Properties

Label 4030.2.a.n.1.8
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
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 1.8
Root \(-3.05324\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.05324 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.05324 q^{6} +4.02288 q^{7} +1.00000 q^{8} +6.32229 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.05324 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.05324 q^{6} +4.02288 q^{7} +1.00000 q^{8} +6.32229 q^{9} -1.00000 q^{10} -0.362988 q^{11} +3.05324 q^{12} -1.00000 q^{13} +4.02288 q^{14} -3.05324 q^{15} +1.00000 q^{16} -1.92409 q^{17} +6.32229 q^{18} -4.56721 q^{19} -1.00000 q^{20} +12.2828 q^{21} -0.362988 q^{22} +1.98562 q^{23} +3.05324 q^{24} +1.00000 q^{25} -1.00000 q^{26} +10.1437 q^{27} +4.02288 q^{28} +6.19189 q^{29} -3.05324 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.10829 q^{33} -1.92409 q^{34} -4.02288 q^{35} +6.32229 q^{36} +3.39085 q^{37} -4.56721 q^{38} -3.05324 q^{39} -1.00000 q^{40} +1.00650 q^{41} +12.2828 q^{42} +1.27528 q^{43} -0.362988 q^{44} -6.32229 q^{45} +1.98562 q^{46} -1.42002 q^{47} +3.05324 q^{48} +9.18360 q^{49} +1.00000 q^{50} -5.87470 q^{51} -1.00000 q^{52} -12.6695 q^{53} +10.1437 q^{54} +0.362988 q^{55} +4.02288 q^{56} -13.9448 q^{57} +6.19189 q^{58} +11.0188 q^{59} -3.05324 q^{60} -13.7464 q^{61} -1.00000 q^{62} +25.4338 q^{63} +1.00000 q^{64} +1.00000 q^{65} -1.10829 q^{66} +3.80933 q^{67} -1.92409 q^{68} +6.06258 q^{69} -4.02288 q^{70} +6.68163 q^{71} +6.32229 q^{72} +7.24069 q^{73} +3.39085 q^{74} +3.05324 q^{75} -4.56721 q^{76} -1.46026 q^{77} -3.05324 q^{78} -16.3027 q^{79} -1.00000 q^{80} +12.0045 q^{81} +1.00650 q^{82} +0.0901385 q^{83} +12.2828 q^{84} +1.92409 q^{85} +1.27528 q^{86} +18.9053 q^{87} -0.362988 q^{88} +1.30520 q^{89} -6.32229 q^{90} -4.02288 q^{91} +1.98562 q^{92} -3.05324 q^{93} -1.42002 q^{94} +4.56721 q^{95} +3.05324 q^{96} -14.5636 q^{97} +9.18360 q^{98} -2.29492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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
\(3\) 3.05324 1.76279 0.881395 0.472380i \(-0.156605\pi\)
0.881395 + 0.472380i \(0.156605\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 3.05324 1.24648
\(7\) 4.02288 1.52051 0.760254 0.649626i \(-0.225075\pi\)
0.760254 + 0.649626i \(0.225075\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.32229 2.10743
\(10\) −1.00000 −0.316228
\(11\) −0.362988 −0.109445 −0.0547226 0.998502i \(-0.517427\pi\)
−0.0547226 + 0.998502i \(0.517427\pi\)
\(12\) 3.05324 0.881395
\(13\) −1.00000 −0.277350
\(14\) 4.02288 1.07516
\(15\) −3.05324 −0.788344
\(16\) 1.00000 0.250000
\(17\) −1.92409 −0.466660 −0.233330 0.972398i \(-0.574962\pi\)
−0.233330 + 0.972398i \(0.574962\pi\)
\(18\) 6.32229 1.49018
\(19\) −4.56721 −1.04779 −0.523895 0.851783i \(-0.675521\pi\)
−0.523895 + 0.851783i \(0.675521\pi\)
\(20\) −1.00000 −0.223607
\(21\) 12.2828 2.68034
\(22\) −0.362988 −0.0773894
\(23\) 1.98562 0.414030 0.207015 0.978338i \(-0.433625\pi\)
0.207015 + 0.978338i \(0.433625\pi\)
\(24\) 3.05324 0.623240
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 10.1437 1.95217
\(28\) 4.02288 0.760254
\(29\) 6.19189 1.14981 0.574903 0.818222i \(-0.305040\pi\)
0.574903 + 0.818222i \(0.305040\pi\)
\(30\) −3.05324 −0.557443
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −1.10829 −0.192929
\(34\) −1.92409 −0.329978
\(35\) −4.02288 −0.679992
\(36\) 6.32229 1.05371
\(37\) 3.39085 0.557452 0.278726 0.960371i \(-0.410088\pi\)
0.278726 + 0.960371i \(0.410088\pi\)
\(38\) −4.56721 −0.740899
\(39\) −3.05324 −0.488910
\(40\) −1.00000 −0.158114
\(41\) 1.00650 0.157189 0.0785945 0.996907i \(-0.474957\pi\)
0.0785945 + 0.996907i \(0.474957\pi\)
\(42\) 12.2828 1.89528
\(43\) 1.27528 0.194478 0.0972390 0.995261i \(-0.468999\pi\)
0.0972390 + 0.995261i \(0.468999\pi\)
\(44\) −0.362988 −0.0547226
\(45\) −6.32229 −0.942471
\(46\) 1.98562 0.292764
\(47\) −1.42002 −0.207132 −0.103566 0.994623i \(-0.533025\pi\)
−0.103566 + 0.994623i \(0.533025\pi\)
\(48\) 3.05324 0.440698
\(49\) 9.18360 1.31194
\(50\) 1.00000 0.141421
\(51\) −5.87470 −0.822623
\(52\) −1.00000 −0.138675
\(53\) −12.6695 −1.74029 −0.870146 0.492794i \(-0.835975\pi\)
−0.870146 + 0.492794i \(0.835975\pi\)
\(54\) 10.1437 1.38039
\(55\) 0.362988 0.0489453
\(56\) 4.02288 0.537581
\(57\) −13.9448 −1.84703
\(58\) 6.19189 0.813035
\(59\) 11.0188 1.43453 0.717265 0.696800i \(-0.245393\pi\)
0.717265 + 0.696800i \(0.245393\pi\)
\(60\) −3.05324 −0.394172
\(61\) −13.7464 −1.76004 −0.880021 0.474936i \(-0.842471\pi\)
−0.880021 + 0.474936i \(0.842471\pi\)
\(62\) −1.00000 −0.127000
\(63\) 25.4338 3.20436
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) −1.10829 −0.136421
\(67\) 3.80933 0.465384 0.232692 0.972550i \(-0.425247\pi\)
0.232692 + 0.972550i \(0.425247\pi\)
\(68\) −1.92409 −0.233330
\(69\) 6.06258 0.729849
\(70\) −4.02288 −0.480827
\(71\) 6.68163 0.792963 0.396482 0.918043i \(-0.370231\pi\)
0.396482 + 0.918043i \(0.370231\pi\)
\(72\) 6.32229 0.745089
\(73\) 7.24069 0.847458 0.423729 0.905789i \(-0.360721\pi\)
0.423729 + 0.905789i \(0.360721\pi\)
\(74\) 3.39085 0.394178
\(75\) 3.05324 0.352558
\(76\) −4.56721 −0.523895
\(77\) −1.46026 −0.166412
\(78\) −3.05324 −0.345712
\(79\) −16.3027 −1.83420 −0.917099 0.398660i \(-0.869475\pi\)
−0.917099 + 0.398660i \(0.869475\pi\)
\(80\) −1.00000 −0.111803
\(81\) 12.0045 1.33383
\(82\) 1.00650 0.111149
\(83\) 0.0901385 0.00989399 0.00494699 0.999988i \(-0.498425\pi\)
0.00494699 + 0.999988i \(0.498425\pi\)
\(84\) 12.2828 1.34017
\(85\) 1.92409 0.208697
\(86\) 1.27528 0.137517
\(87\) 18.9053 2.02687
\(88\) −0.362988 −0.0386947
\(89\) 1.30520 0.138351 0.0691754 0.997605i \(-0.477963\pi\)
0.0691754 + 0.997605i \(0.477963\pi\)
\(90\) −6.32229 −0.666428
\(91\) −4.02288 −0.421713
\(92\) 1.98562 0.207015
\(93\) −3.05324 −0.316606
\(94\) −1.42002 −0.146464
\(95\) 4.56721 0.468586
\(96\) 3.05324 0.311620
\(97\) −14.5636 −1.47871 −0.739355 0.673315i \(-0.764870\pi\)
−0.739355 + 0.673315i \(0.764870\pi\)
\(98\) 9.18360 0.927684
\(99\) −2.29492 −0.230648
\(100\) 1.00000 0.100000
\(101\) 14.6610 1.45882 0.729410 0.684077i \(-0.239795\pi\)
0.729410 + 0.684077i \(0.239795\pi\)
\(102\) −5.87470 −0.581682
\(103\) 5.57050 0.548878 0.274439 0.961605i \(-0.411508\pi\)
0.274439 + 0.961605i \(0.411508\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −12.2828 −1.19868
\(106\) −12.6695 −1.23057
\(107\) −2.41511 −0.233478 −0.116739 0.993163i \(-0.537244\pi\)
−0.116739 + 0.993163i \(0.537244\pi\)
\(108\) 10.1437 0.976083
\(109\) 1.78924 0.171378 0.0856892 0.996322i \(-0.472691\pi\)
0.0856892 + 0.996322i \(0.472691\pi\)
\(110\) 0.362988 0.0346096
\(111\) 10.3531 0.982672
\(112\) 4.02288 0.380127
\(113\) −16.4529 −1.54776 −0.773879 0.633334i \(-0.781686\pi\)
−0.773879 + 0.633334i \(0.781686\pi\)
\(114\) −13.9448 −1.30605
\(115\) −1.98562 −0.185160
\(116\) 6.19189 0.574903
\(117\) −6.32229 −0.584496
\(118\) 11.0188 1.01437
\(119\) −7.74038 −0.709560
\(120\) −3.05324 −0.278722
\(121\) −10.8682 −0.988022
\(122\) −13.7464 −1.24454
\(123\) 3.07309 0.277091
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 25.4338 2.26583
\(127\) −8.39157 −0.744632 −0.372316 0.928106i \(-0.621436\pi\)
−0.372316 + 0.928106i \(0.621436\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.89373 0.342824
\(130\) 1.00000 0.0877058
\(131\) 1.02129 0.0892304 0.0446152 0.999004i \(-0.485794\pi\)
0.0446152 + 0.999004i \(0.485794\pi\)
\(132\) −1.10829 −0.0964644
\(133\) −18.3733 −1.59317
\(134\) 3.80933 0.329076
\(135\) −10.1437 −0.873035
\(136\) −1.92409 −0.164989
\(137\) −1.59838 −0.136559 −0.0682795 0.997666i \(-0.521751\pi\)
−0.0682795 + 0.997666i \(0.521751\pi\)
\(138\) 6.06258 0.516081
\(139\) −3.15038 −0.267212 −0.133606 0.991035i \(-0.542656\pi\)
−0.133606 + 0.991035i \(0.542656\pi\)
\(140\) −4.02288 −0.339996
\(141\) −4.33567 −0.365130
\(142\) 6.68163 0.560710
\(143\) 0.362988 0.0303546
\(144\) 6.32229 0.526857
\(145\) −6.19189 −0.514209
\(146\) 7.24069 0.599243
\(147\) 28.0398 2.31268
\(148\) 3.39085 0.278726
\(149\) −5.40142 −0.442502 −0.221251 0.975217i \(-0.571014\pi\)
−0.221251 + 0.975217i \(0.571014\pi\)
\(150\) 3.05324 0.249296
\(151\) 2.72077 0.221413 0.110707 0.993853i \(-0.464689\pi\)
0.110707 + 0.993853i \(0.464689\pi\)
\(152\) −4.56721 −0.370449
\(153\) −12.1646 −0.983452
\(154\) −1.46026 −0.117671
\(155\) 1.00000 0.0803219
\(156\) −3.05324 −0.244455
\(157\) 14.5902 1.16442 0.582211 0.813038i \(-0.302188\pi\)
0.582211 + 0.813038i \(0.302188\pi\)
\(158\) −16.3027 −1.29697
\(159\) −38.6831 −3.06777
\(160\) −1.00000 −0.0790569
\(161\) 7.98792 0.629536
\(162\) 12.0045 0.943160
\(163\) 1.19269 0.0934187 0.0467094 0.998909i \(-0.485127\pi\)
0.0467094 + 0.998909i \(0.485127\pi\)
\(164\) 1.00650 0.0785945
\(165\) 1.10829 0.0862804
\(166\) 0.0901385 0.00699610
\(167\) −16.4691 −1.27442 −0.637208 0.770692i \(-0.719911\pi\)
−0.637208 + 0.770692i \(0.719911\pi\)
\(168\) 12.2828 0.947642
\(169\) 1.00000 0.0769231
\(170\) 1.92409 0.147571
\(171\) −28.8752 −2.20814
\(172\) 1.27528 0.0972390
\(173\) −1.47452 −0.112106 −0.0560528 0.998428i \(-0.517852\pi\)
−0.0560528 + 0.998428i \(0.517852\pi\)
\(174\) 18.9053 1.43321
\(175\) 4.02288 0.304101
\(176\) −0.362988 −0.0273613
\(177\) 33.6432 2.52878
\(178\) 1.30520 0.0978287
\(179\) −16.8597 −1.26015 −0.630077 0.776532i \(-0.716977\pi\)
−0.630077 + 0.776532i \(0.716977\pi\)
\(180\) −6.32229 −0.471236
\(181\) −4.96502 −0.369047 −0.184524 0.982828i \(-0.559074\pi\)
−0.184524 + 0.982828i \(0.559074\pi\)
\(182\) −4.02288 −0.298196
\(183\) −41.9710 −3.10258
\(184\) 1.98562 0.146382
\(185\) −3.39085 −0.249300
\(186\) −3.05324 −0.223875
\(187\) 0.698421 0.0510736
\(188\) −1.42002 −0.103566
\(189\) 40.8071 2.96828
\(190\) 4.56721 0.331340
\(191\) −15.8620 −1.14773 −0.573867 0.818949i \(-0.694557\pi\)
−0.573867 + 0.818949i \(0.694557\pi\)
\(192\) 3.05324 0.220349
\(193\) −11.9900 −0.863057 −0.431528 0.902099i \(-0.642026\pi\)
−0.431528 + 0.902099i \(0.642026\pi\)
\(194\) −14.5636 −1.04561
\(195\) 3.05324 0.218647
\(196\) 9.18360 0.655972
\(197\) 9.92938 0.707439 0.353719 0.935352i \(-0.384917\pi\)
0.353719 + 0.935352i \(0.384917\pi\)
\(198\) −2.29492 −0.163093
\(199\) −3.49939 −0.248065 −0.124033 0.992278i \(-0.539583\pi\)
−0.124033 + 0.992278i \(0.539583\pi\)
\(200\) 1.00000 0.0707107
\(201\) 11.6308 0.820374
\(202\) 14.6610 1.03154
\(203\) 24.9093 1.74829
\(204\) −5.87470 −0.411312
\(205\) −1.00650 −0.0702971
\(206\) 5.57050 0.388115
\(207\) 12.5537 0.872540
\(208\) −1.00000 −0.0693375
\(209\) 1.65784 0.114675
\(210\) −12.2828 −0.847597
\(211\) 11.2283 0.772989 0.386494 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(212\) −12.6695 −0.870146
\(213\) 20.4006 1.39783
\(214\) −2.41511 −0.165094
\(215\) −1.27528 −0.0869732
\(216\) 10.1437 0.690195
\(217\) −4.02288 −0.273091
\(218\) 1.78924 0.121183
\(219\) 22.1076 1.49389
\(220\) 0.362988 0.0244727
\(221\) 1.92409 0.129428
\(222\) 10.3531 0.694854
\(223\) 11.2109 0.750738 0.375369 0.926875i \(-0.377516\pi\)
0.375369 + 0.926875i \(0.377516\pi\)
\(224\) 4.02288 0.268790
\(225\) 6.32229 0.421486
\(226\) −16.4529 −1.09443
\(227\) −23.1718 −1.53796 −0.768982 0.639270i \(-0.779236\pi\)
−0.768982 + 0.639270i \(0.779236\pi\)
\(228\) −13.9448 −0.923516
\(229\) −3.99256 −0.263836 −0.131918 0.991261i \(-0.542114\pi\)
−0.131918 + 0.991261i \(0.542114\pi\)
\(230\) −1.98562 −0.130928
\(231\) −4.45853 −0.293350
\(232\) 6.19189 0.406518
\(233\) 24.8017 1.62481 0.812406 0.583092i \(-0.198157\pi\)
0.812406 + 0.583092i \(0.198157\pi\)
\(234\) −6.32229 −0.413301
\(235\) 1.42002 0.0926321
\(236\) 11.0188 0.717265
\(237\) −49.7761 −3.23330
\(238\) −7.74038 −0.501734
\(239\) 21.6636 1.40130 0.700651 0.713504i \(-0.252893\pi\)
0.700651 + 0.713504i \(0.252893\pi\)
\(240\) −3.05324 −0.197086
\(241\) 12.7472 0.821118 0.410559 0.911834i \(-0.365334\pi\)
0.410559 + 0.911834i \(0.365334\pi\)
\(242\) −10.8682 −0.698637
\(243\) 6.22128 0.399095
\(244\) −13.7464 −0.880021
\(245\) −9.18360 −0.586719
\(246\) 3.07309 0.195933
\(247\) 4.56721 0.290604
\(248\) −1.00000 −0.0635001
\(249\) 0.275215 0.0174410
\(250\) −1.00000 −0.0632456
\(251\) −8.12191 −0.512650 −0.256325 0.966591i \(-0.582512\pi\)
−0.256325 + 0.966591i \(0.582512\pi\)
\(252\) 25.4338 1.60218
\(253\) −0.720757 −0.0453136
\(254\) −8.39157 −0.526534
\(255\) 5.87470 0.367888
\(256\) 1.00000 0.0625000
\(257\) 6.08771 0.379741 0.189870 0.981809i \(-0.439193\pi\)
0.189870 + 0.981809i \(0.439193\pi\)
\(258\) 3.89373 0.242413
\(259\) 13.6410 0.847611
\(260\) 1.00000 0.0620174
\(261\) 39.1469 2.42313
\(262\) 1.02129 0.0630954
\(263\) 24.9701 1.53972 0.769862 0.638211i \(-0.220325\pi\)
0.769862 + 0.638211i \(0.220325\pi\)
\(264\) −1.10829 −0.0682106
\(265\) 12.6695 0.778282
\(266\) −18.3733 −1.12654
\(267\) 3.98509 0.243883
\(268\) 3.80933 0.232692
\(269\) 13.6867 0.834492 0.417246 0.908793i \(-0.362995\pi\)
0.417246 + 0.908793i \(0.362995\pi\)
\(270\) −10.1437 −0.617329
\(271\) −1.54905 −0.0940984 −0.0470492 0.998893i \(-0.514982\pi\)
−0.0470492 + 0.998893i \(0.514982\pi\)
\(272\) −1.92409 −0.116665
\(273\) −12.2828 −0.743391
\(274\) −1.59838 −0.0965618
\(275\) −0.362988 −0.0218890
\(276\) 6.06258 0.364924
\(277\) −7.48965 −0.450010 −0.225005 0.974358i \(-0.572240\pi\)
−0.225005 + 0.974358i \(0.572240\pi\)
\(278\) −3.15038 −0.188947
\(279\) −6.32229 −0.378505
\(280\) −4.02288 −0.240413
\(281\) 4.80593 0.286698 0.143349 0.989672i \(-0.454213\pi\)
0.143349 + 0.989672i \(0.454213\pi\)
\(282\) −4.33567 −0.258186
\(283\) 5.74155 0.341300 0.170650 0.985332i \(-0.445413\pi\)
0.170650 + 0.985332i \(0.445413\pi\)
\(284\) 6.68163 0.396482
\(285\) 13.9448 0.826018
\(286\) 0.362988 0.0214640
\(287\) 4.04904 0.239007
\(288\) 6.32229 0.372544
\(289\) −13.2979 −0.782229
\(290\) −6.19189 −0.363600
\(291\) −44.4662 −2.60666
\(292\) 7.24069 0.423729
\(293\) 20.9538 1.22413 0.612066 0.790807i \(-0.290339\pi\)
0.612066 + 0.790807i \(0.290339\pi\)
\(294\) 28.0398 1.63531
\(295\) −11.0188 −0.641542
\(296\) 3.39085 0.197089
\(297\) −3.68206 −0.213655
\(298\) −5.40142 −0.312896
\(299\) −1.98562 −0.114831
\(300\) 3.05324 0.176279
\(301\) 5.13029 0.295705
\(302\) 2.72077 0.156563
\(303\) 44.7634 2.57159
\(304\) −4.56721 −0.261947
\(305\) 13.7464 0.787114
\(306\) −12.1646 −0.695406
\(307\) −16.6808 −0.952025 −0.476013 0.879438i \(-0.657918\pi\)
−0.476013 + 0.879438i \(0.657918\pi\)
\(308\) −1.46026 −0.0832061
\(309\) 17.0081 0.967557
\(310\) 1.00000 0.0567962
\(311\) −17.0747 −0.968217 −0.484108 0.875008i \(-0.660856\pi\)
−0.484108 + 0.875008i \(0.660856\pi\)
\(312\) −3.05324 −0.172856
\(313\) −22.6511 −1.28031 −0.640157 0.768244i \(-0.721131\pi\)
−0.640157 + 0.768244i \(0.721131\pi\)
\(314\) 14.5902 0.823370
\(315\) −25.4338 −1.43303
\(316\) −16.3027 −0.917099
\(317\) 5.94274 0.333777 0.166889 0.985976i \(-0.446628\pi\)
0.166889 + 0.985976i \(0.446628\pi\)
\(318\) −38.6831 −2.16924
\(319\) −2.24758 −0.125841
\(320\) −1.00000 −0.0559017
\(321\) −7.37392 −0.411572
\(322\) 7.98792 0.445149
\(323\) 8.78770 0.488961
\(324\) 12.0045 0.666914
\(325\) −1.00000 −0.0554700
\(326\) 1.19269 0.0660570
\(327\) 5.46299 0.302104
\(328\) 1.00650 0.0555747
\(329\) −5.71259 −0.314945
\(330\) 1.10829 0.0610094
\(331\) −12.6907 −0.697544 −0.348772 0.937208i \(-0.613401\pi\)
−0.348772 + 0.937208i \(0.613401\pi\)
\(332\) 0.0901385 0.00494699
\(333\) 21.4379 1.17479
\(334\) −16.4691 −0.901148
\(335\) −3.80933 −0.208126
\(336\) 12.2828 0.670084
\(337\) 13.5891 0.740247 0.370123 0.928983i \(-0.379315\pi\)
0.370123 + 0.928983i \(0.379315\pi\)
\(338\) 1.00000 0.0543928
\(339\) −50.2347 −2.72837
\(340\) 1.92409 0.104348
\(341\) 0.362988 0.0196569
\(342\) −28.8752 −1.56139
\(343\) 8.78438 0.474312
\(344\) 1.27528 0.0687583
\(345\) −6.06258 −0.326398
\(346\) −1.47452 −0.0792706
\(347\) 16.0709 0.862732 0.431366 0.902177i \(-0.358032\pi\)
0.431366 + 0.902177i \(0.358032\pi\)
\(348\) 18.9053 1.01343
\(349\) −18.4294 −0.986501 −0.493250 0.869887i \(-0.664191\pi\)
−0.493250 + 0.869887i \(0.664191\pi\)
\(350\) 4.02288 0.215032
\(351\) −10.1437 −0.541433
\(352\) −0.362988 −0.0193473
\(353\) 32.9845 1.75559 0.877794 0.479038i \(-0.159014\pi\)
0.877794 + 0.479038i \(0.159014\pi\)
\(354\) 33.6432 1.78812
\(355\) −6.68163 −0.354624
\(356\) 1.30520 0.0691754
\(357\) −23.6333 −1.25080
\(358\) −16.8597 −0.891064
\(359\) 26.6487 1.40646 0.703231 0.710961i \(-0.251740\pi\)
0.703231 + 0.710961i \(0.251740\pi\)
\(360\) −6.32229 −0.333214
\(361\) 1.85938 0.0978623
\(362\) −4.96502 −0.260956
\(363\) −33.1834 −1.74168
\(364\) −4.02288 −0.210856
\(365\) −7.24069 −0.378995
\(366\) −41.9710 −2.19386
\(367\) −15.9928 −0.834819 −0.417409 0.908719i \(-0.637062\pi\)
−0.417409 + 0.908719i \(0.637062\pi\)
\(368\) 1.98562 0.103508
\(369\) 6.36339 0.331265
\(370\) −3.39085 −0.176282
\(371\) −50.9680 −2.64613
\(372\) −3.05324 −0.158303
\(373\) 24.9237 1.29050 0.645250 0.763971i \(-0.276753\pi\)
0.645250 + 0.763971i \(0.276753\pi\)
\(374\) 0.698421 0.0361145
\(375\) −3.05324 −0.157669
\(376\) −1.42002 −0.0732321
\(377\) −6.19189 −0.318899
\(378\) 40.8071 2.09889
\(379\) −5.51997 −0.283542 −0.141771 0.989900i \(-0.545280\pi\)
−0.141771 + 0.989900i \(0.545280\pi\)
\(380\) 4.56721 0.234293
\(381\) −25.6215 −1.31263
\(382\) −15.8620 −0.811570
\(383\) −25.7430 −1.31541 −0.657703 0.753278i \(-0.728472\pi\)
−0.657703 + 0.753278i \(0.728472\pi\)
\(384\) 3.05324 0.155810
\(385\) 1.46026 0.0744218
\(386\) −11.9900 −0.610273
\(387\) 8.06267 0.409848
\(388\) −14.5636 −0.739355
\(389\) −14.2448 −0.722238 −0.361119 0.932520i \(-0.617605\pi\)
−0.361119 + 0.932520i \(0.617605\pi\)
\(390\) 3.05324 0.154607
\(391\) −3.82050 −0.193211
\(392\) 9.18360 0.463842
\(393\) 3.11824 0.157294
\(394\) 9.92938 0.500235
\(395\) 16.3027 0.820278
\(396\) −2.29492 −0.115324
\(397\) 1.10409 0.0554125 0.0277063 0.999616i \(-0.491180\pi\)
0.0277063 + 0.999616i \(0.491180\pi\)
\(398\) −3.49939 −0.175408
\(399\) −56.0983 −2.80843
\(400\) 1.00000 0.0500000
\(401\) −8.29815 −0.414390 −0.207195 0.978300i \(-0.566433\pi\)
−0.207195 + 0.978300i \(0.566433\pi\)
\(402\) 11.6308 0.580092
\(403\) 1.00000 0.0498135
\(404\) 14.6610 0.729410
\(405\) −12.0045 −0.596506
\(406\) 24.9093 1.23623
\(407\) −1.23084 −0.0610104
\(408\) −5.87470 −0.290841
\(409\) −12.0948 −0.598052 −0.299026 0.954245i \(-0.596662\pi\)
−0.299026 + 0.954245i \(0.596662\pi\)
\(410\) −1.00650 −0.0497075
\(411\) −4.88025 −0.240725
\(412\) 5.57050 0.274439
\(413\) 44.3275 2.18122
\(414\) 12.5537 0.616979
\(415\) −0.0901385 −0.00442473
\(416\) −1.00000 −0.0490290
\(417\) −9.61887 −0.471038
\(418\) 1.65784 0.0810878
\(419\) 2.03730 0.0995285 0.0497642 0.998761i \(-0.484153\pi\)
0.0497642 + 0.998761i \(0.484153\pi\)
\(420\) −12.2828 −0.599341
\(421\) −1.66569 −0.0811805 −0.0405903 0.999176i \(-0.512924\pi\)
−0.0405903 + 0.999176i \(0.512924\pi\)
\(422\) 11.2283 0.546585
\(423\) −8.97779 −0.436515
\(424\) −12.6695 −0.615286
\(425\) −1.92409 −0.0933319
\(426\) 20.4006 0.988414
\(427\) −55.3000 −2.67616
\(428\) −2.41511 −0.116739
\(429\) 1.10829 0.0535088
\(430\) −1.27528 −0.0614993
\(431\) 20.6268 0.993556 0.496778 0.867878i \(-0.334516\pi\)
0.496778 + 0.867878i \(0.334516\pi\)
\(432\) 10.1437 0.488041
\(433\) −16.1928 −0.778176 −0.389088 0.921201i \(-0.627210\pi\)
−0.389088 + 0.921201i \(0.627210\pi\)
\(434\) −4.02288 −0.193105
\(435\) −18.9053 −0.906442
\(436\) 1.78924 0.0856892
\(437\) −9.06874 −0.433816
\(438\) 22.1076 1.05634
\(439\) −22.9106 −1.09346 −0.546731 0.837308i \(-0.684128\pi\)
−0.546731 + 0.837308i \(0.684128\pi\)
\(440\) 0.362988 0.0173048
\(441\) 58.0614 2.76483
\(442\) 1.92409 0.0915195
\(443\) 35.2284 1.67375 0.836875 0.547394i \(-0.184380\pi\)
0.836875 + 0.547394i \(0.184380\pi\)
\(444\) 10.3531 0.491336
\(445\) −1.30520 −0.0618723
\(446\) 11.2109 0.530852
\(447\) −16.4918 −0.780037
\(448\) 4.02288 0.190063
\(449\) 0.943898 0.0445453 0.0222727 0.999752i \(-0.492910\pi\)
0.0222727 + 0.999752i \(0.492910\pi\)
\(450\) 6.32229 0.298036
\(451\) −0.365348 −0.0172036
\(452\) −16.4529 −0.773879
\(453\) 8.30718 0.390305
\(454\) −23.1718 −1.08750
\(455\) 4.02288 0.188596
\(456\) −13.9448 −0.653025
\(457\) −6.34124 −0.296630 −0.148315 0.988940i \(-0.547385\pi\)
−0.148315 + 0.988940i \(0.547385\pi\)
\(458\) −3.99256 −0.186560
\(459\) −19.5175 −0.910997
\(460\) −1.98562 −0.0925800
\(461\) 10.3511 0.482098 0.241049 0.970513i \(-0.422509\pi\)
0.241049 + 0.970513i \(0.422509\pi\)
\(462\) −4.45853 −0.207430
\(463\) 35.6538 1.65697 0.828486 0.560009i \(-0.189202\pi\)
0.828486 + 0.560009i \(0.189202\pi\)
\(464\) 6.19189 0.287451
\(465\) 3.05324 0.141591
\(466\) 24.8017 1.14892
\(467\) −17.9543 −0.830827 −0.415413 0.909633i \(-0.636363\pi\)
−0.415413 + 0.909633i \(0.636363\pi\)
\(468\) −6.32229 −0.292248
\(469\) 15.3245 0.707620
\(470\) 1.42002 0.0655008
\(471\) 44.5473 2.05263
\(472\) 11.0188 0.507183
\(473\) −0.462911 −0.0212847
\(474\) −49.7761 −2.28629
\(475\) −4.56721 −0.209558
\(476\) −7.74038 −0.354780
\(477\) −80.1003 −3.66754
\(478\) 21.6636 0.990871
\(479\) −10.3445 −0.472654 −0.236327 0.971674i \(-0.575944\pi\)
−0.236327 + 0.971674i \(0.575944\pi\)
\(480\) −3.05324 −0.139361
\(481\) −3.39085 −0.154609
\(482\) 12.7472 0.580618
\(483\) 24.3890 1.10974
\(484\) −10.8682 −0.494011
\(485\) 14.5636 0.661300
\(486\) 6.22128 0.282203
\(487\) −9.36406 −0.424326 −0.212163 0.977234i \(-0.568051\pi\)
−0.212163 + 0.977234i \(0.568051\pi\)
\(488\) −13.7464 −0.622268
\(489\) 3.64157 0.164678
\(490\) −9.18360 −0.414873
\(491\) −14.7056 −0.663657 −0.331828 0.943340i \(-0.607665\pi\)
−0.331828 + 0.943340i \(0.607665\pi\)
\(492\) 3.07309 0.138546
\(493\) −11.9137 −0.536568
\(494\) 4.56721 0.205488
\(495\) 2.29492 0.103149
\(496\) −1.00000 −0.0449013
\(497\) 26.8794 1.20571
\(498\) 0.275215 0.0123327
\(499\) −20.6527 −0.924542 −0.462271 0.886739i \(-0.652965\pi\)
−0.462271 + 0.886739i \(0.652965\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −50.2841 −2.24653
\(502\) −8.12191 −0.362499
\(503\) 7.11242 0.317127 0.158564 0.987349i \(-0.449314\pi\)
0.158564 + 0.987349i \(0.449314\pi\)
\(504\) 25.4338 1.13291
\(505\) −14.6610 −0.652404
\(506\) −0.720757 −0.0320416
\(507\) 3.05324 0.135599
\(508\) −8.39157 −0.372316
\(509\) 40.7482 1.80613 0.903066 0.429502i \(-0.141311\pi\)
0.903066 + 0.429502i \(0.141311\pi\)
\(510\) 5.87470 0.260136
\(511\) 29.1284 1.28857
\(512\) 1.00000 0.0441942
\(513\) −46.3286 −2.04546
\(514\) 6.08771 0.268517
\(515\) −5.57050 −0.245466
\(516\) 3.89373 0.171412
\(517\) 0.515452 0.0226695
\(518\) 13.6410 0.599351
\(519\) −4.50206 −0.197619
\(520\) 1.00000 0.0438529
\(521\) −22.2171 −0.973349 −0.486675 0.873583i \(-0.661790\pi\)
−0.486675 + 0.873583i \(0.661790\pi\)
\(522\) 39.1469 1.71341
\(523\) 25.2843 1.10561 0.552803 0.833312i \(-0.313558\pi\)
0.552803 + 0.833312i \(0.313558\pi\)
\(524\) 1.02129 0.0446152
\(525\) 12.2828 0.536067
\(526\) 24.9701 1.08875
\(527\) 1.92409 0.0838146
\(528\) −1.10829 −0.0482322
\(529\) −19.0573 −0.828579
\(530\) 12.6695 0.550328
\(531\) 69.6643 3.02317
\(532\) −18.3733 −0.796586
\(533\) −1.00650 −0.0435964
\(534\) 3.98509 0.172452
\(535\) 2.41511 0.104414
\(536\) 3.80933 0.164538
\(537\) −51.4768 −2.22139
\(538\) 13.6867 0.590075
\(539\) −3.33354 −0.143586
\(540\) −10.1437 −0.436517
\(541\) 14.2768 0.613809 0.306905 0.951740i \(-0.400707\pi\)
0.306905 + 0.951740i \(0.400707\pi\)
\(542\) −1.54905 −0.0665376
\(543\) −15.1594 −0.650552
\(544\) −1.92409 −0.0824946
\(545\) −1.78924 −0.0766427
\(546\) −12.2828 −0.525657
\(547\) −13.3339 −0.570114 −0.285057 0.958511i \(-0.592013\pi\)
−0.285057 + 0.958511i \(0.592013\pi\)
\(548\) −1.59838 −0.0682795
\(549\) −86.9084 −3.70916
\(550\) −0.362988 −0.0154779
\(551\) −28.2797 −1.20475
\(552\) 6.06258 0.258040
\(553\) −65.5839 −2.78891
\(554\) −7.48965 −0.318205
\(555\) −10.3531 −0.439464
\(556\) −3.15038 −0.133606
\(557\) −40.3054 −1.70780 −0.853898 0.520441i \(-0.825768\pi\)
−0.853898 + 0.520441i \(0.825768\pi\)
\(558\) −6.32229 −0.267644
\(559\) −1.27528 −0.0539385
\(560\) −4.02288 −0.169998
\(561\) 2.13245 0.0900321
\(562\) 4.80593 0.202726
\(563\) 20.0543 0.845187 0.422594 0.906319i \(-0.361120\pi\)
0.422594 + 0.906319i \(0.361120\pi\)
\(564\) −4.33567 −0.182565
\(565\) 16.4529 0.692178
\(566\) 5.74155 0.241336
\(567\) 48.2926 2.02810
\(568\) 6.68163 0.280355
\(569\) −4.45148 −0.186616 −0.0933078 0.995637i \(-0.529744\pi\)
−0.0933078 + 0.995637i \(0.529744\pi\)
\(570\) 13.9448 0.584083
\(571\) −26.4732 −1.10787 −0.553935 0.832560i \(-0.686874\pi\)
−0.553935 + 0.832560i \(0.686874\pi\)
\(572\) 0.362988 0.0151773
\(573\) −48.4305 −2.02321
\(574\) 4.04904 0.169004
\(575\) 1.98562 0.0828061
\(576\) 6.32229 0.263429
\(577\) 20.1640 0.839439 0.419720 0.907654i \(-0.362128\pi\)
0.419720 + 0.907654i \(0.362128\pi\)
\(578\) −13.2979 −0.553119
\(579\) −36.6083 −1.52139
\(580\) −6.19189 −0.257104
\(581\) 0.362617 0.0150439
\(582\) −44.4662 −1.84318
\(583\) 4.59889 0.190466
\(584\) 7.24069 0.299622
\(585\) 6.32229 0.261394
\(586\) 20.9538 0.865592
\(587\) 5.25914 0.217068 0.108534 0.994093i \(-0.465384\pi\)
0.108534 + 0.994093i \(0.465384\pi\)
\(588\) 28.0398 1.15634
\(589\) 4.56721 0.188189
\(590\) −11.0188 −0.453639
\(591\) 30.3168 1.24707
\(592\) 3.39085 0.139363
\(593\) 24.4828 1.00539 0.502694 0.864464i \(-0.332342\pi\)
0.502694 + 0.864464i \(0.332342\pi\)
\(594\) −3.68206 −0.151077
\(595\) 7.74038 0.317325
\(596\) −5.40142 −0.221251
\(597\) −10.6845 −0.437287
\(598\) −1.98562 −0.0811980
\(599\) −32.1433 −1.31334 −0.656670 0.754178i \(-0.728036\pi\)
−0.656670 + 0.754178i \(0.728036\pi\)
\(600\) 3.05324 0.124648
\(601\) −46.2905 −1.88823 −0.944115 0.329618i \(-0.893080\pi\)
−0.944115 + 0.329618i \(0.893080\pi\)
\(602\) 5.13029 0.209095
\(603\) 24.0837 0.980764
\(604\) 2.72077 0.110707
\(605\) 10.8682 0.441857
\(606\) 44.7634 1.81839
\(607\) −39.4658 −1.60187 −0.800935 0.598752i \(-0.795664\pi\)
−0.800935 + 0.598752i \(0.795664\pi\)
\(608\) −4.56721 −0.185225
\(609\) 76.0540 3.08186
\(610\) 13.7464 0.556574
\(611\) 1.42002 0.0574480
\(612\) −12.1646 −0.491726
\(613\) 28.8426 1.16494 0.582471 0.812851i \(-0.302086\pi\)
0.582471 + 0.812851i \(0.302086\pi\)
\(614\) −16.6808 −0.673183
\(615\) −3.07309 −0.123919
\(616\) −1.46026 −0.0588356
\(617\) 3.84755 0.154897 0.0774484 0.996996i \(-0.475323\pi\)
0.0774484 + 0.996996i \(0.475323\pi\)
\(618\) 17.0081 0.684166
\(619\) 31.3732 1.26099 0.630497 0.776191i \(-0.282851\pi\)
0.630497 + 0.776191i \(0.282851\pi\)
\(620\) 1.00000 0.0401610
\(621\) 20.1416 0.808256
\(622\) −17.0747 −0.684632
\(623\) 5.25066 0.210363
\(624\) −3.05324 −0.122228
\(625\) 1.00000 0.0400000
\(626\) −22.6511 −0.905318
\(627\) 5.06180 0.202149
\(628\) 14.5902 0.582211
\(629\) −6.52429 −0.260141
\(630\) −25.4338 −1.01331
\(631\) −23.5400 −0.937113 −0.468557 0.883433i \(-0.655226\pi\)
−0.468557 + 0.883433i \(0.655226\pi\)
\(632\) −16.3027 −0.648487
\(633\) 34.2827 1.36262
\(634\) 5.94274 0.236016
\(635\) 8.39157 0.333009
\(636\) −38.6831 −1.53388
\(637\) −9.18360 −0.363868
\(638\) −2.24758 −0.0889827
\(639\) 42.2432 1.67111
\(640\) −1.00000 −0.0395285
\(641\) −0.308880 −0.0122000 −0.00610001 0.999981i \(-0.501942\pi\)
−0.00610001 + 0.999981i \(0.501942\pi\)
\(642\) −7.37392 −0.291025
\(643\) −40.3424 −1.59095 −0.795474 0.605988i \(-0.792778\pi\)
−0.795474 + 0.605988i \(0.792778\pi\)
\(644\) 7.98792 0.314768
\(645\) −3.89373 −0.153315
\(646\) 8.78770 0.345748
\(647\) −32.2433 −1.26762 −0.633808 0.773490i \(-0.718509\pi\)
−0.633808 + 0.773490i \(0.718509\pi\)
\(648\) 12.0045 0.471580
\(649\) −3.99971 −0.157002
\(650\) −1.00000 −0.0392232
\(651\) −12.2828 −0.481403
\(652\) 1.19269 0.0467094
\(653\) 29.1292 1.13991 0.569956 0.821675i \(-0.306960\pi\)
0.569956 + 0.821675i \(0.306960\pi\)
\(654\) 5.46299 0.213620
\(655\) −1.02129 −0.0399050
\(656\) 1.00650 0.0392973
\(657\) 45.7777 1.78596
\(658\) −5.71259 −0.222700
\(659\) 22.2043 0.864956 0.432478 0.901644i \(-0.357639\pi\)
0.432478 + 0.901644i \(0.357639\pi\)
\(660\) 1.10829 0.0431402
\(661\) 40.1886 1.56316 0.781578 0.623807i \(-0.214415\pi\)
0.781578 + 0.623807i \(0.214415\pi\)
\(662\) −12.6907 −0.493238
\(663\) 5.87470 0.228155
\(664\) 0.0901385 0.00349805
\(665\) 18.3733 0.712488
\(666\) 21.4379 0.830703
\(667\) 12.2947 0.476054
\(668\) −16.4691 −0.637208
\(669\) 34.2296 1.32339
\(670\) −3.80933 −0.147167
\(671\) 4.98977 0.192628
\(672\) 12.2828 0.473821
\(673\) 28.3121 1.09135 0.545675 0.837997i \(-0.316273\pi\)
0.545675 + 0.837997i \(0.316273\pi\)
\(674\) 13.5891 0.523433
\(675\) 10.1437 0.390433
\(676\) 1.00000 0.0384615
\(677\) −25.8809 −0.994685 −0.497342 0.867554i \(-0.665691\pi\)
−0.497342 + 0.867554i \(0.665691\pi\)
\(678\) −50.2347 −1.92925
\(679\) −58.5877 −2.24839
\(680\) 1.92409 0.0737854
\(681\) −70.7490 −2.71111
\(682\) 0.362988 0.0138995
\(683\) −2.71368 −0.103836 −0.0519179 0.998651i \(-0.516533\pi\)
−0.0519179 + 0.998651i \(0.516533\pi\)
\(684\) −28.8752 −1.10407
\(685\) 1.59838 0.0610710
\(686\) 8.78438 0.335389
\(687\) −12.1902 −0.465087
\(688\) 1.27528 0.0486195
\(689\) 12.6695 0.482670
\(690\) −6.06258 −0.230798
\(691\) −26.6259 −1.01290 −0.506448 0.862271i \(-0.669042\pi\)
−0.506448 + 0.862271i \(0.669042\pi\)
\(692\) −1.47452 −0.0560528
\(693\) −9.23219 −0.350702
\(694\) 16.0709 0.610043
\(695\) 3.15038 0.119501
\(696\) 18.9053 0.716605
\(697\) −1.93660 −0.0733538
\(698\) −18.4294 −0.697561
\(699\) 75.7255 2.86420
\(700\) 4.02288 0.152051
\(701\) 29.1342 1.10038 0.550192 0.835038i \(-0.314554\pi\)
0.550192 + 0.835038i \(0.314554\pi\)
\(702\) −10.1437 −0.382851
\(703\) −15.4867 −0.584093
\(704\) −0.362988 −0.0136806
\(705\) 4.33567 0.163291
\(706\) 32.9845 1.24139
\(707\) 58.9793 2.21815
\(708\) 33.6432 1.26439
\(709\) 21.0576 0.790836 0.395418 0.918501i \(-0.370600\pi\)
0.395418 + 0.918501i \(0.370600\pi\)
\(710\) −6.68163 −0.250757
\(711\) −103.070 −3.86544
\(712\) 1.30520 0.0489144
\(713\) −1.98562 −0.0743620
\(714\) −23.6333 −0.884452
\(715\) −0.362988 −0.0135750
\(716\) −16.8597 −0.630077
\(717\) 66.1443 2.47020
\(718\) 26.6487 0.994519
\(719\) 43.3525 1.61677 0.808387 0.588651i \(-0.200341\pi\)
0.808387 + 0.588651i \(0.200341\pi\)
\(720\) −6.32229 −0.235618
\(721\) 22.4095 0.834573
\(722\) 1.85938 0.0691991
\(723\) 38.9202 1.44746
\(724\) −4.96502 −0.184524
\(725\) 6.19189 0.229961
\(726\) −33.1834 −1.23155
\(727\) 43.2037 1.60234 0.801169 0.598438i \(-0.204212\pi\)
0.801169 + 0.598438i \(0.204212\pi\)
\(728\) −4.02288 −0.149098
\(729\) −17.0183 −0.630308
\(730\) −7.24069 −0.267990
\(731\) −2.45374 −0.0907550
\(732\) −41.9710 −1.55129
\(733\) −40.1782 −1.48402 −0.742008 0.670391i \(-0.766126\pi\)
−0.742008 + 0.670391i \(0.766126\pi\)
\(734\) −15.9928 −0.590306
\(735\) −28.0398 −1.03426
\(736\) 1.98562 0.0731909
\(737\) −1.38274 −0.0509340
\(738\) 6.36339 0.234240
\(739\) 34.1465 1.25610 0.628050 0.778173i \(-0.283853\pi\)
0.628050 + 0.778173i \(0.283853\pi\)
\(740\) −3.39085 −0.124650
\(741\) 13.9448 0.512275
\(742\) −50.9680 −1.87109
\(743\) −33.3178 −1.22231 −0.611156 0.791510i \(-0.709295\pi\)
−0.611156 + 0.791510i \(0.709295\pi\)
\(744\) −3.05324 −0.111937
\(745\) 5.40142 0.197893
\(746\) 24.9237 0.912522
\(747\) 0.569882 0.0208509
\(748\) 0.698421 0.0255368
\(749\) −9.71572 −0.355005
\(750\) −3.05324 −0.111489
\(751\) 1.87216 0.0683160 0.0341580 0.999416i \(-0.489125\pi\)
0.0341580 + 0.999416i \(0.489125\pi\)
\(752\) −1.42002 −0.0517829
\(753\) −24.7982 −0.903695
\(754\) −6.19189 −0.225495
\(755\) −2.72077 −0.0990190
\(756\) 40.8071 1.48414
\(757\) 51.2083 1.86120 0.930600 0.366039i \(-0.119286\pi\)
0.930600 + 0.366039i \(0.119286\pi\)
\(758\) −5.51997 −0.200494
\(759\) −2.20065 −0.0798784
\(760\) 4.56721 0.165670
\(761\) −9.04294 −0.327806 −0.163903 0.986476i \(-0.552408\pi\)
−0.163903 + 0.986476i \(0.552408\pi\)
\(762\) −25.6215 −0.928169
\(763\) 7.19792 0.260582
\(764\) −15.8620 −0.573867
\(765\) 12.1646 0.439813
\(766\) −25.7430 −0.930132
\(767\) −11.0188 −0.397867
\(768\) 3.05324 0.110174
\(769\) 21.4816 0.774647 0.387324 0.921944i \(-0.373400\pi\)
0.387324 + 0.921944i \(0.373400\pi\)
\(770\) 1.46026 0.0526241
\(771\) 18.5872 0.669403
\(772\) −11.9900 −0.431528
\(773\) 36.4552 1.31120 0.655602 0.755107i \(-0.272415\pi\)
0.655602 + 0.755107i \(0.272415\pi\)
\(774\) 8.06267 0.289807
\(775\) −1.00000 −0.0359211
\(776\) −14.5636 −0.522803
\(777\) 41.6493 1.49416
\(778\) −14.2448 −0.510699
\(779\) −4.59690 −0.164701
\(780\) 3.05324 0.109324
\(781\) −2.42535 −0.0867860
\(782\) −3.82050 −0.136621
\(783\) 62.8090 2.24461
\(784\) 9.18360 0.327986
\(785\) −14.5902 −0.520745
\(786\) 3.11824 0.111224
\(787\) −32.6924 −1.16536 −0.582679 0.812702i \(-0.697996\pi\)
−0.582679 + 0.812702i \(0.697996\pi\)
\(788\) 9.92938 0.353719
\(789\) 76.2398 2.71421
\(790\) 16.3027 0.580024
\(791\) −66.1881 −2.35338
\(792\) −2.29492 −0.0815463
\(793\) 13.7464 0.488148
\(794\) 1.10409 0.0391826
\(795\) 38.6831 1.37195
\(796\) −3.49939 −0.124033
\(797\) −35.2384 −1.24821 −0.624103 0.781342i \(-0.714536\pi\)
−0.624103 + 0.781342i \(0.714536\pi\)
\(798\) −56.0983 −1.98586
\(799\) 2.73225 0.0966599
\(800\) 1.00000 0.0353553
\(801\) 8.25184 0.291564
\(802\) −8.29815 −0.293018
\(803\) −2.62828 −0.0927502
\(804\) 11.6308 0.410187
\(805\) −7.98792 −0.281537
\(806\) 1.00000 0.0352235
\(807\) 41.7888 1.47104
\(808\) 14.6610 0.515771
\(809\) 16.9030 0.594276 0.297138 0.954835i \(-0.403968\pi\)
0.297138 + 0.954835i \(0.403968\pi\)
\(810\) −12.0045 −0.421794
\(811\) −36.4383 −1.27952 −0.639761 0.768574i \(-0.720966\pi\)
−0.639761 + 0.768574i \(0.720966\pi\)
\(812\) 24.9093 0.874144
\(813\) −4.72964 −0.165876
\(814\) −1.23084 −0.0431409
\(815\) −1.19269 −0.0417781
\(816\) −5.87470 −0.205656
\(817\) −5.82445 −0.203772
\(818\) −12.0948 −0.422887
\(819\) −25.4338 −0.888730
\(820\) −1.00650 −0.0351485
\(821\) −7.89177 −0.275425 −0.137712 0.990472i \(-0.543975\pi\)
−0.137712 + 0.990472i \(0.543975\pi\)
\(822\) −4.88025 −0.170218
\(823\) −27.9250 −0.973404 −0.486702 0.873568i \(-0.661800\pi\)
−0.486702 + 0.873568i \(0.661800\pi\)
\(824\) 5.57050 0.194058
\(825\) −1.10829 −0.0385858
\(826\) 44.3275 1.54235
\(827\) 43.4051 1.50934 0.754671 0.656104i \(-0.227797\pi\)
0.754671 + 0.656104i \(0.227797\pi\)
\(828\) 12.5537 0.436270
\(829\) 35.6001 1.23644 0.618222 0.786004i \(-0.287853\pi\)
0.618222 + 0.786004i \(0.287853\pi\)
\(830\) −0.0901385 −0.00312875
\(831\) −22.8677 −0.793273
\(832\) −1.00000 −0.0346688
\(833\) −17.6700 −0.612231
\(834\) −9.61887 −0.333074
\(835\) 16.4691 0.569936
\(836\) 1.65784 0.0573377
\(837\) −10.1437 −0.350619
\(838\) 2.03730 0.0703773
\(839\) 22.8780 0.789838 0.394919 0.918716i \(-0.370773\pi\)
0.394919 + 0.918716i \(0.370773\pi\)
\(840\) −12.2828 −0.423798
\(841\) 9.33952 0.322052
\(842\) −1.66569 −0.0574033
\(843\) 14.6737 0.505388
\(844\) 11.2283 0.386494
\(845\) −1.00000 −0.0344010
\(846\) −8.97779 −0.308663
\(847\) −43.7217 −1.50229
\(848\) −12.6695 −0.435073
\(849\) 17.5304 0.601640
\(850\) −1.92409 −0.0659956
\(851\) 6.73294 0.230802
\(852\) 20.4006 0.698914
\(853\) 56.1044 1.92098 0.960488 0.278320i \(-0.0897776\pi\)
0.960488 + 0.278320i \(0.0897776\pi\)
\(854\) −55.3000 −1.89233
\(855\) 28.8752 0.987511
\(856\) −2.41511 −0.0825468
\(857\) −26.6440 −0.910143 −0.455071 0.890455i \(-0.650386\pi\)
−0.455071 + 0.890455i \(0.650386\pi\)
\(858\) 1.10829 0.0378365
\(859\) −28.1005 −0.958778 −0.479389 0.877602i \(-0.659142\pi\)
−0.479389 + 0.877602i \(0.659142\pi\)
\(860\) −1.27528 −0.0434866
\(861\) 12.3627 0.421319
\(862\) 20.6268 0.702550
\(863\) 37.9707 1.29254 0.646270 0.763109i \(-0.276328\pi\)
0.646270 + 0.763109i \(0.276328\pi\)
\(864\) 10.1437 0.345097
\(865\) 1.47452 0.0501351
\(866\) −16.1928 −0.550253
\(867\) −40.6017 −1.37891
\(868\) −4.02288 −0.136546
\(869\) 5.91769 0.200744
\(870\) −18.9053 −0.640951
\(871\) −3.80933 −0.129074
\(872\) 1.78924 0.0605914
\(873\) −92.0753 −3.11628
\(874\) −9.06874 −0.306755
\(875\) −4.02288 −0.135998
\(876\) 22.1076 0.746945
\(877\) −24.5344 −0.828467 −0.414234 0.910171i \(-0.635950\pi\)
−0.414234 + 0.910171i \(0.635950\pi\)
\(878\) −22.9106 −0.773195
\(879\) 63.9769 2.15789
\(880\) 0.362988 0.0122363
\(881\) −30.0893 −1.01373 −0.506867 0.862024i \(-0.669197\pi\)
−0.506867 + 0.862024i \(0.669197\pi\)
\(882\) 58.0614 1.95503
\(883\) 15.7495 0.530014 0.265007 0.964246i \(-0.414626\pi\)
0.265007 + 0.964246i \(0.414626\pi\)
\(884\) 1.92409 0.0647141
\(885\) −33.6432 −1.13090
\(886\) 35.2284 1.18352
\(887\) 21.7005 0.728632 0.364316 0.931275i \(-0.381303\pi\)
0.364316 + 0.931275i \(0.381303\pi\)
\(888\) 10.3531 0.347427
\(889\) −33.7583 −1.13222
\(890\) −1.30520 −0.0437503
\(891\) −4.35748 −0.145981
\(892\) 11.2109 0.375369
\(893\) 6.48554 0.217030
\(894\) −16.4918 −0.551570
\(895\) 16.8597 0.563558
\(896\) 4.02288 0.134395
\(897\) −6.06258 −0.202424
\(898\) 0.943898 0.0314983
\(899\) −6.19189 −0.206511
\(900\) 6.32229 0.210743
\(901\) 24.3772 0.812124
\(902\) −0.365348 −0.0121648
\(903\) 15.6640 0.521266
\(904\) −16.4529 −0.547215
\(905\) 4.96502 0.165043
\(906\) 8.30718 0.275987
\(907\) 46.7371 1.55188 0.775940 0.630807i \(-0.217276\pi\)
0.775940 + 0.630807i \(0.217276\pi\)
\(908\) −23.1718 −0.768982
\(909\) 92.6908 3.07436
\(910\) 4.02288 0.133357
\(911\) 57.4858 1.90459 0.952296 0.305177i \(-0.0987158\pi\)
0.952296 + 0.305177i \(0.0987158\pi\)
\(912\) −13.9448 −0.461758
\(913\) −0.0327192 −0.00108285
\(914\) −6.34124 −0.209749
\(915\) 41.9710 1.38752
\(916\) −3.99256 −0.131918
\(917\) 4.10853 0.135675
\(918\) −19.5175 −0.644172
\(919\) −58.8678 −1.94187 −0.970934 0.239346i \(-0.923067\pi\)
−0.970934 + 0.239346i \(0.923067\pi\)
\(920\) −1.98562 −0.0654639
\(921\) −50.9306 −1.67822
\(922\) 10.3511 0.340895
\(923\) −6.68163 −0.219928
\(924\) −4.45853 −0.146675
\(925\) 3.39085 0.111490
\(926\) 35.6538 1.17166
\(927\) 35.2183 1.15672
\(928\) 6.19189 0.203259
\(929\) −40.1191 −1.31627 −0.658133 0.752902i \(-0.728653\pi\)
−0.658133 + 0.752902i \(0.728653\pi\)
\(930\) 3.05324 0.100120
\(931\) −41.9434 −1.37464
\(932\) 24.8017 0.812406
\(933\) −52.1331 −1.70676
\(934\) −17.9543 −0.587483
\(935\) −0.698421 −0.0228408
\(936\) −6.32229 −0.206650
\(937\) −4.91897 −0.160696 −0.0803479 0.996767i \(-0.525603\pi\)
−0.0803479 + 0.996767i \(0.525603\pi\)
\(938\) 15.3245 0.500363
\(939\) −69.1592 −2.25692
\(940\) 1.42002 0.0463160
\(941\) 2.03154 0.0662265 0.0331132 0.999452i \(-0.489458\pi\)
0.0331132 + 0.999452i \(0.489458\pi\)
\(942\) 44.5473 1.45143
\(943\) 1.99853 0.0650810
\(944\) 11.0188 0.358633
\(945\) −40.8071 −1.32746
\(946\) −0.462911 −0.0150505
\(947\) −33.1311 −1.07662 −0.538308 0.842748i \(-0.680936\pi\)
−0.538308 + 0.842748i \(0.680936\pi\)
\(948\) −49.7761 −1.61665
\(949\) −7.24069 −0.235043
\(950\) −4.56721 −0.148180
\(951\) 18.1446 0.588380
\(952\) −7.74038 −0.250867
\(953\) 53.6397 1.73756 0.868780 0.495199i \(-0.164905\pi\)
0.868780 + 0.495199i \(0.164905\pi\)
\(954\) −80.1003 −2.59334
\(955\) 15.8620 0.513282
\(956\) 21.6636 0.700651
\(957\) −6.86242 −0.221831
\(958\) −10.3445 −0.334217
\(959\) −6.43011 −0.207639
\(960\) −3.05324 −0.0985430
\(961\) 1.00000 0.0322581
\(962\) −3.39085 −0.109325
\(963\) −15.2690 −0.492038
\(964\) 12.7472 0.410559
\(965\) 11.9900 0.385971
\(966\) 24.3890 0.784705
\(967\) 56.6954 1.82320 0.911601 0.411076i \(-0.134847\pi\)
0.911601 + 0.411076i \(0.134847\pi\)
\(968\) −10.8682 −0.349318
\(969\) 26.8310 0.861936
\(970\) 14.5636 0.467609
\(971\) −59.5592 −1.91135 −0.955673 0.294429i \(-0.904870\pi\)
−0.955673 + 0.294429i \(0.904870\pi\)
\(972\) 6.22128 0.199548
\(973\) −12.6736 −0.406297
\(974\) −9.36406 −0.300044
\(975\) −3.05324 −0.0977820
\(976\) −13.7464 −0.440010
\(977\) −24.9646 −0.798689 −0.399345 0.916801i \(-0.630762\pi\)
−0.399345 + 0.916801i \(0.630762\pi\)
\(978\) 3.64157 0.116445
\(979\) −0.473772 −0.0151418
\(980\) −9.18360 −0.293359
\(981\) 11.3121 0.361168
\(982\) −14.7056 −0.469276
\(983\) −3.56740 −0.113783 −0.0568913 0.998380i \(-0.518119\pi\)
−0.0568913 + 0.998380i \(0.518119\pi\)
\(984\) 3.07309 0.0979666
\(985\) −9.92938 −0.316376
\(986\) −11.9137 −0.379411
\(987\) −17.4419 −0.555182
\(988\) 4.56721 0.145302
\(989\) 2.53221 0.0805197
\(990\) 2.29492 0.0729373
\(991\) −11.5384 −0.366528 −0.183264 0.983064i \(-0.558666\pi\)
−0.183264 + 0.983064i \(0.558666\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −38.7478 −1.22962
\(994\) 26.8794 0.852563
\(995\) 3.49939 0.110938
\(996\) 0.275215 0.00872051
\(997\) 2.74243 0.0868538 0.0434269 0.999057i \(-0.486172\pi\)
0.0434269 + 0.999057i \(0.486172\pi\)
\(998\) −20.6527 −0.653750
\(999\) 34.3959 1.08824
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 \(a_p\))