Properties

Label 8041.2.a.j.1.4
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

Related objects

Downloads

Learn more about

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 1.4
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62978 q^{2}\) \(+1.21378 q^{3}\) \(+4.91575 q^{4}\) \(+1.03630 q^{5}\) \(-3.19199 q^{6}\) \(+4.97586 q^{7}\) \(-7.66780 q^{8}\) \(-1.52673 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62978 q^{2}\) \(+1.21378 q^{3}\) \(+4.91575 q^{4}\) \(+1.03630 q^{5}\) \(-3.19199 q^{6}\) \(+4.97586 q^{7}\) \(-7.66780 q^{8}\) \(-1.52673 q^{9}\) \(-2.72523 q^{10}\) \(+1.00000 q^{11}\) \(+5.96666 q^{12}\) \(-4.96941 q^{13}\) \(-13.0854 q^{14}\) \(+1.25784 q^{15}\) \(+10.3331 q^{16}\) \(+1.00000 q^{17}\) \(+4.01497 q^{18}\) \(+0.115825 q^{19}\) \(+5.09417 q^{20}\) \(+6.03962 q^{21}\) \(-2.62978 q^{22}\) \(+3.52297 q^{23}\) \(-9.30705 q^{24}\) \(-3.92609 q^{25}\) \(+13.0685 q^{26}\) \(-5.49447 q^{27}\) \(+24.4601 q^{28}\) \(+8.50373 q^{29}\) \(-3.30784 q^{30}\) \(+8.64528 q^{31}\) \(-11.8383 q^{32}\) \(+1.21378 q^{33}\) \(-2.62978 q^{34}\) \(+5.15646 q^{35}\) \(-7.50502 q^{36}\) \(-0.835464 q^{37}\) \(-0.304596 q^{38}\) \(-6.03179 q^{39}\) \(-7.94610 q^{40}\) \(+9.76371 q^{41}\) \(-15.8829 q^{42}\) \(+1.00000 q^{43}\) \(+4.91575 q^{44}\) \(-1.58214 q^{45}\) \(-9.26464 q^{46}\) \(+5.23354 q^{47}\) \(+12.5422 q^{48}\) \(+17.7592 q^{49}\) \(+10.3248 q^{50}\) \(+1.21378 q^{51}\) \(-24.4284 q^{52}\) \(-8.52130 q^{53}\) \(+14.4493 q^{54}\) \(+1.03630 q^{55}\) \(-38.1539 q^{56}\) \(+0.140587 q^{57}\) \(-22.3630 q^{58}\) \(+7.29048 q^{59}\) \(+6.18322 q^{60}\) \(-7.89897 q^{61}\) \(-22.7352 q^{62}\) \(-7.59679 q^{63}\) \(+10.4658 q^{64}\) \(-5.14978 q^{65}\) \(-3.19199 q^{66}\) \(+3.71740 q^{67}\) \(+4.91575 q^{68}\) \(+4.27612 q^{69}\) \(-13.5604 q^{70}\) \(+11.1775 q^{71}\) \(+11.7066 q^{72}\) \(-5.58860 q^{73}\) \(+2.19709 q^{74}\) \(-4.76543 q^{75}\) \(+0.569369 q^{76}\) \(+4.97586 q^{77}\) \(+15.8623 q^{78}\) \(+2.14655 q^{79}\) \(+10.7082 q^{80}\) \(-2.08891 q^{81}\) \(-25.6764 q^{82}\) \(-13.4253 q^{83}\) \(+29.6893 q^{84}\) \(+1.03630 q^{85}\) \(-2.62978 q^{86}\) \(+10.3217 q^{87}\) \(-7.66780 q^{88}\) \(-5.98888 q^{89}\) \(+4.16069 q^{90}\) \(-24.7271 q^{91}\) \(+17.3180 q^{92}\) \(+10.4935 q^{93}\) \(-13.7631 q^{94}\) \(+0.120029 q^{95}\) \(-14.3691 q^{96}\) \(-9.81623 q^{97}\) \(-46.7028 q^{98}\) \(-1.52673 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62978 −1.85954 −0.929768 0.368145i \(-0.879993\pi\)
−0.929768 + 0.368145i \(0.879993\pi\)
\(3\) 1.21378 0.700778 0.350389 0.936604i \(-0.386049\pi\)
0.350389 + 0.936604i \(0.386049\pi\)
\(4\) 4.91575 2.45788
\(5\) 1.03630 0.463445 0.231723 0.972782i \(-0.425564\pi\)
0.231723 + 0.972782i \(0.425564\pi\)
\(6\) −3.19199 −1.30312
\(7\) 4.97586 1.88070 0.940349 0.340211i \(-0.110498\pi\)
0.940349 + 0.340211i \(0.110498\pi\)
\(8\) −7.66780 −2.71098
\(9\) −1.52673 −0.508910
\(10\) −2.72523 −0.861794
\(11\) 1.00000 0.301511
\(12\) 5.96666 1.72243
\(13\) −4.96941 −1.37827 −0.689133 0.724635i \(-0.742009\pi\)
−0.689133 + 0.724635i \(0.742009\pi\)
\(14\) −13.0854 −3.49723
\(15\) 1.25784 0.324772
\(16\) 10.3331 2.58328
\(17\) 1.00000 0.242536
\(18\) 4.01497 0.946336
\(19\) 0.115825 0.0265722 0.0132861 0.999912i \(-0.495771\pi\)
0.0132861 + 0.999912i \(0.495771\pi\)
\(20\) 5.09417 1.13909
\(21\) 6.03962 1.31795
\(22\) −2.62978 −0.560671
\(23\) 3.52297 0.734590 0.367295 0.930105i \(-0.380284\pi\)
0.367295 + 0.930105i \(0.380284\pi\)
\(24\) −9.30705 −1.89979
\(25\) −3.92609 −0.785218
\(26\) 13.0685 2.56294
\(27\) −5.49447 −1.05741
\(28\) 24.4601 4.62253
\(29\) 8.50373 1.57910 0.789551 0.613685i \(-0.210313\pi\)
0.789551 + 0.613685i \(0.210313\pi\)
\(30\) −3.30784 −0.603926
\(31\) 8.64528 1.55274 0.776369 0.630278i \(-0.217059\pi\)
0.776369 + 0.630278i \(0.217059\pi\)
\(32\) −11.8383 −2.09273
\(33\) 1.21378 0.211293
\(34\) −2.62978 −0.451004
\(35\) 5.15646 0.871601
\(36\) −7.50502 −1.25084
\(37\) −0.835464 −0.137350 −0.0686748 0.997639i \(-0.521877\pi\)
−0.0686748 + 0.997639i \(0.521877\pi\)
\(38\) −0.304596 −0.0494119
\(39\) −6.03179 −0.965859
\(40\) −7.94610 −1.25639
\(41\) 9.76371 1.52484 0.762418 0.647085i \(-0.224012\pi\)
0.762418 + 0.647085i \(0.224012\pi\)
\(42\) −15.8829 −2.45078
\(43\) 1.00000 0.152499
\(44\) 4.91575 0.741078
\(45\) −1.58214 −0.235852
\(46\) −9.26464 −1.36600
\(47\) 5.23354 0.763390 0.381695 0.924288i \(-0.375340\pi\)
0.381695 + 0.924288i \(0.375340\pi\)
\(48\) 12.5422 1.81031
\(49\) 17.7592 2.53703
\(50\) 10.3248 1.46014
\(51\) 1.21378 0.169964
\(52\) −24.4284 −3.38761
\(53\) −8.52130 −1.17049 −0.585245 0.810856i \(-0.699002\pi\)
−0.585245 + 0.810856i \(0.699002\pi\)
\(54\) 14.4493 1.96630
\(55\) 1.03630 0.139734
\(56\) −38.1539 −5.09853
\(57\) 0.140587 0.0186212
\(58\) −22.3630 −2.93640
\(59\) 7.29048 0.949140 0.474570 0.880218i \(-0.342604\pi\)
0.474570 + 0.880218i \(0.342604\pi\)
\(60\) 6.18322 0.798251
\(61\) −7.89897 −1.01136 −0.505680 0.862721i \(-0.668758\pi\)
−0.505680 + 0.862721i \(0.668758\pi\)
\(62\) −22.7352 −2.88737
\(63\) −7.59679 −0.957106
\(64\) 10.4658 1.30823
\(65\) −5.14978 −0.638751
\(66\) −3.19199 −0.392906
\(67\) 3.71740 0.454153 0.227076 0.973877i \(-0.427083\pi\)
0.227076 + 0.973877i \(0.427083\pi\)
\(68\) 4.91575 0.596123
\(69\) 4.27612 0.514785
\(70\) −13.5604 −1.62077
\(71\) 11.1775 1.32652 0.663260 0.748389i \(-0.269172\pi\)
0.663260 + 0.748389i \(0.269172\pi\)
\(72\) 11.7066 1.37964
\(73\) −5.58860 −0.654096 −0.327048 0.945008i \(-0.606054\pi\)
−0.327048 + 0.945008i \(0.606054\pi\)
\(74\) 2.19709 0.255406
\(75\) −4.76543 −0.550264
\(76\) 0.569369 0.0653111
\(77\) 4.97586 0.567052
\(78\) 15.8623 1.79605
\(79\) 2.14655 0.241506 0.120753 0.992683i \(-0.461469\pi\)
0.120753 + 0.992683i \(0.461469\pi\)
\(80\) 10.7082 1.19721
\(81\) −2.08891 −0.232101
\(82\) −25.6764 −2.83549
\(83\) −13.4253 −1.47362 −0.736811 0.676098i \(-0.763669\pi\)
−0.736811 + 0.676098i \(0.763669\pi\)
\(84\) 29.6893 3.23937
\(85\) 1.03630 0.112402
\(86\) −2.62978 −0.283577
\(87\) 10.3217 1.10660
\(88\) −7.66780 −0.817390
\(89\) −5.98888 −0.634820 −0.317410 0.948288i \(-0.602813\pi\)
−0.317410 + 0.948288i \(0.602813\pi\)
\(90\) 4.16069 0.438575
\(91\) −24.7271 −2.59210
\(92\) 17.3180 1.80553
\(93\) 10.4935 1.08813
\(94\) −13.7631 −1.41955
\(95\) 0.120029 0.0123148
\(96\) −14.3691 −1.46654
\(97\) −9.81623 −0.996687 −0.498343 0.866980i \(-0.666058\pi\)
−0.498343 + 0.866980i \(0.666058\pi\)
\(98\) −46.7028 −4.71770
\(99\) −1.52673 −0.153442
\(100\) −19.2997 −1.92997
\(101\) 9.49363 0.944651 0.472326 0.881424i \(-0.343415\pi\)
0.472326 + 0.881424i \(0.343415\pi\)
\(102\) −3.19199 −0.316054
\(103\) 16.2610 1.60224 0.801121 0.598503i \(-0.204238\pi\)
0.801121 + 0.598503i \(0.204238\pi\)
\(104\) 38.1044 3.73645
\(105\) 6.25883 0.610799
\(106\) 22.4092 2.17657
\(107\) −5.80470 −0.561162 −0.280581 0.959830i \(-0.590527\pi\)
−0.280581 + 0.959830i \(0.590527\pi\)
\(108\) −27.0095 −2.59899
\(109\) −8.45851 −0.810178 −0.405089 0.914277i \(-0.632760\pi\)
−0.405089 + 0.914277i \(0.632760\pi\)
\(110\) −2.72523 −0.259841
\(111\) −1.01407 −0.0962516
\(112\) 51.4162 4.85837
\(113\) −5.89233 −0.554304 −0.277152 0.960826i \(-0.589390\pi\)
−0.277152 + 0.960826i \(0.589390\pi\)
\(114\) −0.369713 −0.0346268
\(115\) 3.65084 0.340442
\(116\) 41.8022 3.88124
\(117\) 7.58694 0.701413
\(118\) −19.1724 −1.76496
\(119\) 4.97586 0.456136
\(120\) −9.64485 −0.880450
\(121\) 1.00000 0.0909091
\(122\) 20.7726 1.88066
\(123\) 11.8510 1.06857
\(124\) 42.4981 3.81644
\(125\) −9.25007 −0.827351
\(126\) 19.9779 1.77977
\(127\) −14.6467 −1.29968 −0.649841 0.760070i \(-0.725164\pi\)
−0.649841 + 0.760070i \(0.725164\pi\)
\(128\) −3.84631 −0.339969
\(129\) 1.21378 0.106868
\(130\) 13.5428 1.18778
\(131\) 4.12908 0.360759 0.180380 0.983597i \(-0.442267\pi\)
0.180380 + 0.983597i \(0.442267\pi\)
\(132\) 5.96666 0.519331
\(133\) 0.576331 0.0499742
\(134\) −9.77596 −0.844514
\(135\) −5.69389 −0.490052
\(136\) −7.66780 −0.657508
\(137\) 10.1308 0.865536 0.432768 0.901505i \(-0.357537\pi\)
0.432768 + 0.901505i \(0.357537\pi\)
\(138\) −11.2453 −0.957261
\(139\) −10.4483 −0.886215 −0.443107 0.896469i \(-0.646124\pi\)
−0.443107 + 0.896469i \(0.646124\pi\)
\(140\) 25.3479 2.14229
\(141\) 6.35238 0.534967
\(142\) −29.3943 −2.46671
\(143\) −4.96941 −0.415563
\(144\) −15.7759 −1.31466
\(145\) 8.81237 0.731828
\(146\) 14.6968 1.21632
\(147\) 21.5558 1.77789
\(148\) −4.10694 −0.337588
\(149\) −2.82672 −0.231574 −0.115787 0.993274i \(-0.536939\pi\)
−0.115787 + 0.993274i \(0.536939\pi\)
\(150\) 12.5320 1.02324
\(151\) −3.42685 −0.278873 −0.139437 0.990231i \(-0.544529\pi\)
−0.139437 + 0.990231i \(0.544529\pi\)
\(152\) −0.888126 −0.0720365
\(153\) −1.52673 −0.123429
\(154\) −13.0854 −1.05445
\(155\) 8.95907 0.719610
\(156\) −29.6508 −2.37396
\(157\) 10.5845 0.844736 0.422368 0.906424i \(-0.361199\pi\)
0.422368 + 0.906424i \(0.361199\pi\)
\(158\) −5.64497 −0.449090
\(159\) −10.3430 −0.820255
\(160\) −12.2680 −0.969867
\(161\) 17.5298 1.38154
\(162\) 5.49338 0.431601
\(163\) −6.11078 −0.478634 −0.239317 0.970942i \(-0.576923\pi\)
−0.239317 + 0.970942i \(0.576923\pi\)
\(164\) 47.9960 3.74786
\(165\) 1.25784 0.0979226
\(166\) 35.3057 2.74026
\(167\) −4.86491 −0.376458 −0.188229 0.982125i \(-0.560275\pi\)
−0.188229 + 0.982125i \(0.560275\pi\)
\(168\) −46.3106 −3.57294
\(169\) 11.6950 0.899618
\(170\) −2.72523 −0.209016
\(171\) −0.176834 −0.0135228
\(172\) 4.91575 0.374823
\(173\) 5.41350 0.411581 0.205790 0.978596i \(-0.434023\pi\)
0.205790 + 0.978596i \(0.434023\pi\)
\(174\) −27.1438 −2.05776
\(175\) −19.5357 −1.47676
\(176\) 10.3331 0.778889
\(177\) 8.84907 0.665136
\(178\) 15.7495 1.18047
\(179\) 20.5700 1.53747 0.768735 0.639567i \(-0.220886\pi\)
0.768735 + 0.639567i \(0.220886\pi\)
\(180\) −7.77742 −0.579695
\(181\) 20.1776 1.49979 0.749894 0.661558i \(-0.230104\pi\)
0.749894 + 0.661558i \(0.230104\pi\)
\(182\) 65.0269 4.82011
\(183\) −9.58764 −0.708739
\(184\) −27.0134 −1.99145
\(185\) −0.865788 −0.0636540
\(186\) −27.5956 −2.02341
\(187\) 1.00000 0.0731272
\(188\) 25.7268 1.87632
\(189\) −27.3397 −1.98867
\(190\) −0.315651 −0.0228997
\(191\) 23.7258 1.71674 0.858369 0.513033i \(-0.171478\pi\)
0.858369 + 0.513033i \(0.171478\pi\)
\(192\) 12.7033 0.916779
\(193\) 11.6452 0.838236 0.419118 0.907932i \(-0.362339\pi\)
0.419118 + 0.907932i \(0.362339\pi\)
\(194\) 25.8145 1.85338
\(195\) −6.25072 −0.447623
\(196\) 87.2998 6.23570
\(197\) −25.3113 −1.80335 −0.901677 0.432411i \(-0.857663\pi\)
−0.901677 + 0.432411i \(0.857663\pi\)
\(198\) 4.01497 0.285331
\(199\) −12.3856 −0.877992 −0.438996 0.898489i \(-0.644666\pi\)
−0.438996 + 0.898489i \(0.644666\pi\)
\(200\) 30.1045 2.12871
\(201\) 4.51212 0.318260
\(202\) −24.9662 −1.75661
\(203\) 42.3134 2.96982
\(204\) 5.96666 0.417750
\(205\) 10.1181 0.706678
\(206\) −42.7628 −2.97943
\(207\) −5.37862 −0.373840
\(208\) −51.3495 −3.56045
\(209\) 0.115825 0.00801181
\(210\) −16.4594 −1.13580
\(211\) −16.7739 −1.15476 −0.577380 0.816475i \(-0.695925\pi\)
−0.577380 + 0.816475i \(0.695925\pi\)
\(212\) −41.8886 −2.87692
\(213\) 13.5670 0.929597
\(214\) 15.2651 1.04350
\(215\) 1.03630 0.0706748
\(216\) 42.1305 2.86662
\(217\) 43.0177 2.92023
\(218\) 22.2440 1.50656
\(219\) −6.78335 −0.458376
\(220\) 5.09417 0.343449
\(221\) −4.96941 −0.334279
\(222\) 2.66679 0.178983
\(223\) 6.72264 0.450181 0.225091 0.974338i \(-0.427732\pi\)
0.225091 + 0.974338i \(0.427732\pi\)
\(224\) −58.9056 −3.93580
\(225\) 5.99408 0.399605
\(226\) 15.4955 1.03075
\(227\) 7.86616 0.522095 0.261048 0.965326i \(-0.415932\pi\)
0.261048 + 0.965326i \(0.415932\pi\)
\(228\) 0.691091 0.0457686
\(229\) −3.30575 −0.218450 −0.109225 0.994017i \(-0.534837\pi\)
−0.109225 + 0.994017i \(0.534837\pi\)
\(230\) −9.60090 −0.633065
\(231\) 6.03962 0.397378
\(232\) −65.2049 −4.28091
\(233\) 28.8082 1.88729 0.943645 0.330960i \(-0.107372\pi\)
0.943645 + 0.330960i \(0.107372\pi\)
\(234\) −19.9520 −1.30430
\(235\) 5.42349 0.353790
\(236\) 35.8382 2.33287
\(237\) 2.60545 0.169242
\(238\) −13.0854 −0.848202
\(239\) −23.2866 −1.50628 −0.753142 0.657858i \(-0.771463\pi\)
−0.753142 + 0.657858i \(0.771463\pi\)
\(240\) 12.9974 0.838979
\(241\) −9.10383 −0.586429 −0.293215 0.956047i \(-0.594725\pi\)
−0.293215 + 0.956047i \(0.594725\pi\)
\(242\) −2.62978 −0.169049
\(243\) 13.9479 0.894760
\(244\) −38.8294 −2.48580
\(245\) 18.4038 1.17577
\(246\) −31.1656 −1.98705
\(247\) −0.575584 −0.0366235
\(248\) −66.2903 −4.20944
\(249\) −16.2955 −1.03268
\(250\) 24.3257 1.53849
\(251\) 19.9273 1.25780 0.628900 0.777486i \(-0.283505\pi\)
0.628900 + 0.777486i \(0.283505\pi\)
\(252\) −37.3440 −2.35245
\(253\) 3.52297 0.221487
\(254\) 38.5175 2.41681
\(255\) 1.25784 0.0787689
\(256\) −10.8167 −0.676045
\(257\) 14.5013 0.904568 0.452284 0.891874i \(-0.350609\pi\)
0.452284 + 0.891874i \(0.350609\pi\)
\(258\) −3.19199 −0.198724
\(259\) −4.15715 −0.258313
\(260\) −25.3150 −1.56997
\(261\) −12.9829 −0.803621
\(262\) −10.8586 −0.670846
\(263\) −10.9827 −0.677223 −0.338612 0.940926i \(-0.609957\pi\)
−0.338612 + 0.940926i \(0.609957\pi\)
\(264\) −9.30705 −0.572809
\(265\) −8.83059 −0.542459
\(266\) −1.51563 −0.0929289
\(267\) −7.26921 −0.444868
\(268\) 18.2738 1.11625
\(269\) −15.0893 −0.920011 −0.460005 0.887916i \(-0.652152\pi\)
−0.460005 + 0.887916i \(0.652152\pi\)
\(270\) 14.9737 0.911270
\(271\) 6.20822 0.377122 0.188561 0.982061i \(-0.439618\pi\)
0.188561 + 0.982061i \(0.439618\pi\)
\(272\) 10.3331 0.626538
\(273\) −30.0133 −1.81649
\(274\) −26.6419 −1.60950
\(275\) −3.92609 −0.236752
\(276\) 21.0204 1.26528
\(277\) −1.48786 −0.0893970 −0.0446985 0.999001i \(-0.514233\pi\)
−0.0446985 + 0.999001i \(0.514233\pi\)
\(278\) 27.4768 1.64795
\(279\) −13.1990 −0.790204
\(280\) −39.5387 −2.36289
\(281\) −5.10045 −0.304267 −0.152134 0.988360i \(-0.548614\pi\)
−0.152134 + 0.988360i \(0.548614\pi\)
\(282\) −16.7054 −0.994791
\(283\) 22.7387 1.35168 0.675839 0.737050i \(-0.263782\pi\)
0.675839 + 0.737050i \(0.263782\pi\)
\(284\) 54.9456 3.26042
\(285\) 0.145690 0.00862991
\(286\) 13.0685 0.772755
\(287\) 48.5829 2.86776
\(288\) 18.0738 1.06501
\(289\) 1.00000 0.0588235
\(290\) −23.1746 −1.36086
\(291\) −11.9148 −0.698456
\(292\) −27.4722 −1.60769
\(293\) 23.7633 1.38827 0.694133 0.719847i \(-0.255788\pi\)
0.694133 + 0.719847i \(0.255788\pi\)
\(294\) −56.6871 −3.30606
\(295\) 7.55509 0.439874
\(296\) 6.40617 0.372351
\(297\) −5.49447 −0.318821
\(298\) 7.43366 0.430620
\(299\) −17.5071 −1.01246
\(300\) −23.4257 −1.35248
\(301\) 4.97586 0.286804
\(302\) 9.01187 0.518575
\(303\) 11.5232 0.661991
\(304\) 1.19684 0.0686434
\(305\) −8.18567 −0.468710
\(306\) 4.01497 0.229520
\(307\) −10.5867 −0.604216 −0.302108 0.953274i \(-0.597690\pi\)
−0.302108 + 0.953274i \(0.597690\pi\)
\(308\) 24.4601 1.39374
\(309\) 19.7373 1.12282
\(310\) −23.5604 −1.33814
\(311\) 11.8549 0.672232 0.336116 0.941821i \(-0.390887\pi\)
0.336116 + 0.941821i \(0.390887\pi\)
\(312\) 46.2505 2.61842
\(313\) 19.6362 1.10990 0.554952 0.831883i \(-0.312737\pi\)
0.554952 + 0.831883i \(0.312737\pi\)
\(314\) −27.8350 −1.57082
\(315\) −7.87252 −0.443566
\(316\) 10.5519 0.593592
\(317\) −1.81142 −0.101740 −0.0508698 0.998705i \(-0.516199\pi\)
−0.0508698 + 0.998705i \(0.516199\pi\)
\(318\) 27.1999 1.52529
\(319\) 8.50373 0.476117
\(320\) 10.8457 0.606293
\(321\) −7.04565 −0.393250
\(322\) −46.0996 −2.56903
\(323\) 0.115825 0.00644470
\(324\) −10.2686 −0.570476
\(325\) 19.5104 1.08224
\(326\) 16.0700 0.890037
\(327\) −10.2668 −0.567755
\(328\) −74.8661 −4.13379
\(329\) 26.0414 1.43571
\(330\) −3.30784 −0.182091
\(331\) −30.4015 −1.67102 −0.835509 0.549477i \(-0.814827\pi\)
−0.835509 + 0.549477i \(0.814827\pi\)
\(332\) −65.9957 −3.62198
\(333\) 1.27553 0.0698985
\(334\) 12.7937 0.700038
\(335\) 3.85233 0.210475
\(336\) 62.4081 3.40464
\(337\) 30.2858 1.64977 0.824886 0.565299i \(-0.191239\pi\)
0.824886 + 0.565299i \(0.191239\pi\)
\(338\) −30.7554 −1.67287
\(339\) −7.15201 −0.388444
\(340\) 5.09417 0.276270
\(341\) 8.64528 0.468168
\(342\) 0.465035 0.0251462
\(343\) 53.5362 2.89068
\(344\) −7.66780 −0.413420
\(345\) 4.43133 0.238575
\(346\) −14.2363 −0.765350
\(347\) 9.99056 0.536322 0.268161 0.963374i \(-0.413584\pi\)
0.268161 + 0.963374i \(0.413584\pi\)
\(348\) 50.7389 2.71989
\(349\) 14.5474 0.778706 0.389353 0.921089i \(-0.372699\pi\)
0.389353 + 0.921089i \(0.372699\pi\)
\(350\) 51.3746 2.74609
\(351\) 27.3043 1.45739
\(352\) −11.8383 −0.630982
\(353\) 23.1884 1.23420 0.617098 0.786886i \(-0.288308\pi\)
0.617098 + 0.786886i \(0.288308\pi\)
\(354\) −23.2711 −1.23685
\(355\) 11.5832 0.614770
\(356\) −29.4399 −1.56031
\(357\) 6.03962 0.319651
\(358\) −54.0945 −2.85898
\(359\) −9.04820 −0.477546 −0.238773 0.971075i \(-0.576745\pi\)
−0.238773 + 0.971075i \(0.576745\pi\)
\(360\) 12.1315 0.639389
\(361\) −18.9866 −0.999294
\(362\) −53.0627 −2.78891
\(363\) 1.21378 0.0637071
\(364\) −121.552 −6.37107
\(365\) −5.79144 −0.303138
\(366\) 25.2134 1.31793
\(367\) −10.6878 −0.557896 −0.278948 0.960306i \(-0.589986\pi\)
−0.278948 + 0.960306i \(0.589986\pi\)
\(368\) 36.4033 1.89765
\(369\) −14.9065 −0.776003
\(370\) 2.27683 0.118367
\(371\) −42.4008 −2.20134
\(372\) 51.5835 2.67448
\(373\) 13.7908 0.714061 0.357031 0.934093i \(-0.383789\pi\)
0.357031 + 0.934093i \(0.383789\pi\)
\(374\) −2.62978 −0.135983
\(375\) −11.2276 −0.579790
\(376\) −40.1297 −2.06953
\(377\) −42.2585 −2.17642
\(378\) 71.8975 3.69801
\(379\) −16.4202 −0.843449 −0.421725 0.906724i \(-0.638575\pi\)
−0.421725 + 0.906724i \(0.638575\pi\)
\(380\) 0.590035 0.0302681
\(381\) −17.7779 −0.910789
\(382\) −62.3937 −3.19234
\(383\) 20.4116 1.04298 0.521491 0.853257i \(-0.325376\pi\)
0.521491 + 0.853257i \(0.325376\pi\)
\(384\) −4.66859 −0.238243
\(385\) 5.15646 0.262798
\(386\) −30.6242 −1.55873
\(387\) −1.52673 −0.0776080
\(388\) −48.2541 −2.44973
\(389\) −32.2518 −1.63523 −0.817616 0.575764i \(-0.804705\pi\)
−0.817616 + 0.575764i \(0.804705\pi\)
\(390\) 16.4380 0.832371
\(391\) 3.52297 0.178164
\(392\) −136.174 −6.87782
\(393\) 5.01181 0.252812
\(394\) 66.5631 3.35340
\(395\) 2.22446 0.111925
\(396\) −7.50502 −0.377142
\(397\) −30.2330 −1.51735 −0.758676 0.651468i \(-0.774153\pi\)
−0.758676 + 0.651468i \(0.774153\pi\)
\(398\) 32.5714 1.63266
\(399\) 0.699541 0.0350209
\(400\) −40.5688 −2.02844
\(401\) 21.8202 1.08965 0.544825 0.838549i \(-0.316596\pi\)
0.544825 + 0.838549i \(0.316596\pi\)
\(402\) −11.8659 −0.591817
\(403\) −42.9620 −2.14009
\(404\) 46.6683 2.32184
\(405\) −2.16473 −0.107566
\(406\) −111.275 −5.52248
\(407\) −0.835464 −0.0414124
\(408\) −9.30705 −0.460767
\(409\) −24.5741 −1.21511 −0.607555 0.794278i \(-0.707850\pi\)
−0.607555 + 0.794278i \(0.707850\pi\)
\(410\) −26.6084 −1.31409
\(411\) 12.2966 0.606549
\(412\) 79.9349 3.93811
\(413\) 36.2764 1.78505
\(414\) 14.1446 0.695169
\(415\) −13.9126 −0.682944
\(416\) 58.8293 2.88434
\(417\) −12.6820 −0.621040
\(418\) −0.304596 −0.0148983
\(419\) 31.3993 1.53396 0.766978 0.641673i \(-0.221759\pi\)
0.766978 + 0.641673i \(0.221759\pi\)
\(420\) 30.7669 1.50127
\(421\) 22.7285 1.10772 0.553859 0.832611i \(-0.313155\pi\)
0.553859 + 0.832611i \(0.313155\pi\)
\(422\) 44.1116 2.14732
\(423\) −7.99020 −0.388497
\(424\) 65.3396 3.17317
\(425\) −3.92609 −0.190443
\(426\) −35.6783 −1.72862
\(427\) −39.3042 −1.90206
\(428\) −28.5345 −1.37927
\(429\) −6.03179 −0.291218
\(430\) −2.72523 −0.131422
\(431\) 15.3846 0.741049 0.370524 0.928823i \(-0.379178\pi\)
0.370524 + 0.928823i \(0.379178\pi\)
\(432\) −56.7750 −2.73159
\(433\) −9.67705 −0.465049 −0.232525 0.972591i \(-0.574699\pi\)
−0.232525 + 0.972591i \(0.574699\pi\)
\(434\) −113.127 −5.43028
\(435\) 10.6963 0.512849
\(436\) −41.5800 −1.99132
\(437\) 0.408049 0.0195196
\(438\) 17.8387 0.852368
\(439\) 22.7811 1.08728 0.543640 0.839318i \(-0.317046\pi\)
0.543640 + 0.839318i \(0.317046\pi\)
\(440\) −7.94610 −0.378816
\(441\) −27.1135 −1.29112
\(442\) 13.0685 0.621604
\(443\) 14.2396 0.676542 0.338271 0.941049i \(-0.390158\pi\)
0.338271 + 0.941049i \(0.390158\pi\)
\(444\) −4.98493 −0.236574
\(445\) −6.20625 −0.294205
\(446\) −17.6791 −0.837128
\(447\) −3.43103 −0.162282
\(448\) 52.0765 2.46038
\(449\) 29.2643 1.38107 0.690535 0.723299i \(-0.257375\pi\)
0.690535 + 0.723299i \(0.257375\pi\)
\(450\) −15.7631 −0.743081
\(451\) 9.76371 0.459755
\(452\) −28.9652 −1.36241
\(453\) −4.15946 −0.195428
\(454\) −20.6863 −0.970855
\(455\) −25.6246 −1.20130
\(456\) −1.07799 −0.0504816
\(457\) −7.69030 −0.359737 −0.179869 0.983691i \(-0.557567\pi\)
−0.179869 + 0.983691i \(0.557567\pi\)
\(458\) 8.69340 0.406216
\(459\) −5.49447 −0.256460
\(460\) 17.9466 0.836765
\(461\) −6.72941 −0.313420 −0.156710 0.987645i \(-0.550089\pi\)
−0.156710 + 0.987645i \(0.550089\pi\)
\(462\) −15.8829 −0.738938
\(463\) 15.5697 0.723585 0.361792 0.932259i \(-0.382165\pi\)
0.361792 + 0.932259i \(0.382165\pi\)
\(464\) 87.8701 4.07927
\(465\) 10.8744 0.504287
\(466\) −75.7594 −3.50948
\(467\) −19.1722 −0.887182 −0.443591 0.896229i \(-0.646296\pi\)
−0.443591 + 0.896229i \(0.646296\pi\)
\(468\) 37.2955 1.72399
\(469\) 18.4973 0.854125
\(470\) −14.2626 −0.657885
\(471\) 12.8473 0.591973
\(472\) −55.9019 −2.57309
\(473\) 1.00000 0.0459800
\(474\) −6.85177 −0.314712
\(475\) −0.454741 −0.0208650
\(476\) 24.4601 1.12113
\(477\) 13.0097 0.595674
\(478\) 61.2387 2.80099
\(479\) −12.8179 −0.585663 −0.292831 0.956164i \(-0.594597\pi\)
−0.292831 + 0.956164i \(0.594597\pi\)
\(480\) −14.8906 −0.679662
\(481\) 4.15177 0.189304
\(482\) 23.9411 1.09049
\(483\) 21.2774 0.968155
\(484\) 4.91575 0.223443
\(485\) −10.1725 −0.461910
\(486\) −36.6800 −1.66384
\(487\) −13.2869 −0.602085 −0.301042 0.953611i \(-0.597335\pi\)
−0.301042 + 0.953611i \(0.597335\pi\)
\(488\) 60.5677 2.74177
\(489\) −7.41717 −0.335416
\(490\) −48.3979 −2.18639
\(491\) 31.7364 1.43224 0.716122 0.697975i \(-0.245915\pi\)
0.716122 + 0.697975i \(0.245915\pi\)
\(492\) 58.2567 2.62642
\(493\) 8.50373 0.382989
\(494\) 1.51366 0.0681028
\(495\) −1.58214 −0.0711120
\(496\) 89.3328 4.01116
\(497\) 55.6175 2.49479
\(498\) 42.8535 1.92031
\(499\) 37.8117 1.69269 0.846343 0.532638i \(-0.178799\pi\)
0.846343 + 0.532638i \(0.178799\pi\)
\(500\) −45.4711 −2.03353
\(501\) −5.90495 −0.263814
\(502\) −52.4045 −2.33893
\(503\) −11.5504 −0.515009 −0.257504 0.966277i \(-0.582900\pi\)
−0.257504 + 0.966277i \(0.582900\pi\)
\(504\) 58.2507 2.59469
\(505\) 9.83821 0.437794
\(506\) −9.26464 −0.411863
\(507\) 14.1952 0.630433
\(508\) −71.9994 −3.19446
\(509\) −0.790255 −0.0350274 −0.0175137 0.999847i \(-0.505575\pi\)
−0.0175137 + 0.999847i \(0.505575\pi\)
\(510\) −3.30784 −0.146474
\(511\) −27.8081 −1.23016
\(512\) 36.1382 1.59710
\(513\) −0.636399 −0.0280977
\(514\) −38.1353 −1.68208
\(515\) 16.8512 0.742551
\(516\) 5.96666 0.262668
\(517\) 5.23354 0.230171
\(518\) 10.9324 0.480343
\(519\) 6.57082 0.288427
\(520\) 39.4874 1.73164
\(521\) 37.3316 1.63553 0.817763 0.575554i \(-0.195214\pi\)
0.817763 + 0.575554i \(0.195214\pi\)
\(522\) 34.1422 1.49436
\(523\) −23.1091 −1.01049 −0.505246 0.862976i \(-0.668598\pi\)
−0.505246 + 0.862976i \(0.668598\pi\)
\(524\) 20.2975 0.886702
\(525\) −23.7121 −1.03488
\(526\) 28.8821 1.25932
\(527\) 8.64528 0.376594
\(528\) 12.5422 0.545828
\(529\) −10.5887 −0.460378
\(530\) 23.2225 1.00872
\(531\) −11.1306 −0.483026
\(532\) 2.83310 0.122831
\(533\) −48.5199 −2.10163
\(534\) 19.1164 0.827249
\(535\) −6.01539 −0.260068
\(536\) −28.5043 −1.23120
\(537\) 24.9675 1.07743
\(538\) 39.6816 1.71079
\(539\) 17.7592 0.764942
\(540\) −27.9898 −1.20449
\(541\) 36.6252 1.57464 0.787320 0.616545i \(-0.211468\pi\)
0.787320 + 0.616545i \(0.211468\pi\)
\(542\) −16.3263 −0.701273
\(543\) 24.4912 1.05102
\(544\) −11.8383 −0.507562
\(545\) −8.76552 −0.375473
\(546\) 78.9285 3.37783
\(547\) −25.0970 −1.07307 −0.536534 0.843879i \(-0.680267\pi\)
−0.536534 + 0.843879i \(0.680267\pi\)
\(548\) 49.8007 2.12738
\(549\) 12.0596 0.514691
\(550\) 10.3248 0.440249
\(551\) 0.984948 0.0419602
\(552\) −32.7884 −1.39557
\(553\) 10.6810 0.454200
\(554\) 3.91276 0.166237
\(555\) −1.05088 −0.0446073
\(556\) −51.3614 −2.17821
\(557\) 1.55372 0.0658333 0.0329166 0.999458i \(-0.489520\pi\)
0.0329166 + 0.999458i \(0.489520\pi\)
\(558\) 34.7105 1.46941
\(559\) −4.96941 −0.210184
\(560\) 53.2824 2.25159
\(561\) 1.21378 0.0512460
\(562\) 13.4131 0.565796
\(563\) −31.7562 −1.33836 −0.669182 0.743098i \(-0.733355\pi\)
−0.669182 + 0.743098i \(0.733355\pi\)
\(564\) 31.2268 1.31488
\(565\) −6.10619 −0.256889
\(566\) −59.7979 −2.51349
\(567\) −10.3941 −0.436512
\(568\) −85.7065 −3.59616
\(569\) 19.0309 0.797815 0.398907 0.916991i \(-0.369389\pi\)
0.398907 + 0.916991i \(0.369389\pi\)
\(570\) −0.383132 −0.0160476
\(571\) −26.2124 −1.09696 −0.548478 0.836165i \(-0.684793\pi\)
−0.548478 + 0.836165i \(0.684793\pi\)
\(572\) −24.4284 −1.02140
\(573\) 28.7980 1.20305
\(574\) −127.762 −5.33270
\(575\) −13.8315 −0.576813
\(576\) −15.9785 −0.665771
\(577\) −28.9969 −1.20716 −0.603578 0.797304i \(-0.706259\pi\)
−0.603578 + 0.797304i \(0.706259\pi\)
\(578\) −2.62978 −0.109385
\(579\) 14.1347 0.587418
\(580\) 43.3195 1.79874
\(581\) −66.8026 −2.77144
\(582\) 31.3333 1.29881
\(583\) −8.52130 −0.352916
\(584\) 42.8523 1.77324
\(585\) 7.86232 0.325067
\(586\) −62.4923 −2.58153
\(587\) −47.8729 −1.97593 −0.987963 0.154691i \(-0.950562\pi\)
−0.987963 + 0.154691i \(0.950562\pi\)
\(588\) 105.963 4.36984
\(589\) 1.00134 0.0412596
\(590\) −19.8682 −0.817963
\(591\) −30.7224 −1.26375
\(592\) −8.63296 −0.354812
\(593\) 0.231760 0.00951726 0.00475863 0.999989i \(-0.498485\pi\)
0.00475863 + 0.999989i \(0.498485\pi\)
\(594\) 14.4493 0.592860
\(595\) 5.15646 0.211394
\(596\) −13.8955 −0.569180
\(597\) −15.0334 −0.615278
\(598\) 46.0398 1.88271
\(599\) −15.3181 −0.625881 −0.312940 0.949773i \(-0.601314\pi\)
−0.312940 + 0.949773i \(0.601314\pi\)
\(600\) 36.5403 1.49175
\(601\) −22.3648 −0.912277 −0.456139 0.889909i \(-0.650768\pi\)
−0.456139 + 0.889909i \(0.650768\pi\)
\(602\) −13.0854 −0.533322
\(603\) −5.67547 −0.231123
\(604\) −16.8456 −0.685436
\(605\) 1.03630 0.0421314
\(606\) −30.3035 −1.23100
\(607\) −13.6268 −0.553096 −0.276548 0.961000i \(-0.589190\pi\)
−0.276548 + 0.961000i \(0.589190\pi\)
\(608\) −1.37117 −0.0556084
\(609\) 51.3593 2.08118
\(610\) 21.5265 0.871583
\(611\) −26.0076 −1.05216
\(612\) −7.50502 −0.303373
\(613\) 26.8510 1.08450 0.542251 0.840217i \(-0.317572\pi\)
0.542251 + 0.840217i \(0.317572\pi\)
\(614\) 27.8408 1.12356
\(615\) 12.2812 0.495224
\(616\) −38.1539 −1.53726
\(617\) 16.9338 0.681730 0.340865 0.940112i \(-0.389280\pi\)
0.340865 + 0.940112i \(0.389280\pi\)
\(618\) −51.9048 −2.08792
\(619\) 31.8729 1.28108 0.640539 0.767925i \(-0.278711\pi\)
0.640539 + 0.767925i \(0.278711\pi\)
\(620\) 44.0406 1.76871
\(621\) −19.3568 −0.776763
\(622\) −31.1759 −1.25004
\(623\) −29.7999 −1.19391
\(624\) −62.3272 −2.49509
\(625\) 10.0447 0.401786
\(626\) −51.6389 −2.06391
\(627\) 0.140587 0.00561450
\(628\) 52.0309 2.07626
\(629\) −0.835464 −0.0333121
\(630\) 20.7030 0.824828
\(631\) 30.7997 1.22612 0.613059 0.790037i \(-0.289939\pi\)
0.613059 + 0.790037i \(0.289939\pi\)
\(632\) −16.4593 −0.654717
\(633\) −20.3599 −0.809231
\(634\) 4.76364 0.189188
\(635\) −15.1783 −0.602332
\(636\) −50.8437 −2.01608
\(637\) −88.2527 −3.49670
\(638\) −22.3630 −0.885358
\(639\) −17.0650 −0.675079
\(640\) −3.98591 −0.157557
\(641\) 16.7851 0.662973 0.331486 0.943460i \(-0.392450\pi\)
0.331486 + 0.943460i \(0.392450\pi\)
\(642\) 18.5285 0.731263
\(643\) −18.0719 −0.712685 −0.356343 0.934355i \(-0.615976\pi\)
−0.356343 + 0.934355i \(0.615976\pi\)
\(644\) 86.1722 3.39566
\(645\) 1.25784 0.0495273
\(646\) −0.304596 −0.0119842
\(647\) −43.3220 −1.70316 −0.851582 0.524221i \(-0.824356\pi\)
−0.851582 + 0.524221i \(0.824356\pi\)
\(648\) 16.0173 0.629220
\(649\) 7.29048 0.286176
\(650\) −51.3080 −2.01247
\(651\) 52.2142 2.04644
\(652\) −30.0391 −1.17642
\(653\) −26.7302 −1.04603 −0.523017 0.852322i \(-0.675194\pi\)
−0.523017 + 0.852322i \(0.675194\pi\)
\(654\) 26.9995 1.05576
\(655\) 4.27895 0.167192
\(656\) 100.890 3.93908
\(657\) 8.53228 0.332876
\(658\) −68.4831 −2.66975
\(659\) 3.17322 0.123611 0.0618056 0.998088i \(-0.480314\pi\)
0.0618056 + 0.998088i \(0.480314\pi\)
\(660\) 6.18322 0.240682
\(661\) 28.2017 1.09692 0.548460 0.836177i \(-0.315214\pi\)
0.548460 + 0.836177i \(0.315214\pi\)
\(662\) 79.9493 3.10732
\(663\) −6.03179 −0.234255
\(664\) 102.943 3.99496
\(665\) 0.597249 0.0231603
\(666\) −3.35436 −0.129979
\(667\) 29.9584 1.15999
\(668\) −23.9147 −0.925288
\(669\) 8.15983 0.315477
\(670\) −10.1308 −0.391386
\(671\) −7.89897 −0.304936
\(672\) −71.4987 −2.75812
\(673\) −10.2936 −0.396790 −0.198395 0.980122i \(-0.563573\pi\)
−0.198395 + 0.980122i \(0.563573\pi\)
\(674\) −79.6451 −3.06781
\(675\) 21.5718 0.830299
\(676\) 57.4899 2.21115
\(677\) 9.30249 0.357524 0.178762 0.983892i \(-0.442791\pi\)
0.178762 + 0.983892i \(0.442791\pi\)
\(678\) 18.8082 0.722326
\(679\) −48.8442 −1.87447
\(680\) −7.94610 −0.304719
\(681\) 9.54781 0.365873
\(682\) −22.7352 −0.870576
\(683\) −26.7065 −1.02190 −0.510948 0.859611i \(-0.670706\pi\)
−0.510948 + 0.859611i \(0.670706\pi\)
\(684\) −0.869273 −0.0332375
\(685\) 10.4985 0.401129
\(686\) −140.789 −5.37533
\(687\) −4.01246 −0.153085
\(688\) 10.3331 0.393947
\(689\) 42.3458 1.61325
\(690\) −11.6534 −0.443638
\(691\) 33.4352 1.27194 0.635968 0.771715i \(-0.280601\pi\)
0.635968 + 0.771715i \(0.280601\pi\)
\(692\) 26.6114 1.01161
\(693\) −7.59679 −0.288578
\(694\) −26.2730 −0.997310
\(695\) −10.8275 −0.410712
\(696\) −79.1446 −2.99997
\(697\) 9.76371 0.369827
\(698\) −38.2565 −1.44803
\(699\) 34.9670 1.32257
\(700\) −96.0326 −3.62969
\(701\) −7.39066 −0.279142 −0.139571 0.990212i \(-0.544572\pi\)
−0.139571 + 0.990212i \(0.544572\pi\)
\(702\) −71.8043 −2.71008
\(703\) −0.0967680 −0.00364967
\(704\) 10.4658 0.394446
\(705\) 6.58295 0.247928
\(706\) −60.9805 −2.29503
\(707\) 47.2390 1.77660
\(708\) 43.4998 1.63482
\(709\) −45.3080 −1.70158 −0.850788 0.525509i \(-0.823875\pi\)
−0.850788 + 0.525509i \(0.823875\pi\)
\(710\) −30.4612 −1.14319
\(711\) −3.27721 −0.122905
\(712\) 45.9215 1.72098
\(713\) 30.4571 1.14063
\(714\) −15.8829 −0.594402
\(715\) −5.14978 −0.192591
\(716\) 101.117 3.77891
\(717\) −28.2649 −1.05557
\(718\) 23.7948 0.888013
\(719\) −9.05235 −0.337596 −0.168798 0.985651i \(-0.553988\pi\)
−0.168798 + 0.985651i \(0.553988\pi\)
\(720\) −16.3485 −0.609272
\(721\) 80.9123 3.01333
\(722\) 49.9306 1.85822
\(723\) −11.0501 −0.410957
\(724\) 99.1880 3.68629
\(725\) −33.3864 −1.23994
\(726\) −3.19199 −0.118466
\(727\) 34.0948 1.26451 0.632253 0.774762i \(-0.282130\pi\)
0.632253 + 0.774762i \(0.282130\pi\)
\(728\) 189.602 7.02713
\(729\) 23.1965 0.859129
\(730\) 15.2302 0.563696
\(731\) 1.00000 0.0369863
\(732\) −47.1305 −1.74199
\(733\) 10.3204 0.381192 0.190596 0.981669i \(-0.438958\pi\)
0.190596 + 0.981669i \(0.438958\pi\)
\(734\) 28.1065 1.03743
\(735\) 22.3382 0.823957
\(736\) −41.7059 −1.53730
\(737\) 3.71740 0.136932
\(738\) 39.2009 1.44301
\(739\) 17.1350 0.630320 0.315160 0.949039i \(-0.397942\pi\)
0.315160 + 0.949039i \(0.397942\pi\)
\(740\) −4.25600 −0.156454
\(741\) −0.698634 −0.0256650
\(742\) 111.505 4.09347
\(743\) 7.78464 0.285591 0.142795 0.989752i \(-0.454391\pi\)
0.142795 + 0.989752i \(0.454391\pi\)
\(744\) −80.4620 −2.94988
\(745\) −2.92932 −0.107322
\(746\) −36.2668 −1.32782
\(747\) 20.4969 0.749941
\(748\) 4.91575 0.179738
\(749\) −28.8834 −1.05538
\(750\) 29.5261 1.07814
\(751\) 25.2267 0.920535 0.460267 0.887780i \(-0.347754\pi\)
0.460267 + 0.887780i \(0.347754\pi\)
\(752\) 54.0788 1.97205
\(753\) 24.1874 0.881439
\(754\) 111.131 4.04714
\(755\) −3.55123 −0.129243
\(756\) −134.395 −4.88791
\(757\) −49.7924 −1.80974 −0.904868 0.425691i \(-0.860031\pi\)
−0.904868 + 0.425691i \(0.860031\pi\)
\(758\) 43.1815 1.56842
\(759\) 4.27612 0.155213
\(760\) −0.920360 −0.0333850
\(761\) 40.7943 1.47879 0.739397 0.673270i \(-0.235111\pi\)
0.739397 + 0.673270i \(0.235111\pi\)
\(762\) 46.7520 1.69365
\(763\) −42.0884 −1.52370
\(764\) 116.630 4.21953
\(765\) −1.58214 −0.0572025
\(766\) −53.6780 −1.93946
\(767\) −36.2294 −1.30817
\(768\) −13.1291 −0.473757
\(769\) −12.0482 −0.434470 −0.217235 0.976119i \(-0.569704\pi\)
−0.217235 + 0.976119i \(0.569704\pi\)
\(770\) −13.5604 −0.488682
\(771\) 17.6015 0.633902
\(772\) 57.2447 2.06028
\(773\) 53.7991 1.93502 0.967509 0.252835i \(-0.0813629\pi\)
0.967509 + 0.252835i \(0.0813629\pi\)
\(774\) 4.01497 0.144315
\(775\) −33.9422 −1.21924
\(776\) 75.2688 2.70199
\(777\) −5.04589 −0.181020
\(778\) 84.8153 3.04077
\(779\) 1.13089 0.0405182
\(780\) −30.7270 −1.10020
\(781\) 11.1775 0.399961
\(782\) −9.26464 −0.331303
\(783\) −46.7235 −1.66976
\(784\) 183.508 6.55386
\(785\) 10.9687 0.391489
\(786\) −13.1800 −0.470114
\(787\) −1.03362 −0.0368446 −0.0184223 0.999830i \(-0.505864\pi\)
−0.0184223 + 0.999830i \(0.505864\pi\)
\(788\) −124.424 −4.43242
\(789\) −13.3306 −0.474583
\(790\) −5.84986 −0.208129
\(791\) −29.3194 −1.04248
\(792\) 11.7066 0.415978
\(793\) 39.2532 1.39392
\(794\) 79.5063 2.82157
\(795\) −10.7184 −0.380143
\(796\) −60.8846 −2.15800
\(797\) 21.6744 0.767748 0.383874 0.923385i \(-0.374590\pi\)
0.383874 + 0.923385i \(0.374590\pi\)
\(798\) −1.83964 −0.0651226
\(799\) 5.23354 0.185149
\(800\) 46.4782 1.64325
\(801\) 9.14340 0.323066
\(802\) −57.3825 −2.02625
\(803\) −5.58860 −0.197217
\(804\) 22.1805 0.782245
\(805\) 18.1661 0.640269
\(806\) 112.981 3.97957
\(807\) −18.3151 −0.644723
\(808\) −72.7952 −2.56093
\(809\) −52.6705 −1.85180 −0.925898 0.377775i \(-0.876689\pi\)
−0.925898 + 0.377775i \(0.876689\pi\)
\(810\) 5.69276 0.200023
\(811\) −37.1172 −1.30336 −0.651681 0.758493i \(-0.725936\pi\)
−0.651681 + 0.758493i \(0.725936\pi\)
\(812\) 208.002 7.29944
\(813\) 7.53543 0.264279
\(814\) 2.19709 0.0770079
\(815\) −6.33258 −0.221821
\(816\) 12.5422 0.439064
\(817\) 0.115825 0.00405222
\(818\) 64.6245 2.25954
\(819\) 37.7516 1.31915
\(820\) 49.7380 1.73693
\(821\) −7.74209 −0.270201 −0.135100 0.990832i \(-0.543136\pi\)
−0.135100 + 0.990832i \(0.543136\pi\)
\(822\) −32.3375 −1.12790
\(823\) 12.0480 0.419967 0.209983 0.977705i \(-0.432659\pi\)
0.209983 + 0.977705i \(0.432659\pi\)
\(824\) −124.686 −4.34364
\(825\) −4.76543 −0.165911
\(826\) −95.3991 −3.31936
\(827\) 41.7322 1.45117 0.725586 0.688132i \(-0.241569\pi\)
0.725586 + 0.688132i \(0.241569\pi\)
\(828\) −26.4400 −0.918852
\(829\) 29.4084 1.02140 0.510699 0.859760i \(-0.329387\pi\)
0.510699 + 0.859760i \(0.329387\pi\)
\(830\) 36.5872 1.26996
\(831\) −1.80594 −0.0626475
\(832\) −52.0090 −1.80309
\(833\) 17.7592 0.615319
\(834\) 33.3509 1.15485
\(835\) −5.04149 −0.174468
\(836\) 0.569369 0.0196920
\(837\) −47.5012 −1.64188
\(838\) −82.5733 −2.85245
\(839\) 1.86735 0.0644681 0.0322340 0.999480i \(-0.489738\pi\)
0.0322340 + 0.999480i \(0.489738\pi\)
\(840\) −47.9914 −1.65586
\(841\) 43.3134 1.49357
\(842\) −59.7709 −2.05984
\(843\) −6.19084 −0.213224
\(844\) −82.4562 −2.83826
\(845\) 12.1195 0.416924
\(846\) 21.0125 0.722424
\(847\) 4.97586 0.170973
\(848\) −88.0517 −3.02371
\(849\) 27.5999 0.947226
\(850\) 10.3248 0.354137
\(851\) −2.94331 −0.100896
\(852\) 66.6921 2.28483
\(853\) 18.1574 0.621697 0.310848 0.950459i \(-0.399387\pi\)
0.310848 + 0.950459i \(0.399387\pi\)
\(854\) 103.361 3.53695
\(855\) −0.183252 −0.00626710
\(856\) 44.5093 1.52130
\(857\) 27.3385 0.933866 0.466933 0.884293i \(-0.345359\pi\)
0.466933 + 0.884293i \(0.345359\pi\)
\(858\) 15.8623 0.541530
\(859\) −20.6920 −0.706002 −0.353001 0.935623i \(-0.614839\pi\)
−0.353001 + 0.935623i \(0.614839\pi\)
\(860\) 5.09417 0.173710
\(861\) 58.9691 2.00966
\(862\) −40.4581 −1.37801
\(863\) −26.8048 −0.912447 −0.456223 0.889865i \(-0.650798\pi\)
−0.456223 + 0.889865i \(0.650798\pi\)
\(864\) 65.0450 2.21288
\(865\) 5.60998 0.190745
\(866\) 25.4485 0.864776
\(867\) 1.21378 0.0412223
\(868\) 211.465 7.17757
\(869\) 2.14655 0.0728169
\(870\) −28.1290 −0.953662
\(871\) −18.4733 −0.625944
\(872\) 64.8581 2.19637
\(873\) 14.9867 0.507224
\(874\) −1.07308 −0.0362975
\(875\) −46.0271 −1.55600
\(876\) −33.3453 −1.12663
\(877\) −20.9266 −0.706642 −0.353321 0.935502i \(-0.614948\pi\)
−0.353321 + 0.935502i \(0.614948\pi\)
\(878\) −59.9092 −2.02184
\(879\) 28.8435 0.972867
\(880\) 10.7082 0.360972
\(881\) 1.70793 0.0575417 0.0287708 0.999586i \(-0.490841\pi\)
0.0287708 + 0.999586i \(0.490841\pi\)
\(882\) 71.3025 2.40088
\(883\) 23.4126 0.787896 0.393948 0.919133i \(-0.371109\pi\)
0.393948 + 0.919133i \(0.371109\pi\)
\(884\) −24.4284 −0.821616
\(885\) 9.17025 0.308254
\(886\) −37.4470 −1.25806
\(887\) −12.6990 −0.426390 −0.213195 0.977010i \(-0.568387\pi\)
−0.213195 + 0.977010i \(0.568387\pi\)
\(888\) 7.77571 0.260936
\(889\) −72.8798 −2.44431
\(890\) 16.3211 0.547084
\(891\) −2.08891 −0.0699811
\(892\) 33.0468 1.10649
\(893\) 0.606177 0.0202849
\(894\) 9.02285 0.301769
\(895\) 21.3165 0.712534
\(896\) −19.1387 −0.639379
\(897\) −21.2498 −0.709510
\(898\) −76.9589 −2.56815
\(899\) 73.5171 2.45193
\(900\) 29.4654 0.982181
\(901\) −8.52130 −0.283886
\(902\) −25.6764 −0.854931
\(903\) 6.03962 0.200986
\(904\) 45.1812 1.50270
\(905\) 20.9099 0.695070
\(906\) 10.9385 0.363406
\(907\) −30.9849 −1.02884 −0.514418 0.857540i \(-0.671992\pi\)
−0.514418 + 0.857540i \(0.671992\pi\)
\(908\) 38.6681 1.28325
\(909\) −14.4942 −0.480742
\(910\) 67.3870 2.23386
\(911\) 12.2549 0.406022 0.203011 0.979176i \(-0.434927\pi\)
0.203011 + 0.979176i \(0.434927\pi\)
\(912\) 1.45270 0.0481038
\(913\) −13.4253 −0.444314
\(914\) 20.2238 0.668945
\(915\) −9.93563 −0.328462
\(916\) −16.2502 −0.536923
\(917\) 20.5457 0.678480
\(918\) 14.4493 0.476897
\(919\) −27.6284 −0.911378 −0.455689 0.890139i \(-0.650607\pi\)
−0.455689 + 0.890139i \(0.650607\pi\)
\(920\) −27.9939 −0.922930
\(921\) −12.8500 −0.423422
\(922\) 17.6969 0.582816
\(923\) −55.5454 −1.82830
\(924\) 29.6893 0.976705
\(925\) 3.28011 0.107849
\(926\) −40.9449 −1.34553
\(927\) −24.8261 −0.815396
\(928\) −100.669 −3.30464
\(929\) 46.0754 1.51168 0.755842 0.654754i \(-0.227228\pi\)
0.755842 + 0.654754i \(0.227228\pi\)
\(930\) −28.5972 −0.937740
\(931\) 2.05697 0.0674143
\(932\) 141.614 4.63873
\(933\) 14.3893 0.471086
\(934\) 50.4186 1.64975
\(935\) 1.03630 0.0338905
\(936\) −58.1751 −1.90151
\(937\) 5.10047 0.166625 0.0833125 0.996523i \(-0.473450\pi\)
0.0833125 + 0.996523i \(0.473450\pi\)
\(938\) −48.6438 −1.58828
\(939\) 23.8341 0.777796
\(940\) 26.6606 0.869571
\(941\) −31.9030 −1.04001 −0.520004 0.854164i \(-0.674069\pi\)
−0.520004 + 0.854164i \(0.674069\pi\)
\(942\) −33.7856 −1.10080
\(943\) 34.3972 1.12013
\(944\) 75.3334 2.45189
\(945\) −28.3320 −0.921641
\(946\) −2.62978 −0.0855016
\(947\) −59.6795 −1.93932 −0.969662 0.244450i \(-0.921393\pi\)
−0.969662 + 0.244450i \(0.921393\pi\)
\(948\) 12.8078 0.415977
\(949\) 27.7721 0.901519
\(950\) 1.19587 0.0387991
\(951\) −2.19867 −0.0712969
\(952\) −38.1539 −1.23657
\(953\) 52.9918 1.71657 0.858286 0.513172i \(-0.171530\pi\)
0.858286 + 0.513172i \(0.171530\pi\)
\(954\) −34.2127 −1.10768
\(955\) 24.5869 0.795614
\(956\) −114.471 −3.70226
\(957\) 10.3217 0.333653
\(958\) 33.7082 1.08906
\(959\) 50.4097 1.62781
\(960\) 13.1643 0.424877
\(961\) 43.7409 1.41100
\(962\) −10.9182 −0.352018
\(963\) 8.86221 0.285581
\(964\) −44.7522 −1.44137
\(965\) 12.0678 0.388477
\(966\) −55.9549 −1.80032
\(967\) 55.6147 1.78845 0.894224 0.447619i \(-0.147728\pi\)
0.894224 + 0.447619i \(0.147728\pi\)
\(968\) −7.66780 −0.246452
\(969\) 0.140587 0.00451630
\(970\) 26.7515 0.858938
\(971\) −40.8904 −1.31224 −0.656118 0.754658i \(-0.727803\pi\)
−0.656118 + 0.754658i \(0.727803\pi\)
\(972\) 68.5646 2.19921
\(973\) −51.9894 −1.66670
\(974\) 34.9415 1.11960
\(975\) 23.6814 0.758410
\(976\) −81.6211 −2.61263
\(977\) 26.0233 0.832560 0.416280 0.909236i \(-0.363334\pi\)
0.416280 + 0.909236i \(0.363334\pi\)
\(978\) 19.5055 0.623718
\(979\) −5.98888 −0.191406
\(980\) 90.4684 2.88991
\(981\) 12.9139 0.412308
\(982\) −83.4599 −2.66331
\(983\) 12.8524 0.409929 0.204965 0.978769i \(-0.434292\pi\)
0.204965 + 0.978769i \(0.434292\pi\)
\(984\) −90.8713 −2.89687
\(985\) −26.2300 −0.835756
\(986\) −22.3630 −0.712181
\(987\) 31.6086 1.00611
\(988\) −2.82943 −0.0900161
\(989\) 3.52297 0.112024
\(990\) 4.16069 0.132235
\(991\) 51.8628 1.64748 0.823738 0.566970i \(-0.191884\pi\)
0.823738 + 0.566970i \(0.191884\pi\)
\(992\) −102.345 −3.24946
\(993\) −36.9008 −1.17101
\(994\) −146.262 −4.63915
\(995\) −12.8351 −0.406902
\(996\) −80.1045 −2.53821
\(997\) 16.3044 0.516367 0.258183 0.966096i \(-0.416876\pi\)
0.258183 + 0.966096i \(0.416876\pi\)
\(998\) −99.4366 −3.14761
\(999\) 4.59043 0.145235
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 \(a_p\))