Properties

Label 6017.2.a.c.1.8
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} +O(q^{10})\) \(q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} -3.45239 q^{10} +1.00000 q^{11} +13.0550 q^{12} -0.296690 q^{13} +9.30109 q^{14} +3.79217 q^{15} +8.10076 q^{16} -4.19377 q^{17} -12.8297 q^{18} +0.592754 q^{19} +6.19872 q^{20} -10.2165 q^{21} -2.57284 q^{22} +1.33653 q^{23} -19.0464 q^{24} -3.19941 q^{25} +0.763336 q^{26} +5.61428 q^{27} -16.7000 q^{28} +5.99718 q^{29} -9.75665 q^{30} +7.96398 q^{31} -7.36287 q^{32} +2.82606 q^{33} +10.7899 q^{34} -4.85097 q^{35} +23.0356 q^{36} -7.24254 q^{37} -1.52506 q^{38} -0.838464 q^{39} -9.04352 q^{40} -10.4646 q^{41} +26.2854 q^{42} -3.89021 q^{43} +4.61950 q^{44} +6.69133 q^{45} -3.43868 q^{46} -5.62283 q^{47} +22.8932 q^{48} +6.06900 q^{49} +8.23157 q^{50} -11.8518 q^{51} -1.37056 q^{52} -11.7607 q^{53} -14.4446 q^{54} +1.34186 q^{55} +24.3642 q^{56} +1.67516 q^{57} -15.4298 q^{58} -6.98866 q^{59} +17.5179 q^{60} -1.94629 q^{61} -20.4900 q^{62} -18.0271 q^{63} +2.74194 q^{64} -0.398117 q^{65} -7.27099 q^{66} -8.97316 q^{67} -19.3731 q^{68} +3.77711 q^{69} +12.4808 q^{70} +2.79874 q^{71} -33.6075 q^{72} +1.22988 q^{73} +18.6339 q^{74} -9.04173 q^{75} +2.73822 q^{76} -3.61511 q^{77} +2.15723 q^{78} +12.7100 q^{79} +10.8701 q^{80} +0.906459 q^{81} +26.9238 q^{82} -16.2683 q^{83} -47.1951 q^{84} -5.62745 q^{85} +10.0089 q^{86} +16.9484 q^{87} -6.73954 q^{88} +4.80932 q^{89} -17.2157 q^{90} +1.07257 q^{91} +6.17410 q^{92} +22.5067 q^{93} +14.4666 q^{94} +0.795392 q^{95} -20.8079 q^{96} +3.11996 q^{97} -15.6146 q^{98} +4.98661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} + O(q^{10}) \) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} - 30q^{10} + 106q^{11} - 26q^{12} - 72q^{13} + 3q^{14} - 46q^{15} + 75q^{16} - 65q^{17} - 37q^{18} - 63q^{19} - 25q^{20} - 27q^{21} - 13q^{22} - 23q^{23} - 56q^{24} + 74q^{25} + 2q^{26} - 54q^{27} - 115q^{28} - 45q^{29} - 14q^{30} - 89q^{31} - 96q^{32} - 15q^{33} - 26q^{34} - 52q^{35} + 91q^{36} - 35q^{37} + 7q^{38} - 34q^{39} - 74q^{40} - 32q^{41} - 94q^{43} + 93q^{44} - 46q^{45} - 20q^{46} - 105q^{47} - 57q^{48} + 80q^{49} - 60q^{50} - 36q^{51} - 137q^{52} - 61q^{54} - 12q^{55} + 32q^{56} - 71q^{57} - 28q^{58} - 15q^{59} - 21q^{60} - 80q^{61} - 84q^{62} - 182q^{63} + 55q^{64} - 73q^{65} - 22q^{66} - 58q^{67} - 145q^{68} - 8q^{69} - 39q^{70} - 11q^{71} - 100q^{72} - 155q^{73} - 15q^{74} - 15q^{75} - 132q^{76} - 66q^{77} - 45q^{78} - 50q^{79} - 28q^{80} + 114q^{81} - 57q^{82} - 96q^{83} - 27q^{84} - 74q^{85} + 54q^{86} - 182q^{87} - 39q^{88} + 9q^{89} - 53q^{90} + 6q^{91} - 18q^{92} - 26q^{93} - 33q^{94} - 49q^{95} - 56q^{96} - 102q^{97} - 76q^{98} + 97q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57284 −1.81927 −0.909636 0.415407i \(-0.863639\pi\)
−0.909636 + 0.415407i \(0.863639\pi\)
\(3\) 2.82606 1.63163 0.815813 0.578316i \(-0.196290\pi\)
0.815813 + 0.578316i \(0.196290\pi\)
\(4\) 4.61950 2.30975
\(5\) 1.34186 0.600098 0.300049 0.953924i \(-0.402997\pi\)
0.300049 + 0.953924i \(0.402997\pi\)
\(6\) −7.27099 −2.96837
\(7\) −3.61511 −1.36638 −0.683191 0.730240i \(-0.739408\pi\)
−0.683191 + 0.730240i \(0.739408\pi\)
\(8\) −6.73954 −2.38279
\(9\) 4.98661 1.66220
\(10\) −3.45239 −1.09174
\(11\) 1.00000 0.301511
\(12\) 13.0550 3.76865
\(13\) −0.296690 −0.0822871 −0.0411435 0.999153i \(-0.513100\pi\)
−0.0411435 + 0.999153i \(0.513100\pi\)
\(14\) 9.30109 2.48582
\(15\) 3.79217 0.979135
\(16\) 8.10076 2.02519
\(17\) −4.19377 −1.01714 −0.508569 0.861021i \(-0.669825\pi\)
−0.508569 + 0.861021i \(0.669825\pi\)
\(18\) −12.8297 −3.02400
\(19\) 0.592754 0.135987 0.0679935 0.997686i \(-0.478340\pi\)
0.0679935 + 0.997686i \(0.478340\pi\)
\(20\) 6.19872 1.38608
\(21\) −10.2165 −2.22942
\(22\) −2.57284 −0.548531
\(23\) 1.33653 0.278686 0.139343 0.990244i \(-0.455501\pi\)
0.139343 + 0.990244i \(0.455501\pi\)
\(24\) −19.0464 −3.88782
\(25\) −3.19941 −0.639883
\(26\) 0.763336 0.149703
\(27\) 5.61428 1.08047
\(28\) −16.7000 −3.15600
\(29\) 5.99718 1.11365 0.556824 0.830631i \(-0.312020\pi\)
0.556824 + 0.830631i \(0.312020\pi\)
\(30\) −9.75665 −1.78131
\(31\) 7.96398 1.43037 0.715187 0.698933i \(-0.246342\pi\)
0.715187 + 0.698933i \(0.246342\pi\)
\(32\) −7.36287 −1.30158
\(33\) 2.82606 0.491954
\(34\) 10.7899 1.85045
\(35\) −4.85097 −0.819963
\(36\) 23.0356 3.83927
\(37\) −7.24254 −1.19067 −0.595333 0.803479i \(-0.702980\pi\)
−0.595333 + 0.803479i \(0.702980\pi\)
\(38\) −1.52506 −0.247397
\(39\) −0.838464 −0.134262
\(40\) −9.04352 −1.42991
\(41\) −10.4646 −1.63430 −0.817151 0.576424i \(-0.804448\pi\)
−0.817151 + 0.576424i \(0.804448\pi\)
\(42\) 26.2854 4.05593
\(43\) −3.89021 −0.593252 −0.296626 0.954994i \(-0.595861\pi\)
−0.296626 + 0.954994i \(0.595861\pi\)
\(44\) 4.61950 0.696415
\(45\) 6.69133 0.997485
\(46\) −3.43868 −0.507005
\(47\) −5.62283 −0.820175 −0.410087 0.912046i \(-0.634502\pi\)
−0.410087 + 0.912046i \(0.634502\pi\)
\(48\) 22.8932 3.30435
\(49\) 6.06900 0.867000
\(50\) 8.23157 1.16412
\(51\) −11.8518 −1.65959
\(52\) −1.37056 −0.190063
\(53\) −11.7607 −1.61545 −0.807725 0.589559i \(-0.799301\pi\)
−0.807725 + 0.589559i \(0.799301\pi\)
\(54\) −14.4446 −1.96567
\(55\) 1.34186 0.180936
\(56\) 24.3642 3.25580
\(57\) 1.67516 0.221880
\(58\) −15.4298 −2.02603
\(59\) −6.98866 −0.909846 −0.454923 0.890531i \(-0.650333\pi\)
−0.454923 + 0.890531i \(0.650333\pi\)
\(60\) 17.5179 2.26156
\(61\) −1.94629 −0.249196 −0.124598 0.992207i \(-0.539764\pi\)
−0.124598 + 0.992207i \(0.539764\pi\)
\(62\) −20.4900 −2.60224
\(63\) −18.0271 −2.27121
\(64\) 2.74194 0.342743
\(65\) −0.398117 −0.0493803
\(66\) −7.27099 −0.894998
\(67\) −8.97316 −1.09625 −0.548123 0.836398i \(-0.684657\pi\)
−0.548123 + 0.836398i \(0.684657\pi\)
\(68\) −19.3731 −2.34934
\(69\) 3.77711 0.454711
\(70\) 12.4808 1.49174
\(71\) 2.79874 0.332150 0.166075 0.986113i \(-0.446891\pi\)
0.166075 + 0.986113i \(0.446891\pi\)
\(72\) −33.6075 −3.96068
\(73\) 1.22988 0.143947 0.0719734 0.997407i \(-0.477070\pi\)
0.0719734 + 0.997407i \(0.477070\pi\)
\(74\) 18.6339 2.16615
\(75\) −9.04173 −1.04405
\(76\) 2.73822 0.314096
\(77\) −3.61511 −0.411980
\(78\) 2.15723 0.244259
\(79\) 12.7100 1.42998 0.714991 0.699134i \(-0.246431\pi\)
0.714991 + 0.699134i \(0.246431\pi\)
\(80\) 10.8701 1.21531
\(81\) 0.906459 0.100718
\(82\) 26.9238 2.97324
\(83\) −16.2683 −1.78568 −0.892838 0.450379i \(-0.851289\pi\)
−0.892838 + 0.450379i \(0.851289\pi\)
\(84\) −47.1951 −5.14941
\(85\) −5.62745 −0.610383
\(86\) 10.0089 1.07929
\(87\) 16.9484 1.81706
\(88\) −6.73954 −0.718438
\(89\) 4.80932 0.509787 0.254894 0.966969i \(-0.417960\pi\)
0.254894 + 0.966969i \(0.417960\pi\)
\(90\) −17.2157 −1.81470
\(91\) 1.07257 0.112436
\(92\) 6.17410 0.643694
\(93\) 22.5067 2.33384
\(94\) 14.4666 1.49212
\(95\) 0.795392 0.0816055
\(96\) −20.8079 −2.12370
\(97\) 3.11996 0.316784 0.158392 0.987376i \(-0.449369\pi\)
0.158392 + 0.987376i \(0.449369\pi\)
\(98\) −15.6146 −1.57731
\(99\) 4.98661 0.501173
\(100\) −14.7797 −1.47797
\(101\) 14.1519 1.40817 0.704085 0.710116i \(-0.251358\pi\)
0.704085 + 0.710116i \(0.251358\pi\)
\(102\) 30.4929 3.01925
\(103\) −4.84287 −0.477182 −0.238591 0.971120i \(-0.576686\pi\)
−0.238591 + 0.971120i \(0.576686\pi\)
\(104\) 1.99956 0.196073
\(105\) −13.7091 −1.33787
\(106\) 30.2583 2.93894
\(107\) 10.4934 1.01444 0.507219 0.861817i \(-0.330674\pi\)
0.507219 + 0.861817i \(0.330674\pi\)
\(108\) 25.9352 2.49561
\(109\) −1.86581 −0.178712 −0.0893562 0.996000i \(-0.528481\pi\)
−0.0893562 + 0.996000i \(0.528481\pi\)
\(110\) −3.45239 −0.329172
\(111\) −20.4679 −1.94272
\(112\) −29.2851 −2.76719
\(113\) 1.70563 0.160452 0.0802261 0.996777i \(-0.474436\pi\)
0.0802261 + 0.996777i \(0.474436\pi\)
\(114\) −4.30991 −0.403660
\(115\) 1.79344 0.167239
\(116\) 27.7039 2.57225
\(117\) −1.47948 −0.136778
\(118\) 17.9807 1.65526
\(119\) 15.1609 1.38980
\(120\) −25.5575 −2.33307
\(121\) 1.00000 0.0909091
\(122\) 5.00748 0.453356
\(123\) −29.5737 −2.66657
\(124\) 36.7896 3.30380
\(125\) −11.0025 −0.984090
\(126\) 46.3809 4.13194
\(127\) −8.06490 −0.715644 −0.357822 0.933790i \(-0.616481\pi\)
−0.357822 + 0.933790i \(0.616481\pi\)
\(128\) 7.67116 0.678041
\(129\) −10.9940 −0.967965
\(130\) 1.02429 0.0898362
\(131\) 6.62646 0.578956 0.289478 0.957185i \(-0.406518\pi\)
0.289478 + 0.957185i \(0.406518\pi\)
\(132\) 13.0550 1.13629
\(133\) −2.14287 −0.185810
\(134\) 23.0865 1.99437
\(135\) 7.53358 0.648387
\(136\) 28.2641 2.42363
\(137\) 12.2385 1.04561 0.522804 0.852453i \(-0.324886\pi\)
0.522804 + 0.852453i \(0.324886\pi\)
\(138\) −9.71790 −0.827243
\(139\) −10.3449 −0.877440 −0.438720 0.898624i \(-0.644568\pi\)
−0.438720 + 0.898624i \(0.644568\pi\)
\(140\) −22.4090 −1.89391
\(141\) −15.8905 −1.33822
\(142\) −7.20071 −0.604270
\(143\) −0.296690 −0.0248105
\(144\) 40.3954 3.36628
\(145\) 8.04737 0.668297
\(146\) −3.16429 −0.261878
\(147\) 17.1514 1.41462
\(148\) −33.4569 −2.75014
\(149\) −1.88470 −0.154401 −0.0772005 0.997016i \(-0.524598\pi\)
−0.0772005 + 0.997016i \(0.524598\pi\)
\(150\) 23.2629 1.89941
\(151\) −20.1164 −1.63705 −0.818524 0.574472i \(-0.805207\pi\)
−0.818524 + 0.574472i \(0.805207\pi\)
\(152\) −3.99489 −0.324028
\(153\) −20.9127 −1.69069
\(154\) 9.30109 0.749503
\(155\) 10.6865 0.858364
\(156\) −3.87328 −0.310111
\(157\) −8.53604 −0.681250 −0.340625 0.940199i \(-0.610639\pi\)
−0.340625 + 0.940199i \(0.610639\pi\)
\(158\) −32.7007 −2.60152
\(159\) −33.2363 −2.63581
\(160\) −9.87993 −0.781077
\(161\) −4.83170 −0.380791
\(162\) −2.33217 −0.183233
\(163\) 20.3708 1.59557 0.797783 0.602945i \(-0.206006\pi\)
0.797783 + 0.602945i \(0.206006\pi\)
\(164\) −48.3414 −3.77483
\(165\) 3.79217 0.295220
\(166\) 41.8556 3.24863
\(167\) 3.25170 0.251624 0.125812 0.992054i \(-0.459846\pi\)
0.125812 + 0.992054i \(0.459846\pi\)
\(168\) 68.8546 5.31225
\(169\) −12.9120 −0.993229
\(170\) 14.4785 1.11045
\(171\) 2.95583 0.226038
\(172\) −17.9708 −1.37026
\(173\) −13.6488 −1.03770 −0.518851 0.854865i \(-0.673640\pi\)
−0.518851 + 0.854865i \(0.673640\pi\)
\(174\) −43.6054 −3.30572
\(175\) 11.5662 0.874324
\(176\) 8.10076 0.610618
\(177\) −19.7504 −1.48453
\(178\) −12.3736 −0.927441
\(179\) 23.5873 1.76300 0.881499 0.472187i \(-0.156535\pi\)
0.881499 + 0.472187i \(0.156535\pi\)
\(180\) 30.9106 2.30394
\(181\) 8.79771 0.653929 0.326964 0.945037i \(-0.393974\pi\)
0.326964 + 0.945037i \(0.393974\pi\)
\(182\) −2.75954 −0.204551
\(183\) −5.50032 −0.406595
\(184\) −9.00760 −0.664049
\(185\) −9.71847 −0.714516
\(186\) −57.9061 −4.24588
\(187\) −4.19377 −0.306679
\(188\) −25.9747 −1.89440
\(189\) −20.2962 −1.47633
\(190\) −2.04641 −0.148463
\(191\) 0.340337 0.0246259 0.0123130 0.999924i \(-0.496081\pi\)
0.0123130 + 0.999924i \(0.496081\pi\)
\(192\) 7.74889 0.559228
\(193\) 1.18589 0.0853623 0.0426812 0.999089i \(-0.486410\pi\)
0.0426812 + 0.999089i \(0.486410\pi\)
\(194\) −8.02715 −0.576316
\(195\) −1.12510 −0.0805702
\(196\) 28.0357 2.00255
\(197\) −21.7604 −1.55036 −0.775182 0.631739i \(-0.782342\pi\)
−0.775182 + 0.631739i \(0.782342\pi\)
\(198\) −12.8297 −0.911770
\(199\) 0.440890 0.0312539 0.0156269 0.999878i \(-0.495026\pi\)
0.0156269 + 0.999878i \(0.495026\pi\)
\(200\) 21.5626 1.52471
\(201\) −25.3587 −1.78866
\(202\) −36.4106 −2.56184
\(203\) −21.6804 −1.52167
\(204\) −54.7496 −3.83324
\(205\) −14.0421 −0.980741
\(206\) 12.4599 0.868124
\(207\) 6.66476 0.463233
\(208\) −2.40342 −0.166647
\(209\) 0.592754 0.0410016
\(210\) 35.2713 2.43395
\(211\) −26.3894 −1.81672 −0.908362 0.418186i \(-0.862666\pi\)
−0.908362 + 0.418186i \(0.862666\pi\)
\(212\) −54.3283 −3.73128
\(213\) 7.90941 0.541944
\(214\) −26.9979 −1.84554
\(215\) −5.22012 −0.356009
\(216\) −37.8377 −2.57453
\(217\) −28.7907 −1.95444
\(218\) 4.80044 0.325127
\(219\) 3.47572 0.234867
\(220\) 6.19872 0.417917
\(221\) 1.24425 0.0836974
\(222\) 52.6605 3.53434
\(223\) −17.1999 −1.15179 −0.575896 0.817523i \(-0.695347\pi\)
−0.575896 + 0.817523i \(0.695347\pi\)
\(224\) 26.6176 1.77846
\(225\) −15.9542 −1.06362
\(226\) −4.38831 −0.291906
\(227\) 6.51454 0.432385 0.216193 0.976351i \(-0.430636\pi\)
0.216193 + 0.976351i \(0.430636\pi\)
\(228\) 7.73838 0.512487
\(229\) −0.972276 −0.0642498 −0.0321249 0.999484i \(-0.510227\pi\)
−0.0321249 + 0.999484i \(0.510227\pi\)
\(230\) −4.61422 −0.304253
\(231\) −10.2165 −0.672197
\(232\) −40.4182 −2.65359
\(233\) 25.0558 1.64146 0.820732 0.571314i \(-0.193566\pi\)
0.820732 + 0.571314i \(0.193566\pi\)
\(234\) 3.80646 0.248836
\(235\) −7.54505 −0.492185
\(236\) −32.2841 −2.10152
\(237\) 35.9191 2.33320
\(238\) −39.0066 −2.52842
\(239\) 2.80758 0.181607 0.0908037 0.995869i \(-0.471056\pi\)
0.0908037 + 0.995869i \(0.471056\pi\)
\(240\) 30.7195 1.98294
\(241\) −16.3796 −1.05510 −0.527551 0.849523i \(-0.676890\pi\)
−0.527551 + 0.849523i \(0.676890\pi\)
\(242\) −2.57284 −0.165388
\(243\) −14.2811 −0.916135
\(244\) −8.99086 −0.575581
\(245\) 8.14375 0.520285
\(246\) 76.0883 4.85121
\(247\) −0.175864 −0.0111900
\(248\) −53.6736 −3.40828
\(249\) −45.9751 −2.91355
\(250\) 28.3076 1.79033
\(251\) −9.40382 −0.593564 −0.296782 0.954945i \(-0.595913\pi\)
−0.296782 + 0.954945i \(0.595913\pi\)
\(252\) −83.2763 −5.24592
\(253\) 1.33653 0.0840269
\(254\) 20.7497 1.30195
\(255\) −15.9035 −0.995916
\(256\) −25.2205 −1.57628
\(257\) 2.15675 0.134534 0.0672671 0.997735i \(-0.478572\pi\)
0.0672671 + 0.997735i \(0.478572\pi\)
\(258\) 28.2857 1.76099
\(259\) 26.1826 1.62691
\(260\) −1.83910 −0.114056
\(261\) 29.9056 1.85111
\(262\) −17.0488 −1.05328
\(263\) −6.74037 −0.415629 −0.207815 0.978168i \(-0.566635\pi\)
−0.207815 + 0.978168i \(0.566635\pi\)
\(264\) −19.0464 −1.17222
\(265\) −15.7811 −0.969428
\(266\) 5.51325 0.338039
\(267\) 13.5914 0.831782
\(268\) −41.4515 −2.53205
\(269\) 9.58429 0.584365 0.292182 0.956363i \(-0.405619\pi\)
0.292182 + 0.956363i \(0.405619\pi\)
\(270\) −19.3827 −1.17959
\(271\) 9.70651 0.589629 0.294814 0.955555i \(-0.404742\pi\)
0.294814 + 0.955555i \(0.404742\pi\)
\(272\) −33.9728 −2.05990
\(273\) 3.03114 0.183453
\(274\) −31.4877 −1.90224
\(275\) −3.19941 −0.192932
\(276\) 17.4484 1.05027
\(277\) 5.63887 0.338807 0.169404 0.985547i \(-0.445816\pi\)
0.169404 + 0.985547i \(0.445816\pi\)
\(278\) 26.6157 1.59630
\(279\) 39.7133 2.37757
\(280\) 32.6933 1.95380
\(281\) 1.62335 0.0968409 0.0484205 0.998827i \(-0.484581\pi\)
0.0484205 + 0.998827i \(0.484581\pi\)
\(282\) 40.8836 2.43458
\(283\) −13.8259 −0.821864 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(284\) 12.9288 0.767182
\(285\) 2.24782 0.133150
\(286\) 0.763336 0.0451370
\(287\) 37.8308 2.23308
\(288\) −36.7158 −2.16350
\(289\) 0.587717 0.0345716
\(290\) −20.7046 −1.21581
\(291\) 8.81719 0.516873
\(292\) 5.68144 0.332481
\(293\) −19.6258 −1.14655 −0.573277 0.819362i \(-0.694328\pi\)
−0.573277 + 0.819362i \(0.694328\pi\)
\(294\) −44.1277 −2.57358
\(295\) −9.37780 −0.545996
\(296\) 48.8114 2.83711
\(297\) 5.61428 0.325774
\(298\) 4.84904 0.280897
\(299\) −0.396535 −0.0229322
\(300\) −41.7683 −2.41149
\(301\) 14.0635 0.810609
\(302\) 51.7562 2.97824
\(303\) 39.9942 2.29761
\(304\) 4.80176 0.275400
\(305\) −2.61164 −0.149542
\(306\) 53.8050 3.07583
\(307\) 28.8752 1.64799 0.823997 0.566594i \(-0.191739\pi\)
0.823997 + 0.566594i \(0.191739\pi\)
\(308\) −16.7000 −0.951570
\(309\) −13.6862 −0.778583
\(310\) −27.4948 −1.56160
\(311\) −19.4470 −1.10274 −0.551370 0.834261i \(-0.685895\pi\)
−0.551370 + 0.834261i \(0.685895\pi\)
\(312\) 5.65087 0.319917
\(313\) −23.7564 −1.34279 −0.671396 0.741099i \(-0.734305\pi\)
−0.671396 + 0.741099i \(0.734305\pi\)
\(314\) 21.9618 1.23938
\(315\) −24.1899 −1.36295
\(316\) 58.7136 3.30290
\(317\) 9.72984 0.546482 0.273241 0.961946i \(-0.411904\pi\)
0.273241 + 0.961946i \(0.411904\pi\)
\(318\) 85.5116 4.79526
\(319\) 5.99718 0.335777
\(320\) 3.67930 0.205679
\(321\) 29.6550 1.65518
\(322\) 12.4312 0.692763
\(323\) −2.48587 −0.138318
\(324\) 4.18739 0.232633
\(325\) 0.949235 0.0526541
\(326\) −52.4108 −2.90277
\(327\) −5.27290 −0.291592
\(328\) 70.5269 3.89420
\(329\) 20.3272 1.12067
\(330\) −9.75665 −0.537086
\(331\) 8.72398 0.479514 0.239757 0.970833i \(-0.422932\pi\)
0.239757 + 0.970833i \(0.422932\pi\)
\(332\) −75.1513 −4.12446
\(333\) −36.1157 −1.97913
\(334\) −8.36611 −0.457773
\(335\) −12.0407 −0.657854
\(336\) −82.7615 −4.51501
\(337\) 31.8345 1.73413 0.867067 0.498191i \(-0.166002\pi\)
0.867067 + 0.498191i \(0.166002\pi\)
\(338\) 33.2204 1.80695
\(339\) 4.82021 0.261798
\(340\) −25.9960 −1.40983
\(341\) 7.96398 0.431274
\(342\) −7.60488 −0.411225
\(343\) 3.36565 0.181728
\(344\) 26.2183 1.41359
\(345\) 5.06835 0.272871
\(346\) 35.1162 1.88786
\(347\) 29.2943 1.57260 0.786300 0.617845i \(-0.211994\pi\)
0.786300 + 0.617845i \(0.211994\pi\)
\(348\) 78.2930 4.19694
\(349\) −27.2253 −1.45734 −0.728669 0.684866i \(-0.759861\pi\)
−0.728669 + 0.684866i \(0.759861\pi\)
\(350\) −29.7580 −1.59063
\(351\) −1.66570 −0.0889086
\(352\) −7.36287 −0.392442
\(353\) −31.1453 −1.65770 −0.828849 0.559473i \(-0.811004\pi\)
−0.828849 + 0.559473i \(0.811004\pi\)
\(354\) 50.8145 2.70076
\(355\) 3.75552 0.199322
\(356\) 22.2167 1.17748
\(357\) 42.8457 2.26763
\(358\) −60.6863 −3.20737
\(359\) 18.5386 0.978432 0.489216 0.872163i \(-0.337283\pi\)
0.489216 + 0.872163i \(0.337283\pi\)
\(360\) −45.0965 −2.37680
\(361\) −18.6486 −0.981508
\(362\) −22.6351 −1.18967
\(363\) 2.82606 0.148330
\(364\) 4.95472 0.259698
\(365\) 1.65033 0.0863821
\(366\) 14.1514 0.739707
\(367\) −9.18248 −0.479322 −0.239661 0.970857i \(-0.577036\pi\)
−0.239661 + 0.970857i \(0.577036\pi\)
\(368\) 10.8269 0.564392
\(369\) −52.1831 −2.71654
\(370\) 25.0041 1.29990
\(371\) 42.5160 2.20732
\(372\) 103.970 5.39057
\(373\) −22.2419 −1.15164 −0.575820 0.817576i \(-0.695317\pi\)
−0.575820 + 0.817576i \(0.695317\pi\)
\(374\) 10.7899 0.557932
\(375\) −31.0936 −1.60567
\(376\) 37.8953 1.95430
\(377\) −1.77930 −0.0916388
\(378\) 52.2189 2.68585
\(379\) −19.5353 −1.00346 −0.501731 0.865024i \(-0.667303\pi\)
−0.501731 + 0.865024i \(0.667303\pi\)
\(380\) 3.67431 0.188488
\(381\) −22.7919 −1.16766
\(382\) −0.875633 −0.0448013
\(383\) 3.99204 0.203983 0.101992 0.994785i \(-0.467478\pi\)
0.101992 + 0.994785i \(0.467478\pi\)
\(384\) 21.6792 1.10631
\(385\) −4.85097 −0.247228
\(386\) −3.05111 −0.155297
\(387\) −19.3990 −0.986106
\(388\) 14.4126 0.731691
\(389\) 24.8590 1.26040 0.630201 0.776432i \(-0.282973\pi\)
0.630201 + 0.776432i \(0.282973\pi\)
\(390\) 2.89470 0.146579
\(391\) −5.60510 −0.283462
\(392\) −40.9023 −2.06588
\(393\) 18.7268 0.944640
\(394\) 55.9859 2.82053
\(395\) 17.0550 0.858129
\(396\) 23.0356 1.15758
\(397\) −35.2361 −1.76845 −0.884225 0.467060i \(-0.845313\pi\)
−0.884225 + 0.467060i \(0.845313\pi\)
\(398\) −1.13434 −0.0568593
\(399\) −6.05587 −0.303173
\(400\) −25.9177 −1.29588
\(401\) −12.8493 −0.641661 −0.320831 0.947137i \(-0.603962\pi\)
−0.320831 + 0.947137i \(0.603962\pi\)
\(402\) 65.2438 3.25406
\(403\) −2.36284 −0.117701
\(404\) 65.3748 3.25252
\(405\) 1.21634 0.0604404
\(406\) 55.7803 2.76833
\(407\) −7.24254 −0.359000
\(408\) 79.8760 3.95445
\(409\) −8.68451 −0.429421 −0.214711 0.976678i \(-0.568881\pi\)
−0.214711 + 0.976678i \(0.568881\pi\)
\(410\) 36.1280 1.78423
\(411\) 34.5868 1.70604
\(412\) −22.3716 −1.10217
\(413\) 25.2648 1.24320
\(414\) −17.1473 −0.842746
\(415\) −21.8297 −1.07158
\(416\) 2.18449 0.107104
\(417\) −29.2352 −1.43165
\(418\) −1.52506 −0.0745931
\(419\) 3.27758 0.160120 0.0800602 0.996790i \(-0.474489\pi\)
0.0800602 + 0.996790i \(0.474489\pi\)
\(420\) −63.3292 −3.09015
\(421\) 0.278301 0.0135635 0.00678177 0.999977i \(-0.497841\pi\)
0.00678177 + 0.999977i \(0.497841\pi\)
\(422\) 67.8957 3.30511
\(423\) −28.0389 −1.36330
\(424\) 79.2615 3.84928
\(425\) 13.4176 0.650850
\(426\) −20.3496 −0.985943
\(427\) 7.03603 0.340498
\(428\) 48.4743 2.34310
\(429\) −0.838464 −0.0404814
\(430\) 13.4305 0.647677
\(431\) −0.925609 −0.0445850 −0.0222925 0.999751i \(-0.507097\pi\)
−0.0222925 + 0.999751i \(0.507097\pi\)
\(432\) 45.4800 2.18816
\(433\) 5.68063 0.272993 0.136497 0.990641i \(-0.456416\pi\)
0.136497 + 0.990641i \(0.456416\pi\)
\(434\) 74.0737 3.55565
\(435\) 22.7423 1.09041
\(436\) −8.61912 −0.412781
\(437\) 0.792233 0.0378976
\(438\) −8.94246 −0.427287
\(439\) −16.2552 −0.775818 −0.387909 0.921698i \(-0.626803\pi\)
−0.387909 + 0.921698i \(0.626803\pi\)
\(440\) −9.04352 −0.431133
\(441\) 30.2638 1.44113
\(442\) −3.20126 −0.152268
\(443\) 36.8367 1.75016 0.875082 0.483975i \(-0.160807\pi\)
0.875082 + 0.483975i \(0.160807\pi\)
\(444\) −94.5512 −4.48720
\(445\) 6.45343 0.305922
\(446\) 44.2526 2.09542
\(447\) −5.32628 −0.251925
\(448\) −9.91242 −0.468318
\(449\) −37.4233 −1.76612 −0.883058 0.469263i \(-0.844520\pi\)
−0.883058 + 0.469263i \(0.844520\pi\)
\(450\) 41.0477 1.93501
\(451\) −10.4646 −0.492760
\(452\) 7.87916 0.370604
\(453\) −56.8501 −2.67105
\(454\) −16.7609 −0.786626
\(455\) 1.43923 0.0674724
\(456\) −11.2898 −0.528693
\(457\) 28.2903 1.32336 0.661682 0.749784i \(-0.269843\pi\)
0.661682 + 0.749784i \(0.269843\pi\)
\(458\) 2.50151 0.116888
\(459\) −23.5450 −1.09899
\(460\) 8.28477 0.386279
\(461\) 12.0127 0.559488 0.279744 0.960075i \(-0.409750\pi\)
0.279744 + 0.960075i \(0.409750\pi\)
\(462\) 26.2854 1.22291
\(463\) −35.8562 −1.66638 −0.833189 0.552988i \(-0.813488\pi\)
−0.833189 + 0.552988i \(0.813488\pi\)
\(464\) 48.5817 2.25535
\(465\) 30.2008 1.40053
\(466\) −64.4647 −2.98627
\(467\) 1.77727 0.0822424 0.0411212 0.999154i \(-0.486907\pi\)
0.0411212 + 0.999154i \(0.486907\pi\)
\(468\) −6.83445 −0.315923
\(469\) 32.4389 1.49789
\(470\) 19.4122 0.895418
\(471\) −24.1233 −1.11155
\(472\) 47.1004 2.16797
\(473\) −3.89021 −0.178872
\(474\) −92.4140 −4.24472
\(475\) −1.89646 −0.0870157
\(476\) 70.0359 3.21009
\(477\) −58.6458 −2.68521
\(478\) −7.22346 −0.330393
\(479\) −16.8139 −0.768247 −0.384123 0.923282i \(-0.625496\pi\)
−0.384123 + 0.923282i \(0.625496\pi\)
\(480\) −27.9213 −1.27443
\(481\) 2.14879 0.0979765
\(482\) 42.1420 1.91952
\(483\) −13.6547 −0.621309
\(484\) 4.61950 0.209977
\(485\) 4.18655 0.190101
\(486\) 36.7431 1.66670
\(487\) −16.0847 −0.728868 −0.364434 0.931229i \(-0.618737\pi\)
−0.364434 + 0.931229i \(0.618737\pi\)
\(488\) 13.1171 0.593782
\(489\) 57.5692 2.60337
\(490\) −20.9525 −0.946540
\(491\) 12.0568 0.544118 0.272059 0.962281i \(-0.412295\pi\)
0.272059 + 0.962281i \(0.412295\pi\)
\(492\) −136.616 −6.15911
\(493\) −25.1508 −1.13273
\(494\) 0.452470 0.0203576
\(495\) 6.69133 0.300753
\(496\) 64.5144 2.89678
\(497\) −10.1178 −0.453843
\(498\) 118.287 5.30055
\(499\) −11.7110 −0.524257 −0.262128 0.965033i \(-0.584424\pi\)
−0.262128 + 0.965033i \(0.584424\pi\)
\(500\) −50.8258 −2.27300
\(501\) 9.18950 0.410557
\(502\) 24.1945 1.07985
\(503\) 26.1561 1.16624 0.583122 0.812385i \(-0.301831\pi\)
0.583122 + 0.812385i \(0.301831\pi\)
\(504\) 121.495 5.41180
\(505\) 18.9899 0.845039
\(506\) −3.43868 −0.152868
\(507\) −36.4900 −1.62058
\(508\) −37.2558 −1.65296
\(509\) −25.7948 −1.14333 −0.571667 0.820486i \(-0.693703\pi\)
−0.571667 + 0.820486i \(0.693703\pi\)
\(510\) 40.9172 1.81184
\(511\) −4.44615 −0.196686
\(512\) 49.5461 2.18965
\(513\) 3.32789 0.146930
\(514\) −5.54896 −0.244754
\(515\) −6.49845 −0.286356
\(516\) −50.7866 −2.23576
\(517\) −5.62283 −0.247292
\(518\) −67.3635 −2.95978
\(519\) −38.5724 −1.69314
\(520\) 2.68312 0.117663
\(521\) 8.81247 0.386081 0.193041 0.981191i \(-0.438165\pi\)
0.193041 + 0.981191i \(0.438165\pi\)
\(522\) −76.9422 −3.36767
\(523\) 22.4392 0.981200 0.490600 0.871385i \(-0.336778\pi\)
0.490600 + 0.871385i \(0.336778\pi\)
\(524\) 30.6109 1.33724
\(525\) 32.6868 1.42657
\(526\) 17.3419 0.756142
\(527\) −33.3991 −1.45489
\(528\) 22.8932 0.996300
\(529\) −21.2137 −0.922334
\(530\) 40.6023 1.76365
\(531\) −34.8497 −1.51235
\(532\) −9.89897 −0.429175
\(533\) 3.10476 0.134482
\(534\) −34.9686 −1.51324
\(535\) 14.0807 0.608762
\(536\) 60.4750 2.61212
\(537\) 66.6591 2.87655
\(538\) −24.6588 −1.06312
\(539\) 6.06900 0.261410
\(540\) 34.8013 1.49761
\(541\) 16.6249 0.714759 0.357379 0.933959i \(-0.383670\pi\)
0.357379 + 0.933959i \(0.383670\pi\)
\(542\) −24.9733 −1.07269
\(543\) 24.8628 1.06697
\(544\) 30.8782 1.32389
\(545\) −2.50366 −0.107245
\(546\) −7.79863 −0.333751
\(547\) 1.00000 0.0427569
\(548\) 56.5358 2.41509
\(549\) −9.70537 −0.414215
\(550\) 8.23157 0.350996
\(551\) 3.55485 0.151442
\(552\) −25.4560 −1.08348
\(553\) −45.9479 −1.95390
\(554\) −14.5079 −0.616382
\(555\) −27.4650 −1.16582
\(556\) −47.7881 −2.02667
\(557\) 13.2525 0.561526 0.280763 0.959777i \(-0.409413\pi\)
0.280763 + 0.959777i \(0.409413\pi\)
\(558\) −102.176 −4.32545
\(559\) 1.15419 0.0488170
\(560\) −39.2965 −1.66058
\(561\) −11.8518 −0.500385
\(562\) −4.17662 −0.176180
\(563\) −8.96867 −0.377984 −0.188992 0.981979i \(-0.560522\pi\)
−0.188992 + 0.981979i \(0.560522\pi\)
\(564\) −73.4060 −3.09095
\(565\) 2.28872 0.0962870
\(566\) 35.5718 1.49519
\(567\) −3.27695 −0.137619
\(568\) −18.8623 −0.791442
\(569\) 29.4542 1.23478 0.617392 0.786655i \(-0.288189\pi\)
0.617392 + 0.786655i \(0.288189\pi\)
\(570\) −5.78329 −0.242235
\(571\) −14.3825 −0.601891 −0.300945 0.953641i \(-0.597302\pi\)
−0.300945 + 0.953641i \(0.597302\pi\)
\(572\) −1.37056 −0.0573060
\(573\) 0.961813 0.0401803
\(574\) −97.3325 −4.06258
\(575\) −4.27611 −0.178326
\(576\) 13.6730 0.569709
\(577\) 32.8631 1.36811 0.684054 0.729431i \(-0.260215\pi\)
0.684054 + 0.729431i \(0.260215\pi\)
\(578\) −1.51210 −0.0628951
\(579\) 3.35140 0.139279
\(580\) 37.1748 1.54360
\(581\) 58.8116 2.43991
\(582\) −22.6852 −0.940332
\(583\) −11.7607 −0.487077
\(584\) −8.28884 −0.342995
\(585\) −1.98525 −0.0820801
\(586\) 50.4941 2.08589
\(587\) −7.18025 −0.296361 −0.148180 0.988960i \(-0.547342\pi\)
−0.148180 + 0.988960i \(0.547342\pi\)
\(588\) 79.2307 3.26742
\(589\) 4.72068 0.194512
\(590\) 24.1276 0.993316
\(591\) −61.4961 −2.52961
\(592\) −58.6701 −2.41133
\(593\) −35.2885 −1.44912 −0.724562 0.689210i \(-0.757958\pi\)
−0.724562 + 0.689210i \(0.757958\pi\)
\(594\) −14.4446 −0.592671
\(595\) 20.3438 0.834016
\(596\) −8.70638 −0.356627
\(597\) 1.24598 0.0509946
\(598\) 1.02022 0.0417200
\(599\) −29.7188 −1.21428 −0.607138 0.794597i \(-0.707682\pi\)
−0.607138 + 0.794597i \(0.707682\pi\)
\(600\) 60.9372 2.48775
\(601\) 8.84367 0.360741 0.180370 0.983599i \(-0.442270\pi\)
0.180370 + 0.983599i \(0.442270\pi\)
\(602\) −36.1832 −1.47472
\(603\) −44.7456 −1.82218
\(604\) −92.9276 −3.78117
\(605\) 1.34186 0.0545543
\(606\) −102.899 −4.17997
\(607\) −18.5685 −0.753671 −0.376836 0.926280i \(-0.622988\pi\)
−0.376836 + 0.926280i \(0.622988\pi\)
\(608\) −4.36437 −0.176998
\(609\) −61.2702 −2.48279
\(610\) 6.71933 0.272058
\(611\) 1.66824 0.0674898
\(612\) −96.6062 −3.90507
\(613\) −9.85988 −0.398237 −0.199118 0.979975i \(-0.563808\pi\)
−0.199118 + 0.979975i \(0.563808\pi\)
\(614\) −74.2912 −2.99815
\(615\) −39.6837 −1.60020
\(616\) 24.3642 0.981661
\(617\) 28.3609 1.14177 0.570884 0.821030i \(-0.306600\pi\)
0.570884 + 0.821030i \(0.306600\pi\)
\(618\) 35.2125 1.41645
\(619\) −3.90217 −0.156841 −0.0784207 0.996920i \(-0.524988\pi\)
−0.0784207 + 0.996920i \(0.524988\pi\)
\(620\) 49.3665 1.98261
\(621\) 7.50366 0.301111
\(622\) 50.0341 2.00619
\(623\) −17.3862 −0.696564
\(624\) −6.79220 −0.271906
\(625\) 1.23332 0.0493327
\(626\) 61.1214 2.44290
\(627\) 1.67516 0.0668993
\(628\) −39.4322 −1.57352
\(629\) 30.3736 1.21107
\(630\) 62.2367 2.47957
\(631\) 13.8419 0.551038 0.275519 0.961296i \(-0.411150\pi\)
0.275519 + 0.961296i \(0.411150\pi\)
\(632\) −85.6593 −3.40734
\(633\) −74.5781 −2.96421
\(634\) −25.0333 −0.994200
\(635\) −10.8220 −0.429456
\(636\) −153.535 −6.08806
\(637\) −1.80061 −0.0713429
\(638\) −15.4298 −0.610870
\(639\) 13.9562 0.552100
\(640\) 10.2936 0.406891
\(641\) 15.0054 0.592678 0.296339 0.955083i \(-0.404234\pi\)
0.296339 + 0.955083i \(0.404234\pi\)
\(642\) −76.2976 −3.01123
\(643\) 42.4178 1.67279 0.836396 0.548125i \(-0.184658\pi\)
0.836396 + 0.548125i \(0.184658\pi\)
\(644\) −22.3200 −0.879532
\(645\) −14.7524 −0.580874
\(646\) 6.39575 0.251637
\(647\) 29.6448 1.16546 0.582728 0.812667i \(-0.301985\pi\)
0.582728 + 0.812667i \(0.301985\pi\)
\(648\) −6.10912 −0.239989
\(649\) −6.98866 −0.274329
\(650\) −2.44223 −0.0957921
\(651\) −81.3641 −3.18891
\(652\) 94.1030 3.68536
\(653\) 30.7970 1.20518 0.602590 0.798051i \(-0.294135\pi\)
0.602590 + 0.798051i \(0.294135\pi\)
\(654\) 13.5663 0.530485
\(655\) 8.89177 0.347430
\(656\) −84.7716 −3.30977
\(657\) 6.13294 0.239269
\(658\) −52.2985 −2.03881
\(659\) −11.3759 −0.443143 −0.221572 0.975144i \(-0.571119\pi\)
−0.221572 + 0.975144i \(0.571119\pi\)
\(660\) 17.5179 0.681885
\(661\) 12.9902 0.505259 0.252630 0.967563i \(-0.418705\pi\)
0.252630 + 0.967563i \(0.418705\pi\)
\(662\) −22.4454 −0.872365
\(663\) 3.51633 0.136563
\(664\) 109.641 4.25489
\(665\) −2.87543 −0.111504
\(666\) 92.9200 3.60058
\(667\) 8.01541 0.310358
\(668\) 15.0212 0.581189
\(669\) −48.6080 −1.87929
\(670\) 30.9788 1.19682
\(671\) −1.94629 −0.0751355
\(672\) 75.2228 2.90178
\(673\) −19.7802 −0.762470 −0.381235 0.924478i \(-0.624501\pi\)
−0.381235 + 0.924478i \(0.624501\pi\)
\(674\) −81.9050 −3.15486
\(675\) −17.9624 −0.691373
\(676\) −59.6468 −2.29411
\(677\) 37.5273 1.44229 0.721146 0.692783i \(-0.243616\pi\)
0.721146 + 0.692783i \(0.243616\pi\)
\(678\) −12.4016 −0.476282
\(679\) −11.2790 −0.432848
\(680\) 37.9265 1.45441
\(681\) 18.4105 0.705491
\(682\) −20.4900 −0.784604
\(683\) −24.7681 −0.947726 −0.473863 0.880598i \(-0.657141\pi\)
−0.473863 + 0.880598i \(0.657141\pi\)
\(684\) 13.6545 0.522091
\(685\) 16.4224 0.627467
\(686\) −8.65928 −0.330613
\(687\) −2.74771 −0.104832
\(688\) −31.5137 −1.20145
\(689\) 3.48927 0.132931
\(690\) −13.0401 −0.496426
\(691\) 15.7083 0.597574 0.298787 0.954320i \(-0.403418\pi\)
0.298787 + 0.954320i \(0.403418\pi\)
\(692\) −63.0507 −2.39683
\(693\) −18.0271 −0.684794
\(694\) −75.3695 −2.86099
\(695\) −13.8813 −0.526550
\(696\) −114.224 −4.32966
\(697\) 43.8863 1.66231
\(698\) 70.0464 2.65129
\(699\) 70.8093 2.67825
\(700\) 53.4302 2.01947
\(701\) −4.45779 −0.168369 −0.0841843 0.996450i \(-0.526828\pi\)
−0.0841843 + 0.996450i \(0.526828\pi\)
\(702\) 4.28558 0.161749
\(703\) −4.29304 −0.161915
\(704\) 2.74194 0.103341
\(705\) −21.3228 −0.803062
\(706\) 80.1318 3.01580
\(707\) −51.1607 −1.92410
\(708\) −91.2368 −3.42889
\(709\) −3.44233 −0.129280 −0.0646398 0.997909i \(-0.520590\pi\)
−0.0646398 + 0.997909i \(0.520590\pi\)
\(710\) −9.66234 −0.362621
\(711\) 63.3796 2.37692
\(712\) −32.4126 −1.21472
\(713\) 10.6441 0.398625
\(714\) −110.235 −4.12544
\(715\) −0.398117 −0.0148887
\(716\) 108.961 4.07208
\(717\) 7.93439 0.296315
\(718\) −47.6969 −1.78003
\(719\) 1.84667 0.0688693 0.0344347 0.999407i \(-0.489037\pi\)
0.0344347 + 0.999407i \(0.489037\pi\)
\(720\) 54.2049 2.02010
\(721\) 17.5075 0.652013
\(722\) 47.9799 1.78563
\(723\) −46.2897 −1.72153
\(724\) 40.6410 1.51041
\(725\) −19.1874 −0.712604
\(726\) −7.27099 −0.269852
\(727\) −39.2268 −1.45484 −0.727421 0.686191i \(-0.759281\pi\)
−0.727421 + 0.686191i \(0.759281\pi\)
\(728\) −7.22862 −0.267910
\(729\) −43.0787 −1.59551
\(730\) −4.24603 −0.157153
\(731\) 16.3147 0.603420
\(732\) −25.4087 −0.939133
\(733\) 25.1196 0.927814 0.463907 0.885884i \(-0.346447\pi\)
0.463907 + 0.885884i \(0.346447\pi\)
\(734\) 23.6250 0.872016
\(735\) 23.0147 0.848911
\(736\) −9.84070 −0.362733
\(737\) −8.97316 −0.330530
\(738\) 134.259 4.94213
\(739\) −2.20942 −0.0812748 −0.0406374 0.999174i \(-0.512939\pi\)
−0.0406374 + 0.999174i \(0.512939\pi\)
\(740\) −44.8945 −1.65035
\(741\) −0.497003 −0.0182579
\(742\) −109.387 −4.01572
\(743\) 3.99593 0.146596 0.0732982 0.997310i \(-0.476648\pi\)
0.0732982 + 0.997310i \(0.476648\pi\)
\(744\) −151.685 −5.56104
\(745\) −2.52901 −0.0926556
\(746\) 57.2248 2.09515
\(747\) −81.1236 −2.96816
\(748\) −19.3731 −0.708351
\(749\) −37.9349 −1.38611
\(750\) 79.9988 2.92114
\(751\) 14.6502 0.534594 0.267297 0.963614i \(-0.413869\pi\)
0.267297 + 0.963614i \(0.413869\pi\)
\(752\) −45.5493 −1.66101
\(753\) −26.5757 −0.968474
\(754\) 4.57786 0.166716
\(755\) −26.9934 −0.982389
\(756\) −93.7584 −3.40996
\(757\) −23.0916 −0.839278 −0.419639 0.907691i \(-0.637843\pi\)
−0.419639 + 0.907691i \(0.637843\pi\)
\(758\) 50.2612 1.82557
\(759\) 3.77711 0.137101
\(760\) −5.36058 −0.194449
\(761\) 10.0058 0.362709 0.181354 0.983418i \(-0.441952\pi\)
0.181354 + 0.983418i \(0.441952\pi\)
\(762\) 58.6398 2.12430
\(763\) 6.74512 0.244190
\(764\) 1.57219 0.0568797
\(765\) −28.0619 −1.01458
\(766\) −10.2709 −0.371101
\(767\) 2.07347 0.0748686
\(768\) −71.2748 −2.57191
\(769\) 20.8232 0.750905 0.375452 0.926842i \(-0.377487\pi\)
0.375452 + 0.926842i \(0.377487\pi\)
\(770\) 12.4808 0.449775
\(771\) 6.09510 0.219510
\(772\) 5.47822 0.197165
\(773\) −0.517597 −0.0186167 −0.00930834 0.999957i \(-0.502963\pi\)
−0.00930834 + 0.999957i \(0.502963\pi\)
\(774\) 49.9104 1.79399
\(775\) −25.4801 −0.915271
\(776\) −21.0271 −0.754829
\(777\) 73.9935 2.65450
\(778\) −63.9582 −2.29301
\(779\) −6.20295 −0.222244
\(780\) −5.19740 −0.186097
\(781\) 2.79874 0.100147
\(782\) 14.4210 0.515695
\(783\) 33.6698 1.20326
\(784\) 49.1636 1.75584
\(785\) −11.4542 −0.408816
\(786\) −48.1809 −1.71856
\(787\) −50.8626 −1.81305 −0.906527 0.422147i \(-0.861277\pi\)
−0.906527 + 0.422147i \(0.861277\pi\)
\(788\) −100.522 −3.58095
\(789\) −19.0487 −0.678151
\(790\) −43.8797 −1.56117
\(791\) −6.16604 −0.219239
\(792\) −33.6075 −1.19419
\(793\) 0.577444 0.0205056
\(794\) 90.6569 3.21729
\(795\) −44.5984 −1.58174
\(796\) 2.03669 0.0721886
\(797\) −7.05967 −0.250066 −0.125033 0.992153i \(-0.539904\pi\)
−0.125033 + 0.992153i \(0.539904\pi\)
\(798\) 15.5808 0.551554
\(799\) 23.5809 0.834232
\(800\) 23.5569 0.832861
\(801\) 23.9822 0.847370
\(802\) 33.0591 1.16736
\(803\) 1.22988 0.0434016
\(804\) −117.144 −4.13136
\(805\) −6.48346 −0.228512
\(806\) 6.07920 0.214131
\(807\) 27.0858 0.953464
\(808\) −95.3775 −3.35537
\(809\) 25.4973 0.896437 0.448219 0.893924i \(-0.352059\pi\)
0.448219 + 0.893924i \(0.352059\pi\)
\(810\) −3.12945 −0.109958
\(811\) 4.69577 0.164891 0.0824454 0.996596i \(-0.473727\pi\)
0.0824454 + 0.996596i \(0.473727\pi\)
\(812\) −100.153 −3.51467
\(813\) 27.4312 0.962054
\(814\) 18.6339 0.653118
\(815\) 27.3348 0.957495
\(816\) −96.0090 −3.36099
\(817\) −2.30594 −0.0806745
\(818\) 22.3438 0.781234
\(819\) 5.34848 0.186891
\(820\) −64.8673 −2.26526
\(821\) −16.5015 −0.575906 −0.287953 0.957645i \(-0.592975\pi\)
−0.287953 + 0.957645i \(0.592975\pi\)
\(822\) −88.9862 −3.10375
\(823\) 4.93114 0.171889 0.0859444 0.996300i \(-0.472609\pi\)
0.0859444 + 0.996300i \(0.472609\pi\)
\(824\) 32.6387 1.13702
\(825\) −9.04173 −0.314793
\(826\) −65.0021 −2.26171
\(827\) 16.6829 0.580122 0.290061 0.957008i \(-0.406324\pi\)
0.290061 + 0.957008i \(0.406324\pi\)
\(828\) 30.7878 1.06995
\(829\) 42.7677 1.48538 0.742691 0.669634i \(-0.233549\pi\)
0.742691 + 0.669634i \(0.233549\pi\)
\(830\) 56.1644 1.94949
\(831\) 15.9358 0.552806
\(832\) −0.813508 −0.0282033
\(833\) −25.4520 −0.881860
\(834\) 75.2174 2.60457
\(835\) 4.36333 0.150999
\(836\) 2.73822 0.0947034
\(837\) 44.7121 1.54547
\(838\) −8.43269 −0.291302
\(839\) −16.9024 −0.583537 −0.291768 0.956489i \(-0.594244\pi\)
−0.291768 + 0.956489i \(0.594244\pi\)
\(840\) 92.3932 3.18787
\(841\) 6.96611 0.240211
\(842\) −0.716023 −0.0246758
\(843\) 4.58768 0.158008
\(844\) −121.906 −4.19617
\(845\) −17.3261 −0.596034
\(846\) 72.1395 2.48021
\(847\) −3.61511 −0.124217
\(848\) −95.2703 −3.27160
\(849\) −39.0728 −1.34098
\(850\) −34.5213 −1.18407
\(851\) −9.67988 −0.331822
\(852\) 36.5375 1.25175
\(853\) −51.0685 −1.74855 −0.874277 0.485428i \(-0.838664\pi\)
−0.874277 + 0.485428i \(0.838664\pi\)
\(854\) −18.1026 −0.619458
\(855\) 3.96631 0.135645
\(856\) −70.7209 −2.41719
\(857\) −7.49913 −0.256165 −0.128083 0.991763i \(-0.540882\pi\)
−0.128083 + 0.991763i \(0.540882\pi\)
\(858\) 2.15723 0.0736467
\(859\) −10.5597 −0.360291 −0.180145 0.983640i \(-0.557657\pi\)
−0.180145 + 0.983640i \(0.557657\pi\)
\(860\) −24.1143 −0.822292
\(861\) 106.912 3.64355
\(862\) 2.38144 0.0811122
\(863\) −24.1987 −0.823734 −0.411867 0.911244i \(-0.635123\pi\)
−0.411867 + 0.911244i \(0.635123\pi\)
\(864\) −41.3372 −1.40632
\(865\) −18.3148 −0.622722
\(866\) −14.6153 −0.496649
\(867\) 1.66092 0.0564079
\(868\) −132.998 −4.51426
\(869\) 12.7100 0.431156
\(870\) −58.5123 −1.98375
\(871\) 2.66225 0.0902068
\(872\) 12.5747 0.425834
\(873\) 15.5580 0.526559
\(874\) −2.03829 −0.0689461
\(875\) 39.7751 1.34464
\(876\) 16.0561 0.542484
\(877\) 31.0382 1.04808 0.524042 0.851692i \(-0.324423\pi\)
0.524042 + 0.851692i \(0.324423\pi\)
\(878\) 41.8220 1.41142
\(879\) −55.4638 −1.87075
\(880\) 10.8701 0.366431
\(881\) 15.0579 0.507315 0.253657 0.967294i \(-0.418366\pi\)
0.253657 + 0.967294i \(0.418366\pi\)
\(882\) −77.8638 −2.62181
\(883\) 46.0845 1.55087 0.775433 0.631429i \(-0.217531\pi\)
0.775433 + 0.631429i \(0.217531\pi\)
\(884\) 5.74782 0.193320
\(885\) −26.5022 −0.890862
\(886\) −94.7748 −3.18402
\(887\) −27.5919 −0.926445 −0.463223 0.886242i \(-0.653307\pi\)
−0.463223 + 0.886242i \(0.653307\pi\)
\(888\) 137.944 4.62910
\(889\) 29.1555 0.977843
\(890\) −16.6036 −0.556555
\(891\) 0.906459 0.0303675
\(892\) −79.4549 −2.66035
\(893\) −3.33296 −0.111533
\(894\) 13.7037 0.458319
\(895\) 31.6508 1.05797
\(896\) −27.7321 −0.926463
\(897\) −1.12063 −0.0374168
\(898\) 96.2842 3.21305
\(899\) 47.7614 1.59293
\(900\) −73.7005 −2.45668
\(901\) 49.3215 1.64314
\(902\) 26.9238 0.896465
\(903\) 39.7444 1.32261
\(904\) −11.4952 −0.382324
\(905\) 11.8053 0.392421
\(906\) 146.266 4.85937
\(907\) 28.0669 0.931946 0.465973 0.884799i \(-0.345704\pi\)
0.465973 + 0.884799i \(0.345704\pi\)
\(908\) 30.0939 0.998701
\(909\) 70.5702 2.34066
\(910\) −3.70292 −0.122751
\(911\) 16.7853 0.556123 0.278061 0.960563i \(-0.410308\pi\)
0.278061 + 0.960563i \(0.410308\pi\)
\(912\) 13.5700 0.449349
\(913\) −16.2683 −0.538401
\(914\) −72.7864 −2.40756
\(915\) −7.38066 −0.243997
\(916\) −4.49143 −0.148401
\(917\) −23.9553 −0.791075
\(918\) 60.5775 1.99936
\(919\) −55.6147 −1.83456 −0.917281 0.398242i \(-0.869621\pi\)
−0.917281 + 0.398242i \(0.869621\pi\)
\(920\) −12.0869 −0.398495
\(921\) 81.6030 2.68891
\(922\) −30.9068 −1.01786
\(923\) −0.830360 −0.0273316
\(924\) −47.1951 −1.55261
\(925\) 23.1719 0.761887
\(926\) 92.2522 3.03160
\(927\) −24.1495 −0.793174
\(928\) −44.1564 −1.44951
\(929\) −38.8290 −1.27394 −0.636968 0.770890i \(-0.719812\pi\)
−0.636968 + 0.770890i \(0.719812\pi\)
\(930\) −77.7018 −2.54794
\(931\) 3.59742 0.117901
\(932\) 115.745 3.79137
\(933\) −54.9585 −1.79926
\(934\) −4.57264 −0.149621
\(935\) −5.62745 −0.184037
\(936\) 9.97102 0.325913
\(937\) −24.2020 −0.790643 −0.395322 0.918543i \(-0.629367\pi\)
−0.395322 + 0.918543i \(0.629367\pi\)
\(938\) −83.4601 −2.72507
\(939\) −67.1370 −2.19093
\(940\) −34.8544 −1.13682
\(941\) −24.0444 −0.783826 −0.391913 0.920002i \(-0.628187\pi\)
−0.391913 + 0.920002i \(0.628187\pi\)
\(942\) 62.0655 2.02220
\(943\) −13.9863 −0.455457
\(944\) −56.6135 −1.84261
\(945\) −27.2347 −0.885944
\(946\) 10.0089 0.325417
\(947\) −41.1051 −1.33574 −0.667868 0.744280i \(-0.732793\pi\)
−0.667868 + 0.744280i \(0.732793\pi\)
\(948\) 165.928 5.38910
\(949\) −0.364894 −0.0118450
\(950\) 4.87930 0.158305
\(951\) 27.4971 0.891655
\(952\) −102.178 −3.31160
\(953\) 5.03137 0.162982 0.0814910 0.996674i \(-0.474032\pi\)
0.0814910 + 0.996674i \(0.474032\pi\)
\(954\) 150.886 4.88512
\(955\) 0.456685 0.0147780
\(956\) 12.9696 0.419467
\(957\) 16.9484 0.547863
\(958\) 43.2595 1.39765
\(959\) −44.2436 −1.42870
\(960\) 10.3979 0.335592
\(961\) 32.4250 1.04597
\(962\) −5.52850 −0.178246
\(963\) 52.3266 1.68620
\(964\) −75.6655 −2.43702
\(965\) 1.59130 0.0512257
\(966\) 35.1313 1.13033
\(967\) −27.0486 −0.869823 −0.434912 0.900473i \(-0.643220\pi\)
−0.434912 + 0.900473i \(0.643220\pi\)
\(968\) −6.73954 −0.216617
\(969\) −7.02522 −0.225683
\(970\) −10.7713 −0.345846
\(971\) −30.6423 −0.983360 −0.491680 0.870776i \(-0.663617\pi\)
−0.491680 + 0.870776i \(0.663617\pi\)
\(972\) −65.9717 −2.11604
\(973\) 37.3978 1.19892
\(974\) 41.3834 1.32601
\(975\) 2.68259 0.0859118
\(976\) −15.7664 −0.504670
\(977\) 40.3902 1.29220 0.646098 0.763254i \(-0.276400\pi\)
0.646098 + 0.763254i \(0.276400\pi\)
\(978\) −148.116 −4.73623
\(979\) 4.80932 0.153707
\(980\) 37.6200 1.20173
\(981\) −9.30409 −0.297057
\(982\) −31.0203 −0.989898
\(983\) 51.7403 1.65026 0.825130 0.564943i \(-0.191102\pi\)
0.825130 + 0.564943i \(0.191102\pi\)
\(984\) 199.313 6.35387
\(985\) −29.1994 −0.930369
\(986\) 64.7089 2.06075
\(987\) 57.4457 1.82852
\(988\) −0.812404 −0.0258460
\(989\) −5.19939 −0.165331
\(990\) −17.2157 −0.547151
\(991\) 7.94887 0.252504 0.126252 0.991998i \(-0.459705\pi\)
0.126252 + 0.991998i \(0.459705\pi\)
\(992\) −58.6378 −1.86175
\(993\) 24.6545 0.782387
\(994\) 26.0314 0.825664
\(995\) 0.591612 0.0187554
\(996\) −212.382 −6.72958
\(997\) −26.1909 −0.829475 −0.414738 0.909941i \(-0.636127\pi\)
−0.414738 + 0.909941i \(0.636127\pi\)
\(998\) 30.1305 0.953766
\(999\) −40.6617 −1.28648
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 \(a_p\))