Properties

Label 6041.2.a.f.1.20
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.22730 q^{2}\) \(+1.19588 q^{3}\) \(+2.96085 q^{4}\) \(+2.18062 q^{5}\) \(-2.66358 q^{6}\) \(+1.00000 q^{7}\) \(-2.14009 q^{8}\) \(-1.56986 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.22730 q^{2}\) \(+1.19588 q^{3}\) \(+2.96085 q^{4}\) \(+2.18062 q^{5}\) \(-2.66358 q^{6}\) \(+1.00000 q^{7}\) \(-2.14009 q^{8}\) \(-1.56986 q^{9}\) \(-4.85688 q^{10}\) \(-5.84643 q^{11}\) \(+3.54083 q^{12}\) \(-4.49009 q^{13}\) \(-2.22730 q^{14}\) \(+2.60776 q^{15}\) \(-1.15508 q^{16}\) \(+4.28348 q^{17}\) \(+3.49655 q^{18}\) \(+2.48108 q^{19}\) \(+6.45647 q^{20}\) \(+1.19588 q^{21}\) \(+13.0217 q^{22}\) \(-2.32428 q^{23}\) \(-2.55930 q^{24}\) \(-0.244915 q^{25}\) \(+10.0008 q^{26}\) \(-5.46502 q^{27}\) \(+2.96085 q^{28}\) \(+5.18312 q^{29}\) \(-5.80826 q^{30}\) \(-7.27372 q^{31}\) \(+6.85288 q^{32}\) \(-6.99164 q^{33}\) \(-9.54057 q^{34}\) \(+2.18062 q^{35}\) \(-4.64813 q^{36}\) \(+4.26264 q^{37}\) \(-5.52609 q^{38}\) \(-5.36962 q^{39}\) \(-4.66672 q^{40}\) \(+1.15584 q^{41}\) \(-2.66358 q^{42}\) \(+12.7528 q^{43}\) \(-17.3104 q^{44}\) \(-3.42327 q^{45}\) \(+5.17687 q^{46}\) \(+1.87446 q^{47}\) \(-1.38134 q^{48}\) \(+1.00000 q^{49}\) \(+0.545499 q^{50}\) \(+5.12254 q^{51}\) \(-13.2945 q^{52}\) \(+8.62506 q^{53}\) \(+12.1722 q^{54}\) \(-12.7488 q^{55}\) \(-2.14009 q^{56}\) \(+2.96708 q^{57}\) \(-11.5443 q^{58}\) \(+3.08648 q^{59}\) \(+7.72118 q^{60}\) \(-6.77092 q^{61}\) \(+16.2007 q^{62}\) \(-1.56986 q^{63}\) \(-12.9532 q^{64}\) \(-9.79116 q^{65}\) \(+15.5725 q^{66}\) \(-5.38241 q^{67}\) \(+12.6827 q^{68}\) \(-2.77957 q^{69}\) \(-4.85688 q^{70}\) \(-3.33010 q^{71}\) \(+3.35965 q^{72}\) \(-2.43851 q^{73}\) \(-9.49416 q^{74}\) \(-0.292890 q^{75}\) \(+7.34609 q^{76}\) \(-5.84643 q^{77}\) \(+11.9597 q^{78}\) \(+7.22282 q^{79}\) \(-2.51878 q^{80}\) \(-1.82593 q^{81}\) \(-2.57439 q^{82}\) \(-9.50584 q^{83}\) \(+3.54083 q^{84}\) \(+9.34062 q^{85}\) \(-28.4042 q^{86}\) \(+6.19840 q^{87}\) \(+12.5119 q^{88}\) \(-5.53939 q^{89}\) \(+7.62464 q^{90}\) \(-4.49009 q^{91}\) \(-6.88185 q^{92}\) \(-8.69851 q^{93}\) \(-4.17497 q^{94}\) \(+5.41027 q^{95}\) \(+8.19524 q^{96}\) \(-0.269867 q^{97}\) \(-2.22730 q^{98}\) \(+9.17809 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22730 −1.57494 −0.787468 0.616355i \(-0.788608\pi\)
−0.787468 + 0.616355i \(0.788608\pi\)
\(3\) 1.19588 0.690443 0.345222 0.938521i \(-0.387804\pi\)
0.345222 + 0.938521i \(0.387804\pi\)
\(4\) 2.96085 1.48042
\(5\) 2.18062 0.975201 0.487600 0.873067i \(-0.337872\pi\)
0.487600 + 0.873067i \(0.337872\pi\)
\(6\) −2.66358 −1.08740
\(7\) 1.00000 0.377964
\(8\) −2.14009 −0.756637
\(9\) −1.56986 −0.523288
\(10\) −4.85688 −1.53588
\(11\) −5.84643 −1.76276 −0.881382 0.472405i \(-0.843386\pi\)
−0.881382 + 0.472405i \(0.843386\pi\)
\(12\) 3.54083 1.02215
\(13\) −4.49009 −1.24533 −0.622663 0.782490i \(-0.713949\pi\)
−0.622663 + 0.782490i \(0.713949\pi\)
\(14\) −2.22730 −0.595270
\(15\) 2.60776 0.673321
\(16\) −1.15508 −0.288769
\(17\) 4.28348 1.03890 0.519448 0.854502i \(-0.326138\pi\)
0.519448 + 0.854502i \(0.326138\pi\)
\(18\) 3.49655 0.824145
\(19\) 2.48108 0.569198 0.284599 0.958647i \(-0.408140\pi\)
0.284599 + 0.958647i \(0.408140\pi\)
\(20\) 6.45647 1.44371
\(21\) 1.19588 0.260963
\(22\) 13.0217 2.77624
\(23\) −2.32428 −0.484646 −0.242323 0.970196i \(-0.577909\pi\)
−0.242323 + 0.970196i \(0.577909\pi\)
\(24\) −2.55930 −0.522415
\(25\) −0.244915 −0.0489831
\(26\) 10.0008 1.96131
\(27\) −5.46502 −1.05174
\(28\) 2.96085 0.559548
\(29\) 5.18312 0.962481 0.481240 0.876589i \(-0.340186\pi\)
0.481240 + 0.876589i \(0.340186\pi\)
\(30\) −5.80826 −1.06044
\(31\) −7.27372 −1.30640 −0.653199 0.757186i \(-0.726573\pi\)
−0.653199 + 0.757186i \(0.726573\pi\)
\(32\) 6.85288 1.21143
\(33\) −6.99164 −1.21709
\(34\) −9.54057 −1.63619
\(35\) 2.18062 0.368591
\(36\) −4.64813 −0.774688
\(37\) 4.26264 0.700773 0.350387 0.936605i \(-0.386050\pi\)
0.350387 + 0.936605i \(0.386050\pi\)
\(38\) −5.52609 −0.896450
\(39\) −5.36962 −0.859827
\(40\) −4.66672 −0.737873
\(41\) 1.15584 0.180511 0.0902556 0.995919i \(-0.471232\pi\)
0.0902556 + 0.995919i \(0.471232\pi\)
\(42\) −2.66358 −0.411000
\(43\) 12.7528 1.94478 0.972388 0.233369i \(-0.0749750\pi\)
0.972388 + 0.233369i \(0.0749750\pi\)
\(44\) −17.3104 −2.60964
\(45\) −3.42327 −0.510311
\(46\) 5.17687 0.763287
\(47\) 1.87446 0.273418 0.136709 0.990611i \(-0.456348\pi\)
0.136709 + 0.990611i \(0.456348\pi\)
\(48\) −1.38134 −0.199379
\(49\) 1.00000 0.142857
\(50\) 0.545499 0.0771452
\(51\) 5.12254 0.717299
\(52\) −13.2945 −1.84361
\(53\) 8.62506 1.18474 0.592372 0.805665i \(-0.298192\pi\)
0.592372 + 0.805665i \(0.298192\pi\)
\(54\) 12.1722 1.65643
\(55\) −12.7488 −1.71905
\(56\) −2.14009 −0.285982
\(57\) 2.96708 0.392999
\(58\) −11.5443 −1.51585
\(59\) 3.08648 0.401825 0.200913 0.979609i \(-0.435609\pi\)
0.200913 + 0.979609i \(0.435609\pi\)
\(60\) 7.72118 0.996800
\(61\) −6.77092 −0.866928 −0.433464 0.901171i \(-0.642709\pi\)
−0.433464 + 0.901171i \(0.642709\pi\)
\(62\) 16.2007 2.05749
\(63\) −1.56986 −0.197784
\(64\) −12.9532 −1.61916
\(65\) −9.79116 −1.21444
\(66\) 15.5725 1.91684
\(67\) −5.38241 −0.657566 −0.328783 0.944406i \(-0.606638\pi\)
−0.328783 + 0.944406i \(0.606638\pi\)
\(68\) 12.6827 1.53801
\(69\) −2.77957 −0.334621
\(70\) −4.85688 −0.580508
\(71\) −3.33010 −0.395210 −0.197605 0.980282i \(-0.563316\pi\)
−0.197605 + 0.980282i \(0.563316\pi\)
\(72\) 3.35965 0.395939
\(73\) −2.43851 −0.285406 −0.142703 0.989766i \(-0.545579\pi\)
−0.142703 + 0.989766i \(0.545579\pi\)
\(74\) −9.49416 −1.10367
\(75\) −0.292890 −0.0338200
\(76\) 7.34609 0.842654
\(77\) −5.84643 −0.666262
\(78\) 11.9597 1.35417
\(79\) 7.22282 0.812630 0.406315 0.913733i \(-0.366814\pi\)
0.406315 + 0.913733i \(0.366814\pi\)
\(80\) −2.51878 −0.281608
\(81\) −1.82593 −0.202881
\(82\) −2.57439 −0.284294
\(83\) −9.50584 −1.04340 −0.521701 0.853128i \(-0.674702\pi\)
−0.521701 + 0.853128i \(0.674702\pi\)
\(84\) 3.54083 0.386336
\(85\) 9.34062 1.01313
\(86\) −28.4042 −3.06290
\(87\) 6.19840 0.664538
\(88\) 12.5119 1.33377
\(89\) −5.53939 −0.587174 −0.293587 0.955932i \(-0.594849\pi\)
−0.293587 + 0.955932i \(0.594849\pi\)
\(90\) 7.62464 0.803707
\(91\) −4.49009 −0.470689
\(92\) −6.88185 −0.717482
\(93\) −8.69851 −0.901994
\(94\) −4.17497 −0.430615
\(95\) 5.41027 0.555082
\(96\) 8.19524 0.836424
\(97\) −0.269867 −0.0274008 −0.0137004 0.999906i \(-0.504361\pi\)
−0.0137004 + 0.999906i \(0.504361\pi\)
\(98\) −2.22730 −0.224991
\(99\) 9.17809 0.922433
\(100\) −0.725157 −0.0725157
\(101\) −13.0109 −1.29463 −0.647315 0.762222i \(-0.724108\pi\)
−0.647315 + 0.762222i \(0.724108\pi\)
\(102\) −11.4094 −1.12970
\(103\) 15.4070 1.51810 0.759050 0.651032i \(-0.225664\pi\)
0.759050 + 0.651032i \(0.225664\pi\)
\(104\) 9.60920 0.942259
\(105\) 2.60776 0.254491
\(106\) −19.2106 −1.86590
\(107\) 18.6000 1.79813 0.899063 0.437820i \(-0.144249\pi\)
0.899063 + 0.437820i \(0.144249\pi\)
\(108\) −16.1811 −1.55703
\(109\) 12.5373 1.20086 0.600428 0.799679i \(-0.294997\pi\)
0.600428 + 0.799679i \(0.294997\pi\)
\(110\) 28.3954 2.70739
\(111\) 5.09762 0.483844
\(112\) −1.15508 −0.109145
\(113\) 14.6439 1.37759 0.688793 0.724958i \(-0.258141\pi\)
0.688793 + 0.724958i \(0.258141\pi\)
\(114\) −6.60856 −0.618948
\(115\) −5.06837 −0.472628
\(116\) 15.3464 1.42488
\(117\) 7.04883 0.651664
\(118\) −6.87450 −0.632849
\(119\) 4.28348 0.392666
\(120\) −5.58085 −0.509459
\(121\) 23.1807 2.10734
\(122\) 15.0808 1.36536
\(123\) 1.38224 0.124633
\(124\) −21.5364 −1.93402
\(125\) −11.4371 −1.02297
\(126\) 3.49655 0.311498
\(127\) 16.9043 1.50001 0.750007 0.661430i \(-0.230050\pi\)
0.750007 + 0.661430i \(0.230050\pi\)
\(128\) 15.1449 1.33864
\(129\) 15.2508 1.34276
\(130\) 21.8078 1.91267
\(131\) −18.4901 −1.61548 −0.807742 0.589537i \(-0.799310\pi\)
−0.807742 + 0.589537i \(0.799310\pi\)
\(132\) −20.7012 −1.80181
\(133\) 2.48108 0.215137
\(134\) 11.9882 1.03562
\(135\) −11.9171 −1.02566
\(136\) −9.16703 −0.786067
\(137\) −7.50135 −0.640883 −0.320442 0.947268i \(-0.603831\pi\)
−0.320442 + 0.947268i \(0.603831\pi\)
\(138\) 6.19092 0.527006
\(139\) 18.9659 1.60867 0.804334 0.594177i \(-0.202522\pi\)
0.804334 + 0.594177i \(0.202522\pi\)
\(140\) 6.45647 0.545671
\(141\) 2.24163 0.188779
\(142\) 7.41711 0.622430
\(143\) 26.2510 2.19522
\(144\) 1.81332 0.151110
\(145\) 11.3024 0.938612
\(146\) 5.43128 0.449496
\(147\) 1.19588 0.0986348
\(148\) 12.6210 1.03744
\(149\) 19.8707 1.62787 0.813937 0.580954i \(-0.197320\pi\)
0.813937 + 0.580954i \(0.197320\pi\)
\(150\) 0.652353 0.0532644
\(151\) 18.2791 1.48754 0.743768 0.668438i \(-0.233037\pi\)
0.743768 + 0.668438i \(0.233037\pi\)
\(152\) −5.30973 −0.430676
\(153\) −6.72448 −0.543642
\(154\) 13.0217 1.04932
\(155\) −15.8612 −1.27400
\(156\) −15.8986 −1.27291
\(157\) −6.41181 −0.511718 −0.255859 0.966714i \(-0.582358\pi\)
−0.255859 + 0.966714i \(0.582358\pi\)
\(158\) −16.0873 −1.27984
\(159\) 10.3146 0.817998
\(160\) 14.9435 1.18139
\(161\) −2.32428 −0.183179
\(162\) 4.06689 0.319525
\(163\) 17.9690 1.40744 0.703720 0.710477i \(-0.251521\pi\)
0.703720 + 0.710477i \(0.251521\pi\)
\(164\) 3.42225 0.267233
\(165\) −15.2461 −1.18691
\(166\) 21.1723 1.64329
\(167\) 3.51886 0.272297 0.136149 0.990688i \(-0.456527\pi\)
0.136149 + 0.990688i \(0.456527\pi\)
\(168\) −2.55930 −0.197454
\(169\) 7.16089 0.550838
\(170\) −20.8043 −1.59562
\(171\) −3.89495 −0.297855
\(172\) 37.7590 2.87909
\(173\) 18.1529 1.38014 0.690069 0.723744i \(-0.257580\pi\)
0.690069 + 0.723744i \(0.257580\pi\)
\(174\) −13.8057 −1.04661
\(175\) −0.244915 −0.0185139
\(176\) 6.75308 0.509032
\(177\) 3.69106 0.277437
\(178\) 12.3379 0.924761
\(179\) 20.1362 1.50505 0.752524 0.658564i \(-0.228836\pi\)
0.752524 + 0.658564i \(0.228836\pi\)
\(180\) −10.1358 −0.755477
\(181\) −23.3117 −1.73274 −0.866371 0.499401i \(-0.833553\pi\)
−0.866371 + 0.499401i \(0.833553\pi\)
\(182\) 10.0008 0.741305
\(183\) −8.09723 −0.598564
\(184\) 4.97418 0.366701
\(185\) 9.29518 0.683395
\(186\) 19.3742 1.42058
\(187\) −25.0430 −1.83133
\(188\) 5.54998 0.404774
\(189\) −5.46502 −0.397522
\(190\) −12.0503 −0.874219
\(191\) −19.5755 −1.41643 −0.708216 0.705996i \(-0.750500\pi\)
−0.708216 + 0.705996i \(0.750500\pi\)
\(192\) −15.4906 −1.11793
\(193\) 8.22184 0.591821 0.295910 0.955216i \(-0.404377\pi\)
0.295910 + 0.955216i \(0.404377\pi\)
\(194\) 0.601073 0.0431545
\(195\) −11.7091 −0.838504
\(196\) 2.96085 0.211489
\(197\) −18.0713 −1.28753 −0.643764 0.765224i \(-0.722628\pi\)
−0.643764 + 0.765224i \(0.722628\pi\)
\(198\) −20.4423 −1.45277
\(199\) 24.3622 1.72699 0.863495 0.504357i \(-0.168270\pi\)
0.863495 + 0.504357i \(0.168270\pi\)
\(200\) 0.524141 0.0370624
\(201\) −6.43673 −0.454012
\(202\) 28.9791 2.03896
\(203\) 5.18312 0.363784
\(204\) 15.1670 1.06191
\(205\) 2.52043 0.176035
\(206\) −34.3160 −2.39091
\(207\) 3.64881 0.253610
\(208\) 5.18640 0.359612
\(209\) −14.5054 −1.00336
\(210\) −5.80826 −0.400808
\(211\) −8.10524 −0.557987 −0.278994 0.960293i \(-0.590001\pi\)
−0.278994 + 0.960293i \(0.590001\pi\)
\(212\) 25.5375 1.75392
\(213\) −3.98240 −0.272870
\(214\) −41.4276 −2.83193
\(215\) 27.8089 1.89655
\(216\) 11.6956 0.795788
\(217\) −7.27372 −0.493772
\(218\) −27.9243 −1.89127
\(219\) −2.91617 −0.197057
\(220\) −37.7473 −2.54492
\(221\) −19.2332 −1.29376
\(222\) −11.3539 −0.762024
\(223\) 17.8084 1.19254 0.596269 0.802785i \(-0.296649\pi\)
0.596269 + 0.802785i \(0.296649\pi\)
\(224\) 6.85288 0.457877
\(225\) 0.384484 0.0256323
\(226\) −32.6164 −2.16961
\(227\) 13.9969 0.929009 0.464504 0.885571i \(-0.346232\pi\)
0.464504 + 0.885571i \(0.346232\pi\)
\(228\) 8.78506 0.581805
\(229\) −9.21215 −0.608756 −0.304378 0.952551i \(-0.598449\pi\)
−0.304378 + 0.952551i \(0.598449\pi\)
\(230\) 11.2888 0.744358
\(231\) −6.99164 −0.460016
\(232\) −11.0923 −0.728248
\(233\) 11.4843 0.752360 0.376180 0.926547i \(-0.377237\pi\)
0.376180 + 0.926547i \(0.377237\pi\)
\(234\) −15.6998 −1.02633
\(235\) 4.08747 0.266637
\(236\) 9.13859 0.594871
\(237\) 8.63764 0.561075
\(238\) −9.54057 −0.618423
\(239\) −6.88178 −0.445145 −0.222573 0.974916i \(-0.571445\pi\)
−0.222573 + 0.974916i \(0.571445\pi\)
\(240\) −3.01217 −0.194435
\(241\) −2.65568 −0.171067 −0.0855337 0.996335i \(-0.527260\pi\)
−0.0855337 + 0.996335i \(0.527260\pi\)
\(242\) −51.6303 −3.31892
\(243\) 14.2115 0.911666
\(244\) −20.0477 −1.28342
\(245\) 2.18062 0.139314
\(246\) −3.07867 −0.196289
\(247\) −11.1403 −0.708837
\(248\) 15.5664 0.988468
\(249\) −11.3679 −0.720410
\(250\) 25.4739 1.61111
\(251\) −9.92008 −0.626150 −0.313075 0.949728i \(-0.601359\pi\)
−0.313075 + 0.949728i \(0.601359\pi\)
\(252\) −4.64813 −0.292805
\(253\) 13.5887 0.854317
\(254\) −37.6509 −2.36242
\(255\) 11.1703 0.699510
\(256\) −7.82578 −0.489111
\(257\) −7.54536 −0.470667 −0.235333 0.971915i \(-0.575618\pi\)
−0.235333 + 0.971915i \(0.575618\pi\)
\(258\) −33.9680 −2.11476
\(259\) 4.26264 0.264867
\(260\) −28.9901 −1.79789
\(261\) −8.13679 −0.503655
\(262\) 41.1828 2.54428
\(263\) −8.64286 −0.532941 −0.266471 0.963843i \(-0.585858\pi\)
−0.266471 + 0.963843i \(0.585858\pi\)
\(264\) 14.9627 0.920893
\(265\) 18.8079 1.15536
\(266\) −5.52609 −0.338826
\(267\) −6.62446 −0.405410
\(268\) −15.9365 −0.973476
\(269\) 20.7250 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(270\) 26.5429 1.61535
\(271\) −9.67677 −0.587822 −0.293911 0.955833i \(-0.594957\pi\)
−0.293911 + 0.955833i \(0.594957\pi\)
\(272\) −4.94775 −0.300001
\(273\) −5.36962 −0.324984
\(274\) 16.7077 1.00935
\(275\) 1.43188 0.0863456
\(276\) −8.22988 −0.495381
\(277\) 14.8937 0.894877 0.447438 0.894315i \(-0.352336\pi\)
0.447438 + 0.894315i \(0.352336\pi\)
\(278\) −42.2427 −2.53355
\(279\) 11.4187 0.683622
\(280\) −4.66672 −0.278890
\(281\) −31.8158 −1.89797 −0.948987 0.315316i \(-0.897889\pi\)
−0.948987 + 0.315316i \(0.897889\pi\)
\(282\) −4.99277 −0.297315
\(283\) −5.45037 −0.323991 −0.161995 0.986792i \(-0.551793\pi\)
−0.161995 + 0.986792i \(0.551793\pi\)
\(284\) −9.85990 −0.585078
\(285\) 6.47005 0.383253
\(286\) −58.4687 −3.45732
\(287\) 1.15584 0.0682268
\(288\) −10.7581 −0.633927
\(289\) 1.34818 0.0793046
\(290\) −25.1738 −1.47825
\(291\) −0.322729 −0.0189187
\(292\) −7.22005 −0.422522
\(293\) 13.0449 0.762092 0.381046 0.924556i \(-0.375564\pi\)
0.381046 + 0.924556i \(0.375564\pi\)
\(294\) −2.66358 −0.155343
\(295\) 6.73042 0.391860
\(296\) −9.12244 −0.530231
\(297\) 31.9508 1.85398
\(298\) −44.2580 −2.56380
\(299\) 10.4362 0.603543
\(300\) −0.867203 −0.0500680
\(301\) 12.7528 0.735056
\(302\) −40.7130 −2.34277
\(303\) −15.5595 −0.893869
\(304\) −2.86584 −0.164367
\(305\) −14.7648 −0.845429
\(306\) 14.9774 0.856201
\(307\) −0.164746 −0.00940257 −0.00470128 0.999989i \(-0.501496\pi\)
−0.00470128 + 0.999989i \(0.501496\pi\)
\(308\) −17.3104 −0.986350
\(309\) 18.4250 1.04816
\(310\) 35.3275 2.00647
\(311\) −13.4348 −0.761817 −0.380908 0.924613i \(-0.624389\pi\)
−0.380908 + 0.924613i \(0.624389\pi\)
\(312\) 11.4915 0.650577
\(313\) 1.65894 0.0937686 0.0468843 0.998900i \(-0.485071\pi\)
0.0468843 + 0.998900i \(0.485071\pi\)
\(314\) 14.2810 0.805923
\(315\) −3.42327 −0.192879
\(316\) 21.3857 1.20304
\(317\) −15.1120 −0.848774 −0.424387 0.905481i \(-0.639510\pi\)
−0.424387 + 0.905481i \(0.639510\pi\)
\(318\) −22.9736 −1.28829
\(319\) −30.3027 −1.69663
\(320\) −28.2460 −1.57900
\(321\) 22.2434 1.24150
\(322\) 5.17687 0.288495
\(323\) 10.6276 0.591337
\(324\) −5.40631 −0.300350
\(325\) 1.09969 0.0609999
\(326\) −40.0223 −2.21663
\(327\) 14.9931 0.829122
\(328\) −2.47359 −0.136581
\(329\) 1.87446 0.103342
\(330\) 33.9575 1.86930
\(331\) 33.5435 1.84371 0.921857 0.387529i \(-0.126671\pi\)
0.921857 + 0.387529i \(0.126671\pi\)
\(332\) −28.1454 −1.54468
\(333\) −6.69176 −0.366706
\(334\) −7.83754 −0.428851
\(335\) −11.7370 −0.641259
\(336\) −1.38134 −0.0753581
\(337\) 18.1782 0.990232 0.495116 0.868827i \(-0.335126\pi\)
0.495116 + 0.868827i \(0.335126\pi\)
\(338\) −15.9494 −0.867534
\(339\) 17.5124 0.951145
\(340\) 27.6561 1.49986
\(341\) 42.5252 2.30287
\(342\) 8.67521 0.469102
\(343\) 1.00000 0.0539949
\(344\) −27.2921 −1.47149
\(345\) −6.06117 −0.326323
\(346\) −40.4318 −2.17363
\(347\) −25.4729 −1.36746 −0.683730 0.729735i \(-0.739643\pi\)
−0.683730 + 0.729735i \(0.739643\pi\)
\(348\) 18.3525 0.983798
\(349\) −32.4353 −1.73622 −0.868111 0.496371i \(-0.834666\pi\)
−0.868111 + 0.496371i \(0.834666\pi\)
\(350\) 0.545499 0.0291581
\(351\) 24.5384 1.30976
\(352\) −40.0649 −2.13546
\(353\) 6.94211 0.369491 0.184746 0.982786i \(-0.440854\pi\)
0.184746 + 0.982786i \(0.440854\pi\)
\(354\) −8.22109 −0.436946
\(355\) −7.26166 −0.385409
\(356\) −16.4013 −0.869266
\(357\) 5.12254 0.271113
\(358\) −44.8492 −2.37036
\(359\) 16.4892 0.870269 0.435134 0.900366i \(-0.356701\pi\)
0.435134 + 0.900366i \(0.356701\pi\)
\(360\) 7.32611 0.386120
\(361\) −12.8443 −0.676014
\(362\) 51.9219 2.72896
\(363\) 27.7214 1.45500
\(364\) −13.2945 −0.696819
\(365\) −5.31745 −0.278328
\(366\) 18.0349 0.942701
\(367\) −6.28337 −0.327989 −0.163995 0.986461i \(-0.552438\pi\)
−0.163995 + 0.986461i \(0.552438\pi\)
\(368\) 2.68473 0.139951
\(369\) −1.81451 −0.0944594
\(370\) −20.7031 −1.07630
\(371\) 8.62506 0.447791
\(372\) −25.7550 −1.33533
\(373\) −4.66801 −0.241700 −0.120850 0.992671i \(-0.538562\pi\)
−0.120850 + 0.992671i \(0.538562\pi\)
\(374\) 55.7782 2.88422
\(375\) −13.6775 −0.706302
\(376\) −4.01151 −0.206878
\(377\) −23.2727 −1.19860
\(378\) 12.1722 0.626072
\(379\) 15.3002 0.785916 0.392958 0.919556i \(-0.371452\pi\)
0.392958 + 0.919556i \(0.371452\pi\)
\(380\) 16.0190 0.821757
\(381\) 20.2155 1.03567
\(382\) 43.6004 2.23079
\(383\) 25.2108 1.28821 0.644106 0.764936i \(-0.277230\pi\)
0.644106 + 0.764936i \(0.277230\pi\)
\(384\) 18.1116 0.924252
\(385\) −12.7488 −0.649739
\(386\) −18.3125 −0.932080
\(387\) −20.0201 −1.01768
\(388\) −0.799035 −0.0405648
\(389\) 18.5290 0.939455 0.469728 0.882811i \(-0.344352\pi\)
0.469728 + 0.882811i \(0.344352\pi\)
\(390\) 26.0796 1.32059
\(391\) −9.95601 −0.503497
\(392\) −2.14009 −0.108091
\(393\) −22.1119 −1.11540
\(394\) 40.2502 2.02778
\(395\) 15.7502 0.792478
\(396\) 27.1749 1.36559
\(397\) 6.17885 0.310108 0.155054 0.987906i \(-0.450445\pi\)
0.155054 + 0.987906i \(0.450445\pi\)
\(398\) −54.2618 −2.71990
\(399\) 2.96708 0.148540
\(400\) 0.282896 0.0141448
\(401\) 25.8361 1.29019 0.645097 0.764101i \(-0.276817\pi\)
0.645097 + 0.764101i \(0.276817\pi\)
\(402\) 14.3365 0.715040
\(403\) 32.6596 1.62689
\(404\) −38.5232 −1.91660
\(405\) −3.98166 −0.197850
\(406\) −11.5443 −0.572936
\(407\) −24.9212 −1.23530
\(408\) −10.9627 −0.542734
\(409\) −28.8343 −1.42576 −0.712882 0.701284i \(-0.752610\pi\)
−0.712882 + 0.701284i \(0.752610\pi\)
\(410\) −5.61375 −0.277243
\(411\) −8.97073 −0.442493
\(412\) 45.6179 2.24743
\(413\) 3.08648 0.151876
\(414\) −8.12698 −0.399419
\(415\) −20.7286 −1.01753
\(416\) −30.7700 −1.50863
\(417\) 22.6810 1.11069
\(418\) 32.3079 1.58023
\(419\) −3.11865 −0.152356 −0.0761780 0.997094i \(-0.524272\pi\)
−0.0761780 + 0.997094i \(0.524272\pi\)
\(420\) 7.72118 0.376755
\(421\) 28.7995 1.40360 0.701800 0.712374i \(-0.252380\pi\)
0.701800 + 0.712374i \(0.252380\pi\)
\(422\) 18.0528 0.878795
\(423\) −2.94264 −0.143076
\(424\) −18.4584 −0.896420
\(425\) −1.04909 −0.0508883
\(426\) 8.86999 0.429752
\(427\) −6.77092 −0.327668
\(428\) 55.0716 2.66199
\(429\) 31.3931 1.51567
\(430\) −61.9385 −2.98694
\(431\) −31.4626 −1.51550 −0.757750 0.652545i \(-0.773701\pi\)
−0.757750 + 0.652545i \(0.773701\pi\)
\(432\) 6.31253 0.303712
\(433\) 14.3822 0.691164 0.345582 0.938389i \(-0.387681\pi\)
0.345582 + 0.938389i \(0.387681\pi\)
\(434\) 16.2007 0.777659
\(435\) 13.5163 0.648058
\(436\) 37.1210 1.77777
\(437\) −5.76672 −0.275860
\(438\) 6.49517 0.310351
\(439\) 30.2141 1.44204 0.721020 0.692914i \(-0.243673\pi\)
0.721020 + 0.692914i \(0.243673\pi\)
\(440\) 27.2836 1.30070
\(441\) −1.56986 −0.0747554
\(442\) 42.8380 2.03760
\(443\) 25.5218 1.21258 0.606290 0.795244i \(-0.292657\pi\)
0.606290 + 0.795244i \(0.292657\pi\)
\(444\) 15.0933 0.716295
\(445\) −12.0793 −0.572612
\(446\) −39.6645 −1.87817
\(447\) 23.7631 1.12395
\(448\) −12.9532 −0.611983
\(449\) −23.6624 −1.11670 −0.558348 0.829607i \(-0.688565\pi\)
−0.558348 + 0.829607i \(0.688565\pi\)
\(450\) −0.856359 −0.0403692
\(451\) −6.75751 −0.318199
\(452\) 43.3585 2.03941
\(453\) 21.8597 1.02706
\(454\) −31.1753 −1.46313
\(455\) −9.79116 −0.459016
\(456\) −6.34981 −0.297357
\(457\) −7.73181 −0.361679 −0.180839 0.983513i \(-0.557881\pi\)
−0.180839 + 0.983513i \(0.557881\pi\)
\(458\) 20.5182 0.958752
\(459\) −23.4093 −1.09265
\(460\) −15.0067 −0.699689
\(461\) −16.3231 −0.760240 −0.380120 0.924937i \(-0.624117\pi\)
−0.380120 + 0.924937i \(0.624117\pi\)
\(462\) 15.5725 0.724496
\(463\) −1.92773 −0.0895894 −0.0447947 0.998996i \(-0.514263\pi\)
−0.0447947 + 0.998996i \(0.514263\pi\)
\(464\) −5.98690 −0.277935
\(465\) −18.9681 −0.879625
\(466\) −25.5789 −1.18492
\(467\) 18.9733 0.877978 0.438989 0.898492i \(-0.355337\pi\)
0.438989 + 0.898492i \(0.355337\pi\)
\(468\) 20.8705 0.964739
\(469\) −5.38241 −0.248536
\(470\) −9.10400 −0.419936
\(471\) −7.66777 −0.353312
\(472\) −6.60534 −0.304035
\(473\) −74.5580 −3.42818
\(474\) −19.2386 −0.883657
\(475\) −0.607654 −0.0278811
\(476\) 12.6827 0.581312
\(477\) −13.5402 −0.619962
\(478\) 15.3278 0.701075
\(479\) −28.4712 −1.30088 −0.650440 0.759558i \(-0.725416\pi\)
−0.650440 + 0.759558i \(0.725416\pi\)
\(480\) 17.8707 0.815681
\(481\) −19.1396 −0.872692
\(482\) 5.91499 0.269420
\(483\) −2.77957 −0.126475
\(484\) 68.6345 3.11975
\(485\) −0.588476 −0.0267213
\(486\) −31.6531 −1.43582
\(487\) 1.95913 0.0887767 0.0443883 0.999014i \(-0.485866\pi\)
0.0443883 + 0.999014i \(0.485866\pi\)
\(488\) 14.4904 0.655949
\(489\) 21.4888 0.971758
\(490\) −4.85688 −0.219411
\(491\) 25.4213 1.14725 0.573624 0.819119i \(-0.305537\pi\)
0.573624 + 0.819119i \(0.305537\pi\)
\(492\) 4.09261 0.184509
\(493\) 22.2018 0.999917
\(494\) 24.8126 1.11637
\(495\) 20.0139 0.899558
\(496\) 8.40171 0.377248
\(497\) −3.33010 −0.149375
\(498\) 25.3196 1.13460
\(499\) 16.2976 0.729579 0.364790 0.931090i \(-0.381141\pi\)
0.364790 + 0.931090i \(0.381141\pi\)
\(500\) −33.8636 −1.51443
\(501\) 4.20814 0.188006
\(502\) 22.0949 0.986146
\(503\) 17.2582 0.769506 0.384753 0.923019i \(-0.374287\pi\)
0.384753 + 0.923019i \(0.374287\pi\)
\(504\) 3.35965 0.149651
\(505\) −28.3717 −1.26253
\(506\) −30.2662 −1.34549
\(507\) 8.56358 0.380322
\(508\) 50.0510 2.22065
\(509\) −38.2480 −1.69531 −0.847657 0.530544i \(-0.821988\pi\)
−0.847657 + 0.530544i \(0.821988\pi\)
\(510\) −24.8795 −1.10168
\(511\) −2.43851 −0.107873
\(512\) −12.8596 −0.568317
\(513\) −13.5591 −0.598651
\(514\) 16.8058 0.741270
\(515\) 33.5968 1.48045
\(516\) 45.1553 1.98785
\(517\) −10.9589 −0.481971
\(518\) −9.49416 −0.417149
\(519\) 21.7087 0.952906
\(520\) 20.9540 0.918892
\(521\) 36.5144 1.59973 0.799863 0.600183i \(-0.204905\pi\)
0.799863 + 0.600183i \(0.204905\pi\)
\(522\) 18.1230 0.793224
\(523\) −16.1836 −0.707659 −0.353830 0.935310i \(-0.615121\pi\)
−0.353830 + 0.935310i \(0.615121\pi\)
\(524\) −54.7462 −2.39160
\(525\) −0.292890 −0.0127828
\(526\) 19.2502 0.839349
\(527\) −31.1568 −1.35721
\(528\) 8.07589 0.351458
\(529\) −17.5977 −0.765118
\(530\) −41.8909 −1.81962
\(531\) −4.84535 −0.210270
\(532\) 7.34609 0.318493
\(533\) −5.18980 −0.224795
\(534\) 14.7546 0.638495
\(535\) 40.5594 1.75353
\(536\) 11.5188 0.497538
\(537\) 24.0805 1.03915
\(538\) −46.1606 −1.99013
\(539\) −5.84643 −0.251823
\(540\) −35.2848 −1.51841
\(541\) 25.0018 1.07491 0.537455 0.843292i \(-0.319386\pi\)
0.537455 + 0.843292i \(0.319386\pi\)
\(542\) 21.5530 0.925782
\(543\) −27.8780 −1.19636
\(544\) 29.3542 1.25855
\(545\) 27.3390 1.17108
\(546\) 11.9597 0.511829
\(547\) 23.1374 0.989283 0.494642 0.869097i \(-0.335299\pi\)
0.494642 + 0.869097i \(0.335299\pi\)
\(548\) −22.2103 −0.948779
\(549\) 10.6294 0.453653
\(550\) −3.18922 −0.135989
\(551\) 12.8597 0.547842
\(552\) 5.94853 0.253186
\(553\) 7.22282 0.307145
\(554\) −33.1727 −1.40937
\(555\) 11.1159 0.471845
\(556\) 56.1552 2.38151
\(557\) 36.9668 1.56633 0.783167 0.621812i \(-0.213603\pi\)
0.783167 + 0.621812i \(0.213603\pi\)
\(558\) −25.4329 −1.07666
\(559\) −57.2610 −2.42188
\(560\) −2.51878 −0.106438
\(561\) −29.9485 −1.26443
\(562\) 70.8633 2.98919
\(563\) −46.5101 −1.96017 −0.980084 0.198581i \(-0.936367\pi\)
−0.980084 + 0.198581i \(0.936367\pi\)
\(564\) 6.63713 0.279473
\(565\) 31.9328 1.34342
\(566\) 12.1396 0.510265
\(567\) −1.82593 −0.0766820
\(568\) 7.12671 0.299030
\(569\) 26.1957 1.09818 0.549091 0.835762i \(-0.314974\pi\)
0.549091 + 0.835762i \(0.314974\pi\)
\(570\) −14.4107 −0.603599
\(571\) −15.5573 −0.651054 −0.325527 0.945533i \(-0.605542\pi\)
−0.325527 + 0.945533i \(0.605542\pi\)
\(572\) 77.7251 3.24985
\(573\) −23.4100 −0.977966
\(574\) −2.57439 −0.107453
\(575\) 0.569252 0.0237395
\(576\) 20.3348 0.847285
\(577\) −41.1177 −1.71175 −0.855876 0.517181i \(-0.826982\pi\)
−0.855876 + 0.517181i \(0.826982\pi\)
\(578\) −3.00279 −0.124900
\(579\) 9.83236 0.408619
\(580\) 33.4646 1.38954
\(581\) −9.50584 −0.394369
\(582\) 0.718813 0.0297958
\(583\) −50.4258 −2.08842
\(584\) 5.21863 0.215948
\(585\) 15.3708 0.635504
\(586\) −29.0549 −1.20025
\(587\) −4.59120 −0.189499 −0.0947496 0.995501i \(-0.530205\pi\)
−0.0947496 + 0.995501i \(0.530205\pi\)
\(588\) 3.54083 0.146021
\(589\) −18.0466 −0.743599
\(590\) −14.9906 −0.617155
\(591\) −21.6112 −0.888965
\(592\) −4.92368 −0.202362
\(593\) 9.79557 0.402256 0.201128 0.979565i \(-0.435539\pi\)
0.201128 + 0.979565i \(0.435539\pi\)
\(594\) −71.1640 −2.91989
\(595\) 9.34062 0.382928
\(596\) 58.8342 2.40994
\(597\) 29.1343 1.19239
\(598\) −23.2446 −0.950541
\(599\) −10.5584 −0.431404 −0.215702 0.976459i \(-0.569204\pi\)
−0.215702 + 0.976459i \(0.569204\pi\)
\(600\) 0.626811 0.0255895
\(601\) −7.65674 −0.312325 −0.156162 0.987731i \(-0.549912\pi\)
−0.156162 + 0.987731i \(0.549912\pi\)
\(602\) −28.4042 −1.15767
\(603\) 8.44965 0.344096
\(604\) 54.1217 2.20218
\(605\) 50.5482 2.05508
\(606\) 34.6556 1.40779
\(607\) 2.47254 0.100357 0.0501786 0.998740i \(-0.484021\pi\)
0.0501786 + 0.998740i \(0.484021\pi\)
\(608\) 17.0025 0.689543
\(609\) 6.19840 0.251172
\(610\) 32.8855 1.33150
\(611\) −8.41647 −0.340494
\(612\) −19.9102 −0.804820
\(613\) 16.0514 0.648310 0.324155 0.946004i \(-0.394920\pi\)
0.324155 + 0.946004i \(0.394920\pi\)
\(614\) 0.366939 0.0148084
\(615\) 3.01414 0.121542
\(616\) 12.5119 0.504118
\(617\) 33.2170 1.33727 0.668633 0.743592i \(-0.266880\pi\)
0.668633 + 0.743592i \(0.266880\pi\)
\(618\) −41.0379 −1.65079
\(619\) 44.4863 1.78805 0.894027 0.448012i \(-0.147868\pi\)
0.894027 + 0.448012i \(0.147868\pi\)
\(620\) −46.9625 −1.88606
\(621\) 12.7023 0.509724
\(622\) 29.9232 1.19981
\(623\) −5.53939 −0.221931
\(624\) 6.20233 0.248292
\(625\) −23.7154 −0.948618
\(626\) −3.69494 −0.147680
\(627\) −17.3468 −0.692764
\(628\) −18.9844 −0.757559
\(629\) 18.2589 0.728031
\(630\) 7.62464 0.303773
\(631\) 47.6570 1.89719 0.948597 0.316485i \(-0.102503\pi\)
0.948597 + 0.316485i \(0.102503\pi\)
\(632\) −15.4575 −0.614866
\(633\) −9.69291 −0.385259
\(634\) 33.6589 1.33676
\(635\) 36.8618 1.46281
\(636\) 30.5398 1.21098
\(637\) −4.49009 −0.177904
\(638\) 67.4931 2.67208
\(639\) 5.22780 0.206808
\(640\) 33.0253 1.30544
\(641\) 22.0375 0.870429 0.435215 0.900327i \(-0.356673\pi\)
0.435215 + 0.900327i \(0.356673\pi\)
\(642\) −49.5426 −1.95529
\(643\) −23.1274 −0.912055 −0.456028 0.889966i \(-0.650728\pi\)
−0.456028 + 0.889966i \(0.650728\pi\)
\(644\) −6.88185 −0.271183
\(645\) 33.2561 1.30946
\(646\) −23.6709 −0.931319
\(647\) −29.6723 −1.16654 −0.583270 0.812279i \(-0.698227\pi\)
−0.583270 + 0.812279i \(0.698227\pi\)
\(648\) 3.90766 0.153508
\(649\) −18.0449 −0.708322
\(650\) −2.44934 −0.0960709
\(651\) −8.69851 −0.340922
\(652\) 53.2034 2.08361
\(653\) 13.4979 0.528212 0.264106 0.964494i \(-0.414923\pi\)
0.264106 + 0.964494i \(0.414923\pi\)
\(654\) −33.3942 −1.30581
\(655\) −40.3197 −1.57542
\(656\) −1.33508 −0.0521261
\(657\) 3.82813 0.149349
\(658\) −4.17497 −0.162757
\(659\) −18.4992 −0.720628 −0.360314 0.932831i \(-0.617330\pi\)
−0.360314 + 0.932831i \(0.617330\pi\)
\(660\) −45.1413 −1.75712
\(661\) 28.8748 1.12310 0.561550 0.827443i \(-0.310205\pi\)
0.561550 + 0.827443i \(0.310205\pi\)
\(662\) −74.7112 −2.90373
\(663\) −23.0006 −0.893271
\(664\) 20.3434 0.789476
\(665\) 5.41027 0.209801
\(666\) 14.9045 0.577539
\(667\) −12.0470 −0.466463
\(668\) 10.4188 0.403116
\(669\) 21.2967 0.823379
\(670\) 26.1417 1.00994
\(671\) 39.5857 1.52819
\(672\) 8.19524 0.316138
\(673\) −20.5832 −0.793424 −0.396712 0.917943i \(-0.629849\pi\)
−0.396712 + 0.917943i \(0.629849\pi\)
\(674\) −40.4883 −1.55955
\(675\) 1.33847 0.0515176
\(676\) 21.2023 0.815473
\(677\) −33.0179 −1.26898 −0.634490 0.772931i \(-0.718790\pi\)
−0.634490 + 0.772931i \(0.718790\pi\)
\(678\) −39.0054 −1.49799
\(679\) −0.269867 −0.0103565
\(680\) −19.9898 −0.766573
\(681\) 16.7387 0.641428
\(682\) −94.7163 −3.62687
\(683\) −37.2165 −1.42405 −0.712025 0.702154i \(-0.752222\pi\)
−0.712025 + 0.702154i \(0.752222\pi\)
\(684\) −11.5324 −0.440951
\(685\) −16.3576 −0.624990
\(686\) −2.22730 −0.0850386
\(687\) −11.0166 −0.420311
\(688\) −14.7304 −0.561592
\(689\) −38.7273 −1.47539
\(690\) 13.5000 0.513937
\(691\) −38.8762 −1.47892 −0.739460 0.673200i \(-0.764919\pi\)
−0.739460 + 0.673200i \(0.764919\pi\)
\(692\) 53.7479 2.04319
\(693\) 9.17809 0.348647
\(694\) 56.7358 2.15366
\(695\) 41.3574 1.56878
\(696\) −13.2651 −0.502814
\(697\) 4.95100 0.187532
\(698\) 72.2430 2.73444
\(699\) 13.7339 0.519462
\(700\) −0.725157 −0.0274084
\(701\) −44.3377 −1.67461 −0.837307 0.546734i \(-0.815871\pi\)
−0.837307 + 0.546734i \(0.815871\pi\)
\(702\) −54.6543 −2.06280
\(703\) 10.5759 0.398879
\(704\) 75.7302 2.85419
\(705\) 4.88813 0.184098
\(706\) −15.4621 −0.581925
\(707\) −13.0109 −0.489324
\(708\) 10.9287 0.410725
\(709\) 25.8576 0.971104 0.485552 0.874208i \(-0.338619\pi\)
0.485552 + 0.874208i \(0.338619\pi\)
\(710\) 16.1739 0.606994
\(711\) −11.3388 −0.425240
\(712\) 11.8548 0.444277
\(713\) 16.9062 0.633141
\(714\) −11.4094 −0.426986
\(715\) 57.2433 2.14078
\(716\) 59.6201 2.22811
\(717\) −8.22980 −0.307347
\(718\) −36.7264 −1.37062
\(719\) 26.2662 0.979564 0.489782 0.871845i \(-0.337076\pi\)
0.489782 + 0.871845i \(0.337076\pi\)
\(720\) 3.95414 0.147362
\(721\) 15.4070 0.573788
\(722\) 28.6080 1.06468
\(723\) −3.17588 −0.118112
\(724\) −69.0222 −2.56519
\(725\) −1.26942 −0.0471453
\(726\) −61.7437 −2.29152
\(727\) 33.0514 1.22581 0.612905 0.790157i \(-0.290001\pi\)
0.612905 + 0.790157i \(0.290001\pi\)
\(728\) 9.60920 0.356141
\(729\) 22.4730 0.832335
\(730\) 11.8435 0.438349
\(731\) 54.6261 2.02042
\(732\) −23.9747 −0.886129
\(733\) 37.5614 1.38736 0.693681 0.720282i \(-0.255988\pi\)
0.693681 + 0.720282i \(0.255988\pi\)
\(734\) 13.9949 0.516562
\(735\) 2.60776 0.0961887
\(736\) −15.9280 −0.587115
\(737\) 31.4678 1.15913
\(738\) 4.04144 0.148767
\(739\) 8.16143 0.300223 0.150112 0.988669i \(-0.452037\pi\)
0.150112 + 0.988669i \(0.452037\pi\)
\(740\) 27.5216 1.01171
\(741\) −13.3224 −0.489412
\(742\) −19.2106 −0.705242
\(743\) −20.0265 −0.734701 −0.367350 0.930083i \(-0.619735\pi\)
−0.367350 + 0.930083i \(0.619735\pi\)
\(744\) 18.6156 0.682481
\(745\) 43.3304 1.58750
\(746\) 10.3970 0.380662
\(747\) 14.9229 0.546000
\(748\) −74.1486 −2.71114
\(749\) 18.6000 0.679628
\(750\) 30.4638 1.11238
\(751\) −13.1738 −0.480719 −0.240360 0.970684i \(-0.577265\pi\)
−0.240360 + 0.970684i \(0.577265\pi\)
\(752\) −2.16514 −0.0789546
\(753\) −11.8632 −0.432321
\(754\) 51.8351 1.88772
\(755\) 39.8598 1.45065
\(756\) −16.1811 −0.588501
\(757\) 40.4649 1.47072 0.735361 0.677676i \(-0.237013\pi\)
0.735361 + 0.677676i \(0.237013\pi\)
\(758\) −34.0780 −1.23777
\(759\) 16.2505 0.589857
\(760\) −11.5785 −0.419996
\(761\) 27.5598 0.999044 0.499522 0.866301i \(-0.333509\pi\)
0.499522 + 0.866301i \(0.333509\pi\)
\(762\) −45.0260 −1.63112
\(763\) 12.5373 0.453881
\(764\) −57.9600 −2.09692
\(765\) −14.6635 −0.530160
\(766\) −56.1519 −2.02885
\(767\) −13.8586 −0.500403
\(768\) −9.35871 −0.337703
\(769\) 15.7974 0.569668 0.284834 0.958577i \(-0.408062\pi\)
0.284834 + 0.958577i \(0.408062\pi\)
\(770\) 28.3954 1.02330
\(771\) −9.02337 −0.324969
\(772\) 24.3436 0.876146
\(773\) −39.3312 −1.41465 −0.707323 0.706891i \(-0.750097\pi\)
−0.707323 + 0.706891i \(0.750097\pi\)
\(774\) 44.5907 1.60278
\(775\) 1.78144 0.0639914
\(776\) 0.577540 0.0207325
\(777\) 5.09762 0.182876
\(778\) −41.2695 −1.47958
\(779\) 2.86772 0.102747
\(780\) −34.6688 −1.24134
\(781\) 19.4692 0.696661
\(782\) 22.1750 0.792976
\(783\) −28.3259 −1.01228
\(784\) −1.15508 −0.0412528
\(785\) −13.9817 −0.499028
\(786\) 49.2498 1.75668
\(787\) −45.7031 −1.62914 −0.814569 0.580066i \(-0.803027\pi\)
−0.814569 + 0.580066i \(0.803027\pi\)
\(788\) −53.5064 −1.90609
\(789\) −10.3358 −0.367966
\(790\) −35.0803 −1.24810
\(791\) 14.6439 0.520679
\(792\) −19.6420 −0.697947
\(793\) 30.4020 1.07961
\(794\) −13.7621 −0.488400
\(795\) 22.4921 0.797712
\(796\) 72.1327 2.55668
\(797\) 29.3448 1.03945 0.519724 0.854334i \(-0.326035\pi\)
0.519724 + 0.854334i \(0.326035\pi\)
\(798\) −6.60856 −0.233940
\(799\) 8.02919 0.284052
\(800\) −1.67838 −0.0593396
\(801\) 8.69608 0.307261
\(802\) −57.5447 −2.03197
\(803\) 14.2566 0.503103
\(804\) −19.0582 −0.672130
\(805\) −5.06837 −0.178636
\(806\) −72.7426 −2.56225
\(807\) 24.7846 0.872460
\(808\) 27.8445 0.979565
\(809\) −36.2137 −1.27321 −0.636603 0.771192i \(-0.719661\pi\)
−0.636603 + 0.771192i \(0.719661\pi\)
\(810\) 8.86833 0.311601
\(811\) −0.892016 −0.0313229 −0.0156615 0.999877i \(-0.504985\pi\)
−0.0156615 + 0.999877i \(0.504985\pi\)
\(812\) 15.3464 0.538554
\(813\) −11.5723 −0.405857
\(814\) 55.5069 1.94552
\(815\) 39.1835 1.37254
\(816\) −5.91693 −0.207134
\(817\) 31.6406 1.10696
\(818\) 64.2225 2.24549
\(819\) 7.04883 0.246306
\(820\) 7.46262 0.260606
\(821\) −53.3399 −1.86158 −0.930788 0.365559i \(-0.880878\pi\)
−0.930788 + 0.365559i \(0.880878\pi\)
\(822\) 19.9805 0.696899
\(823\) 22.8237 0.795583 0.397792 0.917476i \(-0.369777\pi\)
0.397792 + 0.917476i \(0.369777\pi\)
\(824\) −32.9725 −1.14865
\(825\) 1.71236 0.0596167
\(826\) −6.87450 −0.239194
\(827\) 29.4656 1.02462 0.512310 0.858800i \(-0.328790\pi\)
0.512310 + 0.858800i \(0.328790\pi\)
\(828\) 10.8036 0.375450
\(829\) −4.99904 −0.173624 −0.0868118 0.996225i \(-0.527668\pi\)
−0.0868118 + 0.996225i \(0.527668\pi\)
\(830\) 46.1687 1.60254
\(831\) 17.8111 0.617862
\(832\) 58.1612 2.01638
\(833\) 4.28348 0.148414
\(834\) −50.5173 −1.74927
\(835\) 7.67328 0.265545
\(836\) −42.9484 −1.48540
\(837\) 39.7510 1.37400
\(838\) 6.94615 0.239951
\(839\) −19.4660 −0.672042 −0.336021 0.941854i \(-0.609081\pi\)
−0.336021 + 0.941854i \(0.609081\pi\)
\(840\) −5.58085 −0.192557
\(841\) −2.13530 −0.0736309
\(842\) −64.1449 −2.21058
\(843\) −38.0480 −1.31044
\(844\) −23.9984 −0.826058
\(845\) 15.6151 0.537177
\(846\) 6.55414 0.225336
\(847\) 23.1807 0.796498
\(848\) −9.96262 −0.342118
\(849\) −6.51800 −0.223697
\(850\) 2.33663 0.0801458
\(851\) −9.90758 −0.339627
\(852\) −11.7913 −0.403963
\(853\) −3.92711 −0.134462 −0.0672309 0.997737i \(-0.521416\pi\)
−0.0672309 + 0.997737i \(0.521416\pi\)
\(854\) 15.0808 0.516056
\(855\) −8.49340 −0.290468
\(856\) −39.8056 −1.36053
\(857\) −35.8128 −1.22334 −0.611671 0.791112i \(-0.709503\pi\)
−0.611671 + 0.791112i \(0.709503\pi\)
\(858\) −69.9217 −2.38709
\(859\) 41.0091 1.39921 0.699606 0.714529i \(-0.253359\pi\)
0.699606 + 0.714529i \(0.253359\pi\)
\(860\) 82.3378 2.80769
\(861\) 1.38224 0.0471067
\(862\) 70.0765 2.38682
\(863\) −1.00000 −0.0340404
\(864\) −37.4512 −1.27411
\(865\) 39.5844 1.34591
\(866\) −32.0334 −1.08854
\(867\) 1.61226 0.0547553
\(868\) −21.5364 −0.730992
\(869\) −42.2277 −1.43247
\(870\) −30.1049 −1.02065
\(871\) 24.1675 0.818884
\(872\) −26.8310 −0.908611
\(873\) 0.423654 0.0143385
\(874\) 12.8442 0.434461
\(875\) −11.4371 −0.386646
\(876\) −8.63433 −0.291727
\(877\) −10.6040 −0.358073 −0.179036 0.983842i \(-0.557298\pi\)
−0.179036 + 0.983842i \(0.557298\pi\)
\(878\) −67.2958 −2.27112
\(879\) 15.6002 0.526181
\(880\) 14.7259 0.496409
\(881\) −14.8788 −0.501281 −0.250640 0.968080i \(-0.580641\pi\)
−0.250640 + 0.968080i \(0.580641\pi\)
\(882\) 3.49655 0.117735
\(883\) −44.2645 −1.48962 −0.744809 0.667277i \(-0.767460\pi\)
−0.744809 + 0.667277i \(0.767460\pi\)
\(884\) −56.9465 −1.91532
\(885\) 8.04879 0.270557
\(886\) −56.8447 −1.90974
\(887\) 36.5172 1.22613 0.613064 0.790033i \(-0.289937\pi\)
0.613064 + 0.790033i \(0.289937\pi\)
\(888\) −10.9094 −0.366094
\(889\) 16.9043 0.566952
\(890\) 26.9041 0.901828
\(891\) 10.6752 0.357632
\(892\) 52.7279 1.76546
\(893\) 4.65067 0.155629
\(894\) −52.9274 −1.77016
\(895\) 43.9093 1.46772
\(896\) 15.1449 0.505957
\(897\) 12.4805 0.416712
\(898\) 52.7031 1.75872
\(899\) −37.7005 −1.25738
\(900\) 1.13840 0.0379466
\(901\) 36.9453 1.23082
\(902\) 15.0510 0.501142
\(903\) 15.2508 0.507515
\(904\) −31.3394 −1.04233
\(905\) −50.8338 −1.68977
\(906\) −48.6880 −1.61755
\(907\) −1.12836 −0.0374667 −0.0187333 0.999825i \(-0.505963\pi\)
−0.0187333 + 0.999825i \(0.505963\pi\)
\(908\) 41.4428 1.37533
\(909\) 20.4253 0.677465
\(910\) 21.8078 0.722922
\(911\) −11.5145 −0.381491 −0.190746 0.981640i \(-0.561091\pi\)
−0.190746 + 0.981640i \(0.561091\pi\)
\(912\) −3.42720 −0.113486
\(913\) 55.5752 1.83927
\(914\) 17.2210 0.569621
\(915\) −17.6569 −0.583721
\(916\) −27.2758 −0.901217
\(917\) −18.4901 −0.610595
\(918\) 52.1394 1.72086
\(919\) 1.77145 0.0584348 0.0292174 0.999573i \(-0.490698\pi\)
0.0292174 + 0.999573i \(0.490698\pi\)
\(920\) 10.8468 0.357607
\(921\) −0.197017 −0.00649194
\(922\) 36.3563 1.19733
\(923\) 14.9524 0.492165
\(924\) −20.7012 −0.681019
\(925\) −1.04399 −0.0343260
\(926\) 4.29363 0.141098
\(927\) −24.1870 −0.794404
\(928\) 35.5193 1.16598
\(929\) −22.5707 −0.740522 −0.370261 0.928928i \(-0.620732\pi\)
−0.370261 + 0.928928i \(0.620732\pi\)
\(930\) 42.2476 1.38535
\(931\) 2.48108 0.0813140
\(932\) 34.0032 1.11381
\(933\) −16.0664 −0.525991
\(934\) −42.2591 −1.38276
\(935\) −54.6092 −1.78591
\(936\) −15.0851 −0.493073
\(937\) 32.6902 1.06794 0.533971 0.845503i \(-0.320699\pi\)
0.533971 + 0.845503i \(0.320699\pi\)
\(938\) 11.9882 0.391429
\(939\) 1.98389 0.0647419
\(940\) 12.1024 0.394736
\(941\) 13.9985 0.456337 0.228168 0.973622i \(-0.426726\pi\)
0.228168 + 0.973622i \(0.426726\pi\)
\(942\) 17.0784 0.556444
\(943\) −2.68649 −0.0874841
\(944\) −3.56512 −0.116035
\(945\) −11.9171 −0.387664
\(946\) 166.063 5.39917
\(947\) 17.1140 0.556129 0.278065 0.960562i \(-0.410307\pi\)
0.278065 + 0.960562i \(0.410307\pi\)
\(948\) 25.5747 0.830629
\(949\) 10.9491 0.355423
\(950\) 1.35342 0.0439109
\(951\) −18.0722 −0.586030
\(952\) −9.16703 −0.297105
\(953\) −46.4166 −1.50358 −0.751791 0.659402i \(-0.770810\pi\)
−0.751791 + 0.659402i \(0.770810\pi\)
\(954\) 30.1580 0.976401
\(955\) −42.6866 −1.38131
\(956\) −20.3759 −0.659003
\(957\) −36.2385 −1.17142
\(958\) 63.4137 2.04880
\(959\) −7.50135 −0.242231
\(960\) −33.7790 −1.09021
\(961\) 21.9069 0.706675
\(962\) 42.6296 1.37443
\(963\) −29.1994 −0.940938
\(964\) −7.86307 −0.253252
\(965\) 17.9287 0.577144
\(966\) 6.19092 0.199190
\(967\) 36.6621 1.17897 0.589487 0.807778i \(-0.299330\pi\)
0.589487 + 0.807778i \(0.299330\pi\)
\(968\) −49.6088 −1.59449
\(969\) 12.7094 0.408285
\(970\) 1.31071 0.0420844
\(971\) −23.4903 −0.753840 −0.376920 0.926246i \(-0.623017\pi\)
−0.376920 + 0.926246i \(0.623017\pi\)
\(972\) 42.0780 1.34965
\(973\) 18.9659 0.608020
\(974\) −4.36356 −0.139818
\(975\) 1.31510 0.0421170
\(976\) 7.82094 0.250342
\(977\) 36.4141 1.16499 0.582496 0.812834i \(-0.302076\pi\)
0.582496 + 0.812834i \(0.302076\pi\)
\(978\) −47.8619 −1.53046
\(979\) 32.3856 1.03505
\(980\) 6.45647 0.206244
\(981\) −19.6819 −0.628393
\(982\) −56.6208 −1.80684
\(983\) −40.0144 −1.27626 −0.638130 0.769928i \(-0.720292\pi\)
−0.638130 + 0.769928i \(0.720292\pi\)
\(984\) −2.95813 −0.0943017
\(985\) −39.4066 −1.25560
\(986\) −49.4499 −1.57481
\(987\) 2.24163 0.0713519
\(988\) −32.9846 −1.04938
\(989\) −29.6410 −0.942529
\(990\) −44.5769 −1.41675
\(991\) 20.6691 0.656575 0.328287 0.944578i \(-0.393529\pi\)
0.328287 + 0.944578i \(0.393529\pi\)
\(992\) −49.8459 −1.58261
\(993\) 40.1140 1.27298
\(994\) 7.41711 0.235256
\(995\) 53.1246 1.68416
\(996\) −33.6585 −1.06651
\(997\) 1.77657 0.0562645 0.0281322 0.999604i \(-0.491044\pi\)
0.0281322 + 0.999604i \(0.491044\pi\)
\(998\) −36.2995 −1.14904
\(999\) −23.2954 −0.737034
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 \(a_p\))