Properties

Label 6001.2.a.b.1.12
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.36622 q^{2}\) \(-1.16111 q^{3}\) \(+3.59897 q^{4}\) \(-3.78541 q^{5}\) \(+2.74743 q^{6}\) \(-1.24944 q^{7}\) \(-3.78352 q^{8}\) \(-1.65183 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.36622 q^{2}\) \(-1.16111 q^{3}\) \(+3.59897 q^{4}\) \(-3.78541 q^{5}\) \(+2.74743 q^{6}\) \(-1.24944 q^{7}\) \(-3.78352 q^{8}\) \(-1.65183 q^{9}\) \(+8.95709 q^{10}\) \(+5.90263 q^{11}\) \(-4.17879 q^{12}\) \(-1.18162 q^{13}\) \(+2.95644 q^{14}\) \(+4.39526 q^{15}\) \(+1.75466 q^{16}\) \(+1.00000 q^{17}\) \(+3.90859 q^{18}\) \(-1.27065 q^{19}\) \(-13.6236 q^{20}\) \(+1.45073 q^{21}\) \(-13.9669 q^{22}\) \(-7.24873 q^{23}\) \(+4.39306 q^{24}\) \(+9.32931 q^{25}\) \(+2.79596 q^{26}\) \(+5.40127 q^{27}\) \(-4.49669 q^{28}\) \(-9.12776 q^{29}\) \(-10.4001 q^{30}\) \(+3.49231 q^{31}\) \(+3.41512 q^{32}\) \(-6.85358 q^{33}\) \(-2.36622 q^{34}\) \(+4.72963 q^{35}\) \(-5.94491 q^{36}\) \(+5.41453 q^{37}\) \(+3.00664 q^{38}\) \(+1.37198 q^{39}\) \(+14.3221 q^{40}\) \(-3.88046 q^{41}\) \(-3.43274 q^{42}\) \(-0.876332 q^{43}\) \(+21.2434 q^{44}\) \(+6.25286 q^{45}\) \(+17.1521 q^{46}\) \(-3.03549 q^{47}\) \(-2.03735 q^{48}\) \(-5.43891 q^{49}\) \(-22.0752 q^{50}\) \(-1.16111 q^{51}\) \(-4.25261 q^{52}\) \(+6.64042 q^{53}\) \(-12.7806 q^{54}\) \(-22.3439 q^{55}\) \(+4.72727 q^{56}\) \(+1.47536 q^{57}\) \(+21.5983 q^{58}\) \(+2.21644 q^{59}\) \(+15.8184 q^{60}\) \(-12.5378 q^{61}\) \(-8.26355 q^{62}\) \(+2.06386 q^{63}\) \(-11.5902 q^{64}\) \(+4.47290 q^{65}\) \(+16.2170 q^{66}\) \(+4.23889 q^{67}\) \(+3.59897 q^{68}\) \(+8.41654 q^{69}\) \(-11.1913 q^{70}\) \(-16.2867 q^{71}\) \(+6.24974 q^{72}\) \(-7.52844 q^{73}\) \(-12.8119 q^{74}\) \(-10.8323 q^{75}\) \(-4.57305 q^{76}\) \(-7.37497 q^{77}\) \(-3.24640 q^{78}\) \(+14.7859 q^{79}\) \(-6.64212 q^{80}\) \(-1.31594 q^{81}\) \(+9.18200 q^{82}\) \(+16.6273 q^{83}\) \(+5.22113 q^{84}\) \(-3.78541 q^{85}\) \(+2.07359 q^{86}\) \(+10.5983 q^{87}\) \(-22.3327 q^{88}\) \(+4.50223 q^{89}\) \(-14.7956 q^{90}\) \(+1.47636 q^{91}\) \(-26.0880 q^{92}\) \(-4.05494 q^{93}\) \(+7.18262 q^{94}\) \(+4.80994 q^{95}\) \(-3.96531 q^{96}\) \(+13.0983 q^{97}\) \(+12.8696 q^{98}\) \(-9.75016 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36622 −1.67317 −0.836583 0.547840i \(-0.815450\pi\)
−0.836583 + 0.547840i \(0.815450\pi\)
\(3\) −1.16111 −0.670365 −0.335182 0.942153i \(-0.608798\pi\)
−0.335182 + 0.942153i \(0.608798\pi\)
\(4\) 3.59897 1.79949
\(5\) −3.78541 −1.69289 −0.846443 0.532480i \(-0.821260\pi\)
−0.846443 + 0.532480i \(0.821260\pi\)
\(6\) 2.74743 1.12163
\(7\) −1.24944 −0.472243 −0.236121 0.971724i \(-0.575876\pi\)
−0.236121 + 0.971724i \(0.575876\pi\)
\(8\) −3.78352 −1.33767
\(9\) −1.65183 −0.550611
\(10\) 8.95709 2.83248
\(11\) 5.90263 1.77971 0.889855 0.456244i \(-0.150805\pi\)
0.889855 + 0.456244i \(0.150805\pi\)
\(12\) −4.17879 −1.20631
\(13\) −1.18162 −0.327722 −0.163861 0.986483i \(-0.552395\pi\)
−0.163861 + 0.986483i \(0.552395\pi\)
\(14\) 2.95644 0.790141
\(15\) 4.39526 1.13485
\(16\) 1.75466 0.438666
\(17\) 1.00000 0.242536
\(18\) 3.90859 0.921264
\(19\) −1.27065 −0.291508 −0.145754 0.989321i \(-0.546561\pi\)
−0.145754 + 0.989321i \(0.546561\pi\)
\(20\) −13.6236 −3.04633
\(21\) 1.45073 0.316575
\(22\) −13.9669 −2.97775
\(23\) −7.24873 −1.51146 −0.755732 0.654881i \(-0.772719\pi\)
−0.755732 + 0.654881i \(0.772719\pi\)
\(24\) 4.39306 0.896730
\(25\) 9.32931 1.86586
\(26\) 2.79596 0.548333
\(27\) 5.40127 1.03947
\(28\) −4.49669 −0.849795
\(29\) −9.12776 −1.69498 −0.847492 0.530809i \(-0.821888\pi\)
−0.847492 + 0.530809i \(0.821888\pi\)
\(30\) −10.4001 −1.89879
\(31\) 3.49231 0.627237 0.313618 0.949549i \(-0.398459\pi\)
0.313618 + 0.949549i \(0.398459\pi\)
\(32\) 3.41512 0.603713
\(33\) −6.85358 −1.19305
\(34\) −2.36622 −0.405803
\(35\) 4.72963 0.799453
\(36\) −5.94491 −0.990818
\(37\) 5.41453 0.890143 0.445071 0.895495i \(-0.353178\pi\)
0.445071 + 0.895495i \(0.353178\pi\)
\(38\) 3.00664 0.487741
\(39\) 1.37198 0.219693
\(40\) 14.3221 2.26453
\(41\) −3.88046 −0.606026 −0.303013 0.952986i \(-0.597993\pi\)
−0.303013 + 0.952986i \(0.597993\pi\)
\(42\) −3.43274 −0.529683
\(43\) −0.876332 −0.133639 −0.0668197 0.997765i \(-0.521285\pi\)
−0.0668197 + 0.997765i \(0.521285\pi\)
\(44\) 21.2434 3.20256
\(45\) 6.25286 0.932122
\(46\) 17.1521 2.52893
\(47\) −3.03549 −0.442771 −0.221386 0.975186i \(-0.571058\pi\)
−0.221386 + 0.975186i \(0.571058\pi\)
\(48\) −2.03735 −0.294066
\(49\) −5.43891 −0.776987
\(50\) −22.0752 −3.12190
\(51\) −1.16111 −0.162587
\(52\) −4.25261 −0.589731
\(53\) 6.64042 0.912132 0.456066 0.889946i \(-0.349258\pi\)
0.456066 + 0.889946i \(0.349258\pi\)
\(54\) −12.7806 −1.73921
\(55\) −22.3439 −3.01285
\(56\) 4.72727 0.631708
\(57\) 1.47536 0.195417
\(58\) 21.5983 2.83599
\(59\) 2.21644 0.288555 0.144278 0.989537i \(-0.453914\pi\)
0.144278 + 0.989537i \(0.453914\pi\)
\(60\) 15.8184 2.04215
\(61\) −12.5378 −1.60530 −0.802651 0.596449i \(-0.796578\pi\)
−0.802651 + 0.596449i \(0.796578\pi\)
\(62\) −8.26355 −1.04947
\(63\) 2.06386 0.260022
\(64\) −11.5902 −1.44878
\(65\) 4.47290 0.554795
\(66\) 16.2170 1.99618
\(67\) 4.23889 0.517863 0.258931 0.965896i \(-0.416630\pi\)
0.258931 + 0.965896i \(0.416630\pi\)
\(68\) 3.59897 0.436440
\(69\) 8.41654 1.01323
\(70\) −11.1913 −1.33762
\(71\) −16.2867 −1.93288 −0.966438 0.256901i \(-0.917298\pi\)
−0.966438 + 0.256901i \(0.917298\pi\)
\(72\) 6.24974 0.736539
\(73\) −7.52844 −0.881137 −0.440568 0.897719i \(-0.645223\pi\)
−0.440568 + 0.897719i \(0.645223\pi\)
\(74\) −12.8119 −1.48936
\(75\) −10.8323 −1.25081
\(76\) −4.57305 −0.524565
\(77\) −7.37497 −0.840455
\(78\) −3.24640 −0.367583
\(79\) 14.7859 1.66354 0.831770 0.555120i \(-0.187328\pi\)
0.831770 + 0.555120i \(0.187328\pi\)
\(80\) −6.64212 −0.742612
\(81\) −1.31594 −0.146216
\(82\) 9.18200 1.01398
\(83\) 16.6273 1.82508 0.912540 0.408987i \(-0.134118\pi\)
0.912540 + 0.408987i \(0.134118\pi\)
\(84\) 5.22113 0.569672
\(85\) −3.78541 −0.410585
\(86\) 2.07359 0.223601
\(87\) 10.5983 1.13626
\(88\) −22.3327 −2.38067
\(89\) 4.50223 0.477235 0.238618 0.971114i \(-0.423306\pi\)
0.238618 + 0.971114i \(0.423306\pi\)
\(90\) −14.7956 −1.55960
\(91\) 1.47636 0.154764
\(92\) −26.0880 −2.71986
\(93\) −4.05494 −0.420477
\(94\) 7.18262 0.740831
\(95\) 4.80994 0.493490
\(96\) −3.96531 −0.404708
\(97\) 13.0983 1.32993 0.664964 0.746875i \(-0.268447\pi\)
0.664964 + 0.746875i \(0.268447\pi\)
\(98\) 12.8696 1.30003
\(99\) −9.75016 −0.979928
\(100\) 33.5759 3.35759
\(101\) −6.28784 −0.625663 −0.312832 0.949809i \(-0.601278\pi\)
−0.312832 + 0.949809i \(0.601278\pi\)
\(102\) 2.74743 0.272036
\(103\) 16.7732 1.65272 0.826358 0.563145i \(-0.190409\pi\)
0.826358 + 0.563145i \(0.190409\pi\)
\(104\) 4.47067 0.438385
\(105\) −5.49160 −0.535925
\(106\) −15.7127 −1.52615
\(107\) 12.8320 1.24052 0.620260 0.784396i \(-0.287027\pi\)
0.620260 + 0.784396i \(0.287027\pi\)
\(108\) 19.4390 1.87052
\(109\) 6.74933 0.646469 0.323234 0.946319i \(-0.395230\pi\)
0.323234 + 0.946319i \(0.395230\pi\)
\(110\) 52.8704 5.04099
\(111\) −6.28684 −0.596720
\(112\) −2.19234 −0.207157
\(113\) 0.908526 0.0854670 0.0427335 0.999087i \(-0.486393\pi\)
0.0427335 + 0.999087i \(0.486393\pi\)
\(114\) −3.49103 −0.326965
\(115\) 27.4394 2.55874
\(116\) −32.8506 −3.05010
\(117\) 1.95183 0.180447
\(118\) −5.24457 −0.482801
\(119\) −1.24944 −0.114536
\(120\) −16.6295 −1.51806
\(121\) 23.8410 2.16737
\(122\) 29.6672 2.68594
\(123\) 4.50562 0.406258
\(124\) 12.5687 1.12870
\(125\) −16.3882 −1.46581
\(126\) −4.88354 −0.435061
\(127\) 11.3232 1.00477 0.502387 0.864643i \(-0.332455\pi\)
0.502387 + 0.864643i \(0.332455\pi\)
\(128\) 20.5947 1.82034
\(129\) 1.01751 0.0895871
\(130\) −10.5838 −0.928265
\(131\) −17.2098 −1.50363 −0.751813 0.659377i \(-0.770820\pi\)
−0.751813 + 0.659377i \(0.770820\pi\)
\(132\) −24.6658 −2.14689
\(133\) 1.58760 0.137663
\(134\) −10.0301 −0.866471
\(135\) −20.4460 −1.75971
\(136\) −3.78352 −0.324434
\(137\) 6.33094 0.540888 0.270444 0.962736i \(-0.412829\pi\)
0.270444 + 0.962736i \(0.412829\pi\)
\(138\) −19.9153 −1.69531
\(139\) 10.2409 0.868620 0.434310 0.900764i \(-0.356992\pi\)
0.434310 + 0.900764i \(0.356992\pi\)
\(140\) 17.0218 1.43861
\(141\) 3.52452 0.296818
\(142\) 38.5378 3.23402
\(143\) −6.97465 −0.583249
\(144\) −2.89841 −0.241535
\(145\) 34.5523 2.86941
\(146\) 17.8139 1.47429
\(147\) 6.31514 0.520864
\(148\) 19.4867 1.60180
\(149\) −3.16199 −0.259041 −0.129520 0.991577i \(-0.541344\pi\)
−0.129520 + 0.991577i \(0.541344\pi\)
\(150\) 25.6316 2.09281
\(151\) 0.431101 0.0350825 0.0175412 0.999846i \(-0.494416\pi\)
0.0175412 + 0.999846i \(0.494416\pi\)
\(152\) 4.80754 0.389943
\(153\) −1.65183 −0.133543
\(154\) 17.4508 1.40622
\(155\) −13.2198 −1.06184
\(156\) 4.93773 0.395335
\(157\) −20.6860 −1.65092 −0.825461 0.564459i \(-0.809085\pi\)
−0.825461 + 0.564459i \(0.809085\pi\)
\(158\) −34.9866 −2.78338
\(159\) −7.71023 −0.611461
\(160\) −12.9276 −1.02202
\(161\) 9.05683 0.713779
\(162\) 3.11381 0.244644
\(163\) −5.51060 −0.431624 −0.215812 0.976435i \(-0.569240\pi\)
−0.215812 + 0.976435i \(0.569240\pi\)
\(164\) −13.9657 −1.09054
\(165\) 25.9436 2.01970
\(166\) −39.3437 −3.05366
\(167\) 11.0854 0.857815 0.428908 0.903348i \(-0.358899\pi\)
0.428908 + 0.903348i \(0.358899\pi\)
\(168\) −5.48886 −0.423474
\(169\) −11.6038 −0.892599
\(170\) 8.95709 0.686977
\(171\) 2.09891 0.160508
\(172\) −3.15390 −0.240482
\(173\) −24.1616 −1.83697 −0.918487 0.395452i \(-0.870588\pi\)
−0.918487 + 0.395452i \(0.870588\pi\)
\(174\) −25.0779 −1.90115
\(175\) −11.6564 −0.881140
\(176\) 10.3571 0.780699
\(177\) −2.57352 −0.193437
\(178\) −10.6532 −0.798494
\(179\) 4.36522 0.326272 0.163136 0.986604i \(-0.447839\pi\)
0.163136 + 0.986604i \(0.447839\pi\)
\(180\) 22.5039 1.67734
\(181\) 5.32928 0.396123 0.198061 0.980190i \(-0.436535\pi\)
0.198061 + 0.980190i \(0.436535\pi\)
\(182\) −3.49338 −0.258946
\(183\) 14.5577 1.07614
\(184\) 27.4257 2.02185
\(185\) −20.4962 −1.50691
\(186\) 9.59485 0.703528
\(187\) 5.90263 0.431643
\(188\) −10.9246 −0.796761
\(189\) −6.74855 −0.490885
\(190\) −11.3814 −0.825691
\(191\) −11.3120 −0.818511 −0.409255 0.912420i \(-0.634212\pi\)
−0.409255 + 0.912420i \(0.634212\pi\)
\(192\) 13.4575 0.971210
\(193\) 25.7145 1.85097 0.925486 0.378781i \(-0.123657\pi\)
0.925486 + 0.378781i \(0.123657\pi\)
\(194\) −30.9933 −2.22519
\(195\) −5.19351 −0.371915
\(196\) −19.5745 −1.39818
\(197\) −15.6651 −1.11610 −0.558048 0.829809i \(-0.688449\pi\)
−0.558048 + 0.829809i \(0.688449\pi\)
\(198\) 23.0710 1.63958
\(199\) 17.1364 1.21476 0.607382 0.794410i \(-0.292220\pi\)
0.607382 + 0.794410i \(0.292220\pi\)
\(200\) −35.2976 −2.49592
\(201\) −4.92180 −0.347157
\(202\) 14.8784 1.04684
\(203\) 11.4046 0.800444
\(204\) −4.17879 −0.292574
\(205\) 14.6891 1.02593
\(206\) −39.6891 −2.76527
\(207\) 11.9737 0.832229
\(208\) −2.07334 −0.143760
\(209\) −7.50020 −0.518800
\(210\) 12.9943 0.896692
\(211\) 3.69561 0.254416 0.127208 0.991876i \(-0.459398\pi\)
0.127208 + 0.991876i \(0.459398\pi\)
\(212\) 23.8987 1.64137
\(213\) 18.9106 1.29573
\(214\) −30.3634 −2.07560
\(215\) 3.31727 0.226236
\(216\) −20.4358 −1.39048
\(217\) −4.36342 −0.296208
\(218\) −15.9704 −1.08165
\(219\) 8.74131 0.590683
\(220\) −80.4150 −5.42158
\(221\) −1.18162 −0.0794841
\(222\) 14.8760 0.998413
\(223\) 18.7119 1.25304 0.626520 0.779405i \(-0.284478\pi\)
0.626520 + 0.779405i \(0.284478\pi\)
\(224\) −4.26698 −0.285099
\(225\) −15.4105 −1.02736
\(226\) −2.14977 −0.143000
\(227\) 25.7477 1.70894 0.854468 0.519504i \(-0.173883\pi\)
0.854468 + 0.519504i \(0.173883\pi\)
\(228\) 5.30979 0.351650
\(229\) 12.3676 0.817271 0.408636 0.912698i \(-0.366005\pi\)
0.408636 + 0.912698i \(0.366005\pi\)
\(230\) −64.9275 −4.28119
\(231\) 8.56311 0.563412
\(232\) 34.5350 2.26734
\(233\) 20.9886 1.37501 0.687504 0.726181i \(-0.258706\pi\)
0.687504 + 0.726181i \(0.258706\pi\)
\(234\) −4.61846 −0.301918
\(235\) 11.4906 0.749561
\(236\) 7.97690 0.519252
\(237\) −17.1680 −1.11518
\(238\) 2.95644 0.191637
\(239\) 2.82359 0.182643 0.0913213 0.995821i \(-0.470891\pi\)
0.0913213 + 0.995821i \(0.470891\pi\)
\(240\) 7.71220 0.497821
\(241\) 5.66147 0.364687 0.182344 0.983235i \(-0.441632\pi\)
0.182344 + 0.983235i \(0.441632\pi\)
\(242\) −56.4130 −3.62637
\(243\) −14.6759 −0.941457
\(244\) −45.1232 −2.88872
\(245\) 20.5885 1.31535
\(246\) −10.6613 −0.679738
\(247\) 1.50143 0.0955334
\(248\) −13.2132 −0.839039
\(249\) −19.3060 −1.22347
\(250\) 38.7780 2.45254
\(251\) −22.1361 −1.39722 −0.698609 0.715503i \(-0.746197\pi\)
−0.698609 + 0.715503i \(0.746197\pi\)
\(252\) 7.42779 0.467907
\(253\) −42.7866 −2.68997
\(254\) −26.7932 −1.68115
\(255\) 4.39526 0.275242
\(256\) −25.5511 −1.59695
\(257\) 18.7896 1.17206 0.586032 0.810288i \(-0.300689\pi\)
0.586032 + 0.810288i \(0.300689\pi\)
\(258\) −2.40766 −0.149894
\(259\) −6.76511 −0.420364
\(260\) 16.0979 0.998347
\(261\) 15.0775 0.933277
\(262\) 40.7220 2.51582
\(263\) −12.2967 −0.758245 −0.379122 0.925347i \(-0.623774\pi\)
−0.379122 + 0.925347i \(0.623774\pi\)
\(264\) 25.9306 1.59592
\(265\) −25.1367 −1.54413
\(266\) −3.75661 −0.230332
\(267\) −5.22756 −0.319922
\(268\) 15.2557 0.931887
\(269\) 1.51647 0.0924606 0.0462303 0.998931i \(-0.485279\pi\)
0.0462303 + 0.998931i \(0.485279\pi\)
\(270\) 48.3797 2.94429
\(271\) −7.51629 −0.456582 −0.228291 0.973593i \(-0.573314\pi\)
−0.228291 + 0.973593i \(0.573314\pi\)
\(272\) 1.75466 0.106392
\(273\) −1.71421 −0.103748
\(274\) −14.9804 −0.904996
\(275\) 55.0675 3.32069
\(276\) 30.2909 1.82330
\(277\) 10.8650 0.652815 0.326407 0.945229i \(-0.394162\pi\)
0.326407 + 0.945229i \(0.394162\pi\)
\(278\) −24.2321 −1.45335
\(279\) −5.76871 −0.345364
\(280\) −17.8946 −1.06941
\(281\) −1.28703 −0.0767777 −0.0383888 0.999263i \(-0.512223\pi\)
−0.0383888 + 0.999263i \(0.512223\pi\)
\(282\) −8.33978 −0.496627
\(283\) −13.7280 −0.816047 −0.408024 0.912971i \(-0.633782\pi\)
−0.408024 + 0.912971i \(0.633782\pi\)
\(284\) −58.6154 −3.47818
\(285\) −5.58485 −0.330818
\(286\) 16.5035 0.975873
\(287\) 4.84839 0.286192
\(288\) −5.64121 −0.332411
\(289\) 1.00000 0.0588235
\(290\) −81.7582 −4.80101
\(291\) −15.2085 −0.891537
\(292\) −27.0946 −1.58559
\(293\) −6.24498 −0.364836 −0.182418 0.983221i \(-0.558392\pi\)
−0.182418 + 0.983221i \(0.558392\pi\)
\(294\) −14.9430 −0.871493
\(295\) −8.39012 −0.488491
\(296\) −20.4860 −1.19072
\(297\) 31.8817 1.84996
\(298\) 7.48196 0.433418
\(299\) 8.56522 0.495340
\(300\) −38.9852 −2.25081
\(301\) 1.09492 0.0631103
\(302\) −1.02008 −0.0586988
\(303\) 7.30084 0.419422
\(304\) −2.22957 −0.127875
\(305\) 47.4607 2.71759
\(306\) 3.90859 0.223439
\(307\) 28.0432 1.60051 0.800255 0.599659i \(-0.204697\pi\)
0.800255 + 0.599659i \(0.204697\pi\)
\(308\) −26.5423 −1.51239
\(309\) −19.4755 −1.10792
\(310\) 31.2809 1.77663
\(311\) −3.33887 −0.189330 −0.0946650 0.995509i \(-0.530178\pi\)
−0.0946650 + 0.995509i \(0.530178\pi\)
\(312\) −5.19092 −0.293878
\(313\) 8.82936 0.499065 0.249532 0.968366i \(-0.419723\pi\)
0.249532 + 0.968366i \(0.419723\pi\)
\(314\) 48.9475 2.76227
\(315\) −7.81256 −0.440188
\(316\) 53.2140 2.99352
\(317\) −26.5871 −1.49328 −0.746641 0.665227i \(-0.768335\pi\)
−0.746641 + 0.665227i \(0.768335\pi\)
\(318\) 18.2441 1.02308
\(319\) −53.8778 −3.01658
\(320\) 43.8738 2.45262
\(321\) −14.8994 −0.831601
\(322\) −21.4304 −1.19427
\(323\) −1.27065 −0.0707011
\(324\) −4.73605 −0.263114
\(325\) −11.0237 −0.611483
\(326\) 13.0393 0.722178
\(327\) −7.83668 −0.433370
\(328\) 14.6818 0.810666
\(329\) 3.79265 0.209096
\(330\) −61.3881 −3.37930
\(331\) 2.57328 0.141440 0.0707201 0.997496i \(-0.477470\pi\)
0.0707201 + 0.997496i \(0.477470\pi\)
\(332\) 59.8411 3.28421
\(333\) −8.94390 −0.490123
\(334\) −26.2305 −1.43527
\(335\) −16.0459 −0.876683
\(336\) 2.54554 0.138871
\(337\) −9.06203 −0.493640 −0.246820 0.969061i \(-0.579386\pi\)
−0.246820 + 0.969061i \(0.579386\pi\)
\(338\) 27.4570 1.49347
\(339\) −1.05489 −0.0572940
\(340\) −13.6236 −0.738842
\(341\) 20.6138 1.11630
\(342\) −4.96647 −0.268556
\(343\) 15.5416 0.839169
\(344\) 3.31562 0.178766
\(345\) −31.8600 −1.71529
\(346\) 57.1716 3.07356
\(347\) −3.29621 −0.176950 −0.0884749 0.996078i \(-0.528199\pi\)
−0.0884749 + 0.996078i \(0.528199\pi\)
\(348\) 38.1430 2.04468
\(349\) 23.0758 1.23522 0.617610 0.786485i \(-0.288101\pi\)
0.617610 + 0.786485i \(0.288101\pi\)
\(350\) 27.5815 1.47429
\(351\) −6.38223 −0.340658
\(352\) 20.1582 1.07443
\(353\) 1.00000 0.0532246
\(354\) 6.08950 0.323653
\(355\) 61.6518 3.27214
\(356\) 16.2034 0.858778
\(357\) 1.45073 0.0767807
\(358\) −10.3290 −0.545907
\(359\) 27.7491 1.46454 0.732271 0.681013i \(-0.238460\pi\)
0.732271 + 0.681013i \(0.238460\pi\)
\(360\) −23.6578 −1.24688
\(361\) −17.3854 −0.915023
\(362\) −12.6102 −0.662779
\(363\) −27.6820 −1.45293
\(364\) 5.31337 0.278496
\(365\) 28.4982 1.49166
\(366\) −34.4467 −1.80056
\(367\) 22.2124 1.15948 0.579739 0.814802i \(-0.303155\pi\)
0.579739 + 0.814802i \(0.303155\pi\)
\(368\) −12.7191 −0.663028
\(369\) 6.40988 0.333685
\(370\) 48.4984 2.52131
\(371\) −8.29679 −0.430748
\(372\) −14.5936 −0.756643
\(373\) −33.1205 −1.71491 −0.857456 0.514557i \(-0.827956\pi\)
−0.857456 + 0.514557i \(0.827956\pi\)
\(374\) −13.9669 −0.722211
\(375\) 19.0284 0.982624
\(376\) 11.4848 0.592284
\(377\) 10.7855 0.555483
\(378\) 15.9685 0.821332
\(379\) 31.9877 1.64310 0.821548 0.570139i \(-0.193111\pi\)
0.821548 + 0.570139i \(0.193111\pi\)
\(380\) 17.3109 0.888028
\(381\) −13.1475 −0.673565
\(382\) 26.7667 1.36951
\(383\) −16.2592 −0.830806 −0.415403 0.909638i \(-0.636359\pi\)
−0.415403 + 0.909638i \(0.636359\pi\)
\(384\) −23.9127 −1.22029
\(385\) 27.9173 1.42279
\(386\) −60.8461 −3.09699
\(387\) 1.44756 0.0735834
\(388\) 47.1404 2.39319
\(389\) −16.4340 −0.833237 −0.416618 0.909082i \(-0.636785\pi\)
−0.416618 + 0.909082i \(0.636785\pi\)
\(390\) 12.2890 0.622276
\(391\) −7.24873 −0.366584
\(392\) 20.5782 1.03936
\(393\) 19.9824 1.00798
\(394\) 37.0671 1.86741
\(395\) −55.9706 −2.81618
\(396\) −35.0906 −1.76337
\(397\) −38.1557 −1.91498 −0.957490 0.288467i \(-0.906854\pi\)
−0.957490 + 0.288467i \(0.906854\pi\)
\(398\) −40.5483 −2.03250
\(399\) −1.84337 −0.0922841
\(400\) 16.3698 0.818491
\(401\) −30.7115 −1.53366 −0.766829 0.641852i \(-0.778166\pi\)
−0.766829 + 0.641852i \(0.778166\pi\)
\(402\) 11.6460 0.580851
\(403\) −4.12657 −0.205559
\(404\) −22.6298 −1.12587
\(405\) 4.98138 0.247527
\(406\) −26.9857 −1.33928
\(407\) 31.9600 1.58420
\(408\) 4.39306 0.217489
\(409\) −39.3172 −1.94411 −0.972056 0.234750i \(-0.924573\pi\)
−0.972056 + 0.234750i \(0.924573\pi\)
\(410\) −34.7576 −1.71656
\(411\) −7.35088 −0.362592
\(412\) 60.3664 2.97404
\(413\) −2.76930 −0.136268
\(414\) −28.3323 −1.39246
\(415\) −62.9410 −3.08965
\(416\) −4.03536 −0.197850
\(417\) −11.8907 −0.582292
\(418\) 17.7471 0.868038
\(419\) −33.8350 −1.65295 −0.826473 0.562977i \(-0.809656\pi\)
−0.826473 + 0.562977i \(0.809656\pi\)
\(420\) −19.7641 −0.964390
\(421\) 29.5610 1.44071 0.720357 0.693603i \(-0.243978\pi\)
0.720357 + 0.693603i \(0.243978\pi\)
\(422\) −8.74461 −0.425681
\(423\) 5.01412 0.243795
\(424\) −25.1241 −1.22014
\(425\) 9.32931 0.452538
\(426\) −44.7465 −2.16797
\(427\) 15.6652 0.758093
\(428\) 46.1822 2.23230
\(429\) 8.09830 0.390990
\(430\) −7.84939 −0.378531
\(431\) 33.4447 1.61097 0.805487 0.592613i \(-0.201904\pi\)
0.805487 + 0.592613i \(0.201904\pi\)
\(432\) 9.47742 0.455983
\(433\) −34.8468 −1.67463 −0.837316 0.546719i \(-0.815877\pi\)
−0.837316 + 0.546719i \(0.815877\pi\)
\(434\) 10.3248 0.495605
\(435\) −40.1189 −1.92355
\(436\) 24.2907 1.16331
\(437\) 9.21063 0.440604
\(438\) −20.6838 −0.988311
\(439\) 3.12123 0.148968 0.0744840 0.997222i \(-0.476269\pi\)
0.0744840 + 0.997222i \(0.476269\pi\)
\(440\) 84.5383 4.03021
\(441\) 8.98417 0.427818
\(442\) 2.79596 0.132990
\(443\) 11.4588 0.544424 0.272212 0.962237i \(-0.412245\pi\)
0.272212 + 0.962237i \(0.412245\pi\)
\(444\) −22.6262 −1.07379
\(445\) −17.0428 −0.807904
\(446\) −44.2764 −2.09655
\(447\) 3.67141 0.173652
\(448\) 14.4813 0.684176
\(449\) −1.03249 −0.0487262 −0.0243631 0.999703i \(-0.507756\pi\)
−0.0243631 + 0.999703i \(0.507756\pi\)
\(450\) 36.4645 1.71895
\(451\) −22.9049 −1.07855
\(452\) 3.26976 0.153797
\(453\) −0.500553 −0.0235180
\(454\) −60.9246 −2.85933
\(455\) −5.58861 −0.261998
\(456\) −5.58206 −0.261404
\(457\) −32.5303 −1.52171 −0.760853 0.648925i \(-0.775219\pi\)
−0.760853 + 0.648925i \(0.775219\pi\)
\(458\) −29.2643 −1.36743
\(459\) 5.40127 0.252110
\(460\) 98.7537 4.60441
\(461\) −11.1152 −0.517686 −0.258843 0.965919i \(-0.583341\pi\)
−0.258843 + 0.965919i \(0.583341\pi\)
\(462\) −20.2622 −0.942681
\(463\) −5.01798 −0.233205 −0.116603 0.993179i \(-0.537200\pi\)
−0.116603 + 0.993179i \(0.537200\pi\)
\(464\) −16.0162 −0.743532
\(465\) 15.3496 0.711820
\(466\) −49.6635 −2.30062
\(467\) 26.0334 1.20468 0.602341 0.798239i \(-0.294235\pi\)
0.602341 + 0.798239i \(0.294235\pi\)
\(468\) 7.02460 0.324712
\(469\) −5.29623 −0.244557
\(470\) −27.1891 −1.25414
\(471\) 24.0186 1.10672
\(472\) −8.38592 −0.385993
\(473\) −5.17266 −0.237839
\(474\) 40.6231 1.86588
\(475\) −11.8543 −0.543914
\(476\) −4.49669 −0.206106
\(477\) −10.9689 −0.502230
\(478\) −6.68121 −0.305591
\(479\) −20.6615 −0.944047 −0.472024 0.881586i \(-0.656476\pi\)
−0.472024 + 0.881586i \(0.656476\pi\)
\(480\) 15.0103 0.685124
\(481\) −6.39790 −0.291719
\(482\) −13.3962 −0.610182
\(483\) −10.5159 −0.478492
\(484\) 85.8033 3.90015
\(485\) −49.5823 −2.25142
\(486\) 34.7262 1.57521
\(487\) 9.80661 0.444380 0.222190 0.975003i \(-0.428680\pi\)
0.222190 + 0.975003i \(0.428680\pi\)
\(488\) 47.4370 2.14737
\(489\) 6.39839 0.289345
\(490\) −48.7168 −2.20080
\(491\) 8.56033 0.386322 0.193161 0.981167i \(-0.438126\pi\)
0.193161 + 0.981167i \(0.438126\pi\)
\(492\) 16.2156 0.731057
\(493\) −9.12776 −0.411094
\(494\) −3.55270 −0.159843
\(495\) 36.9083 1.65891
\(496\) 6.12783 0.275147
\(497\) 20.3492 0.912787
\(498\) 45.6822 2.04707
\(499\) 21.0231 0.941125 0.470562 0.882367i \(-0.344051\pi\)
0.470562 + 0.882367i \(0.344051\pi\)
\(500\) −58.9807 −2.63770
\(501\) −12.8713 −0.575049
\(502\) 52.3788 2.33778
\(503\) −27.0043 −1.20406 −0.602031 0.798473i \(-0.705642\pi\)
−0.602031 + 0.798473i \(0.705642\pi\)
\(504\) −7.80866 −0.347825
\(505\) 23.8020 1.05918
\(506\) 101.242 4.50077
\(507\) 13.4732 0.598367
\(508\) 40.7520 1.80808
\(509\) 12.8016 0.567421 0.283711 0.958910i \(-0.408435\pi\)
0.283711 + 0.958910i \(0.408435\pi\)
\(510\) −10.4001 −0.460525
\(511\) 9.40631 0.416111
\(512\) 19.2700 0.851621
\(513\) −6.86314 −0.303015
\(514\) −44.4602 −1.96106
\(515\) −63.4935 −2.79786
\(516\) 3.66201 0.161211
\(517\) −17.9174 −0.788005
\(518\) 16.0077 0.703339
\(519\) 28.0542 1.23144
\(520\) −16.9233 −0.742135
\(521\) 6.65181 0.291421 0.145711 0.989327i \(-0.453453\pi\)
0.145711 + 0.989327i \(0.453453\pi\)
\(522\) −35.6767 −1.56153
\(523\) 35.5738 1.55553 0.777767 0.628553i \(-0.216352\pi\)
0.777767 + 0.628553i \(0.216352\pi\)
\(524\) −61.9376 −2.70575
\(525\) 13.5343 0.590685
\(526\) 29.0966 1.26867
\(527\) 3.49231 0.152127
\(528\) −12.0257 −0.523353
\(529\) 29.5441 1.28453
\(530\) 59.4788 2.58359
\(531\) −3.66119 −0.158882
\(532\) 5.71374 0.247722
\(533\) 4.58522 0.198608
\(534\) 12.3695 0.535282
\(535\) −48.5745 −2.10006
\(536\) −16.0379 −0.692732
\(537\) −5.06848 −0.218721
\(538\) −3.58829 −0.154702
\(539\) −32.1038 −1.38281
\(540\) −73.5846 −3.16658
\(541\) −24.0703 −1.03486 −0.517431 0.855725i \(-0.673112\pi\)
−0.517431 + 0.855725i \(0.673112\pi\)
\(542\) 17.7852 0.763938
\(543\) −6.18786 −0.265547
\(544\) 3.41512 0.146422
\(545\) −25.5490 −1.09440
\(546\) 4.05618 0.173588
\(547\) −5.23013 −0.223624 −0.111812 0.993729i \(-0.535665\pi\)
−0.111812 + 0.993729i \(0.535665\pi\)
\(548\) 22.7849 0.973321
\(549\) 20.7104 0.883897
\(550\) −130.301 −5.55607
\(551\) 11.5982 0.494101
\(552\) −31.8441 −1.35538
\(553\) −18.4740 −0.785595
\(554\) −25.7089 −1.09227
\(555\) 23.7982 1.01018
\(556\) 36.8566 1.56307
\(557\) 11.8901 0.503798 0.251899 0.967754i \(-0.418945\pi\)
0.251899 + 0.967754i \(0.418945\pi\)
\(558\) 13.6500 0.577851
\(559\) 1.03549 0.0437965
\(560\) 8.29891 0.350693
\(561\) −6.85358 −0.289358
\(562\) 3.04539 0.128462
\(563\) −27.9357 −1.17735 −0.588676 0.808369i \(-0.700350\pi\)
−0.588676 + 0.808369i \(0.700350\pi\)
\(564\) 12.6847 0.534121
\(565\) −3.43914 −0.144686
\(566\) 32.4835 1.36538
\(567\) 1.64419 0.0690495
\(568\) 61.6210 2.58556
\(569\) 17.5423 0.735411 0.367705 0.929942i \(-0.380143\pi\)
0.367705 + 0.929942i \(0.380143\pi\)
\(570\) 13.2150 0.553514
\(571\) −21.2859 −0.890786 −0.445393 0.895335i \(-0.646936\pi\)
−0.445393 + 0.895335i \(0.646936\pi\)
\(572\) −25.1016 −1.04955
\(573\) 13.1345 0.548701
\(574\) −11.4723 −0.478846
\(575\) −67.6256 −2.82018
\(576\) 19.1451 0.797714
\(577\) −46.1548 −1.92145 −0.960725 0.277502i \(-0.910493\pi\)
−0.960725 + 0.277502i \(0.910493\pi\)
\(578\) −2.36622 −0.0984216
\(579\) −29.8573 −1.24083
\(580\) 124.353 5.16347
\(581\) −20.7747 −0.861881
\(582\) 35.9865 1.49169
\(583\) 39.1959 1.62333
\(584\) 28.4840 1.17867
\(585\) −7.38849 −0.305476
\(586\) 14.7770 0.610431
\(587\) 29.9086 1.23446 0.617230 0.786783i \(-0.288255\pi\)
0.617230 + 0.786783i \(0.288255\pi\)
\(588\) 22.7280 0.937289
\(589\) −4.43751 −0.182844
\(590\) 19.8528 0.817328
\(591\) 18.1889 0.748191
\(592\) 9.50068 0.390476
\(593\) −13.1448 −0.539792 −0.269896 0.962889i \(-0.586989\pi\)
−0.269896 + 0.962889i \(0.586989\pi\)
\(594\) −75.4390 −3.09530
\(595\) 4.72963 0.193896
\(596\) −11.3799 −0.466140
\(597\) −19.8971 −0.814335
\(598\) −20.2672 −0.828786
\(599\) 35.8873 1.46632 0.733158 0.680059i \(-0.238046\pi\)
0.733158 + 0.680059i \(0.238046\pi\)
\(600\) 40.9842 1.67317
\(601\) 27.8524 1.13612 0.568061 0.822986i \(-0.307694\pi\)
0.568061 + 0.822986i \(0.307694\pi\)
\(602\) −2.59082 −0.105594
\(603\) −7.00194 −0.285141
\(604\) 1.55152 0.0631304
\(605\) −90.2480 −3.66910
\(606\) −17.2754 −0.701764
\(607\) −11.4409 −0.464373 −0.232187 0.972671i \(-0.574588\pi\)
−0.232187 + 0.972671i \(0.574588\pi\)
\(608\) −4.33943 −0.175987
\(609\) −13.2419 −0.536589
\(610\) −112.302 −4.54699
\(611\) 3.58678 0.145106
\(612\) −5.94491 −0.240309
\(613\) 35.9701 1.45282 0.726409 0.687263i \(-0.241188\pi\)
0.726409 + 0.687263i \(0.241188\pi\)
\(614\) −66.3563 −2.67792
\(615\) −17.0556 −0.687749
\(616\) 27.9033 1.12426
\(617\) −44.9639 −1.81018 −0.905088 0.425223i \(-0.860196\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(618\) 46.0832 1.85374
\(619\) −37.1035 −1.49132 −0.745658 0.666328i \(-0.767865\pi\)
−0.745658 + 0.666328i \(0.767865\pi\)
\(620\) −47.5777 −1.91077
\(621\) −39.1524 −1.57113
\(622\) 7.90048 0.316781
\(623\) −5.62525 −0.225371
\(624\) 2.40737 0.0963719
\(625\) 15.3895 0.615579
\(626\) −20.8922 −0.835019
\(627\) 8.70852 0.347785
\(628\) −74.4483 −2.97081
\(629\) 5.41453 0.215891
\(630\) 18.4862 0.736508
\(631\) 6.84676 0.272565 0.136283 0.990670i \(-0.456484\pi\)
0.136283 + 0.990670i \(0.456484\pi\)
\(632\) −55.9426 −2.22528
\(633\) −4.29099 −0.170552
\(634\) 62.9109 2.49851
\(635\) −42.8630 −1.70097
\(636\) −27.7489 −1.10032
\(637\) 6.42670 0.254635
\(638\) 127.486 5.04724
\(639\) 26.9029 1.06426
\(640\) −77.9595 −3.08162
\(641\) −45.0268 −1.77845 −0.889225 0.457470i \(-0.848756\pi\)
−0.889225 + 0.457470i \(0.848756\pi\)
\(642\) 35.2551 1.39141
\(643\) −0.311601 −0.0122883 −0.00614416 0.999981i \(-0.501956\pi\)
−0.00614416 + 0.999981i \(0.501956\pi\)
\(644\) 32.5953 1.28444
\(645\) −3.85171 −0.151661
\(646\) 3.00664 0.118295
\(647\) −15.0049 −0.589902 −0.294951 0.955512i \(-0.595303\pi\)
−0.294951 + 0.955512i \(0.595303\pi\)
\(648\) 4.97889 0.195589
\(649\) 13.0828 0.513545
\(650\) 26.0844 1.02311
\(651\) 5.06639 0.198567
\(652\) −19.8325 −0.776701
\(653\) 30.9778 1.21226 0.606128 0.795367i \(-0.292722\pi\)
0.606128 + 0.795367i \(0.292722\pi\)
\(654\) 18.5433 0.725100
\(655\) 65.1460 2.54547
\(656\) −6.80891 −0.265843
\(657\) 12.4357 0.485164
\(658\) −8.97423 −0.349852
\(659\) 21.3083 0.830052 0.415026 0.909810i \(-0.363772\pi\)
0.415026 + 0.909810i \(0.363772\pi\)
\(660\) 93.3703 3.63443
\(661\) 21.6807 0.843280 0.421640 0.906763i \(-0.361455\pi\)
0.421640 + 0.906763i \(0.361455\pi\)
\(662\) −6.08893 −0.236653
\(663\) 1.37198 0.0532834
\(664\) −62.9095 −2.44136
\(665\) −6.00972 −0.233047
\(666\) 21.1632 0.820057
\(667\) 66.1647 2.56191
\(668\) 39.8961 1.54363
\(669\) −21.7265 −0.839994
\(670\) 37.9681 1.46684
\(671\) −74.0060 −2.85697
\(672\) 4.95441 0.191120
\(673\) −8.15965 −0.314531 −0.157266 0.987556i \(-0.550268\pi\)
−0.157266 + 0.987556i \(0.550268\pi\)
\(674\) 21.4427 0.825943
\(675\) 50.3901 1.93952
\(676\) −41.7617 −1.60622
\(677\) −3.62587 −0.139353 −0.0696767 0.997570i \(-0.522197\pi\)
−0.0696767 + 0.997570i \(0.522197\pi\)
\(678\) 2.49611 0.0958625
\(679\) −16.3655 −0.628049
\(680\) 14.3221 0.549229
\(681\) −29.8958 −1.14561
\(682\) −48.7766 −1.86775
\(683\) 16.0912 0.615714 0.307857 0.951433i \(-0.400388\pi\)
0.307857 + 0.951433i \(0.400388\pi\)
\(684\) 7.55392 0.288831
\(685\) −23.9652 −0.915662
\(686\) −36.7748 −1.40407
\(687\) −14.3600 −0.547870
\(688\) −1.53767 −0.0586231
\(689\) −7.84643 −0.298925
\(690\) 75.3877 2.86996
\(691\) −43.8445 −1.66792 −0.833961 0.551823i \(-0.813932\pi\)
−0.833961 + 0.551823i \(0.813932\pi\)
\(692\) −86.9570 −3.30561
\(693\) 12.1822 0.462764
\(694\) 7.79954 0.296067
\(695\) −38.7659 −1.47047
\(696\) −40.0988 −1.51994
\(697\) −3.88046 −0.146983
\(698\) −54.6023 −2.06673
\(699\) −24.3700 −0.921756
\(700\) −41.9510 −1.58560
\(701\) −42.2851 −1.59709 −0.798543 0.601938i \(-0.794395\pi\)
−0.798543 + 0.601938i \(0.794395\pi\)
\(702\) 15.1017 0.569978
\(703\) −6.87999 −0.259484
\(704\) −68.4128 −2.57841
\(705\) −13.3418 −0.502480
\(706\) −2.36622 −0.0890537
\(707\) 7.85626 0.295465
\(708\) −9.26202 −0.348088
\(709\) 18.7535 0.704304 0.352152 0.935943i \(-0.385450\pi\)
0.352152 + 0.935943i \(0.385450\pi\)
\(710\) −145.881 −5.47483
\(711\) −24.4238 −0.915964
\(712\) −17.0342 −0.638385
\(713\) −25.3148 −0.948046
\(714\) −3.43274 −0.128467
\(715\) 26.4019 0.987374
\(716\) 15.7103 0.587121
\(717\) −3.27848 −0.122437
\(718\) −65.6604 −2.45042
\(719\) −27.1839 −1.01379 −0.506894 0.862008i \(-0.669207\pi\)
−0.506894 + 0.862008i \(0.669207\pi\)
\(720\) 10.9717 0.408890
\(721\) −20.9571 −0.780484
\(722\) 41.1377 1.53099
\(723\) −6.57356 −0.244473
\(724\) 19.1800 0.712817
\(725\) −85.1557 −3.16260
\(726\) 65.5015 2.43099
\(727\) 28.5346 1.05829 0.529144 0.848532i \(-0.322513\pi\)
0.529144 + 0.848532i \(0.322513\pi\)
\(728\) −5.58582 −0.207024
\(729\) 20.9881 0.777335
\(730\) −67.4329 −2.49580
\(731\) −0.876332 −0.0324123
\(732\) 52.3929 1.93650
\(733\) −34.6457 −1.27967 −0.639834 0.768513i \(-0.720997\pi\)
−0.639834 + 0.768513i \(0.720997\pi\)
\(734\) −52.5593 −1.94000
\(735\) −23.9054 −0.881764
\(736\) −24.7553 −0.912491
\(737\) 25.0206 0.921646
\(738\) −15.1671 −0.558310
\(739\) −20.1544 −0.741393 −0.370697 0.928754i \(-0.620881\pi\)
−0.370697 + 0.928754i \(0.620881\pi\)
\(740\) −73.7653 −2.71167
\(741\) −1.74331 −0.0640422
\(742\) 19.6320 0.720713
\(743\) −20.9202 −0.767489 −0.383744 0.923439i \(-0.625366\pi\)
−0.383744 + 0.923439i \(0.625366\pi\)
\(744\) 15.3419 0.562462
\(745\) 11.9694 0.438526
\(746\) 78.3701 2.86933
\(747\) −27.4655 −1.00491
\(748\) 21.2434 0.776736
\(749\) −16.0328 −0.585827
\(750\) −45.0254 −1.64409
\(751\) −43.3456 −1.58170 −0.790852 0.612008i \(-0.790362\pi\)
−0.790852 + 0.612008i \(0.790362\pi\)
\(752\) −5.32626 −0.194229
\(753\) 25.7024 0.936646
\(754\) −25.5209 −0.929415
\(755\) −1.63189 −0.0593906
\(756\) −24.2879 −0.883341
\(757\) 14.2253 0.517026 0.258513 0.966008i \(-0.416768\pi\)
0.258513 + 0.966008i \(0.416768\pi\)
\(758\) −75.6897 −2.74917
\(759\) 49.6797 1.80326
\(760\) −18.1985 −0.660129
\(761\) −5.63185 −0.204154 −0.102077 0.994776i \(-0.532549\pi\)
−0.102077 + 0.994776i \(0.532549\pi\)
\(762\) 31.1097 1.12699
\(763\) −8.43286 −0.305290
\(764\) −40.7118 −1.47290
\(765\) 6.25286 0.226073
\(766\) 38.4727 1.39008
\(767\) −2.61898 −0.0945659
\(768\) 29.6676 1.07054
\(769\) −16.9025 −0.609520 −0.304760 0.952429i \(-0.598576\pi\)
−0.304760 + 0.952429i \(0.598576\pi\)
\(770\) −66.0582 −2.38057
\(771\) −21.8167 −0.785710
\(772\) 92.5459 3.33080
\(773\) −37.5928 −1.35212 −0.676059 0.736847i \(-0.736314\pi\)
−0.676059 + 0.736847i \(0.736314\pi\)
\(774\) −3.42523 −0.123117
\(775\) 32.5808 1.17034
\(776\) −49.5575 −1.77901
\(777\) 7.85501 0.281797
\(778\) 38.8864 1.39414
\(779\) 4.93072 0.176661
\(780\) −18.6913 −0.669256
\(781\) −96.1343 −3.43996
\(782\) 17.1521 0.613356
\(783\) −49.3015 −1.76189
\(784\) −9.54346 −0.340838
\(785\) 78.3049 2.79482
\(786\) −47.2826 −1.68651
\(787\) −14.9019 −0.531195 −0.265597 0.964084i \(-0.585569\pi\)
−0.265597 + 0.964084i \(0.585569\pi\)
\(788\) −56.3785 −2.00840
\(789\) 14.2777 0.508301
\(790\) 132.438 4.71195
\(791\) −1.13515 −0.0403612
\(792\) 36.8899 1.31083
\(793\) 14.8149 0.526092
\(794\) 90.2846 3.20408
\(795\) 29.1864 1.03513
\(796\) 61.6733 2.18595
\(797\) −1.18072 −0.0418233 −0.0209116 0.999781i \(-0.506657\pi\)
−0.0209116 + 0.999781i \(0.506657\pi\)
\(798\) 4.36182 0.154407
\(799\) −3.03549 −0.107388
\(800\) 31.8607 1.12645
\(801\) −7.43693 −0.262771
\(802\) 72.6699 2.56606
\(803\) −44.4376 −1.56817
\(804\) −17.7134 −0.624704
\(805\) −34.2838 −1.20835
\(806\) 9.76434 0.343934
\(807\) −1.76078 −0.0619823
\(808\) 23.7901 0.836934
\(809\) 27.0860 0.952292 0.476146 0.879366i \(-0.342033\pi\)
0.476146 + 0.879366i \(0.342033\pi\)
\(810\) −11.7870 −0.414154
\(811\) 48.9834 1.72004 0.860021 0.510259i \(-0.170451\pi\)
0.860021 + 0.510259i \(0.170451\pi\)
\(812\) 41.0447 1.44039
\(813\) 8.72721 0.306077
\(814\) −75.6241 −2.65062
\(815\) 20.8599 0.730690
\(816\) −2.03735 −0.0713216
\(817\) 1.11351 0.0389570
\(818\) 93.0330 3.25282
\(819\) −2.43870 −0.0852149
\(820\) 52.8658 1.84615
\(821\) 25.4510 0.888247 0.444123 0.895966i \(-0.353515\pi\)
0.444123 + 0.895966i \(0.353515\pi\)
\(822\) 17.3938 0.606678
\(823\) 5.62747 0.196161 0.0980806 0.995178i \(-0.468730\pi\)
0.0980806 + 0.995178i \(0.468730\pi\)
\(824\) −63.4618 −2.21080
\(825\) −63.9391 −2.22607
\(826\) 6.55276 0.228000
\(827\) 44.1025 1.53359 0.766797 0.641890i \(-0.221849\pi\)
0.766797 + 0.641890i \(0.221849\pi\)
\(828\) 43.0930 1.49759
\(829\) 28.1710 0.978420 0.489210 0.872166i \(-0.337285\pi\)
0.489210 + 0.872166i \(0.337285\pi\)
\(830\) 148.932 5.16950
\(831\) −12.6154 −0.437624
\(832\) 13.6952 0.474796
\(833\) −5.43891 −0.188447
\(834\) 28.1360 0.974272
\(835\) −41.9628 −1.45218
\(836\) −26.9930 −0.933573
\(837\) 18.8629 0.651997
\(838\) 80.0608 2.76565
\(839\) 7.19217 0.248301 0.124151 0.992263i \(-0.460379\pi\)
0.124151 + 0.992263i \(0.460379\pi\)
\(840\) 20.7776 0.716894
\(841\) 54.3161 1.87297
\(842\) −69.9477 −2.41056
\(843\) 1.49438 0.0514690
\(844\) 13.3004 0.457819
\(845\) 43.9250 1.51107
\(846\) −11.8645 −0.407910
\(847\) −29.7879 −1.02352
\(848\) 11.6517 0.400121
\(849\) 15.9397 0.547049
\(850\) −22.0752 −0.757171
\(851\) −39.2485 −1.34542
\(852\) 68.0587 2.33165
\(853\) −41.3150 −1.41460 −0.707299 0.706914i \(-0.750087\pi\)
−0.707299 + 0.706914i \(0.750087\pi\)
\(854\) −37.0673 −1.26842
\(855\) −7.94523 −0.271721
\(856\) −48.5503 −1.65941
\(857\) −43.2074 −1.47594 −0.737968 0.674836i \(-0.764214\pi\)
−0.737968 + 0.674836i \(0.764214\pi\)
\(858\) −19.1623 −0.654191
\(859\) −10.9932 −0.375083 −0.187542 0.982257i \(-0.560052\pi\)
−0.187542 + 0.982257i \(0.560052\pi\)
\(860\) 11.9388 0.407109
\(861\) −5.62949 −0.191853
\(862\) −79.1373 −2.69543
\(863\) −18.8729 −0.642440 −0.321220 0.947005i \(-0.604093\pi\)
−0.321220 + 0.947005i \(0.604093\pi\)
\(864\) 18.4460 0.627545
\(865\) 91.4616 3.10979
\(866\) 82.4551 2.80194
\(867\) −1.16111 −0.0394332
\(868\) −15.7038 −0.533022
\(869\) 87.2755 2.96062
\(870\) 94.9299 3.21842
\(871\) −5.00874 −0.169715
\(872\) −25.5362 −0.864765
\(873\) −21.6362 −0.732274
\(874\) −21.7943 −0.737204
\(875\) 20.4760 0.692216
\(876\) 31.4597 1.06293
\(877\) −50.4938 −1.70505 −0.852527 0.522683i \(-0.824931\pi\)
−0.852527 + 0.522683i \(0.824931\pi\)
\(878\) −7.38549 −0.249248
\(879\) 7.25109 0.244573
\(880\) −39.2060 −1.32163
\(881\) −13.7891 −0.464566 −0.232283 0.972648i \(-0.574620\pi\)
−0.232283 + 0.972648i \(0.574620\pi\)
\(882\) −21.2585 −0.715810
\(883\) −24.6986 −0.831174 −0.415587 0.909553i \(-0.636424\pi\)
−0.415587 + 0.909553i \(0.636424\pi\)
\(884\) −4.25261 −0.143031
\(885\) 9.74181 0.327467
\(886\) −27.1140 −0.910912
\(887\) −45.1608 −1.51635 −0.758175 0.652051i \(-0.773909\pi\)
−0.758175 + 0.652051i \(0.773909\pi\)
\(888\) 23.7864 0.798218
\(889\) −14.1477 −0.474498
\(890\) 40.3268 1.35176
\(891\) −7.76753 −0.260222
\(892\) 67.3436 2.25483
\(893\) 3.85705 0.129071
\(894\) −8.68735 −0.290548
\(895\) −16.5241 −0.552340
\(896\) −25.7318 −0.859641
\(897\) −9.94513 −0.332058
\(898\) 2.44309 0.0815270
\(899\) −31.8769 −1.06316
\(900\) −55.4619 −1.84873
\(901\) 6.64042 0.221224
\(902\) 54.1980 1.80459
\(903\) −1.27132 −0.0423069
\(904\) −3.43742 −0.114327
\(905\) −20.1735 −0.670590
\(906\) 1.18442 0.0393496
\(907\) 4.55945 0.151394 0.0756970 0.997131i \(-0.475882\pi\)
0.0756970 + 0.997131i \(0.475882\pi\)
\(908\) 92.6653 3.07521
\(909\) 10.3865 0.344497
\(910\) 13.2239 0.438366
\(911\) 17.8484 0.591344 0.295672 0.955289i \(-0.404456\pi\)
0.295672 + 0.955289i \(0.404456\pi\)
\(912\) 2.58877 0.0857227
\(913\) 98.1446 3.24811
\(914\) 76.9738 2.54607
\(915\) −55.1069 −1.82178
\(916\) 44.5105 1.47067
\(917\) 21.5025 0.710077
\(918\) −12.7806 −0.421822
\(919\) 31.0273 1.02349 0.511747 0.859136i \(-0.328998\pi\)
0.511747 + 0.859136i \(0.328998\pi\)
\(920\) −103.817 −3.42276
\(921\) −32.5611 −1.07293
\(922\) 26.3009 0.866174
\(923\) 19.2446 0.633445
\(924\) 30.8184 1.01385
\(925\) 50.5138 1.66088
\(926\) 11.8736 0.390192
\(927\) −27.7066 −0.910004
\(928\) −31.1724 −1.02328
\(929\) −3.05093 −0.100098 −0.0500489 0.998747i \(-0.515938\pi\)
−0.0500489 + 0.998747i \(0.515938\pi\)
\(930\) −36.3204 −1.19099
\(931\) 6.91097 0.226498
\(932\) 75.5373 2.47431
\(933\) 3.87678 0.126920
\(934\) −61.6006 −2.01563
\(935\) −22.3439 −0.730722
\(936\) −7.38480 −0.241380
\(937\) −13.5621 −0.443056 −0.221528 0.975154i \(-0.571104\pi\)
−0.221528 + 0.975154i \(0.571104\pi\)
\(938\) 12.5320 0.409185
\(939\) −10.2518 −0.334555
\(940\) 41.3542 1.34883
\(941\) −37.2728 −1.21506 −0.607530 0.794297i \(-0.707840\pi\)
−0.607530 + 0.794297i \(0.707840\pi\)
\(942\) −56.8332 −1.85173
\(943\) 28.1284 0.915987
\(944\) 3.88910 0.126580
\(945\) 25.5460 0.831012
\(946\) 12.2396 0.397945
\(947\) −35.7023 −1.16017 −0.580084 0.814556i \(-0.696980\pi\)
−0.580084 + 0.814556i \(0.696980\pi\)
\(948\) −61.7870 −2.00675
\(949\) 8.89573 0.288768
\(950\) 28.0499 0.910058
\(951\) 30.8705 1.00104
\(952\) 4.72727 0.153212
\(953\) 44.2404 1.43309 0.716544 0.697542i \(-0.245723\pi\)
0.716544 + 0.697542i \(0.245723\pi\)
\(954\) 25.9547 0.840314
\(955\) 42.8207 1.38565
\(956\) 10.1620 0.328663
\(957\) 62.5578 2.02221
\(958\) 48.8895 1.57955
\(959\) −7.91011 −0.255431
\(960\) −50.9421 −1.64415
\(961\) −18.8038 −0.606574
\(962\) 15.1388 0.488095
\(963\) −21.1964 −0.683045
\(964\) 20.3755 0.656250
\(965\) −97.3400 −3.13348
\(966\) 24.8830 0.800597
\(967\) −33.2839 −1.07034 −0.535168 0.844745i \(-0.679752\pi\)
−0.535168 + 0.844745i \(0.679752\pi\)
\(968\) −90.2029 −2.89923
\(969\) 1.47536 0.0473955
\(970\) 117.322 3.76700
\(971\) −9.43881 −0.302906 −0.151453 0.988464i \(-0.548395\pi\)
−0.151453 + 0.988464i \(0.548395\pi\)
\(972\) −52.8180 −1.69414
\(973\) −12.7953 −0.410200
\(974\) −23.2045 −0.743521
\(975\) 12.7996 0.409917
\(976\) −21.9997 −0.704192
\(977\) −2.48911 −0.0796336 −0.0398168 0.999207i \(-0.512677\pi\)
−0.0398168 + 0.999207i \(0.512677\pi\)
\(978\) −15.1400 −0.484123
\(979\) 26.5750 0.849340
\(980\) 74.0974 2.36695
\(981\) −11.1488 −0.355953
\(982\) −20.2556 −0.646382
\(983\) 19.4578 0.620606 0.310303 0.950638i \(-0.399569\pi\)
0.310303 + 0.950638i \(0.399569\pi\)
\(984\) −17.0471 −0.543442
\(985\) 59.2990 1.88942
\(986\) 21.5983 0.687828
\(987\) −4.40367 −0.140170
\(988\) 5.40359 0.171911
\(989\) 6.35230 0.201991
\(990\) −87.3331 −2.77563
\(991\) 32.0699 1.01873 0.509366 0.860550i \(-0.329880\pi\)
0.509366 + 0.860550i \(0.329880\pi\)
\(992\) 11.9266 0.378671
\(993\) −2.98785 −0.0948165
\(994\) −48.1506 −1.52724
\(995\) −64.8681 −2.05646
\(996\) −69.4818 −2.20162
\(997\) 52.5668 1.66481 0.832404 0.554169i \(-0.186964\pi\)
0.832404 + 0.554169i \(0.186964\pi\)
\(998\) −49.7453 −1.57466
\(999\) 29.2453 0.925281
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 \(a_p\))