Properties

Label 8001.2.a.z.1.1
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69601 q^{2} +5.26849 q^{4} +3.35934 q^{5} -1.00000 q^{7} -8.81189 q^{8} +O(q^{10})\) \(q-2.69601 q^{2} +5.26849 q^{4} +3.35934 q^{5} -1.00000 q^{7} -8.81189 q^{8} -9.05682 q^{10} -2.89389 q^{11} -2.10825 q^{13} +2.69601 q^{14} +13.2200 q^{16} +6.29317 q^{17} -0.167183 q^{19} +17.6986 q^{20} +7.80197 q^{22} +4.03441 q^{23} +6.28516 q^{25} +5.68387 q^{26} -5.26849 q^{28} -0.392019 q^{29} -7.54513 q^{31} -18.0175 q^{32} -16.9665 q^{34} -3.35934 q^{35} -2.42977 q^{37} +0.450728 q^{38} -29.6021 q^{40} +0.160937 q^{41} -6.15714 q^{43} -15.2464 q^{44} -10.8768 q^{46} -8.81645 q^{47} +1.00000 q^{49} -16.9449 q^{50} -11.1073 q^{52} +2.87949 q^{53} -9.72156 q^{55} +8.81189 q^{56} +1.05689 q^{58} +3.45891 q^{59} -12.0314 q^{61} +20.3418 q^{62} +22.1354 q^{64} -7.08233 q^{65} +9.36114 q^{67} +33.1555 q^{68} +9.05682 q^{70} +12.0277 q^{71} -11.2562 q^{73} +6.55069 q^{74} -0.880801 q^{76} +2.89389 q^{77} +3.36380 q^{79} +44.4104 q^{80} -0.433889 q^{82} -17.3020 q^{83} +21.1409 q^{85} +16.5997 q^{86} +25.5006 q^{88} -14.6779 q^{89} +2.10825 q^{91} +21.2552 q^{92} +23.7693 q^{94} -0.561624 q^{95} -1.23267 q^{97} -2.69601 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 30q^{4} - 32q^{7} + O(q^{10}) \) \( 32q + 30q^{4} - 32q^{7} - 16q^{10} - 14q^{13} + 18q^{16} - 30q^{19} - 10q^{22} + 36q^{25} - 30q^{28} - 58q^{31} - 34q^{34} + 8q^{37} - 34q^{40} + 6q^{43} - 36q^{46} + 32q^{49} - 56q^{52} - 88q^{55} - 22q^{58} - 46q^{61} + 20q^{64} - 8q^{67} + 16q^{70} - 60q^{73} - 128q^{76} - 74q^{79} - 52q^{82} - 16q^{85} - 64q^{88} + 14q^{91} - 58q^{94} - 44q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69601 −1.90637 −0.953185 0.302389i \(-0.902216\pi\)
−0.953185 + 0.302389i \(0.902216\pi\)
\(3\) 0 0
\(4\) 5.26849 2.63424
\(5\) 3.35934 1.50234 0.751171 0.660107i \(-0.229489\pi\)
0.751171 + 0.660107i \(0.229489\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −8.81189 −3.11547
\(9\) 0 0
\(10\) −9.05682 −2.86402
\(11\) −2.89389 −0.872541 −0.436271 0.899816i \(-0.643701\pi\)
−0.436271 + 0.899816i \(0.643701\pi\)
\(12\) 0 0
\(13\) −2.10825 −0.584723 −0.292362 0.956308i \(-0.594441\pi\)
−0.292362 + 0.956308i \(0.594441\pi\)
\(14\) 2.69601 0.720540
\(15\) 0 0
\(16\) 13.2200 3.30500
\(17\) 6.29317 1.52632 0.763160 0.646210i \(-0.223647\pi\)
0.763160 + 0.646210i \(0.223647\pi\)
\(18\) 0 0
\(19\) −0.167183 −0.0383544 −0.0191772 0.999816i \(-0.506105\pi\)
−0.0191772 + 0.999816i \(0.506105\pi\)
\(20\) 17.6986 3.95754
\(21\) 0 0
\(22\) 7.80197 1.66339
\(23\) 4.03441 0.841233 0.420616 0.907239i \(-0.361814\pi\)
0.420616 + 0.907239i \(0.361814\pi\)
\(24\) 0 0
\(25\) 6.28516 1.25703
\(26\) 5.68387 1.11470
\(27\) 0 0
\(28\) −5.26849 −0.995651
\(29\) −0.392019 −0.0727961 −0.0363981 0.999337i \(-0.511588\pi\)
−0.0363981 + 0.999337i \(0.511588\pi\)
\(30\) 0 0
\(31\) −7.54513 −1.35514 −0.677572 0.735456i \(-0.736968\pi\)
−0.677572 + 0.735456i \(0.736968\pi\)
\(32\) −18.0175 −3.18507
\(33\) 0 0
\(34\) −16.9665 −2.90973
\(35\) −3.35934 −0.567832
\(36\) 0 0
\(37\) −2.42977 −0.399452 −0.199726 0.979852i \(-0.564005\pi\)
−0.199726 + 0.979852i \(0.564005\pi\)
\(38\) 0.450728 0.0731177
\(39\) 0 0
\(40\) −29.6021 −4.68051
\(41\) 0.160937 0.0251342 0.0125671 0.999921i \(-0.496000\pi\)
0.0125671 + 0.999921i \(0.496000\pi\)
\(42\) 0 0
\(43\) −6.15714 −0.938955 −0.469478 0.882944i \(-0.655558\pi\)
−0.469478 + 0.882944i \(0.655558\pi\)
\(44\) −15.2464 −2.29849
\(45\) 0 0
\(46\) −10.8768 −1.60370
\(47\) −8.81645 −1.28601 −0.643006 0.765861i \(-0.722313\pi\)
−0.643006 + 0.765861i \(0.722313\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −16.9449 −2.39637
\(51\) 0 0
\(52\) −11.1073 −1.54030
\(53\) 2.87949 0.395528 0.197764 0.980250i \(-0.436632\pi\)
0.197764 + 0.980250i \(0.436632\pi\)
\(54\) 0 0
\(55\) −9.72156 −1.31086
\(56\) 8.81189 1.17754
\(57\) 0 0
\(58\) 1.05689 0.138776
\(59\) 3.45891 0.450312 0.225156 0.974323i \(-0.427711\pi\)
0.225156 + 0.974323i \(0.427711\pi\)
\(60\) 0 0
\(61\) −12.0314 −1.54046 −0.770232 0.637763i \(-0.779860\pi\)
−0.770232 + 0.637763i \(0.779860\pi\)
\(62\) 20.3418 2.58341
\(63\) 0 0
\(64\) 22.1354 2.76693
\(65\) −7.08233 −0.878455
\(66\) 0 0
\(67\) 9.36114 1.14364 0.571822 0.820377i \(-0.306237\pi\)
0.571822 + 0.820377i \(0.306237\pi\)
\(68\) 33.1555 4.02070
\(69\) 0 0
\(70\) 9.05682 1.08250
\(71\) 12.0277 1.42742 0.713710 0.700441i \(-0.247013\pi\)
0.713710 + 0.700441i \(0.247013\pi\)
\(72\) 0 0
\(73\) −11.2562 −1.31743 −0.658717 0.752390i \(-0.728901\pi\)
−0.658717 + 0.752390i \(0.728901\pi\)
\(74\) 6.55069 0.761503
\(75\) 0 0
\(76\) −0.880801 −0.101035
\(77\) 2.89389 0.329790
\(78\) 0 0
\(79\) 3.36380 0.378457 0.189228 0.981933i \(-0.439401\pi\)
0.189228 + 0.981933i \(0.439401\pi\)
\(80\) 44.4104 4.96524
\(81\) 0 0
\(82\) −0.433889 −0.0479150
\(83\) −17.3020 −1.89914 −0.949569 0.313559i \(-0.898479\pi\)
−0.949569 + 0.313559i \(0.898479\pi\)
\(84\) 0 0
\(85\) 21.1409 2.29305
\(86\) 16.5997 1.79000
\(87\) 0 0
\(88\) 25.5006 2.71838
\(89\) −14.6779 −1.55585 −0.777927 0.628355i \(-0.783729\pi\)
−0.777927 + 0.628355i \(0.783729\pi\)
\(90\) 0 0
\(91\) 2.10825 0.221005
\(92\) 21.2552 2.21601
\(93\) 0 0
\(94\) 23.7693 2.45161
\(95\) −0.561624 −0.0576215
\(96\) 0 0
\(97\) −1.23267 −0.125159 −0.0625793 0.998040i \(-0.519933\pi\)
−0.0625793 + 0.998040i \(0.519933\pi\)
\(98\) −2.69601 −0.272338
\(99\) 0 0
\(100\) 33.1133 3.31133
\(101\) 12.2730 1.22121 0.610603 0.791937i \(-0.290927\pi\)
0.610603 + 0.791937i \(0.290927\pi\)
\(102\) 0 0
\(103\) −3.50168 −0.345030 −0.172515 0.985007i \(-0.555189\pi\)
−0.172515 + 0.985007i \(0.555189\pi\)
\(104\) 18.5777 1.82169
\(105\) 0 0
\(106\) −7.76314 −0.754023
\(107\) 11.7913 1.13991 0.569953 0.821677i \(-0.306961\pi\)
0.569953 + 0.821677i \(0.306961\pi\)
\(108\) 0 0
\(109\) −8.25140 −0.790341 −0.395170 0.918608i \(-0.629314\pi\)
−0.395170 + 0.918608i \(0.629314\pi\)
\(110\) 26.2095 2.49897
\(111\) 0 0
\(112\) −13.2200 −1.24917
\(113\) 13.2805 1.24932 0.624662 0.780895i \(-0.285237\pi\)
0.624662 + 0.780895i \(0.285237\pi\)
\(114\) 0 0
\(115\) 13.5530 1.26382
\(116\) −2.06535 −0.191763
\(117\) 0 0
\(118\) −9.32528 −0.858462
\(119\) −6.29317 −0.576894
\(120\) 0 0
\(121\) −2.62539 −0.238672
\(122\) 32.4368 2.93669
\(123\) 0 0
\(124\) −39.7514 −3.56978
\(125\) 4.31730 0.386151
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −23.6424 −2.08971
\(129\) 0 0
\(130\) 19.0940 1.67466
\(131\) −19.3595 −1.69145 −0.845726 0.533618i \(-0.820832\pi\)
−0.845726 + 0.533618i \(0.820832\pi\)
\(132\) 0 0
\(133\) 0.167183 0.0144966
\(134\) −25.2378 −2.18021
\(135\) 0 0
\(136\) −55.4547 −4.75520
\(137\) −15.6936 −1.34079 −0.670397 0.742003i \(-0.733876\pi\)
−0.670397 + 0.742003i \(0.733876\pi\)
\(138\) 0 0
\(139\) −7.82773 −0.663939 −0.331970 0.943290i \(-0.607713\pi\)
−0.331970 + 0.943290i \(0.607713\pi\)
\(140\) −17.6986 −1.49581
\(141\) 0 0
\(142\) −32.4267 −2.72119
\(143\) 6.10105 0.510195
\(144\) 0 0
\(145\) −1.31693 −0.109365
\(146\) 30.3468 2.51152
\(147\) 0 0
\(148\) −12.8012 −1.05225
\(149\) 15.7545 1.29066 0.645328 0.763905i \(-0.276721\pi\)
0.645328 + 0.763905i \(0.276721\pi\)
\(150\) 0 0
\(151\) −1.99541 −0.162384 −0.0811922 0.996698i \(-0.525873\pi\)
−0.0811922 + 0.996698i \(0.525873\pi\)
\(152\) 1.47320 0.119492
\(153\) 0 0
\(154\) −7.80197 −0.628701
\(155\) −25.3466 −2.03589
\(156\) 0 0
\(157\) 4.40954 0.351919 0.175960 0.984397i \(-0.443697\pi\)
0.175960 + 0.984397i \(0.443697\pi\)
\(158\) −9.06884 −0.721478
\(159\) 0 0
\(160\) −60.5269 −4.78507
\(161\) −4.03441 −0.317956
\(162\) 0 0
\(163\) −9.81692 −0.768921 −0.384460 0.923142i \(-0.625612\pi\)
−0.384460 + 0.923142i \(0.625612\pi\)
\(164\) 0.847896 0.0662095
\(165\) 0 0
\(166\) 46.6463 3.62046
\(167\) 15.3402 1.18706 0.593531 0.804811i \(-0.297734\pi\)
0.593531 + 0.804811i \(0.297734\pi\)
\(168\) 0 0
\(169\) −8.55528 −0.658099
\(170\) −56.9962 −4.37141
\(171\) 0 0
\(172\) −32.4388 −2.47344
\(173\) −12.7598 −0.970110 −0.485055 0.874484i \(-0.661200\pi\)
−0.485055 + 0.874484i \(0.661200\pi\)
\(174\) 0 0
\(175\) −6.28516 −0.475114
\(176\) −38.2572 −2.88375
\(177\) 0 0
\(178\) 39.5718 2.96603
\(179\) −1.20349 −0.0899531 −0.0449766 0.998988i \(-0.514321\pi\)
−0.0449766 + 0.998988i \(0.514321\pi\)
\(180\) 0 0
\(181\) −8.27628 −0.615171 −0.307585 0.951520i \(-0.599521\pi\)
−0.307585 + 0.951520i \(0.599521\pi\)
\(182\) −5.68387 −0.421316
\(183\) 0 0
\(184\) −35.5508 −2.62084
\(185\) −8.16243 −0.600113
\(186\) 0 0
\(187\) −18.2118 −1.33178
\(188\) −46.4494 −3.38767
\(189\) 0 0
\(190\) 1.51415 0.109848
\(191\) 16.1586 1.16920 0.584598 0.811323i \(-0.301252\pi\)
0.584598 + 0.811323i \(0.301252\pi\)
\(192\) 0 0
\(193\) 10.3243 0.743159 0.371579 0.928401i \(-0.378816\pi\)
0.371579 + 0.928401i \(0.378816\pi\)
\(194\) 3.32329 0.238598
\(195\) 0 0
\(196\) 5.26849 0.376321
\(197\) 19.7255 1.40539 0.702693 0.711493i \(-0.251981\pi\)
0.702693 + 0.711493i \(0.251981\pi\)
\(198\) 0 0
\(199\) 1.25357 0.0888634 0.0444317 0.999012i \(-0.485852\pi\)
0.0444317 + 0.999012i \(0.485852\pi\)
\(200\) −55.3841 −3.91625
\(201\) 0 0
\(202\) −33.0881 −2.32807
\(203\) 0.392019 0.0275144
\(204\) 0 0
\(205\) 0.540643 0.0377601
\(206\) 9.44056 0.657755
\(207\) 0 0
\(208\) −27.8710 −1.93251
\(209\) 0.483809 0.0334658
\(210\) 0 0
\(211\) 1.81620 0.125032 0.0625162 0.998044i \(-0.480088\pi\)
0.0625162 + 0.998044i \(0.480088\pi\)
\(212\) 15.1706 1.04192
\(213\) 0 0
\(214\) −31.7894 −2.17308
\(215\) −20.6839 −1.41063
\(216\) 0 0
\(217\) 7.54513 0.512197
\(218\) 22.2459 1.50668
\(219\) 0 0
\(220\) −51.2179 −3.45311
\(221\) −13.2676 −0.892474
\(222\) 0 0
\(223\) 0.622163 0.0416631 0.0208316 0.999783i \(-0.493369\pi\)
0.0208316 + 0.999783i \(0.493369\pi\)
\(224\) 18.0175 1.20384
\(225\) 0 0
\(226\) −35.8044 −2.38167
\(227\) −25.3816 −1.68464 −0.842319 0.538980i \(-0.818810\pi\)
−0.842319 + 0.538980i \(0.818810\pi\)
\(228\) 0 0
\(229\) −0.702452 −0.0464193 −0.0232097 0.999731i \(-0.507389\pi\)
−0.0232097 + 0.999731i \(0.507389\pi\)
\(230\) −36.5389 −2.40931
\(231\) 0 0
\(232\) 3.45443 0.226794
\(233\) −16.1341 −1.05698 −0.528490 0.848939i \(-0.677242\pi\)
−0.528490 + 0.848939i \(0.677242\pi\)
\(234\) 0 0
\(235\) −29.6175 −1.93203
\(236\) 18.2232 1.18623
\(237\) 0 0
\(238\) 16.9665 1.09977
\(239\) −8.34664 −0.539899 −0.269949 0.962874i \(-0.587007\pi\)
−0.269949 + 0.962874i \(0.587007\pi\)
\(240\) 0 0
\(241\) 11.7059 0.754043 0.377021 0.926205i \(-0.376948\pi\)
0.377021 + 0.926205i \(0.376948\pi\)
\(242\) 7.07809 0.454997
\(243\) 0 0
\(244\) −63.3873 −4.05796
\(245\) 3.35934 0.214620
\(246\) 0 0
\(247\) 0.352463 0.0224267
\(248\) 66.4868 4.22192
\(249\) 0 0
\(250\) −11.6395 −0.736146
\(251\) −17.8668 −1.12774 −0.563871 0.825863i \(-0.690689\pi\)
−0.563871 + 0.825863i \(0.690689\pi\)
\(252\) 0 0
\(253\) −11.6751 −0.734010
\(254\) 2.69601 0.169163
\(255\) 0 0
\(256\) 19.4694 1.21683
\(257\) 9.30841 0.580643 0.290321 0.956929i \(-0.406238\pi\)
0.290321 + 0.956929i \(0.406238\pi\)
\(258\) 0 0
\(259\) 2.42977 0.150979
\(260\) −37.3131 −2.31406
\(261\) 0 0
\(262\) 52.1936 3.22453
\(263\) −12.0727 −0.744435 −0.372217 0.928146i \(-0.621402\pi\)
−0.372217 + 0.928146i \(0.621402\pi\)
\(264\) 0 0
\(265\) 9.67318 0.594219
\(266\) −0.450728 −0.0276359
\(267\) 0 0
\(268\) 49.3190 3.01264
\(269\) 27.9575 1.70460 0.852299 0.523056i \(-0.175208\pi\)
0.852299 + 0.523056i \(0.175208\pi\)
\(270\) 0 0
\(271\) −11.6402 −0.707089 −0.353545 0.935418i \(-0.615024\pi\)
−0.353545 + 0.935418i \(0.615024\pi\)
\(272\) 83.1957 5.04448
\(273\) 0 0
\(274\) 42.3101 2.55605
\(275\) −18.1886 −1.09681
\(276\) 0 0
\(277\) 26.0313 1.56407 0.782036 0.623234i \(-0.214181\pi\)
0.782036 + 0.623234i \(0.214181\pi\)
\(278\) 21.1037 1.26571
\(279\) 0 0
\(280\) 29.6021 1.76906
\(281\) −17.6693 −1.05406 −0.527031 0.849846i \(-0.676695\pi\)
−0.527031 + 0.849846i \(0.676695\pi\)
\(282\) 0 0
\(283\) −9.81022 −0.583157 −0.291579 0.956547i \(-0.594180\pi\)
−0.291579 + 0.956547i \(0.594180\pi\)
\(284\) 63.3676 3.76017
\(285\) 0 0
\(286\) −16.4485 −0.972620
\(287\) −0.160937 −0.00949982
\(288\) 0 0
\(289\) 22.6041 1.32965
\(290\) 3.55045 0.208490
\(291\) 0 0
\(292\) −59.3030 −3.47044
\(293\) −18.0827 −1.05641 −0.528203 0.849118i \(-0.677134\pi\)
−0.528203 + 0.849118i \(0.677134\pi\)
\(294\) 0 0
\(295\) 11.6197 0.676523
\(296\) 21.4109 1.24448
\(297\) 0 0
\(298\) −42.4743 −2.46047
\(299\) −8.50554 −0.491888
\(300\) 0 0
\(301\) 6.15714 0.354892
\(302\) 5.37966 0.309565
\(303\) 0 0
\(304\) −2.21016 −0.126761
\(305\) −40.4176 −2.31431
\(306\) 0 0
\(307\) 4.05704 0.231547 0.115774 0.993276i \(-0.463065\pi\)
0.115774 + 0.993276i \(0.463065\pi\)
\(308\) 15.2464 0.868746
\(309\) 0 0
\(310\) 68.3349 3.88116
\(311\) −13.5710 −0.769543 −0.384772 0.923012i \(-0.625720\pi\)
−0.384772 + 0.923012i \(0.625720\pi\)
\(312\) 0 0
\(313\) 23.3786 1.32144 0.660719 0.750633i \(-0.270251\pi\)
0.660719 + 0.750633i \(0.270251\pi\)
\(314\) −11.8882 −0.670888
\(315\) 0 0
\(316\) 17.7221 0.996947
\(317\) 31.8794 1.79053 0.895263 0.445537i \(-0.146987\pi\)
0.895263 + 0.445537i \(0.146987\pi\)
\(318\) 0 0
\(319\) 1.13446 0.0635176
\(320\) 74.3603 4.15687
\(321\) 0 0
\(322\) 10.8768 0.606142
\(323\) −1.05211 −0.0585411
\(324\) 0 0
\(325\) −13.2507 −0.735016
\(326\) 26.4666 1.46585
\(327\) 0 0
\(328\) −1.41816 −0.0783048
\(329\) 8.81645 0.486067
\(330\) 0 0
\(331\) −32.8969 −1.80818 −0.904090 0.427343i \(-0.859450\pi\)
−0.904090 + 0.427343i \(0.859450\pi\)
\(332\) −91.1552 −5.00279
\(333\) 0 0
\(334\) −41.3574 −2.26298
\(335\) 31.4472 1.71815
\(336\) 0 0
\(337\) 12.2361 0.666544 0.333272 0.942831i \(-0.391847\pi\)
0.333272 + 0.942831i \(0.391847\pi\)
\(338\) 23.0652 1.25458
\(339\) 0 0
\(340\) 111.381 6.04046
\(341\) 21.8348 1.18242
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 54.2560 2.92529
\(345\) 0 0
\(346\) 34.4006 1.84939
\(347\) 4.98147 0.267419 0.133710 0.991021i \(-0.457311\pi\)
0.133710 + 0.991021i \(0.457311\pi\)
\(348\) 0 0
\(349\) −7.29876 −0.390693 −0.195347 0.980734i \(-0.562583\pi\)
−0.195347 + 0.980734i \(0.562583\pi\)
\(350\) 16.9449 0.905742
\(351\) 0 0
\(352\) 52.1406 2.77911
\(353\) 12.2191 0.650356 0.325178 0.945653i \(-0.394576\pi\)
0.325178 + 0.945653i \(0.394576\pi\)
\(354\) 0 0
\(355\) 40.4050 2.14447
\(356\) −77.3303 −4.09850
\(357\) 0 0
\(358\) 3.24463 0.171484
\(359\) −36.0746 −1.90395 −0.951973 0.306181i \(-0.900949\pi\)
−0.951973 + 0.306181i \(0.900949\pi\)
\(360\) 0 0
\(361\) −18.9720 −0.998529
\(362\) 22.3130 1.17274
\(363\) 0 0
\(364\) 11.1073 0.582180
\(365\) −37.8133 −1.97924
\(366\) 0 0
\(367\) −25.0223 −1.30616 −0.653078 0.757291i \(-0.726523\pi\)
−0.653078 + 0.757291i \(0.726523\pi\)
\(368\) 53.3348 2.78027
\(369\) 0 0
\(370\) 22.0060 1.14404
\(371\) −2.87949 −0.149496
\(372\) 0 0
\(373\) −12.9187 −0.668905 −0.334452 0.942413i \(-0.608551\pi\)
−0.334452 + 0.942413i \(0.608551\pi\)
\(374\) 49.0992 2.53886
\(375\) 0 0
\(376\) 77.6896 4.00653
\(377\) 0.826474 0.0425656
\(378\) 0 0
\(379\) 1.07672 0.0553076 0.0276538 0.999618i \(-0.491196\pi\)
0.0276538 + 0.999618i \(0.491196\pi\)
\(380\) −2.95891 −0.151789
\(381\) 0 0
\(382\) −43.5638 −2.22892
\(383\) −14.0723 −0.719060 −0.359530 0.933133i \(-0.617063\pi\)
−0.359530 + 0.933133i \(0.617063\pi\)
\(384\) 0 0
\(385\) 9.72156 0.495457
\(386\) −27.8344 −1.41674
\(387\) 0 0
\(388\) −6.49430 −0.329698
\(389\) −0.896424 −0.0454505 −0.0227253 0.999742i \(-0.507234\pi\)
−0.0227253 + 0.999742i \(0.507234\pi\)
\(390\) 0 0
\(391\) 25.3892 1.28399
\(392\) −8.81189 −0.445067
\(393\) 0 0
\(394\) −53.1803 −2.67918
\(395\) 11.3001 0.568571
\(396\) 0 0
\(397\) 15.5645 0.781158 0.390579 0.920569i \(-0.372275\pi\)
0.390579 + 0.920569i \(0.372275\pi\)
\(398\) −3.37965 −0.169406
\(399\) 0 0
\(400\) 83.0898 4.15449
\(401\) 21.5171 1.07451 0.537257 0.843419i \(-0.319461\pi\)
0.537257 + 0.843419i \(0.319461\pi\)
\(402\) 0 0
\(403\) 15.9070 0.792385
\(404\) 64.6600 3.21696
\(405\) 0 0
\(406\) −1.05689 −0.0524525
\(407\) 7.03149 0.348538
\(408\) 0 0
\(409\) −0.413177 −0.0204303 −0.0102151 0.999948i \(-0.503252\pi\)
−0.0102151 + 0.999948i \(0.503252\pi\)
\(410\) −1.45758 −0.0719848
\(411\) 0 0
\(412\) −18.4485 −0.908894
\(413\) −3.45891 −0.170202
\(414\) 0 0
\(415\) −58.1232 −2.85316
\(416\) 37.9854 1.86239
\(417\) 0 0
\(418\) −1.30436 −0.0637982
\(419\) −36.4195 −1.77921 −0.889605 0.456730i \(-0.849020\pi\)
−0.889605 + 0.456730i \(0.849020\pi\)
\(420\) 0 0
\(421\) −13.2124 −0.643934 −0.321967 0.946751i \(-0.604344\pi\)
−0.321967 + 0.946751i \(0.604344\pi\)
\(422\) −4.89650 −0.238358
\(423\) 0 0
\(424\) −25.3737 −1.23226
\(425\) 39.5536 1.91863
\(426\) 0 0
\(427\) 12.0314 0.582241
\(428\) 62.1222 3.00279
\(429\) 0 0
\(430\) 55.7642 2.68919
\(431\) −33.8851 −1.63219 −0.816095 0.577918i \(-0.803865\pi\)
−0.816095 + 0.577918i \(0.803865\pi\)
\(432\) 0 0
\(433\) −4.57030 −0.219635 −0.109817 0.993952i \(-0.535027\pi\)
−0.109817 + 0.993952i \(0.535027\pi\)
\(434\) −20.3418 −0.976436
\(435\) 0 0
\(436\) −43.4724 −2.08195
\(437\) −0.674485 −0.0322650
\(438\) 0 0
\(439\) −15.1264 −0.721945 −0.360973 0.932576i \(-0.617555\pi\)
−0.360973 + 0.932576i \(0.617555\pi\)
\(440\) 85.6653 4.08393
\(441\) 0 0
\(442\) 35.7696 1.70139
\(443\) 21.4687 1.02001 0.510005 0.860171i \(-0.329643\pi\)
0.510005 + 0.860171i \(0.329643\pi\)
\(444\) 0 0
\(445\) −49.3080 −2.33743
\(446\) −1.67736 −0.0794253
\(447\) 0 0
\(448\) −22.1354 −1.04580
\(449\) −27.3231 −1.28945 −0.644727 0.764413i \(-0.723029\pi\)
−0.644727 + 0.764413i \(0.723029\pi\)
\(450\) 0 0
\(451\) −0.465735 −0.0219306
\(452\) 69.9681 3.29102
\(453\) 0 0
\(454\) 68.4292 3.21154
\(455\) 7.08233 0.332025
\(456\) 0 0
\(457\) 17.8679 0.835826 0.417913 0.908487i \(-0.362762\pi\)
0.417913 + 0.908487i \(0.362762\pi\)
\(458\) 1.89382 0.0884924
\(459\) 0 0
\(460\) 71.4036 3.32921
\(461\) 5.37461 0.250320 0.125160 0.992137i \(-0.460056\pi\)
0.125160 + 0.992137i \(0.460056\pi\)
\(462\) 0 0
\(463\) 21.8586 1.01586 0.507928 0.861399i \(-0.330411\pi\)
0.507928 + 0.861399i \(0.330411\pi\)
\(464\) −5.18249 −0.240591
\(465\) 0 0
\(466\) 43.4978 2.01500
\(467\) 32.8761 1.52133 0.760663 0.649147i \(-0.224874\pi\)
0.760663 + 0.649147i \(0.224874\pi\)
\(468\) 0 0
\(469\) −9.36114 −0.432257
\(470\) 79.8491 3.68316
\(471\) 0 0
\(472\) −30.4796 −1.40294
\(473\) 17.8181 0.819277
\(474\) 0 0
\(475\) −1.05077 −0.0482127
\(476\) −33.1555 −1.51968
\(477\) 0 0
\(478\) 22.5026 1.02925
\(479\) −15.8690 −0.725073 −0.362536 0.931970i \(-0.618089\pi\)
−0.362536 + 0.931970i \(0.618089\pi\)
\(480\) 0 0
\(481\) 5.12256 0.233569
\(482\) −31.5592 −1.43748
\(483\) 0 0
\(484\) −13.8318 −0.628720
\(485\) −4.14095 −0.188031
\(486\) 0 0
\(487\) 8.98925 0.407342 0.203671 0.979039i \(-0.434713\pi\)
0.203671 + 0.979039i \(0.434713\pi\)
\(488\) 106.019 4.79927
\(489\) 0 0
\(490\) −9.05682 −0.409146
\(491\) −1.39367 −0.0628953 −0.0314476 0.999505i \(-0.510012\pi\)
−0.0314476 + 0.999505i \(0.510012\pi\)
\(492\) 0 0
\(493\) −2.46705 −0.111110
\(494\) −0.950246 −0.0427536
\(495\) 0 0
\(496\) −99.7465 −4.47875
\(497\) −12.0277 −0.539514
\(498\) 0 0
\(499\) −5.96722 −0.267129 −0.133565 0.991040i \(-0.542642\pi\)
−0.133565 + 0.991040i \(0.542642\pi\)
\(500\) 22.7456 1.01722
\(501\) 0 0
\(502\) 48.1691 2.14989
\(503\) −28.1974 −1.25726 −0.628630 0.777704i \(-0.716384\pi\)
−0.628630 + 0.777704i \(0.716384\pi\)
\(504\) 0 0
\(505\) 41.2291 1.83467
\(506\) 31.4763 1.39929
\(507\) 0 0
\(508\) −5.26849 −0.233751
\(509\) −19.4653 −0.862786 −0.431393 0.902164i \(-0.641978\pi\)
−0.431393 + 0.902164i \(0.641978\pi\)
\(510\) 0 0
\(511\) 11.2562 0.497944
\(512\) −5.20488 −0.230026
\(513\) 0 0
\(514\) −25.0956 −1.10692
\(515\) −11.7633 −0.518354
\(516\) 0 0
\(517\) 25.5139 1.12210
\(518\) −6.55069 −0.287821
\(519\) 0 0
\(520\) 62.4087 2.73680
\(521\) 18.0600 0.791221 0.395611 0.918418i \(-0.370533\pi\)
0.395611 + 0.918418i \(0.370533\pi\)
\(522\) 0 0
\(523\) −0.634346 −0.0277380 −0.0138690 0.999904i \(-0.504415\pi\)
−0.0138690 + 0.999904i \(0.504415\pi\)
\(524\) −101.996 −4.45570
\(525\) 0 0
\(526\) 32.5482 1.41917
\(527\) −47.4828 −2.06838
\(528\) 0 0
\(529\) −6.72353 −0.292328
\(530\) −26.0790 −1.13280
\(531\) 0 0
\(532\) 0.880801 0.0381876
\(533\) −0.339296 −0.0146965
\(534\) 0 0
\(535\) 39.6109 1.71253
\(536\) −82.4893 −3.56299
\(537\) 0 0
\(538\) −75.3737 −3.24959
\(539\) −2.89389 −0.124649
\(540\) 0 0
\(541\) 12.8668 0.553186 0.276593 0.960987i \(-0.410795\pi\)
0.276593 + 0.960987i \(0.410795\pi\)
\(542\) 31.3820 1.34797
\(543\) 0 0
\(544\) −113.387 −4.86144
\(545\) −27.7193 −1.18736
\(546\) 0 0
\(547\) 25.5679 1.09320 0.546602 0.837393i \(-0.315921\pi\)
0.546602 + 0.837393i \(0.315921\pi\)
\(548\) −82.6814 −3.53198
\(549\) 0 0
\(550\) 49.0367 2.09093
\(551\) 0.0655389 0.00279205
\(552\) 0 0
\(553\) −3.36380 −0.143043
\(554\) −70.1808 −2.98170
\(555\) 0 0
\(556\) −41.2403 −1.74898
\(557\) −40.7860 −1.72816 −0.864079 0.503357i \(-0.832098\pi\)
−0.864079 + 0.503357i \(0.832098\pi\)
\(558\) 0 0
\(559\) 12.9808 0.549029
\(560\) −44.4104 −1.87668
\(561\) 0 0
\(562\) 47.6367 2.00943
\(563\) −10.0286 −0.422657 −0.211329 0.977415i \(-0.567779\pi\)
−0.211329 + 0.977415i \(0.567779\pi\)
\(564\) 0 0
\(565\) 44.6137 1.87691
\(566\) 26.4485 1.11171
\(567\) 0 0
\(568\) −105.986 −4.44709
\(569\) 29.2372 1.22569 0.612844 0.790204i \(-0.290025\pi\)
0.612844 + 0.790204i \(0.290025\pi\)
\(570\) 0 0
\(571\) 10.8647 0.454672 0.227336 0.973816i \(-0.426998\pi\)
0.227336 + 0.973816i \(0.426998\pi\)
\(572\) 32.1433 1.34398
\(573\) 0 0
\(574\) 0.433889 0.0181102
\(575\) 25.3569 1.05746
\(576\) 0 0
\(577\) −3.53035 −0.146971 −0.0734853 0.997296i \(-0.523412\pi\)
−0.0734853 + 0.997296i \(0.523412\pi\)
\(578\) −60.9408 −2.53480
\(579\) 0 0
\(580\) −6.93821 −0.288093
\(581\) 17.3020 0.717807
\(582\) 0 0
\(583\) −8.33293 −0.345115
\(584\) 99.1881 4.10443
\(585\) 0 0
\(586\) 48.7513 2.01390
\(587\) −30.2595 −1.24894 −0.624472 0.781048i \(-0.714686\pi\)
−0.624472 + 0.781048i \(0.714686\pi\)
\(588\) 0 0
\(589\) 1.26142 0.0519758
\(590\) −31.3268 −1.28970
\(591\) 0 0
\(592\) −32.1215 −1.32019
\(593\) 31.0070 1.27330 0.636652 0.771151i \(-0.280319\pi\)
0.636652 + 0.771151i \(0.280319\pi\)
\(594\) 0 0
\(595\) −21.1409 −0.866693
\(596\) 83.0022 3.39990
\(597\) 0 0
\(598\) 22.9311 0.937721
\(599\) −35.9127 −1.46735 −0.733676 0.679499i \(-0.762197\pi\)
−0.733676 + 0.679499i \(0.762197\pi\)
\(600\) 0 0
\(601\) −46.4045 −1.89288 −0.946440 0.322879i \(-0.895349\pi\)
−0.946440 + 0.322879i \(0.895349\pi\)
\(602\) −16.5997 −0.676555
\(603\) 0 0
\(604\) −10.5128 −0.427760
\(605\) −8.81958 −0.358567
\(606\) 0 0
\(607\) −13.7737 −0.559058 −0.279529 0.960137i \(-0.590178\pi\)
−0.279529 + 0.960137i \(0.590178\pi\)
\(608\) 3.01222 0.122162
\(609\) 0 0
\(610\) 108.966 4.41192
\(611\) 18.5873 0.751961
\(612\) 0 0
\(613\) −33.4089 −1.34937 −0.674686 0.738105i \(-0.735721\pi\)
−0.674686 + 0.738105i \(0.735721\pi\)
\(614\) −10.9378 −0.441415
\(615\) 0 0
\(616\) −25.5006 −1.02745
\(617\) 26.6250 1.07188 0.535941 0.844256i \(-0.319957\pi\)
0.535941 + 0.844256i \(0.319957\pi\)
\(618\) 0 0
\(619\) −3.87967 −0.155937 −0.0779686 0.996956i \(-0.524843\pi\)
−0.0779686 + 0.996956i \(0.524843\pi\)
\(620\) −133.538 −5.36303
\(621\) 0 0
\(622\) 36.5877 1.46703
\(623\) 14.6779 0.588058
\(624\) 0 0
\(625\) −16.9225 −0.676902
\(626\) −63.0291 −2.51915
\(627\) 0 0
\(628\) 23.2316 0.927041
\(629\) −15.2910 −0.609691
\(630\) 0 0
\(631\) 24.1518 0.961467 0.480733 0.876867i \(-0.340370\pi\)
0.480733 + 0.876867i \(0.340370\pi\)
\(632\) −29.6414 −1.17907
\(633\) 0 0
\(634\) −85.9473 −3.41340
\(635\) −3.35934 −0.133311
\(636\) 0 0
\(637\) −2.10825 −0.0835319
\(638\) −3.05852 −0.121088
\(639\) 0 0
\(640\) −79.4228 −3.13946
\(641\) 3.52432 0.139202 0.0696012 0.997575i \(-0.477827\pi\)
0.0696012 + 0.997575i \(0.477827\pi\)
\(642\) 0 0
\(643\) 19.9282 0.785890 0.392945 0.919562i \(-0.371456\pi\)
0.392945 + 0.919562i \(0.371456\pi\)
\(644\) −21.2552 −0.837574
\(645\) 0 0
\(646\) 2.83651 0.111601
\(647\) −38.7661 −1.52405 −0.762027 0.647546i \(-0.775795\pi\)
−0.762027 + 0.647546i \(0.775795\pi\)
\(648\) 0 0
\(649\) −10.0097 −0.392916
\(650\) 35.7240 1.40121
\(651\) 0 0
\(652\) −51.7203 −2.02552
\(653\) 23.5705 0.922386 0.461193 0.887300i \(-0.347421\pi\)
0.461193 + 0.887300i \(0.347421\pi\)
\(654\) 0 0
\(655\) −65.0353 −2.54114
\(656\) 2.12759 0.0830683
\(657\) 0 0
\(658\) −23.7693 −0.926623
\(659\) −7.43377 −0.289579 −0.144789 0.989463i \(-0.546250\pi\)
−0.144789 + 0.989463i \(0.546250\pi\)
\(660\) 0 0
\(661\) 3.67368 0.142890 0.0714449 0.997445i \(-0.477239\pi\)
0.0714449 + 0.997445i \(0.477239\pi\)
\(662\) 88.6906 3.44706
\(663\) 0 0
\(664\) 152.463 5.91671
\(665\) 0.561624 0.0217789
\(666\) 0 0
\(667\) −1.58157 −0.0612385
\(668\) 80.8197 3.12701
\(669\) 0 0
\(670\) −84.7822 −3.27542
\(671\) 34.8176 1.34412
\(672\) 0 0
\(673\) 45.7468 1.76341 0.881706 0.471800i \(-0.156396\pi\)
0.881706 + 0.471800i \(0.156396\pi\)
\(674\) −32.9888 −1.27068
\(675\) 0 0
\(676\) −45.0734 −1.73359
\(677\) 49.9400 1.91935 0.959674 0.281114i \(-0.0907039\pi\)
0.959674 + 0.281114i \(0.0907039\pi\)
\(678\) 0 0
\(679\) 1.23267 0.0473055
\(680\) −186.291 −7.14395
\(681\) 0 0
\(682\) −58.8668 −2.25413
\(683\) 31.8312 1.21799 0.608993 0.793176i \(-0.291574\pi\)
0.608993 + 0.793176i \(0.291574\pi\)
\(684\) 0 0
\(685\) −52.7201 −2.01433
\(686\) 2.69601 0.102934
\(687\) 0 0
\(688\) −81.3973 −3.10324
\(689\) −6.07068 −0.231275
\(690\) 0 0
\(691\) 15.3903 0.585475 0.292737 0.956193i \(-0.405434\pi\)
0.292737 + 0.956193i \(0.405434\pi\)
\(692\) −67.2249 −2.55551
\(693\) 0 0
\(694\) −13.4301 −0.509800
\(695\) −26.2960 −0.997464
\(696\) 0 0
\(697\) 1.01281 0.0383628
\(698\) 19.6775 0.744806
\(699\) 0 0
\(700\) −33.1133 −1.25157
\(701\) −16.6857 −0.630210 −0.315105 0.949057i \(-0.602040\pi\)
−0.315105 + 0.949057i \(0.602040\pi\)
\(702\) 0 0
\(703\) 0.406216 0.0153207
\(704\) −64.0575 −2.41426
\(705\) 0 0
\(706\) −32.9428 −1.23982
\(707\) −12.2730 −0.461573
\(708\) 0 0
\(709\) 13.3407 0.501022 0.250511 0.968114i \(-0.419401\pi\)
0.250511 + 0.968114i \(0.419401\pi\)
\(710\) −108.932 −4.08816
\(711\) 0 0
\(712\) 129.340 4.84722
\(713\) −30.4401 −1.13999
\(714\) 0 0
\(715\) 20.4955 0.766488
\(716\) −6.34058 −0.236958
\(717\) 0 0
\(718\) 97.2577 3.62962
\(719\) 20.3493 0.758903 0.379451 0.925212i \(-0.376113\pi\)
0.379451 + 0.925212i \(0.376113\pi\)
\(720\) 0 0
\(721\) 3.50168 0.130409
\(722\) 51.1489 1.90356
\(723\) 0 0
\(724\) −43.6035 −1.62051
\(725\) −2.46390 −0.0915071
\(726\) 0 0
\(727\) 6.19761 0.229856 0.114928 0.993374i \(-0.463336\pi\)
0.114928 + 0.993374i \(0.463336\pi\)
\(728\) −18.5777 −0.688534
\(729\) 0 0
\(730\) 101.945 3.77316
\(731\) −38.7480 −1.43315
\(732\) 0 0
\(733\) −20.4599 −0.755703 −0.377851 0.925866i \(-0.623337\pi\)
−0.377851 + 0.925866i \(0.623337\pi\)
\(734\) 67.4606 2.49001
\(735\) 0 0
\(736\) −72.6899 −2.67939
\(737\) −27.0901 −0.997877
\(738\) 0 0
\(739\) −40.7478 −1.49893 −0.749466 0.662042i \(-0.769690\pi\)
−0.749466 + 0.662042i \(0.769690\pi\)
\(740\) −43.0036 −1.58085
\(741\) 0 0
\(742\) 7.76314 0.284994
\(743\) −4.75496 −0.174443 −0.0872213 0.996189i \(-0.527799\pi\)
−0.0872213 + 0.996189i \(0.527799\pi\)
\(744\) 0 0
\(745\) 52.9246 1.93901
\(746\) 34.8290 1.27518
\(747\) 0 0
\(748\) −95.9485 −3.50822
\(749\) −11.7913 −0.430844
\(750\) 0 0
\(751\) 30.3761 1.10844 0.554220 0.832370i \(-0.313017\pi\)
0.554220 + 0.832370i \(0.313017\pi\)
\(752\) −116.553 −4.25026
\(753\) 0 0
\(754\) −2.22819 −0.0811457
\(755\) −6.70327 −0.243957
\(756\) 0 0
\(757\) 2.83567 0.103064 0.0515321 0.998671i \(-0.483590\pi\)
0.0515321 + 0.998671i \(0.483590\pi\)
\(758\) −2.90286 −0.105437
\(759\) 0 0
\(760\) 4.94897 0.179518
\(761\) 10.8152 0.392052 0.196026 0.980599i \(-0.437196\pi\)
0.196026 + 0.980599i \(0.437196\pi\)
\(762\) 0 0
\(763\) 8.25140 0.298721
\(764\) 85.1314 3.07994
\(765\) 0 0
\(766\) 37.9391 1.37079
\(767\) −7.29226 −0.263308
\(768\) 0 0
\(769\) −12.8275 −0.462571 −0.231286 0.972886i \(-0.574293\pi\)
−0.231286 + 0.972886i \(0.574293\pi\)
\(770\) −26.2095 −0.944524
\(771\) 0 0
\(772\) 54.3934 1.95766
\(773\) 34.8329 1.25285 0.626427 0.779480i \(-0.284517\pi\)
0.626427 + 0.779480i \(0.284517\pi\)
\(774\) 0 0
\(775\) −47.4223 −1.70346
\(776\) 10.8621 0.389928
\(777\) 0 0
\(778\) 2.41677 0.0866455
\(779\) −0.0269060 −0.000964006 0
\(780\) 0 0
\(781\) −34.8067 −1.24548
\(782\) −68.4498 −2.44776
\(783\) 0 0
\(784\) 13.2200 0.472142
\(785\) 14.8131 0.528703
\(786\) 0 0
\(787\) 7.06256 0.251753 0.125876 0.992046i \(-0.459826\pi\)
0.125876 + 0.992046i \(0.459826\pi\)
\(788\) 103.924 3.70213
\(789\) 0 0
\(790\) −30.4653 −1.08391
\(791\) −13.2805 −0.472200
\(792\) 0 0
\(793\) 25.3652 0.900745
\(794\) −41.9620 −1.48918
\(795\) 0 0
\(796\) 6.60443 0.234088
\(797\) −4.18736 −0.148324 −0.0741619 0.997246i \(-0.523628\pi\)
−0.0741619 + 0.997246i \(0.523628\pi\)
\(798\) 0 0
\(799\) −55.4835 −1.96286
\(800\) −113.243 −4.00374
\(801\) 0 0
\(802\) −58.0104 −2.04842
\(803\) 32.5741 1.14952
\(804\) 0 0
\(805\) −13.5530 −0.477679
\(806\) −42.8855 −1.51058
\(807\) 0 0
\(808\) −108.148 −3.80463
\(809\) −5.20778 −0.183096 −0.0915479 0.995801i \(-0.529181\pi\)
−0.0915479 + 0.995801i \(0.529181\pi\)
\(810\) 0 0
\(811\) 40.9326 1.43734 0.718668 0.695353i \(-0.244752\pi\)
0.718668 + 0.695353i \(0.244752\pi\)
\(812\) 2.06535 0.0724795
\(813\) 0 0
\(814\) −18.9570 −0.664442
\(815\) −32.9784 −1.15518
\(816\) 0 0
\(817\) 1.02937 0.0360131
\(818\) 1.11393 0.0389476
\(819\) 0 0
\(820\) 2.84837 0.0994694
\(821\) −9.27823 −0.323813 −0.161906 0.986806i \(-0.551764\pi\)
−0.161906 + 0.986806i \(0.551764\pi\)
\(822\) 0 0
\(823\) −33.4733 −1.16681 −0.583404 0.812182i \(-0.698279\pi\)
−0.583404 + 0.812182i \(0.698279\pi\)
\(824\) 30.8564 1.07493
\(825\) 0 0
\(826\) 9.32528 0.324468
\(827\) −11.0635 −0.384716 −0.192358 0.981325i \(-0.561613\pi\)
−0.192358 + 0.981325i \(0.561613\pi\)
\(828\) 0 0
\(829\) −18.5732 −0.645075 −0.322538 0.946557i \(-0.604536\pi\)
−0.322538 + 0.946557i \(0.604536\pi\)
\(830\) 156.701 5.43917
\(831\) 0 0
\(832\) −46.6670 −1.61789
\(833\) 6.29317 0.218046
\(834\) 0 0
\(835\) 51.5330 1.78337
\(836\) 2.54894 0.0881571
\(837\) 0 0
\(838\) 98.1875 3.39183
\(839\) −43.0577 −1.48652 −0.743258 0.669004i \(-0.766721\pi\)
−0.743258 + 0.669004i \(0.766721\pi\)
\(840\) 0 0
\(841\) −28.8463 −0.994701
\(842\) 35.6209 1.22758
\(843\) 0 0
\(844\) 9.56862 0.329366
\(845\) −28.7401 −0.988690
\(846\) 0 0
\(847\) 2.62539 0.0902095
\(848\) 38.0668 1.30722
\(849\) 0 0
\(850\) −106.637 −3.65762
\(851\) −9.80269 −0.336032
\(852\) 0 0
\(853\) 17.7530 0.607850 0.303925 0.952696i \(-0.401703\pi\)
0.303925 + 0.952696i \(0.401703\pi\)
\(854\) −32.4368 −1.10997
\(855\) 0 0
\(856\) −103.903 −3.55134
\(857\) 2.85537 0.0975377 0.0487688 0.998810i \(-0.484470\pi\)
0.0487688 + 0.998810i \(0.484470\pi\)
\(858\) 0 0
\(859\) 19.0355 0.649485 0.324742 0.945803i \(-0.394722\pi\)
0.324742 + 0.945803i \(0.394722\pi\)
\(860\) −108.973 −3.71595
\(861\) 0 0
\(862\) 91.3548 3.11156
\(863\) 24.5348 0.835173 0.417586 0.908637i \(-0.362876\pi\)
0.417586 + 0.908637i \(0.362876\pi\)
\(864\) 0 0
\(865\) −42.8645 −1.45744
\(866\) 12.3216 0.418705
\(867\) 0 0
\(868\) 39.7514 1.34925
\(869\) −9.73446 −0.330219
\(870\) 0 0
\(871\) −19.7356 −0.668716
\(872\) 72.7104 2.46229
\(873\) 0 0
\(874\) 1.81842 0.0615090
\(875\) −4.31730 −0.145951
\(876\) 0 0
\(877\) 0.731536 0.0247022 0.0123511 0.999924i \(-0.496068\pi\)
0.0123511 + 0.999924i \(0.496068\pi\)
\(878\) 40.7810 1.37629
\(879\) 0 0
\(880\) −128.519 −4.33237
\(881\) 24.2382 0.816605 0.408302 0.912847i \(-0.366121\pi\)
0.408302 + 0.912847i \(0.366121\pi\)
\(882\) 0 0
\(883\) −24.7304 −0.832245 −0.416122 0.909309i \(-0.636611\pi\)
−0.416122 + 0.909309i \(0.636611\pi\)
\(884\) −69.9001 −2.35099
\(885\) 0 0
\(886\) −57.8800 −1.94452
\(887\) 2.92462 0.0981992 0.0490996 0.998794i \(-0.484365\pi\)
0.0490996 + 0.998794i \(0.484365\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 132.935 4.45600
\(891\) 0 0
\(892\) 3.27786 0.109751
\(893\) 1.47396 0.0493242
\(894\) 0 0
\(895\) −4.04293 −0.135140
\(896\) 23.6424 0.789836
\(897\) 0 0
\(898\) 73.6633 2.45818
\(899\) 2.95783 0.0986493
\(900\) 0 0
\(901\) 18.1211 0.603702
\(902\) 1.25563 0.0418078
\(903\) 0 0
\(904\) −117.026 −3.89223
\(905\) −27.8028 −0.924197
\(906\) 0 0
\(907\) 22.1789 0.736440 0.368220 0.929739i \(-0.379967\pi\)
0.368220 + 0.929739i \(0.379967\pi\)
\(908\) −133.723 −4.43774
\(909\) 0 0
\(910\) −19.0940 −0.632961
\(911\) −4.10731 −0.136081 −0.0680406 0.997683i \(-0.521675\pi\)
−0.0680406 + 0.997683i \(0.521675\pi\)
\(912\) 0 0
\(913\) 50.0700 1.65708
\(914\) −48.1721 −1.59339
\(915\) 0 0
\(916\) −3.70086 −0.122280
\(917\) 19.3595 0.639309
\(918\) 0 0
\(919\) 18.2568 0.602238 0.301119 0.953587i \(-0.402640\pi\)
0.301119 + 0.953587i \(0.402640\pi\)
\(920\) −119.427 −3.93739
\(921\) 0 0
\(922\) −14.4900 −0.477203
\(923\) −25.3573 −0.834646
\(924\) 0 0
\(925\) −15.2715 −0.502124
\(926\) −58.9312 −1.93660
\(927\) 0 0
\(928\) 7.06320 0.231861
\(929\) −48.7368 −1.59900 −0.799501 0.600665i \(-0.794903\pi\)
−0.799501 + 0.600665i \(0.794903\pi\)
\(930\) 0 0
\(931\) −0.167183 −0.00547920
\(932\) −85.0023 −2.78434
\(933\) 0 0
\(934\) −88.6345 −2.90021
\(935\) −61.1795 −2.00078
\(936\) 0 0
\(937\) −18.6686 −0.609875 −0.304938 0.952372i \(-0.598636\pi\)
−0.304938 + 0.952372i \(0.598636\pi\)
\(938\) 25.2378 0.824042
\(939\) 0 0
\(940\) −156.039 −5.08944
\(941\) −51.5302 −1.67984 −0.839918 0.542713i \(-0.817397\pi\)
−0.839918 + 0.542713i \(0.817397\pi\)
\(942\) 0 0
\(943\) 0.649287 0.0211437
\(944\) 45.7268 1.48828
\(945\) 0 0
\(946\) −48.0378 −1.56184
\(947\) −27.8818 −0.906036 −0.453018 0.891501i \(-0.649653\pi\)
−0.453018 + 0.891501i \(0.649653\pi\)
\(948\) 0 0
\(949\) 23.7308 0.770335
\(950\) 2.83290 0.0919113
\(951\) 0 0
\(952\) 55.4547 1.79730
\(953\) −39.2006 −1.26983 −0.634916 0.772582i \(-0.718965\pi\)
−0.634916 + 0.772582i \(0.718965\pi\)
\(954\) 0 0
\(955\) 54.2822 1.75653
\(956\) −43.9741 −1.42223
\(957\) 0 0
\(958\) 42.7830 1.38226
\(959\) 15.6936 0.506772
\(960\) 0 0
\(961\) 25.9289 0.836417
\(962\) −13.8105 −0.445268
\(963\) 0 0
\(964\) 61.6724 1.98633
\(965\) 34.6828 1.11648
\(966\) 0 0
\(967\) 31.0201 0.997539 0.498770 0.866735i \(-0.333785\pi\)
0.498770 + 0.866735i \(0.333785\pi\)
\(968\) 23.1347 0.743576
\(969\) 0 0
\(970\) 11.1641 0.358456
\(971\) −7.85796 −0.252174 −0.126087 0.992019i \(-0.540242\pi\)
−0.126087 + 0.992019i \(0.540242\pi\)
\(972\) 0 0
\(973\) 7.82773 0.250945
\(974\) −24.2351 −0.776544
\(975\) 0 0
\(976\) −159.055 −5.09123
\(977\) −33.1002 −1.05897 −0.529484 0.848320i \(-0.677615\pi\)
−0.529484 + 0.848320i \(0.677615\pi\)
\(978\) 0 0
\(979\) 42.4762 1.35755
\(980\) 17.6986 0.565362
\(981\) 0 0
\(982\) 3.75734 0.119902
\(983\) −5.35215 −0.170707 −0.0853535 0.996351i \(-0.527202\pi\)
−0.0853535 + 0.996351i \(0.527202\pi\)
\(984\) 0 0
\(985\) 66.2647 2.11137
\(986\) 6.65119 0.211817
\(987\) 0 0
\(988\) 1.85695 0.0590774
\(989\) −24.8404 −0.789880
\(990\) 0 0
\(991\) 31.1999 0.991097 0.495549 0.868580i \(-0.334967\pi\)
0.495549 + 0.868580i \(0.334967\pi\)
\(992\) 135.944 4.31623
\(993\) 0 0
\(994\) 32.4267 1.02851
\(995\) 4.21118 0.133503
\(996\) 0 0
\(997\) −62.0455 −1.96500 −0.982501 0.186257i \(-0.940364\pi\)
−0.982501 + 0.186257i \(0.940364\pi\)
\(998\) 16.0877 0.509247
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))