Properties

Label 8041.2.a.j.1.13
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 1.13
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.22059 q^{2}\) \(-3.23881 q^{3}\) \(+2.93104 q^{4}\) \(-1.33112 q^{5}\) \(+7.19209 q^{6}\) \(-0.932335 q^{7}\) \(-2.06746 q^{8}\) \(+7.48990 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.22059 q^{2}\) \(-3.23881 q^{3}\) \(+2.93104 q^{4}\) \(-1.33112 q^{5}\) \(+7.19209 q^{6}\) \(-0.932335 q^{7}\) \(-2.06746 q^{8}\) \(+7.48990 q^{9}\) \(+2.95587 q^{10}\) \(+1.00000 q^{11}\) \(-9.49308 q^{12}\) \(+4.80259 q^{13}\) \(+2.07034 q^{14}\) \(+4.31124 q^{15}\) \(-1.27109 q^{16}\) \(+1.00000 q^{17}\) \(-16.6320 q^{18}\) \(+0.807270 q^{19}\) \(-3.90156 q^{20}\) \(+3.01966 q^{21}\) \(-2.22059 q^{22}\) \(-8.62067 q^{23}\) \(+6.69612 q^{24}\) \(-3.22813 q^{25}\) \(-10.6646 q^{26}\) \(-14.5419 q^{27}\) \(-2.73271 q^{28}\) \(-7.30946 q^{29}\) \(-9.57351 q^{30}\) \(+8.01755 q^{31}\) \(+6.95749 q^{32}\) \(-3.23881 q^{33}\) \(-2.22059 q^{34}\) \(+1.24105 q^{35}\) \(+21.9532 q^{36}\) \(-10.7508 q^{37}\) \(-1.79262 q^{38}\) \(-15.5547 q^{39}\) \(+2.75203 q^{40}\) \(+8.36668 q^{41}\) \(-6.70543 q^{42}\) \(+1.00000 q^{43}\) \(+2.93104 q^{44}\) \(-9.96994 q^{45}\) \(+19.1430 q^{46}\) \(+11.5760 q^{47}\) \(+4.11681 q^{48}\) \(-6.13075 q^{49}\) \(+7.16836 q^{50}\) \(-3.23881 q^{51}\) \(+14.0766 q^{52}\) \(+10.7135 q^{53}\) \(+32.2918 q^{54}\) \(-1.33112 q^{55}\) \(+1.92757 q^{56}\) \(-2.61460 q^{57}\) \(+16.2314 q^{58}\) \(+10.2059 q^{59}\) \(+12.6364 q^{60}\) \(-0.149587 q^{61}\) \(-17.8037 q^{62}\) \(-6.98310 q^{63}\) \(-12.9076 q^{64}\) \(-6.39281 q^{65}\) \(+7.19209 q^{66}\) \(-9.07168 q^{67}\) \(+2.93104 q^{68}\) \(+27.9207 q^{69}\) \(-2.75586 q^{70}\) \(+10.2411 q^{71}\) \(-15.4851 q^{72}\) \(+13.5574 q^{73}\) \(+23.8732 q^{74}\) \(+10.4553 q^{75}\) \(+2.36614 q^{76}\) \(-0.932335 q^{77}\) \(+34.5407 q^{78}\) \(+2.14236 q^{79}\) \(+1.69197 q^{80}\) \(+24.6289 q^{81}\) \(-18.5790 q^{82}\) \(+8.57869 q^{83}\) \(+8.85073 q^{84}\) \(-1.33112 q^{85}\) \(-2.22059 q^{86}\) \(+23.6740 q^{87}\) \(-2.06746 q^{88}\) \(-8.59733 q^{89}\) \(+22.1392 q^{90}\) \(-4.47762 q^{91}\) \(-25.2675 q^{92}\) \(-25.9673 q^{93}\) \(-25.7057 q^{94}\) \(-1.07457 q^{95}\) \(-22.5340 q^{96}\) \(-19.2144 q^{97}\) \(+13.6139 q^{98}\) \(+7.48990 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22059 −1.57020 −0.785099 0.619371i \(-0.787388\pi\)
−0.785099 + 0.619371i \(0.787388\pi\)
\(3\) −3.23881 −1.86993 −0.934964 0.354741i \(-0.884569\pi\)
−0.934964 + 0.354741i \(0.884569\pi\)
\(4\) 2.93104 1.46552
\(5\) −1.33112 −0.595294 −0.297647 0.954676i \(-0.596202\pi\)
−0.297647 + 0.954676i \(0.596202\pi\)
\(6\) 7.19209 2.93616
\(7\) −0.932335 −0.352389 −0.176195 0.984355i \(-0.556379\pi\)
−0.176195 + 0.984355i \(0.556379\pi\)
\(8\) −2.06746 −0.730958
\(9\) 7.48990 2.49663
\(10\) 2.95587 0.934729
\(11\) 1.00000 0.301511
\(12\) −9.49308 −2.74042
\(13\) 4.80259 1.33200 0.666000 0.745952i \(-0.268005\pi\)
0.666000 + 0.745952i \(0.268005\pi\)
\(14\) 2.07034 0.553321
\(15\) 4.31124 1.11316
\(16\) −1.27109 −0.317772
\(17\) 1.00000 0.242536
\(18\) −16.6320 −3.92021
\(19\) 0.807270 0.185201 0.0926003 0.995703i \(-0.470482\pi\)
0.0926003 + 0.995703i \(0.470482\pi\)
\(20\) −3.90156 −0.872415
\(21\) 3.01966 0.658943
\(22\) −2.22059 −0.473432
\(23\) −8.62067 −1.79753 −0.898767 0.438427i \(-0.855536\pi\)
−0.898767 + 0.438427i \(0.855536\pi\)
\(24\) 6.69612 1.36684
\(25\) −3.22813 −0.645625
\(26\) −10.6646 −2.09150
\(27\) −14.5419 −2.79860
\(28\) −2.73271 −0.516434
\(29\) −7.30946 −1.35733 −0.678667 0.734446i \(-0.737442\pi\)
−0.678667 + 0.734446i \(0.737442\pi\)
\(30\) −9.57351 −1.74788
\(31\) 8.01755 1.43999 0.719997 0.693977i \(-0.244143\pi\)
0.719997 + 0.693977i \(0.244143\pi\)
\(32\) 6.95749 1.22992
\(33\) −3.23881 −0.563805
\(34\) −2.22059 −0.380829
\(35\) 1.24105 0.209775
\(36\) 21.9532 3.65887
\(37\) −10.7508 −1.76742 −0.883712 0.468030i \(-0.844964\pi\)
−0.883712 + 0.468030i \(0.844964\pi\)
\(38\) −1.79262 −0.290801
\(39\) −15.5547 −2.49074
\(40\) 2.75203 0.435135
\(41\) 8.36668 1.30666 0.653328 0.757075i \(-0.273372\pi\)
0.653328 + 0.757075i \(0.273372\pi\)
\(42\) −6.70543 −1.03467
\(43\) 1.00000 0.152499
\(44\) 2.93104 0.441871
\(45\) −9.96994 −1.48623
\(46\) 19.1430 2.82248
\(47\) 11.5760 1.68854 0.844268 0.535920i \(-0.180035\pi\)
0.844268 + 0.535920i \(0.180035\pi\)
\(48\) 4.11681 0.594211
\(49\) −6.13075 −0.875822
\(50\) 7.16836 1.01376
\(51\) −3.23881 −0.453524
\(52\) 14.0766 1.95207
\(53\) 10.7135 1.47162 0.735808 0.677190i \(-0.236803\pi\)
0.735808 + 0.677190i \(0.236803\pi\)
\(54\) 32.2918 4.39435
\(55\) −1.33112 −0.179488
\(56\) 1.92757 0.257582
\(57\) −2.61460 −0.346312
\(58\) 16.2314 2.13128
\(59\) 10.2059 1.32870 0.664349 0.747423i \(-0.268709\pi\)
0.664349 + 0.747423i \(0.268709\pi\)
\(60\) 12.6364 1.63135
\(61\) −0.149587 −0.0191527 −0.00957636 0.999954i \(-0.503048\pi\)
−0.00957636 + 0.999954i \(0.503048\pi\)
\(62\) −17.8037 −2.26108
\(63\) −6.98310 −0.879788
\(64\) −12.9076 −1.61345
\(65\) −6.39281 −0.792931
\(66\) 7.19209 0.885285
\(67\) −9.07168 −1.10828 −0.554141 0.832423i \(-0.686953\pi\)
−0.554141 + 0.832423i \(0.686953\pi\)
\(68\) 2.93104 0.355441
\(69\) 27.9207 3.36126
\(70\) −2.75586 −0.329389
\(71\) 10.2411 1.21540 0.607700 0.794167i \(-0.292093\pi\)
0.607700 + 0.794167i \(0.292093\pi\)
\(72\) −15.4851 −1.82493
\(73\) 13.5574 1.58677 0.793387 0.608718i \(-0.208316\pi\)
0.793387 + 0.608718i \(0.208316\pi\)
\(74\) 23.8732 2.77521
\(75\) 10.4553 1.20727
\(76\) 2.36614 0.271415
\(77\) −0.932335 −0.106249
\(78\) 34.5407 3.91096
\(79\) 2.14236 0.241034 0.120517 0.992711i \(-0.461545\pi\)
0.120517 + 0.992711i \(0.461545\pi\)
\(80\) 1.69197 0.189168
\(81\) 24.6289 2.73655
\(82\) −18.5790 −2.05171
\(83\) 8.57869 0.941634 0.470817 0.882231i \(-0.343959\pi\)
0.470817 + 0.882231i \(0.343959\pi\)
\(84\) 8.85073 0.965694
\(85\) −1.33112 −0.144380
\(86\) −2.22059 −0.239453
\(87\) 23.6740 2.53812
\(88\) −2.06746 −0.220392
\(89\) −8.59733 −0.911315 −0.455658 0.890155i \(-0.650596\pi\)
−0.455658 + 0.890155i \(0.650596\pi\)
\(90\) 22.1392 2.33368
\(91\) −4.47762 −0.469383
\(92\) −25.2675 −2.63432
\(93\) −25.9673 −2.69269
\(94\) −25.7057 −2.65134
\(95\) −1.07457 −0.110249
\(96\) −22.5340 −2.29987
\(97\) −19.2144 −1.95092 −0.975461 0.220170i \(-0.929339\pi\)
−0.975461 + 0.220170i \(0.929339\pi\)
\(98\) 13.6139 1.37521
\(99\) 7.48990 0.752763
\(100\) −9.46176 −0.946176
\(101\) 11.7453 1.16870 0.584349 0.811503i \(-0.301350\pi\)
0.584349 + 0.811503i \(0.301350\pi\)
\(102\) 7.19209 0.712123
\(103\) 0.676477 0.0666553 0.0333276 0.999444i \(-0.489390\pi\)
0.0333276 + 0.999444i \(0.489390\pi\)
\(104\) −9.92917 −0.973635
\(105\) −4.01952 −0.392265
\(106\) −23.7904 −2.31073
\(107\) −7.43546 −0.718813 −0.359406 0.933181i \(-0.617021\pi\)
−0.359406 + 0.933181i \(0.617021\pi\)
\(108\) −42.6230 −4.10140
\(109\) −14.3239 −1.37198 −0.685990 0.727611i \(-0.740630\pi\)
−0.685990 + 0.727611i \(0.740630\pi\)
\(110\) 2.95587 0.281831
\(111\) 34.8199 3.30496
\(112\) 1.18508 0.111979
\(113\) −12.6686 −1.19176 −0.595879 0.803074i \(-0.703196\pi\)
−0.595879 + 0.803074i \(0.703196\pi\)
\(114\) 5.80596 0.543778
\(115\) 11.4751 1.07006
\(116\) −21.4243 −1.98920
\(117\) 35.9709 3.32551
\(118\) −22.6632 −2.08632
\(119\) −0.932335 −0.0854670
\(120\) −8.91332 −0.813671
\(121\) 1.00000 0.0909091
\(122\) 0.332173 0.0300735
\(123\) −27.0981 −2.44336
\(124\) 23.4998 2.11034
\(125\) 10.9526 0.979631
\(126\) 15.5066 1.38144
\(127\) 10.5483 0.936013 0.468007 0.883725i \(-0.344972\pi\)
0.468007 + 0.883725i \(0.344972\pi\)
\(128\) 14.7475 1.30351
\(129\) −3.23881 −0.285161
\(130\) 14.1958 1.24506
\(131\) 9.37849 0.819403 0.409701 0.912220i \(-0.365633\pi\)
0.409701 + 0.912220i \(0.365633\pi\)
\(132\) −9.49308 −0.826267
\(133\) −0.752646 −0.0652627
\(134\) 20.1445 1.74022
\(135\) 19.3570 1.66599
\(136\) −2.06746 −0.177283
\(137\) −5.92747 −0.506418 −0.253209 0.967412i \(-0.581486\pi\)
−0.253209 + 0.967412i \(0.581486\pi\)
\(138\) −62.0006 −5.27784
\(139\) −1.05055 −0.0891066 −0.0445533 0.999007i \(-0.514186\pi\)
−0.0445533 + 0.999007i \(0.514186\pi\)
\(140\) 3.63756 0.307430
\(141\) −37.4926 −3.15744
\(142\) −22.7414 −1.90842
\(143\) 4.80259 0.401613
\(144\) −9.52032 −0.793360
\(145\) 9.72975 0.808012
\(146\) −30.1055 −2.49155
\(147\) 19.8564 1.63772
\(148\) −31.5111 −2.59020
\(149\) 8.26366 0.676985 0.338493 0.940969i \(-0.390083\pi\)
0.338493 + 0.940969i \(0.390083\pi\)
\(150\) −23.2170 −1.89566
\(151\) 9.80243 0.797710 0.398855 0.917014i \(-0.369408\pi\)
0.398855 + 0.917014i \(0.369408\pi\)
\(152\) −1.66900 −0.135374
\(153\) 7.48990 0.605523
\(154\) 2.07034 0.166833
\(155\) −10.6723 −0.857220
\(156\) −45.5914 −3.65023
\(157\) −10.6114 −0.846884 −0.423442 0.905923i \(-0.639178\pi\)
−0.423442 + 0.905923i \(0.639178\pi\)
\(158\) −4.75731 −0.378471
\(159\) −34.6991 −2.75182
\(160\) −9.26124 −0.732165
\(161\) 8.03735 0.633432
\(162\) −54.6909 −4.29692
\(163\) −17.3561 −1.35943 −0.679716 0.733475i \(-0.737897\pi\)
−0.679716 + 0.733475i \(0.737897\pi\)
\(164\) 24.5231 1.91493
\(165\) 4.31124 0.335630
\(166\) −19.0498 −1.47855
\(167\) −21.3077 −1.64884 −0.824421 0.565978i \(-0.808499\pi\)
−0.824421 + 0.565978i \(0.808499\pi\)
\(168\) −6.24302 −0.481660
\(169\) 10.0649 0.774222
\(170\) 2.95587 0.226705
\(171\) 6.04638 0.462378
\(172\) 2.93104 0.223490
\(173\) 24.2718 1.84535 0.922676 0.385575i \(-0.125997\pi\)
0.922676 + 0.385575i \(0.125997\pi\)
\(174\) −52.5703 −3.98534
\(175\) 3.00969 0.227512
\(176\) −1.27109 −0.0958118
\(177\) −33.0551 −2.48457
\(178\) 19.0912 1.43094
\(179\) 11.1232 0.831389 0.415694 0.909504i \(-0.363539\pi\)
0.415694 + 0.909504i \(0.363539\pi\)
\(180\) −29.2223 −2.17810
\(181\) −6.48195 −0.481799 −0.240900 0.970550i \(-0.577442\pi\)
−0.240900 + 0.970550i \(0.577442\pi\)
\(182\) 9.94299 0.737023
\(183\) 0.484486 0.0358142
\(184\) 17.8229 1.31392
\(185\) 14.3106 1.05214
\(186\) 57.6629 4.22805
\(187\) 1.00000 0.0731272
\(188\) 33.9298 2.47458
\(189\) 13.5580 0.986197
\(190\) 2.38619 0.173112
\(191\) 5.43991 0.393618 0.196809 0.980442i \(-0.436942\pi\)
0.196809 + 0.980442i \(0.436942\pi\)
\(192\) 41.8053 3.01703
\(193\) −4.53753 −0.326619 −0.163309 0.986575i \(-0.552217\pi\)
−0.163309 + 0.986575i \(0.552217\pi\)
\(194\) 42.6673 3.06333
\(195\) 20.7051 1.48272
\(196\) −17.9695 −1.28353
\(197\) −16.0137 −1.14093 −0.570466 0.821322i \(-0.693237\pi\)
−0.570466 + 0.821322i \(0.693237\pi\)
\(198\) −16.6320 −1.18199
\(199\) 8.62260 0.611240 0.305620 0.952154i \(-0.401136\pi\)
0.305620 + 0.952154i \(0.401136\pi\)
\(200\) 6.67402 0.471925
\(201\) 29.3815 2.07241
\(202\) −26.0815 −1.83509
\(203\) 6.81487 0.478310
\(204\) −9.49308 −0.664649
\(205\) −11.1370 −0.777845
\(206\) −1.50218 −0.104662
\(207\) −64.5680 −4.48778
\(208\) −6.10451 −0.423272
\(209\) 0.807270 0.0558401
\(210\) 8.92572 0.615933
\(211\) 17.3751 1.19615 0.598074 0.801441i \(-0.295933\pi\)
0.598074 + 0.801441i \(0.295933\pi\)
\(212\) 31.4018 2.15668
\(213\) −33.1691 −2.27271
\(214\) 16.5111 1.12868
\(215\) −1.33112 −0.0907815
\(216\) 30.0649 2.04566
\(217\) −7.47504 −0.507439
\(218\) 31.8075 2.15428
\(219\) −43.9099 −2.96715
\(220\) −3.90156 −0.263043
\(221\) 4.80259 0.323057
\(222\) −77.3209 −5.18944
\(223\) 15.5189 1.03922 0.519611 0.854403i \(-0.326077\pi\)
0.519611 + 0.854403i \(0.326077\pi\)
\(224\) −6.48671 −0.433412
\(225\) −24.1783 −1.61189
\(226\) 28.1318 1.87130
\(227\) −1.61241 −0.107019 −0.0535097 0.998567i \(-0.517041\pi\)
−0.0535097 + 0.998567i \(0.517041\pi\)
\(228\) −7.66349 −0.507527
\(229\) −14.9324 −0.986759 −0.493380 0.869814i \(-0.664239\pi\)
−0.493380 + 0.869814i \(0.664239\pi\)
\(230\) −25.4816 −1.68021
\(231\) 3.01966 0.198679
\(232\) 15.1120 0.992153
\(233\) 13.9882 0.916398 0.458199 0.888850i \(-0.348495\pi\)
0.458199 + 0.888850i \(0.348495\pi\)
\(234\) −79.8769 −5.22171
\(235\) −15.4091 −1.00518
\(236\) 29.9140 1.94723
\(237\) −6.93870 −0.450717
\(238\) 2.07034 0.134200
\(239\) 2.07630 0.134304 0.0671522 0.997743i \(-0.478609\pi\)
0.0671522 + 0.997743i \(0.478609\pi\)
\(240\) −5.47996 −0.353730
\(241\) 16.4376 1.05884 0.529421 0.848359i \(-0.322409\pi\)
0.529421 + 0.848359i \(0.322409\pi\)
\(242\) −2.22059 −0.142745
\(243\) −36.1426 −2.31855
\(244\) −0.438447 −0.0280687
\(245\) 8.16075 0.521371
\(246\) 60.1739 3.83655
\(247\) 3.87699 0.246687
\(248\) −16.5760 −1.05257
\(249\) −27.7848 −1.76079
\(250\) −24.3213 −1.53821
\(251\) −23.5430 −1.48602 −0.743010 0.669281i \(-0.766602\pi\)
−0.743010 + 0.669281i \(0.766602\pi\)
\(252\) −20.4677 −1.28935
\(253\) −8.62067 −0.541977
\(254\) −23.4236 −1.46973
\(255\) 4.31124 0.269980
\(256\) −6.93312 −0.433320
\(257\) −1.99334 −0.124341 −0.0621705 0.998066i \(-0.519802\pi\)
−0.0621705 + 0.998066i \(0.519802\pi\)
\(258\) 7.19209 0.447760
\(259\) 10.0234 0.622822
\(260\) −18.7376 −1.16206
\(261\) −54.7472 −3.38876
\(262\) −20.8258 −1.28662
\(263\) −18.8731 −1.16376 −0.581882 0.813273i \(-0.697684\pi\)
−0.581882 + 0.813273i \(0.697684\pi\)
\(264\) 6.69612 0.412117
\(265\) −14.2610 −0.876044
\(266\) 1.67132 0.102475
\(267\) 27.8451 1.70409
\(268\) −26.5894 −1.62421
\(269\) −19.1525 −1.16775 −0.583873 0.811845i \(-0.698463\pi\)
−0.583873 + 0.811845i \(0.698463\pi\)
\(270\) −42.9841 −2.61593
\(271\) 9.31968 0.566130 0.283065 0.959101i \(-0.408649\pi\)
0.283065 + 0.959101i \(0.408649\pi\)
\(272\) −1.27109 −0.0770710
\(273\) 14.5022 0.877712
\(274\) 13.1625 0.795176
\(275\) −3.22813 −0.194663
\(276\) 81.8367 4.92599
\(277\) 9.57319 0.575197 0.287599 0.957751i \(-0.407143\pi\)
0.287599 + 0.957751i \(0.407143\pi\)
\(278\) 2.33285 0.139915
\(279\) 60.0507 3.59514
\(280\) −2.56582 −0.153337
\(281\) 3.93684 0.234852 0.117426 0.993082i \(-0.462536\pi\)
0.117426 + 0.993082i \(0.462536\pi\)
\(282\) 83.2558 4.95781
\(283\) 21.8578 1.29931 0.649654 0.760230i \(-0.274914\pi\)
0.649654 + 0.760230i \(0.274914\pi\)
\(284\) 30.0172 1.78119
\(285\) 3.48034 0.206157
\(286\) −10.6646 −0.630612
\(287\) −7.80055 −0.460452
\(288\) 52.1109 3.07067
\(289\) 1.00000 0.0588235
\(290\) −21.6058 −1.26874
\(291\) 62.2317 3.64809
\(292\) 39.7373 2.32545
\(293\) −17.4790 −1.02113 −0.510567 0.859838i \(-0.670565\pi\)
−0.510567 + 0.859838i \(0.670565\pi\)
\(294\) −44.0929 −2.57155
\(295\) −13.5853 −0.790966
\(296\) 22.2269 1.29191
\(297\) −14.5419 −0.843809
\(298\) −18.3502 −1.06300
\(299\) −41.4015 −2.39431
\(300\) 30.6449 1.76928
\(301\) −0.932335 −0.0537389
\(302\) −21.7672 −1.25256
\(303\) −38.0407 −2.18538
\(304\) −1.02611 −0.0588515
\(305\) 0.199119 0.0114015
\(306\) −16.6320 −0.950790
\(307\) 3.32392 0.189706 0.0948530 0.995491i \(-0.469762\pi\)
0.0948530 + 0.995491i \(0.469762\pi\)
\(308\) −2.73271 −0.155711
\(309\) −2.19098 −0.124641
\(310\) 23.6988 1.34600
\(311\) 14.0796 0.798379 0.399190 0.916868i \(-0.369291\pi\)
0.399190 + 0.916868i \(0.369291\pi\)
\(312\) 32.1587 1.82063
\(313\) −1.65434 −0.0935086 −0.0467543 0.998906i \(-0.514888\pi\)
−0.0467543 + 0.998906i \(0.514888\pi\)
\(314\) 23.5637 1.32977
\(315\) 9.29532 0.523732
\(316\) 6.27934 0.353240
\(317\) 9.77596 0.549072 0.274536 0.961577i \(-0.411476\pi\)
0.274536 + 0.961577i \(0.411476\pi\)
\(318\) 77.0526 4.32090
\(319\) −7.30946 −0.409251
\(320\) 17.1815 0.960476
\(321\) 24.0820 1.34413
\(322\) −17.8477 −0.994613
\(323\) 0.807270 0.0449177
\(324\) 72.1884 4.01046
\(325\) −15.5034 −0.859972
\(326\) 38.5408 2.13458
\(327\) 46.3924 2.56550
\(328\) −17.2978 −0.955111
\(329\) −10.7927 −0.595023
\(330\) −9.57351 −0.527005
\(331\) −7.80926 −0.429236 −0.214618 0.976698i \(-0.568851\pi\)
−0.214618 + 0.976698i \(0.568851\pi\)
\(332\) 25.1445 1.37998
\(333\) −80.5226 −4.41261
\(334\) 47.3158 2.58901
\(335\) 12.0755 0.659753
\(336\) −3.83825 −0.209394
\(337\) −8.72374 −0.475213 −0.237606 0.971362i \(-0.576363\pi\)
−0.237606 + 0.971362i \(0.576363\pi\)
\(338\) −22.3500 −1.21568
\(339\) 41.0311 2.22850
\(340\) −3.90156 −0.211592
\(341\) 8.01755 0.434175
\(342\) −13.4266 −0.726025
\(343\) 12.2423 0.661020
\(344\) −2.06746 −0.111470
\(345\) −37.1658 −2.00094
\(346\) −53.8979 −2.89757
\(347\) 14.5666 0.781976 0.390988 0.920396i \(-0.372133\pi\)
0.390988 + 0.920396i \(0.372133\pi\)
\(348\) 69.3894 3.71966
\(349\) −25.6913 −1.37522 −0.687612 0.726079i \(-0.741341\pi\)
−0.687612 + 0.726079i \(0.741341\pi\)
\(350\) −6.68331 −0.357238
\(351\) −69.8390 −3.72773
\(352\) 6.95749 0.370835
\(353\) 18.5988 0.989915 0.494958 0.868917i \(-0.335184\pi\)
0.494958 + 0.868917i \(0.335184\pi\)
\(354\) 73.4019 3.90126
\(355\) −13.6322 −0.723520
\(356\) −25.1991 −1.33555
\(357\) 3.01966 0.159817
\(358\) −24.7002 −1.30544
\(359\) 3.74162 0.197475 0.0987375 0.995114i \(-0.468520\pi\)
0.0987375 + 0.995114i \(0.468520\pi\)
\(360\) 20.6125 1.08637
\(361\) −18.3483 −0.965701
\(362\) 14.3938 0.756520
\(363\) −3.23881 −0.169994
\(364\) −13.1241 −0.687889
\(365\) −18.0465 −0.944596
\(366\) −1.07585 −0.0562354
\(367\) −13.3254 −0.695581 −0.347790 0.937572i \(-0.613068\pi\)
−0.347790 + 0.937572i \(0.613068\pi\)
\(368\) 10.9576 0.571205
\(369\) 62.6657 3.26224
\(370\) −31.7781 −1.65206
\(371\) −9.98860 −0.518582
\(372\) −76.1113 −3.94619
\(373\) −26.2400 −1.35866 −0.679328 0.733834i \(-0.737729\pi\)
−0.679328 + 0.733834i \(0.737729\pi\)
\(374\) −2.22059 −0.114824
\(375\) −35.4734 −1.83184
\(376\) −23.9330 −1.23425
\(377\) −35.1044 −1.80797
\(378\) −30.1067 −1.54852
\(379\) 25.4656 1.30808 0.654040 0.756460i \(-0.273073\pi\)
0.654040 + 0.756460i \(0.273073\pi\)
\(380\) −3.14961 −0.161572
\(381\) −34.1641 −1.75028
\(382\) −12.0798 −0.618059
\(383\) −7.17364 −0.366556 −0.183278 0.983061i \(-0.558671\pi\)
−0.183278 + 0.983061i \(0.558671\pi\)
\(384\) −47.7645 −2.43747
\(385\) 1.24105 0.0632496
\(386\) 10.0760 0.512856
\(387\) 7.48990 0.380733
\(388\) −56.3181 −2.85912
\(389\) 16.9227 0.858012 0.429006 0.903302i \(-0.358864\pi\)
0.429006 + 0.903302i \(0.358864\pi\)
\(390\) −45.9777 −2.32817
\(391\) −8.62067 −0.435966
\(392\) 12.6751 0.640189
\(393\) −30.3752 −1.53222
\(394\) 35.5600 1.79149
\(395\) −2.85173 −0.143486
\(396\) 21.9532 1.10319
\(397\) −17.5239 −0.879498 −0.439749 0.898121i \(-0.644933\pi\)
−0.439749 + 0.898121i \(0.644933\pi\)
\(398\) −19.1473 −0.959768
\(399\) 2.43768 0.122037
\(400\) 4.10323 0.205161
\(401\) −10.5042 −0.524554 −0.262277 0.964993i \(-0.584473\pi\)
−0.262277 + 0.964993i \(0.584473\pi\)
\(402\) −65.2443 −3.25409
\(403\) 38.5050 1.91807
\(404\) 34.4258 1.71275
\(405\) −32.7840 −1.62905
\(406\) −15.1331 −0.751041
\(407\) −10.7508 −0.532899
\(408\) 6.69612 0.331507
\(409\) −15.4454 −0.763724 −0.381862 0.924219i \(-0.624717\pi\)
−0.381862 + 0.924219i \(0.624717\pi\)
\(410\) 24.7309 1.22137
\(411\) 19.1980 0.946965
\(412\) 1.98278 0.0976846
\(413\) −9.51533 −0.468219
\(414\) 143.379 7.04671
\(415\) −11.4192 −0.560549
\(416\) 33.4140 1.63826
\(417\) 3.40254 0.166623
\(418\) −1.79262 −0.0876799
\(419\) 11.3979 0.556826 0.278413 0.960461i \(-0.410192\pi\)
0.278413 + 0.960461i \(0.410192\pi\)
\(420\) −11.7814 −0.574872
\(421\) −25.9949 −1.26691 −0.633457 0.773778i \(-0.718365\pi\)
−0.633457 + 0.773778i \(0.718365\pi\)
\(422\) −38.5830 −1.87819
\(423\) 86.7033 4.21566
\(424\) −22.1498 −1.07569
\(425\) −3.22813 −0.156587
\(426\) 73.6551 3.56860
\(427\) 0.139466 0.00674921
\(428\) −21.7936 −1.05343
\(429\) −15.5547 −0.750988
\(430\) 2.95587 0.142545
\(431\) 22.2699 1.07271 0.536353 0.843994i \(-0.319802\pi\)
0.536353 + 0.843994i \(0.319802\pi\)
\(432\) 18.4841 0.889316
\(433\) 37.6567 1.80966 0.904832 0.425769i \(-0.139996\pi\)
0.904832 + 0.425769i \(0.139996\pi\)
\(434\) 16.5990 0.796779
\(435\) −31.5128 −1.51093
\(436\) −41.9839 −2.01066
\(437\) −6.95921 −0.332904
\(438\) 97.5060 4.65902
\(439\) 15.9729 0.762347 0.381173 0.924504i \(-0.375520\pi\)
0.381173 + 0.924504i \(0.375520\pi\)
\(440\) 2.75203 0.131198
\(441\) −45.9187 −2.18661
\(442\) −10.6646 −0.507264
\(443\) −2.44955 −0.116382 −0.0581908 0.998305i \(-0.518533\pi\)
−0.0581908 + 0.998305i \(0.518533\pi\)
\(444\) 102.058 4.84348
\(445\) 11.4441 0.542500
\(446\) −34.4612 −1.63178
\(447\) −26.7644 −1.26591
\(448\) 12.0342 0.568562
\(449\) −20.0298 −0.945265 −0.472632 0.881260i \(-0.656696\pi\)
−0.472632 + 0.881260i \(0.656696\pi\)
\(450\) 53.6903 2.53099
\(451\) 8.36668 0.393972
\(452\) −37.1321 −1.74655
\(453\) −31.7482 −1.49166
\(454\) 3.58051 0.168041
\(455\) 5.96024 0.279421
\(456\) 5.40558 0.253139
\(457\) −22.2696 −1.04173 −0.520864 0.853640i \(-0.674390\pi\)
−0.520864 + 0.853640i \(0.674390\pi\)
\(458\) 33.1588 1.54941
\(459\) −14.5419 −0.678760
\(460\) 33.6340 1.56819
\(461\) 1.41068 0.0657018 0.0328509 0.999460i \(-0.489541\pi\)
0.0328509 + 0.999460i \(0.489541\pi\)
\(462\) −6.70543 −0.311965
\(463\) −25.3233 −1.17687 −0.588436 0.808544i \(-0.700256\pi\)
−0.588436 + 0.808544i \(0.700256\pi\)
\(464\) 9.29096 0.431322
\(465\) 34.5656 1.60294
\(466\) −31.0621 −1.43893
\(467\) 0.313198 0.0144931 0.00724654 0.999974i \(-0.497693\pi\)
0.00724654 + 0.999974i \(0.497693\pi\)
\(468\) 105.432 4.87361
\(469\) 8.45784 0.390547
\(470\) 34.2173 1.57832
\(471\) 34.3684 1.58361
\(472\) −21.1003 −0.971222
\(473\) 1.00000 0.0459800
\(474\) 15.4080 0.707715
\(475\) −2.60597 −0.119570
\(476\) −2.73271 −0.125254
\(477\) 80.2433 3.67409
\(478\) −4.61061 −0.210884
\(479\) −1.08888 −0.0497524 −0.0248762 0.999691i \(-0.507919\pi\)
−0.0248762 + 0.999691i \(0.507919\pi\)
\(480\) 29.9954 1.36910
\(481\) −51.6318 −2.35421
\(482\) −36.5013 −1.66259
\(483\) −26.0315 −1.18447
\(484\) 2.93104 0.133229
\(485\) 25.5766 1.16137
\(486\) 80.2581 3.64058
\(487\) −37.3112 −1.69073 −0.845367 0.534186i \(-0.820618\pi\)
−0.845367 + 0.534186i \(0.820618\pi\)
\(488\) 0.309266 0.0139998
\(489\) 56.2131 2.54204
\(490\) −18.1217 −0.818656
\(491\) −30.7080 −1.38583 −0.692917 0.721017i \(-0.743675\pi\)
−0.692917 + 0.721017i \(0.743675\pi\)
\(492\) −79.4256 −3.58078
\(493\) −7.30946 −0.329202
\(494\) −8.60922 −0.387347
\(495\) −9.96994 −0.448115
\(496\) −10.1910 −0.457590
\(497\) −9.54817 −0.428294
\(498\) 61.6987 2.76479
\(499\) 22.7886 1.02016 0.510080 0.860127i \(-0.329616\pi\)
0.510080 + 0.860127i \(0.329616\pi\)
\(500\) 32.1025 1.43567
\(501\) 69.0117 3.08322
\(502\) 52.2794 2.33334
\(503\) −20.9566 −0.934408 −0.467204 0.884149i \(-0.654739\pi\)
−0.467204 + 0.884149i \(0.654739\pi\)
\(504\) 14.4373 0.643087
\(505\) −15.6343 −0.695718
\(506\) 19.1430 0.851010
\(507\) −32.5983 −1.44774
\(508\) 30.9176 1.37175
\(509\) −35.8907 −1.59083 −0.795414 0.606066i \(-0.792747\pi\)
−0.795414 + 0.606066i \(0.792747\pi\)
\(510\) −9.57351 −0.423922
\(511\) −12.6400 −0.559162
\(512\) −14.0994 −0.623112
\(513\) −11.7393 −0.518302
\(514\) 4.42639 0.195240
\(515\) −0.900471 −0.0396795
\(516\) −9.49308 −0.417910
\(517\) 11.5760 0.509113
\(518\) −22.2578 −0.977953
\(519\) −78.6119 −3.45068
\(520\) 13.2169 0.579599
\(521\) −4.88369 −0.213958 −0.106979 0.994261i \(-0.534118\pi\)
−0.106979 + 0.994261i \(0.534118\pi\)
\(522\) 121.571 5.32103
\(523\) −3.63027 −0.158741 −0.0793704 0.996845i \(-0.525291\pi\)
−0.0793704 + 0.996845i \(0.525291\pi\)
\(524\) 27.4887 1.20085
\(525\) −9.74783 −0.425430
\(526\) 41.9095 1.82734
\(527\) 8.01755 0.349250
\(528\) 4.11681 0.179161
\(529\) 51.3159 2.23113
\(530\) 31.6678 1.37556
\(531\) 76.4413 3.31727
\(532\) −2.20604 −0.0956438
\(533\) 40.1818 1.74047
\(534\) −61.8328 −2.67576
\(535\) 9.89747 0.427905
\(536\) 18.7553 0.810107
\(537\) −36.0260 −1.55464
\(538\) 42.5298 1.83359
\(539\) −6.13075 −0.264070
\(540\) 56.7363 2.44154
\(541\) 27.6169 1.18734 0.593672 0.804707i \(-0.297678\pi\)
0.593672 + 0.804707i \(0.297678\pi\)
\(542\) −20.6952 −0.888936
\(543\) 20.9938 0.900931
\(544\) 6.95749 0.298300
\(545\) 19.0668 0.816731
\(546\) −32.2035 −1.37818
\(547\) −5.88658 −0.251692 −0.125846 0.992050i \(-0.540165\pi\)
−0.125846 + 0.992050i \(0.540165\pi\)
\(548\) −17.3736 −0.742165
\(549\) −1.12040 −0.0478173
\(550\) 7.16836 0.305660
\(551\) −5.90071 −0.251379
\(552\) −57.7250 −2.45694
\(553\) −1.99740 −0.0849379
\(554\) −21.2582 −0.903174
\(555\) −46.3494 −1.96742
\(556\) −3.07921 −0.130588
\(557\) −17.7215 −0.750886 −0.375443 0.926846i \(-0.622509\pi\)
−0.375443 + 0.926846i \(0.622509\pi\)
\(558\) −133.348 −5.64508
\(559\) 4.80259 0.203128
\(560\) −1.57748 −0.0666607
\(561\) −3.23881 −0.136743
\(562\) −8.74213 −0.368765
\(563\) −19.5992 −0.826006 −0.413003 0.910730i \(-0.635520\pi\)
−0.413003 + 0.910730i \(0.635520\pi\)
\(564\) −109.892 −4.62730
\(565\) 16.8634 0.709447
\(566\) −48.5372 −2.04017
\(567\) −22.9624 −0.964330
\(568\) −21.1731 −0.888405
\(569\) 23.8377 0.999327 0.499664 0.866219i \(-0.333457\pi\)
0.499664 + 0.866219i \(0.333457\pi\)
\(570\) −7.72842 −0.323708
\(571\) −15.1843 −0.635445 −0.317722 0.948184i \(-0.602918\pi\)
−0.317722 + 0.948184i \(0.602918\pi\)
\(572\) 14.0766 0.588572
\(573\) −17.6189 −0.736038
\(574\) 17.3219 0.723001
\(575\) 27.8286 1.16053
\(576\) −96.6766 −4.02819
\(577\) −12.8644 −0.535552 −0.267776 0.963481i \(-0.586289\pi\)
−0.267776 + 0.963481i \(0.586289\pi\)
\(578\) −2.22059 −0.0923645
\(579\) 14.6962 0.610754
\(580\) 28.5183 1.18416
\(581\) −7.99822 −0.331822
\(582\) −138.191 −5.72822
\(583\) 10.7135 0.443709
\(584\) −28.0294 −1.15986
\(585\) −47.8816 −1.97966
\(586\) 38.8138 1.60338
\(587\) 27.1321 1.11986 0.559931 0.828539i \(-0.310827\pi\)
0.559931 + 0.828539i \(0.310827\pi\)
\(588\) 58.1997 2.40012
\(589\) 6.47233 0.266688
\(590\) 30.1674 1.24197
\(591\) 51.8655 2.13346
\(592\) 13.6652 0.561638
\(593\) 18.9468 0.778054 0.389027 0.921226i \(-0.372811\pi\)
0.389027 + 0.921226i \(0.372811\pi\)
\(594\) 32.2918 1.32495
\(595\) 1.24105 0.0508780
\(596\) 24.2211 0.992135
\(597\) −27.9270 −1.14298
\(598\) 91.9360 3.75954
\(599\) 4.37119 0.178602 0.0893010 0.996005i \(-0.471537\pi\)
0.0893010 + 0.996005i \(0.471537\pi\)
\(600\) −21.6159 −0.882466
\(601\) 31.4728 1.28380 0.641901 0.766787i \(-0.278146\pi\)
0.641901 + 0.766787i \(0.278146\pi\)
\(602\) 2.07034 0.0843807
\(603\) −67.9460 −2.76697
\(604\) 28.7313 1.16906
\(605\) −1.33112 −0.0541176
\(606\) 84.4729 3.43148
\(607\) 13.6521 0.554121 0.277061 0.960852i \(-0.410640\pi\)
0.277061 + 0.960852i \(0.410640\pi\)
\(608\) 5.61658 0.227782
\(609\) −22.0721 −0.894406
\(610\) −0.442161 −0.0179026
\(611\) 55.5949 2.24913
\(612\) 21.9532 0.887405
\(613\) 7.09513 0.286570 0.143285 0.989681i \(-0.454234\pi\)
0.143285 + 0.989681i \(0.454234\pi\)
\(614\) −7.38107 −0.297876
\(615\) 36.0708 1.45451
\(616\) 1.92757 0.0776638
\(617\) 25.3337 1.01990 0.509949 0.860205i \(-0.329664\pi\)
0.509949 + 0.860205i \(0.329664\pi\)
\(618\) 4.86528 0.195710
\(619\) 25.3955 1.02073 0.510366 0.859957i \(-0.329510\pi\)
0.510366 + 0.859957i \(0.329510\pi\)
\(620\) −31.2809 −1.25627
\(621\) 125.361 5.03058
\(622\) −31.2650 −1.25361
\(623\) 8.01559 0.321138
\(624\) 19.7714 0.791488
\(625\) 1.56143 0.0624571
\(626\) 3.67361 0.146827
\(627\) −2.61460 −0.104417
\(628\) −31.1025 −1.24113
\(629\) −10.7508 −0.428663
\(630\) −20.6411 −0.822363
\(631\) −24.7758 −0.986310 −0.493155 0.869941i \(-0.664156\pi\)
−0.493155 + 0.869941i \(0.664156\pi\)
\(632\) −4.42924 −0.176186
\(633\) −56.2746 −2.23671
\(634\) −21.7084 −0.862152
\(635\) −14.0411 −0.557203
\(636\) −101.704 −4.03284
\(637\) −29.4435 −1.16659
\(638\) 16.2314 0.642605
\(639\) 76.7051 3.03441
\(640\) −19.6307 −0.775972
\(641\) −19.9885 −0.789497 −0.394748 0.918789i \(-0.629168\pi\)
−0.394748 + 0.918789i \(0.629168\pi\)
\(642\) −53.4765 −2.11055
\(643\) −31.7736 −1.25303 −0.626514 0.779410i \(-0.715519\pi\)
−0.626514 + 0.779410i \(0.715519\pi\)
\(644\) 23.5578 0.928307
\(645\) 4.31124 0.169755
\(646\) −1.79262 −0.0705297
\(647\) 42.1715 1.65793 0.828966 0.559300i \(-0.188930\pi\)
0.828966 + 0.559300i \(0.188930\pi\)
\(648\) −50.9193 −2.00030
\(649\) 10.2059 0.400617
\(650\) 34.4267 1.35033
\(651\) 24.2102 0.948874
\(652\) −50.8713 −1.99228
\(653\) −45.5674 −1.78319 −0.891595 0.452833i \(-0.850413\pi\)
−0.891595 + 0.452833i \(0.850413\pi\)
\(654\) −103.019 −4.02835
\(655\) −12.4839 −0.487785
\(656\) −10.6348 −0.415219
\(657\) 101.544 3.96159
\(658\) 23.9663 0.934303
\(659\) 6.89142 0.268452 0.134226 0.990951i \(-0.457145\pi\)
0.134226 + 0.990951i \(0.457145\pi\)
\(660\) 12.6364 0.491872
\(661\) −16.1336 −0.627526 −0.313763 0.949501i \(-0.601590\pi\)
−0.313763 + 0.949501i \(0.601590\pi\)
\(662\) 17.3412 0.673985
\(663\) −15.5547 −0.604094
\(664\) −17.7361 −0.688295
\(665\) 1.00186 0.0388505
\(666\) 178.808 6.92867
\(667\) 63.0124 2.43985
\(668\) −62.4538 −2.41641
\(669\) −50.2628 −1.94327
\(670\) −26.8147 −1.03594
\(671\) −0.149587 −0.00577476
\(672\) 21.0092 0.810449
\(673\) 9.63893 0.371554 0.185777 0.982592i \(-0.440520\pi\)
0.185777 + 0.982592i \(0.440520\pi\)
\(674\) 19.3719 0.746178
\(675\) 46.9432 1.80685
\(676\) 29.5006 1.13464
\(677\) 30.9794 1.19064 0.595318 0.803490i \(-0.297026\pi\)
0.595318 + 0.803490i \(0.297026\pi\)
\(678\) −91.1135 −3.49919
\(679\) 17.9142 0.687485
\(680\) 2.75203 0.105536
\(681\) 5.22229 0.200119
\(682\) −17.8037 −0.681740
\(683\) 9.47005 0.362361 0.181181 0.983450i \(-0.442008\pi\)
0.181181 + 0.983450i \(0.442008\pi\)
\(684\) 17.7222 0.677624
\(685\) 7.89016 0.301467
\(686\) −27.1851 −1.03793
\(687\) 48.3632 1.84517
\(688\) −1.27109 −0.0484597
\(689\) 51.4527 1.96019
\(690\) 82.5301 3.14187
\(691\) −12.7430 −0.484766 −0.242383 0.970181i \(-0.577929\pi\)
−0.242383 + 0.970181i \(0.577929\pi\)
\(692\) 71.1417 2.70440
\(693\) −6.98310 −0.265266
\(694\) −32.3465 −1.22786
\(695\) 1.39841 0.0530446
\(696\) −48.9450 −1.85526
\(697\) 8.36668 0.316911
\(698\) 57.0499 2.15937
\(699\) −45.3052 −1.71360
\(700\) 8.82153 0.333423
\(701\) 0.760299 0.0287161 0.0143580 0.999897i \(-0.495430\pi\)
0.0143580 + 0.999897i \(0.495430\pi\)
\(702\) 155.084 5.85328
\(703\) −8.67882 −0.327328
\(704\) −12.9076 −0.486473
\(705\) 49.9070 1.87961
\(706\) −41.3004 −1.55436
\(707\) −10.9505 −0.411837
\(708\) −96.8857 −3.64119
\(709\) 31.7702 1.19316 0.596578 0.802555i \(-0.296527\pi\)
0.596578 + 0.802555i \(0.296527\pi\)
\(710\) 30.2715 1.13607
\(711\) 16.0461 0.601774
\(712\) 17.7746 0.666133
\(713\) −69.1166 −2.58844
\(714\) −6.70543 −0.250945
\(715\) −6.39281 −0.239078
\(716\) 32.6026 1.21842
\(717\) −6.72473 −0.251140
\(718\) −8.30861 −0.310075
\(719\) −36.0100 −1.34295 −0.671474 0.741028i \(-0.734338\pi\)
−0.671474 + 0.741028i \(0.734338\pi\)
\(720\) 12.6727 0.472282
\(721\) −0.630703 −0.0234886
\(722\) 40.7442 1.51634
\(723\) −53.2384 −1.97996
\(724\) −18.9988 −0.706087
\(725\) 23.5959 0.876329
\(726\) 7.19209 0.266923
\(727\) −38.0910 −1.41272 −0.706359 0.707854i \(-0.749664\pi\)
−0.706359 + 0.707854i \(0.749664\pi\)
\(728\) 9.25731 0.343099
\(729\) 43.1724 1.59898
\(730\) 40.0739 1.48320
\(731\) 1.00000 0.0369863
\(732\) 1.42005 0.0524864
\(733\) 28.7771 1.06291 0.531454 0.847087i \(-0.321646\pi\)
0.531454 + 0.847087i \(0.321646\pi\)
\(734\) 29.5903 1.09220
\(735\) −26.4311 −0.974927
\(736\) −59.9782 −2.21083
\(737\) −9.07168 −0.334159
\(738\) −139.155 −5.12237
\(739\) −24.1005 −0.886549 −0.443275 0.896386i \(-0.646183\pi\)
−0.443275 + 0.896386i \(0.646183\pi\)
\(740\) 41.9450 1.54193
\(741\) −12.5568 −0.461287
\(742\) 22.1806 0.814276
\(743\) −22.3442 −0.819728 −0.409864 0.912147i \(-0.634424\pi\)
−0.409864 + 0.912147i \(0.634424\pi\)
\(744\) 53.6864 1.96824
\(745\) −10.9999 −0.403005
\(746\) 58.2684 2.13336
\(747\) 64.2536 2.35092
\(748\) 2.93104 0.107169
\(749\) 6.93234 0.253302
\(750\) 78.7721 2.87635
\(751\) 28.9494 1.05638 0.528189 0.849127i \(-0.322871\pi\)
0.528189 + 0.849127i \(0.322871\pi\)
\(752\) −14.7141 −0.536569
\(753\) 76.2512 2.77875
\(754\) 77.9526 2.83886
\(755\) −13.0482 −0.474872
\(756\) 39.7389 1.44529
\(757\) −20.4138 −0.741952 −0.370976 0.928642i \(-0.620977\pi\)
−0.370976 + 0.928642i \(0.620977\pi\)
\(758\) −56.5488 −2.05394
\(759\) 27.9207 1.01346
\(760\) 2.22164 0.0805872
\(761\) 46.3201 1.67910 0.839551 0.543280i \(-0.182818\pi\)
0.839551 + 0.543280i \(0.182818\pi\)
\(762\) 75.8645 2.74828
\(763\) 13.3547 0.483471
\(764\) 15.9446 0.576856
\(765\) −9.96994 −0.360464
\(766\) 15.9297 0.575565
\(767\) 49.0149 1.76982
\(768\) 22.4551 0.810278
\(769\) −20.9153 −0.754223 −0.377112 0.926168i \(-0.623083\pi\)
−0.377112 + 0.926168i \(0.623083\pi\)
\(770\) −2.75586 −0.0993144
\(771\) 6.45604 0.232509
\(772\) −13.2997 −0.478666
\(773\) −14.1945 −0.510542 −0.255271 0.966870i \(-0.582165\pi\)
−0.255271 + 0.966870i \(0.582165\pi\)
\(774\) −16.6320 −0.597826
\(775\) −25.8817 −0.929697
\(776\) 39.7249 1.42604
\(777\) −32.4638 −1.16463
\(778\) −37.5783 −1.34725
\(779\) 6.75418 0.241994
\(780\) 60.6875 2.17296
\(781\) 10.2411 0.366457
\(782\) 19.1430 0.684552
\(783\) 106.294 3.79863
\(784\) 7.79272 0.278311
\(785\) 14.1251 0.504145
\(786\) 67.4509 2.40590
\(787\) 22.0557 0.786201 0.393100 0.919496i \(-0.371402\pi\)
0.393100 + 0.919496i \(0.371402\pi\)
\(788\) −46.9369 −1.67206
\(789\) 61.1264 2.17616
\(790\) 6.33254 0.225302
\(791\) 11.8114 0.419963
\(792\) −15.4851 −0.550238
\(793\) −0.718408 −0.0255114
\(794\) 38.9134 1.38099
\(795\) 46.1886 1.63814
\(796\) 25.2732 0.895784
\(797\) 1.90962 0.0676423 0.0338212 0.999428i \(-0.489232\pi\)
0.0338212 + 0.999428i \(0.489232\pi\)
\(798\) −5.41310 −0.191622
\(799\) 11.5760 0.409530
\(800\) −22.4597 −0.794069
\(801\) −64.3932 −2.27522
\(802\) 23.3255 0.823654
\(803\) 13.5574 0.478430
\(804\) 86.1182 3.03715
\(805\) −10.6987 −0.377078
\(806\) −85.5040 −3.01175
\(807\) 62.0312 2.18360
\(808\) −24.2829 −0.854268
\(809\) −16.0469 −0.564180 −0.282090 0.959388i \(-0.591028\pi\)
−0.282090 + 0.959388i \(0.591028\pi\)
\(810\) 72.8000 2.55793
\(811\) −17.8474 −0.626708 −0.313354 0.949636i \(-0.601453\pi\)
−0.313354 + 0.949636i \(0.601453\pi\)
\(812\) 19.9746 0.700973
\(813\) −30.1847 −1.05862
\(814\) 23.8732 0.836756
\(815\) 23.1030 0.809262
\(816\) 4.11681 0.144117
\(817\) 0.807270 0.0282428
\(818\) 34.2979 1.19920
\(819\) −33.5370 −1.17188
\(820\) −32.6431 −1.13995
\(821\) 27.8197 0.970915 0.485458 0.874260i \(-0.338653\pi\)
0.485458 + 0.874260i \(0.338653\pi\)
\(822\) −42.6309 −1.48692
\(823\) −28.2474 −0.984643 −0.492321 0.870413i \(-0.663852\pi\)
−0.492321 + 0.870413i \(0.663852\pi\)
\(824\) −1.39859 −0.0487222
\(825\) 10.4553 0.364007
\(826\) 21.1297 0.735196
\(827\) −13.0110 −0.452436 −0.226218 0.974077i \(-0.572636\pi\)
−0.226218 + 0.974077i \(0.572636\pi\)
\(828\) −189.251 −6.57693
\(829\) −0.125222 −0.00434914 −0.00217457 0.999998i \(-0.500692\pi\)
−0.00217457 + 0.999998i \(0.500692\pi\)
\(830\) 25.3575 0.880172
\(831\) −31.0058 −1.07558
\(832\) −61.9899 −2.14911
\(833\) −6.13075 −0.212418
\(834\) −7.55566 −0.261631
\(835\) 28.3631 0.981545
\(836\) 2.36614 0.0818347
\(837\) −116.591 −4.02997
\(838\) −25.3102 −0.874327
\(839\) 44.9381 1.55143 0.775717 0.631080i \(-0.217388\pi\)
0.775717 + 0.631080i \(0.217388\pi\)
\(840\) 8.31020 0.286729
\(841\) 24.4282 0.842353
\(842\) 57.7241 1.98931
\(843\) −12.7507 −0.439157
\(844\) 50.9270 1.75298
\(845\) −13.3976 −0.460890
\(846\) −192.533 −6.61942
\(847\) −0.932335 −0.0320354
\(848\) −13.6178 −0.467638
\(849\) −70.7932 −2.42961
\(850\) 7.16836 0.245873
\(851\) 92.6793 3.17701
\(852\) −97.2200 −3.33070
\(853\) −10.8932 −0.372977 −0.186488 0.982457i \(-0.559711\pi\)
−0.186488 + 0.982457i \(0.559711\pi\)
\(854\) −0.309697 −0.0105976
\(855\) −8.04844 −0.275251
\(856\) 15.3725 0.525422
\(857\) −19.4913 −0.665809 −0.332904 0.942961i \(-0.608029\pi\)
−0.332904 + 0.942961i \(0.608029\pi\)
\(858\) 34.5407 1.17920
\(859\) −37.7299 −1.28733 −0.643664 0.765308i \(-0.722587\pi\)
−0.643664 + 0.765308i \(0.722587\pi\)
\(860\) −3.90156 −0.133042
\(861\) 25.2645 0.861013
\(862\) −49.4525 −1.68436
\(863\) 54.9779 1.87147 0.935734 0.352707i \(-0.114739\pi\)
0.935734 + 0.352707i \(0.114739\pi\)
\(864\) −101.175 −3.44206
\(865\) −32.3087 −1.09853
\(866\) −83.6202 −2.84153
\(867\) −3.23881 −0.109996
\(868\) −21.9096 −0.743662
\(869\) 2.14236 0.0726746
\(870\) 69.9772 2.37245
\(871\) −43.5676 −1.47623
\(872\) 29.6141 1.00286
\(873\) −143.914 −4.87074
\(874\) 15.4536 0.522725
\(875\) −10.2115 −0.345212
\(876\) −128.701 −4.34842
\(877\) −10.5383 −0.355852 −0.177926 0.984044i \(-0.556939\pi\)
−0.177926 + 0.984044i \(0.556939\pi\)
\(878\) −35.4694 −1.19704
\(879\) 56.6112 1.90945
\(880\) 1.69197 0.0570362
\(881\) −1.28919 −0.0434338 −0.0217169 0.999764i \(-0.506913\pi\)
−0.0217169 + 0.999764i \(0.506913\pi\)
\(882\) 101.967 3.43340
\(883\) 13.3197 0.448245 0.224122 0.974561i \(-0.428048\pi\)
0.224122 + 0.974561i \(0.428048\pi\)
\(884\) 14.0766 0.473447
\(885\) 44.0002 1.47905
\(886\) 5.43946 0.182742
\(887\) 31.0808 1.04359 0.521796 0.853070i \(-0.325262\pi\)
0.521796 + 0.853070i \(0.325262\pi\)
\(888\) −71.9888 −2.41579
\(889\) −9.83458 −0.329841
\(890\) −25.4126 −0.851833
\(891\) 24.6289 0.825100
\(892\) 45.4865 1.52300
\(893\) 9.34498 0.312718
\(894\) 59.4330 1.98774
\(895\) −14.8063 −0.494921
\(896\) −13.7496 −0.459343
\(897\) 134.092 4.47720
\(898\) 44.4781 1.48425
\(899\) −58.6040 −1.95455
\(900\) −70.8677 −2.36226
\(901\) 10.7135 0.356919
\(902\) −18.5790 −0.618613
\(903\) 3.01966 0.100488
\(904\) 26.1918 0.871125
\(905\) 8.62824 0.286812
\(906\) 70.4999 2.34220
\(907\) −31.0511 −1.03104 −0.515518 0.856879i \(-0.672400\pi\)
−0.515518 + 0.856879i \(0.672400\pi\)
\(908\) −4.72603 −0.156839
\(909\) 87.9709 2.91781
\(910\) −13.2353 −0.438745
\(911\) 1.94022 0.0642823 0.0321411 0.999483i \(-0.489767\pi\)
0.0321411 + 0.999483i \(0.489767\pi\)
\(912\) 3.32338 0.110048
\(913\) 8.57869 0.283913
\(914\) 49.4517 1.63572
\(915\) −0.644907 −0.0213200
\(916\) −43.7674 −1.44612
\(917\) −8.74390 −0.288749
\(918\) 32.2918 1.06579
\(919\) 6.35911 0.209768 0.104884 0.994484i \(-0.466553\pi\)
0.104884 + 0.994484i \(0.466553\pi\)
\(920\) −23.7244 −0.782169
\(921\) −10.7655 −0.354737
\(922\) −3.13254 −0.103165
\(923\) 49.1840 1.61891
\(924\) 8.85073 0.291168
\(925\) 34.7050 1.14109
\(926\) 56.2327 1.84792
\(927\) 5.06675 0.166414
\(928\) −50.8555 −1.66941
\(929\) 4.10078 0.134542 0.0672712 0.997735i \(-0.478571\pi\)
0.0672712 + 0.997735i \(0.478571\pi\)
\(930\) −76.7561 −2.51693
\(931\) −4.94917 −0.162203
\(932\) 41.0000 1.34300
\(933\) −45.6011 −1.49291
\(934\) −0.695486 −0.0227570
\(935\) −1.33112 −0.0435322
\(936\) −74.3685 −2.43081
\(937\) 31.6315 1.03335 0.516677 0.856180i \(-0.327169\pi\)
0.516677 + 0.856180i \(0.327169\pi\)
\(938\) −18.7814 −0.613235
\(939\) 5.35808 0.174854
\(940\) −45.1645 −1.47310
\(941\) −19.8860 −0.648266 −0.324133 0.946011i \(-0.605073\pi\)
−0.324133 + 0.946011i \(0.605073\pi\)
\(942\) −76.3183 −2.48658
\(943\) −72.1264 −2.34876
\(944\) −12.9726 −0.422223
\(945\) −18.0472 −0.587077
\(946\) −2.22059 −0.0721978
\(947\) 31.8193 1.03399 0.516994 0.855989i \(-0.327051\pi\)
0.516994 + 0.855989i \(0.327051\pi\)
\(948\) −20.3376 −0.660535
\(949\) 65.1106 2.11358
\(950\) 5.78680 0.187749
\(951\) −31.6625 −1.02673
\(952\) 1.92757 0.0624728
\(953\) −39.9062 −1.29269 −0.646344 0.763046i \(-0.723703\pi\)
−0.646344 + 0.763046i \(0.723703\pi\)
\(954\) −178.188 −5.76904
\(955\) −7.24117 −0.234319
\(956\) 6.08571 0.196826
\(957\) 23.6740 0.765271
\(958\) 2.41797 0.0781211
\(959\) 5.52639 0.178456
\(960\) −55.6477 −1.79602
\(961\) 33.2811 1.07358
\(962\) 114.653 3.69657
\(963\) −55.6908 −1.79461
\(964\) 48.1794 1.55175
\(965\) 6.03999 0.194434
\(966\) 57.8053 1.85986
\(967\) 0.987880 0.0317681 0.0158840 0.999874i \(-0.494944\pi\)
0.0158840 + 0.999874i \(0.494944\pi\)
\(968\) −2.06746 −0.0664507
\(969\) −2.61460 −0.0839930
\(970\) −56.7952 −1.82358
\(971\) −6.56596 −0.210712 −0.105356 0.994435i \(-0.533598\pi\)
−0.105356 + 0.994435i \(0.533598\pi\)
\(972\) −105.935 −3.39788
\(973\) 0.979466 0.0314002
\(974\) 82.8531 2.65479
\(975\) 50.2125 1.60809
\(976\) 0.190139 0.00608619
\(977\) 23.3104 0.745765 0.372882 0.927879i \(-0.378369\pi\)
0.372882 + 0.927879i \(0.378369\pi\)
\(978\) −124.826 −3.99151
\(979\) −8.59733 −0.274772
\(980\) 23.9195 0.764080
\(981\) −107.284 −3.42533
\(982\) 68.1901 2.17603
\(983\) 2.26795 0.0723365 0.0361682 0.999346i \(-0.488485\pi\)
0.0361682 + 0.999346i \(0.488485\pi\)
\(984\) 56.0243 1.78599
\(985\) 21.3162 0.679189
\(986\) 16.2314 0.516912
\(987\) 34.9556 1.11265
\(988\) 11.3636 0.361525
\(989\) −8.62067 −0.274121
\(990\) 22.1392 0.703630
\(991\) 10.1142 0.321289 0.160645 0.987012i \(-0.448643\pi\)
0.160645 + 0.987012i \(0.448643\pi\)
\(992\) 55.7820 1.77108
\(993\) 25.2927 0.802641
\(994\) 21.2026 0.672506
\(995\) −11.4777 −0.363868
\(996\) −81.4383 −2.58047
\(997\) 40.8609 1.29408 0.647038 0.762458i \(-0.276007\pi\)
0.647038 + 0.762458i \(0.276007\pi\)
\(998\) −50.6043 −1.60185
\(999\) 156.338 4.94631
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 \(a_p\))