Properties

Label 8007.2.a.j.1.14
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.70394 q^{2}\) \(-1.00000 q^{3}\) \(+0.903397 q^{4}\) \(+3.92360 q^{5}\) \(+1.70394 q^{6}\) \(-2.84859 q^{7}\) \(+1.86854 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.70394 q^{2}\) \(-1.00000 q^{3}\) \(+0.903397 q^{4}\) \(+3.92360 q^{5}\) \(+1.70394 q^{6}\) \(-2.84859 q^{7}\) \(+1.86854 q^{8}\) \(+1.00000 q^{9}\) \(-6.68557 q^{10}\) \(-1.86713 q^{11}\) \(-0.903397 q^{12}\) \(+6.59965 q^{13}\) \(+4.85382 q^{14}\) \(-3.92360 q^{15}\) \(-4.99067 q^{16}\) \(+1.00000 q^{17}\) \(-1.70394 q^{18}\) \(+5.88070 q^{19}\) \(+3.54457 q^{20}\) \(+2.84859 q^{21}\) \(+3.18147 q^{22}\) \(+8.09177 q^{23}\) \(-1.86854 q^{24}\) \(+10.3947 q^{25}\) \(-11.2454 q^{26}\) \(-1.00000 q^{27}\) \(-2.57341 q^{28}\) \(+7.49767 q^{29}\) \(+6.68557 q^{30}\) \(-0.0109314 q^{31}\) \(+4.76669 q^{32}\) \(+1.86713 q^{33}\) \(-1.70394 q^{34}\) \(-11.1767 q^{35}\) \(+0.903397 q^{36}\) \(-3.18729 q^{37}\) \(-10.0203 q^{38}\) \(-6.59965 q^{39}\) \(+7.33141 q^{40}\) \(+8.13433 q^{41}\) \(-4.85382 q^{42}\) \(+8.10773 q^{43}\) \(-1.68676 q^{44}\) \(+3.92360 q^{45}\) \(-13.7879 q^{46}\) \(+5.27611 q^{47}\) \(+4.99067 q^{48}\) \(+1.11447 q^{49}\) \(-17.7118 q^{50}\) \(-1.00000 q^{51}\) \(+5.96210 q^{52}\) \(+1.77834 q^{53}\) \(+1.70394 q^{54}\) \(-7.32587 q^{55}\) \(-5.32271 q^{56}\) \(-5.88070 q^{57}\) \(-12.7755 q^{58}\) \(+6.72972 q^{59}\) \(-3.54457 q^{60}\) \(+9.82087 q^{61}\) \(+0.0186265 q^{62}\) \(-2.84859 q^{63}\) \(+1.85920 q^{64}\) \(+25.8944 q^{65}\) \(-3.18147 q^{66}\) \(-4.68216 q^{67}\) \(+0.903397 q^{68}\) \(-8.09177 q^{69}\) \(+19.0444 q^{70}\) \(-7.18037 q^{71}\) \(+1.86854 q^{72}\) \(+3.29779 q^{73}\) \(+5.43093 q^{74}\) \(-10.3947 q^{75}\) \(+5.31261 q^{76}\) \(+5.31869 q^{77}\) \(+11.2454 q^{78}\) \(-9.25247 q^{79}\) \(-19.5814 q^{80}\) \(+1.00000 q^{81}\) \(-13.8604 q^{82}\) \(+5.74483 q^{83}\) \(+2.57341 q^{84}\) \(+3.92360 q^{85}\) \(-13.8151 q^{86}\) \(-7.49767 q^{87}\) \(-3.48881 q^{88}\) \(-3.90125 q^{89}\) \(-6.68557 q^{90}\) \(-18.7997 q^{91}\) \(+7.31008 q^{92}\) \(+0.0109314 q^{93}\) \(-8.99015 q^{94}\) \(+23.0735 q^{95}\) \(-4.76669 q^{96}\) \(-10.7592 q^{97}\) \(-1.89899 q^{98}\) \(-1.86713 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70394 −1.20486 −0.602432 0.798170i \(-0.705802\pi\)
−0.602432 + 0.798170i \(0.705802\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.903397 0.451698
\(5\) 3.92360 1.75469 0.877344 0.479862i \(-0.159313\pi\)
0.877344 + 0.479862i \(0.159313\pi\)
\(6\) 1.70394 0.695629
\(7\) −2.84859 −1.07667 −0.538333 0.842732i \(-0.680946\pi\)
−0.538333 + 0.842732i \(0.680946\pi\)
\(8\) 1.86854 0.660629
\(9\) 1.00000 0.333333
\(10\) −6.68557 −2.11416
\(11\) −1.86713 −0.562961 −0.281480 0.959567i \(-0.590825\pi\)
−0.281480 + 0.959567i \(0.590825\pi\)
\(12\) −0.903397 −0.260788
\(13\) 6.59965 1.83041 0.915207 0.402984i \(-0.132027\pi\)
0.915207 + 0.402984i \(0.132027\pi\)
\(14\) 4.85382 1.29724
\(15\) −3.92360 −1.01307
\(16\) −4.99067 −1.24767
\(17\) 1.00000 0.242536
\(18\) −1.70394 −0.401621
\(19\) 5.88070 1.34913 0.674563 0.738218i \(-0.264332\pi\)
0.674563 + 0.738218i \(0.264332\pi\)
\(20\) 3.54457 0.792590
\(21\) 2.84859 0.621614
\(22\) 3.18147 0.678291
\(23\) 8.09177 1.68725 0.843625 0.536933i \(-0.180417\pi\)
0.843625 + 0.536933i \(0.180417\pi\)
\(24\) −1.86854 −0.381414
\(25\) 10.3947 2.07893
\(26\) −11.2454 −2.20540
\(27\) −1.00000 −0.192450
\(28\) −2.57341 −0.486328
\(29\) 7.49767 1.39228 0.696141 0.717905i \(-0.254899\pi\)
0.696141 + 0.717905i \(0.254899\pi\)
\(30\) 6.68557 1.22061
\(31\) −0.0109314 −0.00196334 −0.000981672 1.00000i \(-0.500312\pi\)
−0.000981672 1.00000i \(0.500312\pi\)
\(32\) 4.76669 0.842640
\(33\) 1.86713 0.325025
\(34\) −1.70394 −0.292223
\(35\) −11.1767 −1.88921
\(36\) 0.903397 0.150566
\(37\) −3.18729 −0.523987 −0.261993 0.965070i \(-0.584380\pi\)
−0.261993 + 0.965070i \(0.584380\pi\)
\(38\) −10.0203 −1.62551
\(39\) −6.59965 −1.05679
\(40\) 7.33141 1.15920
\(41\) 8.13433 1.27037 0.635184 0.772361i \(-0.280924\pi\)
0.635184 + 0.772361i \(0.280924\pi\)
\(42\) −4.85382 −0.748960
\(43\) 8.10773 1.23642 0.618209 0.786014i \(-0.287859\pi\)
0.618209 + 0.786014i \(0.287859\pi\)
\(44\) −1.68676 −0.254288
\(45\) 3.92360 0.584896
\(46\) −13.7879 −2.03291
\(47\) 5.27611 0.769600 0.384800 0.923000i \(-0.374270\pi\)
0.384800 + 0.923000i \(0.374270\pi\)
\(48\) 4.99067 0.720341
\(49\) 1.11447 0.159211
\(50\) −17.7118 −2.50483
\(51\) −1.00000 −0.140028
\(52\) 5.96210 0.826795
\(53\) 1.77834 0.244274 0.122137 0.992513i \(-0.461025\pi\)
0.122137 + 0.992513i \(0.461025\pi\)
\(54\) 1.70394 0.231876
\(55\) −7.32587 −0.987820
\(56\) −5.32271 −0.711277
\(57\) −5.88070 −0.778918
\(58\) −12.7755 −1.67751
\(59\) 6.72972 0.876134 0.438067 0.898942i \(-0.355663\pi\)
0.438067 + 0.898942i \(0.355663\pi\)
\(60\) −3.54457 −0.457602
\(61\) 9.82087 1.25743 0.628717 0.777635i \(-0.283581\pi\)
0.628717 + 0.777635i \(0.283581\pi\)
\(62\) 0.0186265 0.00236556
\(63\) −2.84859 −0.358889
\(64\) 1.85920 0.232400
\(65\) 25.8944 3.21181
\(66\) −3.18147 −0.391612
\(67\) −4.68216 −0.572017 −0.286008 0.958227i \(-0.592329\pi\)
−0.286008 + 0.958227i \(0.592329\pi\)
\(68\) 0.903397 0.109553
\(69\) −8.09177 −0.974134
\(70\) 19.0444 2.27625
\(71\) −7.18037 −0.852153 −0.426077 0.904687i \(-0.640105\pi\)
−0.426077 + 0.904687i \(0.640105\pi\)
\(72\) 1.86854 0.220210
\(73\) 3.29779 0.385977 0.192988 0.981201i \(-0.438182\pi\)
0.192988 + 0.981201i \(0.438182\pi\)
\(74\) 5.43093 0.631333
\(75\) −10.3947 −1.20027
\(76\) 5.31261 0.609398
\(77\) 5.31869 0.606121
\(78\) 11.2454 1.27329
\(79\) −9.25247 −1.04098 −0.520492 0.853866i \(-0.674252\pi\)
−0.520492 + 0.853866i \(0.674252\pi\)
\(80\) −19.5814 −2.18927
\(81\) 1.00000 0.111111
\(82\) −13.8604 −1.53062
\(83\) 5.74483 0.630577 0.315288 0.948996i \(-0.397899\pi\)
0.315288 + 0.948996i \(0.397899\pi\)
\(84\) 2.57341 0.280782
\(85\) 3.92360 0.425574
\(86\) −13.8151 −1.48972
\(87\) −7.49767 −0.803834
\(88\) −3.48881 −0.371908
\(89\) −3.90125 −0.413531 −0.206766 0.978390i \(-0.566294\pi\)
−0.206766 + 0.978390i \(0.566294\pi\)
\(90\) −6.68557 −0.704721
\(91\) −18.7997 −1.97075
\(92\) 7.31008 0.762128
\(93\) 0.0109314 0.00113354
\(94\) −8.99015 −0.927264
\(95\) 23.0735 2.36729
\(96\) −4.76669 −0.486499
\(97\) −10.7592 −1.09243 −0.546215 0.837645i \(-0.683932\pi\)
−0.546215 + 0.837645i \(0.683932\pi\)
\(98\) −1.89899 −0.191827
\(99\) −1.86713 −0.187654
\(100\) 9.39050 0.939050
\(101\) 4.23881 0.421777 0.210889 0.977510i \(-0.432364\pi\)
0.210889 + 0.977510i \(0.432364\pi\)
\(102\) 1.70394 0.168715
\(103\) −18.0364 −1.77718 −0.888592 0.458698i \(-0.848316\pi\)
−0.888592 + 0.458698i \(0.848316\pi\)
\(104\) 12.3317 1.20923
\(105\) 11.1767 1.09074
\(106\) −3.03018 −0.294317
\(107\) −15.1586 −1.46544 −0.732720 0.680530i \(-0.761750\pi\)
−0.732720 + 0.680530i \(0.761750\pi\)
\(108\) −0.903397 −0.0869294
\(109\) −0.691952 −0.0662770 −0.0331385 0.999451i \(-0.510550\pi\)
−0.0331385 + 0.999451i \(0.510550\pi\)
\(110\) 12.4828 1.19019
\(111\) 3.18729 0.302524
\(112\) 14.2164 1.34332
\(113\) 1.75574 0.165167 0.0825833 0.996584i \(-0.473683\pi\)
0.0825833 + 0.996584i \(0.473683\pi\)
\(114\) 10.0203 0.938490
\(115\) 31.7489 2.96060
\(116\) 6.77337 0.628891
\(117\) 6.59965 0.610138
\(118\) −11.4670 −1.05562
\(119\) −2.84859 −0.261130
\(120\) −7.33141 −0.669264
\(121\) −7.51383 −0.683075
\(122\) −16.7341 −1.51504
\(123\) −8.13433 −0.733448
\(124\) −0.00987543 −0.000886840 0
\(125\) 21.1665 1.89319
\(126\) 4.85382 0.432412
\(127\) 6.68609 0.593294 0.296647 0.954987i \(-0.404131\pi\)
0.296647 + 0.954987i \(0.404131\pi\)
\(128\) −12.7013 −1.12265
\(129\) −8.10773 −0.713846
\(130\) −44.1224 −3.86979
\(131\) 2.41675 0.211152 0.105576 0.994411i \(-0.466331\pi\)
0.105576 + 0.994411i \(0.466331\pi\)
\(132\) 1.68676 0.146813
\(133\) −16.7517 −1.45256
\(134\) 7.97810 0.689203
\(135\) −3.92360 −0.337690
\(136\) 1.86854 0.160226
\(137\) 7.72990 0.660410 0.330205 0.943909i \(-0.392882\pi\)
0.330205 + 0.943909i \(0.392882\pi\)
\(138\) 13.7879 1.17370
\(139\) 11.0080 0.933688 0.466844 0.884340i \(-0.345391\pi\)
0.466844 + 0.884340i \(0.345391\pi\)
\(140\) −10.0970 −0.853355
\(141\) −5.27611 −0.444329
\(142\) 12.2349 1.02673
\(143\) −12.3224 −1.03045
\(144\) −4.99067 −0.415889
\(145\) 29.4179 2.44302
\(146\) −5.61922 −0.465050
\(147\) −1.11447 −0.0919203
\(148\) −2.87939 −0.236684
\(149\) 14.3407 1.17483 0.587417 0.809284i \(-0.300145\pi\)
0.587417 + 0.809284i \(0.300145\pi\)
\(150\) 17.7118 1.44616
\(151\) 4.08244 0.332224 0.166112 0.986107i \(-0.446879\pi\)
0.166112 + 0.986107i \(0.446879\pi\)
\(152\) 10.9883 0.891272
\(153\) 1.00000 0.0808452
\(154\) −9.06270 −0.730293
\(155\) −0.0428906 −0.00344506
\(156\) −5.96210 −0.477350
\(157\) −1.00000 −0.0798087
\(158\) 15.7656 1.25425
\(159\) −1.77834 −0.141032
\(160\) 18.7026 1.47857
\(161\) −23.0501 −1.81661
\(162\) −1.70394 −0.133874
\(163\) −23.0729 −1.80721 −0.903605 0.428366i \(-0.859090\pi\)
−0.903605 + 0.428366i \(0.859090\pi\)
\(164\) 7.34853 0.573823
\(165\) 7.32587 0.570318
\(166\) −9.78882 −0.759760
\(167\) 19.7822 1.53079 0.765394 0.643562i \(-0.222544\pi\)
0.765394 + 0.643562i \(0.222544\pi\)
\(168\) 5.32271 0.410656
\(169\) 30.5554 2.35042
\(170\) −6.68557 −0.512760
\(171\) 5.88070 0.449708
\(172\) 7.32450 0.558488
\(173\) 5.37235 0.408452 0.204226 0.978924i \(-0.434532\pi\)
0.204226 + 0.978924i \(0.434532\pi\)
\(174\) 12.7755 0.968511
\(175\) −29.6101 −2.23832
\(176\) 9.31822 0.702387
\(177\) −6.72972 −0.505836
\(178\) 6.64747 0.498249
\(179\) −24.1181 −1.80267 −0.901334 0.433124i \(-0.857411\pi\)
−0.901334 + 0.433124i \(0.857411\pi\)
\(180\) 3.54457 0.264197
\(181\) 7.99070 0.593944 0.296972 0.954886i \(-0.404023\pi\)
0.296972 + 0.954886i \(0.404023\pi\)
\(182\) 32.0335 2.37448
\(183\) −9.82087 −0.725979
\(184\) 15.1198 1.11465
\(185\) −12.5057 −0.919434
\(186\) −0.0186265 −0.00136576
\(187\) −1.86713 −0.136538
\(188\) 4.76642 0.347627
\(189\) 2.84859 0.207205
\(190\) −39.3158 −2.85227
\(191\) 17.5796 1.27201 0.636007 0.771683i \(-0.280585\pi\)
0.636007 + 0.771683i \(0.280585\pi\)
\(192\) −1.85920 −0.134176
\(193\) 3.15164 0.226860 0.113430 0.993546i \(-0.463816\pi\)
0.113430 + 0.993546i \(0.463816\pi\)
\(194\) 18.3330 1.31623
\(195\) −25.8944 −1.85434
\(196\) 1.00681 0.0719152
\(197\) 22.4682 1.60079 0.800397 0.599470i \(-0.204622\pi\)
0.800397 + 0.599470i \(0.204622\pi\)
\(198\) 3.18147 0.226097
\(199\) 2.71973 0.192796 0.0963982 0.995343i \(-0.469268\pi\)
0.0963982 + 0.995343i \(0.469268\pi\)
\(200\) 19.4229 1.37340
\(201\) 4.68216 0.330254
\(202\) −7.22265 −0.508184
\(203\) −21.3578 −1.49902
\(204\) −0.903397 −0.0632504
\(205\) 31.9159 2.22910
\(206\) 30.7329 2.14127
\(207\) 8.09177 0.562417
\(208\) −32.9367 −2.28375
\(209\) −10.9800 −0.759504
\(210\) −19.0444 −1.31419
\(211\) 7.38613 0.508482 0.254241 0.967141i \(-0.418174\pi\)
0.254241 + 0.967141i \(0.418174\pi\)
\(212\) 1.60655 0.110338
\(213\) 7.18037 0.491991
\(214\) 25.8293 1.76566
\(215\) 31.8115 2.16953
\(216\) −1.86854 −0.127138
\(217\) 0.0311392 0.00211387
\(218\) 1.17904 0.0798548
\(219\) −3.29779 −0.222844
\(220\) −6.61817 −0.446197
\(221\) 6.59965 0.443941
\(222\) −5.43093 −0.364500
\(223\) −6.08366 −0.407392 −0.203696 0.979034i \(-0.565295\pi\)
−0.203696 + 0.979034i \(0.565295\pi\)
\(224\) −13.5784 −0.907243
\(225\) 10.3947 0.692977
\(226\) −2.99168 −0.199003
\(227\) −4.28514 −0.284415 −0.142207 0.989837i \(-0.545420\pi\)
−0.142207 + 0.989837i \(0.545420\pi\)
\(228\) −5.31261 −0.351836
\(229\) −5.26508 −0.347926 −0.173963 0.984752i \(-0.555657\pi\)
−0.173963 + 0.984752i \(0.555657\pi\)
\(230\) −54.0980 −3.56712
\(231\) −5.31869 −0.349944
\(232\) 14.0097 0.919782
\(233\) −27.2502 −1.78522 −0.892610 0.450830i \(-0.851128\pi\)
−0.892610 + 0.450830i \(0.851128\pi\)
\(234\) −11.2454 −0.735134
\(235\) 20.7014 1.35041
\(236\) 6.07960 0.395748
\(237\) 9.25247 0.601013
\(238\) 4.85382 0.314626
\(239\) −15.0549 −0.973818 −0.486909 0.873453i \(-0.661876\pi\)
−0.486909 + 0.873453i \(0.661876\pi\)
\(240\) 19.5814 1.26397
\(241\) −4.87483 −0.314015 −0.157008 0.987597i \(-0.550185\pi\)
−0.157008 + 0.987597i \(0.550185\pi\)
\(242\) 12.8031 0.823013
\(243\) −1.00000 −0.0641500
\(244\) 8.87214 0.567980
\(245\) 4.37276 0.279365
\(246\) 13.8604 0.883705
\(247\) 38.8106 2.46946
\(248\) −0.0204258 −0.00129704
\(249\) −5.74483 −0.364064
\(250\) −36.0663 −2.28104
\(251\) −22.6448 −1.42933 −0.714665 0.699467i \(-0.753421\pi\)
−0.714665 + 0.699467i \(0.753421\pi\)
\(252\) −2.57341 −0.162109
\(253\) −15.1084 −0.949855
\(254\) −11.3927 −0.714839
\(255\) −3.92360 −0.245706
\(256\) 17.9239 1.12024
\(257\) −24.0439 −1.49982 −0.749910 0.661540i \(-0.769903\pi\)
−0.749910 + 0.661540i \(0.769903\pi\)
\(258\) 13.8151 0.860088
\(259\) 9.07928 0.564159
\(260\) 23.3929 1.45077
\(261\) 7.49767 0.464094
\(262\) −4.11799 −0.254410
\(263\) −31.2083 −1.92439 −0.962194 0.272364i \(-0.912195\pi\)
−0.962194 + 0.272364i \(0.912195\pi\)
\(264\) 3.48881 0.214721
\(265\) 6.97752 0.428625
\(266\) 28.5438 1.75014
\(267\) 3.90125 0.238752
\(268\) −4.22985 −0.258379
\(269\) −19.1859 −1.16978 −0.584892 0.811111i \(-0.698863\pi\)
−0.584892 + 0.811111i \(0.698863\pi\)
\(270\) 6.68557 0.406871
\(271\) −23.1038 −1.40346 −0.701728 0.712445i \(-0.747588\pi\)
−0.701728 + 0.712445i \(0.747588\pi\)
\(272\) −4.99067 −0.302604
\(273\) 18.7997 1.13781
\(274\) −13.1713 −0.795704
\(275\) −19.4082 −1.17036
\(276\) −7.31008 −0.440015
\(277\) −19.4800 −1.17044 −0.585220 0.810874i \(-0.698992\pi\)
−0.585220 + 0.810874i \(0.698992\pi\)
\(278\) −18.7570 −1.12497
\(279\) −0.0109314 −0.000654448 0
\(280\) −20.8842 −1.24807
\(281\) −27.0046 −1.61096 −0.805480 0.592623i \(-0.798092\pi\)
−0.805480 + 0.592623i \(0.798092\pi\)
\(282\) 8.99015 0.535356
\(283\) −8.08803 −0.480784 −0.240392 0.970676i \(-0.577276\pi\)
−0.240392 + 0.970676i \(0.577276\pi\)
\(284\) −6.48672 −0.384916
\(285\) −23.0735 −1.36676
\(286\) 20.9966 1.24155
\(287\) −23.1714 −1.36776
\(288\) 4.76669 0.280880
\(289\) 1.00000 0.0588235
\(290\) −50.1261 −2.94351
\(291\) 10.7592 0.630714
\(292\) 2.97921 0.174345
\(293\) −14.9382 −0.872696 −0.436348 0.899778i \(-0.643728\pi\)
−0.436348 + 0.899778i \(0.643728\pi\)
\(294\) 1.89899 0.110752
\(295\) 26.4047 1.53734
\(296\) −5.95558 −0.346161
\(297\) 1.86713 0.108342
\(298\) −24.4356 −1.41552
\(299\) 53.4029 3.08837
\(300\) −9.39050 −0.542161
\(301\) −23.0956 −1.33121
\(302\) −6.95622 −0.400285
\(303\) −4.23881 −0.243513
\(304\) −29.3486 −1.68326
\(305\) 38.5332 2.20640
\(306\) −1.70394 −0.0974075
\(307\) 9.47468 0.540749 0.270374 0.962755i \(-0.412853\pi\)
0.270374 + 0.962755i \(0.412853\pi\)
\(308\) 4.80489 0.273784
\(309\) 18.0364 1.02606
\(310\) 0.0730829 0.00415083
\(311\) −18.9615 −1.07521 −0.537604 0.843198i \(-0.680670\pi\)
−0.537604 + 0.843198i \(0.680670\pi\)
\(312\) −12.3317 −0.698146
\(313\) −10.1151 −0.571739 −0.285870 0.958268i \(-0.592282\pi\)
−0.285870 + 0.958268i \(0.592282\pi\)
\(314\) 1.70394 0.0961587
\(315\) −11.1767 −0.629738
\(316\) −8.35865 −0.470211
\(317\) −30.6649 −1.72231 −0.861156 0.508340i \(-0.830259\pi\)
−0.861156 + 0.508340i \(0.830259\pi\)
\(318\) 3.03018 0.169924
\(319\) −13.9991 −0.783800
\(320\) 7.29475 0.407789
\(321\) 15.1586 0.846072
\(322\) 39.2760 2.18876
\(323\) 5.88070 0.327211
\(324\) 0.903397 0.0501887
\(325\) 68.6011 3.80531
\(326\) 39.3148 2.17744
\(327\) 0.691952 0.0382651
\(328\) 15.1993 0.839243
\(329\) −15.0295 −0.828602
\(330\) −12.4828 −0.687156
\(331\) −25.0913 −1.37914 −0.689571 0.724218i \(-0.742201\pi\)
−0.689571 + 0.724218i \(0.742201\pi\)
\(332\) 5.18986 0.284831
\(333\) −3.18729 −0.174662
\(334\) −33.7075 −1.84439
\(335\) −18.3709 −1.00371
\(336\) −14.2164 −0.775567
\(337\) 9.12503 0.497072 0.248536 0.968623i \(-0.420051\pi\)
0.248536 + 0.968623i \(0.420051\pi\)
\(338\) −52.0645 −2.83193
\(339\) −1.75574 −0.0953590
\(340\) 3.54457 0.192231
\(341\) 0.0204104 0.00110529
\(342\) −10.0203 −0.541838
\(343\) 16.7655 0.905250
\(344\) 15.1496 0.816813
\(345\) −31.7489 −1.70930
\(346\) −9.15414 −0.492130
\(347\) 15.1352 0.812498 0.406249 0.913763i \(-0.366837\pi\)
0.406249 + 0.913763i \(0.366837\pi\)
\(348\) −6.77337 −0.363091
\(349\) 10.1377 0.542657 0.271328 0.962487i \(-0.412537\pi\)
0.271328 + 0.962487i \(0.412537\pi\)
\(350\) 50.4538 2.69687
\(351\) −6.59965 −0.352263
\(352\) −8.90003 −0.474373
\(353\) 6.83008 0.363528 0.181764 0.983342i \(-0.441819\pi\)
0.181764 + 0.983342i \(0.441819\pi\)
\(354\) 11.4670 0.609464
\(355\) −28.1729 −1.49526
\(356\) −3.52437 −0.186791
\(357\) 2.84859 0.150763
\(358\) 41.0956 2.17197
\(359\) −16.9878 −0.896582 −0.448291 0.893888i \(-0.647967\pi\)
−0.448291 + 0.893888i \(0.647967\pi\)
\(360\) 7.33141 0.386399
\(361\) 15.5826 0.820139
\(362\) −13.6156 −0.715622
\(363\) 7.51383 0.394374
\(364\) −16.9836 −0.890183
\(365\) 12.9392 0.677269
\(366\) 16.7341 0.874707
\(367\) −10.2984 −0.537571 −0.268786 0.963200i \(-0.586622\pi\)
−0.268786 + 0.963200i \(0.586622\pi\)
\(368\) −40.3833 −2.10513
\(369\) 8.13433 0.423456
\(370\) 21.3088 1.10779
\(371\) −5.06578 −0.263002
\(372\) 0.00987543 0.000512017 0
\(373\) −2.30087 −0.119135 −0.0595674 0.998224i \(-0.518972\pi\)
−0.0595674 + 0.998224i \(0.518972\pi\)
\(374\) 3.18147 0.164510
\(375\) −21.1665 −1.09303
\(376\) 9.85863 0.508420
\(377\) 49.4820 2.54845
\(378\) −4.85382 −0.249653
\(379\) 30.1533 1.54887 0.774436 0.632652i \(-0.218034\pi\)
0.774436 + 0.632652i \(0.218034\pi\)
\(380\) 20.8446 1.06930
\(381\) −6.68609 −0.342539
\(382\) −29.9545 −1.53260
\(383\) 19.1114 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(384\) 12.7013 0.648162
\(385\) 20.8684 1.06355
\(386\) −5.37019 −0.273336
\(387\) 8.10773 0.412139
\(388\) −9.71981 −0.493449
\(389\) −1.84952 −0.0937743 −0.0468872 0.998900i \(-0.514930\pi\)
−0.0468872 + 0.998900i \(0.514930\pi\)
\(390\) 44.1224 2.23423
\(391\) 8.09177 0.409218
\(392\) 2.08244 0.105179
\(393\) −2.41675 −0.121909
\(394\) −38.2844 −1.92874
\(395\) −36.3030 −1.82660
\(396\) −1.68676 −0.0847628
\(397\) 23.2381 1.16629 0.583145 0.812368i \(-0.301822\pi\)
0.583145 + 0.812368i \(0.301822\pi\)
\(398\) −4.63424 −0.232294
\(399\) 16.7517 0.838635
\(400\) −51.8763 −2.59381
\(401\) −35.5020 −1.77289 −0.886444 0.462837i \(-0.846832\pi\)
−0.886444 + 0.462837i \(0.846832\pi\)
\(402\) −7.97810 −0.397911
\(403\) −0.0721437 −0.00359373
\(404\) 3.82932 0.190516
\(405\) 3.92360 0.194965
\(406\) 36.3923 1.80612
\(407\) 5.95108 0.294984
\(408\) −1.86854 −0.0925066
\(409\) 30.7424 1.52011 0.760057 0.649856i \(-0.225171\pi\)
0.760057 + 0.649856i \(0.225171\pi\)
\(410\) −54.3826 −2.68577
\(411\) −7.72990 −0.381288
\(412\) −16.2941 −0.802751
\(413\) −19.1702 −0.943305
\(414\) −13.7879 −0.677636
\(415\) 22.5404 1.10647
\(416\) 31.4585 1.54238
\(417\) −11.0080 −0.539065
\(418\) 18.7093 0.915100
\(419\) −18.9779 −0.927132 −0.463566 0.886062i \(-0.653430\pi\)
−0.463566 + 0.886062i \(0.653430\pi\)
\(420\) 10.0970 0.492685
\(421\) −22.6584 −1.10430 −0.552151 0.833744i \(-0.686193\pi\)
−0.552151 + 0.833744i \(0.686193\pi\)
\(422\) −12.5855 −0.612652
\(423\) 5.27611 0.256533
\(424\) 3.32291 0.161375
\(425\) 10.3947 0.504215
\(426\) −12.2349 −0.592782
\(427\) −27.9756 −1.35384
\(428\) −13.6943 −0.661937
\(429\) 12.3224 0.594931
\(430\) −54.2048 −2.61399
\(431\) −19.7395 −0.950819 −0.475410 0.879765i \(-0.657700\pi\)
−0.475410 + 0.879765i \(0.657700\pi\)
\(432\) 4.99067 0.240114
\(433\) 21.3127 1.02422 0.512110 0.858920i \(-0.328864\pi\)
0.512110 + 0.858920i \(0.328864\pi\)
\(434\) −0.0530592 −0.00254692
\(435\) −29.4179 −1.41048
\(436\) −0.625108 −0.0299372
\(437\) 47.5853 2.27631
\(438\) 5.61922 0.268497
\(439\) −17.1388 −0.817990 −0.408995 0.912537i \(-0.634121\pi\)
−0.408995 + 0.912537i \(0.634121\pi\)
\(440\) −13.6887 −0.652583
\(441\) 1.11447 0.0530702
\(442\) −11.2454 −0.534888
\(443\) 34.7595 1.65147 0.825737 0.564055i \(-0.190759\pi\)
0.825737 + 0.564055i \(0.190759\pi\)
\(444\) 2.87939 0.136650
\(445\) −15.3069 −0.725619
\(446\) 10.3662 0.490852
\(447\) −14.3407 −0.678291
\(448\) −5.29609 −0.250217
\(449\) 8.18046 0.386060 0.193030 0.981193i \(-0.438169\pi\)
0.193030 + 0.981193i \(0.438169\pi\)
\(450\) −17.7118 −0.834944
\(451\) −15.1878 −0.715168
\(452\) 1.58613 0.0746055
\(453\) −4.08244 −0.191810
\(454\) 7.30161 0.342681
\(455\) −73.7626 −3.45804
\(456\) −10.9883 −0.514576
\(457\) 7.74931 0.362497 0.181249 0.983437i \(-0.441986\pi\)
0.181249 + 0.983437i \(0.441986\pi\)
\(458\) 8.97136 0.419204
\(459\) −1.00000 −0.0466760
\(460\) 28.6818 1.33730
\(461\) 1.32226 0.0615838 0.0307919 0.999526i \(-0.490197\pi\)
0.0307919 + 0.999526i \(0.490197\pi\)
\(462\) 9.06270 0.421635
\(463\) 22.0058 1.02270 0.511348 0.859374i \(-0.329146\pi\)
0.511348 + 0.859374i \(0.329146\pi\)
\(464\) −37.4184 −1.73710
\(465\) 0.0428906 0.00198901
\(466\) 46.4326 2.15095
\(467\) 25.8450 1.19596 0.597981 0.801510i \(-0.295970\pi\)
0.597981 + 0.801510i \(0.295970\pi\)
\(468\) 5.96210 0.275598
\(469\) 13.3376 0.615871
\(470\) −35.2738 −1.62706
\(471\) 1.00000 0.0460776
\(472\) 12.5748 0.578800
\(473\) −15.1382 −0.696054
\(474\) −15.7656 −0.724139
\(475\) 61.1279 2.80474
\(476\) −2.57341 −0.117952
\(477\) 1.77834 0.0814248
\(478\) 25.6525 1.17332
\(479\) 0.381457 0.0174292 0.00871460 0.999962i \(-0.497226\pi\)
0.00871460 + 0.999962i \(0.497226\pi\)
\(480\) −18.7026 −0.853654
\(481\) −21.0350 −0.959113
\(482\) 8.30639 0.378346
\(483\) 23.0501 1.04882
\(484\) −6.78797 −0.308544
\(485\) −42.2148 −1.91687
\(486\) 1.70394 0.0772921
\(487\) −17.0150 −0.771022 −0.385511 0.922703i \(-0.625975\pi\)
−0.385511 + 0.922703i \(0.625975\pi\)
\(488\) 18.3507 0.830697
\(489\) 23.0729 1.04339
\(490\) −7.45090 −0.336597
\(491\) −44.0172 −1.98647 −0.993234 0.116133i \(-0.962950\pi\)
−0.993234 + 0.116133i \(0.962950\pi\)
\(492\) −7.34853 −0.331297
\(493\) 7.49767 0.337678
\(494\) −66.1307 −2.97536
\(495\) −7.32587 −0.329273
\(496\) 0.0545552 0.00244960
\(497\) 20.4539 0.917485
\(498\) 9.78882 0.438647
\(499\) 13.0678 0.584995 0.292497 0.956266i \(-0.405514\pi\)
0.292497 + 0.956266i \(0.405514\pi\)
\(500\) 19.1217 0.855150
\(501\) −19.7822 −0.883801
\(502\) 38.5853 1.72215
\(503\) 18.5410 0.826702 0.413351 0.910572i \(-0.364358\pi\)
0.413351 + 0.910572i \(0.364358\pi\)
\(504\) −5.32271 −0.237092
\(505\) 16.6314 0.740087
\(506\) 25.7437 1.14445
\(507\) −30.5554 −1.35701
\(508\) 6.04019 0.267990
\(509\) −1.90452 −0.0844165 −0.0422082 0.999109i \(-0.513439\pi\)
−0.0422082 + 0.999109i \(0.513439\pi\)
\(510\) 6.68557 0.296042
\(511\) −9.39405 −0.415568
\(512\) −5.13845 −0.227089
\(513\) −5.88070 −0.259639
\(514\) 40.9693 1.80708
\(515\) −70.7679 −3.11840
\(516\) −7.32450 −0.322443
\(517\) −9.85118 −0.433254
\(518\) −15.4705 −0.679735
\(519\) −5.37235 −0.235820
\(520\) 48.3848 2.12181
\(521\) −15.0690 −0.660185 −0.330093 0.943949i \(-0.607080\pi\)
−0.330093 + 0.943949i \(0.607080\pi\)
\(522\) −12.7755 −0.559170
\(523\) 20.5686 0.899403 0.449701 0.893179i \(-0.351530\pi\)
0.449701 + 0.893179i \(0.351530\pi\)
\(524\) 2.18328 0.0953772
\(525\) 29.6101 1.29229
\(526\) 53.1770 2.31863
\(527\) −0.0109314 −0.000476181 0
\(528\) −9.31822 −0.405523
\(529\) 42.4767 1.84681
\(530\) −11.8892 −0.516435
\(531\) 6.72972 0.292045
\(532\) −15.1334 −0.656118
\(533\) 53.6837 2.32530
\(534\) −6.64747 −0.287664
\(535\) −59.4765 −2.57139
\(536\) −8.74881 −0.377891
\(537\) 24.1181 1.04077
\(538\) 32.6915 1.40943
\(539\) −2.08087 −0.0896293
\(540\) −3.54457 −0.152534
\(541\) −42.1834 −1.81360 −0.906802 0.421556i \(-0.861484\pi\)
−0.906802 + 0.421556i \(0.861484\pi\)
\(542\) 39.3674 1.69097
\(543\) −7.99070 −0.342914
\(544\) 4.76669 0.204370
\(545\) −2.71495 −0.116296
\(546\) −32.0335 −1.37091
\(547\) 22.9966 0.983262 0.491631 0.870804i \(-0.336401\pi\)
0.491631 + 0.870804i \(0.336401\pi\)
\(548\) 6.98317 0.298306
\(549\) 9.82087 0.419144
\(550\) 33.0703 1.41012
\(551\) 44.0915 1.87836
\(552\) −15.1198 −0.643542
\(553\) 26.3565 1.12079
\(554\) 33.1927 1.41022
\(555\) 12.5057 0.530835
\(556\) 9.94461 0.421745
\(557\) 19.7995 0.838932 0.419466 0.907771i \(-0.362217\pi\)
0.419466 + 0.907771i \(0.362217\pi\)
\(558\) 0.0186265 0.000788521 0
\(559\) 53.5082 2.26316
\(560\) 55.7794 2.35711
\(561\) 1.86713 0.0788302
\(562\) 46.0141 1.94099
\(563\) 27.2447 1.14823 0.574114 0.818776i \(-0.305347\pi\)
0.574114 + 0.818776i \(0.305347\pi\)
\(564\) −4.76642 −0.200703
\(565\) 6.88885 0.289816
\(566\) 13.7815 0.579279
\(567\) −2.84859 −0.119630
\(568\) −13.4168 −0.562957
\(569\) 9.46666 0.396863 0.198431 0.980115i \(-0.436415\pi\)
0.198431 + 0.980115i \(0.436415\pi\)
\(570\) 39.3158 1.64676
\(571\) 2.92871 0.122563 0.0612814 0.998121i \(-0.480481\pi\)
0.0612814 + 0.998121i \(0.480481\pi\)
\(572\) −11.1320 −0.465453
\(573\) −17.5796 −0.734398
\(574\) 39.4825 1.64797
\(575\) 84.1112 3.50768
\(576\) 1.85920 0.0774665
\(577\) −8.37754 −0.348761 −0.174381 0.984678i \(-0.555792\pi\)
−0.174381 + 0.984678i \(0.555792\pi\)
\(578\) −1.70394 −0.0708744
\(579\) −3.15164 −0.130978
\(580\) 26.5760 1.10351
\(581\) −16.3647 −0.678921
\(582\) −18.3330 −0.759925
\(583\) −3.32040 −0.137517
\(584\) 6.16205 0.254987
\(585\) 25.8944 1.07060
\(586\) 25.4536 1.05148
\(587\) 9.53243 0.393445 0.196723 0.980459i \(-0.436970\pi\)
0.196723 + 0.980459i \(0.436970\pi\)
\(588\) −1.00681 −0.0415203
\(589\) −0.0642845 −0.00264880
\(590\) −44.9920 −1.85229
\(591\) −22.4682 −0.924219
\(592\) 15.9067 0.653761
\(593\) −32.0305 −1.31534 −0.657668 0.753308i \(-0.728457\pi\)
−0.657668 + 0.753308i \(0.728457\pi\)
\(594\) −3.18147 −0.130537
\(595\) −11.1767 −0.458202
\(596\) 12.9553 0.530671
\(597\) −2.71973 −0.111311
\(598\) −90.9950 −3.72106
\(599\) −27.8490 −1.13788 −0.568939 0.822380i \(-0.692646\pi\)
−0.568939 + 0.822380i \(0.692646\pi\)
\(600\) −19.4229 −0.792935
\(601\) −2.18062 −0.0889495 −0.0444748 0.999011i \(-0.514161\pi\)
−0.0444748 + 0.999011i \(0.514161\pi\)
\(602\) 39.3534 1.60393
\(603\) −4.68216 −0.190672
\(604\) 3.68806 0.150065
\(605\) −29.4813 −1.19858
\(606\) 7.22265 0.293400
\(607\) −41.3614 −1.67881 −0.839403 0.543509i \(-0.817095\pi\)
−0.839403 + 0.543509i \(0.817095\pi\)
\(608\) 28.0315 1.13683
\(609\) 21.3578 0.865461
\(610\) −65.6581 −2.65842
\(611\) 34.8205 1.40869
\(612\) 0.903397 0.0365176
\(613\) −10.3646 −0.418623 −0.209312 0.977849i \(-0.567122\pi\)
−0.209312 + 0.977849i \(0.567122\pi\)
\(614\) −16.1443 −0.651529
\(615\) −31.9159 −1.28697
\(616\) 9.93819 0.400421
\(617\) 32.6854 1.31586 0.657932 0.753077i \(-0.271431\pi\)
0.657932 + 0.753077i \(0.271431\pi\)
\(618\) −30.7329 −1.23626
\(619\) −22.3478 −0.898235 −0.449118 0.893473i \(-0.648262\pi\)
−0.449118 + 0.893473i \(0.648262\pi\)
\(620\) −0.0387473 −0.00155613
\(621\) −8.09177 −0.324711
\(622\) 32.3092 1.29548
\(623\) 11.1131 0.445235
\(624\) 32.9367 1.31852
\(625\) 31.0756 1.24303
\(626\) 17.2355 0.688868
\(627\) 10.9800 0.438500
\(628\) −0.903397 −0.0360495
\(629\) −3.18729 −0.127086
\(630\) 19.0444 0.758749
\(631\) 24.9048 0.991443 0.495722 0.868482i \(-0.334904\pi\)
0.495722 + 0.868482i \(0.334904\pi\)
\(632\) −17.2886 −0.687705
\(633\) −7.38613 −0.293572
\(634\) 52.2510 2.07515
\(635\) 26.2336 1.04105
\(636\) −1.60655 −0.0637039
\(637\) 7.35515 0.291422
\(638\) 23.8536 0.944372
\(639\) −7.18037 −0.284051
\(640\) −49.8350 −1.96990
\(641\) −21.7337 −0.858431 −0.429216 0.903202i \(-0.641210\pi\)
−0.429216 + 0.903202i \(0.641210\pi\)
\(642\) −25.8293 −1.01940
\(643\) −11.8093 −0.465712 −0.232856 0.972511i \(-0.574807\pi\)
−0.232856 + 0.972511i \(0.574807\pi\)
\(644\) −20.8234 −0.820558
\(645\) −31.8115 −1.25258
\(646\) −10.0203 −0.394245
\(647\) −24.2154 −0.952006 −0.476003 0.879444i \(-0.657915\pi\)
−0.476003 + 0.879444i \(0.657915\pi\)
\(648\) 1.86854 0.0734032
\(649\) −12.5652 −0.493229
\(650\) −116.892 −4.58488
\(651\) −0.0311392 −0.00122044
\(652\) −20.8440 −0.816314
\(653\) −37.1471 −1.45368 −0.726839 0.686808i \(-0.759011\pi\)
−0.726839 + 0.686808i \(0.759011\pi\)
\(654\) −1.17904 −0.0461042
\(655\) 9.48237 0.370507
\(656\) −40.5957 −1.58500
\(657\) 3.29779 0.128659
\(658\) 25.6093 0.998354
\(659\) 23.1020 0.899925 0.449962 0.893047i \(-0.351437\pi\)
0.449962 + 0.893047i \(0.351437\pi\)
\(660\) 6.61817 0.257612
\(661\) 25.4491 0.989857 0.494929 0.868934i \(-0.335194\pi\)
0.494929 + 0.868934i \(0.335194\pi\)
\(662\) 42.7540 1.66168
\(663\) −6.59965 −0.256309
\(664\) 10.7345 0.416578
\(665\) −65.7271 −2.54879
\(666\) 5.43093 0.210444
\(667\) 60.6694 2.34913
\(668\) 17.8711 0.691455
\(669\) 6.08366 0.235208
\(670\) 31.3029 1.20934
\(671\) −18.3368 −0.707885
\(672\) 13.5784 0.523797
\(673\) −7.73474 −0.298152 −0.149076 0.988826i \(-0.547630\pi\)
−0.149076 + 0.988826i \(0.547630\pi\)
\(674\) −15.5485 −0.598904
\(675\) −10.3947 −0.400091
\(676\) 27.6037 1.06168
\(677\) −10.8148 −0.415645 −0.207822 0.978167i \(-0.566638\pi\)
−0.207822 + 0.978167i \(0.566638\pi\)
\(678\) 2.99168 0.114895
\(679\) 30.6485 1.17618
\(680\) 7.33141 0.281147
\(681\) 4.28514 0.164207
\(682\) −0.0347780 −0.00133172
\(683\) 0.380002 0.0145404 0.00727018 0.999974i \(-0.497686\pi\)
0.00727018 + 0.999974i \(0.497686\pi\)
\(684\) 5.31261 0.203133
\(685\) 30.3291 1.15881
\(686\) −28.5673 −1.09070
\(687\) 5.26508 0.200875
\(688\) −40.4630 −1.54264
\(689\) 11.7365 0.447123
\(690\) 54.0980 2.05948
\(691\) 38.2297 1.45433 0.727163 0.686465i \(-0.240839\pi\)
0.727163 + 0.686465i \(0.240839\pi\)
\(692\) 4.85336 0.184497
\(693\) 5.31869 0.202040
\(694\) −25.7893 −0.978949
\(695\) 43.1911 1.63833
\(696\) −14.0097 −0.531036
\(697\) 8.13433 0.308110
\(698\) −17.2739 −0.653828
\(699\) 27.2502 1.03070
\(700\) −26.7497 −1.01104
\(701\) 36.5737 1.38137 0.690684 0.723156i \(-0.257309\pi\)
0.690684 + 0.723156i \(0.257309\pi\)
\(702\) 11.2454 0.424430
\(703\) −18.7435 −0.706924
\(704\) −3.47136 −0.130832
\(705\) −20.7014 −0.779658
\(706\) −11.6380 −0.438002
\(707\) −12.0746 −0.454113
\(708\) −6.07960 −0.228486
\(709\) −34.2094 −1.28476 −0.642380 0.766386i \(-0.722053\pi\)
−0.642380 + 0.766386i \(0.722053\pi\)
\(710\) 48.0048 1.80159
\(711\) −9.25247 −0.346995
\(712\) −7.28964 −0.273191
\(713\) −0.0884547 −0.00331265
\(714\) −4.85382 −0.181650
\(715\) −48.3482 −1.80812
\(716\) −21.7882 −0.814262
\(717\) 15.0549 0.562234
\(718\) 28.9461 1.08026
\(719\) 19.4549 0.725546 0.362773 0.931878i \(-0.381830\pi\)
0.362773 + 0.931878i \(0.381830\pi\)
\(720\) −19.5814 −0.729756
\(721\) 51.3785 1.91343
\(722\) −26.5518 −0.988156
\(723\) 4.87483 0.181297
\(724\) 7.21877 0.268283
\(725\) 77.9357 2.89446
\(726\) −12.8031 −0.475167
\(727\) 29.2804 1.08595 0.542974 0.839749i \(-0.317298\pi\)
0.542974 + 0.839749i \(0.317298\pi\)
\(728\) −35.1281 −1.30193
\(729\) 1.00000 0.0370370
\(730\) −22.0476 −0.816017
\(731\) 8.10773 0.299875
\(732\) −8.87214 −0.327924
\(733\) 44.0076 1.62546 0.812728 0.582643i \(-0.197981\pi\)
0.812728 + 0.582643i \(0.197981\pi\)
\(734\) 17.5478 0.647700
\(735\) −4.37276 −0.161292
\(736\) 38.5710 1.42175
\(737\) 8.74220 0.322023
\(738\) −13.8604 −0.510207
\(739\) 3.03536 0.111658 0.0558288 0.998440i \(-0.482220\pi\)
0.0558288 + 0.998440i \(0.482220\pi\)
\(740\) −11.2976 −0.415307
\(741\) −38.8106 −1.42574
\(742\) 8.63176 0.316882
\(743\) −46.0920 −1.69095 −0.845476 0.534013i \(-0.820683\pi\)
−0.845476 + 0.534013i \(0.820683\pi\)
\(744\) 0.0204258 0.000748848 0
\(745\) 56.2671 2.06147
\(746\) 3.92054 0.143541
\(747\) 5.74483 0.210192
\(748\) −1.68676 −0.0616740
\(749\) 43.1808 1.57779
\(750\) 36.0663 1.31696
\(751\) −12.3363 −0.450158 −0.225079 0.974341i \(-0.572264\pi\)
−0.225079 + 0.974341i \(0.572264\pi\)
\(752\) −26.3313 −0.960204
\(753\) 22.6448 0.825224
\(754\) −84.3141 −3.07054
\(755\) 16.0179 0.582950
\(756\) 2.57341 0.0935940
\(757\) 0.328579 0.0119424 0.00597120 0.999982i \(-0.498099\pi\)
0.00597120 + 0.999982i \(0.498099\pi\)
\(758\) −51.3793 −1.86618
\(759\) 15.1084 0.548399
\(760\) 43.1139 1.56390
\(761\) 6.16435 0.223457 0.111729 0.993739i \(-0.464361\pi\)
0.111729 + 0.993739i \(0.464361\pi\)
\(762\) 11.3927 0.412713
\(763\) 1.97109 0.0713582
\(764\) 15.8813 0.574567
\(765\) 3.92360 0.141858
\(766\) −32.5646 −1.17661
\(767\) 44.4138 1.60369
\(768\) −17.9239 −0.646772
\(769\) −19.5054 −0.703382 −0.351691 0.936116i \(-0.614393\pi\)
−0.351691 + 0.936116i \(0.614393\pi\)
\(770\) −35.5584 −1.28144
\(771\) 24.0439 0.865921
\(772\) 2.84718 0.102472
\(773\) 38.4023 1.38124 0.690618 0.723220i \(-0.257339\pi\)
0.690618 + 0.723220i \(0.257339\pi\)
\(774\) −13.8151 −0.496572
\(775\) −0.113629 −0.00408166
\(776\) −20.1040 −0.721691
\(777\) −9.07928 −0.325717
\(778\) 3.15146 0.112985
\(779\) 47.8356 1.71389
\(780\) −23.3929 −0.837601
\(781\) 13.4067 0.479729
\(782\) −13.7879 −0.493053
\(783\) −7.49767 −0.267945
\(784\) −5.56197 −0.198642
\(785\) −3.92360 −0.140039
\(786\) 4.11799 0.146884
\(787\) −14.0214 −0.499808 −0.249904 0.968271i \(-0.580399\pi\)
−0.249904 + 0.968271i \(0.580399\pi\)
\(788\) 20.2977 0.723076
\(789\) 31.2083 1.11105
\(790\) 61.8580 2.20081
\(791\) −5.00140 −0.177829
\(792\) −3.48881 −0.123969
\(793\) 64.8143 2.30162
\(794\) −39.5963 −1.40522
\(795\) −6.97752 −0.247467
\(796\) 2.45699 0.0870858
\(797\) 10.7655 0.381332 0.190666 0.981655i \(-0.438935\pi\)
0.190666 + 0.981655i \(0.438935\pi\)
\(798\) −28.5438 −1.01044
\(799\) 5.27611 0.186655
\(800\) 49.5482 1.75179
\(801\) −3.90125 −0.137844
\(802\) 60.4932 2.13609
\(803\) −6.15739 −0.217290
\(804\) 4.22985 0.149175
\(805\) −90.4396 −3.18758
\(806\) 0.122928 0.00432996
\(807\) 19.1859 0.675376
\(808\) 7.92039 0.278638
\(809\) 1.56251 0.0549349 0.0274675 0.999623i \(-0.491256\pi\)
0.0274675 + 0.999623i \(0.491256\pi\)
\(810\) −6.68557 −0.234907
\(811\) −20.2601 −0.711430 −0.355715 0.934595i \(-0.615763\pi\)
−0.355715 + 0.934595i \(0.615763\pi\)
\(812\) −19.2946 −0.677106
\(813\) 23.1038 0.810286
\(814\) −10.1403 −0.355416
\(815\) −90.5290 −3.17109
\(816\) 4.99067 0.174708
\(817\) 47.6791 1.66808
\(818\) −52.3831 −1.83153
\(819\) −18.7997 −0.656915
\(820\) 28.8327 1.00688
\(821\) −26.5636 −0.927075 −0.463538 0.886077i \(-0.653420\pi\)
−0.463538 + 0.886077i \(0.653420\pi\)
\(822\) 13.1713 0.459400
\(823\) 48.7647 1.69983 0.849916 0.526919i \(-0.176653\pi\)
0.849916 + 0.526919i \(0.176653\pi\)
\(824\) −33.7019 −1.17406
\(825\) 19.4082 0.675706
\(826\) 32.6648 1.13655
\(827\) −18.2547 −0.634780 −0.317390 0.948295i \(-0.602806\pi\)
−0.317390 + 0.948295i \(0.602806\pi\)
\(828\) 7.31008 0.254043
\(829\) −21.2287 −0.737303 −0.368652 0.929568i \(-0.620180\pi\)
−0.368652 + 0.929568i \(0.620180\pi\)
\(830\) −38.4074 −1.33314
\(831\) 19.4800 0.675754
\(832\) 12.2700 0.425387
\(833\) 1.11447 0.0386143
\(834\) 18.7570 0.649500
\(835\) 77.6173 2.68606
\(836\) −9.91932 −0.343067
\(837\) 0.0109314 0.000377846 0
\(838\) 32.3372 1.11707
\(839\) 11.1966 0.386548 0.193274 0.981145i \(-0.438089\pi\)
0.193274 + 0.981145i \(0.438089\pi\)
\(840\) 20.8842 0.720574
\(841\) 27.2150 0.938448
\(842\) 38.6084 1.33053
\(843\) 27.0046 0.930088
\(844\) 6.67261 0.229681
\(845\) 119.887 4.12425
\(846\) −8.99015 −0.309088
\(847\) 21.4038 0.735444
\(848\) −8.87512 −0.304773
\(849\) 8.08803 0.277580
\(850\) −17.7118 −0.607511
\(851\) −25.7908 −0.884097
\(852\) 6.48672 0.222231
\(853\) 2.77793 0.0951146 0.0475573 0.998869i \(-0.484856\pi\)
0.0475573 + 0.998869i \(0.484856\pi\)
\(854\) 47.6687 1.63119
\(855\) 23.0735 0.789098
\(856\) −28.3245 −0.968113
\(857\) −20.5496 −0.701960 −0.350980 0.936383i \(-0.614151\pi\)
−0.350980 + 0.936383i \(0.614151\pi\)
\(858\) −20.9966 −0.716811
\(859\) −2.19682 −0.0749545 −0.0374772 0.999297i \(-0.511932\pi\)
−0.0374772 + 0.999297i \(0.511932\pi\)
\(860\) 28.7384 0.979972
\(861\) 23.1714 0.789679
\(862\) 33.6349 1.14561
\(863\) 10.1013 0.343854 0.171927 0.985110i \(-0.445001\pi\)
0.171927 + 0.985110i \(0.445001\pi\)
\(864\) −4.76669 −0.162166
\(865\) 21.0790 0.716707
\(866\) −36.3154 −1.23405
\(867\) −1.00000 −0.0339618
\(868\) 0.0281311 0.000954830 0
\(869\) 17.2756 0.586033
\(870\) 50.1261 1.69944
\(871\) −30.9006 −1.04703
\(872\) −1.29294 −0.0437845
\(873\) −10.7592 −0.364143
\(874\) −81.0822 −2.74265
\(875\) −60.2947 −2.03833
\(876\) −2.97921 −0.100658
\(877\) 5.15256 0.173990 0.0869948 0.996209i \(-0.472274\pi\)
0.0869948 + 0.996209i \(0.472274\pi\)
\(878\) 29.2034 0.985567
\(879\) 14.9382 0.503851
\(880\) 36.5610 1.23247
\(881\) −16.3677 −0.551441 −0.275720 0.961238i \(-0.588916\pi\)
−0.275720 + 0.961238i \(0.588916\pi\)
\(882\) −1.89899 −0.0639424
\(883\) 35.0608 1.17989 0.589944 0.807444i \(-0.299150\pi\)
0.589944 + 0.807444i \(0.299150\pi\)
\(884\) 5.96210 0.200527
\(885\) −26.4047 −0.887585
\(886\) −59.2280 −1.98980
\(887\) 46.3982 1.55790 0.778950 0.627086i \(-0.215752\pi\)
0.778950 + 0.627086i \(0.215752\pi\)
\(888\) 5.95558 0.199856
\(889\) −19.0459 −0.638780
\(890\) 26.0820 0.874272
\(891\) −1.86713 −0.0625512
\(892\) −5.49596 −0.184018
\(893\) 31.0272 1.03829
\(894\) 24.4356 0.817249
\(895\) −94.6297 −3.16312
\(896\) 36.1809 1.20872
\(897\) −53.4029 −1.78307
\(898\) −13.9390 −0.465150
\(899\) −0.0819603 −0.00273353
\(900\) 9.39050 0.313017
\(901\) 1.77834 0.0592452
\(902\) 25.8791 0.861680
\(903\) 23.0956 0.768574
\(904\) 3.28068 0.109114
\(905\) 31.3523 1.04219
\(906\) 6.95622 0.231105
\(907\) −55.9541 −1.85792 −0.928962 0.370175i \(-0.879298\pi\)
−0.928962 + 0.370175i \(0.879298\pi\)
\(908\) −3.87118 −0.128470
\(909\) 4.23881 0.140592
\(910\) 125.687 4.16648
\(911\) −28.4904 −0.943930 −0.471965 0.881617i \(-0.656455\pi\)
−0.471965 + 0.881617i \(0.656455\pi\)
\(912\) 29.3486 0.971830
\(913\) −10.7263 −0.354990
\(914\) −13.2043 −0.436760
\(915\) −38.5332 −1.27387
\(916\) −4.75646 −0.157158
\(917\) −6.88434 −0.227341
\(918\) 1.70394 0.0562383
\(919\) 28.0612 0.925654 0.462827 0.886449i \(-0.346835\pi\)
0.462827 + 0.886449i \(0.346835\pi\)
\(920\) 59.3241 1.95586
\(921\) −9.47468 −0.312201
\(922\) −2.25305 −0.0742001
\(923\) −47.3880 −1.55979
\(924\) −4.80489 −0.158069
\(925\) −33.1308 −1.08933
\(926\) −37.4964 −1.23221
\(927\) −18.0364 −0.592395
\(928\) 35.7391 1.17319
\(929\) 19.6650 0.645186 0.322593 0.946538i \(-0.395445\pi\)
0.322593 + 0.946538i \(0.395445\pi\)
\(930\) −0.0730829 −0.00239648
\(931\) 6.55389 0.214795
\(932\) −24.6177 −0.806381
\(933\) 18.9615 0.620771
\(934\) −44.0382 −1.44097
\(935\) −7.32587 −0.239582
\(936\) 12.3317 0.403075
\(937\) −13.2346 −0.432354 −0.216177 0.976354i \(-0.569359\pi\)
−0.216177 + 0.976354i \(0.569359\pi\)
\(938\) −22.7264 −0.742042
\(939\) 10.1151 0.330094
\(940\) 18.7015 0.609977
\(941\) 24.2665 0.791064 0.395532 0.918452i \(-0.370560\pi\)
0.395532 + 0.918452i \(0.370560\pi\)
\(942\) −1.70394 −0.0555172
\(943\) 65.8211 2.14343
\(944\) −33.5858 −1.09312
\(945\) 11.1767 0.363579
\(946\) 25.7945 0.838651
\(947\) −2.65087 −0.0861418 −0.0430709 0.999072i \(-0.513714\pi\)
−0.0430709 + 0.999072i \(0.513714\pi\)
\(948\) 8.35865 0.271476
\(949\) 21.7642 0.706497
\(950\) −104.158 −3.37933
\(951\) 30.6649 0.994378
\(952\) −5.32271 −0.172510
\(953\) 17.2406 0.558478 0.279239 0.960222i \(-0.409918\pi\)
0.279239 + 0.960222i \(0.409918\pi\)
\(954\) −3.03018 −0.0981058
\(955\) 68.9753 2.23199
\(956\) −13.6005 −0.439872
\(957\) 13.9991 0.452527
\(958\) −0.649978 −0.0209998
\(959\) −22.0193 −0.711041
\(960\) −7.29475 −0.235437
\(961\) −30.9999 −0.999996
\(962\) 35.8423 1.15560
\(963\) −15.1586 −0.488480
\(964\) −4.40390 −0.141840
\(965\) 12.3658 0.398069
\(966\) −39.2760 −1.26368
\(967\) −32.7996 −1.05476 −0.527381 0.849629i \(-0.676826\pi\)
−0.527381 + 0.849629i \(0.676826\pi\)
\(968\) −14.0399 −0.451260
\(969\) −5.88070 −0.188915
\(970\) 71.9312 2.30957
\(971\) 25.9416 0.832504 0.416252 0.909249i \(-0.363343\pi\)
0.416252 + 0.909249i \(0.363343\pi\)
\(972\) −0.903397 −0.0289765
\(973\) −31.3574 −1.00527
\(974\) 28.9924 0.928977
\(975\) −68.6011 −2.19699
\(976\) −49.0127 −1.56886
\(977\) 20.2416 0.647587 0.323794 0.946128i \(-0.395042\pi\)
0.323794 + 0.946128i \(0.395042\pi\)
\(978\) −39.3148 −1.25715
\(979\) 7.28413 0.232802
\(980\) 3.95033 0.126189
\(981\) −0.691952 −0.0220923
\(982\) 75.0024 2.39342
\(983\) −25.4260 −0.810963 −0.405481 0.914103i \(-0.632896\pi\)
−0.405481 + 0.914103i \(0.632896\pi\)
\(984\) −15.1993 −0.484537
\(985\) 88.1563 2.80889
\(986\) −12.7755 −0.406856
\(987\) 15.0295 0.478394
\(988\) 35.0614 1.11545
\(989\) 65.6059 2.08615
\(990\) 12.4828 0.396730
\(991\) 61.1192 1.94151 0.970757 0.240063i \(-0.0771680\pi\)
0.970757 + 0.240063i \(0.0771680\pi\)
\(992\) −0.0521068 −0.00165439
\(993\) 25.0913 0.796248
\(994\) −34.8522 −1.10544
\(995\) 10.6711 0.338298
\(996\) −5.18986 −0.164447
\(997\) 51.7981 1.64046 0.820231 0.572032i \(-0.193845\pi\)
0.820231 + 0.572032i \(0.193845\pi\)
\(998\) −22.2667 −0.704839
\(999\) 3.18729 0.100841
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 \(a_p\))