0.0313596
\(43\) −3.20309 −0.488467 −0.244233 0.969716i \(-0.578536\pi\)
−0.244233 + 0.969716i \(0.578536\pi\)
\(44\) −1.05946 −0.159720
\(45\) 0.0923708 0.0137698
\(46\) −0.155960 −0.0229951
\(47\) 5.42049 0.790660 0.395330 0.918539i \(-0.370630\pi\)
0.395330 + 0.918539i \(0.370630\pi\)
\(48\) 1.75851 0.253820
\(49\) −6.98664 −0.998092
\(50\) 1.00000 0.141421
\(51\) −13.4606 −1.88486
\(52\) −5.92506 −0.821658
\(53\) 4.44313 0.610311 0.305156 0.952303i \(-0.401292\pi\)
0.305156 + 0.952303i \(0.401292\pi\)
\(54\) −5.11311 −0.695806
\(55\) −1.05946 −0.142858
\(56\) −0.115571 −0.0154438
\(57\) −10.5711 −1.40017
\(58\) 3.22489 0.423449
\(59\) 2.13926 0.278508 0.139254 0.990257i \(-0.455530\pi\)
0.139254 + 0.990257i \(0.455530\pi\)
\(60\) 1.75851 0.227023
\(61\) 5.01100 0.641593 0.320796 0.947148i \(-0.396050\pi\)
0.320796 + 0.947148i \(0.396050\pi\)
\(62\) −3.14463 −0.399368
\(63\) −0.0106754 −0.00134497
\(64\) 1.00000 0.125000
\(65\) −5.92506 −0.734913
\(66\) −1.86308 −0.229329
\(67\) −15.5059 −1.89434 −0.947171 0.320729i \(-0.896072\pi\)
−0.947171 + 0.320729i \(0.896072\pi\)
\(68\) −7.65454 −0.928249
\(69\) −0.274258 −0.0330168
\(70\) −0.115571 −0.0138134
\(71\) 8.80287 1.04471 0.522354 0.852728i \(-0.325054\pi\)
0.522354 + 0.852728i \(0.325054\pi\)
\(72\) 0.0923708 0.0108860
\(73\) −11.1478 −1.30475 −0.652376 0.757896i \(-0.726228\pi\)
−0.652376 + 0.757896i \(0.726228\pi\)
\(74\) 6.44860 0.749634
\(75\) 1.75851 0.203056
\(76\) −6.01137 −0.689551
\(77\) 0.122443 0.0139537
\(78\) −10.4193 −1.17975
\(79\) −2.78887 −0.313773 −0.156886 0.987617i \(-0.550146\pi\)
−0.156886 + 0.987617i \(0.550146\pi\)
\(80\) 1.00000 0.111803
\(81\) −9.26858 −1.02984
\(82\) −0.499853 −0.0551995
\(83\) 5.34566 0.586762 0.293381 0.955996i \(-0.405220\pi\)
0.293381 + 0.955996i \(0.405220\pi\)
\(84\) −0.203233 −0.0221746
\(85\) −7.65454 −0.830251
\(86\) −3.20309 −0.345398
\(87\) 5.67101 0.607996
\(88\) −1.05946 −0.112939
\(89\) −3.18269 −0.337364 −0.168682 0.985670i \(-0.553951\pi\)
−0.168682 + 0.985670i \(0.553951\pi\)
\(90\) 0.0923708 0.00973674
\(91\) 0.684765 0.0717829
\(92\) −0.155960 −0.0162600
\(93\) −5.52987 −0.573420
\(94\) 5.42049 0.559081
\(95\) −6.01137 −0.616753
\(96\) 1.75851 0.179478
\(97\) −7.38623 −0.749959 −0.374979 0.927033i \(-0.622350\pi\)
−0.374979 + 0.927033i \(0.622350\pi\)
\(98\) −6.98664 −0.705758
\(99\) −0.0978633 −0.00983564
\(100\) 1.00000 0.100000
\(101\) −3.05060 −0.303546 −0.151773 0.988415i \(-0.548498\pi\)
−0.151773 + 0.988415i \(0.548498\pi\)
\(102\) −13.4606 −1.33280
\(103\) 14.5891 1.43750 0.718752 0.695266i \(-0.244713\pi\)
0.718752 + 0.695266i \(0.244713\pi\)
\(104\) −5.92506 −0.581000
\(105\) −0.203233 −0.0198335
\(106\) 4.44313 0.431555
\(107\) 1.34607 0.130129 0.0650647 0.997881i \(-0.479275\pi\)
0.0650647 + 0.997881i \(0.479275\pi\)
\(108\) −5.11311 −0.492009
\(109\) −4.06826 −0.389669 −0.194834 0.980836i \(-0.562417\pi\)
−0.194834 + 0.980836i \(0.562417\pi\)
\(110\) −1.05946 −0.101016
\(111\) 11.3399 1.07634
\(112\) −0.115571 −0.0109204
\(113\) −3.26230 −0.306891 −0.153446 0.988157i \(-0.549037\pi\)
−0.153446 + 0.988157i \(0.549037\pi\)
\(114\) −10.5711 −0.990072
\(115\) −0.155960 −0.0145434
\(116\) 3.22489 0.299423
\(117\) −0.547303 −0.0505981
\(118\) 2.13926 0.196935
\(119\) 0.884643 0.0810951
\(120\) 1.75851 0.160530
\(121\) −9.87754 −0.897958
\(122\) 5.01100 0.453674
\(123\) −0.878998 −0.0792566
\(124\) −3.14463 −0.282396
\(125\) 1.00000 0.0894427
\(126\) −0.0106754 −0.000951040 0
\(127\) 6.50795 0.577487 0.288744 0.957406i \(-0.406762\pi\)
0.288744 + 0.957406i \(0.406762\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.63268 −0.495930
\(130\) −5.92506 −0.519662
\(131\) −1.43515 −0.125390 −0.0626949 0.998033i \(-0.519970\pi\)
−0.0626949 + 0.998033i \(0.519970\pi\)
\(132\) −1.86308 −0.162160
\(133\) 0.694740 0.0602416
\(134\) −15.5059 −1.33950
\(135\) −5.11311 −0.440066
\(136\) −7.65454 −0.656371
\(137\) 13.7923 1.17836 0.589179 0.808002i \(-0.299451\pi\)
0.589179 + 0.808002i \(0.299451\pi\)
\(138\) −0.274258 −0.0233464
\(139\) 3.68639 0.312675 0.156338 0.987704i \(-0.450031\pi\)
0.156338 + 0.987704i \(0.450031\pi\)
\(140\) −0.115571 −0.00976754
\(141\) 9.53201 0.802740
\(142\) 8.80287 0.738721
\(143\) 6.27737 0.524940
\(144\) 0.0923708 0.00769757
\(145\) 3.22489 0.267812
\(146\) −11.1478 −0.922599
\(147\) −12.2861 −1.01334
\(148\) 6.44860 0.530072
\(149\) −2.57210 −0.210714 −0.105357 0.994434i \(-0.533599\pi\)
−0.105357 + 0.994434i \(0.533599\pi\)
\(150\) 1.75851 0.143582
\(151\) −3.91016 −0.318204 −0.159102 0.987262i \(-0.550860\pi\)
−0.159102 + 0.987262i \(0.550860\pi\)
\(152\) −6.01137 −0.487586
\(153\) −0.707056 −0.0571621
\(154\) 0.122443 0.00986674
\(155\) −3.14463 −0.252582
\(156\) −10.4193 −0.834211
\(157\) 12.1974 0.973461 0.486730 0.873552i \(-0.338189\pi\)
0.486730 + 0.873552i \(0.338189\pi\)
\(158\) −2.78887 −0.221871
\(159\) 7.81331 0.619636
\(160\) 1.00000 0.0790569
\(161\) 0.0180245 0.00142053
\(162\) −9.26858 −0.728208
\(163\) 4.00892 0.314003 0.157002 0.987598i \(-0.449817\pi\)
0.157002 + 0.987598i \(0.449817\pi\)
\(164\) −0.499853 −0.0390319
\(165\) −1.86308 −0.145040
\(166\) 5.34566 0.414904
\(167\) 8.33064 0.644644 0.322322 0.946630i \(-0.395537\pi\)
0.322322 + 0.946630i \(0.395537\pi\)
\(168\) −0.203233 −0.0156798
\(169\) 22.1063 1.70048
\(170\) −7.65454 −0.587076
\(171\) −0.555275 −0.0424630
\(172\) −3.20309 −0.244233
\(173\) 4.92679 0.374577 0.187289 0.982305i \(-0.440030\pi\)
0.187289 + 0.982305i \(0.440030\pi\)
\(174\) 5.67101 0.429918
\(175\) −0.115571 −0.00873635
\(176\) −1.05946 −0.0798599
\(177\) 3.76192 0.282763
\(178\) −3.18269 −0.238553
\(179\) −22.8285 −1.70628 −0.853140 0.521682i \(-0.825305\pi\)
−0.853140 + 0.521682i \(0.825305\pi\)
\(180\) 0.0923708 0.00688492
\(181\) −2.34240 −0.174109 −0.0870545 0.996204i \(-0.527745\pi\)
−0.0870545 + 0.996204i \(0.527745\pi\)
\(182\) 0.684765 0.0507582
\(183\) 8.81191 0.651395
\(184\) −0.155960 −0.0114975
\(185\) 6.44860 0.474110
\(186\) −5.52987 −0.405470
\(187\) 8.10969 0.593039
\(188\) 5.42049 0.395330
\(189\) 0.590927 0.0429836
\(190\) −6.01137 −0.436111
\(191\) 3.88368 0.281013 0.140507 0.990080i \(-0.455127\pi\)
0.140507 + 0.990080i \(0.455127\pi\)
\(192\) 1.75851 0.126910
\(193\) 9.37592 0.674894 0.337447 0.941345i \(-0.390437\pi\)
0.337447 + 0.941345i \(0.390437\pi\)
\(194\) −7.38623 −0.530301
\(195\) −10.4193 −0.746141
\(196\) −6.98664 −0.499046
\(197\) 8.09795 0.576955 0.288478 0.957487i \(-0.406851\pi\)
0.288478 + 0.957487i \(0.406851\pi\)
\(198\) −0.0978633 −0.00695485
\(199\) −2.33970 −0.165857 −0.0829286 0.996555i \(-0.526427\pi\)
−0.0829286 + 0.996555i \(0.526427\pi\)
\(200\) 1.00000 0.0707107
\(201\) −27.2673 −1.92328
\(202\) −3.05060 −0.214640
\(203\) −0.372704 −0.0261587
\(204\) −13.4606 −0.942431
\(205\) −0.499853 −0.0349112
\(206\) 14.5891 1.01647
\(207\) −0.0144062 −0.00100130
\(208\) −5.92506 −0.410829
\(209\) 6.36881 0.440540
\(210\) −0.203233 −0.0140244
\(211\) 6.78067 0.466800 0.233400 0.972381i \(-0.425015\pi\)
0.233400 + 0.972381i \(0.425015\pi\)
\(212\) 4.44313 0.305156
\(213\) 15.4800 1.06067
\(214\) 1.34607 0.0920154
\(215\) −3.20309 −0.218449
\(216\) −5.11311 −0.347903
\(217\) 0.363428 0.0246711
\(218\) −4.06826 −0.275538
\(219\) −19.6036 −1.32469
\(220\) −1.05946 −0.0714289
\(221\) 45.3536 3.05081
\(222\) 11.3399 0.761088
\(223\) 6.50219 0.435419 0.217709 0.976014i \(-0.430142\pi\)
0.217709 + 0.976014i \(0.430142\pi\)
\(224\) −0.115571 −0.00772192
\(225\) 0.0923708 0.00615806
\(226\) −3.26230 −0.217005
\(227\) −10.9040 −0.723726 −0.361863 0.932231i \(-0.617859\pi\)
−0.361863 + 0.932231i \(0.617859\pi\)
\(228\) −10.5711 −0.700087
\(229\) 4.98442 0.329380 0.164690 0.986345i \(-0.447338\pi\)
0.164690 + 0.986345i \(0.447338\pi\)
\(230\) −0.155960 −0.0102837
\(231\) 0.215318 0.0141669
\(232\) 3.22489 0.211724
\(233\) 17.9641 1.17687 0.588435 0.808544i \(-0.299744\pi\)
0.588435 + 0.808544i \(0.299744\pi\)
\(234\) −0.547303 −0.0357783
\(235\) 5.42049 0.353594
\(236\) 2.13926 0.139254
\(237\) −4.90427 −0.318567
\(238\) 0.884643 0.0573429
\(239\) −13.1816 −0.852645 −0.426322 0.904571i \(-0.640191\pi\)
−0.426322 + 0.904571i \(0.640191\pi\)
\(240\) 1.75851 0.113512
\(241\) 14.7855 0.952420 0.476210 0.879332i \(-0.342010\pi\)
0.476210 + 0.879332i \(0.342010\pi\)
\(242\) −9.87754 −0.634952
\(243\) −0.959608 −0.0615589
\(244\) 5.01100 0.320796
\(245\) −6.98664 −0.446360
\(246\) −0.878998 −0.0560429
\(247\) 35.6177 2.26630
\(248\) −3.14463 −0.199684
\(249\) 9.40041 0.595727
\(250\) 1.00000 0.0632456
\(251\) −7.44387 −0.469853 −0.234926 0.972013i \(-0.575485\pi\)
−0.234926 + 0.972013i \(0.575485\pi\)
\(252\) −0.0106754 −0.000672487 0
\(253\) 0.165234 0.0103882
\(254\) 6.50795 0.408345
\(255\) −13.4606 −0.842936
\(256\) 1.00000 0.0625000
\(257\) 3.60615 0.224945 0.112473 0.993655i \(-0.464123\pi\)
0.112473 + 0.993655i \(0.464123\pi\)
\(258\) −5.63268 −0.350675
\(259\) −0.745271 −0.0463089
\(260\) −5.92506 −0.367456
\(261\) 0.297886 0.0184387
\(262\) −1.43515 −0.0886640
\(263\) −23.5575 −1.45262 −0.726308 0.687369i \(-0.758766\pi\)
−0.726308 + 0.687369i \(0.758766\pi\)
\(264\) −1.86308 −0.114665
\(265\) 4.44313 0.272939
\(266\) 0.694740 0.0425973
\(267\) −5.59680 −0.342519
\(268\) −15.5059 −0.947171
\(269\) −19.8168 −1.20825 −0.604126 0.796889i \(-0.706478\pi\)
−0.604126 + 0.796889i \(0.706478\pi\)
\(270\) −5.11311 −0.311174
\(271\) −22.7798 −1.38378 −0.691888 0.722005i \(-0.743221\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(272\) −7.65454 −0.464124
\(273\) 1.20417 0.0728796
\(274\) 13.7923 0.833225
\(275\) −1.05946 −0.0638879
\(276\) −0.274258 −0.0165084
\(277\) 1.03363 0.0621049 0.0310524 0.999518i \(-0.490114\pi\)
0.0310524 + 0.999518i \(0.490114\pi\)
\(278\) 3.68639 0.221095
\(279\) −0.290472 −0.0173901
\(280\) −0.115571 −0.00690669
\(281\) 4.30491 0.256810 0.128405 0.991722i \(-0.459014\pi\)
0.128405 + 0.991722i \(0.459014\pi\)
\(282\) 9.53201 0.567623
\(283\) −18.7648 −1.11545 −0.557727 0.830025i \(-0.688326\pi\)
−0.557727 + 0.830025i \(0.688326\pi\)
\(284\) 8.80287 0.522354
\(285\) −10.5711 −0.626176
\(286\) 6.27737 0.371189
\(287\) 0.0577685 0.00340997
\(288\) 0.0923708 0.00544300
\(289\) 41.5919 2.44658
\(290\) 3.22489 0.189372
\(291\) −12.9888 −0.761417
\(292\) −11.1478 −0.652376
\(293\) 10.7236 0.626480 0.313240 0.949674i \(-0.398586\pi\)
0.313240 + 0.949674i \(0.398586\pi\)
\(294\) −12.2861 −0.716540
\(295\) 2.13926 0.124552
\(296\) 6.44860 0.374817
\(297\) 5.41714 0.314334
\(298\) −2.57210 −0.148998
\(299\) 0.924073 0.0534405
\(300\) 1.75851 0.101528
\(301\) 0.370185 0.0213371
\(302\) −3.91016 −0.225004
\(303\) −5.36453 −0.308184
\(304\) −6.01137 −0.344776
\(305\) 5.01100 0.286929
\(306\) −0.707056 −0.0404197
\(307\) 7.68431 0.438567 0.219283 0.975661i \(-0.429628\pi\)
0.219283 + 0.975661i \(0.429628\pi\)
\(308\) 0.122443 0.00697684
\(309\) 25.6551 1.45947
\(310\) −3.14463 −0.178603
\(311\) 23.6752 1.34250 0.671248 0.741233i \(-0.265759\pi\)
0.671248 + 0.741233i \(0.265759\pi\)
\(312\) −10.4193 −0.589876
\(313\) −27.7398 −1.56794 −0.783972 0.620796i \(-0.786810\pi\)
−0.783972 + 0.620796i \(0.786810\pi\)
\(314\) 12.1974 0.688341
\(315\) −0.0106754 −0.000601490 0
\(316\) −2.78887 −0.156886
\(317\) −20.9930 −1.17908 −0.589541 0.807738i \(-0.700691\pi\)
−0.589541 + 0.807738i \(0.700691\pi\)
\(318\) 7.81331 0.438149
\(319\) −3.41664 −0.191295
\(320\) 1.00000 0.0559017
\(321\) 2.36708 0.132118
\(322\) 0.0180245 0.00100447
\(323\) 46.0142 2.56030
\(324\) −9.26858 −0.514921
\(325\) −5.92506 −0.328663
\(326\) 4.00892 0.222034
\(327\) −7.15410 −0.395622
\(328\) −0.499853 −0.0275997
\(329\) −0.626452 −0.0345374
\(330\) −1.86308 −0.102559
\(331\) −30.1815 −1.65892 −0.829462 0.558563i \(-0.811353\pi\)
−0.829462 + 0.558563i \(0.811353\pi\)
\(332\) 5.34566 0.293381
\(333\) 0.595662 0.0326421
\(334\) 8.33064 0.455832
\(335\) −15.5059 −0.847175
\(336\) −0.203233 −0.0110873
\(337\) −10.3899 −0.565975 −0.282988 0.959124i \(-0.591326\pi\)
−0.282988 + 0.959124i \(0.591326\pi\)
\(338\) 22.1063 1.20242
\(339\) −5.73680 −0.311580
\(340\) −7.65454 −0.415126
\(341\) 3.33161 0.180417
\(342\) −0.555275 −0.0300258
\(343\) 1.61645 0.0872802
\(344\) −3.20309 −0.172699
\(345\) −0.274258 −0.0147656
\(346\) 4.92679 0.264866
\(347\) −3.12197 −0.167596 −0.0837980 0.996483i \(-0.526705\pi\)
−0.0837980 + 0.996483i \(0.526705\pi\)
\(348\) 5.67101 0.303998
\(349\) −19.8255 −1.06123 −0.530617 0.847612i \(-0.678040\pi\)
−0.530617 + 0.847612i \(0.678040\pi\)
\(350\) −0.115571 −0.00617753
\(351\) 30.2954 1.61705
\(352\) −1.05946 −0.0564695
\(353\) −27.2823 −1.45209 −0.726045 0.687648i \(-0.758643\pi\)
−0.726045 + 0.687648i \(0.758643\pi\)
\(354\) 3.76192 0.199944
\(355\) 8.80287 0.467208
\(356\) −3.18269 −0.168682
\(357\) 1.55566 0.0823341
\(358\) −22.8285 −1.20652
\(359\) −25.2933 −1.33493 −0.667466 0.744641i \(-0.732621\pi\)
−0.667466 + 0.744641i \(0.732621\pi\)
\(360\) 0.0923708 0.00486837
\(361\) 17.1366 0.901924
\(362\) −2.34240 −0.123114
\(363\) −17.3698 −0.911678
\(364\) 0.684765 0.0358914
\(365\) −11.1478 −0.583503
\(366\) 8.81191 0.460606
\(367\) −32.2471 −1.68329 −0.841644 0.540033i \(-0.818412\pi\)
−0.841644 + 0.540033i \(0.818412\pi\)
\(368\) −0.155960 −0.00812999
\(369\) −0.0461718 −0.00240361
\(370\) 6.44860 0.335247
\(371\) −0.513497 −0.0266595
\(372\) −5.52987 −0.286710
\(373\) 17.7463 0.918868 0.459434 0.888212i \(-0.348052\pi\)
0.459434 + 0.888212i \(0.348052\pi\)
\(374\) 8.10969 0.419342
\(375\) 1.75851 0.0908093
\(376\) 5.42049 0.279540
\(377\) −19.1076 −0.984094
\(378\) 0.590927 0.0303940
\(379\) 8.59889 0.441695 0.220848 0.975308i \(-0.429118\pi\)
0.220848 + 0.975308i \(0.429118\pi\)
\(380\) −6.01137 −0.308377
\(381\) 11.4443 0.586310
\(382\) 3.88368 0.198706
\(383\) 29.4587 1.50527 0.752636 0.658437i \(-0.228782\pi\)
0.752636 + 0.658437i \(0.228782\pi\)
\(384\) 1.75851 0.0897388
\(385\) 0.122443 0.00624028
\(386\) 9.37592 0.477222
\(387\) −0.295872 −0.0150400
\(388\) −7.38623 −0.374979
\(389\) 0.0800026 0.00405629 0.00202815 0.999998i \(-0.499354\pi\)
0.00202815 + 0.999998i \(0.499354\pi\)
\(390\) −10.4193 −0.527602
\(391\) 1.19380 0.0603732
\(392\) −6.98664 −0.352879
\(393\) −2.52373 −0.127306
\(394\) 8.09795 0.407969
\(395\) −2.78887 −0.140323
\(396\) −0.0978633 −0.00491782
\(397\) −9.52087 −0.477839 −0.238919 0.971039i \(-0.576793\pi\)
−0.238919 + 0.971039i \(0.576793\pi\)
\(398\) −2.33970 −0.117279
\(399\) 1.22171 0.0611620
\(400\) 1.00000 0.0500000
\(401\) 38.3647 1.91584 0.957921 0.287034i \(-0.0926691\pi\)
0.957921 + 0.287034i \(0.0926691\pi\)
\(402\) −27.2673 −1.35997
\(403\) 18.6321 0.928130
\(404\) −3.05060 −0.151773
\(405\) −9.26858 −0.460559
\(406\) −0.372704 −0.0184970
\(407\) −6.83204 −0.338652
\(408\) −13.4606 −0.666399
\(409\) −22.0031 −1.08798 −0.543991 0.839091i \(-0.683087\pi\)
−0.543991 + 0.839091i \(0.683087\pi\)
\(410\) −0.499853 −0.0246860
\(411\) 24.2540 1.19636
\(412\) 14.5891 0.718752
\(413\) −0.247236 −0.0121657
\(414\) −0.0144062 −0.000708025 0
\(415\) 5.34566 0.262408
\(416\) −5.92506 −0.290500
\(417\) 6.48257 0.317453
\(418\) 6.36881 0.311509
\(419\) −16.8407 −0.822723 −0.411362 0.911472i \(-0.634947\pi\)
−0.411362 + 0.911472i \(0.634947\pi\)
\(420\) −0.203233 −0.00991677
\(421\) 34.2753 1.67047 0.835237 0.549890i \(-0.185330\pi\)
0.835237 + 0.549890i \(0.185330\pi\)
\(422\) 6.78067 0.330078
\(423\) 0.500695 0.0243446
\(424\) 4.44313 0.215778
\(425\) −7.65454 −0.371300
\(426\) 15.4800 0.750007
\(427\) −0.579126 −0.0280259
\(428\) 1.34607 0.0650647
\(429\) 11.0388 0.532960
\(430\) −3.20309 −0.154467
\(431\) −35.8069 −1.72476 −0.862379 0.506263i \(-0.831026\pi\)
−0.862379 + 0.506263i \(0.831026\pi\)
\(432\) −5.11311 −0.246004
\(433\) −9.67497 −0.464949 −0.232475 0.972602i \(-0.574682\pi\)
−0.232475 + 0.972602i \(0.574682\pi\)
\(434\) 0.363428 0.0174451
\(435\) 5.67101 0.271904
\(436\) −4.06826 −0.194834
\(437\) 0.937534 0.0448483
\(438\) −19.6036 −0.936694
\(439\) −14.6670 −0.700020 −0.350010 0.936746i \(-0.613822\pi\)
−0.350010 + 0.936746i \(0.613822\pi\)
\(440\) −1.05946 −0.0505078
\(441\) −0.645362 −0.0307315
\(442\) 45.3536 2.15725
\(443\) 13.3396 0.633783 0.316891 0.948462i \(-0.397361\pi\)
0.316891 + 0.948462i \(0.397361\pi\)
\(444\) 11.3399 0.538170
\(445\) −3.18269 −0.150874
\(446\) 6.50219 0.307887
\(447\) −4.52307 −0.213934
\(448\) −0.115571 −0.00546022
\(449\) 18.3476 0.865878 0.432939 0.901423i \(-0.357476\pi\)
0.432939 + 0.901423i \(0.357476\pi\)
\(450\) 0.0923708 0.00435440
\(451\) 0.529575 0.0249367
\(452\) −3.26230 −0.153446
\(453\) −6.87607 −0.323066
\(454\) −10.9040 −0.511752
\(455\) 0.684765 0.0321023
\(456\) −10.5711 −0.495036
\(457\) −37.0376 −1.73254 −0.866272 0.499573i \(-0.833490\pi\)
−0.866272 + 0.499573i \(0.833490\pi\)
\(458\) 4.98442 0.232907
\(459\) 39.1385 1.82683
\(460\) −0.155960 −0.00727168
\(461\) −3.57261 −0.166393 −0.0831965 0.996533i \(-0.526513\pi\)
−0.0831965 + 0.996533i \(0.526513\pi\)
\(462\) 0.215318 0.0100175
\(463\) −17.6931 −0.822267 −0.411134 0.911575i \(-0.634867\pi\)
−0.411134 + 0.911575i \(0.634867\pi\)
\(464\) 3.22489 0.149712
\(465\) −5.52987 −0.256441
\(466\) 17.9641 0.832173
\(467\) −32.7445 −1.51523 −0.757617 0.652699i \(-0.773637\pi\)
−0.757617 + 0.652699i \(0.773637\pi\)
\(468\) −0.547303 −0.0252991
\(469\) 1.79203 0.0827482
\(470\) 5.42049 0.250029
\(471\) 21.4493 0.988334
\(472\) 2.13926 0.0984674
\(473\) 3.39355 0.156036
\(474\) −4.90427 −0.225261
\(475\) −6.01137 −0.275821
\(476\) 0.884643 0.0405475
\(477\) 0.410416 0.0187917
\(478\) −13.1816 −0.602911
\(479\) −5.78661 −0.264397 −0.132198 0.991223i \(-0.542204\pi\)
−0.132198 + 0.991223i \(0.542204\pi\)
\(480\) 1.75851 0.0802648
\(481\) −38.2083 −1.74215
\(482\) 14.7855 0.673462
\(483\) 0.0316963 0.00144223
\(484\) −9.87754 −0.448979
\(485\) −7.38623 −0.335392
\(486\) −0.959608 −0.0435287
\(487\) 23.4387 1.06211 0.531055 0.847338i \(-0.321796\pi\)
0.531055 + 0.847338i \(0.321796\pi\)
\(488\) 5.01100 0.226837
\(489\) 7.04975 0.318801
\(490\) −6.98664 −0.315624
\(491\) −4.03449 −0.182074 −0.0910369 0.995848i \(-0.529018\pi\)
−0.0910369 + 0.995848i \(0.529018\pi\)
\(492\) −0.878998 −0.0396283
\(493\) −24.6850 −1.11176
\(494\) 35.6177 1.60252
\(495\) −0.0978633 −0.00439863
\(496\) −3.14463 −0.141198
\(497\) −1.01736 −0.0456347
\(498\) 9.40041 0.421243
\(499\) −3.14365 −0.140729 −0.0703646 0.997521i \(-0.522416\pi\)
−0.0703646 + 0.997521i \(0.522416\pi\)
\(500\) 1.00000 0.0447214
\(501\) 14.6495 0.654493
\(502\) −7.44387 −0.332236
\(503\) 17.0587 0.760612 0.380306 0.924861i \(-0.375819\pi\)
0.380306 + 0.924861i \(0.375819\pi\)
\(504\) −0.0106754 −0.000475520 0
\(505\) −3.05060 −0.135750
\(506\) 0.165234 0.00734554
\(507\) 38.8742 1.72647
\(508\) 6.50795 0.288744
\(509\) 11.4905 0.509307 0.254653 0.967032i \(-0.418039\pi\)
0.254653 + 0.967032i \(0.418039\pi\)
\(510\) −13.4606 −0.596046
\(511\) 1.28836 0.0569938
\(512\) 1.00000 0.0441942
\(513\) 30.7368 1.35706
\(514\) 3.60615 0.159060
\(515\) 14.5891 0.642872
\(516\) −5.63268 −0.247965
\(517\) −5.74280 −0.252568
\(518\) −0.745271 −0.0327453
\(519\) 8.66383 0.380300
\(520\) −5.92506 −0.259831
\(521\) 13.6864 0.599614 0.299807 0.954000i \(-0.403078\pi\)
0.299807 + 0.954000i \(0.403078\pi\)
\(522\) 0.297886 0.0130381
\(523\) 38.3083 1.67511 0.837553 0.546356i \(-0.183985\pi\)
0.837553 + 0.546356i \(0.183985\pi\)
\(524\) −1.43515 −0.0626949
\(525\) −0.203233 −0.00886983
\(526\) −23.5575 −1.02716
\(527\) 24.0706 1.04853
\(528\) −1.86308 −0.0810800
\(529\) −22.9757 −0.998942
\(530\) 4.44313 0.192997
\(531\) 0.197605 0.00857533
\(532\) 0.694740 0.0301208
\(533\) 2.96166 0.128284
\(534\) −5.59680 −0.242197
\(535\) 1.34607 0.0581956
\(536\) −15.5059 −0.669751
\(537\) −40.1442 −1.73235
\(538\) −19.8168 −0.854363
\(539\) 7.40208 0.318830
\(540\) −5.11311 −0.220033
\(541\) −43.4449 −1.86784 −0.933922 0.357477i \(-0.883637\pi\)
−0.933922 + 0.357477i \(0.883637\pi\)
\(542\) −22.7798 −0.978477
\(543\) −4.11914 −0.176769
\(544\) −7.65454 −0.328186
\(545\) −4.06826 −0.174265
\(546\) 1.20417 0.0515337
\(547\) 39.8275 1.70290 0.851450 0.524437i \(-0.175724\pi\)
0.851450 + 0.524437i \(0.175724\pi\)
\(548\) 13.7923 0.589179
\(549\) 0.462870 0.0197548
\(550\) −1.05946 −0.0451756
\(551\) −19.3860 −0.825871
\(552\) −0.274258 −0.0116732
\(553\) 0.322313 0.0137061
\(554\) 1.03363 0.0439148
\(555\) 11.3399 0.481354
\(556\) 3.68639 0.156338
\(557\) 16.3993 0.694863 0.347431 0.937705i \(-0.387054\pi\)
0.347431 + 0.937705i \(0.387054\pi\)
\(558\) −0.290472 −0.0122966
\(559\) 18.9785 0.802705
\(560\) −0.115571 −0.00488377
\(561\) 14.2610 0.602100
\(562\) 4.30491 0.181592
\(563\) −25.7493 −1.08520 −0.542602 0.839990i \(-0.682561\pi\)
−0.542602 + 0.839990i \(0.682561\pi\)
\(564\) 9.53201 0.401370
\(565\) −3.26230 −0.137246
\(566\) −18.7648 −0.788745
\(567\) 1.07118 0.0449853
\(568\) 8.80287 0.369360
\(569\) 16.2960 0.683163 0.341582 0.939852i \(-0.389037\pi\)
0.341582 + 0.939852i \(0.389037\pi\)
\(570\) −10.5711 −0.442774
\(571\) 5.28775 0.221286 0.110643 0.993860i \(-0.464709\pi\)
0.110643 + 0.993860i \(0.464709\pi\)
\(572\) 6.27737 0.262470
\(573\) 6.82950 0.285307
\(574\) 0.0577685 0.00241121
\(575\) −0.155960 −0.00650399
\(576\) 0.0923708 0.00384878
\(577\) 22.6166 0.941540 0.470770 0.882256i \(-0.343976\pi\)
0.470770 + 0.882256i \(0.343976\pi\)
\(578\) 41.5919 1.73000
\(579\) 16.4877 0.685205
\(580\) 3.22489 0.133906
\(581\) −0.617803 −0.0256308
\(582\) −12.9888 −0.538403
\(583\) −4.70733 −0.194958
\(584\) −11.1478 −0.461299
\(585\) −0.547303 −0.0226282
\(586\) 10.7236 0.442988
\(587\) 17.5749 0.725392 0.362696 0.931907i \(-0.381856\pi\)
0.362696 + 0.931907i \(0.381856\pi\)
\(588\) −12.2861 −0.506671
\(589\) 18.9035 0.778905
\(590\) 2.13926 0.0880719
\(591\) 14.2404 0.585770
\(592\) 6.44860 0.265036
\(593\) −33.9525 −1.39426 −0.697132 0.716943i \(-0.745541\pi\)
−0.697132 + 0.716943i \(0.745541\pi\)
\(594\) 5.41714 0.222268
\(595\) 0.884643 0.0362668
\(596\) −2.57210 −0.105357
\(597\) −4.11440 −0.168391
\(598\) 0.924073 0.0377882
\(599\) −10.5128 −0.429540 −0.214770 0.976665i \(-0.568900\pi\)
−0.214770 + 0.976665i \(0.568900\pi\)
\(600\) 1.75851 0.0717910
\(601\) −1.00000 −0.0407909
\(602\) 0.370185 0.0150876
\(603\) −1.43229 −0.0583273
\(604\) −3.91016 −0.159102
\(605\) −9.87754 −0.401579
\(606\) −5.36453 −0.217919
\(607\) 0.0255091 0.00103538 0.000517691 1.00000i \(-0.499835\pi\)
0.000517691 1.00000i \(0.499835\pi\)
\(608\) −6.01137 −0.243793
\(609\) −0.655405 −0.0265583
\(610\) 5.01100 0.202889
\(611\) −32.1167 −1.29930
\(612\) −0.707056 −0.0285810
\(613\) −24.0389 −0.970924 −0.485462 0.874258i \(-0.661349\pi\)
−0.485462 + 0.874258i \(0.661349\pi\)
\(614\) 7.68431 0.310113
\(615\) −0.878998 −0.0354446
\(616\) 0.122443 0.00493337
\(617\) −16.0653 −0.646767 −0.323383 0.946268i \(-0.604820\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(618\) 25.6551 1.03200
\(619\) −11.7331 −0.471593 −0.235797 0.971802i \(-0.575770\pi\)
−0.235797 + 0.971802i \(0.575770\pi\)
\(620\) −3.14463 −0.126291
\(621\) 0.797441 0.0320002
\(622\) 23.6752 0.949287
\(623\) 0.367827 0.0147367
\(624\) −10.4193 −0.417106
\(625\) 1.00000 0.0400000
\(626\) −27.7398 −1.10870
\(627\) 11.1996 0.447271
\(628\) 12.1974 0.486730
\(629\) −49.3610 −1.96815
\(630\) −0.0106754 −0.000425318 0
\(631\) 33.0265 1.31477 0.657383 0.753557i \(-0.271663\pi\)
0.657383 + 0.753557i \(0.271663\pi\)
\(632\) −2.78887 −0.110935
\(633\) 11.9239 0.473932
\(634\) −20.9930 −0.833737
\(635\) 6.50795 0.258260
\(636\) 7.81331 0.309818
\(637\) 41.3963 1.64018
\(638\) −3.41664 −0.135266
\(639\) 0.813129 0.0321669
\(640\) 1.00000 0.0395285
\(641\) 37.7607 1.49146 0.745729 0.666250i \(-0.232102\pi\)
0.745729 + 0.666250i \(0.232102\pi\)
\(642\) 2.36708 0.0934212
\(643\) −13.2655 −0.523142 −0.261571 0.965184i \(-0.584241\pi\)
−0.261571 + 0.965184i \(0.584241\pi\)
\(644\) 0.0180245 0.000710264 0
\(645\) −5.63268 −0.221787
\(646\) 46.0142 1.81041
\(647\) −12.3466 −0.485396 −0.242698 0.970102i \(-0.578032\pi\)
−0.242698 + 0.970102i \(0.578032\pi\)
\(648\) −9.26858 −0.364104
\(649\) −2.26646 −0.0889665
\(650\) −5.92506 −0.232400
\(651\) 0.639093 0.0250480
\(652\) 4.00892 0.157002
\(653\) −7.03367 −0.275249 −0.137624 0.990485i \(-0.543947\pi\)
−0.137624 + 0.990485i \(0.543947\pi\)
\(654\) −7.15410 −0.279747
\(655\) −1.43515 −0.0560760
\(656\) −0.499853 −0.0195160
\(657\) −1.02973 −0.0401737
\(658\) −0.626452 −0.0244216
\(659\) −7.03423 −0.274015 −0.137007 0.990570i \(-0.543748\pi\)
−0.137007 + 0.990570i \(0.543748\pi\)
\(660\) −1.86308 −0.0725202
\(661\) −0.591861 −0.0230207 −0.0115104 0.999934i \(-0.503664\pi\)
−0.0115104 + 0.999934i \(0.503664\pi\)
\(662\) −30.1815 −1.17304
\(663\) 79.7549 3.09742
\(664\) 5.34566 0.207452
\(665\) 0.694740 0.0269409
\(666\) 0.595662 0.0230815
\(667\) −0.502954 −0.0194745
\(668\) 8.33064 0.322322
\(669\) 11.4342 0.442071
\(670\) −15.5059 −0.599044
\(671\) −5.30896 −0.204950
\(672\) −0.203233 −0.00783989
\(673\) −17.6471 −0.680246 −0.340123 0.940381i \(-0.610469\pi\)
−0.340123 + 0.940381i \(0.610469\pi\)
\(674\) −10.3899 −0.400205
\(675\) −5.11311 −0.196804
\(676\) 22.1063 0.850242
\(677\) 11.5061 0.442216 0.221108 0.975249i \(-0.429033\pi\)
0.221108 + 0.975249i \(0.429033\pi\)
\(678\) −5.73680 −0.220320
\(679\) 0.853635 0.0327595
\(680\) −7.65454 −0.293538
\(681\) −19.1749 −0.734783
\(682\) 3.33161 0.127574
\(683\) −25.1718 −0.963171 −0.481586 0.876399i \(-0.659939\pi\)
−0.481586 + 0.876399i \(0.659939\pi\)
\(684\) −0.555275 −0.0212315
\(685\) 13.7923 0.526978
\(686\) 1.61645 0.0617164
\(687\) 8.76517 0.334412
\(688\) −3.20309 −0.122117
\(689\) −26.3258 −1.00293
\(690\) −0.274258 −0.0104408
\(691\) 1.02855 0.0391278 0.0195639 0.999809i \(-0.493772\pi\)
0.0195639 + 0.999809i \(0.493772\pi\)
\(692\) 4.92679 0.187289
\(693\) 0.0113102 0.000429638 0
\(694\) −3.12197 −0.118508
\(695\) 3.68639 0.139833
\(696\) 5.67101 0.214959
\(697\) 3.82614 0.144925
\(698\) −19.8255 −0.750406
\(699\) 31.5902 1.19485
\(700\) −0.115571 −0.00436818
\(701\) −7.99077 −0.301807 −0.150904 0.988548i \(-0.548218\pi\)
−0.150904 + 0.988548i \(0.548218\pi\)
\(702\) 30.2954 1.14343
\(703\) −38.7649 −1.46205
\(704\) −1.05946 −0.0399300
\(705\) 9.53201 0.358996
\(706\) −27.2823 −1.02678
\(707\) 0.352561 0.0132594
\(708\) 3.76192 0.141382
\(709\) −27.5073 −1.03306 −0.516529 0.856270i \(-0.672776\pi\)
−0.516529 + 0.856270i \(0.672776\pi\)
\(710\) 8.80287 0.330366
\(711\) −0.257611 −0.00966115
\(712\) −3.18269 −0.119276
\(713\) 0.490436 0.0183670
\(714\) 1.55566 0.0582190
\(715\) 6.27737 0.234760
\(716\) −22.8285 −0.853140
\(717\) −23.1800 −0.865672
\(718\) −25.2933 −0.943939
\(719\) −25.5509 −0.952889 −0.476444 0.879205i \(-0.658075\pi\)
−0.476444 + 0.879205i \(0.658075\pi\)
\(720\) 0.0923708 0.00344246
\(721\) −1.68608 −0.0627927
\(722\) 17.1366 0.637757
\(723\) 26.0006 0.966971
\(724\) −2.34240 −0.0870545
\(725\) 3.22489 0.119769
\(726\) −17.3698 −0.644653
\(727\) −11.7504 −0.435800 −0.217900 0.975971i \(-0.569921\pi\)
−0.217900 + 0.975971i \(0.569921\pi\)
\(728\) 0.684765 0.0253791
\(729\) 26.1183 0.967343
\(730\) −11.1478 −0.412599
\(731\) 24.5182 0.906837
\(732\) 8.81191 0.325698
\(733\) 3.36788 0.124396 0.0621978 0.998064i \(-0.480189\pi\)
0.0621978 + 0.998064i \(0.480189\pi\)
\(734\) −32.2471 −1.19026
\(735\) −12.2861 −0.453180
\(736\) −0.155960 −0.00574877
\(737\) 16.4279 0.605128
\(738\) −0.0461718 −0.00169961
\(739\) 11.1562 0.410389 0.205195 0.978721i \(-0.434217\pi\)
0.205195 + 0.978721i \(0.434217\pi\)
\(740\) 6.44860 0.237055
\(741\) 62.6342 2.30093
\(742\) −0.513497 −0.0188511
\(743\) 12.9513 0.475139 0.237569 0.971371i \(-0.423649\pi\)
0.237569 + 0.971371i \(0.423649\pi\)
\(744\) −5.52987 −0.202735
\(745\) −2.57210 −0.0942343
\(746\) 17.7463 0.649738
\(747\) 0.493783 0.0180666
\(748\) 8.10969 0.296520
\(749\) −0.155567 −0.00568428
\(750\) 1.75851 0.0642118
\(751\) −38.3680 −1.40007 −0.700035 0.714109i \(-0.746832\pi\)
−0.700035 + 0.714109i \(0.746832\pi\)
\(752\) 5.42049 0.197665
\(753\) −13.0901 −0.477032
\(754\) −19.1076 −0.695859
\(755\) −3.91016 −0.142305
\(756\) 0.590927 0.0214918
\(757\) 4.16306 0.151309 0.0756545 0.997134i \(-0.475895\pi\)
0.0756545 + 0.997134i \(0.475895\pi\)
\(758\) 8.59889 0.312326
\(759\) 0.290566 0.0105469
\(760\) −6.01137 −0.218055
\(761\) 21.9747 0.796581 0.398291 0.917259i \(-0.369604\pi\)
0.398291 + 0.917259i \(0.369604\pi\)
\(762\) 11.4443 0.414584
\(763\) 0.470173 0.0170214
\(764\) 3.88368 0.140507
\(765\) −0.707056 −0.0255637
\(766\) 29.4587 1.06439
\(767\) −12.6752 −0.457676
\(768\) 1.75851 0.0634549
\(769\) 16.8733 0.608468 0.304234 0.952597i \(-0.401599\pi\)
0.304234 + 0.952597i \(0.401599\pi\)
\(770\) 0.122443 0.00441254
\(771\) 6.34146 0.228382
\(772\) 9.37592 0.337447
\(773\) −31.9352 −1.14863 −0.574315 0.818634i \(-0.694732\pi\)
−0.574315 + 0.818634i \(0.694732\pi\)
\(774\) −0.295872 −0.0106349
\(775\) −3.14463 −0.112958
\(776\) −7.38623 −0.265150
\(777\) −1.31057 −0.0470164
\(778\) 0.0800026 0.00286823
\(779\) 3.00480 0.107658
\(780\) −10.4193 −0.373071
\(781\) −9.32631 −0.333721
\(782\) 1.19380 0.0426903
\(783\) −16.4892 −0.589276
\(784\) −6.98664 −0.249523
\(785\) 12.1974 0.435345
\(786\) −2.52373 −0.0900186
\(787\) 6.04218 0.215380 0.107690 0.994184i \(-0.465655\pi\)
0.107690 + 0.994184i \(0.465655\pi\)
\(788\) 8.09795 0.288478
\(789\) −41.4262 −1.47481
\(790\) −2.78887 −0.0992237
\(791\) 0.377027 0.0134056
\(792\) −0.0978633 −0.00347742
\(793\) −29.6904 −1.05434
\(794\) −9.52087 −0.337883
\(795\) 7.81331 0.277110
\(796\) −2.33970 −0.0829286
\(797\) −13.5925 −0.481473 −0.240736 0.970591i \(-0.577389\pi\)
−0.240736 + 0.970591i \(0.577389\pi\)
\(798\) 1.22171 0.0432481
\(799\) −41.4913 −1.46786
\(800\) 1.00000 0.0353553
\(801\) −0.293988 −0.0103875
\(802\) 38.3647 1.35470
\(803\) 11.8107 0.416789
\(804\) −27.2673 −0.961642
\(805\) 0.0180245 0.000635280 0
\(806\) 18.6321 0.656287
\(807\) −34.8481 −1.22671
\(808\) −3.05060 −0.107320
\(809\) 49.6483 1.74554 0.872771 0.488130i \(-0.162321\pi\)
0.872771 + 0.488130i \(0.162321\pi\)
\(810\) −9.26858 −0.325665
\(811\) 12.6727 0.444999 0.222499 0.974933i \(-0.428578\pi\)
0.222499 + 0.974933i \(0.428578\pi\)
\(812\) −0.372704 −0.0130793
\(813\) −40.0586 −1.40492
\(814\) −6.83204 −0.239463
\(815\) 4.00892 0.140426
\(816\) −13.4606 −0.471216
\(817\) 19.2550 0.673646
\(818\) −22.0031 −0.769319
\(819\) 0.0632523 0.00221022
\(820\) −0.499853 −0.0174556
\(821\) 31.7128 1.10678 0.553392 0.832921i \(-0.313333\pi\)
0.553392 + 0.832921i \(0.313333\pi\)
\(822\) 24.2540 0.845956
\(823\) 45.1045 1.57224 0.786122 0.618071i \(-0.212086\pi\)
0.786122 + 0.618071i \(0.212086\pi\)
\(824\) 14.5891 0.508235
\(825\) −1.86308 −0.0648640
\(826\) −0.247236 −0.00860246
\(827\) 10.0656 0.350016 0.175008 0.984567i \(-0.444005\pi\)
0.175008 + 0.984567i \(0.444005\pi\)
\(828\) −0.0144062 −0.000500649 0
\(829\) −15.2100 −0.528266 −0.264133 0.964486i \(-0.585086\pi\)
−0.264133 + 0.964486i \(0.585086\pi\)
\(830\) 5.34566 0.185550
\(831\) 1.81765 0.0630537
\(832\) −5.92506 −0.205414
\(833\) 53.4795 1.85296
\(834\) 6.48257 0.224473
\(835\) 8.33064 0.288294
\(836\) 6.36881 0.220270
\(837\) 16.0788 0.555765
\(838\) −16.8407 −0.581753
\(839\) −28.1900 −0.973228 −0.486614 0.873617i \(-0.661768\pi\)
−0.486614 + 0.873617i \(0.661768\pi\)
\(840\) −0.203233 −0.00701221
\(841\) −18.6001 −0.641383
\(842\) 34.2753 1.18120
\(843\) 7.57025 0.260733
\(844\) 6.78067 0.233400
\(845\) 22.1063 0.760480
\(846\) 0.500695 0.0172143
\(847\) 1.14156 0.0392244
\(848\) 4.44313 0.152578
\(849\) −32.9982 −1.13250
\(850\) −7.65454 −0.262548
\(851\) −1.00572 −0.0344758
\(852\) 15.4800 0.530335
\(853\) −17.1029 −0.585591 −0.292796 0.956175i \(-0.594586\pi\)
−0.292796 + 0.956175i \(0.594586\pi\)
\(854\) −0.579126 −0.0198173
\(855\) −0.555275 −0.0189900
\(856\) 1.34607 0.0460077
\(857\) −35.5869 −1.21563 −0.607813 0.794080i \(-0.707953\pi\)
−0.607813 + 0.794080i \(0.707953\pi\)
\(858\) 11.0388 0.376860
\(859\) 52.2232 1.78183 0.890916 0.454169i \(-0.150064\pi\)
0.890916 + 0.454169i \(0.150064\pi\)
\(860\) −3.20309 −0.109224
\(861\) 0.101587 0.00346207
\(862\) −35.8069 −1.21959
\(863\) 42.7203 1.45422 0.727108 0.686523i \(-0.240864\pi\)
0.727108 + 0.686523i \(0.240864\pi\)
\(864\) −5.11311 −0.173951
\(865\) 4.92679 0.167516
\(866\) −9.67497 −0.328769
\(867\) 73.1400 2.48396
\(868\) 0.363428 0.0123355
\(869\) 2.95470 0.100231
\(870\) 5.67101 0.192265
\(871\) 91.8731 3.11300
\(872\) −4.06826 −0.137769
\(873\) −0.682273 −0.0230914
\(874\) 0.937534 0.0317126
\(875\) −0.115571 −0.00390701
\(876\) −19.6036 −0.662343
\(877\) −28.3762 −0.958198 −0.479099 0.877761i \(-0.659036\pi\)
−0.479099 + 0.877761i \(0.659036\pi\)
\(878\) −14.6670 −0.494989
\(879\) 18.8576 0.636051
\(880\) −1.05946 −0.0357144
\(881\) −54.2295 −1.82704 −0.913519 0.406797i \(-0.866646\pi\)
−0.913519 + 0.406797i \(0.866646\pi\)
\(882\) −0.645362 −0.0217305
\(883\) 16.0177 0.539038 0.269519 0.962995i \(-0.413135\pi\)
0.269519 + 0.962995i \(0.413135\pi\)
\(884\) 45.3536 1.52541
\(885\) 3.76192 0.126455
\(886\) 13.3396 0.448152
\(887\) −34.0395 −1.14293 −0.571467 0.820625i \(-0.693625\pi\)
−0.571467 + 0.820625i \(0.693625\pi\)
\(888\) 11.3399 0.380544
\(889\) −0.752131 −0.0252257
\(890\) −3.18269 −0.106684
\(891\) 9.81970 0.328972
\(892\) 6.50219 0.217709
\(893\) −32.5846 −1.09040
\(894\) −4.52307 −0.151274
\(895\) −22.8285 −0.763072
\(896\) −0.115571 −0.00386096
\(897\) 1.62500 0.0542570
\(898\) 18.3476 0.612268
\(899\) −10.1411 −0.338223
\(900\) 0.0923708 0.00307903
\(901\) −34.0101 −1.13304
\(902\) 0.529575 0.0176329
\(903\) 0.650975 0.0216631
\(904\) −3.26230 −0.108502
\(905\) −2.34240 −0.0778639
\(906\) −6.87607 −0.228442
\(907\) 2.37458 0.0788468 0.0394234 0.999223i \(-0.487448\pi\)
0.0394234 + 0.999223i \(0.487448\pi\)
\(908\) −10.9040 −0.361863
\(909\) −0.281787 −0.00934627
\(910\) 0.684765 0.0226997
\(911\) 46.0411 1.52541 0.762705 0.646747i \(-0.223871\pi\)
0.762705 + 0.646747i \(0.223871\pi\)
\(912\) −10.5711 −0.350043
\(913\) −5.66352 −0.187435
\(914\) −37.0376 −1.22509
\(915\) 8.81191 0.291313
\(916\) 4.98442 0.164690
\(917\) 0.165862 0.00547725
\(918\) 39.1385 1.29176
\(919\) −43.1275 −1.42265 −0.711323 0.702866i \(-0.751904\pi\)
−0.711323 + 0.702866i \(0.751904\pi\)
\(920\) −0.155960 −0.00514186
\(921\) 13.5130 0.445267
\(922\) −3.57261 −0.117658
\(923\) −52.1575 −1.71679
\(924\) 0.215318 0.00708344
\(925\) 6.44860 0.212029
\(926\) −17.6931 −0.581431
\(927\) 1.34761 0.0442612
\(928\) 3.22489 0.105862
\(929\) −53.0317 −1.73991 −0.869957 0.493128i \(-0.835853\pi\)
−0.869957 + 0.493128i \(0.835853\pi\)
\(930\) −5.52987 −0.181331
\(931\) 41.9993 1.37647
\(932\) 17.9641 0.588435
\(933\) 41.6331 1.36301
\(934\) −32.7445 −1.07143
\(935\) 8.10969 0.265215
\(936\) −0.547303 −0.0178891
\(937\) 2.80676 0.0916929 0.0458464 0.998948i \(-0.485402\pi\)
0.0458464 + 0.998948i \(0.485402\pi\)
\(938\) 1.79203 0.0585118
\(939\) −48.7808 −1.59190
\(940\) 5.42049 0.176797
\(941\) 16.5716 0.540218 0.270109 0.962830i \(-0.412940\pi\)
0.270109 + 0.962830i \(0.412940\pi\)
\(942\) 21.4493 0.698858
\(943\) 0.0779571 0.00253863
\(944\) 2.13926 0.0696270
\(945\) 0.590927 0.0192229
\(946\) 3.39355 0.110334
\(947\) −0.688425 −0.0223708 −0.0111854 0.999937i \(-0.503560\pi\)
−0.0111854 + 0.999937i \(0.503560\pi\)
\(948\) −4.90427 −0.159283
\(949\) 66.0514 2.14412
\(950\) −6.01137 −0.195035
\(951\) −36.9164 −1.19710
\(952\) 0.884643 0.0286714
\(953\) −6.54144 −0.211898 −0.105949 0.994372i \(-0.533788\pi\)
−0.105949 + 0.994372i \(0.533788\pi\)
\(954\) 0.410416 0.0132877
\(955\) 3.88368 0.125673
\(956\) −13.1816 −0.426322
\(957\) −6.00822 −0.194218
\(958\) −5.78661 −0.186957
\(959\) −1.59399 −0.0514728
\(960\) 1.75851 0.0567558
\(961\) −21.1113 −0.681011
\(962\) −38.2083 −1.23189
\(963\) 0.124338 0.00400672
\(964\) 14.7855 0.476210
\(965\) 9.37592 0.301822
\(966\) 0.0316963 0.00101981
\(967\) −25.4310 −0.817805 −0.408903 0.912578i \(-0.634088\pi\)
−0.408903 + 0.912578i \(0.634088\pi\)
\(968\) −9.87754 −0.317476
\(969\) 80.9167 2.59942
\(970\) −7.38623 −0.237158
\(971\) 25.4416 0.816460 0.408230 0.912879i \(-0.366146\pi\)
0.408230 + 0.912879i \(0.366146\pi\)
\(972\) −0.959608 −0.0307794
\(973\) −0.426040 −0.0136582
\(974\) 23.4387 0.751025
\(975\) −10.4193 −0.333685
\(976\) 5.01100 0.160398
\(977\) −43.9535 −1.40620 −0.703098 0.711093i \(-0.748200\pi\)
−0.703098 + 0.711093i \(0.748200\pi\)
\(978\) 7.04975 0.225426
\(979\) 3.37194 0.107768
\(980\) −6.98664 −0.223180
\(981\) −0.375789 −0.0119980
\(982\) −4.03449 −0.128746
\(983\) 12.4179 0.396068 0.198034 0.980195i \(-0.436544\pi\)
0.198034 + 0.980195i \(0.436544\pi\)
\(984\) −0.878998 −0.0280214
\(985\) 8.09795 0.258022
\(986\) −24.6850 −0.786131
\(987\) −1.10162 −0.0350651
\(988\) 35.6177 1.13315
\(989\) 0.499555 0.0158849
\(990\) −0.0978633 −0.00311030
\(991\) −4.64070 −0.147417 −0.0737084 0.997280i \(-0.523483\pi\)
−0.0737084 + 0.997280i \(0.523483\pi\)
\(992\) −3.14463 −0.0998420
\(993\) −53.0746 −1.68427
\(994\) −1.01736 −0.0322686
\(995\) −2.33970 −0.0741736
\(996\) 9.40041 0.297863
\(997\) 36.3901 1.15249 0.576243 0.817278i \(-0.304518\pi\)
0.576243 + 0.817278i \(0.304518\pi\)
\(998\) −3.14365 −0.0995105
\(999\) −32.9724 −1.04320
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 \(a_p\))