Properties

Label 8041.2.a.j.1.6
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55417 q^{2}\) \(-3.23448 q^{3}\) \(+4.52378 q^{4}\) \(-3.35627 q^{5}\) \(+8.26140 q^{6}\) \(+1.37818 q^{7}\) \(-6.44616 q^{8}\) \(+7.46183 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55417 q^{2}\) \(-3.23448 q^{3}\) \(+4.52378 q^{4}\) \(-3.35627 q^{5}\) \(+8.26140 q^{6}\) \(+1.37818 q^{7}\) \(-6.44616 q^{8}\) \(+7.46183 q^{9}\) \(+8.57249 q^{10}\) \(+1.00000 q^{11}\) \(-14.6321 q^{12}\) \(-5.93482 q^{13}\) \(-3.52011 q^{14}\) \(+10.8558 q^{15}\) \(+7.41702 q^{16}\) \(+1.00000 q^{17}\) \(-19.0588 q^{18}\) \(+0.524776 q^{19}\) \(-15.1830 q^{20}\) \(-4.45770 q^{21}\) \(-2.55417 q^{22}\) \(+5.85725 q^{23}\) \(+20.8499 q^{24}\) \(+6.26457 q^{25}\) \(+15.1585 q^{26}\) \(-14.4317 q^{27}\) \(+6.23460 q^{28}\) \(-0.806143 q^{29}\) \(-27.7275 q^{30}\) \(-8.85305 q^{31}\) \(-6.05200 q^{32}\) \(-3.23448 q^{33}\) \(-2.55417 q^{34}\) \(-4.62556 q^{35}\) \(+33.7557 q^{36}\) \(-1.29326 q^{37}\) \(-1.34037 q^{38}\) \(+19.1960 q^{39}\) \(+21.6351 q^{40}\) \(+11.2002 q^{41}\) \(+11.3857 q^{42}\) \(+1.00000 q^{43}\) \(+4.52378 q^{44}\) \(-25.0440 q^{45}\) \(-14.9604 q^{46}\) \(-9.73357 q^{47}\) \(-23.9902 q^{48}\) \(-5.10061 q^{49}\) \(-16.0008 q^{50}\) \(-3.23448 q^{51}\) \(-26.8478 q^{52}\) \(+5.69213 q^{53}\) \(+36.8610 q^{54}\) \(-3.35627 q^{55}\) \(-8.88399 q^{56}\) \(-1.69738 q^{57}\) \(+2.05903 q^{58}\) \(+10.4120 q^{59}\) \(+49.1092 q^{60}\) \(-2.19688 q^{61}\) \(+22.6122 q^{62}\) \(+10.2838 q^{63}\) \(+0.623802 q^{64}\) \(+19.9189 q^{65}\) \(+8.26140 q^{66}\) \(+2.89361 q^{67}\) \(+4.52378 q^{68}\) \(-18.9451 q^{69}\) \(+11.8145 q^{70}\) \(+8.86691 q^{71}\) \(-48.1002 q^{72}\) \(-11.0044 q^{73}\) \(+3.30320 q^{74}\) \(-20.2626 q^{75}\) \(+2.37397 q^{76}\) \(+1.37818 q^{77}\) \(-49.0299 q^{78}\) \(+11.8348 q^{79}\) \(-24.8935 q^{80}\) \(+24.2935 q^{81}\) \(-28.6071 q^{82}\) \(-15.7774 q^{83}\) \(-20.1657 q^{84}\) \(-3.35627 q^{85}\) \(-2.55417 q^{86}\) \(+2.60745 q^{87}\) \(-6.44616 q^{88}\) \(-1.57241 q^{89}\) \(+63.9665 q^{90}\) \(-8.17928 q^{91}\) \(+26.4969 q^{92}\) \(+28.6350 q^{93}\) \(+24.8612 q^{94}\) \(-1.76129 q^{95}\) \(+19.5751 q^{96}\) \(+12.2296 q^{97}\) \(+13.0278 q^{98}\) \(+7.46183 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55417 −1.80607 −0.903035 0.429567i \(-0.858666\pi\)
−0.903035 + 0.429567i \(0.858666\pi\)
\(3\) −3.23448 −1.86743 −0.933713 0.358023i \(-0.883451\pi\)
−0.933713 + 0.358023i \(0.883451\pi\)
\(4\) 4.52378 2.26189
\(5\) −3.35627 −1.50097 −0.750486 0.660887i \(-0.770180\pi\)
−0.750486 + 0.660887i \(0.770180\pi\)
\(6\) 8.26140 3.37270
\(7\) 1.37818 0.520905 0.260452 0.965487i \(-0.416128\pi\)
0.260452 + 0.965487i \(0.416128\pi\)
\(8\) −6.44616 −2.27906
\(9\) 7.46183 2.48728
\(10\) 8.57249 2.71086
\(11\) 1.00000 0.301511
\(12\) −14.6321 −4.22391
\(13\) −5.93482 −1.64602 −0.823012 0.568024i \(-0.807708\pi\)
−0.823012 + 0.568024i \(0.807708\pi\)
\(14\) −3.52011 −0.940790
\(15\) 10.8558 2.80295
\(16\) 7.41702 1.85425
\(17\) 1.00000 0.242536
\(18\) −19.0588 −4.49220
\(19\) 0.524776 0.120392 0.0601960 0.998187i \(-0.480827\pi\)
0.0601960 + 0.998187i \(0.480827\pi\)
\(20\) −15.1830 −3.39503
\(21\) −4.45770 −0.972750
\(22\) −2.55417 −0.544551
\(23\) 5.85725 1.22132 0.610661 0.791892i \(-0.290904\pi\)
0.610661 + 0.791892i \(0.290904\pi\)
\(24\) 20.8499 4.25598
\(25\) 6.26457 1.25291
\(26\) 15.1585 2.97283
\(27\) −14.4317 −2.77738
\(28\) 6.23460 1.17823
\(29\) −0.806143 −0.149697 −0.0748485 0.997195i \(-0.523847\pi\)
−0.0748485 + 0.997195i \(0.523847\pi\)
\(30\) −27.7275 −5.06233
\(31\) −8.85305 −1.59005 −0.795027 0.606574i \(-0.792543\pi\)
−0.795027 + 0.606574i \(0.792543\pi\)
\(32\) −6.05200 −1.06985
\(33\) −3.23448 −0.563050
\(34\) −2.55417 −0.438036
\(35\) −4.62556 −0.781863
\(36\) 33.7557 5.62595
\(37\) −1.29326 −0.212610 −0.106305 0.994334i \(-0.533902\pi\)
−0.106305 + 0.994334i \(0.533902\pi\)
\(38\) −1.34037 −0.217436
\(39\) 19.1960 3.07383
\(40\) 21.6351 3.42080
\(41\) 11.2002 1.74917 0.874587 0.484870i \(-0.161133\pi\)
0.874587 + 0.484870i \(0.161133\pi\)
\(42\) 11.3857 1.75686
\(43\) 1.00000 0.152499
\(44\) 4.52378 0.681985
\(45\) −25.0440 −3.73333
\(46\) −14.9604 −2.20579
\(47\) −9.73357 −1.41979 −0.709893 0.704309i \(-0.751257\pi\)
−0.709893 + 0.704309i \(0.751257\pi\)
\(48\) −23.9902 −3.46268
\(49\) −5.10061 −0.728658
\(50\) −16.0008 −2.26285
\(51\) −3.23448 −0.452917
\(52\) −26.8478 −3.72312
\(53\) 5.69213 0.781874 0.390937 0.920417i \(-0.372151\pi\)
0.390937 + 0.920417i \(0.372151\pi\)
\(54\) 36.8610 5.01615
\(55\) −3.35627 −0.452560
\(56\) −8.88399 −1.18717
\(57\) −1.69738 −0.224823
\(58\) 2.05903 0.270363
\(59\) 10.4120 1.35553 0.677763 0.735281i \(-0.262950\pi\)
0.677763 + 0.735281i \(0.262950\pi\)
\(60\) 49.1092 6.33997
\(61\) −2.19688 −0.281282 −0.140641 0.990061i \(-0.544916\pi\)
−0.140641 + 0.990061i \(0.544916\pi\)
\(62\) 22.6122 2.87175
\(63\) 10.2838 1.29563
\(64\) 0.623802 0.0779752
\(65\) 19.9189 2.47063
\(66\) 8.26140 1.01691
\(67\) 2.89361 0.353511 0.176755 0.984255i \(-0.443440\pi\)
0.176755 + 0.984255i \(0.443440\pi\)
\(68\) 4.52378 0.548589
\(69\) −18.9451 −2.28073
\(70\) 11.8145 1.41210
\(71\) 8.86691 1.05231 0.526154 0.850389i \(-0.323633\pi\)
0.526154 + 0.850389i \(0.323633\pi\)
\(72\) −48.1002 −5.66866
\(73\) −11.0044 −1.28796 −0.643981 0.765041i \(-0.722719\pi\)
−0.643981 + 0.765041i \(0.722719\pi\)
\(74\) 3.30320 0.383989
\(75\) −20.2626 −2.33972
\(76\) 2.37397 0.272313
\(77\) 1.37818 0.157059
\(78\) −49.0299 −5.55155
\(79\) 11.8348 1.33152 0.665758 0.746167i \(-0.268108\pi\)
0.665758 + 0.746167i \(0.268108\pi\)
\(80\) −24.8935 −2.78318
\(81\) 24.2935 2.69927
\(82\) −28.6071 −3.15913
\(83\) −15.7774 −1.73179 −0.865895 0.500226i \(-0.833250\pi\)
−0.865895 + 0.500226i \(0.833250\pi\)
\(84\) −20.1657 −2.20025
\(85\) −3.35627 −0.364039
\(86\) −2.55417 −0.275423
\(87\) 2.60745 0.279548
\(88\) −6.44616 −0.687163
\(89\) −1.57241 −0.166675 −0.0833376 0.996521i \(-0.526558\pi\)
−0.0833376 + 0.996521i \(0.526558\pi\)
\(90\) 63.9665 6.74266
\(91\) −8.17928 −0.857421
\(92\) 26.4969 2.76249
\(93\) 28.6350 2.96931
\(94\) 24.8612 2.56423
\(95\) −1.76129 −0.180705
\(96\) 19.5751 1.99787
\(97\) 12.2296 1.24173 0.620864 0.783918i \(-0.286782\pi\)
0.620864 + 0.783918i \(0.286782\pi\)
\(98\) 13.0278 1.31601
\(99\) 7.46183 0.749943
\(100\) 28.3395 2.83395
\(101\) 13.2908 1.32249 0.661243 0.750172i \(-0.270029\pi\)
0.661243 + 0.750172i \(0.270029\pi\)
\(102\) 8.26140 0.818000
\(103\) 14.7617 1.45451 0.727257 0.686365i \(-0.240795\pi\)
0.727257 + 0.686365i \(0.240795\pi\)
\(104\) 38.2568 3.75139
\(105\) 14.9613 1.46007
\(106\) −14.5387 −1.41212
\(107\) 1.55105 0.149946 0.0749730 0.997186i \(-0.476113\pi\)
0.0749730 + 0.997186i \(0.476113\pi\)
\(108\) −65.2858 −6.28213
\(109\) 7.67263 0.734904 0.367452 0.930042i \(-0.380230\pi\)
0.367452 + 0.930042i \(0.380230\pi\)
\(110\) 8.57249 0.817355
\(111\) 4.18301 0.397034
\(112\) 10.2220 0.965890
\(113\) 7.41517 0.697561 0.348780 0.937205i \(-0.386596\pi\)
0.348780 + 0.937205i \(0.386596\pi\)
\(114\) 4.33539 0.406046
\(115\) −19.6585 −1.83317
\(116\) −3.64681 −0.338598
\(117\) −44.2847 −4.09412
\(118\) −26.5940 −2.44817
\(119\) 1.37818 0.126338
\(120\) −69.9781 −6.38810
\(121\) 1.00000 0.0909091
\(122\) 5.61120 0.508014
\(123\) −36.2267 −3.26645
\(124\) −40.0492 −3.59653
\(125\) −4.24425 −0.379617
\(126\) −26.2665 −2.34001
\(127\) 0.552737 0.0490474 0.0245237 0.999699i \(-0.492193\pi\)
0.0245237 + 0.999699i \(0.492193\pi\)
\(128\) 10.5107 0.929025
\(129\) −3.23448 −0.284780
\(130\) −50.8762 −4.46214
\(131\) 1.76387 0.154110 0.0770548 0.997027i \(-0.475448\pi\)
0.0770548 + 0.997027i \(0.475448\pi\)
\(132\) −14.6321 −1.27356
\(133\) 0.723239 0.0627127
\(134\) −7.39077 −0.638465
\(135\) 48.4367 4.16877
\(136\) −6.44616 −0.552754
\(137\) 4.44502 0.379764 0.189882 0.981807i \(-0.439189\pi\)
0.189882 + 0.981807i \(0.439189\pi\)
\(138\) 48.3891 4.11915
\(139\) −2.58705 −0.219431 −0.109715 0.993963i \(-0.534994\pi\)
−0.109715 + 0.993963i \(0.534994\pi\)
\(140\) −20.9250 −1.76849
\(141\) 31.4830 2.65135
\(142\) −22.6476 −1.90054
\(143\) −5.93482 −0.496295
\(144\) 55.3446 4.61205
\(145\) 2.70564 0.224691
\(146\) 28.1070 2.32615
\(147\) 16.4978 1.36072
\(148\) −5.85041 −0.480901
\(149\) 0.313474 0.0256808 0.0128404 0.999918i \(-0.495913\pi\)
0.0128404 + 0.999918i \(0.495913\pi\)
\(150\) 51.7541 4.22571
\(151\) 5.19538 0.422794 0.211397 0.977400i \(-0.432199\pi\)
0.211397 + 0.977400i \(0.432199\pi\)
\(152\) −3.38279 −0.274381
\(153\) 7.46183 0.603254
\(154\) −3.52011 −0.283659
\(155\) 29.7132 2.38662
\(156\) 86.8387 6.95266
\(157\) −3.30167 −0.263502 −0.131751 0.991283i \(-0.542060\pi\)
−0.131751 + 0.991283i \(0.542060\pi\)
\(158\) −30.2280 −2.40481
\(159\) −18.4111 −1.46009
\(160\) 20.3122 1.60582
\(161\) 8.07237 0.636192
\(162\) −62.0496 −4.87508
\(163\) −22.4799 −1.76076 −0.880380 0.474269i \(-0.842712\pi\)
−0.880380 + 0.474269i \(0.842712\pi\)
\(164\) 50.6671 3.95644
\(165\) 10.8558 0.845122
\(166\) 40.2980 3.12773
\(167\) 1.31422 0.101697 0.0508486 0.998706i \(-0.483807\pi\)
0.0508486 + 0.998706i \(0.483807\pi\)
\(168\) 28.7351 2.21696
\(169\) 22.2221 1.70939
\(170\) 8.57249 0.657480
\(171\) 3.91580 0.299448
\(172\) 4.52378 0.344935
\(173\) −21.0326 −1.59908 −0.799540 0.600613i \(-0.794923\pi\)
−0.799540 + 0.600613i \(0.794923\pi\)
\(174\) −6.65987 −0.504883
\(175\) 8.63373 0.652649
\(176\) 7.41702 0.559079
\(177\) −33.6773 −2.53134
\(178\) 4.01620 0.301027
\(179\) −3.94618 −0.294952 −0.147476 0.989066i \(-0.547115\pi\)
−0.147476 + 0.989066i \(0.547115\pi\)
\(180\) −113.293 −8.44439
\(181\) −15.3567 −1.14145 −0.570727 0.821140i \(-0.693338\pi\)
−0.570727 + 0.821140i \(0.693338\pi\)
\(182\) 20.8913 1.54856
\(183\) 7.10575 0.525272
\(184\) −37.7568 −2.78347
\(185\) 4.34052 0.319122
\(186\) −73.1385 −5.36278
\(187\) 1.00000 0.0731272
\(188\) −44.0325 −3.21140
\(189\) −19.8895 −1.44675
\(190\) 4.49864 0.326366
\(191\) 4.06337 0.294015 0.147008 0.989135i \(-0.453036\pi\)
0.147008 + 0.989135i \(0.453036\pi\)
\(192\) −2.01767 −0.145613
\(193\) −13.1024 −0.943133 −0.471566 0.881831i \(-0.656311\pi\)
−0.471566 + 0.881831i \(0.656311\pi\)
\(194\) −31.2365 −2.24265
\(195\) −64.4272 −4.61373
\(196\) −23.0740 −1.64814
\(197\) 20.1168 1.43327 0.716633 0.697451i \(-0.245682\pi\)
0.716633 + 0.697451i \(0.245682\pi\)
\(198\) −19.0588 −1.35445
\(199\) −16.5753 −1.17499 −0.587496 0.809227i \(-0.699886\pi\)
−0.587496 + 0.809227i \(0.699886\pi\)
\(200\) −40.3824 −2.85547
\(201\) −9.35931 −0.660155
\(202\) −33.9470 −2.38850
\(203\) −1.11101 −0.0779778
\(204\) −14.6321 −1.02445
\(205\) −37.5908 −2.62546
\(206\) −37.7039 −2.62696
\(207\) 43.7058 3.03777
\(208\) −44.0187 −3.05215
\(209\) 0.524776 0.0362995
\(210\) −38.2136 −2.63699
\(211\) −0.334550 −0.0230314 −0.0115157 0.999934i \(-0.503666\pi\)
−0.0115157 + 0.999934i \(0.503666\pi\)
\(212\) 25.7499 1.76851
\(213\) −28.6798 −1.96511
\(214\) −3.96165 −0.270813
\(215\) −3.35627 −0.228896
\(216\) 93.0290 6.32982
\(217\) −12.2011 −0.828266
\(218\) −19.5972 −1.32729
\(219\) 35.5933 2.40517
\(220\) −15.1830 −1.02364
\(221\) −5.93482 −0.399219
\(222\) −10.6841 −0.717071
\(223\) −5.22511 −0.349899 −0.174950 0.984577i \(-0.555976\pi\)
−0.174950 + 0.984577i \(0.555976\pi\)
\(224\) −8.34077 −0.557291
\(225\) 46.7452 3.11635
\(226\) −18.9396 −1.25984
\(227\) −9.06116 −0.601410 −0.300705 0.953717i \(-0.597222\pi\)
−0.300705 + 0.953717i \(0.597222\pi\)
\(228\) −7.67856 −0.508525
\(229\) −2.89718 −0.191451 −0.0957257 0.995408i \(-0.530517\pi\)
−0.0957257 + 0.995408i \(0.530517\pi\)
\(230\) 50.2112 3.31083
\(231\) −4.45770 −0.293295
\(232\) 5.19652 0.341169
\(233\) −24.5253 −1.60671 −0.803354 0.595502i \(-0.796953\pi\)
−0.803354 + 0.595502i \(0.796953\pi\)
\(234\) 113.111 7.39427
\(235\) 32.6685 2.13106
\(236\) 47.1015 3.06605
\(237\) −38.2793 −2.48651
\(238\) −3.52011 −0.228175
\(239\) −8.04199 −0.520193 −0.260096 0.965583i \(-0.583754\pi\)
−0.260096 + 0.965583i \(0.583754\pi\)
\(240\) 80.5176 5.19739
\(241\) −17.3835 −1.11977 −0.559885 0.828570i \(-0.689155\pi\)
−0.559885 + 0.828570i \(0.689155\pi\)
\(242\) −2.55417 −0.164188
\(243\) −35.2815 −2.26331
\(244\) −9.93819 −0.636228
\(245\) 17.1190 1.09370
\(246\) 92.5291 5.89944
\(247\) −3.11446 −0.198168
\(248\) 57.0681 3.62383
\(249\) 51.0315 3.23399
\(250\) 10.8405 0.685615
\(251\) −23.3782 −1.47562 −0.737810 0.675009i \(-0.764140\pi\)
−0.737810 + 0.675009i \(0.764140\pi\)
\(252\) 46.5216 2.93058
\(253\) 5.85725 0.368242
\(254\) −1.41178 −0.0885831
\(255\) 10.8558 0.679816
\(256\) −28.0937 −1.75586
\(257\) 9.17874 0.572554 0.286277 0.958147i \(-0.407582\pi\)
0.286277 + 0.958147i \(0.407582\pi\)
\(258\) 8.26140 0.514332
\(259\) −1.78235 −0.110750
\(260\) 90.1087 5.58830
\(261\) −6.01530 −0.372338
\(262\) −4.50521 −0.278333
\(263\) −25.7970 −1.59071 −0.795355 0.606143i \(-0.792716\pi\)
−0.795355 + 0.606143i \(0.792716\pi\)
\(264\) 20.8499 1.28323
\(265\) −19.1044 −1.17357
\(266\) −1.84727 −0.113264
\(267\) 5.08592 0.311254
\(268\) 13.0901 0.799602
\(269\) 8.71268 0.531222 0.265611 0.964080i \(-0.414426\pi\)
0.265611 + 0.964080i \(0.414426\pi\)
\(270\) −123.716 −7.52909
\(271\) 31.9214 1.93909 0.969543 0.244923i \(-0.0787626\pi\)
0.969543 + 0.244923i \(0.0787626\pi\)
\(272\) 7.41702 0.449723
\(273\) 26.4557 1.60117
\(274\) −11.3533 −0.685880
\(275\) 6.26457 0.377768
\(276\) −85.7036 −5.15875
\(277\) −22.4204 −1.34711 −0.673557 0.739135i \(-0.735234\pi\)
−0.673557 + 0.739135i \(0.735234\pi\)
\(278\) 6.60776 0.396307
\(279\) −66.0600 −3.95491
\(280\) 29.8171 1.78191
\(281\) −6.59654 −0.393516 −0.196758 0.980452i \(-0.563041\pi\)
−0.196758 + 0.980452i \(0.563041\pi\)
\(282\) −80.4129 −4.78852
\(283\) 1.26338 0.0750999 0.0375500 0.999295i \(-0.488045\pi\)
0.0375500 + 0.999295i \(0.488045\pi\)
\(284\) 40.1119 2.38021
\(285\) 5.69686 0.337453
\(286\) 15.1585 0.896343
\(287\) 15.4359 0.911152
\(288\) −45.1590 −2.66102
\(289\) 1.00000 0.0588235
\(290\) −6.91065 −0.405807
\(291\) −39.5564 −2.31884
\(292\) −49.7813 −2.91323
\(293\) 31.0522 1.81409 0.907043 0.421037i \(-0.138334\pi\)
0.907043 + 0.421037i \(0.138334\pi\)
\(294\) −42.1382 −2.45755
\(295\) −34.9455 −2.03460
\(296\) 8.33654 0.484552
\(297\) −14.4317 −0.837412
\(298\) −0.800665 −0.0463813
\(299\) −34.7617 −2.01032
\(300\) −91.6636 −5.29220
\(301\) 1.37818 0.0794372
\(302\) −13.2699 −0.763596
\(303\) −42.9888 −2.46964
\(304\) 3.89228 0.223237
\(305\) 7.37333 0.422195
\(306\) −19.0588 −1.08952
\(307\) 20.5178 1.17101 0.585506 0.810668i \(-0.300896\pi\)
0.585506 + 0.810668i \(0.300896\pi\)
\(308\) 6.23460 0.355249
\(309\) −47.7464 −2.71620
\(310\) −75.8926 −4.31041
\(311\) −14.8101 −0.839806 −0.419903 0.907569i \(-0.637936\pi\)
−0.419903 + 0.907569i \(0.637936\pi\)
\(312\) −123.741 −7.00544
\(313\) 32.8935 1.85925 0.929626 0.368505i \(-0.120130\pi\)
0.929626 + 0.368505i \(0.120130\pi\)
\(314\) 8.43303 0.475903
\(315\) −34.5152 −1.94471
\(316\) 53.5379 3.01174
\(317\) 7.02870 0.394771 0.197386 0.980326i \(-0.436755\pi\)
0.197386 + 0.980326i \(0.436755\pi\)
\(318\) 47.0250 2.63703
\(319\) −0.806143 −0.0451353
\(320\) −2.09365 −0.117039
\(321\) −5.01684 −0.280013
\(322\) −20.6182 −1.14901
\(323\) 0.524776 0.0291993
\(324\) 109.898 6.10546
\(325\) −37.1791 −2.06233
\(326\) 57.4174 3.18006
\(327\) −24.8169 −1.37238
\(328\) −72.1981 −3.98647
\(329\) −13.4146 −0.739574
\(330\) −27.7275 −1.52635
\(331\) 12.0888 0.664463 0.332231 0.943198i \(-0.392199\pi\)
0.332231 + 0.943198i \(0.392199\pi\)
\(332\) −71.3733 −3.91712
\(333\) −9.65007 −0.528821
\(334\) −3.35673 −0.183672
\(335\) −9.71175 −0.530610
\(336\) −33.0629 −1.80373
\(337\) −13.8127 −0.752424 −0.376212 0.926534i \(-0.622774\pi\)
−0.376212 + 0.926534i \(0.622774\pi\)
\(338\) −56.7591 −3.08729
\(339\) −23.9842 −1.30264
\(340\) −15.1830 −0.823416
\(341\) −8.85305 −0.479419
\(342\) −10.0016 −0.540825
\(343\) −16.6769 −0.900466
\(344\) −6.44616 −0.347554
\(345\) 63.5850 3.42330
\(346\) 53.7209 2.88805
\(347\) −8.94658 −0.480277 −0.240139 0.970739i \(-0.577193\pi\)
−0.240139 + 0.970739i \(0.577193\pi\)
\(348\) 11.7955 0.632307
\(349\) 8.83961 0.473174 0.236587 0.971610i \(-0.423971\pi\)
0.236587 + 0.971610i \(0.423971\pi\)
\(350\) −22.0520 −1.17873
\(351\) 85.6496 4.57164
\(352\) −6.05200 −0.322573
\(353\) −11.6584 −0.620513 −0.310257 0.950653i \(-0.600415\pi\)
−0.310257 + 0.950653i \(0.600415\pi\)
\(354\) 86.0176 4.57178
\(355\) −29.7598 −1.57948
\(356\) −7.11324 −0.377001
\(357\) −4.45770 −0.235927
\(358\) 10.0792 0.532703
\(359\) 7.79998 0.411667 0.205834 0.978587i \(-0.434009\pi\)
0.205834 + 0.978587i \(0.434009\pi\)
\(360\) 161.437 8.50849
\(361\) −18.7246 −0.985506
\(362\) 39.2236 2.06154
\(363\) −3.23448 −0.169766
\(364\) −37.0013 −1.93939
\(365\) 36.9336 1.93319
\(366\) −18.1493 −0.948679
\(367\) −18.7115 −0.976731 −0.488366 0.872639i \(-0.662407\pi\)
−0.488366 + 0.872639i \(0.662407\pi\)
\(368\) 43.4433 2.26464
\(369\) 83.5738 4.35068
\(370\) −11.0864 −0.576356
\(371\) 7.84481 0.407282
\(372\) 129.538 6.71624
\(373\) −15.9039 −0.823475 −0.411738 0.911302i \(-0.635078\pi\)
−0.411738 + 0.911302i \(0.635078\pi\)
\(374\) −2.55417 −0.132073
\(375\) 13.7279 0.708907
\(376\) 62.7441 3.23578
\(377\) 4.78432 0.246405
\(378\) 50.8012 2.61293
\(379\) 11.1411 0.572278 0.286139 0.958188i \(-0.407628\pi\)
0.286139 + 0.958188i \(0.407628\pi\)
\(380\) −7.96770 −0.408735
\(381\) −1.78781 −0.0915925
\(382\) −10.3785 −0.531012
\(383\) −3.19351 −0.163181 −0.0815905 0.996666i \(-0.526000\pi\)
−0.0815905 + 0.996666i \(0.526000\pi\)
\(384\) −33.9966 −1.73488
\(385\) −4.62556 −0.235740
\(386\) 33.4658 1.70336
\(387\) 7.46183 0.379306
\(388\) 55.3240 2.80865
\(389\) 1.08134 0.0548260 0.0274130 0.999624i \(-0.491273\pi\)
0.0274130 + 0.999624i \(0.491273\pi\)
\(390\) 164.558 8.33271
\(391\) 5.85725 0.296214
\(392\) 32.8793 1.66066
\(393\) −5.70518 −0.287788
\(394\) −51.3818 −2.58858
\(395\) −39.7208 −1.99857
\(396\) 33.7557 1.69629
\(397\) −31.7452 −1.59325 −0.796624 0.604475i \(-0.793383\pi\)
−0.796624 + 0.604475i \(0.793383\pi\)
\(398\) 42.3361 2.12212
\(399\) −2.33930 −0.117111
\(400\) 46.4644 2.32322
\(401\) −27.3622 −1.36640 −0.683201 0.730231i \(-0.739413\pi\)
−0.683201 + 0.730231i \(0.739413\pi\)
\(402\) 23.9053 1.19229
\(403\) 52.5413 2.61727
\(404\) 60.1247 2.99132
\(405\) −81.5355 −4.05153
\(406\) 2.83772 0.140833
\(407\) −1.29326 −0.0641044
\(408\) 20.8499 1.03223
\(409\) 10.0088 0.494903 0.247451 0.968900i \(-0.420407\pi\)
0.247451 + 0.968900i \(0.420407\pi\)
\(410\) 96.0134 4.74176
\(411\) −14.3773 −0.709181
\(412\) 66.7787 3.28995
\(413\) 14.3496 0.706100
\(414\) −111.632 −5.48642
\(415\) 52.9531 2.59937
\(416\) 35.9176 1.76100
\(417\) 8.36775 0.409771
\(418\) −1.34037 −0.0655595
\(419\) −30.7938 −1.50438 −0.752188 0.658948i \(-0.771002\pi\)
−0.752188 + 0.658948i \(0.771002\pi\)
\(420\) 67.6815 3.30252
\(421\) −20.8669 −1.01699 −0.508495 0.861065i \(-0.669798\pi\)
−0.508495 + 0.861065i \(0.669798\pi\)
\(422\) 0.854497 0.0415963
\(423\) −72.6303 −3.53140
\(424\) −36.6924 −1.78194
\(425\) 6.26457 0.303876
\(426\) 73.2530 3.54912
\(427\) −3.02770 −0.146521
\(428\) 7.01662 0.339161
\(429\) 19.1960 0.926794
\(430\) 8.57249 0.413402
\(431\) 5.79030 0.278909 0.139455 0.990228i \(-0.455465\pi\)
0.139455 + 0.990228i \(0.455465\pi\)
\(432\) −107.040 −5.14997
\(433\) −23.5918 −1.13375 −0.566875 0.823804i \(-0.691848\pi\)
−0.566875 + 0.823804i \(0.691848\pi\)
\(434\) 31.1637 1.49591
\(435\) −8.75131 −0.419593
\(436\) 34.7093 1.66227
\(437\) 3.07375 0.147037
\(438\) −90.9114 −4.34391
\(439\) −16.9166 −0.807388 −0.403694 0.914894i \(-0.632274\pi\)
−0.403694 + 0.914894i \(0.632274\pi\)
\(440\) 21.6351 1.03141
\(441\) −38.0599 −1.81238
\(442\) 15.1585 0.721018
\(443\) 6.90701 0.328162 0.164081 0.986447i \(-0.447534\pi\)
0.164081 + 0.986447i \(0.447534\pi\)
\(444\) 18.9230 0.898046
\(445\) 5.27744 0.250175
\(446\) 13.3458 0.631942
\(447\) −1.01392 −0.0479569
\(448\) 0.859714 0.0406176
\(449\) 34.7352 1.63926 0.819628 0.572897i \(-0.194180\pi\)
0.819628 + 0.572897i \(0.194180\pi\)
\(450\) −119.395 −5.62834
\(451\) 11.2002 0.527396
\(452\) 33.5446 1.57781
\(453\) −16.8043 −0.789537
\(454\) 23.1437 1.08619
\(455\) 27.4519 1.28696
\(456\) 10.9416 0.512385
\(457\) 32.3147 1.51162 0.755809 0.654793i \(-0.227244\pi\)
0.755809 + 0.654793i \(0.227244\pi\)
\(458\) 7.39990 0.345775
\(459\) −14.4317 −0.673614
\(460\) −88.9309 −4.14642
\(461\) 10.8304 0.504422 0.252211 0.967672i \(-0.418842\pi\)
0.252211 + 0.967672i \(0.418842\pi\)
\(462\) 11.3857 0.529712
\(463\) 24.5364 1.14030 0.570152 0.821539i \(-0.306884\pi\)
0.570152 + 0.821539i \(0.306884\pi\)
\(464\) −5.97918 −0.277576
\(465\) −96.1068 −4.45684
\(466\) 62.6419 2.90183
\(467\) −26.1616 −1.21062 −0.605308 0.795991i \(-0.706950\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(468\) −200.334 −9.26045
\(469\) 3.98793 0.184145
\(470\) −83.4409 −3.84884
\(471\) 10.6792 0.492071
\(472\) −67.1173 −3.08933
\(473\) 1.00000 0.0459800
\(474\) 97.7718 4.49081
\(475\) 3.28750 0.150841
\(476\) 6.23460 0.285762
\(477\) 42.4737 1.94474
\(478\) 20.5406 0.939505
\(479\) 18.2621 0.834415 0.417208 0.908811i \(-0.363009\pi\)
0.417208 + 0.908811i \(0.363009\pi\)
\(480\) −65.6993 −2.99875
\(481\) 7.67525 0.349961
\(482\) 44.4004 2.02238
\(483\) −26.1099 −1.18804
\(484\) 4.52378 0.205626
\(485\) −41.0459 −1.86380
\(486\) 90.1150 4.08770
\(487\) 21.4633 0.972597 0.486298 0.873793i \(-0.338347\pi\)
0.486298 + 0.873793i \(0.338347\pi\)
\(488\) 14.1614 0.641058
\(489\) 72.7106 3.28809
\(490\) −43.7249 −1.97529
\(491\) −32.7277 −1.47698 −0.738490 0.674264i \(-0.764461\pi\)
−0.738490 + 0.674264i \(0.764461\pi\)
\(492\) −163.882 −7.38835
\(493\) −0.806143 −0.0363068
\(494\) 7.95485 0.357905
\(495\) −25.0440 −1.12564
\(496\) −65.6632 −2.94836
\(497\) 12.2202 0.548152
\(498\) −130.343 −5.84081
\(499\) −35.9455 −1.60914 −0.804571 0.593857i \(-0.797605\pi\)
−0.804571 + 0.593857i \(0.797605\pi\)
\(500\) −19.2000 −0.858652
\(501\) −4.25080 −0.189912
\(502\) 59.7119 2.66507
\(503\) 21.9715 0.979662 0.489831 0.871818i \(-0.337059\pi\)
0.489831 + 0.871818i \(0.337059\pi\)
\(504\) −66.2909 −2.95283
\(505\) −44.6076 −1.98501
\(506\) −14.9604 −0.665071
\(507\) −71.8770 −3.19217
\(508\) 2.50046 0.110940
\(509\) 20.5308 0.910010 0.455005 0.890489i \(-0.349637\pi\)
0.455005 + 0.890489i \(0.349637\pi\)
\(510\) −27.7275 −1.22779
\(511\) −15.1660 −0.670906
\(512\) 50.7347 2.24218
\(513\) −7.57341 −0.334374
\(514\) −23.4441 −1.03407
\(515\) −49.5443 −2.18318
\(516\) −14.6321 −0.644140
\(517\) −9.73357 −0.428082
\(518\) 4.55241 0.200022
\(519\) 68.0295 2.98616
\(520\) −128.400 −5.63073
\(521\) 26.5945 1.16512 0.582562 0.812786i \(-0.302050\pi\)
0.582562 + 0.812786i \(0.302050\pi\)
\(522\) 15.3641 0.672469
\(523\) −9.86949 −0.431563 −0.215781 0.976442i \(-0.569230\pi\)
−0.215781 + 0.976442i \(0.569230\pi\)
\(524\) 7.97934 0.348579
\(525\) −27.9256 −1.21877
\(526\) 65.8899 2.87294
\(527\) −8.85305 −0.385645
\(528\) −23.9902 −1.04404
\(529\) 11.3074 0.491625
\(530\) 48.7957 2.11955
\(531\) 77.6925 3.37157
\(532\) 3.27177 0.141849
\(533\) −66.4710 −2.87918
\(534\) −12.9903 −0.562146
\(535\) −5.20576 −0.225065
\(536\) −18.6527 −0.805673
\(537\) 12.7638 0.550800
\(538\) −22.2537 −0.959423
\(539\) −5.10061 −0.219699
\(540\) 219.117 9.42929
\(541\) 0.336012 0.0144463 0.00722315 0.999974i \(-0.497701\pi\)
0.00722315 + 0.999974i \(0.497701\pi\)
\(542\) −81.5326 −3.50212
\(543\) 49.6708 2.13158
\(544\) −6.05200 −0.259478
\(545\) −25.7514 −1.10307
\(546\) −67.5723 −2.89183
\(547\) −21.9888 −0.940172 −0.470086 0.882621i \(-0.655777\pi\)
−0.470086 + 0.882621i \(0.655777\pi\)
\(548\) 20.1083 0.858984
\(549\) −16.3927 −0.699625
\(550\) −16.0008 −0.682275
\(551\) −0.423045 −0.0180223
\(552\) 122.123 5.19791
\(553\) 16.3105 0.693593
\(554\) 57.2656 2.43298
\(555\) −14.0393 −0.595936
\(556\) −11.7032 −0.496328
\(557\) 5.51343 0.233611 0.116806 0.993155i \(-0.462735\pi\)
0.116806 + 0.993155i \(0.462735\pi\)
\(558\) 168.728 7.14284
\(559\) −5.93482 −0.251016
\(560\) −34.3079 −1.44977
\(561\) −3.23448 −0.136560
\(562\) 16.8487 0.710718
\(563\) 10.9402 0.461075 0.230537 0.973063i \(-0.425952\pi\)
0.230537 + 0.973063i \(0.425952\pi\)
\(564\) 142.422 5.99705
\(565\) −24.8873 −1.04702
\(566\) −3.22688 −0.135636
\(567\) 33.4809 1.40606
\(568\) −57.1575 −2.39827
\(569\) −46.1074 −1.93292 −0.966462 0.256809i \(-0.917329\pi\)
−0.966462 + 0.256809i \(0.917329\pi\)
\(570\) −14.5507 −0.609464
\(571\) −10.8126 −0.452493 −0.226247 0.974070i \(-0.572646\pi\)
−0.226247 + 0.974070i \(0.572646\pi\)
\(572\) −26.8478 −1.12256
\(573\) −13.1429 −0.549052
\(574\) −39.4259 −1.64560
\(575\) 36.6932 1.53021
\(576\) 4.65471 0.193946
\(577\) 28.4683 1.18515 0.592575 0.805515i \(-0.298111\pi\)
0.592575 + 0.805515i \(0.298111\pi\)
\(578\) −2.55417 −0.106239
\(579\) 42.3795 1.76123
\(580\) 12.2397 0.508226
\(581\) −21.7441 −0.902097
\(582\) 101.034 4.18798
\(583\) 5.69213 0.235744
\(584\) 70.9358 2.93535
\(585\) 148.631 6.14515
\(586\) −79.3125 −3.27637
\(587\) 48.2610 1.99194 0.995971 0.0896706i \(-0.0285814\pi\)
0.995971 + 0.0896706i \(0.0285814\pi\)
\(588\) 74.6324 3.07779
\(589\) −4.64587 −0.191430
\(590\) 89.2567 3.67464
\(591\) −65.0674 −2.67652
\(592\) −9.59211 −0.394233
\(593\) 37.0365 1.52091 0.760454 0.649392i \(-0.224977\pi\)
0.760454 + 0.649392i \(0.224977\pi\)
\(594\) 36.8610 1.51242
\(595\) −4.62556 −0.189630
\(596\) 1.41809 0.0580871
\(597\) 53.6124 2.19421
\(598\) 88.7874 3.63079
\(599\) 23.3037 0.952165 0.476082 0.879401i \(-0.342056\pi\)
0.476082 + 0.879401i \(0.342056\pi\)
\(600\) 130.616 5.33237
\(601\) 36.3416 1.48240 0.741202 0.671282i \(-0.234256\pi\)
0.741202 + 0.671282i \(0.234256\pi\)
\(602\) −3.52011 −0.143469
\(603\) 21.5916 0.879280
\(604\) 23.5028 0.956314
\(605\) −3.35627 −0.136452
\(606\) 109.801 4.46035
\(607\) −44.7723 −1.81725 −0.908627 0.417609i \(-0.862868\pi\)
−0.908627 + 0.417609i \(0.862868\pi\)
\(608\) −3.17595 −0.128802
\(609\) 3.59355 0.145618
\(610\) −18.8327 −0.762515
\(611\) 57.7670 2.33700
\(612\) 33.7557 1.36449
\(613\) 22.4024 0.904823 0.452411 0.891809i \(-0.350564\pi\)
0.452411 + 0.891809i \(0.350564\pi\)
\(614\) −52.4059 −2.11493
\(615\) 121.587 4.90285
\(616\) −8.88399 −0.357946
\(617\) −24.7601 −0.996805 −0.498403 0.866946i \(-0.666080\pi\)
−0.498403 + 0.866946i \(0.666080\pi\)
\(618\) 121.952 4.90564
\(619\) 5.72666 0.230174 0.115087 0.993355i \(-0.463285\pi\)
0.115087 + 0.993355i \(0.463285\pi\)
\(620\) 134.416 5.39828
\(621\) −84.5300 −3.39207
\(622\) 37.8276 1.51675
\(623\) −2.16707 −0.0868219
\(624\) 142.377 5.69966
\(625\) −17.0780 −0.683120
\(626\) −84.0156 −3.35794
\(627\) −1.69738 −0.0677867
\(628\) −14.9360 −0.596013
\(629\) −1.29326 −0.0515655
\(630\) 88.1576 3.51228
\(631\) −17.6119 −0.701118 −0.350559 0.936541i \(-0.614008\pi\)
−0.350559 + 0.936541i \(0.614008\pi\)
\(632\) −76.2889 −3.03461
\(633\) 1.08209 0.0430094
\(634\) −17.9525 −0.712984
\(635\) −1.85514 −0.0736188
\(636\) −83.2876 −3.30257
\(637\) 30.2712 1.19939
\(638\) 2.05903 0.0815176
\(639\) 66.1634 2.61738
\(640\) −35.2768 −1.39444
\(641\) −5.36006 −0.211710 −0.105855 0.994382i \(-0.533758\pi\)
−0.105855 + 0.994382i \(0.533758\pi\)
\(642\) 12.8139 0.505723
\(643\) −23.4496 −0.924760 −0.462380 0.886682i \(-0.653004\pi\)
−0.462380 + 0.886682i \(0.653004\pi\)
\(644\) 36.5176 1.43900
\(645\) 10.8558 0.427446
\(646\) −1.34037 −0.0527361
\(647\) 21.7715 0.855926 0.427963 0.903796i \(-0.359231\pi\)
0.427963 + 0.903796i \(0.359231\pi\)
\(648\) −156.600 −6.15181
\(649\) 10.4120 0.408706
\(650\) 94.9618 3.72471
\(651\) 39.4642 1.54673
\(652\) −101.694 −3.98264
\(653\) 7.20019 0.281765 0.140883 0.990026i \(-0.455006\pi\)
0.140883 + 0.990026i \(0.455006\pi\)
\(654\) 63.3866 2.47861
\(655\) −5.92001 −0.231314
\(656\) 83.0719 3.24341
\(657\) −82.1127 −3.20352
\(658\) 34.2633 1.33572
\(659\) 7.27702 0.283472 0.141736 0.989904i \(-0.454732\pi\)
0.141736 + 0.989904i \(0.454732\pi\)
\(660\) 49.1092 1.91157
\(661\) −8.85333 −0.344355 −0.172177 0.985066i \(-0.555080\pi\)
−0.172177 + 0.985066i \(0.555080\pi\)
\(662\) −30.8769 −1.20007
\(663\) 19.1960 0.745513
\(664\) 101.703 3.94686
\(665\) −2.42739 −0.0941300
\(666\) 24.6479 0.955087
\(667\) −4.72178 −0.182828
\(668\) 5.94523 0.230028
\(669\) 16.9005 0.653411
\(670\) 24.8054 0.958318
\(671\) −2.19688 −0.0848096
\(672\) 26.9780 1.04070
\(673\) −40.1144 −1.54630 −0.773148 0.634225i \(-0.781319\pi\)
−0.773148 + 0.634225i \(0.781319\pi\)
\(674\) 35.2799 1.35893
\(675\) −90.4084 −3.47982
\(676\) 100.528 3.86646
\(677\) −38.9840 −1.49828 −0.749139 0.662413i \(-0.769532\pi\)
−0.749139 + 0.662413i \(0.769532\pi\)
\(678\) 61.2597 2.35266
\(679\) 16.8546 0.646822
\(680\) 21.6351 0.829667
\(681\) 29.3081 1.12309
\(682\) 22.6122 0.865865
\(683\) −25.9123 −0.991506 −0.495753 0.868464i \(-0.665108\pi\)
−0.495753 + 0.868464i \(0.665108\pi\)
\(684\) 17.7142 0.677319
\(685\) −14.9187 −0.570015
\(686\) 42.5955 1.62630
\(687\) 9.37087 0.357521
\(688\) 7.41702 0.282771
\(689\) −33.7818 −1.28698
\(690\) −162.407 −6.18273
\(691\) 10.3583 0.394049 0.197025 0.980399i \(-0.436872\pi\)
0.197025 + 0.980399i \(0.436872\pi\)
\(692\) −95.1469 −3.61694
\(693\) 10.2838 0.390649
\(694\) 22.8511 0.867415
\(695\) 8.68285 0.329359
\(696\) −16.8080 −0.637107
\(697\) 11.2002 0.424237
\(698\) −22.5779 −0.854585
\(699\) 79.3266 3.00041
\(700\) 39.0571 1.47622
\(701\) −13.2522 −0.500529 −0.250265 0.968178i \(-0.580518\pi\)
−0.250265 + 0.968178i \(0.580518\pi\)
\(702\) −218.763 −8.25670
\(703\) −0.678671 −0.0255966
\(704\) 0.623802 0.0235104
\(705\) −105.666 −3.97959
\(706\) 29.7775 1.12069
\(707\) 18.3172 0.688889
\(708\) −152.349 −5.72562
\(709\) 1.18051 0.0443348 0.0221674 0.999754i \(-0.492943\pi\)
0.0221674 + 0.999754i \(0.492943\pi\)
\(710\) 76.0115 2.85266
\(711\) 88.3092 3.31185
\(712\) 10.1360 0.379863
\(713\) −51.8545 −1.94197
\(714\) 11.3857 0.426100
\(715\) 19.9189 0.744924
\(716\) −17.8517 −0.667148
\(717\) 26.0116 0.971422
\(718\) −19.9225 −0.743500
\(719\) 26.7223 0.996572 0.498286 0.867013i \(-0.333963\pi\)
0.498286 + 0.867013i \(0.333963\pi\)
\(720\) −185.752 −6.92255
\(721\) 20.3444 0.757663
\(722\) 47.8258 1.77989
\(723\) 56.2266 2.09109
\(724\) −69.4702 −2.58184
\(725\) −5.05014 −0.187557
\(726\) 8.26140 0.306609
\(727\) 22.8693 0.848175 0.424088 0.905621i \(-0.360595\pi\)
0.424088 + 0.905621i \(0.360595\pi\)
\(728\) 52.7249 1.95412
\(729\) 41.2369 1.52729
\(730\) −94.3348 −3.49149
\(731\) 1.00000 0.0369863
\(732\) 32.1449 1.18811
\(733\) −4.91443 −0.181518 −0.0907592 0.995873i \(-0.528929\pi\)
−0.0907592 + 0.995873i \(0.528929\pi\)
\(734\) 47.7923 1.76404
\(735\) −55.3711 −2.04239
\(736\) −35.4481 −1.30663
\(737\) 2.89361 0.106588
\(738\) −213.462 −7.85763
\(739\) 5.04742 0.185672 0.0928362 0.995681i \(-0.470407\pi\)
0.0928362 + 0.995681i \(0.470407\pi\)
\(740\) 19.6356 0.721818
\(741\) 10.0736 0.370064
\(742\) −20.0370 −0.735580
\(743\) 17.9495 0.658504 0.329252 0.944242i \(-0.393203\pi\)
0.329252 + 0.944242i \(0.393203\pi\)
\(744\) −184.585 −6.76723
\(745\) −1.05210 −0.0385461
\(746\) 40.6214 1.48725
\(747\) −117.728 −4.30744
\(748\) 4.52378 0.165406
\(749\) 2.13764 0.0781075
\(750\) −35.0634 −1.28034
\(751\) 17.7075 0.646156 0.323078 0.946372i \(-0.395282\pi\)
0.323078 + 0.946372i \(0.395282\pi\)
\(752\) −72.1941 −2.63265
\(753\) 75.6162 2.75561
\(754\) −12.2200 −0.445024
\(755\) −17.4371 −0.634602
\(756\) −89.9758 −3.27239
\(757\) 32.9132 1.19625 0.598126 0.801402i \(-0.295912\pi\)
0.598126 + 0.801402i \(0.295912\pi\)
\(758\) −28.4561 −1.03357
\(759\) −18.9451 −0.687665
\(760\) 11.3536 0.411837
\(761\) −23.0245 −0.834636 −0.417318 0.908760i \(-0.637030\pi\)
−0.417318 + 0.908760i \(0.637030\pi\)
\(762\) 4.56638 0.165422
\(763\) 10.5743 0.382815
\(764\) 18.3818 0.665030
\(765\) −25.0440 −0.905466
\(766\) 8.15677 0.294716
\(767\) −61.7933 −2.23123
\(768\) 90.8685 3.27894
\(769\) −13.7130 −0.494503 −0.247251 0.968951i \(-0.579527\pi\)
−0.247251 + 0.968951i \(0.579527\pi\)
\(770\) 11.8145 0.425764
\(771\) −29.6884 −1.06920
\(772\) −59.2725 −2.13326
\(773\) 2.20396 0.0792708 0.0396354 0.999214i \(-0.487380\pi\)
0.0396354 + 0.999214i \(0.487380\pi\)
\(774\) −19.0588 −0.685054
\(775\) −55.4605 −1.99220
\(776\) −78.8340 −2.82998
\(777\) 5.76496 0.206817
\(778\) −2.76192 −0.0990196
\(779\) 5.87759 0.210586
\(780\) −291.454 −10.4357
\(781\) 8.86691 0.317283
\(782\) −14.9604 −0.534983
\(783\) 11.6340 0.415766
\(784\) −37.8313 −1.35112
\(785\) 11.0813 0.395509
\(786\) 14.5720 0.519766
\(787\) 17.9522 0.639927 0.319964 0.947430i \(-0.396329\pi\)
0.319964 + 0.947430i \(0.396329\pi\)
\(788\) 91.0042 3.24189
\(789\) 83.4398 2.97053
\(790\) 101.454 3.60955
\(791\) 10.2195 0.363363
\(792\) −48.1002 −1.70916
\(793\) 13.0381 0.462996
\(794\) 81.0827 2.87752
\(795\) 61.7926 2.19156
\(796\) −74.9830 −2.65770
\(797\) −38.7993 −1.37434 −0.687170 0.726497i \(-0.741147\pi\)
−0.687170 + 0.726497i \(0.741147\pi\)
\(798\) 5.97496 0.211511
\(799\) −9.73357 −0.344349
\(800\) −37.9132 −1.34043
\(801\) −11.7331 −0.414568
\(802\) 69.8876 2.46782
\(803\) −11.0044 −0.388335
\(804\) −42.3395 −1.49320
\(805\) −27.0931 −0.954905
\(806\) −134.199 −4.72697
\(807\) −28.1810 −0.992017
\(808\) −85.6747 −3.01402
\(809\) 44.1907 1.55366 0.776831 0.629709i \(-0.216826\pi\)
0.776831 + 0.629709i \(0.216826\pi\)
\(810\) 208.255 7.31735
\(811\) 48.8606 1.71573 0.857864 0.513877i \(-0.171791\pi\)
0.857864 + 0.513877i \(0.171791\pi\)
\(812\) −5.02598 −0.176377
\(813\) −103.249 −3.62110
\(814\) 3.30320 0.115777
\(815\) 75.4486 2.64285
\(816\) −23.9902 −0.839824
\(817\) 0.524776 0.0183596
\(818\) −25.5641 −0.893829
\(819\) −61.0324 −2.13265
\(820\) −170.053 −5.93850
\(821\) −38.4371 −1.34147 −0.670733 0.741699i \(-0.734020\pi\)
−0.670733 + 0.741699i \(0.734020\pi\)
\(822\) 36.7221 1.28083
\(823\) 28.2441 0.984527 0.492263 0.870446i \(-0.336170\pi\)
0.492263 + 0.870446i \(0.336170\pi\)
\(824\) −95.1563 −3.31493
\(825\) −20.2626 −0.705453
\(826\) −36.6514 −1.27527
\(827\) −18.6964 −0.650137 −0.325069 0.945690i \(-0.605387\pi\)
−0.325069 + 0.945690i \(0.605387\pi\)
\(828\) 197.716 6.87109
\(829\) 17.8475 0.619870 0.309935 0.950758i \(-0.399693\pi\)
0.309935 + 0.950758i \(0.399693\pi\)
\(830\) −135.251 −4.69464
\(831\) 72.5184 2.51563
\(832\) −3.70215 −0.128349
\(833\) −5.10061 −0.176726
\(834\) −21.3727 −0.740074
\(835\) −4.41087 −0.152645
\(836\) 2.37397 0.0821056
\(837\) 127.764 4.41619
\(838\) 78.6526 2.71701
\(839\) 49.5585 1.71095 0.855474 0.517845i \(-0.173266\pi\)
0.855474 + 0.517845i \(0.173266\pi\)
\(840\) −96.4427 −3.32759
\(841\) −28.3501 −0.977591
\(842\) 53.2976 1.83676
\(843\) 21.3363 0.734863
\(844\) −1.51343 −0.0520944
\(845\) −74.5836 −2.56575
\(846\) 185.510 6.37797
\(847\) 1.37818 0.0473550
\(848\) 42.2187 1.44979
\(849\) −4.08636 −0.140244
\(850\) −16.0008 −0.548822
\(851\) −7.57493 −0.259665
\(852\) −129.741 −4.44486
\(853\) 18.4565 0.631939 0.315970 0.948769i \(-0.397670\pi\)
0.315970 + 0.948769i \(0.397670\pi\)
\(854\) 7.73327 0.264627
\(855\) −13.1425 −0.449463
\(856\) −9.99833 −0.341736
\(857\) −43.3772 −1.48174 −0.740869 0.671650i \(-0.765586\pi\)
−0.740869 + 0.671650i \(0.765586\pi\)
\(858\) −49.0299 −1.67385
\(859\) 26.9066 0.918041 0.459020 0.888426i \(-0.348201\pi\)
0.459020 + 0.888426i \(0.348201\pi\)
\(860\) −15.1830 −0.517737
\(861\) −49.9270 −1.70151
\(862\) −14.7894 −0.503729
\(863\) 26.1250 0.889306 0.444653 0.895703i \(-0.353327\pi\)
0.444653 + 0.895703i \(0.353327\pi\)
\(864\) 87.3407 2.97139
\(865\) 70.5912 2.40017
\(866\) 60.2575 2.04763
\(867\) −3.23448 −0.109849
\(868\) −55.1952 −1.87345
\(869\) 11.8348 0.401467
\(870\) 22.3523 0.757815
\(871\) −17.1731 −0.581887
\(872\) −49.4590 −1.67489
\(873\) 91.2553 3.08852
\(874\) −7.85087 −0.265560
\(875\) −5.84935 −0.197744
\(876\) 161.016 5.44024
\(877\) 4.20254 0.141910 0.0709548 0.997480i \(-0.477395\pi\)
0.0709548 + 0.997480i \(0.477395\pi\)
\(878\) 43.2080 1.45820
\(879\) −100.437 −3.38767
\(880\) −24.8935 −0.839161
\(881\) −38.0143 −1.28073 −0.640367 0.768069i \(-0.721218\pi\)
−0.640367 + 0.768069i \(0.721218\pi\)
\(882\) 97.2114 3.27328
\(883\) −11.5452 −0.388528 −0.194264 0.980949i \(-0.562232\pi\)
−0.194264 + 0.980949i \(0.562232\pi\)
\(884\) −26.8478 −0.902990
\(885\) 113.030 3.79947
\(886\) −17.6417 −0.592684
\(887\) 16.4918 0.553741 0.276871 0.960907i \(-0.410703\pi\)
0.276871 + 0.960907i \(0.410703\pi\)
\(888\) −26.9643 −0.904864
\(889\) 0.761773 0.0255490
\(890\) −13.4795 −0.451833
\(891\) 24.2935 0.813862
\(892\) −23.6372 −0.791433
\(893\) −5.10795 −0.170931
\(894\) 2.58973 0.0866136
\(895\) 13.2445 0.442714
\(896\) 14.4857 0.483933
\(897\) 112.436 3.75413
\(898\) −88.7196 −2.96061
\(899\) 7.13682 0.238026
\(900\) 211.465 7.04883
\(901\) 5.69213 0.189632
\(902\) −28.6071 −0.952513
\(903\) −4.45770 −0.148343
\(904\) −47.7994 −1.58978
\(905\) 51.5412 1.71329
\(906\) 42.9211 1.42596
\(907\) 16.3851 0.544059 0.272029 0.962289i \(-0.412305\pi\)
0.272029 + 0.962289i \(0.412305\pi\)
\(908\) −40.9907 −1.36032
\(909\) 99.1738 3.28939
\(910\) −70.1168 −2.32435
\(911\) −52.2144 −1.72994 −0.864970 0.501824i \(-0.832662\pi\)
−0.864970 + 0.501824i \(0.832662\pi\)
\(912\) −12.5895 −0.416879
\(913\) −15.7774 −0.522154
\(914\) −82.5372 −2.73009
\(915\) −23.8488 −0.788419
\(916\) −13.1062 −0.433042
\(917\) 2.43093 0.0802764
\(918\) 36.8610 1.21659
\(919\) 29.8832 0.985757 0.492879 0.870098i \(-0.335945\pi\)
0.492879 + 0.870098i \(0.335945\pi\)
\(920\) 126.722 4.17790
\(921\) −66.3643 −2.18678
\(922\) −27.6627 −0.911022
\(923\) −52.6235 −1.73212
\(924\) −20.1657 −0.663402
\(925\) −8.10170 −0.266382
\(926\) −62.6701 −2.05947
\(927\) 110.149 3.61778
\(928\) 4.87878 0.160154
\(929\) −47.7925 −1.56802 −0.784011 0.620747i \(-0.786829\pi\)
−0.784011 + 0.620747i \(0.786829\pi\)
\(930\) 245.473 8.04937
\(931\) −2.67668 −0.0877246
\(932\) −110.947 −3.63420
\(933\) 47.9030 1.56827
\(934\) 66.8212 2.18646
\(935\) −3.35627 −0.109762
\(936\) 285.466 9.33075
\(937\) −19.2335 −0.628332 −0.314166 0.949368i \(-0.601725\pi\)
−0.314166 + 0.949368i \(0.601725\pi\)
\(938\) −10.1858 −0.332580
\(939\) −106.393 −3.47201
\(940\) 147.785 4.82022
\(941\) −49.3214 −1.60783 −0.803916 0.594743i \(-0.797254\pi\)
−0.803916 + 0.594743i \(0.797254\pi\)
\(942\) −27.2764 −0.888714
\(943\) 65.6022 2.13630
\(944\) 77.2259 2.51349
\(945\) 66.7547 2.17153
\(946\) −2.55417 −0.0830432
\(947\) 30.1197 0.978759 0.489379 0.872071i \(-0.337223\pi\)
0.489379 + 0.872071i \(0.337223\pi\)
\(948\) −173.167 −5.62421
\(949\) 65.3089 2.12002
\(950\) −8.39683 −0.272429
\(951\) −22.7342 −0.737206
\(952\) −8.88399 −0.287932
\(953\) −32.0301 −1.03756 −0.518778 0.854909i \(-0.673613\pi\)
−0.518778 + 0.854909i \(0.673613\pi\)
\(954\) −108.485 −3.51234
\(955\) −13.6378 −0.441308
\(956\) −36.3802 −1.17662
\(957\) 2.60745 0.0842869
\(958\) −46.6444 −1.50701
\(959\) 6.12606 0.197821
\(960\) 6.77186 0.218561
\(961\) 47.3764 1.52827
\(962\) −19.6039 −0.632055
\(963\) 11.5737 0.372957
\(964\) −78.6392 −2.53280
\(965\) 43.9753 1.41562
\(966\) 66.6890 2.14568
\(967\) −46.4739 −1.49450 −0.747250 0.664543i \(-0.768626\pi\)
−0.747250 + 0.664543i \(0.768626\pi\)
\(968\) −6.44616 −0.207187
\(969\) −1.69738 −0.0545276
\(970\) 104.838 3.36615
\(971\) −21.2545 −0.682090 −0.341045 0.940047i \(-0.610781\pi\)
−0.341045 + 0.940047i \(0.610781\pi\)
\(972\) −159.606 −5.11936
\(973\) −3.56543 −0.114302
\(974\) −54.8210 −1.75658
\(975\) 120.255 3.85124
\(976\) −16.2943 −0.521568
\(977\) 33.8197 1.08199 0.540994 0.841027i \(-0.318048\pi\)
0.540994 + 0.841027i \(0.318048\pi\)
\(978\) −185.715 −5.93852
\(979\) −1.57241 −0.0502545
\(980\) 77.4427 2.47382
\(981\) 57.2519 1.82791
\(982\) 83.5921 2.66753
\(983\) 17.4845 0.557668 0.278834 0.960339i \(-0.410052\pi\)
0.278834 + 0.960339i \(0.410052\pi\)
\(984\) 233.523 7.44444
\(985\) −67.5176 −2.15129
\(986\) 2.05903 0.0655727
\(987\) 43.3894 1.38110
\(988\) −14.0891 −0.448234
\(989\) 5.85725 0.186250
\(990\) 63.9665 2.03299
\(991\) −19.4549 −0.618005 −0.309003 0.951061i \(-0.599995\pi\)
−0.309003 + 0.951061i \(0.599995\pi\)
\(992\) 53.5787 1.70112
\(993\) −39.1011 −1.24083
\(994\) −31.2125 −0.990001
\(995\) 55.6312 1.76363
\(996\) 230.855 7.31493
\(997\) 4.47879 0.141845 0.0709224 0.997482i \(-0.477406\pi\)
0.0709224 + 0.997482i \(0.477406\pi\)
\(998\) 91.8109 2.90622
\(999\) 18.6639 0.590499
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 \(a_p\))