Properties

Label 6026.2.a.h.1.4
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.41227 q^{3}\) \(+1.00000 q^{4}\) \(+0.460247 q^{5}\) \(+2.41227 q^{6}\) \(-4.49457 q^{7}\) \(-1.00000 q^{8}\) \(+2.81904 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.41227 q^{3}\) \(+1.00000 q^{4}\) \(+0.460247 q^{5}\) \(+2.41227 q^{6}\) \(-4.49457 q^{7}\) \(-1.00000 q^{8}\) \(+2.81904 q^{9}\) \(-0.460247 q^{10}\) \(-2.62582 q^{11}\) \(-2.41227 q^{12}\) \(+0.877859 q^{13}\) \(+4.49457 q^{14}\) \(-1.11024 q^{15}\) \(+1.00000 q^{16}\) \(+0.794105 q^{17}\) \(-2.81904 q^{18}\) \(+0.648378 q^{19}\) \(+0.460247 q^{20}\) \(+10.8421 q^{21}\) \(+2.62582 q^{22}\) \(-1.00000 q^{23}\) \(+2.41227 q^{24}\) \(-4.78817 q^{25}\) \(-0.877859 q^{26}\) \(+0.436529 q^{27}\) \(-4.49457 q^{28}\) \(+2.58114 q^{29}\) \(+1.11024 q^{30}\) \(-6.97168 q^{31}\) \(-1.00000 q^{32}\) \(+6.33418 q^{33}\) \(-0.794105 q^{34}\) \(-2.06861 q^{35}\) \(+2.81904 q^{36}\) \(+7.43390 q^{37}\) \(-0.648378 q^{38}\) \(-2.11763 q^{39}\) \(-0.460247 q^{40}\) \(+1.59484 q^{41}\) \(-10.8421 q^{42}\) \(-1.00435 q^{43}\) \(-2.62582 q^{44}\) \(+1.29745 q^{45}\) \(+1.00000 q^{46}\) \(-8.71767 q^{47}\) \(-2.41227 q^{48}\) \(+13.2012 q^{49}\) \(+4.78817 q^{50}\) \(-1.91559 q^{51}\) \(+0.877859 q^{52}\) \(+8.84706 q^{53}\) \(-0.436529 q^{54}\) \(-1.20853 q^{55}\) \(+4.49457 q^{56}\) \(-1.56406 q^{57}\) \(-2.58114 q^{58}\) \(+3.77789 q^{59}\) \(-1.11024 q^{60}\) \(+3.78698 q^{61}\) \(+6.97168 q^{62}\) \(-12.6704 q^{63}\) \(+1.00000 q^{64}\) \(+0.404032 q^{65}\) \(-6.33418 q^{66}\) \(+14.9876 q^{67}\) \(+0.794105 q^{68}\) \(+2.41227 q^{69}\) \(+2.06861 q^{70}\) \(-6.81686 q^{71}\) \(-2.81904 q^{72}\) \(+8.09734 q^{73}\) \(-7.43390 q^{74}\) \(+11.5504 q^{75}\) \(+0.648378 q^{76}\) \(+11.8019 q^{77}\) \(+2.11763 q^{78}\) \(-11.8233 q^{79}\) \(+0.460247 q^{80}\) \(-9.51014 q^{81}\) \(-1.59484 q^{82}\) \(+14.8328 q^{83}\) \(+10.8421 q^{84}\) \(+0.365484 q^{85}\) \(+1.00435 q^{86}\) \(-6.22639 q^{87}\) \(+2.62582 q^{88}\) \(-9.69816 q^{89}\) \(-1.29745 q^{90}\) \(-3.94560 q^{91}\) \(-1.00000 q^{92}\) \(+16.8176 q^{93}\) \(+8.71767 q^{94}\) \(+0.298414 q^{95}\) \(+2.41227 q^{96}\) \(-3.98455 q^{97}\) \(-13.2012 q^{98}\) \(-7.40229 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.41227 −1.39272 −0.696362 0.717691i \(-0.745199\pi\)
−0.696362 + 0.717691i \(0.745199\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.460247 0.205829 0.102914 0.994690i \(-0.467183\pi\)
0.102914 + 0.994690i \(0.467183\pi\)
\(6\) 2.41227 0.984804
\(7\) −4.49457 −1.69879 −0.849395 0.527758i \(-0.823033\pi\)
−0.849395 + 0.527758i \(0.823033\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.81904 0.939679
\(10\) −0.460247 −0.145543
\(11\) −2.62582 −0.791714 −0.395857 0.918312i \(-0.629552\pi\)
−0.395857 + 0.918312i \(0.629552\pi\)
\(12\) −2.41227 −0.696362
\(13\) 0.877859 0.243474 0.121737 0.992562i \(-0.461153\pi\)
0.121737 + 0.992562i \(0.461153\pi\)
\(14\) 4.49457 1.20123
\(15\) −1.11024 −0.286662
\(16\) 1.00000 0.250000
\(17\) 0.794105 0.192599 0.0962994 0.995352i \(-0.469299\pi\)
0.0962994 + 0.995352i \(0.469299\pi\)
\(18\) −2.81904 −0.664454
\(19\) 0.648378 0.148748 0.0743741 0.997230i \(-0.476304\pi\)
0.0743741 + 0.997230i \(0.476304\pi\)
\(20\) 0.460247 0.102914
\(21\) 10.8421 2.36594
\(22\) 2.62582 0.559827
\(23\) −1.00000 −0.208514
\(24\) 2.41227 0.492402
\(25\) −4.78817 −0.957635
\(26\) −0.877859 −0.172162
\(27\) 0.436529 0.0840101
\(28\) −4.49457 −0.849395
\(29\) 2.58114 0.479305 0.239652 0.970859i \(-0.422967\pi\)
0.239652 + 0.970859i \(0.422967\pi\)
\(30\) 1.11024 0.202701
\(31\) −6.97168 −1.25215 −0.626075 0.779763i \(-0.715340\pi\)
−0.626075 + 0.779763i \(0.715340\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.33418 1.10264
\(34\) −0.794105 −0.136188
\(35\) −2.06861 −0.349659
\(36\) 2.81904 0.469840
\(37\) 7.43390 1.22213 0.611063 0.791582i \(-0.290742\pi\)
0.611063 + 0.791582i \(0.290742\pi\)
\(38\) −0.648378 −0.105181
\(39\) −2.11763 −0.339093
\(40\) −0.460247 −0.0727714
\(41\) 1.59484 0.249072 0.124536 0.992215i \(-0.460256\pi\)
0.124536 + 0.992215i \(0.460256\pi\)
\(42\) −10.8421 −1.67298
\(43\) −1.00435 −0.153161 −0.0765807 0.997063i \(-0.524400\pi\)
−0.0765807 + 0.997063i \(0.524400\pi\)
\(44\) −2.62582 −0.395857
\(45\) 1.29745 0.193413
\(46\) 1.00000 0.147442
\(47\) −8.71767 −1.27160 −0.635802 0.771853i \(-0.719330\pi\)
−0.635802 + 0.771853i \(0.719330\pi\)
\(48\) −2.41227 −0.348181
\(49\) 13.2012 1.88589
\(50\) 4.78817 0.677150
\(51\) −1.91559 −0.268237
\(52\) 0.877859 0.121737
\(53\) 8.84706 1.21524 0.607619 0.794229i \(-0.292125\pi\)
0.607619 + 0.794229i \(0.292125\pi\)
\(54\) −0.436529 −0.0594041
\(55\) −1.20853 −0.162958
\(56\) 4.49457 0.600613
\(57\) −1.56406 −0.207165
\(58\) −2.58114 −0.338920
\(59\) 3.77789 0.491840 0.245920 0.969290i \(-0.420910\pi\)
0.245920 + 0.969290i \(0.420910\pi\)
\(60\) −1.11024 −0.143331
\(61\) 3.78698 0.484873 0.242437 0.970167i \(-0.422053\pi\)
0.242437 + 0.970167i \(0.422053\pi\)
\(62\) 6.97168 0.885404
\(63\) −12.6704 −1.59632
\(64\) 1.00000 0.125000
\(65\) 0.404032 0.0501140
\(66\) −6.33418 −0.779684
\(67\) 14.9876 1.83103 0.915515 0.402285i \(-0.131784\pi\)
0.915515 + 0.402285i \(0.131784\pi\)
\(68\) 0.794105 0.0962994
\(69\) 2.41227 0.290403
\(70\) 2.06861 0.247247
\(71\) −6.81686 −0.809012 −0.404506 0.914535i \(-0.632557\pi\)
−0.404506 + 0.914535i \(0.632557\pi\)
\(72\) −2.81904 −0.332227
\(73\) 8.09734 0.947723 0.473861 0.880600i \(-0.342860\pi\)
0.473861 + 0.880600i \(0.342860\pi\)
\(74\) −7.43390 −0.864173
\(75\) 11.5504 1.33372
\(76\) 0.648378 0.0743741
\(77\) 11.8019 1.34496
\(78\) 2.11763 0.239775
\(79\) −11.8233 −1.33022 −0.665110 0.746745i \(-0.731615\pi\)
−0.665110 + 0.746745i \(0.731615\pi\)
\(80\) 0.460247 0.0514572
\(81\) −9.51014 −1.05668
\(82\) −1.59484 −0.176121
\(83\) 14.8328 1.62811 0.814054 0.580789i \(-0.197256\pi\)
0.814054 + 0.580789i \(0.197256\pi\)
\(84\) 10.8421 1.18297
\(85\) 0.365484 0.0396423
\(86\) 1.00435 0.108301
\(87\) −6.22639 −0.667539
\(88\) 2.62582 0.279913
\(89\) −9.69816 −1.02800 −0.514001 0.857789i \(-0.671837\pi\)
−0.514001 + 0.857789i \(0.671837\pi\)
\(90\) −1.29745 −0.136764
\(91\) −3.94560 −0.413612
\(92\) −1.00000 −0.104257
\(93\) 16.8176 1.74390
\(94\) 8.71767 0.899159
\(95\) 0.298414 0.0306166
\(96\) 2.41227 0.246201
\(97\) −3.98455 −0.404570 −0.202285 0.979327i \(-0.564837\pi\)
−0.202285 + 0.979327i \(0.564837\pi\)
\(98\) −13.2012 −1.33352
\(99\) −7.40229 −0.743958
\(100\) −4.78817 −0.478817
\(101\) 2.57846 0.256566 0.128283 0.991738i \(-0.459053\pi\)
0.128283 + 0.991738i \(0.459053\pi\)
\(102\) 1.91559 0.189672
\(103\) 11.5301 1.13610 0.568049 0.822995i \(-0.307699\pi\)
0.568049 + 0.822995i \(0.307699\pi\)
\(104\) −0.877859 −0.0860812
\(105\) 4.99005 0.486979
\(106\) −8.84706 −0.859303
\(107\) −0.677536 −0.0654999 −0.0327499 0.999464i \(-0.510426\pi\)
−0.0327499 + 0.999464i \(0.510426\pi\)
\(108\) 0.436529 0.0420050
\(109\) 13.4069 1.28415 0.642074 0.766643i \(-0.278074\pi\)
0.642074 + 0.766643i \(0.278074\pi\)
\(110\) 1.20853 0.115228
\(111\) −17.9326 −1.70208
\(112\) −4.49457 −0.424697
\(113\) −2.04836 −0.192693 −0.0963467 0.995348i \(-0.530716\pi\)
−0.0963467 + 0.995348i \(0.530716\pi\)
\(114\) 1.56406 0.146488
\(115\) −0.460247 −0.0429182
\(116\) 2.58114 0.239652
\(117\) 2.47472 0.228788
\(118\) −3.77789 −0.347783
\(119\) −3.56916 −0.327185
\(120\) 1.11024 0.101350
\(121\) −4.10507 −0.373188
\(122\) −3.78698 −0.342857
\(123\) −3.84718 −0.346889
\(124\) −6.97168 −0.626075
\(125\) −4.50498 −0.402937
\(126\) 12.6704 1.12877
\(127\) 6.60663 0.586244 0.293122 0.956075i \(-0.405306\pi\)
0.293122 + 0.956075i \(0.405306\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.42275 0.213312
\(130\) −0.404032 −0.0354359
\(131\) −1.00000 −0.0873704
\(132\) 6.33418 0.551320
\(133\) −2.91418 −0.252692
\(134\) −14.9876 −1.29473
\(135\) 0.200911 0.0172917
\(136\) −0.794105 −0.0680939
\(137\) 8.31080 0.710039 0.355020 0.934859i \(-0.384474\pi\)
0.355020 + 0.934859i \(0.384474\pi\)
\(138\) −2.41227 −0.205346
\(139\) −0.604721 −0.0512918 −0.0256459 0.999671i \(-0.508164\pi\)
−0.0256459 + 0.999671i \(0.508164\pi\)
\(140\) −2.06861 −0.174830
\(141\) 21.0294 1.77099
\(142\) 6.81686 0.572058
\(143\) −2.30510 −0.192762
\(144\) 2.81904 0.234920
\(145\) 1.18796 0.0986547
\(146\) −8.09734 −0.670141
\(147\) −31.8448 −2.62652
\(148\) 7.43390 0.611063
\(149\) −2.18608 −0.179091 −0.0895455 0.995983i \(-0.528541\pi\)
−0.0895455 + 0.995983i \(0.528541\pi\)
\(150\) −11.5504 −0.943083
\(151\) −15.3419 −1.24851 −0.624253 0.781222i \(-0.714597\pi\)
−0.624253 + 0.781222i \(0.714597\pi\)
\(152\) −0.648378 −0.0525904
\(153\) 2.23861 0.180981
\(154\) −11.8019 −0.951028
\(155\) −3.20869 −0.257728
\(156\) −2.11763 −0.169546
\(157\) −11.1164 −0.887185 −0.443593 0.896229i \(-0.646296\pi\)
−0.443593 + 0.896229i \(0.646296\pi\)
\(158\) 11.8233 0.940608
\(159\) −21.3415 −1.69249
\(160\) −0.460247 −0.0363857
\(161\) 4.49457 0.354222
\(162\) 9.51014 0.747187
\(163\) 12.8532 1.00674 0.503371 0.864070i \(-0.332093\pi\)
0.503371 + 0.864070i \(0.332093\pi\)
\(164\) 1.59484 0.124536
\(165\) 2.91529 0.226955
\(166\) −14.8328 −1.15125
\(167\) 17.0085 1.31616 0.658080 0.752948i \(-0.271369\pi\)
0.658080 + 0.752948i \(0.271369\pi\)
\(168\) −10.8421 −0.836488
\(169\) −12.2294 −0.940720
\(170\) −0.365484 −0.0280314
\(171\) 1.82780 0.139776
\(172\) −1.00435 −0.0765807
\(173\) 11.7883 0.896245 0.448122 0.893972i \(-0.352093\pi\)
0.448122 + 0.893972i \(0.352093\pi\)
\(174\) 6.22639 0.472022
\(175\) 21.5208 1.62682
\(176\) −2.62582 −0.197929
\(177\) −9.11329 −0.684997
\(178\) 9.69816 0.726908
\(179\) −20.8338 −1.55719 −0.778596 0.627525i \(-0.784068\pi\)
−0.778596 + 0.627525i \(0.784068\pi\)
\(180\) 1.29745 0.0967064
\(181\) −6.87479 −0.510999 −0.255499 0.966809i \(-0.582240\pi\)
−0.255499 + 0.966809i \(0.582240\pi\)
\(182\) 3.94560 0.292468
\(183\) −9.13522 −0.675295
\(184\) 1.00000 0.0737210
\(185\) 3.42143 0.251548
\(186\) −16.8176 −1.23312
\(187\) −2.08518 −0.152483
\(188\) −8.71767 −0.635802
\(189\) −1.96201 −0.142715
\(190\) −0.298414 −0.0216492
\(191\) 17.1231 1.23898 0.619492 0.785003i \(-0.287339\pi\)
0.619492 + 0.785003i \(0.287339\pi\)
\(192\) −2.41227 −0.174090
\(193\) 22.0959 1.59050 0.795250 0.606281i \(-0.207339\pi\)
0.795250 + 0.606281i \(0.207339\pi\)
\(194\) 3.98455 0.286074
\(195\) −0.974634 −0.0697950
\(196\) 13.2012 0.942943
\(197\) −4.27109 −0.304303 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(198\) 7.40229 0.526058
\(199\) 19.0104 1.34761 0.673807 0.738907i \(-0.264658\pi\)
0.673807 + 0.738907i \(0.264658\pi\)
\(200\) 4.78817 0.338575
\(201\) −36.1542 −2.55012
\(202\) −2.57846 −0.181420
\(203\) −11.6011 −0.814238
\(204\) −1.91559 −0.134118
\(205\) 0.734020 0.0512662
\(206\) −11.5301 −0.803342
\(207\) −2.81904 −0.195937
\(208\) 0.877859 0.0608686
\(209\) −1.70252 −0.117766
\(210\) −4.99005 −0.344346
\(211\) −7.08629 −0.487840 −0.243920 0.969795i \(-0.578433\pi\)
−0.243920 + 0.969795i \(0.578433\pi\)
\(212\) 8.84706 0.607619
\(213\) 16.4441 1.12673
\(214\) 0.677536 0.0463154
\(215\) −0.462247 −0.0315250
\(216\) −0.436529 −0.0297020
\(217\) 31.3347 2.12714
\(218\) −13.4069 −0.908029
\(219\) −19.5330 −1.31992
\(220\) −1.20853 −0.0814788
\(221\) 0.697112 0.0468929
\(222\) 17.9326 1.20355
\(223\) −26.3899 −1.76720 −0.883598 0.468246i \(-0.844886\pi\)
−0.883598 + 0.468246i \(0.844886\pi\)
\(224\) 4.49457 0.300306
\(225\) −13.4980 −0.899869
\(226\) 2.04836 0.136255
\(227\) 12.4452 0.826015 0.413008 0.910728i \(-0.364478\pi\)
0.413008 + 0.910728i \(0.364478\pi\)
\(228\) −1.56406 −0.103583
\(229\) 4.70486 0.310906 0.155453 0.987843i \(-0.450316\pi\)
0.155453 + 0.987843i \(0.450316\pi\)
\(230\) 0.460247 0.0303478
\(231\) −28.4695 −1.87315
\(232\) −2.58114 −0.169460
\(233\) 0.200287 0.0131212 0.00656061 0.999978i \(-0.497912\pi\)
0.00656061 + 0.999978i \(0.497912\pi\)
\(234\) −2.47472 −0.161777
\(235\) −4.01228 −0.261732
\(236\) 3.77789 0.245920
\(237\) 28.5209 1.85263
\(238\) 3.56916 0.231355
\(239\) 18.1759 1.17570 0.587852 0.808969i \(-0.299974\pi\)
0.587852 + 0.808969i \(0.299974\pi\)
\(240\) −1.11024 −0.0716656
\(241\) −17.1104 −1.10218 −0.551088 0.834447i \(-0.685787\pi\)
−0.551088 + 0.834447i \(0.685787\pi\)
\(242\) 4.10507 0.263884
\(243\) 21.6314 1.38766
\(244\) 3.78698 0.242437
\(245\) 6.07581 0.388169
\(246\) 3.84718 0.245287
\(247\) 0.569185 0.0362164
\(248\) 6.97168 0.442702
\(249\) −35.7806 −2.26750
\(250\) 4.50498 0.284920
\(251\) −17.2290 −1.08748 −0.543741 0.839253i \(-0.682993\pi\)
−0.543741 + 0.839253i \(0.682993\pi\)
\(252\) −12.6704 −0.798159
\(253\) 2.62582 0.165084
\(254\) −6.60663 −0.414537
\(255\) −0.881646 −0.0552108
\(256\) 1.00000 0.0625000
\(257\) −16.4630 −1.02694 −0.513468 0.858109i \(-0.671639\pi\)
−0.513468 + 0.858109i \(0.671639\pi\)
\(258\) −2.42275 −0.150834
\(259\) −33.4122 −2.07613
\(260\) 0.404032 0.0250570
\(261\) 7.27632 0.450393
\(262\) 1.00000 0.0617802
\(263\) 14.2504 0.878719 0.439359 0.898311i \(-0.355205\pi\)
0.439359 + 0.898311i \(0.355205\pi\)
\(264\) −6.33418 −0.389842
\(265\) 4.07183 0.250131
\(266\) 2.91418 0.178680
\(267\) 23.3946 1.43172
\(268\) 14.9876 0.915515
\(269\) 21.1869 1.29179 0.645895 0.763426i \(-0.276484\pi\)
0.645895 + 0.763426i \(0.276484\pi\)
\(270\) −0.200911 −0.0122271
\(271\) 29.9437 1.81895 0.909474 0.415760i \(-0.136484\pi\)
0.909474 + 0.415760i \(0.136484\pi\)
\(272\) 0.794105 0.0481497
\(273\) 9.51786 0.576047
\(274\) −8.31080 −0.502074
\(275\) 12.5729 0.758173
\(276\) 2.41227 0.145201
\(277\) 15.5132 0.932101 0.466050 0.884758i \(-0.345677\pi\)
0.466050 + 0.884758i \(0.345677\pi\)
\(278\) 0.604721 0.0362688
\(279\) −19.6534 −1.17662
\(280\) 2.06861 0.123623
\(281\) −18.9578 −1.13093 −0.565464 0.824773i \(-0.691303\pi\)
−0.565464 + 0.824773i \(0.691303\pi\)
\(282\) −21.0294 −1.25228
\(283\) 1.24346 0.0739157 0.0369579 0.999317i \(-0.488233\pi\)
0.0369579 + 0.999317i \(0.488233\pi\)
\(284\) −6.81686 −0.404506
\(285\) −0.719855 −0.0426405
\(286\) 2.30510 0.136303
\(287\) −7.16813 −0.423121
\(288\) −2.81904 −0.166113
\(289\) −16.3694 −0.962906
\(290\) −1.18796 −0.0697594
\(291\) 9.61180 0.563454
\(292\) 8.09734 0.473861
\(293\) 2.83227 0.165463 0.0827316 0.996572i \(-0.473636\pi\)
0.0827316 + 0.996572i \(0.473636\pi\)
\(294\) 31.8448 1.85723
\(295\) 1.73876 0.101235
\(296\) −7.43390 −0.432086
\(297\) −1.14625 −0.0665120
\(298\) 2.18608 0.126636
\(299\) −0.877859 −0.0507679
\(300\) 11.5504 0.666860
\(301\) 4.51411 0.260189
\(302\) 15.3419 0.882827
\(303\) −6.21993 −0.357326
\(304\) 0.648378 0.0371870
\(305\) 1.74295 0.0998008
\(306\) −2.23861 −0.127973
\(307\) −8.47363 −0.483616 −0.241808 0.970324i \(-0.577740\pi\)
−0.241808 + 0.970324i \(0.577740\pi\)
\(308\) 11.8019 0.672478
\(309\) −27.8138 −1.58227
\(310\) 3.20869 0.182241
\(311\) −29.8126 −1.69052 −0.845259 0.534357i \(-0.820554\pi\)
−0.845259 + 0.534357i \(0.820554\pi\)
\(312\) 2.11763 0.119887
\(313\) 11.8646 0.670624 0.335312 0.942107i \(-0.391158\pi\)
0.335312 + 0.942107i \(0.391158\pi\)
\(314\) 11.1164 0.627335
\(315\) −5.83150 −0.328568
\(316\) −11.8233 −0.665110
\(317\) −28.4403 −1.59737 −0.798683 0.601752i \(-0.794470\pi\)
−0.798683 + 0.601752i \(0.794470\pi\)
\(318\) 21.3415 1.19677
\(319\) −6.77760 −0.379473
\(320\) 0.460247 0.0257286
\(321\) 1.63440 0.0912233
\(322\) −4.49457 −0.250473
\(323\) 0.514880 0.0286487
\(324\) −9.51014 −0.528341
\(325\) −4.20334 −0.233160
\(326\) −12.8532 −0.711874
\(327\) −32.3410 −1.78846
\(328\) −1.59484 −0.0880603
\(329\) 39.1822 2.16019
\(330\) −2.91529 −0.160481
\(331\) 17.2305 0.947077 0.473538 0.880773i \(-0.342977\pi\)
0.473538 + 0.880773i \(0.342977\pi\)
\(332\) 14.8328 0.814054
\(333\) 20.9564 1.14841
\(334\) −17.0085 −0.930665
\(335\) 6.89800 0.376878
\(336\) 10.8421 0.591486
\(337\) −29.6804 −1.61679 −0.808396 0.588639i \(-0.799664\pi\)
−0.808396 + 0.588639i \(0.799664\pi\)
\(338\) 12.2294 0.665190
\(339\) 4.94119 0.268369
\(340\) 0.365484 0.0198212
\(341\) 18.3064 0.991345
\(342\) −1.82780 −0.0988363
\(343\) −27.8718 −1.50493
\(344\) 1.00435 0.0541507
\(345\) 1.11024 0.0597732
\(346\) −11.7883 −0.633741
\(347\) 17.7986 0.955479 0.477740 0.878501i \(-0.341456\pi\)
0.477740 + 0.878501i \(0.341456\pi\)
\(348\) −6.22639 −0.333770
\(349\) −18.4127 −0.985610 −0.492805 0.870140i \(-0.664028\pi\)
−0.492805 + 0.870140i \(0.664028\pi\)
\(350\) −21.5208 −1.15034
\(351\) 0.383211 0.0204543
\(352\) 2.62582 0.139957
\(353\) −15.5953 −0.830054 −0.415027 0.909809i \(-0.636228\pi\)
−0.415027 + 0.909809i \(0.636228\pi\)
\(354\) 9.11329 0.484366
\(355\) −3.13744 −0.166518
\(356\) −9.69816 −0.514001
\(357\) 8.60978 0.455678
\(358\) 20.8338 1.10110
\(359\) −18.7690 −0.990588 −0.495294 0.868726i \(-0.664940\pi\)
−0.495294 + 0.868726i \(0.664940\pi\)
\(360\) −1.29745 −0.0683818
\(361\) −18.5796 −0.977874
\(362\) 6.87479 0.361331
\(363\) 9.90253 0.519748
\(364\) −3.94560 −0.206806
\(365\) 3.72678 0.195068
\(366\) 9.13522 0.477505
\(367\) −4.46882 −0.233271 −0.116635 0.993175i \(-0.537211\pi\)
−0.116635 + 0.993175i \(0.537211\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 4.49592 0.234048
\(370\) −3.42143 −0.177872
\(371\) −39.7638 −2.06443
\(372\) 16.8176 0.871950
\(373\) −33.7315 −1.74655 −0.873277 0.487225i \(-0.838009\pi\)
−0.873277 + 0.487225i \(0.838009\pi\)
\(374\) 2.08518 0.107822
\(375\) 10.8672 0.561180
\(376\) 8.71767 0.449580
\(377\) 2.26587 0.116698
\(378\) 1.96201 0.100915
\(379\) 24.9988 1.28410 0.642050 0.766663i \(-0.278084\pi\)
0.642050 + 0.766663i \(0.278084\pi\)
\(380\) 0.298414 0.0153083
\(381\) −15.9370 −0.816475
\(382\) −17.1231 −0.876094
\(383\) 6.41793 0.327941 0.163970 0.986465i \(-0.447570\pi\)
0.163970 + 0.986465i \(0.447570\pi\)
\(384\) 2.41227 0.123101
\(385\) 5.43181 0.276830
\(386\) −22.0959 −1.12465
\(387\) −2.83129 −0.143923
\(388\) −3.98455 −0.202285
\(389\) 27.5282 1.39573 0.697867 0.716228i \(-0.254133\pi\)
0.697867 + 0.716228i \(0.254133\pi\)
\(390\) 0.974634 0.0493525
\(391\) −0.794105 −0.0401596
\(392\) −13.2012 −0.666761
\(393\) 2.41227 0.121683
\(394\) 4.27109 0.215174
\(395\) −5.44162 −0.273797
\(396\) −7.40229 −0.371979
\(397\) −13.5398 −0.679542 −0.339771 0.940508i \(-0.610350\pi\)
−0.339771 + 0.940508i \(0.610350\pi\)
\(398\) −19.0104 −0.952907
\(399\) 7.02979 0.351930
\(400\) −4.78817 −0.239409
\(401\) 24.2827 1.21262 0.606310 0.795228i \(-0.292649\pi\)
0.606310 + 0.795228i \(0.292649\pi\)
\(402\) 36.1542 1.80321
\(403\) −6.12015 −0.304866
\(404\) 2.57846 0.128283
\(405\) −4.37701 −0.217495
\(406\) 11.6011 0.575753
\(407\) −19.5201 −0.967574
\(408\) 1.91559 0.0948360
\(409\) 32.3561 1.59990 0.799952 0.600064i \(-0.204858\pi\)
0.799952 + 0.600064i \(0.204858\pi\)
\(410\) −0.734020 −0.0362507
\(411\) −20.0479 −0.988889
\(412\) 11.5301 0.568049
\(413\) −16.9800 −0.835532
\(414\) 2.81904 0.138548
\(415\) 6.82673 0.335111
\(416\) −0.877859 −0.0430406
\(417\) 1.45875 0.0714353
\(418\) 1.70252 0.0832732
\(419\) −4.87191 −0.238008 −0.119004 0.992894i \(-0.537970\pi\)
−0.119004 + 0.992894i \(0.537970\pi\)
\(420\) 4.99005 0.243490
\(421\) −6.76788 −0.329847 −0.164923 0.986306i \(-0.552738\pi\)
−0.164923 + 0.986306i \(0.552738\pi\)
\(422\) 7.08629 0.344955
\(423\) −24.5754 −1.19490
\(424\) −8.84706 −0.429651
\(425\) −3.80231 −0.184439
\(426\) −16.4441 −0.796719
\(427\) −17.0209 −0.823698
\(428\) −0.677536 −0.0327499
\(429\) 5.56052 0.268465
\(430\) 0.462247 0.0222915
\(431\) 17.4799 0.841976 0.420988 0.907066i \(-0.361683\pi\)
0.420988 + 0.907066i \(0.361683\pi\)
\(432\) 0.436529 0.0210025
\(433\) −10.8029 −0.519153 −0.259576 0.965723i \(-0.583583\pi\)
−0.259576 + 0.965723i \(0.583583\pi\)
\(434\) −31.3347 −1.50411
\(435\) −2.86568 −0.137399
\(436\) 13.4069 0.642074
\(437\) −0.648378 −0.0310161
\(438\) 19.5330 0.933321
\(439\) −25.7481 −1.22889 −0.614444 0.788960i \(-0.710620\pi\)
−0.614444 + 0.788960i \(0.710620\pi\)
\(440\) 1.20853 0.0576142
\(441\) 37.2147 1.77213
\(442\) −0.697112 −0.0331583
\(443\) −1.98805 −0.0944553 −0.0472277 0.998884i \(-0.515039\pi\)
−0.0472277 + 0.998884i \(0.515039\pi\)
\(444\) −17.9326 −0.851041
\(445\) −4.46355 −0.211592
\(446\) 26.3899 1.24960
\(447\) 5.27342 0.249424
\(448\) −4.49457 −0.212349
\(449\) −30.6524 −1.44658 −0.723289 0.690545i \(-0.757371\pi\)
−0.723289 + 0.690545i \(0.757371\pi\)
\(450\) 13.4980 0.636304
\(451\) −4.18776 −0.197194
\(452\) −2.04836 −0.0963467
\(453\) 37.0088 1.73882
\(454\) −12.4452 −0.584081
\(455\) −1.81595 −0.0851331
\(456\) 1.56406 0.0732439
\(457\) −15.4859 −0.724401 −0.362201 0.932100i \(-0.617975\pi\)
−0.362201 + 0.932100i \(0.617975\pi\)
\(458\) −4.70486 −0.219844
\(459\) 0.346650 0.0161802
\(460\) −0.460247 −0.0214591
\(461\) −29.4029 −1.36943 −0.684715 0.728811i \(-0.740074\pi\)
−0.684715 + 0.728811i \(0.740074\pi\)
\(462\) 28.4695 1.32452
\(463\) −27.9058 −1.29689 −0.648447 0.761260i \(-0.724581\pi\)
−0.648447 + 0.761260i \(0.724581\pi\)
\(464\) 2.58114 0.119826
\(465\) 7.74022 0.358944
\(466\) −0.200287 −0.00927810
\(467\) −20.3053 −0.939616 −0.469808 0.882769i \(-0.655677\pi\)
−0.469808 + 0.882769i \(0.655677\pi\)
\(468\) 2.47472 0.114394
\(469\) −67.3630 −3.11053
\(470\) 4.01228 0.185073
\(471\) 26.8157 1.23560
\(472\) −3.77789 −0.173892
\(473\) 2.63723 0.121260
\(474\) −28.5209 −1.31001
\(475\) −3.10455 −0.142446
\(476\) −3.56916 −0.163592
\(477\) 24.9402 1.14193
\(478\) −18.1759 −0.831348
\(479\) −12.9549 −0.591925 −0.295962 0.955200i \(-0.595640\pi\)
−0.295962 + 0.955200i \(0.595640\pi\)
\(480\) 1.11024 0.0506752
\(481\) 6.52592 0.297556
\(482\) 17.1104 0.779356
\(483\) −10.8421 −0.493334
\(484\) −4.10507 −0.186594
\(485\) −1.83388 −0.0832720
\(486\) −21.6314 −0.981221
\(487\) −27.1150 −1.22870 −0.614349 0.789034i \(-0.710581\pi\)
−0.614349 + 0.789034i \(0.710581\pi\)
\(488\) −3.78698 −0.171429
\(489\) −31.0054 −1.40211
\(490\) −6.07581 −0.274477
\(491\) −10.5565 −0.476406 −0.238203 0.971215i \(-0.576558\pi\)
−0.238203 + 0.971215i \(0.576558\pi\)
\(492\) −3.84718 −0.173444
\(493\) 2.04969 0.0923135
\(494\) −0.569185 −0.0256088
\(495\) −3.40688 −0.153128
\(496\) −6.97168 −0.313038
\(497\) 30.6389 1.37434
\(498\) 35.7806 1.60337
\(499\) −11.9256 −0.533865 −0.266933 0.963715i \(-0.586010\pi\)
−0.266933 + 0.963715i \(0.586010\pi\)
\(500\) −4.50498 −0.201469
\(501\) −41.0291 −1.83305
\(502\) 17.2290 0.768966
\(503\) −14.8762 −0.663296 −0.331648 0.943403i \(-0.607605\pi\)
−0.331648 + 0.943403i \(0.607605\pi\)
\(504\) 12.6704 0.564383
\(505\) 1.18673 0.0528087
\(506\) −2.62582 −0.116732
\(507\) 29.5005 1.31016
\(508\) 6.60663 0.293122
\(509\) −11.3539 −0.503255 −0.251627 0.967824i \(-0.580966\pi\)
−0.251627 + 0.967824i \(0.580966\pi\)
\(510\) 0.881646 0.0390399
\(511\) −36.3941 −1.60998
\(512\) −1.00000 −0.0441942
\(513\) 0.283036 0.0124963
\(514\) 16.4630 0.726153
\(515\) 5.30670 0.233841
\(516\) 2.42275 0.106656
\(517\) 22.8910 1.00675
\(518\) 33.4122 1.46805
\(519\) −28.4364 −1.24822
\(520\) −0.404032 −0.0177180
\(521\) 23.4108 1.02565 0.512824 0.858494i \(-0.328600\pi\)
0.512824 + 0.858494i \(0.328600\pi\)
\(522\) −7.27632 −0.318476
\(523\) −36.3521 −1.58957 −0.794783 0.606894i \(-0.792415\pi\)
−0.794783 + 0.606894i \(0.792415\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −51.9139 −2.26571
\(526\) −14.2504 −0.621348
\(527\) −5.53624 −0.241163
\(528\) 6.33418 0.275660
\(529\) 1.00000 0.0434783
\(530\) −4.07183 −0.176869
\(531\) 10.6500 0.462172
\(532\) −2.91418 −0.126346
\(533\) 1.40005 0.0606427
\(534\) −23.3946 −1.01238
\(535\) −0.311834 −0.0134818
\(536\) −14.9876 −0.647367
\(537\) 50.2567 2.16874
\(538\) −21.1869 −0.913434
\(539\) −34.6640 −1.49308
\(540\) 0.200911 0.00864584
\(541\) 44.6482 1.91958 0.959789 0.280723i \(-0.0905743\pi\)
0.959789 + 0.280723i \(0.0905743\pi\)
\(542\) −29.9437 −1.28619
\(543\) 16.5838 0.711680
\(544\) −0.794105 −0.0340470
\(545\) 6.17048 0.264314
\(546\) −9.51786 −0.407327
\(547\) −19.6844 −0.841643 −0.420821 0.907144i \(-0.638258\pi\)
−0.420821 + 0.907144i \(0.638258\pi\)
\(548\) 8.31080 0.355020
\(549\) 10.6756 0.455625
\(550\) −12.5729 −0.536109
\(551\) 1.67355 0.0712957
\(552\) −2.41227 −0.102673
\(553\) 53.1405 2.25976
\(554\) −15.5132 −0.659095
\(555\) −8.25340 −0.350337
\(556\) −0.604721 −0.0256459
\(557\) 4.58050 0.194082 0.0970411 0.995280i \(-0.469062\pi\)
0.0970411 + 0.995280i \(0.469062\pi\)
\(558\) 19.6534 0.831996
\(559\) −0.881675 −0.0372909
\(560\) −2.06861 −0.0874149
\(561\) 5.03001 0.212367
\(562\) 18.9578 0.799687
\(563\) −36.9245 −1.55618 −0.778092 0.628151i \(-0.783812\pi\)
−0.778092 + 0.628151i \(0.783812\pi\)
\(564\) 21.0294 0.885496
\(565\) −0.942751 −0.0396618
\(566\) −1.24346 −0.0522663
\(567\) 42.7440 1.79508
\(568\) 6.81686 0.286029
\(569\) 19.3897 0.812860 0.406430 0.913682i \(-0.366774\pi\)
0.406430 + 0.913682i \(0.366774\pi\)
\(570\) 0.719855 0.0301514
\(571\) −8.12576 −0.340053 −0.170026 0.985440i \(-0.554385\pi\)
−0.170026 + 0.985440i \(0.554385\pi\)
\(572\) −2.30510 −0.0963811
\(573\) −41.3055 −1.72556
\(574\) 7.16813 0.299192
\(575\) 4.78817 0.199681
\(576\) 2.81904 0.117460
\(577\) 13.7070 0.570631 0.285315 0.958434i \(-0.407902\pi\)
0.285315 + 0.958434i \(0.407902\pi\)
\(578\) 16.3694 0.680877
\(579\) −53.3013 −2.21513
\(580\) 1.18796 0.0493273
\(581\) −66.6670 −2.76581
\(582\) −9.61180 −0.398422
\(583\) −23.2308 −0.962121
\(584\) −8.09734 −0.335071
\(585\) 1.13898 0.0470911
\(586\) −2.83227 −0.117000
\(587\) −10.5966 −0.437370 −0.218685 0.975795i \(-0.570177\pi\)
−0.218685 + 0.975795i \(0.570177\pi\)
\(588\) −31.8448 −1.31326
\(589\) −4.52028 −0.186255
\(590\) −1.73876 −0.0715837
\(591\) 10.3030 0.423809
\(592\) 7.43390 0.305531
\(593\) 10.7539 0.441610 0.220805 0.975318i \(-0.429132\pi\)
0.220805 + 0.975318i \(0.429132\pi\)
\(594\) 1.14625 0.0470311
\(595\) −1.64270 −0.0673440
\(596\) −2.18608 −0.0895455
\(597\) −45.8583 −1.87685
\(598\) 0.877859 0.0358983
\(599\) 28.3027 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(600\) −11.5504 −0.471541
\(601\) −37.9573 −1.54831 −0.774156 0.632995i \(-0.781825\pi\)
−0.774156 + 0.632995i \(0.781825\pi\)
\(602\) −4.51411 −0.183981
\(603\) 42.2507 1.72058
\(604\) −15.3419 −0.624253
\(605\) −1.88935 −0.0768128
\(606\) 6.21993 0.252667
\(607\) −16.3774 −0.664738 −0.332369 0.943149i \(-0.607848\pi\)
−0.332369 + 0.943149i \(0.607848\pi\)
\(608\) −0.648378 −0.0262952
\(609\) 27.9850 1.13401
\(610\) −1.74295 −0.0705698
\(611\) −7.65289 −0.309603
\(612\) 2.23861 0.0904905
\(613\) −32.8644 −1.32738 −0.663690 0.748008i \(-0.731011\pi\)
−0.663690 + 0.748008i \(0.731011\pi\)
\(614\) 8.47363 0.341968
\(615\) −1.77065 −0.0713996
\(616\) −11.8019 −0.475514
\(617\) 10.9973 0.442734 0.221367 0.975191i \(-0.428948\pi\)
0.221367 + 0.975191i \(0.428948\pi\)
\(618\) 27.8138 1.11883
\(619\) 4.89692 0.196824 0.0984119 0.995146i \(-0.468624\pi\)
0.0984119 + 0.995146i \(0.468624\pi\)
\(620\) −3.20869 −0.128864
\(621\) −0.436529 −0.0175173
\(622\) 29.8126 1.19538
\(623\) 43.5891 1.74636
\(624\) −2.11763 −0.0847731
\(625\) 21.8675 0.874699
\(626\) −11.8646 −0.474203
\(627\) 4.10695 0.164016
\(628\) −11.1164 −0.443593
\(629\) 5.90329 0.235380
\(630\) 5.83150 0.232333
\(631\) −32.4013 −1.28988 −0.644938 0.764235i \(-0.723117\pi\)
−0.644938 + 0.764235i \(0.723117\pi\)
\(632\) 11.8233 0.470304
\(633\) 17.0940 0.679427
\(634\) 28.4403 1.12951
\(635\) 3.04068 0.120666
\(636\) −21.3415 −0.846245
\(637\) 11.5888 0.459165
\(638\) 6.77760 0.268328
\(639\) −19.2170 −0.760212
\(640\) −0.460247 −0.0181929
\(641\) −16.0119 −0.632431 −0.316215 0.948687i \(-0.602412\pi\)
−0.316215 + 0.948687i \(0.602412\pi\)
\(642\) −1.63440 −0.0645046
\(643\) 7.40926 0.292193 0.146096 0.989270i \(-0.453329\pi\)
0.146096 + 0.989270i \(0.453329\pi\)
\(644\) 4.49457 0.177111
\(645\) 1.11506 0.0439056
\(646\) −0.514880 −0.0202577
\(647\) −10.2470 −0.402851 −0.201425 0.979504i \(-0.564557\pi\)
−0.201425 + 0.979504i \(0.564557\pi\)
\(648\) 9.51014 0.373594
\(649\) −9.92007 −0.389397
\(650\) 4.20334 0.164869
\(651\) −75.5877 −2.96252
\(652\) 12.8532 0.503371
\(653\) 38.1379 1.49245 0.746226 0.665693i \(-0.231864\pi\)
0.746226 + 0.665693i \(0.231864\pi\)
\(654\) 32.3410 1.26463
\(655\) −0.460247 −0.0179833
\(656\) 1.59484 0.0622681
\(657\) 22.8267 0.890555
\(658\) −39.1822 −1.52748
\(659\) −40.2282 −1.56707 −0.783534 0.621349i \(-0.786585\pi\)
−0.783534 + 0.621349i \(0.786585\pi\)
\(660\) 2.91529 0.113477
\(661\) 22.8208 0.887626 0.443813 0.896120i \(-0.353626\pi\)
0.443813 + 0.896120i \(0.353626\pi\)
\(662\) −17.2305 −0.669684
\(663\) −1.68162 −0.0653088
\(664\) −14.8328 −0.575623
\(665\) −1.34124 −0.0520112
\(666\) −20.9564 −0.812045
\(667\) −2.58114 −0.0999420
\(668\) 17.0085 0.658080
\(669\) 63.6595 2.46122
\(670\) −6.89800 −0.266493
\(671\) −9.94393 −0.383881
\(672\) −10.8421 −0.418244
\(673\) −1.88147 −0.0725255 −0.0362628 0.999342i \(-0.511545\pi\)
−0.0362628 + 0.999342i \(0.511545\pi\)
\(674\) 29.6804 1.14324
\(675\) −2.09018 −0.0804509
\(676\) −12.2294 −0.470360
\(677\) 23.0777 0.886949 0.443474 0.896287i \(-0.353746\pi\)
0.443474 + 0.896287i \(0.353746\pi\)
\(678\) −4.94119 −0.189765
\(679\) 17.9089 0.687279
\(680\) −0.365484 −0.0140157
\(681\) −30.0211 −1.15041
\(682\) −18.3064 −0.700987
\(683\) 48.0500 1.83858 0.919291 0.393578i \(-0.128763\pi\)
0.919291 + 0.393578i \(0.128763\pi\)
\(684\) 1.82780 0.0698878
\(685\) 3.82502 0.146146
\(686\) 27.8718 1.06415
\(687\) −11.3494 −0.433006
\(688\) −1.00435 −0.0382903
\(689\) 7.76648 0.295879
\(690\) −1.11024 −0.0422661
\(691\) −13.7851 −0.524409 −0.262204 0.965012i \(-0.584449\pi\)
−0.262204 + 0.965012i \(0.584449\pi\)
\(692\) 11.7883 0.448122
\(693\) 33.2701 1.26383
\(694\) −17.7986 −0.675626
\(695\) −0.278321 −0.0105573
\(696\) 6.22639 0.236011
\(697\) 1.26647 0.0479710
\(698\) 18.4127 0.696931
\(699\) −0.483145 −0.0182742
\(700\) 21.5208 0.813410
\(701\) 51.8058 1.95668 0.978340 0.207005i \(-0.0663718\pi\)
0.978340 + 0.207005i \(0.0663718\pi\)
\(702\) −0.383211 −0.0144634
\(703\) 4.81998 0.181789
\(704\) −2.62582 −0.0989643
\(705\) 9.67870 0.364521
\(706\) 15.5953 0.586937
\(707\) −11.5891 −0.435852
\(708\) −9.11329 −0.342498
\(709\) −13.6097 −0.511123 −0.255561 0.966793i \(-0.582260\pi\)
−0.255561 + 0.966793i \(0.582260\pi\)
\(710\) 3.13744 0.117746
\(711\) −33.3302 −1.24998
\(712\) 9.69816 0.363454
\(713\) 6.97168 0.261091
\(714\) −8.60978 −0.322213
\(715\) −1.06092 −0.0396760
\(716\) −20.8338 −0.778596
\(717\) −43.8452 −1.63743
\(718\) 18.7690 0.700451
\(719\) 43.6103 1.62639 0.813194 0.581993i \(-0.197727\pi\)
0.813194 + 0.581993i \(0.197727\pi\)
\(720\) 1.29745 0.0483532
\(721\) −51.8230 −1.92999
\(722\) 18.5796 0.691461
\(723\) 41.2748 1.53503
\(724\) −6.87479 −0.255499
\(725\) −12.3589 −0.458999
\(726\) −9.90253 −0.367517
\(727\) 41.2105 1.52841 0.764207 0.644972i \(-0.223131\pi\)
0.764207 + 0.644972i \(0.223131\pi\)
\(728\) 3.94560 0.146234
\(729\) −23.6504 −0.875939
\(730\) −3.72678 −0.137934
\(731\) −0.797556 −0.0294987
\(732\) −9.13522 −0.337647
\(733\) −27.5284 −1.01679 −0.508393 0.861125i \(-0.669760\pi\)
−0.508393 + 0.861125i \(0.669760\pi\)
\(734\) 4.46882 0.164947
\(735\) −14.6565 −0.540613
\(736\) 1.00000 0.0368605
\(737\) −39.3548 −1.44965
\(738\) −4.49592 −0.165497
\(739\) −12.9950 −0.478028 −0.239014 0.971016i \(-0.576824\pi\)
−0.239014 + 0.971016i \(0.576824\pi\)
\(740\) 3.42143 0.125774
\(741\) −1.37303 −0.0504394
\(742\) 39.7638 1.45977
\(743\) −23.7409 −0.870968 −0.435484 0.900197i \(-0.643423\pi\)
−0.435484 + 0.900197i \(0.643423\pi\)
\(744\) −16.8176 −0.616561
\(745\) −1.00614 −0.0368621
\(746\) 33.7315 1.23500
\(747\) 41.8141 1.52990
\(748\) −2.08518 −0.0762416
\(749\) 3.04524 0.111271
\(750\) −10.8672 −0.396814
\(751\) 5.75838 0.210126 0.105063 0.994466i \(-0.466496\pi\)
0.105063 + 0.994466i \(0.466496\pi\)
\(752\) −8.71767 −0.317901
\(753\) 41.5609 1.51456
\(754\) −2.26587 −0.0825183
\(755\) −7.06106 −0.256978
\(756\) −1.96201 −0.0713577
\(757\) −19.4332 −0.706311 −0.353156 0.935565i \(-0.614891\pi\)
−0.353156 + 0.935565i \(0.614891\pi\)
\(758\) −24.9988 −0.907996
\(759\) −6.33418 −0.229916
\(760\) −0.298414 −0.0108246
\(761\) 18.9672 0.687561 0.343780 0.939050i \(-0.388292\pi\)
0.343780 + 0.939050i \(0.388292\pi\)
\(762\) 15.9370 0.577335
\(763\) −60.2583 −2.18150
\(764\) 17.1231 0.619492
\(765\) 1.03031 0.0372511
\(766\) −6.41793 −0.231889
\(767\) 3.31646 0.119750
\(768\) −2.41227 −0.0870452
\(769\) 2.24872 0.0810908 0.0405454 0.999178i \(-0.487090\pi\)
0.0405454 + 0.999178i \(0.487090\pi\)
\(770\) −5.43181 −0.195749
\(771\) 39.7133 1.43024
\(772\) 22.0959 0.795250
\(773\) −25.4305 −0.914672 −0.457336 0.889294i \(-0.651196\pi\)
−0.457336 + 0.889294i \(0.651196\pi\)
\(774\) 2.83129 0.101769
\(775\) 33.3816 1.19910
\(776\) 3.98455 0.143037
\(777\) 80.5992 2.89148
\(778\) −27.5282 −0.986932
\(779\) 1.03406 0.0370490
\(780\) −0.974634 −0.0348975
\(781\) 17.8998 0.640507
\(782\) 0.794105 0.0283971
\(783\) 1.12674 0.0402664
\(784\) 13.2012 0.471471
\(785\) −5.11629 −0.182608
\(786\) −2.41227 −0.0860428
\(787\) −53.0282 −1.89025 −0.945125 0.326708i \(-0.894061\pi\)
−0.945125 + 0.326708i \(0.894061\pi\)
\(788\) −4.27109 −0.152151
\(789\) −34.3758 −1.22381
\(790\) 5.44162 0.193604
\(791\) 9.20651 0.327346
\(792\) 7.40229 0.263029
\(793\) 3.32444 0.118054
\(794\) 13.5398 0.480509
\(795\) −9.82235 −0.348363
\(796\) 19.0104 0.673807
\(797\) −30.1499 −1.06797 −0.533983 0.845495i \(-0.679305\pi\)
−0.533983 + 0.845495i \(0.679305\pi\)
\(798\) −7.02979 −0.248852
\(799\) −6.92275 −0.244909
\(800\) 4.78817 0.169287
\(801\) −27.3395 −0.965993
\(802\) −24.2827 −0.857452
\(803\) −21.2622 −0.750326
\(804\) −36.1542 −1.27506
\(805\) 2.06861 0.0729090
\(806\) 6.12015 0.215573
\(807\) −51.1086 −1.79911
\(808\) −2.57846 −0.0907098
\(809\) 16.5344 0.581320 0.290660 0.956826i \(-0.406125\pi\)
0.290660 + 0.956826i \(0.406125\pi\)
\(810\) 4.37701 0.153792
\(811\) −9.87120 −0.346625 −0.173312 0.984867i \(-0.555447\pi\)
−0.173312 + 0.984867i \(0.555447\pi\)
\(812\) −11.6011 −0.407119
\(813\) −72.2322 −2.53329
\(814\) 19.5201 0.684178
\(815\) 5.91566 0.207216
\(816\) −1.91559 −0.0670592
\(817\) −0.651196 −0.0227825
\(818\) −32.3561 −1.13130
\(819\) −11.1228 −0.388662
\(820\) 0.734020 0.0256331
\(821\) −35.5947 −1.24226 −0.621132 0.783706i \(-0.713327\pi\)
−0.621132 + 0.783706i \(0.713327\pi\)
\(822\) 20.0479 0.699250
\(823\) 0.783110 0.0272975 0.0136488 0.999907i \(-0.495655\pi\)
0.0136488 + 0.999907i \(0.495655\pi\)
\(824\) −11.5301 −0.401671
\(825\) −30.3292 −1.05593
\(826\) 16.9800 0.590811
\(827\) −31.0859 −1.08096 −0.540481 0.841356i \(-0.681758\pi\)
−0.540481 + 0.841356i \(0.681758\pi\)
\(828\) −2.81904 −0.0979683
\(829\) 0.945704 0.0328457 0.0164228 0.999865i \(-0.494772\pi\)
0.0164228 + 0.999865i \(0.494772\pi\)
\(830\) −6.82673 −0.236959
\(831\) −37.4221 −1.29816
\(832\) 0.877859 0.0304343
\(833\) 10.4831 0.363219
\(834\) −1.45875 −0.0505124
\(835\) 7.82812 0.270903
\(836\) −1.70252 −0.0588830
\(837\) −3.04334 −0.105193
\(838\) 4.87191 0.168297
\(839\) 14.8816 0.513768 0.256884 0.966442i \(-0.417304\pi\)
0.256884 + 0.966442i \(0.417304\pi\)
\(840\) −4.99005 −0.172173
\(841\) −22.3377 −0.770267
\(842\) 6.76788 0.233237
\(843\) 45.7314 1.57507
\(844\) −7.08629 −0.243920
\(845\) −5.62852 −0.193627
\(846\) 24.5754 0.844921
\(847\) 18.4505 0.633968
\(848\) 8.84706 0.303809
\(849\) −2.99955 −0.102944
\(850\) 3.80231 0.130418
\(851\) −7.43390 −0.254831
\(852\) 16.4441 0.563365
\(853\) −15.1927 −0.520190 −0.260095 0.965583i \(-0.583754\pi\)
−0.260095 + 0.965583i \(0.583754\pi\)
\(854\) 17.0209 0.582442
\(855\) 0.841240 0.0287698
\(856\) 0.677536 0.0231577
\(857\) −16.3065 −0.557018 −0.278509 0.960434i \(-0.589840\pi\)
−0.278509 + 0.960434i \(0.589840\pi\)
\(858\) −5.56052 −0.189833
\(859\) 36.4736 1.24446 0.622232 0.782833i \(-0.286226\pi\)
0.622232 + 0.782833i \(0.286226\pi\)
\(860\) −0.462247 −0.0157625
\(861\) 17.2914 0.589291
\(862\) −17.4799 −0.595367
\(863\) −35.0893 −1.19445 −0.597227 0.802072i \(-0.703731\pi\)
−0.597227 + 0.802072i \(0.703731\pi\)
\(864\) −0.436529 −0.0148510
\(865\) 5.42551 0.184473
\(866\) 10.8029 0.367096
\(867\) 39.4874 1.34106
\(868\) 31.3347 1.06357
\(869\) 31.0457 1.05315
\(870\) 2.86568 0.0971556
\(871\) 13.1570 0.445809
\(872\) −13.4069 −0.454015
\(873\) −11.2326 −0.380166
\(874\) 0.648378 0.0219317
\(875\) 20.2479 0.684506
\(876\) −19.5330 −0.659958
\(877\) 6.29673 0.212626 0.106313 0.994333i \(-0.466096\pi\)
0.106313 + 0.994333i \(0.466096\pi\)
\(878\) 25.7481 0.868956
\(879\) −6.83220 −0.230444
\(880\) −1.20853 −0.0407394
\(881\) 2.75278 0.0927434 0.0463717 0.998924i \(-0.485234\pi\)
0.0463717 + 0.998924i \(0.485234\pi\)
\(882\) −37.2147 −1.25308
\(883\) −43.4094 −1.46084 −0.730422 0.682996i \(-0.760677\pi\)
−0.730422 + 0.682996i \(0.760677\pi\)
\(884\) 0.697112 0.0234464
\(885\) −4.19436 −0.140992
\(886\) 1.98805 0.0667900
\(887\) 50.3513 1.69063 0.845315 0.534268i \(-0.179413\pi\)
0.845315 + 0.534268i \(0.179413\pi\)
\(888\) 17.9326 0.601777
\(889\) −29.6940 −0.995905
\(890\) 4.46355 0.149618
\(891\) 24.9719 0.836591
\(892\) −26.3899 −0.883598
\(893\) −5.65235 −0.189149
\(894\) −5.27342 −0.176370
\(895\) −9.58870 −0.320515
\(896\) 4.49457 0.150153
\(897\) 2.11763 0.0707057
\(898\) 30.6524 1.02289
\(899\) −17.9948 −0.600162
\(900\) −13.4980 −0.449935
\(901\) 7.02549 0.234053
\(902\) 4.18776 0.139437
\(903\) −10.8892 −0.362371
\(904\) 2.04836 0.0681274
\(905\) −3.16410 −0.105178
\(906\) −37.0088 −1.22953
\(907\) 29.2600 0.971562 0.485781 0.874080i \(-0.338535\pi\)
0.485781 + 0.874080i \(0.338535\pi\)
\(908\) 12.4452 0.413008
\(909\) 7.26877 0.241090
\(910\) 1.81595 0.0601982
\(911\) −19.1451 −0.634307 −0.317153 0.948374i \(-0.602727\pi\)
−0.317153 + 0.948374i \(0.602727\pi\)
\(912\) −1.56406 −0.0517913
\(913\) −38.9482 −1.28900
\(914\) 15.4859 0.512229
\(915\) −4.20445 −0.138995
\(916\) 4.70486 0.155453
\(917\) 4.49457 0.148424
\(918\) −0.346650 −0.0114412
\(919\) −24.2888 −0.801214 −0.400607 0.916250i \(-0.631201\pi\)
−0.400607 + 0.916250i \(0.631201\pi\)
\(920\) 0.460247 0.0151739
\(921\) 20.4407 0.673543
\(922\) 29.4029 0.968334
\(923\) −5.98425 −0.196974
\(924\) −28.4695 −0.936576
\(925\) −35.5948 −1.17035
\(926\) 27.9058 0.917042
\(927\) 32.5039 1.06757
\(928\) −2.58114 −0.0847299
\(929\) −4.87805 −0.160044 −0.0800218 0.996793i \(-0.525499\pi\)
−0.0800218 + 0.996793i \(0.525499\pi\)
\(930\) −7.74022 −0.253812
\(931\) 8.55937 0.280522
\(932\) 0.200287 0.00656061
\(933\) 71.9160 2.35442
\(934\) 20.3053 0.664409
\(935\) −0.959696 −0.0313854
\(936\) −2.47472 −0.0808887
\(937\) 11.8812 0.388142 0.194071 0.980988i \(-0.437831\pi\)
0.194071 + 0.980988i \(0.437831\pi\)
\(938\) 67.3630 2.19948
\(939\) −28.6205 −0.933994
\(940\) −4.01228 −0.130866
\(941\) −8.35763 −0.272451 −0.136225 0.990678i \(-0.543497\pi\)
−0.136225 + 0.990678i \(0.543497\pi\)
\(942\) −26.8157 −0.873704
\(943\) −1.59484 −0.0519351
\(944\) 3.77789 0.122960
\(945\) −0.903010 −0.0293749
\(946\) −2.63723 −0.0857438
\(947\) 42.1854 1.37084 0.685420 0.728148i \(-0.259619\pi\)
0.685420 + 0.728148i \(0.259619\pi\)
\(948\) 28.5209 0.926315
\(949\) 7.10833 0.230746
\(950\) 3.10455 0.100725
\(951\) 68.6056 2.22469
\(952\) 3.56916 0.115677
\(953\) 10.8419 0.351202 0.175601 0.984461i \(-0.443813\pi\)
0.175601 + 0.984461i \(0.443813\pi\)
\(954\) −24.9402 −0.807469
\(955\) 7.88085 0.255018
\(956\) 18.1759 0.587852
\(957\) 16.3494 0.528501
\(958\) 12.9549 0.418554
\(959\) −37.3535 −1.20621
\(960\) −1.11024 −0.0358328
\(961\) 17.6043 0.567880
\(962\) −6.52592 −0.210404
\(963\) −1.91000 −0.0615489
\(964\) −17.1104 −0.551088
\(965\) 10.1696 0.327371
\(966\) 10.8421 0.348839
\(967\) −57.4506 −1.84749 −0.923743 0.383014i \(-0.874886\pi\)
−0.923743 + 0.383014i \(0.874886\pi\)
\(968\) 4.10507 0.131942
\(969\) −1.24203 −0.0398997
\(970\) 1.83388 0.0588822
\(971\) −20.9322 −0.671747 −0.335874 0.941907i \(-0.609032\pi\)
−0.335874 + 0.941907i \(0.609032\pi\)
\(972\) 21.6314 0.693828
\(973\) 2.71796 0.0871339
\(974\) 27.1150 0.868821
\(975\) 10.1396 0.324727
\(976\) 3.78698 0.121218
\(977\) −19.0775 −0.610345 −0.305172 0.952297i \(-0.598714\pi\)
−0.305172 + 0.952297i \(0.598714\pi\)
\(978\) 31.0054 0.991444
\(979\) 25.4656 0.813885
\(980\) 6.07581 0.194085
\(981\) 37.7945 1.20669
\(982\) 10.5565 0.336870
\(983\) 1.24712 0.0397768 0.0198884 0.999802i \(-0.493669\pi\)
0.0198884 + 0.999802i \(0.493669\pi\)
\(984\) 3.84718 0.122644
\(985\) −1.96576 −0.0626342
\(986\) −2.04969 −0.0652755
\(987\) −94.5180 −3.00854
\(988\) 0.569185 0.0181082
\(989\) 1.00435 0.0319364
\(990\) 3.40688 0.108278
\(991\) 52.3126 1.66177 0.830883 0.556447i \(-0.187836\pi\)
0.830883 + 0.556447i \(0.187836\pi\)
\(992\) 6.97168 0.221351
\(993\) −41.5647 −1.31902
\(994\) −30.6389 −0.971806
\(995\) 8.74949 0.277378
\(996\) −35.7806 −1.13375
\(997\) 46.5551 1.47441 0.737207 0.675666i \(-0.236144\pi\)
0.737207 + 0.675666i \(0.236144\pi\)
\(998\) 11.9256 0.377500
\(999\) 3.24511 0.102671
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 \(a_p\))