Properties

Label 4030.2.a.f.1.1
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
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: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.95223\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} -1.00000 q^{10} -2.84568 q^{11} -2.58368 q^{12} +1.00000 q^{13} -0.667536 q^{14} +2.58368 q^{15} +1.00000 q^{16} +1.37374 q^{17} +3.67538 q^{18} +1.12705 q^{19} -1.00000 q^{20} +1.72470 q^{21} -2.84568 q^{22} -0.435841 q^{23} -2.58368 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.74496 q^{27} -0.667536 q^{28} +3.39742 q^{29} +2.58368 q^{30} -1.00000 q^{31} +1.00000 q^{32} +7.35231 q^{33} +1.37374 q^{34} +0.667536 q^{35} +3.67538 q^{36} +6.66636 q^{37} +1.12705 q^{38} -2.58368 q^{39} -1.00000 q^{40} -4.55705 q^{41} +1.72470 q^{42} -8.44112 q^{43} -2.84568 q^{44} -3.67538 q^{45} -0.435841 q^{46} +1.87000 q^{47} -2.58368 q^{48} -6.55440 q^{49} +1.00000 q^{50} -3.54931 q^{51} +1.00000 q^{52} +6.09399 q^{53} -1.74496 q^{54} +2.84568 q^{55} -0.667536 q^{56} -2.91193 q^{57} +3.39742 q^{58} +9.16780 q^{59} +2.58368 q^{60} +0.621446 q^{61} -1.00000 q^{62} -2.45345 q^{63} +1.00000 q^{64} -1.00000 q^{65} +7.35231 q^{66} -15.1922 q^{67} +1.37374 q^{68} +1.12607 q^{69} +0.667536 q^{70} -0.573489 q^{71} +3.67538 q^{72} +15.1539 q^{73} +6.66636 q^{74} -2.58368 q^{75} +1.12705 q^{76} +1.89959 q^{77} -2.58368 q^{78} -8.71493 q^{79} -1.00000 q^{80} -6.51773 q^{81} -4.55705 q^{82} -14.9770 q^{83} +1.72470 q^{84} -1.37374 q^{85} -8.44112 q^{86} -8.77782 q^{87} -2.84568 q^{88} +0.261768 q^{89} -3.67538 q^{90} -0.667536 q^{91} -0.435841 q^{92} +2.58368 q^{93} +1.87000 q^{94} -1.12705 q^{95} -2.58368 q^{96} -14.0327 q^{97} -6.55440 q^{98} -10.4589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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
\(3\) −2.58368 −1.49169 −0.745843 0.666122i \(-0.767953\pi\)
−0.745843 + 0.666122i \(0.767953\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.58368 −1.05478
\(7\) −0.667536 −0.252305 −0.126152 0.992011i \(-0.540263\pi\)
−0.126152 + 0.992011i \(0.540263\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.67538 1.22513
\(10\) −1.00000 −0.316228
\(11\) −2.84568 −0.858004 −0.429002 0.903304i \(-0.641135\pi\)
−0.429002 + 0.903304i \(0.641135\pi\)
\(12\) −2.58368 −0.745843
\(13\) 1.00000 0.277350
\(14\) −0.667536 −0.178406
\(15\) 2.58368 0.667102
\(16\) 1.00000 0.250000
\(17\) 1.37374 0.333182 0.166591 0.986026i \(-0.446724\pi\)
0.166591 + 0.986026i \(0.446724\pi\)
\(18\) 3.67538 0.866295
\(19\) 1.12705 0.258563 0.129282 0.991608i \(-0.458733\pi\)
0.129282 + 0.991608i \(0.458733\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.72470 0.376359
\(22\) −2.84568 −0.606700
\(23\) −0.435841 −0.0908791 −0.0454396 0.998967i \(-0.514469\pi\)
−0.0454396 + 0.998967i \(0.514469\pi\)
\(24\) −2.58368 −0.527391
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) −1.74496 −0.335817
\(28\) −0.667536 −0.126152
\(29\) 3.39742 0.630885 0.315442 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(30\) 2.58368 0.471712
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 7.35231 1.27987
\(34\) 1.37374 0.235595
\(35\) 0.667536 0.112834
\(36\) 3.67538 0.612563
\(37\) 6.66636 1.09594 0.547971 0.836497i \(-0.315400\pi\)
0.547971 + 0.836497i \(0.315400\pi\)
\(38\) 1.12705 0.182832
\(39\) −2.58368 −0.413719
\(40\) −1.00000 −0.158114
\(41\) −4.55705 −0.711692 −0.355846 0.934545i \(-0.615807\pi\)
−0.355846 + 0.934545i \(0.615807\pi\)
\(42\) 1.72470 0.266126
\(43\) −8.44112 −1.28726 −0.643629 0.765337i \(-0.722572\pi\)
−0.643629 + 0.765337i \(0.722572\pi\)
\(44\) −2.84568 −0.429002
\(45\) −3.67538 −0.547893
\(46\) −0.435841 −0.0642613
\(47\) 1.87000 0.272768 0.136384 0.990656i \(-0.456452\pi\)
0.136384 + 0.990656i \(0.456452\pi\)
\(48\) −2.58368 −0.372921
\(49\) −6.55440 −0.936342
\(50\) 1.00000 0.141421
\(51\) −3.54931 −0.497002
\(52\) 1.00000 0.138675
\(53\) 6.09399 0.837074 0.418537 0.908200i \(-0.362543\pi\)
0.418537 + 0.908200i \(0.362543\pi\)
\(54\) −1.74496 −0.237459
\(55\) 2.84568 0.383711
\(56\) −0.667536 −0.0892032
\(57\) −2.91193 −0.385695
\(58\) 3.39742 0.446103
\(59\) 9.16780 1.19355 0.596773 0.802410i \(-0.296449\pi\)
0.596773 + 0.802410i \(0.296449\pi\)
\(60\) 2.58368 0.333551
\(61\) 0.621446 0.0795680 0.0397840 0.999208i \(-0.487333\pi\)
0.0397840 + 0.999208i \(0.487333\pi\)
\(62\) −1.00000 −0.127000
\(63\) −2.45345 −0.309105
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 7.35231 0.905006
\(67\) −15.1922 −1.85602 −0.928011 0.372553i \(-0.878482\pi\)
−0.928011 + 0.372553i \(0.878482\pi\)
\(68\) 1.37374 0.166591
\(69\) 1.12607 0.135563
\(70\) 0.667536 0.0797858
\(71\) −0.573489 −0.0680606 −0.0340303 0.999421i \(-0.510834\pi\)
−0.0340303 + 0.999421i \(0.510834\pi\)
\(72\) 3.67538 0.433147
\(73\) 15.1539 1.77363 0.886815 0.462125i \(-0.152913\pi\)
0.886815 + 0.462125i \(0.152913\pi\)
\(74\) 6.66636 0.774949
\(75\) −2.58368 −0.298337
\(76\) 1.12705 0.129282
\(77\) 1.89959 0.216479
\(78\) −2.58368 −0.292544
\(79\) −8.71493 −0.980507 −0.490253 0.871580i \(-0.663096\pi\)
−0.490253 + 0.871580i \(0.663096\pi\)
\(80\) −1.00000 −0.111803
\(81\) −6.51773 −0.724192
\(82\) −4.55705 −0.503242
\(83\) −14.9770 −1.64394 −0.821971 0.569529i \(-0.807126\pi\)
−0.821971 + 0.569529i \(0.807126\pi\)
\(84\) 1.72470 0.188180
\(85\) −1.37374 −0.149003
\(86\) −8.44112 −0.910229
\(87\) −8.77782 −0.941081
\(88\) −2.84568 −0.303350
\(89\) 0.261768 0.0277474 0.0138737 0.999904i \(-0.495584\pi\)
0.0138737 + 0.999904i \(0.495584\pi\)
\(90\) −3.67538 −0.387419
\(91\) −0.667536 −0.0699768
\(92\) −0.435841 −0.0454396
\(93\) 2.58368 0.267915
\(94\) 1.87000 0.192876
\(95\) −1.12705 −0.115633
\(96\) −2.58368 −0.263695
\(97\) −14.0327 −1.42480 −0.712402 0.701772i \(-0.752393\pi\)
−0.712402 + 0.701772i \(0.752393\pi\)
\(98\) −6.55440 −0.662094
\(99\) −10.4589 −1.05116
\(100\) 1.00000 0.100000
\(101\) −6.89933 −0.686509 −0.343254 0.939242i \(-0.611529\pi\)
−0.343254 + 0.939242i \(0.611529\pi\)
\(102\) −3.54931 −0.351434
\(103\) 19.0139 1.87349 0.936745 0.350012i \(-0.113822\pi\)
0.936745 + 0.350012i \(0.113822\pi\)
\(104\) 1.00000 0.0980581
\(105\) −1.72470 −0.168313
\(106\) 6.09399 0.591900
\(107\) 5.32124 0.514424 0.257212 0.966355i \(-0.417196\pi\)
0.257212 + 0.966355i \(0.417196\pi\)
\(108\) −1.74496 −0.167909
\(109\) −0.774663 −0.0741992 −0.0370996 0.999312i \(-0.511812\pi\)
−0.0370996 + 0.999312i \(0.511812\pi\)
\(110\) 2.84568 0.271325
\(111\) −17.2237 −1.63480
\(112\) −0.667536 −0.0630762
\(113\) 0.172180 0.0161973 0.00809865 0.999967i \(-0.497422\pi\)
0.00809865 + 0.999967i \(0.497422\pi\)
\(114\) −2.91193 −0.272727
\(115\) 0.435841 0.0406424
\(116\) 3.39742 0.315442
\(117\) 3.67538 0.339789
\(118\) 9.16780 0.843965
\(119\) −0.917023 −0.0840633
\(120\) 2.58368 0.235856
\(121\) −2.90212 −0.263829
\(122\) 0.621446 0.0562631
\(123\) 11.7739 1.06162
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −2.45345 −0.218570
\(127\) 9.77114 0.867048 0.433524 0.901142i \(-0.357270\pi\)
0.433524 + 0.901142i \(0.357270\pi\)
\(128\) 1.00000 0.0883883
\(129\) 21.8091 1.92018
\(130\) −1.00000 −0.0877058
\(131\) −15.1936 −1.32747 −0.663735 0.747968i \(-0.731030\pi\)
−0.663735 + 0.747968i \(0.731030\pi\)
\(132\) 7.35231 0.639936
\(133\) −0.752347 −0.0652367
\(134\) −15.1922 −1.31241
\(135\) 1.74496 0.150182
\(136\) 1.37374 0.117798
\(137\) −21.8397 −1.86589 −0.932945 0.360019i \(-0.882770\pi\)
−0.932945 + 0.360019i \(0.882770\pi\)
\(138\) 1.12607 0.0958576
\(139\) −18.7401 −1.58952 −0.794759 0.606926i \(-0.792403\pi\)
−0.794759 + 0.606926i \(0.792403\pi\)
\(140\) 0.667536 0.0564171
\(141\) −4.83147 −0.406883
\(142\) −0.573489 −0.0481261
\(143\) −2.84568 −0.237967
\(144\) 3.67538 0.306281
\(145\) −3.39742 −0.282140
\(146\) 15.1539 1.25415
\(147\) 16.9344 1.39673
\(148\) 6.66636 0.547971
\(149\) −1.27180 −0.104190 −0.0520948 0.998642i \(-0.516590\pi\)
−0.0520948 + 0.998642i \(0.516590\pi\)
\(150\) −2.58368 −0.210956
\(151\) −3.32959 −0.270958 −0.135479 0.990780i \(-0.543257\pi\)
−0.135479 + 0.990780i \(0.543257\pi\)
\(152\) 1.12705 0.0914159
\(153\) 5.04903 0.408189
\(154\) 1.89959 0.153073
\(155\) 1.00000 0.0803219
\(156\) −2.58368 −0.206860
\(157\) −1.80308 −0.143902 −0.0719508 0.997408i \(-0.522922\pi\)
−0.0719508 + 0.997408i \(0.522922\pi\)
\(158\) −8.71493 −0.693323
\(159\) −15.7449 −1.24865
\(160\) −1.00000 −0.0790569
\(161\) 0.290939 0.0229292
\(162\) −6.51773 −0.512081
\(163\) 10.9449 0.857267 0.428633 0.903478i \(-0.358995\pi\)
0.428633 + 0.903478i \(0.358995\pi\)
\(164\) −4.55705 −0.355846
\(165\) −7.35231 −0.572376
\(166\) −14.9770 −1.16244
\(167\) −7.15082 −0.553347 −0.276674 0.960964i \(-0.589232\pi\)
−0.276674 + 0.960964i \(0.589232\pi\)
\(168\) 1.72470 0.133063
\(169\) 1.00000 0.0769231
\(170\) −1.37374 −0.105361
\(171\) 4.14234 0.316772
\(172\) −8.44112 −0.643629
\(173\) −14.1002 −1.07202 −0.536011 0.844211i \(-0.680069\pi\)
−0.536011 + 0.844211i \(0.680069\pi\)
\(174\) −8.77782 −0.665445
\(175\) −0.667536 −0.0504610
\(176\) −2.84568 −0.214501
\(177\) −23.6866 −1.78040
\(178\) 0.261768 0.0196203
\(179\) −22.3539 −1.67081 −0.835403 0.549638i \(-0.814766\pi\)
−0.835403 + 0.549638i \(0.814766\pi\)
\(180\) −3.67538 −0.273946
\(181\) 3.13201 0.232800 0.116400 0.993202i \(-0.462865\pi\)
0.116400 + 0.993202i \(0.462865\pi\)
\(182\) −0.667536 −0.0494810
\(183\) −1.60561 −0.118690
\(184\) −0.435841 −0.0321306
\(185\) −6.66636 −0.490121
\(186\) 2.58368 0.189444
\(187\) −3.90923 −0.285871
\(188\) 1.87000 0.136384
\(189\) 1.16482 0.0847283
\(190\) −1.12705 −0.0817648
\(191\) −11.9729 −0.866328 −0.433164 0.901315i \(-0.642603\pi\)
−0.433164 + 0.901315i \(0.642603\pi\)
\(192\) −2.58368 −0.186461
\(193\) −3.99866 −0.287830 −0.143915 0.989590i \(-0.545969\pi\)
−0.143915 + 0.989590i \(0.545969\pi\)
\(194\) −14.0327 −1.00749
\(195\) 2.58368 0.185021
\(196\) −6.55440 −0.468171
\(197\) 13.0147 0.927256 0.463628 0.886030i \(-0.346547\pi\)
0.463628 + 0.886030i \(0.346547\pi\)
\(198\) −10.4589 −0.743284
\(199\) 12.8215 0.908893 0.454447 0.890774i \(-0.349837\pi\)
0.454447 + 0.890774i \(0.349837\pi\)
\(200\) 1.00000 0.0707107
\(201\) 39.2517 2.76860
\(202\) −6.89933 −0.485435
\(203\) −2.26790 −0.159175
\(204\) −3.54931 −0.248501
\(205\) 4.55705 0.318278
\(206\) 19.0139 1.32476
\(207\) −1.60188 −0.111338
\(208\) 1.00000 0.0693375
\(209\) −3.20722 −0.221848
\(210\) −1.72470 −0.119015
\(211\) −27.0211 −1.86021 −0.930105 0.367292i \(-0.880285\pi\)
−0.930105 + 0.367292i \(0.880285\pi\)
\(212\) 6.09399 0.418537
\(213\) 1.48171 0.101525
\(214\) 5.32124 0.363753
\(215\) 8.44112 0.575679
\(216\) −1.74496 −0.118729
\(217\) 0.667536 0.0453153
\(218\) −0.774663 −0.0524668
\(219\) −39.1528 −2.64570
\(220\) 2.84568 0.191856
\(221\) 1.37374 0.0924080
\(222\) −17.2237 −1.15598
\(223\) 4.99819 0.334704 0.167352 0.985897i \(-0.446478\pi\)
0.167352 + 0.985897i \(0.446478\pi\)
\(224\) −0.667536 −0.0446016
\(225\) 3.67538 0.245025
\(226\) 0.172180 0.0114532
\(227\) −10.0209 −0.665112 −0.332556 0.943084i \(-0.607911\pi\)
−0.332556 + 0.943084i \(0.607911\pi\)
\(228\) −2.91193 −0.192847
\(229\) −11.8143 −0.780710 −0.390355 0.920664i \(-0.627648\pi\)
−0.390355 + 0.920664i \(0.627648\pi\)
\(230\) 0.435841 0.0287385
\(231\) −4.90793 −0.322918
\(232\) 3.39742 0.223051
\(233\) 18.3641 1.20308 0.601538 0.798845i \(-0.294555\pi\)
0.601538 + 0.798845i \(0.294555\pi\)
\(234\) 3.67538 0.240267
\(235\) −1.87000 −0.121985
\(236\) 9.16780 0.596773
\(237\) 22.5166 1.46261
\(238\) −0.917023 −0.0594417
\(239\) −15.7543 −1.01906 −0.509531 0.860452i \(-0.670181\pi\)
−0.509531 + 0.860452i \(0.670181\pi\)
\(240\) 2.58368 0.166776
\(241\) 26.3281 1.69594 0.847970 0.530043i \(-0.177824\pi\)
0.847970 + 0.530043i \(0.177824\pi\)
\(242\) −2.90212 −0.186555
\(243\) 22.0746 1.41608
\(244\) 0.621446 0.0397840
\(245\) 6.55440 0.418745
\(246\) 11.7739 0.750679
\(247\) 1.12705 0.0717125
\(248\) −1.00000 −0.0635001
\(249\) 38.6958 2.45224
\(250\) −1.00000 −0.0632456
\(251\) −11.4360 −0.721835 −0.360918 0.932598i \(-0.617536\pi\)
−0.360918 + 0.932598i \(0.617536\pi\)
\(252\) −2.45345 −0.154553
\(253\) 1.24026 0.0779747
\(254\) 9.77114 0.613096
\(255\) 3.54931 0.222266
\(256\) 1.00000 0.0625000
\(257\) −26.1966 −1.63410 −0.817051 0.576566i \(-0.804392\pi\)
−0.817051 + 0.576566i \(0.804392\pi\)
\(258\) 21.8091 1.35778
\(259\) −4.45003 −0.276512
\(260\) −1.00000 −0.0620174
\(261\) 12.4868 0.772913
\(262\) −15.1936 −0.938663
\(263\) −5.32719 −0.328489 −0.164244 0.986420i \(-0.552519\pi\)
−0.164244 + 0.986420i \(0.552519\pi\)
\(264\) 7.35231 0.452503
\(265\) −6.09399 −0.374351
\(266\) −0.752347 −0.0461293
\(267\) −0.676324 −0.0413903
\(268\) −15.1922 −0.928011
\(269\) −14.8195 −0.903562 −0.451781 0.892129i \(-0.649211\pi\)
−0.451781 + 0.892129i \(0.649211\pi\)
\(270\) 1.74496 0.106195
\(271\) 9.36508 0.568888 0.284444 0.958693i \(-0.408191\pi\)
0.284444 + 0.958693i \(0.408191\pi\)
\(272\) 1.37374 0.0832954
\(273\) 1.72470 0.104383
\(274\) −21.8397 −1.31938
\(275\) −2.84568 −0.171601
\(276\) 1.12607 0.0677815
\(277\) −9.53219 −0.572734 −0.286367 0.958120i \(-0.592448\pi\)
−0.286367 + 0.958120i \(0.592448\pi\)
\(278\) −18.7401 −1.12396
\(279\) −3.67538 −0.220039
\(280\) 0.667536 0.0398929
\(281\) −16.5401 −0.986701 −0.493350 0.869831i \(-0.664228\pi\)
−0.493350 + 0.869831i \(0.664228\pi\)
\(282\) −4.83147 −0.287710
\(283\) −16.8986 −1.00452 −0.502258 0.864718i \(-0.667497\pi\)
−0.502258 + 0.864718i \(0.667497\pi\)
\(284\) −0.573489 −0.0340303
\(285\) 2.91193 0.172488
\(286\) −2.84568 −0.168268
\(287\) 3.04200 0.179563
\(288\) 3.67538 0.216574
\(289\) −15.1128 −0.888990
\(290\) −3.39742 −0.199503
\(291\) 36.2559 2.12536
\(292\) 15.1539 0.886815
\(293\) −20.1637 −1.17798 −0.588989 0.808141i \(-0.700474\pi\)
−0.588989 + 0.808141i \(0.700474\pi\)
\(294\) 16.9344 0.987636
\(295\) −9.16780 −0.533770
\(296\) 6.66636 0.387474
\(297\) 4.96558 0.288132
\(298\) −1.27180 −0.0736732
\(299\) −0.435841 −0.0252053
\(300\) −2.58368 −0.149169
\(301\) 5.63475 0.324781
\(302\) −3.32959 −0.191597
\(303\) 17.8256 1.02406
\(304\) 1.12705 0.0646408
\(305\) −0.621446 −0.0355839
\(306\) 5.04903 0.288634
\(307\) 1.63537 0.0933357 0.0466678 0.998910i \(-0.485140\pi\)
0.0466678 + 0.998910i \(0.485140\pi\)
\(308\) 1.89959 0.108239
\(309\) −49.1256 −2.79466
\(310\) 1.00000 0.0567962
\(311\) 30.0340 1.70307 0.851536 0.524296i \(-0.175671\pi\)
0.851536 + 0.524296i \(0.175671\pi\)
\(312\) −2.58368 −0.146272
\(313\) 14.6006 0.825273 0.412637 0.910896i \(-0.364608\pi\)
0.412637 + 0.910896i \(0.364608\pi\)
\(314\) −1.80308 −0.101754
\(315\) 2.45345 0.138236
\(316\) −8.71493 −0.490253
\(317\) 1.04173 0.0585095 0.0292547 0.999572i \(-0.490687\pi\)
0.0292547 + 0.999572i \(0.490687\pi\)
\(318\) −15.7449 −0.882929
\(319\) −9.66795 −0.541301
\(320\) −1.00000 −0.0559017
\(321\) −13.7484 −0.767359
\(322\) 0.290939 0.0162134
\(323\) 1.54828 0.0861485
\(324\) −6.51773 −0.362096
\(325\) 1.00000 0.0554700
\(326\) 10.9449 0.606179
\(327\) 2.00148 0.110682
\(328\) −4.55705 −0.251621
\(329\) −1.24829 −0.0688206
\(330\) −7.35231 −0.404731
\(331\) −26.6829 −1.46662 −0.733312 0.679892i \(-0.762026\pi\)
−0.733312 + 0.679892i \(0.762026\pi\)
\(332\) −14.9770 −0.821971
\(333\) 24.5014 1.34267
\(334\) −7.15082 −0.391275
\(335\) 15.1922 0.830038
\(336\) 1.72470 0.0940899
\(337\) 21.0760 1.14808 0.574042 0.818826i \(-0.305375\pi\)
0.574042 + 0.818826i \(0.305375\pi\)
\(338\) 1.00000 0.0543928
\(339\) −0.444857 −0.0241613
\(340\) −1.37374 −0.0745017
\(341\) 2.84568 0.154102
\(342\) 4.14234 0.223992
\(343\) 9.04804 0.488548
\(344\) −8.44112 −0.455115
\(345\) −1.12607 −0.0606257
\(346\) −14.1002 −0.758034
\(347\) 15.1484 0.813210 0.406605 0.913604i \(-0.366713\pi\)
0.406605 + 0.913604i \(0.366713\pi\)
\(348\) −8.77782 −0.470541
\(349\) 4.81220 0.257591 0.128796 0.991671i \(-0.458889\pi\)
0.128796 + 0.991671i \(0.458889\pi\)
\(350\) −0.667536 −0.0356813
\(351\) −1.74496 −0.0931389
\(352\) −2.84568 −0.151675
\(353\) −2.98394 −0.158819 −0.0794096 0.996842i \(-0.525304\pi\)
−0.0794096 + 0.996842i \(0.525304\pi\)
\(354\) −23.6866 −1.25893
\(355\) 0.573489 0.0304376
\(356\) 0.261768 0.0138737
\(357\) 2.36929 0.125396
\(358\) −22.3539 −1.18144
\(359\) −30.3642 −1.60256 −0.801281 0.598289i \(-0.795848\pi\)
−0.801281 + 0.598289i \(0.795848\pi\)
\(360\) −3.67538 −0.193709
\(361\) −17.7298 −0.933145
\(362\) 3.13201 0.164615
\(363\) 7.49814 0.393550
\(364\) −0.667536 −0.0349884
\(365\) −15.1539 −0.793191
\(366\) −1.60561 −0.0839268
\(367\) 15.0688 0.786585 0.393293 0.919413i \(-0.371336\pi\)
0.393293 + 0.919413i \(0.371336\pi\)
\(368\) −0.435841 −0.0227198
\(369\) −16.7489 −0.871912
\(370\) −6.66636 −0.346568
\(371\) −4.06796 −0.211198
\(372\) 2.58368 0.133957
\(373\) 1.32323 0.0685141 0.0342571 0.999413i \(-0.489094\pi\)
0.0342571 + 0.999413i \(0.489094\pi\)
\(374\) −3.90923 −0.202141
\(375\) 2.58368 0.133420
\(376\) 1.87000 0.0964379
\(377\) 3.39742 0.174976
\(378\) 1.16482 0.0599119
\(379\) −30.1419 −1.54829 −0.774144 0.633010i \(-0.781819\pi\)
−0.774144 + 0.633010i \(0.781819\pi\)
\(380\) −1.12705 −0.0578165
\(381\) −25.2455 −1.29336
\(382\) −11.9729 −0.612587
\(383\) −14.0592 −0.718394 −0.359197 0.933262i \(-0.616949\pi\)
−0.359197 + 0.933262i \(0.616949\pi\)
\(384\) −2.58368 −0.131848
\(385\) −1.89959 −0.0968121
\(386\) −3.99866 −0.203526
\(387\) −31.0243 −1.57705
\(388\) −14.0327 −0.712402
\(389\) 6.48024 0.328561 0.164281 0.986414i \(-0.447470\pi\)
0.164281 + 0.986414i \(0.447470\pi\)
\(390\) 2.58368 0.130829
\(391\) −0.598734 −0.0302793
\(392\) −6.55440 −0.331047
\(393\) 39.2553 1.98017
\(394\) 13.0147 0.655669
\(395\) 8.71493 0.438496
\(396\) −10.4589 −0.525581
\(397\) 28.0958 1.41009 0.705043 0.709165i \(-0.250928\pi\)
0.705043 + 0.709165i \(0.250928\pi\)
\(398\) 12.8215 0.642684
\(399\) 1.94382 0.0973127
\(400\) 1.00000 0.0500000
\(401\) 31.9072 1.59337 0.796684 0.604396i \(-0.206585\pi\)
0.796684 + 0.604396i \(0.206585\pi\)
\(402\) 39.2517 1.95770
\(403\) −1.00000 −0.0498135
\(404\) −6.89933 −0.343254
\(405\) 6.51773 0.323869
\(406\) −2.26790 −0.112554
\(407\) −18.9703 −0.940323
\(408\) −3.54931 −0.175717
\(409\) 32.7128 1.61755 0.808773 0.588121i \(-0.200132\pi\)
0.808773 + 0.588121i \(0.200132\pi\)
\(410\) 4.55705 0.225057
\(411\) 56.4266 2.78332
\(412\) 19.0139 0.936745
\(413\) −6.11984 −0.301137
\(414\) −1.60188 −0.0787281
\(415\) 14.9770 0.735193
\(416\) 1.00000 0.0490290
\(417\) 48.4184 2.37106
\(418\) −3.20722 −0.156870
\(419\) 22.4404 1.09628 0.548142 0.836385i \(-0.315335\pi\)
0.548142 + 0.836385i \(0.315335\pi\)
\(420\) −1.72470 −0.0841565
\(421\) 9.40354 0.458301 0.229150 0.973391i \(-0.426405\pi\)
0.229150 + 0.973391i \(0.426405\pi\)
\(422\) −27.0211 −1.31537
\(423\) 6.87296 0.334175
\(424\) 6.09399 0.295950
\(425\) 1.37374 0.0666363
\(426\) 1.48171 0.0717890
\(427\) −0.414837 −0.0200754
\(428\) 5.32124 0.257212
\(429\) 7.35231 0.354973
\(430\) 8.44112 0.407067
\(431\) −23.5643 −1.13505 −0.567526 0.823356i \(-0.692099\pi\)
−0.567526 + 0.823356i \(0.692099\pi\)
\(432\) −1.74496 −0.0839543
\(433\) 11.9152 0.572606 0.286303 0.958139i \(-0.407574\pi\)
0.286303 + 0.958139i \(0.407574\pi\)
\(434\) 0.667536 0.0320427
\(435\) 8.77782 0.420864
\(436\) −0.774663 −0.0370996
\(437\) −0.491215 −0.0234980
\(438\) −39.1528 −1.87079
\(439\) −40.6319 −1.93926 −0.969628 0.244583i \(-0.921349\pi\)
−0.969628 + 0.244583i \(0.921349\pi\)
\(440\) 2.84568 0.135662
\(441\) −24.0899 −1.14714
\(442\) 1.37374 0.0653423
\(443\) −21.8424 −1.03776 −0.518882 0.854846i \(-0.673652\pi\)
−0.518882 + 0.854846i \(0.673652\pi\)
\(444\) −17.2237 −0.817401
\(445\) −0.261768 −0.0124090
\(446\) 4.99819 0.236671
\(447\) 3.28591 0.155418
\(448\) −0.667536 −0.0315381
\(449\) 5.96092 0.281313 0.140657 0.990058i \(-0.455079\pi\)
0.140657 + 0.990058i \(0.455079\pi\)
\(450\) 3.67538 0.173259
\(451\) 12.9679 0.610635
\(452\) 0.172180 0.00809865
\(453\) 8.60259 0.404185
\(454\) −10.0209 −0.470305
\(455\) 0.667536 0.0312946
\(456\) −2.91193 −0.136364
\(457\) 28.0231 1.31086 0.655432 0.755254i \(-0.272487\pi\)
0.655432 + 0.755254i \(0.272487\pi\)
\(458\) −11.8143 −0.552045
\(459\) −2.39712 −0.111888
\(460\) 0.435841 0.0203212
\(461\) 9.15109 0.426209 0.213104 0.977029i \(-0.431643\pi\)
0.213104 + 0.977029i \(0.431643\pi\)
\(462\) −4.90793 −0.228337
\(463\) 16.0997 0.748217 0.374109 0.927385i \(-0.377949\pi\)
0.374109 + 0.927385i \(0.377949\pi\)
\(464\) 3.39742 0.157721
\(465\) −2.58368 −0.119815
\(466\) 18.3641 0.850703
\(467\) 1.88462 0.0872100 0.0436050 0.999049i \(-0.486116\pi\)
0.0436050 + 0.999049i \(0.486116\pi\)
\(468\) 3.67538 0.169894
\(469\) 10.1413 0.468283
\(470\) −1.87000 −0.0862567
\(471\) 4.65858 0.214656
\(472\) 9.16780 0.421982
\(473\) 24.0207 1.10447
\(474\) 22.5166 1.03422
\(475\) 1.12705 0.0517126
\(476\) −0.917023 −0.0420317
\(477\) 22.3977 1.02552
\(478\) −15.7543 −0.720586
\(479\) 33.4694 1.52926 0.764628 0.644472i \(-0.222923\pi\)
0.764628 + 0.644472i \(0.222923\pi\)
\(480\) 2.58368 0.117928
\(481\) 6.66636 0.303960
\(482\) 26.3281 1.19921
\(483\) −0.751693 −0.0342032
\(484\) −2.90212 −0.131915
\(485\) 14.0327 0.637191
\(486\) 22.0746 1.00132
\(487\) 26.8466 1.21654 0.608268 0.793732i \(-0.291865\pi\)
0.608268 + 0.793732i \(0.291865\pi\)
\(488\) 0.621446 0.0281315
\(489\) −28.2779 −1.27877
\(490\) 6.55440 0.296097
\(491\) 18.1787 0.820393 0.410196 0.911997i \(-0.365460\pi\)
0.410196 + 0.911997i \(0.365460\pi\)
\(492\) 11.7739 0.530810
\(493\) 4.66718 0.210199
\(494\) 1.12705 0.0507084
\(495\) 10.4589 0.470094
\(496\) −1.00000 −0.0449013
\(497\) 0.382824 0.0171720
\(498\) 38.6958 1.73400
\(499\) −2.88109 −0.128975 −0.0644877 0.997919i \(-0.520541\pi\)
−0.0644877 + 0.997919i \(0.520541\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 18.4754 0.825420
\(502\) −11.4360 −0.510414
\(503\) 27.4648 1.22460 0.612298 0.790627i \(-0.290245\pi\)
0.612298 + 0.790627i \(0.290245\pi\)
\(504\) −2.45345 −0.109285
\(505\) 6.89933 0.307016
\(506\) 1.24026 0.0551364
\(507\) −2.58368 −0.114745
\(508\) 9.77114 0.433524
\(509\) −23.1987 −1.02826 −0.514132 0.857711i \(-0.671886\pi\)
−0.514132 + 0.857711i \(0.671886\pi\)
\(510\) 3.54931 0.157166
\(511\) −10.1158 −0.447495
\(512\) 1.00000 0.0441942
\(513\) −1.96665 −0.0868299
\(514\) −26.1966 −1.15548
\(515\) −19.0139 −0.837851
\(516\) 21.8091 0.960092
\(517\) −5.32142 −0.234036
\(518\) −4.45003 −0.195523
\(519\) 36.4305 1.59912
\(520\) −1.00000 −0.0438529
\(521\) −13.7819 −0.603797 −0.301899 0.953340i \(-0.597620\pi\)
−0.301899 + 0.953340i \(0.597620\pi\)
\(522\) 12.4868 0.546532
\(523\) −23.4117 −1.02372 −0.511861 0.859068i \(-0.671044\pi\)
−0.511861 + 0.859068i \(0.671044\pi\)
\(524\) −15.1936 −0.663735
\(525\) 1.72470 0.0752719
\(526\) −5.32719 −0.232276
\(527\) −1.37374 −0.0598412
\(528\) 7.35231 0.319968
\(529\) −22.8100 −0.991741
\(530\) −6.09399 −0.264706
\(531\) 33.6951 1.46224
\(532\) −0.752347 −0.0326184
\(533\) −4.55705 −0.197388
\(534\) −0.676324 −0.0292674
\(535\) −5.32124 −0.230057
\(536\) −15.1922 −0.656203
\(537\) 57.7551 2.49232
\(538\) −14.8195 −0.638915
\(539\) 18.6517 0.803385
\(540\) 1.74496 0.0750910
\(541\) −7.63228 −0.328137 −0.164069 0.986449i \(-0.552462\pi\)
−0.164069 + 0.986449i \(0.552462\pi\)
\(542\) 9.36508 0.402265
\(543\) −8.09209 −0.347265
\(544\) 1.37374 0.0588988
\(545\) 0.774663 0.0331829
\(546\) 1.72470 0.0738102
\(547\) −8.05877 −0.344568 −0.172284 0.985047i \(-0.555115\pi\)
−0.172284 + 0.985047i \(0.555115\pi\)
\(548\) −21.8397 −0.932945
\(549\) 2.28405 0.0974808
\(550\) −2.84568 −0.121340
\(551\) 3.82906 0.163123
\(552\) 1.12607 0.0479288
\(553\) 5.81753 0.247386
\(554\) −9.53219 −0.404984
\(555\) 17.2237 0.731106
\(556\) −18.7401 −0.794759
\(557\) −9.73541 −0.412503 −0.206251 0.978499i \(-0.566126\pi\)
−0.206251 + 0.978499i \(0.566126\pi\)
\(558\) −3.67538 −0.155591
\(559\) −8.44112 −0.357021
\(560\) 0.667536 0.0282085
\(561\) 10.1002 0.426430
\(562\) −16.5401 −0.697703
\(563\) −26.7207 −1.12614 −0.563072 0.826408i \(-0.690381\pi\)
−0.563072 + 0.826408i \(0.690381\pi\)
\(564\) −4.83147 −0.203442
\(565\) −0.172180 −0.00724366
\(566\) −16.8986 −0.710300
\(567\) 4.35082 0.182717
\(568\) −0.573489 −0.0240630
\(569\) −24.1738 −1.01342 −0.506710 0.862117i \(-0.669138\pi\)
−0.506710 + 0.862117i \(0.669138\pi\)
\(570\) 2.91193 0.121967
\(571\) −11.2901 −0.472475 −0.236238 0.971695i \(-0.575914\pi\)
−0.236238 + 0.971695i \(0.575914\pi\)
\(572\) −2.84568 −0.118984
\(573\) 30.9341 1.29229
\(574\) 3.04200 0.126970
\(575\) −0.435841 −0.0181758
\(576\) 3.67538 0.153141
\(577\) 26.3661 1.09764 0.548818 0.835942i \(-0.315078\pi\)
0.548818 + 0.835942i \(0.315078\pi\)
\(578\) −15.1128 −0.628611
\(579\) 10.3312 0.429351
\(580\) −3.39742 −0.141070
\(581\) 9.99770 0.414774
\(582\) 36.2559 1.50286
\(583\) −17.3415 −0.718213
\(584\) 15.1539 0.627073
\(585\) −3.67538 −0.151958
\(586\) −20.1637 −0.832956
\(587\) −6.94172 −0.286515 −0.143258 0.989685i \(-0.545758\pi\)
−0.143258 + 0.989685i \(0.545758\pi\)
\(588\) 16.9344 0.698364
\(589\) −1.12705 −0.0464393
\(590\) −9.16780 −0.377432
\(591\) −33.6256 −1.38317
\(592\) 6.66636 0.273986
\(593\) 20.0038 0.821458 0.410729 0.911757i \(-0.365274\pi\)
0.410729 + 0.911757i \(0.365274\pi\)
\(594\) 4.96558 0.203740
\(595\) 0.917023 0.0375943
\(596\) −1.27180 −0.0520948
\(597\) −33.1266 −1.35578
\(598\) −0.435841 −0.0178229
\(599\) −34.0007 −1.38923 −0.694615 0.719382i \(-0.744425\pi\)
−0.694615 + 0.719382i \(0.744425\pi\)
\(600\) −2.58368 −0.105478
\(601\) 45.0090 1.83595 0.917977 0.396634i \(-0.129822\pi\)
0.917977 + 0.396634i \(0.129822\pi\)
\(602\) 5.63475 0.229655
\(603\) −55.8370 −2.27386
\(604\) −3.32959 −0.135479
\(605\) 2.90212 0.117988
\(606\) 17.8256 0.724117
\(607\) −25.3651 −1.02954 −0.514768 0.857330i \(-0.672122\pi\)
−0.514768 + 0.857330i \(0.672122\pi\)
\(608\) 1.12705 0.0457079
\(609\) 5.85951 0.237439
\(610\) −0.621446 −0.0251616
\(611\) 1.87000 0.0756521
\(612\) 5.04903 0.204095
\(613\) −3.70474 −0.149633 −0.0748166 0.997197i \(-0.523837\pi\)
−0.0748166 + 0.997197i \(0.523837\pi\)
\(614\) 1.63537 0.0659983
\(615\) −11.7739 −0.474771
\(616\) 1.89959 0.0765367
\(617\) −14.0120 −0.564101 −0.282051 0.959400i \(-0.591015\pi\)
−0.282051 + 0.959400i \(0.591015\pi\)
\(618\) −49.1256 −1.97612
\(619\) 29.1480 1.17156 0.585778 0.810472i \(-0.300789\pi\)
0.585778 + 0.810472i \(0.300789\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0.760524 0.0305188
\(622\) 30.0340 1.20425
\(623\) −0.174740 −0.00700079
\(624\) −2.58368 −0.103430
\(625\) 1.00000 0.0400000
\(626\) 14.6006 0.583556
\(627\) 8.28642 0.330928
\(628\) −1.80308 −0.0719508
\(629\) 9.15787 0.365148
\(630\) 2.45345 0.0977476
\(631\) 39.1209 1.55738 0.778689 0.627411i \(-0.215885\pi\)
0.778689 + 0.627411i \(0.215885\pi\)
\(632\) −8.71493 −0.346661
\(633\) 69.8138 2.77485
\(634\) 1.04173 0.0413724
\(635\) −9.77114 −0.387756
\(636\) −15.7449 −0.624325
\(637\) −6.55440 −0.259695
\(638\) −9.66795 −0.382758
\(639\) −2.10779 −0.0833828
\(640\) −1.00000 −0.0395285
\(641\) 24.1876 0.955351 0.477675 0.878536i \(-0.341480\pi\)
0.477675 + 0.878536i \(0.341480\pi\)
\(642\) −13.7484 −0.542605
\(643\) 35.0258 1.38128 0.690642 0.723197i \(-0.257328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(644\) 0.290939 0.0114646
\(645\) −21.8091 −0.858733
\(646\) 1.54828 0.0609162
\(647\) 8.28752 0.325816 0.162908 0.986641i \(-0.447913\pi\)
0.162908 + 0.986641i \(0.447913\pi\)
\(648\) −6.51773 −0.256041
\(649\) −26.0886 −1.02407
\(650\) 1.00000 0.0392232
\(651\) −1.72470 −0.0675961
\(652\) 10.9449 0.428633
\(653\) −14.5057 −0.567650 −0.283825 0.958876i \(-0.591603\pi\)
−0.283825 + 0.958876i \(0.591603\pi\)
\(654\) 2.00148 0.0782639
\(655\) 15.1936 0.593663
\(656\) −4.55705 −0.177923
\(657\) 55.6963 2.17292
\(658\) −1.24829 −0.0486635
\(659\) −26.9167 −1.04853 −0.524263 0.851556i \(-0.675659\pi\)
−0.524263 + 0.851556i \(0.675659\pi\)
\(660\) −7.35231 −0.286188
\(661\) 6.37499 0.247958 0.123979 0.992285i \(-0.460434\pi\)
0.123979 + 0.992285i \(0.460434\pi\)
\(662\) −26.6829 −1.03706
\(663\) −3.54931 −0.137844
\(664\) −14.9770 −0.581221
\(665\) 0.752347 0.0291747
\(666\) 24.5014 0.949410
\(667\) −1.48073 −0.0573342
\(668\) −7.15082 −0.276674
\(669\) −12.9137 −0.499273
\(670\) 15.1922 0.586926
\(671\) −1.76843 −0.0682696
\(672\) 1.72470 0.0665316
\(673\) −36.2686 −1.39805 −0.699027 0.715096i \(-0.746383\pi\)
−0.699027 + 0.715096i \(0.746383\pi\)
\(674\) 21.0760 0.811817
\(675\) −1.74496 −0.0671634
\(676\) 1.00000 0.0384615
\(677\) −1.21930 −0.0468617 −0.0234308 0.999725i \(-0.507459\pi\)
−0.0234308 + 0.999725i \(0.507459\pi\)
\(678\) −0.444857 −0.0170846
\(679\) 9.36732 0.359485
\(680\) −1.37374 −0.0526806
\(681\) 25.8908 0.992138
\(682\) 2.84568 0.108967
\(683\) 14.6388 0.560138 0.280069 0.959980i \(-0.409643\pi\)
0.280069 + 0.959980i \(0.409643\pi\)
\(684\) 4.14234 0.158386
\(685\) 21.8397 0.834451
\(686\) 9.04804 0.345456
\(687\) 30.5243 1.16457
\(688\) −8.44112 −0.321815
\(689\) 6.09399 0.232162
\(690\) −1.12607 −0.0428688
\(691\) 40.2830 1.53244 0.766218 0.642580i \(-0.222136\pi\)
0.766218 + 0.642580i \(0.222136\pi\)
\(692\) −14.1002 −0.536011
\(693\) 6.98172 0.265213
\(694\) 15.1484 0.575026
\(695\) 18.7401 0.710854
\(696\) −8.77782 −0.332722
\(697\) −6.26022 −0.237123
\(698\) 4.81220 0.182144
\(699\) −47.4470 −1.79461
\(700\) −0.667536 −0.0252305
\(701\) 48.5761 1.83470 0.917348 0.398087i \(-0.130326\pi\)
0.917348 + 0.398087i \(0.130326\pi\)
\(702\) −1.74496 −0.0658592
\(703\) 7.51333 0.283370
\(704\) −2.84568 −0.107250
\(705\) 4.83147 0.181964
\(706\) −2.98394 −0.112302
\(707\) 4.60555 0.173209
\(708\) −23.6866 −0.890198
\(709\) −43.4382 −1.63136 −0.815679 0.578505i \(-0.803636\pi\)
−0.815679 + 0.578505i \(0.803636\pi\)
\(710\) 0.573489 0.0215226
\(711\) −32.0307 −1.20124
\(712\) 0.261768 0.00981017
\(713\) 0.435841 0.0163224
\(714\) 2.36929 0.0886684
\(715\) 2.84568 0.106422
\(716\) −22.3539 −0.835403
\(717\) 40.7041 1.52012
\(718\) −30.3642 −1.13318
\(719\) 0.909886 0.0339330 0.0169665 0.999856i \(-0.494599\pi\)
0.0169665 + 0.999856i \(0.494599\pi\)
\(720\) −3.67538 −0.136973
\(721\) −12.6924 −0.472691
\(722\) −17.7298 −0.659833
\(723\) −68.0232 −2.52981
\(724\) 3.13201 0.116400
\(725\) 3.39742 0.126177
\(726\) 7.49814 0.278282
\(727\) 12.8509 0.476612 0.238306 0.971190i \(-0.423408\pi\)
0.238306 + 0.971190i \(0.423408\pi\)
\(728\) −0.667536 −0.0247405
\(729\) −37.4803 −1.38816
\(730\) −15.1539 −0.560871
\(731\) −11.5959 −0.428891
\(732\) −1.60561 −0.0593452
\(733\) 46.8785 1.73150 0.865748 0.500480i \(-0.166843\pi\)
0.865748 + 0.500480i \(0.166843\pi\)
\(734\) 15.0688 0.556200
\(735\) −16.9344 −0.624636
\(736\) −0.435841 −0.0160653
\(737\) 43.2321 1.59247
\(738\) −16.7489 −0.616535
\(739\) −32.3595 −1.19036 −0.595181 0.803591i \(-0.702920\pi\)
−0.595181 + 0.803591i \(0.702920\pi\)
\(740\) −6.66636 −0.245060
\(741\) −2.91193 −0.106973
\(742\) −4.06796 −0.149339
\(743\) 34.3768 1.26116 0.630582 0.776123i \(-0.282816\pi\)
0.630582 + 0.776123i \(0.282816\pi\)
\(744\) 2.58368 0.0947221
\(745\) 1.27180 0.0465950
\(746\) 1.32323 0.0484468
\(747\) −55.0462 −2.01404
\(748\) −3.90923 −0.142936
\(749\) −3.55212 −0.129792
\(750\) 2.58368 0.0943425
\(751\) 4.71021 0.171878 0.0859390 0.996300i \(-0.472611\pi\)
0.0859390 + 0.996300i \(0.472611\pi\)
\(752\) 1.87000 0.0681919
\(753\) 29.5470 1.07675
\(754\) 3.39742 0.123727
\(755\) 3.32959 0.121176
\(756\) 1.16482 0.0423641
\(757\) −42.1212 −1.53092 −0.765461 0.643483i \(-0.777489\pi\)
−0.765461 + 0.643483i \(0.777489\pi\)
\(758\) −30.1419 −1.09480
\(759\) −3.20444 −0.116314
\(760\) −1.12705 −0.0408824
\(761\) −16.0350 −0.581269 −0.290635 0.956834i \(-0.593866\pi\)
−0.290635 + 0.956834i \(0.593866\pi\)
\(762\) −25.2455 −0.914546
\(763\) 0.517115 0.0187208
\(764\) −11.9729 −0.433164
\(765\) −5.04903 −0.182548
\(766\) −14.0592 −0.507981
\(767\) 9.16780 0.331030
\(768\) −2.58368 −0.0932304
\(769\) 18.5000 0.667128 0.333564 0.942727i \(-0.391749\pi\)
0.333564 + 0.942727i \(0.391749\pi\)
\(770\) −1.89959 −0.0684565
\(771\) 67.6836 2.43757
\(772\) −3.99866 −0.143915
\(773\) 37.4399 1.34662 0.673309 0.739361i \(-0.264872\pi\)
0.673309 + 0.739361i \(0.264872\pi\)
\(774\) −31.0243 −1.11515
\(775\) −1.00000 −0.0359211
\(776\) −14.0327 −0.503744
\(777\) 11.4974 0.412468
\(778\) 6.48024 0.232328
\(779\) −5.13603 −0.184017
\(780\) 2.58368 0.0925104
\(781\) 1.63196 0.0583962
\(782\) −0.598734 −0.0214107
\(783\) −5.92835 −0.211862
\(784\) −6.55440 −0.234086
\(785\) 1.80308 0.0643548
\(786\) 39.2553 1.40019
\(787\) −31.8429 −1.13508 −0.567538 0.823347i \(-0.692104\pi\)
−0.567538 + 0.823347i \(0.692104\pi\)
\(788\) 13.0147 0.463628
\(789\) 13.7637 0.490002
\(790\) 8.71493 0.310063
\(791\) −0.114936 −0.00408666
\(792\) −10.4589 −0.371642
\(793\) 0.621446 0.0220682
\(794\) 28.0958 0.997081
\(795\) 15.7449 0.558414
\(796\) 12.8215 0.454447
\(797\) −26.5286 −0.939692 −0.469846 0.882748i \(-0.655691\pi\)
−0.469846 + 0.882748i \(0.655691\pi\)
\(798\) 1.94382 0.0688105
\(799\) 2.56890 0.0908812
\(800\) 1.00000 0.0353553
\(801\) 0.962097 0.0339940
\(802\) 31.9072 1.12668
\(803\) −43.1231 −1.52178
\(804\) 39.2517 1.38430
\(805\) −0.290939 −0.0102543
\(806\) −1.00000 −0.0352235
\(807\) 38.2888 1.34783
\(808\) −6.89933 −0.242718
\(809\) −39.7194 −1.39646 −0.698229 0.715874i \(-0.746028\pi\)
−0.698229 + 0.715874i \(0.746028\pi\)
\(810\) 6.51773 0.229010
\(811\) −16.4908 −0.579071 −0.289536 0.957167i \(-0.593501\pi\)
−0.289536 + 0.957167i \(0.593501\pi\)
\(812\) −2.26790 −0.0795876
\(813\) −24.1963 −0.848602
\(814\) −18.9703 −0.664909
\(815\) −10.9449 −0.383381
\(816\) −3.54931 −0.124251
\(817\) −9.51357 −0.332838
\(818\) 32.7128 1.14378
\(819\) −2.45345 −0.0857303
\(820\) 4.55705 0.159139
\(821\) −51.5885 −1.80045 −0.900226 0.435423i \(-0.856599\pi\)
−0.900226 + 0.435423i \(0.856599\pi\)
\(822\) 56.4266 1.96811
\(823\) 24.9637 0.870179 0.435089 0.900387i \(-0.356717\pi\)
0.435089 + 0.900387i \(0.356717\pi\)
\(824\) 19.0139 0.662379
\(825\) 7.35231 0.255974
\(826\) −6.11984 −0.212936
\(827\) 13.0834 0.454954 0.227477 0.973783i \(-0.426952\pi\)
0.227477 + 0.973783i \(0.426952\pi\)
\(828\) −1.60188 −0.0556692
\(829\) −3.65472 −0.126934 −0.0634669 0.997984i \(-0.520216\pi\)
−0.0634669 + 0.997984i \(0.520216\pi\)
\(830\) 14.9770 0.519860
\(831\) 24.6281 0.854339
\(832\) 1.00000 0.0346688
\(833\) −9.00406 −0.311972
\(834\) 48.4184 1.67659
\(835\) 7.15082 0.247464
\(836\) −3.20722 −0.110924
\(837\) 1.74496 0.0603145
\(838\) 22.4404 0.775190
\(839\) −6.68690 −0.230857 −0.115429 0.993316i \(-0.536824\pi\)
−0.115429 + 0.993316i \(0.536824\pi\)
\(840\) −1.72470 −0.0595077
\(841\) −17.4576 −0.601985
\(842\) 9.40354 0.324067
\(843\) 42.7343 1.47185
\(844\) −27.0211 −0.930105
\(845\) −1.00000 −0.0344010
\(846\) 6.87296 0.236297
\(847\) 1.93727 0.0665654
\(848\) 6.09399 0.209268
\(849\) 43.6604 1.49842
\(850\) 1.37374 0.0471190
\(851\) −2.90547 −0.0995983
\(852\) 1.48171 0.0507625
\(853\) −29.7239 −1.01773 −0.508864 0.860847i \(-0.669934\pi\)
−0.508864 + 0.860847i \(0.669934\pi\)
\(854\) −0.414837 −0.0141954
\(855\) −4.14234 −0.141665
\(856\) 5.32124 0.181876
\(857\) −16.5202 −0.564320 −0.282160 0.959367i \(-0.591051\pi\)
−0.282160 + 0.959367i \(0.591051\pi\)
\(858\) 7.35231 0.251004
\(859\) 27.6703 0.944099 0.472049 0.881572i \(-0.343514\pi\)
0.472049 + 0.881572i \(0.343514\pi\)
\(860\) 8.44112 0.287840
\(861\) −7.85953 −0.267852
\(862\) −23.5643 −0.802603
\(863\) 15.7292 0.535427 0.267713 0.963499i \(-0.413732\pi\)
0.267713 + 0.963499i \(0.413732\pi\)
\(864\) −1.74496 −0.0593646
\(865\) 14.1002 0.479423
\(866\) 11.9152 0.404893
\(867\) 39.0466 1.32609
\(868\) 0.667536 0.0226576
\(869\) 24.7999 0.841279
\(870\) 8.77782 0.297596
\(871\) −15.1922 −0.514768
\(872\) −0.774663 −0.0262334
\(873\) −51.5754 −1.74556
\(874\) −0.491215 −0.0166156
\(875\) 0.667536 0.0225668
\(876\) −39.1528 −1.32285
\(877\) −25.8797 −0.873896 −0.436948 0.899487i \(-0.643941\pi\)
−0.436948 + 0.899487i \(0.643941\pi\)
\(878\) −40.6319 −1.37126
\(879\) 52.0965 1.75717
\(880\) 2.84568 0.0959278
\(881\) −5.80538 −0.195588 −0.0977941 0.995207i \(-0.531179\pi\)
−0.0977941 + 0.995207i \(0.531179\pi\)
\(882\) −24.0899 −0.811149
\(883\) 0.215006 0.00723552 0.00361776 0.999993i \(-0.498848\pi\)
0.00361776 + 0.999993i \(0.498848\pi\)
\(884\) 1.37374 0.0462040
\(885\) 23.6866 0.796217
\(886\) −21.8424 −0.733811
\(887\) 49.7454 1.67029 0.835144 0.550031i \(-0.185384\pi\)
0.835144 + 0.550031i \(0.185384\pi\)
\(888\) −17.2237 −0.577990
\(889\) −6.52258 −0.218760
\(890\) −0.261768 −0.00877449
\(891\) 18.5474 0.621360
\(892\) 4.99819 0.167352
\(893\) 2.10759 0.0705276
\(894\) 3.28591 0.109897
\(895\) 22.3539 0.747207
\(896\) −0.667536 −0.0223008
\(897\) 1.12607 0.0375984
\(898\) 5.96092 0.198919
\(899\) −3.39742 −0.113310
\(900\) 3.67538 0.122513
\(901\) 8.37157 0.278898
\(902\) 12.9679 0.431784
\(903\) −14.5584 −0.484472
\(904\) 0.172180 0.00572661
\(905\) −3.13201 −0.104111
\(906\) 8.60259 0.285802
\(907\) 8.64404 0.287021 0.143510 0.989649i \(-0.454161\pi\)
0.143510 + 0.989649i \(0.454161\pi\)
\(908\) −10.0209 −0.332556
\(909\) −25.3576 −0.841060
\(910\) 0.667536 0.0221286
\(911\) −18.2160 −0.603524 −0.301762 0.953383i \(-0.597575\pi\)
−0.301762 + 0.953383i \(0.597575\pi\)
\(912\) −2.91193 −0.0964237
\(913\) 42.6198 1.41051
\(914\) 28.0231 0.926920
\(915\) 1.60561 0.0530800
\(916\) −11.8143 −0.390355
\(917\) 10.1423 0.334927
\(918\) −2.39712 −0.0791168
\(919\) 0.0211494 0.000697654 0 0.000348827 1.00000i \(-0.499889\pi\)
0.000348827 1.00000i \(0.499889\pi\)
\(920\) 0.435841 0.0143693
\(921\) −4.22527 −0.139227
\(922\) 9.15109 0.301375
\(923\) −0.573489 −0.0188766
\(924\) −4.90793 −0.161459
\(925\) 6.66636 0.219189
\(926\) 16.0997 0.529069
\(927\) 69.8831 2.29526
\(928\) 3.39742 0.111526
\(929\) 33.7466 1.10719 0.553596 0.832785i \(-0.313255\pi\)
0.553596 + 0.832785i \(0.313255\pi\)
\(930\) −2.58368 −0.0847220
\(931\) −7.38714 −0.242104
\(932\) 18.3641 0.601538
\(933\) −77.5981 −2.54045
\(934\) 1.88462 0.0616668
\(935\) 3.90923 0.127845
\(936\) 3.67538 0.120133
\(937\) 6.07998 0.198624 0.0993122 0.995056i \(-0.468336\pi\)
0.0993122 + 0.995056i \(0.468336\pi\)
\(938\) 10.1413 0.331126
\(939\) −37.7232 −1.23105
\(940\) −1.87000 −0.0609927
\(941\) −20.2623 −0.660531 −0.330266 0.943888i \(-0.607138\pi\)
−0.330266 + 0.943888i \(0.607138\pi\)
\(942\) 4.65858 0.151785
\(943\) 1.98615 0.0646780
\(944\) 9.16780 0.298387
\(945\) −1.16482 −0.0378916
\(946\) 24.0207 0.780980
\(947\) −39.3941 −1.28014 −0.640069 0.768318i \(-0.721094\pi\)
−0.640069 + 0.768318i \(0.721094\pi\)
\(948\) 22.5166 0.731304
\(949\) 15.1539 0.491916
\(950\) 1.12705 0.0365664
\(951\) −2.69150 −0.0872777
\(952\) −0.917023 −0.0297209
\(953\) −0.213052 −0.00690142 −0.00345071 0.999994i \(-0.501098\pi\)
−0.00345071 + 0.999994i \(0.501098\pi\)
\(954\) 22.3977 0.725153
\(955\) 11.9729 0.387434
\(956\) −15.7543 −0.509531
\(957\) 24.9788 0.807452
\(958\) 33.4694 1.08135
\(959\) 14.5788 0.470773
\(960\) 2.58368 0.0833878
\(961\) 1.00000 0.0322581
\(962\) 6.66636 0.214932
\(963\) 19.5576 0.630234
\(964\) 26.3281 0.847970
\(965\) 3.99866 0.128721
\(966\) −0.751693 −0.0241853
\(967\) −46.6253 −1.49937 −0.749685 0.661795i \(-0.769795\pi\)
−0.749685 + 0.661795i \(0.769795\pi\)
\(968\) −2.90212 −0.0932777
\(969\) −4.00025 −0.128506
\(970\) 14.0327 0.450562
\(971\) 26.2579 0.842657 0.421328 0.906908i \(-0.361564\pi\)
0.421328 + 0.906908i \(0.361564\pi\)
\(972\) 22.0746 0.708042
\(973\) 12.5097 0.401043
\(974\) 26.8466 0.860220
\(975\) −2.58368 −0.0827438
\(976\) 0.621446 0.0198920
\(977\) 7.45597 0.238538 0.119269 0.992862i \(-0.461945\pi\)
0.119269 + 0.992862i \(0.461945\pi\)
\(978\) −28.2779 −0.904229
\(979\) −0.744908 −0.0238073
\(980\) 6.55440 0.209373
\(981\) −2.84718 −0.0909034
\(982\) 18.1787 0.580105
\(983\) −16.0620 −0.512298 −0.256149 0.966637i \(-0.582454\pi\)
−0.256149 + 0.966637i \(0.582454\pi\)
\(984\) 11.7739 0.375340
\(985\) −13.0147 −0.414681
\(986\) 4.66718 0.148633
\(987\) 3.22518 0.102659
\(988\) 1.12705 0.0358563
\(989\) 3.67899 0.116985
\(990\) 10.4589 0.332407
\(991\) 35.1127 1.11539 0.557696 0.830045i \(-0.311686\pi\)
0.557696 + 0.830045i \(0.311686\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 68.9399 2.18774
\(994\) 0.382824 0.0121424
\(995\) −12.8215 −0.406469
\(996\) 38.6958 1.22612
\(997\) 6.23411 0.197436 0.0987181 0.995115i \(-0.468526\pi\)
0.0987181 + 0.995115i \(0.468526\pi\)
\(998\) −2.88109 −0.0911994
\(999\) −11.6325 −0.368036
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 \(a_p\))