Properties

Label 8041.2.a.j.1.8
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 1.8
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34655 q^{2}\) \(+3.28622 q^{3}\) \(+3.50630 q^{4}\) \(+3.73933 q^{5}\) \(-7.71129 q^{6}\) \(+3.13477 q^{7}\) \(-3.53461 q^{8}\) \(+7.79927 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34655 q^{2}\) \(+3.28622 q^{3}\) \(+3.50630 q^{4}\) \(+3.73933 q^{5}\) \(-7.71129 q^{6}\) \(+3.13477 q^{7}\) \(-3.53461 q^{8}\) \(+7.79927 q^{9}\) \(-8.77452 q^{10}\) \(+1.00000 q^{11}\) \(+11.5225 q^{12}\) \(+0.157450 q^{13}\) \(-7.35589 q^{14}\) \(+12.2883 q^{15}\) \(+1.28155 q^{16}\) \(+1.00000 q^{17}\) \(-18.3014 q^{18}\) \(-5.83875 q^{19}\) \(+13.1112 q^{20}\) \(+10.3015 q^{21}\) \(-2.34655 q^{22}\) \(+0.802293 q^{23}\) \(-11.6155 q^{24}\) \(+8.98258 q^{25}\) \(-0.369464 q^{26}\) \(+15.7715 q^{27}\) \(+10.9914 q^{28}\) \(+1.68678 q^{29}\) \(-28.8351 q^{30}\) \(+0.923264 q^{31}\) \(+4.06201 q^{32}\) \(+3.28622 q^{33}\) \(-2.34655 q^{34}\) \(+11.7219 q^{35}\) \(+27.3466 q^{36}\) \(+7.42808 q^{37}\) \(+13.7009 q^{38}\) \(+0.517416 q^{39}\) \(-13.2171 q^{40}\) \(-5.49809 q^{41}\) \(-24.1731 q^{42}\) \(+1.00000 q^{43}\) \(+3.50630 q^{44}\) \(+29.1640 q^{45}\) \(-1.88262 q^{46}\) \(-6.58511 q^{47}\) \(+4.21145 q^{48}\) \(+2.82675 q^{49}\) \(-21.0781 q^{50}\) \(+3.28622 q^{51}\) \(+0.552067 q^{52}\) \(-4.16982 q^{53}\) \(-37.0086 q^{54}\) \(+3.73933 q^{55}\) \(-11.0802 q^{56}\) \(-19.1874 q^{57}\) \(-3.95812 q^{58}\) \(-0.00333073 q^{59}\) \(+43.0864 q^{60}\) \(+7.96347 q^{61}\) \(-2.16649 q^{62}\) \(+24.4489 q^{63}\) \(-12.0948 q^{64}\) \(+0.588757 q^{65}\) \(-7.71129 q^{66}\) \(-2.69073 q^{67}\) \(+3.50630 q^{68}\) \(+2.63651 q^{69}\) \(-27.5061 q^{70}\) \(-0.778687 q^{71}\) \(-27.5674 q^{72}\) \(-13.6854 q^{73}\) \(-17.4304 q^{74}\) \(+29.5188 q^{75}\) \(-20.4724 q^{76}\) \(+3.13477 q^{77}\) \(-1.21414 q^{78}\) \(-7.37260 q^{79}\) \(+4.79212 q^{80}\) \(+28.4308 q^{81}\) \(+12.9016 q^{82}\) \(+6.85470 q^{83}\) \(+36.1203 q^{84}\) \(+3.73933 q^{85}\) \(-2.34655 q^{86}\) \(+5.54314 q^{87}\) \(-3.53461 q^{88}\) \(-9.62399 q^{89}\) \(-68.4349 q^{90}\) \(+0.493568 q^{91}\) \(+2.81308 q^{92}\) \(+3.03405 q^{93}\) \(+15.4523 q^{94}\) \(-21.8330 q^{95}\) \(+13.3487 q^{96}\) \(+5.96564 q^{97}\) \(-6.63312 q^{98}\) \(+7.79927 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34655 −1.65926 −0.829631 0.558312i \(-0.811449\pi\)
−0.829631 + 0.558312i \(0.811449\pi\)
\(3\) 3.28622 1.89730 0.948651 0.316324i \(-0.102449\pi\)
0.948651 + 0.316324i \(0.102449\pi\)
\(4\) 3.50630 1.75315
\(5\) 3.73933 1.67228 0.836139 0.548517i \(-0.184807\pi\)
0.836139 + 0.548517i \(0.184807\pi\)
\(6\) −7.71129 −3.14812
\(7\) 3.13477 1.18483 0.592415 0.805633i \(-0.298175\pi\)
0.592415 + 0.805633i \(0.298175\pi\)
\(8\) −3.53461 −1.24967
\(9\) 7.79927 2.59976
\(10\) −8.77452 −2.77475
\(11\) 1.00000 0.301511
\(12\) 11.5225 3.32626
\(13\) 0.157450 0.0436687 0.0218344 0.999762i \(-0.493049\pi\)
0.0218344 + 0.999762i \(0.493049\pi\)
\(14\) −7.35589 −1.96594
\(15\) 12.2883 3.17282
\(16\) 1.28155 0.320386
\(17\) 1.00000 0.242536
\(18\) −18.3014 −4.31368
\(19\) −5.83875 −1.33950 −0.669750 0.742587i \(-0.733599\pi\)
−0.669750 + 0.742587i \(0.733599\pi\)
\(20\) 13.1112 2.93176
\(21\) 10.3015 2.24798
\(22\) −2.34655 −0.500286
\(23\) 0.802293 0.167290 0.0836448 0.996496i \(-0.473344\pi\)
0.0836448 + 0.996496i \(0.473344\pi\)
\(24\) −11.6155 −2.37101
\(25\) 8.98258 1.79652
\(26\) −0.369464 −0.0724579
\(27\) 15.7715 3.03522
\(28\) 10.9914 2.07719
\(29\) 1.68678 0.313227 0.156614 0.987660i \(-0.449942\pi\)
0.156614 + 0.987660i \(0.449942\pi\)
\(30\) −28.8351 −5.26454
\(31\) 0.923264 0.165823 0.0829116 0.996557i \(-0.473578\pi\)
0.0829116 + 0.996557i \(0.473578\pi\)
\(32\) 4.06201 0.718069
\(33\) 3.28622 0.572058
\(34\) −2.34655 −0.402430
\(35\) 11.7219 1.98137
\(36\) 27.3466 4.55776
\(37\) 7.42808 1.22117 0.610585 0.791951i \(-0.290935\pi\)
0.610585 + 0.791951i \(0.290935\pi\)
\(38\) 13.7009 2.22258
\(39\) 0.517416 0.0828528
\(40\) −13.2171 −2.08980
\(41\) −5.49809 −0.858658 −0.429329 0.903148i \(-0.641250\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(42\) −24.1731 −3.72999
\(43\) 1.00000 0.152499
\(44\) 3.50630 0.528595
\(45\) 29.1640 4.34752
\(46\) −1.88262 −0.277577
\(47\) −6.58511 −0.960537 −0.480269 0.877121i \(-0.659461\pi\)
−0.480269 + 0.877121i \(0.659461\pi\)
\(48\) 4.21145 0.607870
\(49\) 2.82675 0.403822
\(50\) −21.0781 −2.98089
\(51\) 3.28622 0.460163
\(52\) 0.552067 0.0765579
\(53\) −4.16982 −0.572768 −0.286384 0.958115i \(-0.592453\pi\)
−0.286384 + 0.958115i \(0.592453\pi\)
\(54\) −37.0086 −5.03623
\(55\) 3.73933 0.504211
\(56\) −11.0802 −1.48065
\(57\) −19.1874 −2.54144
\(58\) −3.95812 −0.519726
\(59\) −0.00333073 −0.000433624 0 −0.000216812 1.00000i \(-0.500069\pi\)
−0.000216812 1.00000i \(0.500069\pi\)
\(60\) 43.0864 5.56243
\(61\) 7.96347 1.01962 0.509809 0.860288i \(-0.329716\pi\)
0.509809 + 0.860288i \(0.329716\pi\)
\(62\) −2.16649 −0.275144
\(63\) 24.4489 3.08027
\(64\) −12.0948 −1.51185
\(65\) 0.588757 0.0730263
\(66\) −7.71129 −0.949194
\(67\) −2.69073 −0.328724 −0.164362 0.986400i \(-0.552557\pi\)
−0.164362 + 0.986400i \(0.552557\pi\)
\(68\) 3.50630 0.425201
\(69\) 2.63651 0.317399
\(70\) −27.5061 −3.28760
\(71\) −0.778687 −0.0924131 −0.0462066 0.998932i \(-0.514713\pi\)
−0.0462066 + 0.998932i \(0.514713\pi\)
\(72\) −27.5674 −3.24885
\(73\) −13.6854 −1.60175 −0.800875 0.598831i \(-0.795632\pi\)
−0.800875 + 0.598831i \(0.795632\pi\)
\(74\) −17.4304 −2.02624
\(75\) 29.5188 3.40853
\(76\) −20.4724 −2.34835
\(77\) 3.13477 0.357240
\(78\) −1.21414 −0.137475
\(79\) −7.37260 −0.829482 −0.414741 0.909940i \(-0.636128\pi\)
−0.414741 + 0.909940i \(0.636128\pi\)
\(80\) 4.79212 0.535775
\(81\) 28.4308 3.15897
\(82\) 12.9016 1.42474
\(83\) 6.85470 0.752401 0.376200 0.926538i \(-0.377230\pi\)
0.376200 + 0.926538i \(0.377230\pi\)
\(84\) 36.1203 3.94105
\(85\) 3.73933 0.405587
\(86\) −2.34655 −0.253035
\(87\) 5.54314 0.594287
\(88\) −3.53461 −0.376791
\(89\) −9.62399 −1.02014 −0.510070 0.860133i \(-0.670381\pi\)
−0.510070 + 0.860133i \(0.670381\pi\)
\(90\) −68.4349 −7.21367
\(91\) 0.493568 0.0517400
\(92\) 2.81308 0.293284
\(93\) 3.03405 0.314617
\(94\) 15.4523 1.59378
\(95\) −21.8330 −2.24002
\(96\) 13.3487 1.36239
\(97\) 5.96564 0.605719 0.302860 0.953035i \(-0.402059\pi\)
0.302860 + 0.953035i \(0.402059\pi\)
\(98\) −6.63312 −0.670046
\(99\) 7.79927 0.783856
\(100\) 31.4956 3.14956
\(101\) −17.7077 −1.76198 −0.880989 0.473136i \(-0.843122\pi\)
−0.880989 + 0.473136i \(0.843122\pi\)
\(102\) −7.71129 −0.763532
\(103\) 2.17627 0.214435 0.107217 0.994236i \(-0.465806\pi\)
0.107217 + 0.994236i \(0.465806\pi\)
\(104\) −0.556524 −0.0545717
\(105\) 38.5208 3.75925
\(106\) 9.78469 0.950373
\(107\) −13.6880 −1.32327 −0.661634 0.749827i \(-0.730137\pi\)
−0.661634 + 0.749827i \(0.730137\pi\)
\(108\) 55.2995 5.32120
\(109\) −5.90381 −0.565482 −0.282741 0.959196i \(-0.591244\pi\)
−0.282741 + 0.959196i \(0.591244\pi\)
\(110\) −8.77452 −0.836618
\(111\) 24.4103 2.31693
\(112\) 4.01735 0.379603
\(113\) 11.0631 1.04073 0.520365 0.853944i \(-0.325796\pi\)
0.520365 + 0.853944i \(0.325796\pi\)
\(114\) 45.0243 4.21691
\(115\) 3.00004 0.279755
\(116\) 5.91436 0.549135
\(117\) 1.22799 0.113528
\(118\) 0.00781573 0.000719496 0
\(119\) 3.13477 0.287363
\(120\) −43.4343 −3.96499
\(121\) 1.00000 0.0909091
\(122\) −18.6867 −1.69181
\(123\) −18.0680 −1.62913
\(124\) 3.23724 0.290713
\(125\) 14.8922 1.33200
\(126\) −57.3705 −5.11097
\(127\) −4.94357 −0.438671 −0.219336 0.975649i \(-0.570389\pi\)
−0.219336 + 0.975649i \(0.570389\pi\)
\(128\) 20.2571 1.79049
\(129\) 3.28622 0.289336
\(130\) −1.38155 −0.121170
\(131\) 8.20749 0.717092 0.358546 0.933512i \(-0.383273\pi\)
0.358546 + 0.933512i \(0.383273\pi\)
\(132\) 11.5225 1.00290
\(133\) −18.3031 −1.58708
\(134\) 6.31392 0.545440
\(135\) 58.9747 5.07573
\(136\) −3.53461 −0.303091
\(137\) 13.7948 1.17857 0.589286 0.807925i \(-0.299409\pi\)
0.589286 + 0.807925i \(0.299409\pi\)
\(138\) −6.18671 −0.526648
\(139\) −18.4278 −1.56303 −0.781515 0.623887i \(-0.785553\pi\)
−0.781515 + 0.623887i \(0.785553\pi\)
\(140\) 41.1006 3.47363
\(141\) −21.6402 −1.82243
\(142\) 1.82723 0.153338
\(143\) 0.157450 0.0131666
\(144\) 9.99512 0.832927
\(145\) 6.30743 0.523803
\(146\) 32.1134 2.65772
\(147\) 9.28935 0.766172
\(148\) 26.0451 2.14089
\(149\) −4.72476 −0.387067 −0.193534 0.981094i \(-0.561995\pi\)
−0.193534 + 0.981094i \(0.561995\pi\)
\(150\) −69.2673 −5.65565
\(151\) 13.3970 1.09024 0.545118 0.838359i \(-0.316485\pi\)
0.545118 + 0.838359i \(0.316485\pi\)
\(152\) 20.6377 1.67394
\(153\) 7.79927 0.630533
\(154\) −7.35589 −0.592754
\(155\) 3.45239 0.277302
\(156\) 1.81422 0.145253
\(157\) −7.86577 −0.627757 −0.313879 0.949463i \(-0.601628\pi\)
−0.313879 + 0.949463i \(0.601628\pi\)
\(158\) 17.3002 1.37633
\(159\) −13.7029 −1.08671
\(160\) 15.1892 1.20081
\(161\) 2.51500 0.198210
\(162\) −66.7143 −5.24157
\(163\) −10.0524 −0.787365 −0.393683 0.919246i \(-0.628799\pi\)
−0.393683 + 0.919246i \(0.628799\pi\)
\(164\) −19.2780 −1.50536
\(165\) 12.2883 0.956641
\(166\) −16.0849 −1.24843
\(167\) −4.54613 −0.351790 −0.175895 0.984409i \(-0.556282\pi\)
−0.175895 + 0.984409i \(0.556282\pi\)
\(168\) −36.4120 −2.80924
\(169\) −12.9752 −0.998093
\(170\) −8.77452 −0.672975
\(171\) −45.5379 −3.48237
\(172\) 3.50630 0.267353
\(173\) −22.8399 −1.73649 −0.868244 0.496138i \(-0.834751\pi\)
−0.868244 + 0.496138i \(0.834751\pi\)
\(174\) −13.0073 −0.986078
\(175\) 28.1583 2.12857
\(176\) 1.28155 0.0966002
\(177\) −0.0109455 −0.000822716 0
\(178\) 22.5832 1.69268
\(179\) −17.7864 −1.32942 −0.664709 0.747102i \(-0.731445\pi\)
−0.664709 + 0.747102i \(0.731445\pi\)
\(180\) 102.258 7.62185
\(181\) −6.89009 −0.512137 −0.256068 0.966659i \(-0.582427\pi\)
−0.256068 + 0.966659i \(0.582427\pi\)
\(182\) −1.15818 −0.0858503
\(183\) 26.1698 1.93452
\(184\) −2.83579 −0.209057
\(185\) 27.7760 2.04213
\(186\) −7.11956 −0.522031
\(187\) 1.00000 0.0731272
\(188\) −23.0894 −1.68397
\(189\) 49.4399 3.59622
\(190\) 51.2322 3.71678
\(191\) −5.22557 −0.378109 −0.189055 0.981967i \(-0.560542\pi\)
−0.189055 + 0.981967i \(0.560542\pi\)
\(192\) −39.7463 −2.86844
\(193\) 12.8224 0.922978 0.461489 0.887146i \(-0.347315\pi\)
0.461489 + 0.887146i \(0.347315\pi\)
\(194\) −13.9987 −1.00505
\(195\) 1.93479 0.138553
\(196\) 9.91145 0.707961
\(197\) 6.03779 0.430175 0.215087 0.976595i \(-0.430996\pi\)
0.215087 + 0.976595i \(0.430996\pi\)
\(198\) −18.3014 −1.30062
\(199\) 9.39589 0.666057 0.333028 0.942917i \(-0.391930\pi\)
0.333028 + 0.942917i \(0.391930\pi\)
\(200\) −31.7499 −2.24506
\(201\) −8.84233 −0.623690
\(202\) 41.5519 2.92358
\(203\) 5.28766 0.371121
\(204\) 11.5225 0.806736
\(205\) −20.5592 −1.43591
\(206\) −5.10674 −0.355803
\(207\) 6.25729 0.434912
\(208\) 0.201779 0.0139909
\(209\) −5.83875 −0.403874
\(210\) −90.3911 −6.23758
\(211\) 27.6908 1.90631 0.953157 0.302477i \(-0.0978136\pi\)
0.953157 + 0.302477i \(0.0978136\pi\)
\(212\) −14.6206 −1.00415
\(213\) −2.55894 −0.175336
\(214\) 32.1196 2.19565
\(215\) 3.73933 0.255020
\(216\) −55.7460 −3.79304
\(217\) 2.89422 0.196472
\(218\) 13.8536 0.938284
\(219\) −44.9732 −3.03900
\(220\) 13.1112 0.883958
\(221\) 0.157450 0.0105912
\(222\) −57.2801 −3.84439
\(223\) 1.64128 0.109908 0.0549541 0.998489i \(-0.482499\pi\)
0.0549541 + 0.998489i \(0.482499\pi\)
\(224\) 12.7335 0.850790
\(225\) 70.0575 4.67050
\(226\) −25.9602 −1.72684
\(227\) 12.2734 0.814612 0.407306 0.913292i \(-0.366468\pi\)
0.407306 + 0.913292i \(0.366468\pi\)
\(228\) −67.2769 −4.45552
\(229\) −14.6293 −0.966730 −0.483365 0.875419i \(-0.660586\pi\)
−0.483365 + 0.875419i \(0.660586\pi\)
\(230\) −7.03974 −0.464186
\(231\) 10.3015 0.677792
\(232\) −5.96212 −0.391432
\(233\) 17.3190 1.13460 0.567301 0.823510i \(-0.307988\pi\)
0.567301 + 0.823510i \(0.307988\pi\)
\(234\) −2.88155 −0.188373
\(235\) −24.6239 −1.60629
\(236\) −0.0116785 −0.000760209 0
\(237\) −24.2280 −1.57378
\(238\) −7.35589 −0.476811
\(239\) 24.2707 1.56994 0.784969 0.619535i \(-0.212679\pi\)
0.784969 + 0.619535i \(0.212679\pi\)
\(240\) 15.7480 1.01653
\(241\) 2.60739 0.167957 0.0839783 0.996468i \(-0.473237\pi\)
0.0839783 + 0.996468i \(0.473237\pi\)
\(242\) −2.34655 −0.150842
\(243\) 46.1155 2.95831
\(244\) 27.9223 1.78754
\(245\) 10.5702 0.675303
\(246\) 42.3974 2.70316
\(247\) −0.919310 −0.0584943
\(248\) −3.26338 −0.207225
\(249\) 22.5261 1.42753
\(250\) −34.9452 −2.21013
\(251\) −17.4595 −1.10203 −0.551016 0.834495i \(-0.685760\pi\)
−0.551016 + 0.834495i \(0.685760\pi\)
\(252\) 85.7251 5.40017
\(253\) 0.802293 0.0504397
\(254\) 11.6003 0.727870
\(255\) 12.2883 0.769521
\(256\) −23.3446 −1.45904
\(257\) 25.9458 1.61845 0.809227 0.587496i \(-0.199886\pi\)
0.809227 + 0.587496i \(0.199886\pi\)
\(258\) −7.71129 −0.480084
\(259\) 23.2853 1.44688
\(260\) 2.06436 0.128026
\(261\) 13.1557 0.814314
\(262\) −19.2593 −1.18984
\(263\) 17.4395 1.07536 0.537682 0.843148i \(-0.319300\pi\)
0.537682 + 0.843148i \(0.319300\pi\)
\(264\) −11.6155 −0.714886
\(265\) −15.5923 −0.957828
\(266\) 42.9491 2.63338
\(267\) −31.6266 −1.93552
\(268\) −9.43449 −0.576303
\(269\) 1.26835 0.0773325 0.0386662 0.999252i \(-0.487689\pi\)
0.0386662 + 0.999252i \(0.487689\pi\)
\(270\) −138.387 −8.42197
\(271\) −9.05410 −0.549997 −0.274999 0.961445i \(-0.588677\pi\)
−0.274999 + 0.961445i \(0.588677\pi\)
\(272\) 1.28155 0.0777051
\(273\) 1.62198 0.0981665
\(274\) −32.3703 −1.95556
\(275\) 8.98258 0.541670
\(276\) 9.24441 0.556448
\(277\) −25.0642 −1.50596 −0.752982 0.658042i \(-0.771385\pi\)
−0.752982 + 0.658042i \(0.771385\pi\)
\(278\) 43.2419 2.59348
\(279\) 7.20078 0.431100
\(280\) −41.4324 −2.47606
\(281\) −26.0912 −1.55647 −0.778235 0.627973i \(-0.783885\pi\)
−0.778235 + 0.627973i \(0.783885\pi\)
\(282\) 50.7797 3.02389
\(283\) 13.6420 0.810932 0.405466 0.914110i \(-0.367109\pi\)
0.405466 + 0.914110i \(0.367109\pi\)
\(284\) −2.73031 −0.162014
\(285\) −71.7481 −4.24999
\(286\) −0.369464 −0.0218469
\(287\) −17.2352 −1.01736
\(288\) 31.6807 1.86680
\(289\) 1.00000 0.0588235
\(290\) −14.8007 −0.869127
\(291\) 19.6044 1.14923
\(292\) −47.9850 −2.80811
\(293\) 22.7130 1.32691 0.663453 0.748218i \(-0.269090\pi\)
0.663453 + 0.748218i \(0.269090\pi\)
\(294\) −21.7979 −1.27128
\(295\) −0.0124547 −0.000725141 0
\(296\) −26.2554 −1.52606
\(297\) 15.7715 0.915153
\(298\) 11.0869 0.642246
\(299\) 0.126321 0.00730533
\(300\) 103.502 5.97567
\(301\) 3.13477 0.180685
\(302\) −31.4368 −1.80899
\(303\) −58.1913 −3.34301
\(304\) −7.48262 −0.429158
\(305\) 29.7780 1.70509
\(306\) −18.3014 −1.04622
\(307\) 3.04953 0.174046 0.0870231 0.996206i \(-0.472265\pi\)
0.0870231 + 0.996206i \(0.472265\pi\)
\(308\) 10.9914 0.626295
\(309\) 7.15172 0.406847
\(310\) −8.10120 −0.460117
\(311\) 9.36660 0.531131 0.265565 0.964093i \(-0.414441\pi\)
0.265565 + 0.964093i \(0.414441\pi\)
\(312\) −1.82886 −0.103539
\(313\) −25.8421 −1.46068 −0.730342 0.683082i \(-0.760639\pi\)
−0.730342 + 0.683082i \(0.760639\pi\)
\(314\) 18.4574 1.04161
\(315\) 91.4224 5.15107
\(316\) −25.8505 −1.45421
\(317\) 21.8487 1.22714 0.613572 0.789639i \(-0.289732\pi\)
0.613572 + 0.789639i \(0.289732\pi\)
\(318\) 32.1547 1.80314
\(319\) 1.68678 0.0944416
\(320\) −45.2265 −2.52824
\(321\) −44.9818 −2.51064
\(322\) −5.90157 −0.328882
\(323\) −5.83875 −0.324876
\(324\) 99.6869 5.53816
\(325\) 1.41431 0.0784516
\(326\) 23.5885 1.30645
\(327\) −19.4012 −1.07289
\(328\) 19.4336 1.07304
\(329\) −20.6428 −1.13807
\(330\) −28.8351 −1.58732
\(331\) −21.5290 −1.18334 −0.591670 0.806180i \(-0.701531\pi\)
−0.591670 + 0.806180i \(0.701531\pi\)
\(332\) 24.0346 1.31907
\(333\) 57.9336 3.17474
\(334\) 10.6677 0.583711
\(335\) −10.0615 −0.549719
\(336\) 13.2019 0.720223
\(337\) −18.2913 −0.996391 −0.498195 0.867065i \(-0.666004\pi\)
−0.498195 + 0.867065i \(0.666004\pi\)
\(338\) 30.4470 1.65610
\(339\) 36.3559 1.97458
\(340\) 13.1112 0.711055
\(341\) 0.923264 0.0499975
\(342\) 106.857 5.77817
\(343\) −13.0821 −0.706370
\(344\) −3.53461 −0.190574
\(345\) 9.85879 0.530779
\(346\) 53.5951 2.88129
\(347\) 19.3085 1.03653 0.518266 0.855219i \(-0.326578\pi\)
0.518266 + 0.855219i \(0.326578\pi\)
\(348\) 19.4359 1.04187
\(349\) −3.10537 −0.166226 −0.0831132 0.996540i \(-0.526486\pi\)
−0.0831132 + 0.996540i \(0.526486\pi\)
\(350\) −66.0748 −3.53185
\(351\) 2.48322 0.132544
\(352\) 4.06201 0.216506
\(353\) 8.28086 0.440746 0.220373 0.975416i \(-0.429273\pi\)
0.220373 + 0.975416i \(0.429273\pi\)
\(354\) 0.0256842 0.00136510
\(355\) −2.91177 −0.154540
\(356\) −33.7446 −1.78846
\(357\) 10.3015 0.545215
\(358\) 41.7367 2.20585
\(359\) 18.7141 0.987693 0.493846 0.869549i \(-0.335590\pi\)
0.493846 + 0.869549i \(0.335590\pi\)
\(360\) −103.084 −5.43298
\(361\) 15.0909 0.794260
\(362\) 16.1680 0.849769
\(363\) 3.28622 0.172482
\(364\) 1.73060 0.0907081
\(365\) −51.1741 −2.67857
\(366\) −61.4087 −3.20988
\(367\) 2.88918 0.150814 0.0754069 0.997153i \(-0.475974\pi\)
0.0754069 + 0.997153i \(0.475974\pi\)
\(368\) 1.02817 0.0535973
\(369\) −42.8811 −2.23230
\(370\) −65.1779 −3.38844
\(371\) −13.0714 −0.678633
\(372\) 10.6383 0.551570
\(373\) 0.725098 0.0375442 0.0187721 0.999824i \(-0.494024\pi\)
0.0187721 + 0.999824i \(0.494024\pi\)
\(374\) −2.34655 −0.121337
\(375\) 48.9390 2.52720
\(376\) 23.2758 1.20036
\(377\) 0.265583 0.0136782
\(378\) −116.013 −5.96707
\(379\) 18.9756 0.974711 0.487355 0.873204i \(-0.337962\pi\)
0.487355 + 0.873204i \(0.337962\pi\)
\(380\) −76.5530 −3.92709
\(381\) −16.2457 −0.832292
\(382\) 12.2621 0.627382
\(383\) 19.1017 0.976049 0.488025 0.872830i \(-0.337718\pi\)
0.488025 + 0.872830i \(0.337718\pi\)
\(384\) 66.5692 3.39710
\(385\) 11.7219 0.597404
\(386\) −30.0885 −1.53146
\(387\) 7.79927 0.396459
\(388\) 20.9173 1.06192
\(389\) −36.8471 −1.86822 −0.934111 0.356984i \(-0.883805\pi\)
−0.934111 + 0.356984i \(0.883805\pi\)
\(390\) −4.54008 −0.229896
\(391\) 0.802293 0.0405737
\(392\) −9.99148 −0.504646
\(393\) 26.9717 1.36054
\(394\) −14.1680 −0.713772
\(395\) −27.5686 −1.38712
\(396\) 27.3466 1.37422
\(397\) 30.6800 1.53978 0.769892 0.638174i \(-0.220310\pi\)
0.769892 + 0.638174i \(0.220310\pi\)
\(398\) −22.0479 −1.10516
\(399\) −60.1481 −3.01117
\(400\) 11.5116 0.575579
\(401\) −25.1078 −1.25382 −0.626911 0.779091i \(-0.715681\pi\)
−0.626911 + 0.779091i \(0.715681\pi\)
\(402\) 20.7490 1.03486
\(403\) 0.145368 0.00724129
\(404\) −62.0884 −3.08901
\(405\) 106.312 5.28269
\(406\) −12.4078 −0.615787
\(407\) 7.42808 0.368196
\(408\) −11.6155 −0.575054
\(409\) 30.7734 1.52165 0.760823 0.648960i \(-0.224796\pi\)
0.760823 + 0.648960i \(0.224796\pi\)
\(410\) 48.2431 2.38256
\(411\) 45.3329 2.23611
\(412\) 7.63067 0.375936
\(413\) −0.0104411 −0.000513771 0
\(414\) −14.6831 −0.721633
\(415\) 25.6320 1.25822
\(416\) 0.639563 0.0313572
\(417\) −60.5580 −2.96554
\(418\) 13.7009 0.670134
\(419\) 35.2436 1.72176 0.860882 0.508805i \(-0.169913\pi\)
0.860882 + 0.508805i \(0.169913\pi\)
\(420\) 135.066 6.59053
\(421\) −40.2018 −1.95931 −0.979657 0.200680i \(-0.935685\pi\)
−0.979657 + 0.200680i \(0.935685\pi\)
\(422\) −64.9779 −3.16307
\(423\) −51.3591 −2.49716
\(424\) 14.7387 0.715774
\(425\) 8.98258 0.435719
\(426\) 6.00468 0.290928
\(427\) 24.9636 1.20807
\(428\) −47.9942 −2.31989
\(429\) 0.517416 0.0249811
\(430\) −8.77452 −0.423145
\(431\) 24.9486 1.20173 0.600867 0.799349i \(-0.294822\pi\)
0.600867 + 0.799349i \(0.294822\pi\)
\(432\) 20.2119 0.972444
\(433\) −14.7226 −0.707525 −0.353763 0.935335i \(-0.615098\pi\)
−0.353763 + 0.935335i \(0.615098\pi\)
\(434\) −6.79143 −0.325999
\(435\) 20.7276 0.993813
\(436\) −20.7005 −0.991376
\(437\) −4.68438 −0.224084
\(438\) 105.532 5.04250
\(439\) −40.9925 −1.95646 −0.978232 0.207514i \(-0.933463\pi\)
−0.978232 + 0.207514i \(0.933463\pi\)
\(440\) −13.2171 −0.630099
\(441\) 22.0466 1.04984
\(442\) −0.369464 −0.0175736
\(443\) −22.5415 −1.07098 −0.535490 0.844541i \(-0.679873\pi\)
−0.535490 + 0.844541i \(0.679873\pi\)
\(444\) 85.5900 4.06192
\(445\) −35.9873 −1.70596
\(446\) −3.85134 −0.182366
\(447\) −15.5266 −0.734383
\(448\) −37.9144 −1.79129
\(449\) 16.0252 0.756275 0.378137 0.925749i \(-0.376565\pi\)
0.378137 + 0.925749i \(0.376565\pi\)
\(450\) −164.394 −7.74959
\(451\) −5.49809 −0.258895
\(452\) 38.7906 1.82456
\(453\) 44.0257 2.06851
\(454\) −28.8001 −1.35165
\(455\) 1.84561 0.0865238
\(456\) 67.8201 3.17597
\(457\) −7.64623 −0.357675 −0.178838 0.983879i \(-0.557234\pi\)
−0.178838 + 0.983879i \(0.557234\pi\)
\(458\) 34.3283 1.60406
\(459\) 15.7715 0.736149
\(460\) 10.5190 0.490452
\(461\) −25.2790 −1.17736 −0.588680 0.808366i \(-0.700352\pi\)
−0.588680 + 0.808366i \(0.700352\pi\)
\(462\) −24.1731 −1.12463
\(463\) 1.44153 0.0669935 0.0334968 0.999439i \(-0.489336\pi\)
0.0334968 + 0.999439i \(0.489336\pi\)
\(464\) 2.16169 0.100354
\(465\) 11.3453 0.526127
\(466\) −40.6398 −1.88260
\(467\) 41.1549 1.90442 0.952210 0.305445i \(-0.0988052\pi\)
0.952210 + 0.305445i \(0.0988052\pi\)
\(468\) 4.30572 0.199032
\(469\) −8.43479 −0.389483
\(470\) 57.7812 2.66525
\(471\) −25.8487 −1.19104
\(472\) 0.0117728 0.000541889 0
\(473\) 1.00000 0.0459800
\(474\) 56.8522 2.61131
\(475\) −52.4470 −2.40643
\(476\) 10.9914 0.503791
\(477\) −32.5215 −1.48906
\(478\) −56.9523 −2.60494
\(479\) −32.5566 −1.48755 −0.743774 0.668432i \(-0.766966\pi\)
−0.743774 + 0.668432i \(0.766966\pi\)
\(480\) 49.9151 2.27830
\(481\) 1.16955 0.0533269
\(482\) −6.11837 −0.278684
\(483\) 8.26485 0.376064
\(484\) 3.50630 0.159377
\(485\) 22.3075 1.01293
\(486\) −108.212 −4.90861
\(487\) −26.9786 −1.22251 −0.611257 0.791432i \(-0.709336\pi\)
−0.611257 + 0.791432i \(0.709336\pi\)
\(488\) −28.1478 −1.27419
\(489\) −33.0345 −1.49387
\(490\) −24.8034 −1.12050
\(491\) 8.77555 0.396035 0.198018 0.980198i \(-0.436550\pi\)
0.198018 + 0.980198i \(0.436550\pi\)
\(492\) −63.3517 −2.85612
\(493\) 1.68678 0.0759688
\(494\) 2.15721 0.0970573
\(495\) 29.1640 1.31083
\(496\) 1.18321 0.0531275
\(497\) −2.44100 −0.109494
\(498\) −52.8586 −2.36865
\(499\) 1.75861 0.0787261 0.0393630 0.999225i \(-0.487467\pi\)
0.0393630 + 0.999225i \(0.487467\pi\)
\(500\) 52.2164 2.33519
\(501\) −14.9396 −0.667452
\(502\) 40.9695 1.82856
\(503\) −42.9646 −1.91570 −0.957849 0.287274i \(-0.907251\pi\)
−0.957849 + 0.287274i \(0.907251\pi\)
\(504\) −86.4173 −3.84933
\(505\) −66.2148 −2.94652
\(506\) −1.88262 −0.0836927
\(507\) −42.6394 −1.89368
\(508\) −17.3337 −0.769057
\(509\) 28.3483 1.25652 0.628258 0.778005i \(-0.283768\pi\)
0.628258 + 0.778005i \(0.283768\pi\)
\(510\) −28.8351 −1.27684
\(511\) −42.9004 −1.89780
\(512\) 14.2652 0.630438
\(513\) −92.0856 −4.06568
\(514\) −60.8831 −2.68544
\(515\) 8.13780 0.358594
\(516\) 11.5225 0.507249
\(517\) −6.58511 −0.289613
\(518\) −54.6401 −2.40075
\(519\) −75.0571 −3.29464
\(520\) −2.08103 −0.0912591
\(521\) 2.17196 0.0951553 0.0475777 0.998868i \(-0.484850\pi\)
0.0475777 + 0.998868i \(0.484850\pi\)
\(522\) −30.8704 −1.35116
\(523\) 20.5959 0.900595 0.450298 0.892878i \(-0.351318\pi\)
0.450298 + 0.892878i \(0.351318\pi\)
\(524\) 28.7779 1.25717
\(525\) 92.5344 4.03853
\(526\) −40.9226 −1.78431
\(527\) 0.923264 0.0402180
\(528\) 4.21145 0.183280
\(529\) −22.3563 −0.972014
\(530\) 36.5882 1.58929
\(531\) −0.0259773 −0.00112732
\(532\) −64.1762 −2.78239
\(533\) −0.865674 −0.0374965
\(534\) 74.2134 3.21153
\(535\) −51.1839 −2.21287
\(536\) 9.51067 0.410798
\(537\) −58.4501 −2.52231
\(538\) −2.97624 −0.128315
\(539\) 2.82675 0.121757
\(540\) 206.783 8.89853
\(541\) 16.0554 0.690277 0.345139 0.938552i \(-0.387832\pi\)
0.345139 + 0.938552i \(0.387832\pi\)
\(542\) 21.2459 0.912590
\(543\) −22.6424 −0.971678
\(544\) 4.06201 0.174157
\(545\) −22.0763 −0.945644
\(546\) −3.80605 −0.162884
\(547\) 8.15397 0.348639 0.174319 0.984689i \(-0.444227\pi\)
0.174319 + 0.984689i \(0.444227\pi\)
\(548\) 48.3688 2.06621
\(549\) 62.1093 2.65076
\(550\) −21.0781 −0.898772
\(551\) −9.84868 −0.419568
\(552\) −9.31905 −0.396645
\(553\) −23.1114 −0.982795
\(554\) 58.8145 2.49879
\(555\) 91.2783 3.87455
\(556\) −64.6136 −2.74023
\(557\) −17.6992 −0.749940 −0.374970 0.927037i \(-0.622347\pi\)
−0.374970 + 0.927037i \(0.622347\pi\)
\(558\) −16.8970 −0.715307
\(559\) 0.157450 0.00665942
\(560\) 15.0222 0.634803
\(561\) 3.28622 0.138744
\(562\) 61.2243 2.58259
\(563\) 5.34456 0.225246 0.112623 0.993638i \(-0.464075\pi\)
0.112623 + 0.993638i \(0.464075\pi\)
\(564\) −75.8769 −3.19499
\(565\) 41.3686 1.74039
\(566\) −32.0116 −1.34555
\(567\) 89.1238 3.74285
\(568\) 2.75236 0.115486
\(569\) 23.1252 0.969457 0.484729 0.874665i \(-0.338918\pi\)
0.484729 + 0.874665i \(0.338918\pi\)
\(570\) 168.361 7.05185
\(571\) −34.6881 −1.45165 −0.725825 0.687879i \(-0.758542\pi\)
−0.725825 + 0.687879i \(0.758542\pi\)
\(572\) 0.552067 0.0230831
\(573\) −17.1724 −0.717388
\(574\) 40.4433 1.68807
\(575\) 7.20666 0.300538
\(576\) −94.3307 −3.93044
\(577\) 4.35115 0.181141 0.0905705 0.995890i \(-0.471131\pi\)
0.0905705 + 0.995890i \(0.471131\pi\)
\(578\) −2.34655 −0.0976037
\(579\) 42.1374 1.75117
\(580\) 22.1157 0.918306
\(581\) 21.4879 0.891467
\(582\) −46.0028 −1.90688
\(583\) −4.16982 −0.172696
\(584\) 48.3724 2.00167
\(585\) 4.59187 0.189851
\(586\) −53.2971 −2.20168
\(587\) 13.1832 0.544130 0.272065 0.962279i \(-0.412293\pi\)
0.272065 + 0.962279i \(0.412293\pi\)
\(588\) 32.5712 1.34322
\(589\) −5.39070 −0.222120
\(590\) 0.0292256 0.00120320
\(591\) 19.8415 0.816171
\(592\) 9.51943 0.391246
\(593\) −12.5264 −0.514398 −0.257199 0.966358i \(-0.582800\pi\)
−0.257199 + 0.966358i \(0.582800\pi\)
\(594\) −37.0086 −1.51848
\(595\) 11.7219 0.480552
\(596\) −16.5664 −0.678587
\(597\) 30.8770 1.26371
\(598\) −0.296418 −0.0121215
\(599\) 44.7035 1.82654 0.913268 0.407358i \(-0.133550\pi\)
0.913268 + 0.407358i \(0.133550\pi\)
\(600\) −104.337 −4.25956
\(601\) 3.71184 0.151409 0.0757045 0.997130i \(-0.475879\pi\)
0.0757045 + 0.997130i \(0.475879\pi\)
\(602\) −7.35589 −0.299804
\(603\) −20.9857 −0.854603
\(604\) 46.9741 1.91135
\(605\) 3.73933 0.152025
\(606\) 136.549 5.54692
\(607\) 48.1253 1.95334 0.976672 0.214735i \(-0.0688887\pi\)
0.976672 + 0.214735i \(0.0688887\pi\)
\(608\) −23.7171 −0.961854
\(609\) 17.3764 0.704129
\(610\) −69.8757 −2.82918
\(611\) −1.03683 −0.0419455
\(612\) 27.3466 1.10542
\(613\) −21.7624 −0.878976 −0.439488 0.898248i \(-0.644840\pi\)
−0.439488 + 0.898248i \(0.644840\pi\)
\(614\) −7.15589 −0.288788
\(615\) −67.5620 −2.72436
\(616\) −11.0802 −0.446433
\(617\) 18.1265 0.729745 0.364872 0.931058i \(-0.381113\pi\)
0.364872 + 0.931058i \(0.381113\pi\)
\(618\) −16.7819 −0.675066
\(619\) −40.9507 −1.64595 −0.822973 0.568080i \(-0.807686\pi\)
−0.822973 + 0.568080i \(0.807686\pi\)
\(620\) 12.1051 0.486153
\(621\) 12.6533 0.507761
\(622\) −21.9792 −0.881285
\(623\) −30.1689 −1.20869
\(624\) 0.663092 0.0265449
\(625\) 10.7738 0.430953
\(626\) 60.6399 2.42366
\(627\) −19.1874 −0.766272
\(628\) −27.5798 −1.10055
\(629\) 7.42808 0.296177
\(630\) −214.527 −8.54697
\(631\) −12.3015 −0.489714 −0.244857 0.969559i \(-0.578741\pi\)
−0.244857 + 0.969559i \(0.578741\pi\)
\(632\) 26.0593 1.03658
\(633\) 90.9982 3.61685
\(634\) −51.2690 −2.03615
\(635\) −18.4856 −0.733580
\(636\) −48.0467 −1.90517
\(637\) 0.445072 0.0176344
\(638\) −3.95812 −0.156703
\(639\) −6.07319 −0.240252
\(640\) 75.7478 2.99420
\(641\) 34.9917 1.38209 0.691044 0.722813i \(-0.257151\pi\)
0.691044 + 0.722813i \(0.257151\pi\)
\(642\) 105.552 4.16581
\(643\) −17.7621 −0.700468 −0.350234 0.936662i \(-0.613898\pi\)
−0.350234 + 0.936662i \(0.613898\pi\)
\(644\) 8.81834 0.347491
\(645\) 12.2883 0.483850
\(646\) 13.7009 0.539055
\(647\) −8.70847 −0.342365 −0.171183 0.985239i \(-0.554759\pi\)
−0.171183 + 0.985239i \(0.554759\pi\)
\(648\) −100.492 −3.94769
\(649\) −0.00333073 −0.000130743 0
\(650\) −3.31874 −0.130172
\(651\) 9.51104 0.372767
\(652\) −35.2468 −1.38037
\(653\) −17.5676 −0.687472 −0.343736 0.939066i \(-0.611693\pi\)
−0.343736 + 0.939066i \(0.611693\pi\)
\(654\) 45.5260 1.78021
\(655\) 30.6905 1.19918
\(656\) −7.04606 −0.275102
\(657\) −106.736 −4.16416
\(658\) 48.4393 1.88836
\(659\) 0.809846 0.0315471 0.0157736 0.999876i \(-0.494979\pi\)
0.0157736 + 0.999876i \(0.494979\pi\)
\(660\) 43.0864 1.67714
\(661\) −27.3586 −1.06412 −0.532062 0.846705i \(-0.678583\pi\)
−0.532062 + 0.846705i \(0.678583\pi\)
\(662\) 50.5188 1.96347
\(663\) 0.517416 0.0200948
\(664\) −24.2287 −0.940256
\(665\) −68.4413 −2.65404
\(666\) −135.944 −5.26773
\(667\) 1.35329 0.0523997
\(668\) −15.9401 −0.616740
\(669\) 5.39361 0.208529
\(670\) 23.6098 0.912128
\(671\) 7.96347 0.307426
\(672\) 41.8450 1.61421
\(673\) 0.243284 0.00937789 0.00468895 0.999989i \(-0.498507\pi\)
0.00468895 + 0.999989i \(0.498507\pi\)
\(674\) 42.9215 1.65327
\(675\) 141.668 5.45282
\(676\) −45.4950 −1.74981
\(677\) −48.9083 −1.87970 −0.939849 0.341591i \(-0.889034\pi\)
−0.939849 + 0.341591i \(0.889034\pi\)
\(678\) −85.3109 −3.27635
\(679\) 18.7009 0.717674
\(680\) −13.2171 −0.506852
\(681\) 40.3330 1.54556
\(682\) −2.16649 −0.0829590
\(683\) 0.445464 0.0170452 0.00852260 0.999964i \(-0.497287\pi\)
0.00852260 + 0.999964i \(0.497287\pi\)
\(684\) −159.670 −6.10512
\(685\) 51.5834 1.97090
\(686\) 30.6979 1.17205
\(687\) −48.0751 −1.83418
\(688\) 1.28155 0.0488585
\(689\) −0.656537 −0.0250121
\(690\) −23.1342 −0.880702
\(691\) −29.9516 −1.13941 −0.569706 0.821849i \(-0.692943\pi\)
−0.569706 + 0.821849i \(0.692943\pi\)
\(692\) −80.0837 −3.04432
\(693\) 24.4489 0.928736
\(694\) −45.3083 −1.71988
\(695\) −68.9078 −2.61382
\(696\) −19.5928 −0.742665
\(697\) −5.49809 −0.208255
\(698\) 7.28690 0.275813
\(699\) 56.9140 2.15268
\(700\) 98.7314 3.73170
\(701\) 16.9462 0.640048 0.320024 0.947409i \(-0.396309\pi\)
0.320024 + 0.947409i \(0.396309\pi\)
\(702\) −5.82699 −0.219926
\(703\) −43.3707 −1.63576
\(704\) −12.0948 −0.455840
\(705\) −80.9196 −3.04761
\(706\) −19.4315 −0.731312
\(707\) −55.5094 −2.08764
\(708\) −0.0383783 −0.00144235
\(709\) 1.38862 0.0521508 0.0260754 0.999660i \(-0.491699\pi\)
0.0260754 + 0.999660i \(0.491699\pi\)
\(710\) 6.83261 0.256423
\(711\) −57.5009 −2.15645
\(712\) 34.0171 1.27484
\(713\) 0.740728 0.0277405
\(714\) −24.1731 −0.904655
\(715\) 0.588757 0.0220183
\(716\) −62.3645 −2.33067
\(717\) 79.7588 2.97865
\(718\) −43.9136 −1.63884
\(719\) 10.8162 0.403377 0.201688 0.979450i \(-0.435357\pi\)
0.201688 + 0.979450i \(0.435357\pi\)
\(720\) 37.3750 1.39289
\(721\) 6.82211 0.254069
\(722\) −35.4117 −1.31789
\(723\) 8.56846 0.318664
\(724\) −24.1587 −0.897853
\(725\) 15.1516 0.562718
\(726\) −7.71129 −0.286193
\(727\) 45.9183 1.70301 0.851507 0.524343i \(-0.175689\pi\)
0.851507 + 0.524343i \(0.175689\pi\)
\(728\) −1.74457 −0.0646582
\(729\) 66.2535 2.45383
\(730\) 120.083 4.44445
\(731\) 1.00000 0.0369863
\(732\) 91.7590 3.39151
\(733\) 39.0237 1.44137 0.720687 0.693260i \(-0.243826\pi\)
0.720687 + 0.693260i \(0.243826\pi\)
\(734\) −6.77960 −0.250240
\(735\) 34.7359 1.28125
\(736\) 3.25892 0.120125
\(737\) −2.69073 −0.0991141
\(738\) 100.623 3.70397
\(739\) 30.7395 1.13077 0.565385 0.824827i \(-0.308728\pi\)
0.565385 + 0.824827i \(0.308728\pi\)
\(740\) 97.3912 3.58017
\(741\) −3.02106 −0.110981
\(742\) 30.6727 1.12603
\(743\) 11.9117 0.436999 0.218499 0.975837i \(-0.429884\pi\)
0.218499 + 0.975837i \(0.429884\pi\)
\(744\) −10.7242 −0.393168
\(745\) −17.6674 −0.647284
\(746\) −1.70148 −0.0622956
\(747\) 53.4616 1.95606
\(748\) 3.50630 0.128203
\(749\) −42.9087 −1.56785
\(750\) −114.838 −4.19329
\(751\) −19.7493 −0.720660 −0.360330 0.932825i \(-0.617336\pi\)
−0.360330 + 0.932825i \(0.617336\pi\)
\(752\) −8.43912 −0.307743
\(753\) −57.3757 −2.09089
\(754\) −0.623205 −0.0226958
\(755\) 50.0960 1.82318
\(756\) 173.351 6.30472
\(757\) 0.0478783 0.00174017 0.000870084 1.00000i \(-0.499723\pi\)
0.000870084 1.00000i \(0.499723\pi\)
\(758\) −44.5272 −1.61730
\(759\) 2.63651 0.0956994
\(760\) 77.1711 2.79929
\(761\) 45.9562 1.66591 0.832955 0.553340i \(-0.186647\pi\)
0.832955 + 0.553340i \(0.186647\pi\)
\(762\) 38.1213 1.38099
\(763\) −18.5071 −0.670001
\(764\) −18.3224 −0.662882
\(765\) 29.1640 1.05443
\(766\) −44.8230 −1.61952
\(767\) −0.000524423 0 −1.89358e−5 0
\(768\) −76.7156 −2.76824
\(769\) −27.1374 −0.978600 −0.489300 0.872116i \(-0.662748\pi\)
−0.489300 + 0.872116i \(0.662748\pi\)
\(770\) −27.5061 −0.991250
\(771\) 85.2637 3.07070
\(772\) 44.9593 1.61812
\(773\) −41.1983 −1.48180 −0.740899 0.671616i \(-0.765600\pi\)
−0.740899 + 0.671616i \(0.765600\pi\)
\(774\) −18.3014 −0.657829
\(775\) 8.29329 0.297904
\(776\) −21.0862 −0.756951
\(777\) 76.5207 2.74516
\(778\) 86.4636 3.09987
\(779\) 32.1020 1.15017
\(780\) 6.78395 0.242904
\(781\) −0.778687 −0.0278636
\(782\) −1.88262 −0.0673224
\(783\) 26.6030 0.950714
\(784\) 3.62261 0.129379
\(785\) −29.4127 −1.04978
\(786\) −63.2904 −2.25749
\(787\) 12.6871 0.452247 0.226124 0.974099i \(-0.427395\pi\)
0.226124 + 0.974099i \(0.427395\pi\)
\(788\) 21.1703 0.754161
\(789\) 57.3100 2.04029
\(790\) 64.6910 2.30160
\(791\) 34.6803 1.23309
\(792\) −27.5674 −0.979565
\(793\) 1.25385 0.0445255
\(794\) −71.9922 −2.55491
\(795\) −51.2398 −1.81729
\(796\) 32.9448 1.16770
\(797\) 8.09034 0.286575 0.143287 0.989681i \(-0.454233\pi\)
0.143287 + 0.989681i \(0.454233\pi\)
\(798\) 141.141 4.99632
\(799\) −6.58511 −0.232965
\(800\) 36.4873 1.29002
\(801\) −75.0601 −2.65212
\(802\) 58.9167 2.08042
\(803\) −13.6854 −0.482946
\(804\) −31.0039 −1.09342
\(805\) 9.40441 0.331462
\(806\) −0.341113 −0.0120152
\(807\) 4.16807 0.146723
\(808\) 62.5897 2.20190
\(809\) −8.82110 −0.310134 −0.155067 0.987904i \(-0.549559\pi\)
−0.155067 + 0.987904i \(0.549559\pi\)
\(810\) −249.467 −8.76536
\(811\) 2.71442 0.0953163 0.0476581 0.998864i \(-0.484824\pi\)
0.0476581 + 0.998864i \(0.484824\pi\)
\(812\) 18.5401 0.650631
\(813\) −29.7538 −1.04351
\(814\) −17.4304 −0.610934
\(815\) −37.5893 −1.31669
\(816\) 4.21145 0.147430
\(817\) −5.83875 −0.204272
\(818\) −72.2113 −2.52481
\(819\) 3.84947 0.134511
\(820\) −72.0866 −2.51737
\(821\) −25.3175 −0.883588 −0.441794 0.897116i \(-0.645658\pi\)
−0.441794 + 0.897116i \(0.645658\pi\)
\(822\) −106.376 −3.71029
\(823\) 45.2475 1.57723 0.788614 0.614889i \(-0.210799\pi\)
0.788614 + 0.614889i \(0.210799\pi\)
\(824\) −7.69228 −0.267973
\(825\) 29.5188 1.02771
\(826\) 0.0245005 0.000852481 0
\(827\) 27.4728 0.955322 0.477661 0.878544i \(-0.341485\pi\)
0.477661 + 0.878544i \(0.341485\pi\)
\(828\) 21.9400 0.762466
\(829\) 10.2452 0.355832 0.177916 0.984046i \(-0.443065\pi\)
0.177916 + 0.984046i \(0.443065\pi\)
\(830\) −60.1467 −2.08772
\(831\) −82.3666 −2.85727
\(832\) −1.90433 −0.0660207
\(833\) 2.82675 0.0979412
\(834\) 142.102 4.92061
\(835\) −16.9995 −0.588291
\(836\) −20.4724 −0.708053
\(837\) 14.5612 0.503310
\(838\) −82.7009 −2.85686
\(839\) 9.46425 0.326742 0.163371 0.986565i \(-0.447763\pi\)
0.163371 + 0.986565i \(0.447763\pi\)
\(840\) −136.156 −4.69784
\(841\) −26.1548 −0.901889
\(842\) 94.3355 3.25101
\(843\) −85.7415 −2.95309
\(844\) 97.0923 3.34205
\(845\) −48.5186 −1.66909
\(846\) 120.517 4.14345
\(847\) 3.13477 0.107712
\(848\) −5.34381 −0.183507
\(849\) 44.8306 1.53858
\(850\) −21.0781 −0.722972
\(851\) 5.95949 0.204289
\(852\) −8.97241 −0.307390
\(853\) 18.6804 0.639605 0.319802 0.947484i \(-0.396383\pi\)
0.319802 + 0.947484i \(0.396383\pi\)
\(854\) −58.5784 −2.00451
\(855\) −170.281 −5.82350
\(856\) 48.3818 1.65365
\(857\) −20.8450 −0.712050 −0.356025 0.934476i \(-0.615868\pi\)
−0.356025 + 0.934476i \(0.615868\pi\)
\(858\) −1.21414 −0.0414501
\(859\) −25.1809 −0.859161 −0.429581 0.903028i \(-0.641339\pi\)
−0.429581 + 0.903028i \(0.641339\pi\)
\(860\) 13.1112 0.447089
\(861\) −56.6388 −1.93025
\(862\) −58.5432 −1.99399
\(863\) −40.0323 −1.36272 −0.681358 0.731950i \(-0.738610\pi\)
−0.681358 + 0.731950i \(0.738610\pi\)
\(864\) 64.0639 2.17950
\(865\) −85.4060 −2.90389
\(866\) 34.5474 1.17397
\(867\) 3.28622 0.111606
\(868\) 10.1480 0.344445
\(869\) −7.37260 −0.250098
\(870\) −48.6384 −1.64900
\(871\) −0.423654 −0.0143550
\(872\) 20.8677 0.706669
\(873\) 46.5276 1.57472
\(874\) 10.9921 0.371815
\(875\) 46.6834 1.57819
\(876\) −157.689 −5.32783
\(877\) 1.55572 0.0525328 0.0262664 0.999655i \(-0.491638\pi\)
0.0262664 + 0.999655i \(0.491638\pi\)
\(878\) 96.1909 3.24629
\(879\) 74.6399 2.51754
\(880\) 4.79212 0.161542
\(881\) 17.1664 0.578351 0.289175 0.957276i \(-0.406619\pi\)
0.289175 + 0.957276i \(0.406619\pi\)
\(882\) −51.7335 −1.74196
\(883\) −55.0298 −1.85190 −0.925949 0.377647i \(-0.876733\pi\)
−0.925949 + 0.377647i \(0.876733\pi\)
\(884\) 0.552067 0.0185680
\(885\) −0.0409289 −0.00137581
\(886\) 52.8948 1.77704
\(887\) −1.81992 −0.0611070 −0.0305535 0.999533i \(-0.509727\pi\)
−0.0305535 + 0.999533i \(0.509727\pi\)
\(888\) −86.2811 −2.89540
\(889\) −15.4969 −0.519751
\(890\) 84.4459 2.83063
\(891\) 28.4308 0.952467
\(892\) 5.75482 0.192686
\(893\) 38.4488 1.28664
\(894\) 36.4340 1.21853
\(895\) −66.5092 −2.22316
\(896\) 63.5011 2.12142
\(897\) 0.415119 0.0138604
\(898\) −37.6039 −1.25486
\(899\) 1.55734 0.0519403
\(900\) 245.643 8.18809
\(901\) −4.16982 −0.138917
\(902\) 12.9016 0.429575
\(903\) 10.3015 0.342814
\(904\) −39.1038 −1.30057
\(905\) −25.7643 −0.856435
\(906\) −103.309 −3.43220
\(907\) 40.4476 1.34304 0.671520 0.740986i \(-0.265642\pi\)
0.671520 + 0.740986i \(0.265642\pi\)
\(908\) 43.0341 1.42814
\(909\) −138.107 −4.58071
\(910\) −4.33083 −0.143566
\(911\) 18.5804 0.615597 0.307798 0.951452i \(-0.400408\pi\)
0.307798 + 0.951452i \(0.400408\pi\)
\(912\) −24.5896 −0.814242
\(913\) 6.85470 0.226857
\(914\) 17.9423 0.593477
\(915\) 97.8573 3.23506
\(916\) −51.2946 −1.69482
\(917\) 25.7286 0.849632
\(918\) −37.0086 −1.22146
\(919\) 43.0843 1.42122 0.710610 0.703586i \(-0.248419\pi\)
0.710610 + 0.703586i \(0.248419\pi\)
\(920\) −10.6040 −0.349602
\(921\) 10.0215 0.330218
\(922\) 59.3184 1.95355
\(923\) −0.122604 −0.00403557
\(924\) 36.1203 1.18827
\(925\) 66.7233 2.19385
\(926\) −3.38262 −0.111160
\(927\) 16.9733 0.557478
\(928\) 6.85172 0.224919
\(929\) −18.1144 −0.594314 −0.297157 0.954829i \(-0.596039\pi\)
−0.297157 + 0.954829i \(0.596039\pi\)
\(930\) −26.6224 −0.872982
\(931\) −16.5047 −0.540920
\(932\) 60.7255 1.98913
\(933\) 30.7807 1.00772
\(934\) −96.5720 −3.15993
\(935\) 3.73933 0.122289
\(936\) −4.34048 −0.141873
\(937\) 57.6138 1.88216 0.941081 0.338182i \(-0.109812\pi\)
0.941081 + 0.338182i \(0.109812\pi\)
\(938\) 19.7927 0.646254
\(939\) −84.9230 −2.77136
\(940\) −86.3388 −2.81606
\(941\) 28.0969 0.915932 0.457966 0.888970i \(-0.348578\pi\)
0.457966 + 0.888970i \(0.348578\pi\)
\(942\) 60.6553 1.97626
\(943\) −4.41108 −0.143644
\(944\) −0.00426849 −0.000138927 0
\(945\) 184.872 6.01388
\(946\) −2.34655 −0.0762930
\(947\) −36.2630 −1.17839 −0.589195 0.807991i \(-0.700555\pi\)
−0.589195 + 0.807991i \(0.700555\pi\)
\(948\) −84.9507 −2.75907
\(949\) −2.15476 −0.0699464
\(950\) 123.070 3.99290
\(951\) 71.7996 2.32826
\(952\) −11.0802 −0.359111
\(953\) −3.68408 −0.119339 −0.0596695 0.998218i \(-0.519005\pi\)
−0.0596695 + 0.998218i \(0.519005\pi\)
\(954\) 76.3134 2.47074
\(955\) −19.5401 −0.632304
\(956\) 85.1003 2.75234
\(957\) 5.54314 0.179184
\(958\) 76.3956 2.46823
\(959\) 43.2435 1.39641
\(960\) −148.624 −4.79683
\(961\) −30.1476 −0.972503
\(962\) −2.74441 −0.0884833
\(963\) −106.756 −3.44018
\(964\) 9.14229 0.294453
\(965\) 47.9473 1.54348
\(966\) −19.3939 −0.623988
\(967\) 56.4893 1.81657 0.908286 0.418350i \(-0.137391\pi\)
0.908286 + 0.418350i \(0.137391\pi\)
\(968\) −3.53461 −0.113607
\(969\) −19.1874 −0.616389
\(970\) −52.3457 −1.68072
\(971\) 55.3772 1.77714 0.888570 0.458741i \(-0.151699\pi\)
0.888570 + 0.458741i \(0.151699\pi\)
\(972\) 161.695 5.18636
\(973\) −57.7670 −1.85192
\(974\) 63.3066 2.02847
\(975\) 4.64773 0.148846
\(976\) 10.2056 0.326672
\(977\) 25.9519 0.830276 0.415138 0.909759i \(-0.363733\pi\)
0.415138 + 0.909759i \(0.363733\pi\)
\(978\) 77.5170 2.47872
\(979\) −9.62399 −0.307584
\(980\) 37.0622 1.18391
\(981\) −46.0454 −1.47012
\(982\) −20.5923 −0.657126
\(983\) 47.2667 1.50757 0.753787 0.657118i \(-0.228225\pi\)
0.753787 + 0.657118i \(0.228225\pi\)
\(984\) 63.8632 2.03589
\(985\) 22.5773 0.719372
\(986\) −3.95812 −0.126052
\(987\) −67.8368 −2.15927
\(988\) −3.22338 −0.102549
\(989\) 0.802293 0.0255114
\(990\) −68.4349 −2.17500
\(991\) 4.73933 0.150550 0.0752748 0.997163i \(-0.476017\pi\)
0.0752748 + 0.997163i \(0.476017\pi\)
\(992\) 3.75031 0.119072
\(993\) −70.7490 −2.24515
\(994\) 5.72793 0.181679
\(995\) 35.1343 1.11383
\(996\) 78.9832 2.50268
\(997\) 42.3144 1.34011 0.670055 0.742312i \(-0.266271\pi\)
0.670055 + 0.742312i \(0.266271\pi\)
\(998\) −4.12666 −0.130627
\(999\) 117.152 3.70652
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 \(a_p\))