Properties

Label 6001.2.a.b.1.8
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56595 q^{2}\) \(+1.01181 q^{3}\) \(+4.58410 q^{4}\) \(+2.09874 q^{5}\) \(-2.59626 q^{6}\) \(+3.20271 q^{7}\) \(-6.63067 q^{8}\) \(-1.97623 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56595 q^{2}\) \(+1.01181 q^{3}\) \(+4.58410 q^{4}\) \(+2.09874 q^{5}\) \(-2.59626 q^{6}\) \(+3.20271 q^{7}\) \(-6.63067 q^{8}\) \(-1.97623 q^{9}\) \(-5.38525 q^{10}\) \(-3.82268 q^{11}\) \(+4.63825 q^{12}\) \(+3.94710 q^{13}\) \(-8.21799 q^{14}\) \(+2.12353 q^{15}\) \(+7.84578 q^{16}\) \(+1.00000 q^{17}\) \(+5.07092 q^{18}\) \(-1.67377 q^{19}\) \(+9.62082 q^{20}\) \(+3.24054 q^{21}\) \(+9.80881 q^{22}\) \(-6.51560 q^{23}\) \(-6.70900 q^{24}\) \(-0.595305 q^{25}\) \(-10.1281 q^{26}\) \(-5.03502 q^{27}\) \(+14.6815 q^{28}\) \(-7.47480 q^{29}\) \(-5.44887 q^{30}\) \(+5.60264 q^{31}\) \(-6.87052 q^{32}\) \(-3.86784 q^{33}\) \(-2.56595 q^{34}\) \(+6.72164 q^{35}\) \(-9.05926 q^{36}\) \(-0.965190 q^{37}\) \(+4.29482 q^{38}\) \(+3.99373 q^{39}\) \(-13.9160 q^{40}\) \(-1.71017 q^{41}\) \(-8.31506 q^{42}\) \(-5.00992 q^{43}\) \(-17.5236 q^{44}\) \(-4.14760 q^{45}\) \(+16.7187 q^{46}\) \(-8.53728 q^{47}\) \(+7.93846 q^{48}\) \(+3.25733 q^{49}\) \(+1.52752 q^{50}\) \(+1.01181 q^{51}\) \(+18.0939 q^{52}\) \(-1.22573 q^{53}\) \(+12.9196 q^{54}\) \(-8.02280 q^{55}\) \(-21.2361 q^{56}\) \(-1.69354 q^{57}\) \(+19.1800 q^{58}\) \(+12.4681 q^{59}\) \(+9.73447 q^{60}\) \(-4.75996 q^{61}\) \(-14.3761 q^{62}\) \(-6.32930 q^{63}\) \(+1.93787 q^{64}\) \(+8.28392 q^{65}\) \(+9.92468 q^{66}\) \(+10.3637 q^{67}\) \(+4.58410 q^{68}\) \(-6.59257 q^{69}\) \(-17.2474 q^{70}\) \(-0.894207 q^{71}\) \(+13.1038 q^{72}\) \(+2.09406 q^{73}\) \(+2.47663 q^{74}\) \(-0.602337 q^{75}\) \(-7.67274 q^{76}\) \(-12.2429 q^{77}\) \(-10.2477 q^{78}\) \(-8.36190 q^{79}\) \(+16.4662 q^{80}\) \(+0.834207 q^{81}\) \(+4.38820 q^{82}\) \(-9.04787 q^{83}\) \(+14.8550 q^{84}\) \(+2.09874 q^{85}\) \(+12.8552 q^{86}\) \(-7.56310 q^{87}\) \(+25.3470 q^{88}\) \(+1.32155 q^{89}\) \(+10.6425 q^{90}\) \(+12.6414 q^{91}\) \(-29.8682 q^{92}\) \(+5.66882 q^{93}\) \(+21.9062 q^{94}\) \(-3.51281 q^{95}\) \(-6.95169 q^{96}\) \(-0.597503 q^{97}\) \(-8.35814 q^{98}\) \(+7.55452 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56595 −1.81440 −0.907200 0.420699i \(-0.861785\pi\)
−0.907200 + 0.420699i \(0.861785\pi\)
\(3\) 1.01181 0.584170 0.292085 0.956392i \(-0.405651\pi\)
0.292085 + 0.956392i \(0.405651\pi\)
\(4\) 4.58410 2.29205
\(5\) 2.09874 0.938584 0.469292 0.883043i \(-0.344509\pi\)
0.469292 + 0.883043i \(0.344509\pi\)
\(6\) −2.59626 −1.05992
\(7\) 3.20271 1.21051 0.605255 0.796032i \(-0.293071\pi\)
0.605255 + 0.796032i \(0.293071\pi\)
\(8\) −6.63067 −2.34430
\(9\) −1.97623 −0.658745
\(10\) −5.38525 −1.70297
\(11\) −3.82268 −1.15258 −0.576291 0.817245i \(-0.695500\pi\)
−0.576291 + 0.817245i \(0.695500\pi\)
\(12\) 4.63825 1.33895
\(13\) 3.94710 1.09473 0.547364 0.836894i \(-0.315631\pi\)
0.547364 + 0.836894i \(0.315631\pi\)
\(14\) −8.21799 −2.19635
\(15\) 2.12353 0.548293
\(16\) 7.84578 1.96144
\(17\) 1.00000 0.242536
\(18\) 5.07092 1.19523
\(19\) −1.67377 −0.383990 −0.191995 0.981396i \(-0.561496\pi\)
−0.191995 + 0.981396i \(0.561496\pi\)
\(20\) 9.62082 2.15128
\(21\) 3.24054 0.707144
\(22\) 9.80881 2.09125
\(23\) −6.51560 −1.35860 −0.679298 0.733862i \(-0.737716\pi\)
−0.679298 + 0.733862i \(0.737716\pi\)
\(24\) −6.70900 −1.36947
\(25\) −0.595305 −0.119061
\(26\) −10.1281 −1.98628
\(27\) −5.03502 −0.968990
\(28\) 14.6815 2.77455
\(29\) −7.47480 −1.38804 −0.694018 0.719958i \(-0.744161\pi\)
−0.694018 + 0.719958i \(0.744161\pi\)
\(30\) −5.44887 −0.994823
\(31\) 5.60264 1.00626 0.503132 0.864210i \(-0.332181\pi\)
0.503132 + 0.864210i \(0.332181\pi\)
\(32\) −6.87052 −1.21455
\(33\) −3.86784 −0.673304
\(34\) −2.56595 −0.440057
\(35\) 6.72164 1.13616
\(36\) −9.05926 −1.50988
\(37\) −0.965190 −0.158676 −0.0793381 0.996848i \(-0.525281\pi\)
−0.0793381 + 0.996848i \(0.525281\pi\)
\(38\) 4.29482 0.696711
\(39\) 3.99373 0.639508
\(40\) −13.9160 −2.20032
\(41\) −1.71017 −0.267083 −0.133542 0.991043i \(-0.542635\pi\)
−0.133542 + 0.991043i \(0.542635\pi\)
\(42\) −8.31506 −1.28304
\(43\) −5.00992 −0.764005 −0.382003 0.924161i \(-0.624766\pi\)
−0.382003 + 0.924161i \(0.624766\pi\)
\(44\) −17.5236 −2.64178
\(45\) −4.14760 −0.618287
\(46\) 16.7187 2.46504
\(47\) −8.53728 −1.24529 −0.622645 0.782504i \(-0.713942\pi\)
−0.622645 + 0.782504i \(0.713942\pi\)
\(48\) 7.93846 1.14582
\(49\) 3.25733 0.465333
\(50\) 1.52752 0.216024
\(51\) 1.01181 0.141682
\(52\) 18.0939 2.50917
\(53\) −1.22573 −0.168367 −0.0841836 0.996450i \(-0.526828\pi\)
−0.0841836 + 0.996450i \(0.526828\pi\)
\(54\) 12.9196 1.75814
\(55\) −8.02280 −1.08179
\(56\) −21.2361 −2.83779
\(57\) −1.69354 −0.224315
\(58\) 19.1800 2.51845
\(59\) 12.4681 1.62321 0.811605 0.584207i \(-0.198594\pi\)
0.811605 + 0.584207i \(0.198594\pi\)
\(60\) 9.73447 1.25671
\(61\) −4.75996 −0.609450 −0.304725 0.952440i \(-0.598565\pi\)
−0.304725 + 0.952440i \(0.598565\pi\)
\(62\) −14.3761 −1.82577
\(63\) −6.32930 −0.797417
\(64\) 1.93787 0.242234
\(65\) 8.28392 1.02749
\(66\) 9.92468 1.22164
\(67\) 10.3637 1.26613 0.633063 0.774101i \(-0.281798\pi\)
0.633063 + 0.774101i \(0.281798\pi\)
\(68\) 4.58410 0.555904
\(69\) −6.59257 −0.793652
\(70\) −17.2474 −2.06146
\(71\) −0.894207 −0.106123 −0.0530614 0.998591i \(-0.516898\pi\)
−0.0530614 + 0.998591i \(0.516898\pi\)
\(72\) 13.1038 1.54429
\(73\) 2.09406 0.245091 0.122546 0.992463i \(-0.460894\pi\)
0.122546 + 0.992463i \(0.460894\pi\)
\(74\) 2.47663 0.287902
\(75\) −0.602337 −0.0695519
\(76\) −7.67274 −0.880124
\(77\) −12.2429 −1.39521
\(78\) −10.2477 −1.16032
\(79\) −8.36190 −0.940788 −0.470394 0.882457i \(-0.655888\pi\)
−0.470394 + 0.882457i \(0.655888\pi\)
\(80\) 16.4662 1.84098
\(81\) 0.834207 0.0926897
\(82\) 4.38820 0.484596
\(83\) −9.04787 −0.993133 −0.496566 0.867999i \(-0.665406\pi\)
−0.496566 + 0.867999i \(0.665406\pi\)
\(84\) 14.8550 1.62081
\(85\) 2.09874 0.227640
\(86\) 12.8552 1.38621
\(87\) −7.56310 −0.810850
\(88\) 25.3470 2.70199
\(89\) 1.32155 0.140084 0.0700419 0.997544i \(-0.477687\pi\)
0.0700419 + 0.997544i \(0.477687\pi\)
\(90\) 10.6425 1.12182
\(91\) 12.6414 1.32518
\(92\) −29.8682 −3.11397
\(93\) 5.66882 0.587830
\(94\) 21.9062 2.25946
\(95\) −3.51281 −0.360406
\(96\) −6.95169 −0.709503
\(97\) −0.597503 −0.0606672 −0.0303336 0.999540i \(-0.509657\pi\)
−0.0303336 + 0.999540i \(0.509657\pi\)
\(98\) −8.35814 −0.844300
\(99\) 7.55452 0.759257
\(100\) −2.72894 −0.272894
\(101\) −7.55936 −0.752185 −0.376092 0.926582i \(-0.622732\pi\)
−0.376092 + 0.926582i \(0.622732\pi\)
\(102\) −2.59626 −0.257068
\(103\) −0.360037 −0.0354755 −0.0177378 0.999843i \(-0.505646\pi\)
−0.0177378 + 0.999843i \(0.505646\pi\)
\(104\) −26.1719 −2.56637
\(105\) 6.80104 0.663713
\(106\) 3.14517 0.305485
\(107\) 6.53257 0.631527 0.315764 0.948838i \(-0.397739\pi\)
0.315764 + 0.948838i \(0.397739\pi\)
\(108\) −23.0810 −2.22097
\(109\) 15.8041 1.51376 0.756880 0.653554i \(-0.226723\pi\)
0.756880 + 0.653554i \(0.226723\pi\)
\(110\) 20.5861 1.96281
\(111\) −0.976592 −0.0926940
\(112\) 25.1277 2.37435
\(113\) −16.5645 −1.55826 −0.779129 0.626863i \(-0.784339\pi\)
−0.779129 + 0.626863i \(0.784339\pi\)
\(114\) 4.34555 0.406998
\(115\) −13.6745 −1.27516
\(116\) −34.2653 −3.18145
\(117\) −7.80040 −0.721147
\(118\) −31.9926 −2.94515
\(119\) 3.20271 0.293592
\(120\) −14.0804 −1.28536
\(121\) 3.61290 0.328445
\(122\) 12.2138 1.10579
\(123\) −1.73037 −0.156022
\(124\) 25.6831 2.30641
\(125\) −11.7431 −1.05033
\(126\) 16.2407 1.44683
\(127\) −17.6884 −1.56959 −0.784797 0.619753i \(-0.787233\pi\)
−0.784797 + 0.619753i \(0.787233\pi\)
\(128\) 8.76857 0.775039
\(129\) −5.06910 −0.446309
\(130\) −21.2561 −1.86429
\(131\) −5.57770 −0.487326 −0.243663 0.969860i \(-0.578349\pi\)
−0.243663 + 0.969860i \(0.578349\pi\)
\(132\) −17.7306 −1.54325
\(133\) −5.36060 −0.464823
\(134\) −26.5927 −2.29726
\(135\) −10.5672 −0.909478
\(136\) −6.63067 −0.568576
\(137\) 10.3835 0.887121 0.443561 0.896244i \(-0.353715\pi\)
0.443561 + 0.896244i \(0.353715\pi\)
\(138\) 16.9162 1.44000
\(139\) −8.57191 −0.727060 −0.363530 0.931583i \(-0.618429\pi\)
−0.363530 + 0.931583i \(0.618429\pi\)
\(140\) 30.8127 2.60415
\(141\) −8.63813 −0.727462
\(142\) 2.29449 0.192549
\(143\) −15.0885 −1.26176
\(144\) −15.5051 −1.29209
\(145\) −15.6876 −1.30279
\(146\) −5.37325 −0.444694
\(147\) 3.29581 0.271834
\(148\) −4.42453 −0.363694
\(149\) 7.17404 0.587721 0.293860 0.955848i \(-0.405060\pi\)
0.293860 + 0.955848i \(0.405060\pi\)
\(150\) 1.54557 0.126195
\(151\) −0.183450 −0.0149289 −0.00746446 0.999972i \(-0.502376\pi\)
−0.00746446 + 0.999972i \(0.502376\pi\)
\(152\) 11.0982 0.900186
\(153\) −1.97623 −0.159769
\(154\) 31.4147 2.53147
\(155\) 11.7585 0.944463
\(156\) 18.3076 1.46578
\(157\) −11.8164 −0.943049 −0.471524 0.881853i \(-0.656296\pi\)
−0.471524 + 0.881853i \(0.656296\pi\)
\(158\) 21.4562 1.70697
\(159\) −1.24021 −0.0983551
\(160\) −14.4194 −1.13996
\(161\) −20.8676 −1.64459
\(162\) −2.14053 −0.168176
\(163\) −18.0441 −1.41333 −0.706663 0.707550i \(-0.749800\pi\)
−0.706663 + 0.707550i \(0.749800\pi\)
\(164\) −7.83957 −0.612168
\(165\) −8.11757 −0.631952
\(166\) 23.2164 1.80194
\(167\) −19.9628 −1.54477 −0.772383 0.635157i \(-0.780935\pi\)
−0.772383 + 0.635157i \(0.780935\pi\)
\(168\) −21.4870 −1.65775
\(169\) 2.57960 0.198431
\(170\) −5.38525 −0.413030
\(171\) 3.30777 0.252951
\(172\) −22.9660 −1.75114
\(173\) −21.5280 −1.63674 −0.818372 0.574689i \(-0.805123\pi\)
−0.818372 + 0.574689i \(0.805123\pi\)
\(174\) 19.4065 1.47121
\(175\) −1.90659 −0.144124
\(176\) −29.9919 −2.26072
\(177\) 12.6154 0.948231
\(178\) −3.39103 −0.254168
\(179\) 6.95315 0.519703 0.259851 0.965649i \(-0.416326\pi\)
0.259851 + 0.965649i \(0.416326\pi\)
\(180\) −19.0130 −1.41715
\(181\) −10.9817 −0.816265 −0.408133 0.912923i \(-0.633820\pi\)
−0.408133 + 0.912923i \(0.633820\pi\)
\(182\) −32.4372 −2.40441
\(183\) −4.81618 −0.356023
\(184\) 43.2028 3.18495
\(185\) −2.02568 −0.148931
\(186\) −14.5459 −1.06656
\(187\) −3.82268 −0.279542
\(188\) −39.1358 −2.85427
\(189\) −16.1257 −1.17297
\(190\) 9.01369 0.653922
\(191\) −8.89162 −0.643375 −0.321688 0.946846i \(-0.604250\pi\)
−0.321688 + 0.946846i \(0.604250\pi\)
\(192\) 1.96076 0.141506
\(193\) −5.65444 −0.407015 −0.203508 0.979073i \(-0.565234\pi\)
−0.203508 + 0.979073i \(0.565234\pi\)
\(194\) 1.53316 0.110075
\(195\) 8.38178 0.600232
\(196\) 14.9319 1.06657
\(197\) 12.9768 0.924556 0.462278 0.886735i \(-0.347032\pi\)
0.462278 + 0.886735i \(0.347032\pi\)
\(198\) −19.3845 −1.37760
\(199\) 17.3327 1.22868 0.614340 0.789041i \(-0.289422\pi\)
0.614340 + 0.789041i \(0.289422\pi\)
\(200\) 3.94727 0.279114
\(201\) 10.4861 0.739633
\(202\) 19.3969 1.36476
\(203\) −23.9396 −1.68023
\(204\) 4.63825 0.324743
\(205\) −3.58919 −0.250680
\(206\) 0.923838 0.0643669
\(207\) 12.8764 0.894969
\(208\) 30.9681 2.14725
\(209\) 6.39830 0.442580
\(210\) −17.4511 −1.20424
\(211\) 11.3135 0.778855 0.389428 0.921057i \(-0.372673\pi\)
0.389428 + 0.921057i \(0.372673\pi\)
\(212\) −5.61888 −0.385906
\(213\) −0.904770 −0.0619938
\(214\) −16.7622 −1.14584
\(215\) −10.5145 −0.717083
\(216\) 33.3856 2.27160
\(217\) 17.9436 1.21809
\(218\) −40.5526 −2.74657
\(219\) 2.11880 0.143175
\(220\) −36.7773 −2.47953
\(221\) 3.94710 0.265511
\(222\) 2.50589 0.168184
\(223\) 11.5423 0.772927 0.386464 0.922305i \(-0.373696\pi\)
0.386464 + 0.922305i \(0.373696\pi\)
\(224\) −22.0043 −1.47022
\(225\) 1.17646 0.0784308
\(226\) 42.5037 2.82731
\(227\) −4.31227 −0.286215 −0.143108 0.989707i \(-0.545710\pi\)
−0.143108 + 0.989707i \(0.545710\pi\)
\(228\) −7.76338 −0.514142
\(229\) −23.6117 −1.56031 −0.780153 0.625589i \(-0.784859\pi\)
−0.780153 + 0.625589i \(0.784859\pi\)
\(230\) 35.0882 2.31364
\(231\) −12.3876 −0.815041
\(232\) 49.5630 3.25397
\(233\) 17.7062 1.15997 0.579986 0.814626i \(-0.303058\pi\)
0.579986 + 0.814626i \(0.303058\pi\)
\(234\) 20.0154 1.30845
\(235\) −17.9175 −1.16881
\(236\) 57.1551 3.72048
\(237\) −8.46068 −0.549580
\(238\) −8.21799 −0.532693
\(239\) 6.24485 0.403946 0.201973 0.979391i \(-0.435265\pi\)
0.201973 + 0.979391i \(0.435265\pi\)
\(240\) 16.6607 1.07545
\(241\) 18.3152 1.17979 0.589894 0.807481i \(-0.299169\pi\)
0.589894 + 0.807481i \(0.299169\pi\)
\(242\) −9.27051 −0.595931
\(243\) 15.9491 1.02314
\(244\) −21.8201 −1.39689
\(245\) 6.83627 0.436754
\(246\) 4.44004 0.283086
\(247\) −6.60655 −0.420365
\(248\) −37.1493 −2.35898
\(249\) −9.15475 −0.580159
\(250\) 30.1321 1.90572
\(251\) −18.5827 −1.17293 −0.586465 0.809975i \(-0.699481\pi\)
−0.586465 + 0.809975i \(0.699481\pi\)
\(252\) −29.0141 −1.82772
\(253\) 24.9071 1.56589
\(254\) 45.3876 2.84787
\(255\) 2.12353 0.132981
\(256\) −26.3754 −1.64847
\(257\) 25.6265 1.59854 0.799269 0.600973i \(-0.205220\pi\)
0.799269 + 0.600973i \(0.205220\pi\)
\(258\) 13.0071 0.809784
\(259\) −3.09122 −0.192079
\(260\) 37.9743 2.35507
\(261\) 14.7720 0.914362
\(262\) 14.3121 0.884204
\(263\) 6.44143 0.397196 0.198598 0.980081i \(-0.436361\pi\)
0.198598 + 0.980081i \(0.436361\pi\)
\(264\) 25.6464 1.57843
\(265\) −2.57249 −0.158027
\(266\) 13.7550 0.843376
\(267\) 1.33716 0.0818329
\(268\) 47.5082 2.90202
\(269\) −3.96363 −0.241666 −0.120833 0.992673i \(-0.538557\pi\)
−0.120833 + 0.992673i \(0.538557\pi\)
\(270\) 27.1149 1.65016
\(271\) −1.76321 −0.107107 −0.0535536 0.998565i \(-0.517055\pi\)
−0.0535536 + 0.998565i \(0.517055\pi\)
\(272\) 7.84578 0.475720
\(273\) 12.7907 0.774131
\(274\) −26.6435 −1.60959
\(275\) 2.27566 0.137227
\(276\) −30.2210 −1.81909
\(277\) −7.39485 −0.444314 −0.222157 0.975011i \(-0.571310\pi\)
−0.222157 + 0.975011i \(0.571310\pi\)
\(278\) 21.9951 1.31918
\(279\) −11.0721 −0.662871
\(280\) −44.5690 −2.66351
\(281\) 6.18579 0.369013 0.184507 0.982831i \(-0.440931\pi\)
0.184507 + 0.982831i \(0.440931\pi\)
\(282\) 22.1650 1.31991
\(283\) −19.2937 −1.14689 −0.573446 0.819244i \(-0.694394\pi\)
−0.573446 + 0.819244i \(0.694394\pi\)
\(284\) −4.09914 −0.243239
\(285\) −3.55430 −0.210539
\(286\) 38.7164 2.28935
\(287\) −5.47716 −0.323306
\(288\) 13.5778 0.800078
\(289\) 1.00000 0.0588235
\(290\) 40.2537 2.36378
\(291\) −0.604561 −0.0354400
\(292\) 9.59938 0.561761
\(293\) 20.8941 1.22065 0.610324 0.792152i \(-0.291039\pi\)
0.610324 + 0.792152i \(0.291039\pi\)
\(294\) −8.45688 −0.493215
\(295\) 26.1673 1.52352
\(296\) 6.39986 0.371984
\(297\) 19.2473 1.11684
\(298\) −18.4082 −1.06636
\(299\) −25.7177 −1.48729
\(300\) −2.76117 −0.159416
\(301\) −16.0453 −0.924836
\(302\) 0.470723 0.0270870
\(303\) −7.64866 −0.439404
\(304\) −13.1320 −0.753174
\(305\) −9.98989 −0.572020
\(306\) 5.07092 0.289885
\(307\) −8.83425 −0.504198 −0.252099 0.967702i \(-0.581121\pi\)
−0.252099 + 0.967702i \(0.581121\pi\)
\(308\) −56.1228 −3.19789
\(309\) −0.364291 −0.0207238
\(310\) −30.1716 −1.71363
\(311\) −7.75695 −0.439857 −0.219928 0.975516i \(-0.570582\pi\)
−0.219928 + 0.975516i \(0.570582\pi\)
\(312\) −26.4811 −1.49920
\(313\) −17.0734 −0.965048 −0.482524 0.875883i \(-0.660280\pi\)
−0.482524 + 0.875883i \(0.660280\pi\)
\(314\) 30.3202 1.71107
\(315\) −13.2835 −0.748442
\(316\) −38.3318 −2.15633
\(317\) 0.765824 0.0430129 0.0215065 0.999769i \(-0.493154\pi\)
0.0215065 + 0.999769i \(0.493154\pi\)
\(318\) 3.18232 0.178456
\(319\) 28.5738 1.59983
\(320\) 4.06708 0.227357
\(321\) 6.60974 0.368920
\(322\) 53.5451 2.98395
\(323\) −1.67377 −0.0931312
\(324\) 3.82409 0.212449
\(325\) −2.34973 −0.130339
\(326\) 46.3004 2.56434
\(327\) 15.9908 0.884294
\(328\) 11.3396 0.626122
\(329\) −27.3424 −1.50744
\(330\) 20.8293 1.14661
\(331\) 23.0643 1.26773 0.633864 0.773445i \(-0.281468\pi\)
0.633864 + 0.773445i \(0.281468\pi\)
\(332\) −41.4763 −2.27631
\(333\) 1.90744 0.104527
\(334\) 51.2235 2.80283
\(335\) 21.7506 1.18836
\(336\) 25.4245 1.38702
\(337\) −3.46411 −0.188702 −0.0943509 0.995539i \(-0.530078\pi\)
−0.0943509 + 0.995539i \(0.530078\pi\)
\(338\) −6.61914 −0.360034
\(339\) −16.7602 −0.910289
\(340\) 9.62082 0.521762
\(341\) −21.4171 −1.15980
\(342\) −8.48757 −0.458955
\(343\) −11.9867 −0.647220
\(344\) 33.2191 1.79106
\(345\) −13.8361 −0.744909
\(346\) 55.2398 2.96971
\(347\) 27.7595 1.49021 0.745104 0.666948i \(-0.232400\pi\)
0.745104 + 0.666948i \(0.232400\pi\)
\(348\) −34.6700 −1.85851
\(349\) −3.75441 −0.200969 −0.100485 0.994939i \(-0.532039\pi\)
−0.100485 + 0.994939i \(0.532039\pi\)
\(350\) 4.89221 0.261499
\(351\) −19.8737 −1.06078
\(352\) 26.2638 1.39987
\(353\) 1.00000 0.0532246
\(354\) −32.3705 −1.72047
\(355\) −1.87671 −0.0996052
\(356\) 6.05811 0.321079
\(357\) 3.24054 0.171508
\(358\) −17.8414 −0.942949
\(359\) 23.5434 1.24257 0.621287 0.783583i \(-0.286610\pi\)
0.621287 + 0.783583i \(0.286610\pi\)
\(360\) 27.5014 1.44945
\(361\) −16.1985 −0.852552
\(362\) 28.1786 1.48103
\(363\) 3.65557 0.191868
\(364\) 57.9495 3.03738
\(365\) 4.39488 0.230039
\(366\) 12.3581 0.645968
\(367\) −2.59748 −0.135587 −0.0677935 0.997699i \(-0.521596\pi\)
−0.0677935 + 0.997699i \(0.521596\pi\)
\(368\) −51.1199 −2.66481
\(369\) 3.37969 0.175940
\(370\) 5.19779 0.270220
\(371\) −3.92566 −0.203810
\(372\) 25.9865 1.34733
\(373\) 13.5699 0.702624 0.351312 0.936258i \(-0.385736\pi\)
0.351312 + 0.936258i \(0.385736\pi\)
\(374\) 9.80881 0.507202
\(375\) −11.8818 −0.613573
\(376\) 56.6079 2.91933
\(377\) −29.5038 −1.51952
\(378\) 41.3777 2.12824
\(379\) 11.2451 0.577620 0.288810 0.957386i \(-0.406740\pi\)
0.288810 + 0.957386i \(0.406740\pi\)
\(380\) −16.1031 −0.826070
\(381\) −17.8974 −0.916911
\(382\) 22.8155 1.16734
\(383\) −18.0813 −0.923911 −0.461956 0.886903i \(-0.652852\pi\)
−0.461956 + 0.886903i \(0.652852\pi\)
\(384\) 8.87215 0.452755
\(385\) −25.6947 −1.30952
\(386\) 14.5090 0.738489
\(387\) 9.90078 0.503285
\(388\) −2.73901 −0.139052
\(389\) −30.4014 −1.54141 −0.770705 0.637192i \(-0.780096\pi\)
−0.770705 + 0.637192i \(0.780096\pi\)
\(390\) −21.5072 −1.08906
\(391\) −6.51560 −0.329508
\(392\) −21.5983 −1.09088
\(393\) −5.64359 −0.284681
\(394\) −33.2977 −1.67752
\(395\) −17.5494 −0.883008
\(396\) 34.6307 1.74026
\(397\) 11.9092 0.597704 0.298852 0.954299i \(-0.403396\pi\)
0.298852 + 0.954299i \(0.403396\pi\)
\(398\) −44.4748 −2.22932
\(399\) −5.42393 −0.271536
\(400\) −4.67063 −0.233531
\(401\) 26.7870 1.33768 0.668840 0.743406i \(-0.266791\pi\)
0.668840 + 0.743406i \(0.266791\pi\)
\(402\) −26.9068 −1.34199
\(403\) 22.1142 1.10159
\(404\) −34.6529 −1.72405
\(405\) 1.75078 0.0869970
\(406\) 61.4278 3.04861
\(407\) 3.68961 0.182887
\(408\) −6.70900 −0.332145
\(409\) 20.5877 1.01800 0.508998 0.860768i \(-0.330016\pi\)
0.508998 + 0.860768i \(0.330016\pi\)
\(410\) 9.20968 0.454834
\(411\) 10.5061 0.518230
\(412\) −1.65045 −0.0813117
\(413\) 39.9317 1.96491
\(414\) −33.0401 −1.62383
\(415\) −18.9891 −0.932138
\(416\) −27.1187 −1.32960
\(417\) −8.67317 −0.424727
\(418\) −16.4177 −0.803017
\(419\) 9.73118 0.475399 0.237700 0.971339i \(-0.423607\pi\)
0.237700 + 0.971339i \(0.423607\pi\)
\(420\) 31.1766 1.52126
\(421\) 14.9330 0.727789 0.363895 0.931440i \(-0.381447\pi\)
0.363895 + 0.931440i \(0.381447\pi\)
\(422\) −29.0299 −1.41316
\(423\) 16.8717 0.820329
\(424\) 8.12742 0.394703
\(425\) −0.595305 −0.0288765
\(426\) 2.32160 0.112482
\(427\) −15.2447 −0.737745
\(428\) 29.9460 1.44749
\(429\) −15.2667 −0.737086
\(430\) 26.9797 1.30108
\(431\) −32.2126 −1.55163 −0.775814 0.630962i \(-0.782660\pi\)
−0.775814 + 0.630962i \(0.782660\pi\)
\(432\) −39.5036 −1.90062
\(433\) 33.4394 1.60699 0.803497 0.595309i \(-0.202970\pi\)
0.803497 + 0.595309i \(0.202970\pi\)
\(434\) −46.0424 −2.21011
\(435\) −15.8730 −0.761050
\(436\) 72.4477 3.46961
\(437\) 10.9056 0.521687
\(438\) −5.43673 −0.259777
\(439\) 1.51622 0.0723653 0.0361826 0.999345i \(-0.488480\pi\)
0.0361826 + 0.999345i \(0.488480\pi\)
\(440\) 53.1966 2.53605
\(441\) −6.43725 −0.306536
\(442\) −10.1281 −0.481743
\(443\) −18.9931 −0.902388 −0.451194 0.892426i \(-0.649002\pi\)
−0.451194 + 0.892426i \(0.649002\pi\)
\(444\) −4.47679 −0.212459
\(445\) 2.77358 0.131480
\(446\) −29.6169 −1.40240
\(447\) 7.25879 0.343329
\(448\) 6.20644 0.293227
\(449\) 21.6013 1.01943 0.509715 0.860343i \(-0.329751\pi\)
0.509715 + 0.860343i \(0.329751\pi\)
\(450\) −3.01874 −0.142305
\(451\) 6.53742 0.307835
\(452\) −75.9334 −3.57161
\(453\) −0.185617 −0.00872103
\(454\) 11.0651 0.519309
\(455\) 26.5310 1.24379
\(456\) 11.2293 0.525862
\(457\) −2.15994 −0.101038 −0.0505188 0.998723i \(-0.516087\pi\)
−0.0505188 + 0.998723i \(0.516087\pi\)
\(458\) 60.5865 2.83102
\(459\) −5.03502 −0.235015
\(460\) −62.6854 −2.92272
\(461\) −2.17997 −0.101531 −0.0507657 0.998711i \(-0.516166\pi\)
−0.0507657 + 0.998711i \(0.516166\pi\)
\(462\) 31.7858 1.47881
\(463\) 17.2753 0.802852 0.401426 0.915892i \(-0.368515\pi\)
0.401426 + 0.915892i \(0.368515\pi\)
\(464\) −58.6456 −2.72256
\(465\) 11.8974 0.551727
\(466\) −45.4333 −2.10466
\(467\) 6.33017 0.292925 0.146463 0.989216i \(-0.453211\pi\)
0.146463 + 0.989216i \(0.453211\pi\)
\(468\) −35.7578 −1.65291
\(469\) 33.1918 1.53266
\(470\) 45.9754 2.12069
\(471\) −11.9560 −0.550901
\(472\) −82.6720 −3.80529
\(473\) 19.1513 0.880579
\(474\) 21.7097 0.997159
\(475\) 0.996405 0.0457182
\(476\) 14.6815 0.672927
\(477\) 2.42233 0.110911
\(478\) −16.0240 −0.732920
\(479\) −10.1565 −0.464062 −0.232031 0.972708i \(-0.574537\pi\)
−0.232031 + 0.972708i \(0.574537\pi\)
\(480\) −14.5898 −0.665928
\(481\) −3.80970 −0.173707
\(482\) −46.9960 −2.14061
\(483\) −21.1141 −0.960723
\(484\) 16.5619 0.752813
\(485\) −1.25400 −0.0569413
\(486\) −40.9246 −1.85638
\(487\) −14.4559 −0.655060 −0.327530 0.944841i \(-0.606216\pi\)
−0.327530 + 0.944841i \(0.606216\pi\)
\(488\) 31.5617 1.42873
\(489\) −18.2573 −0.825623
\(490\) −17.5415 −0.792446
\(491\) 12.9210 0.583118 0.291559 0.956553i \(-0.405826\pi\)
0.291559 + 0.956553i \(0.405826\pi\)
\(492\) −7.93218 −0.357610
\(493\) −7.47480 −0.336648
\(494\) 16.9521 0.762710
\(495\) 15.8549 0.712627
\(496\) 43.9571 1.97373
\(497\) −2.86388 −0.128463
\(498\) 23.4906 1.05264
\(499\) −7.27621 −0.325728 −0.162864 0.986649i \(-0.552073\pi\)
−0.162864 + 0.986649i \(0.552073\pi\)
\(500\) −53.8314 −2.40741
\(501\) −20.1986 −0.902407
\(502\) 47.6823 2.12817
\(503\) −3.94145 −0.175740 −0.0878702 0.996132i \(-0.528006\pi\)
−0.0878702 + 0.996132i \(0.528006\pi\)
\(504\) 41.9675 1.86938
\(505\) −15.8651 −0.705988
\(506\) −63.9103 −2.84116
\(507\) 2.61008 0.115918
\(508\) −81.0856 −3.59759
\(509\) −3.99573 −0.177108 −0.0885539 0.996071i \(-0.528225\pi\)
−0.0885539 + 0.996071i \(0.528225\pi\)
\(510\) −5.44887 −0.241280
\(511\) 6.70666 0.296685
\(512\) 50.1410 2.21594
\(513\) 8.42748 0.372082
\(514\) −65.7564 −2.90039
\(515\) −0.755624 −0.0332968
\(516\) −23.2373 −1.02296
\(517\) 32.6353 1.43530
\(518\) 7.93192 0.348508
\(519\) −21.7823 −0.956138
\(520\) −54.9280 −2.40875
\(521\) −24.9472 −1.09296 −0.546478 0.837473i \(-0.684032\pi\)
−0.546478 + 0.837473i \(0.684032\pi\)
\(522\) −37.9041 −1.65902
\(523\) −14.6359 −0.639982 −0.319991 0.947421i \(-0.603680\pi\)
−0.319991 + 0.947421i \(0.603680\pi\)
\(524\) −25.5687 −1.11698
\(525\) −1.92911 −0.0841932
\(526\) −16.5284 −0.720672
\(527\) 5.60264 0.244055
\(528\) −30.3462 −1.32065
\(529\) 19.4531 0.845785
\(530\) 6.60087 0.286724
\(531\) −24.6399 −1.06928
\(532\) −24.5735 −1.06540
\(533\) −6.75020 −0.292383
\(534\) −3.43109 −0.148478
\(535\) 13.7101 0.592741
\(536\) −68.7182 −2.96817
\(537\) 7.03528 0.303595
\(538\) 10.1705 0.438480
\(539\) −12.4517 −0.536334
\(540\) −48.4410 −2.08457
\(541\) −29.7724 −1.28002 −0.640008 0.768368i \(-0.721069\pi\)
−0.640008 + 0.768368i \(0.721069\pi\)
\(542\) 4.52430 0.194335
\(543\) −11.1114 −0.476838
\(544\) −6.87052 −0.294571
\(545\) 33.1687 1.42079
\(546\) −32.8204 −1.40458
\(547\) −30.0474 −1.28473 −0.642367 0.766397i \(-0.722047\pi\)
−0.642367 + 0.766397i \(0.722047\pi\)
\(548\) 47.5990 2.03333
\(549\) 9.40679 0.401472
\(550\) −5.83923 −0.248986
\(551\) 12.5111 0.532992
\(552\) 43.7132 1.86056
\(553\) −26.7807 −1.13883
\(554\) 18.9748 0.806163
\(555\) −2.04961 −0.0870011
\(556\) −39.2945 −1.66646
\(557\) 27.6137 1.17003 0.585015 0.811023i \(-0.301089\pi\)
0.585015 + 0.811023i \(0.301089\pi\)
\(558\) 28.4105 1.20271
\(559\) −19.7747 −0.836379
\(560\) 52.7365 2.22852
\(561\) −3.86784 −0.163300
\(562\) −15.8724 −0.669538
\(563\) −9.37010 −0.394903 −0.197451 0.980313i \(-0.563266\pi\)
−0.197451 + 0.980313i \(0.563266\pi\)
\(564\) −39.5981 −1.66738
\(565\) −34.7646 −1.46256
\(566\) 49.5067 2.08092
\(567\) 2.67172 0.112202
\(568\) 5.92920 0.248784
\(569\) −20.7864 −0.871413 −0.435706 0.900089i \(-0.643501\pi\)
−0.435706 + 0.900089i \(0.643501\pi\)
\(570\) 9.12017 0.382002
\(571\) 5.69563 0.238355 0.119177 0.992873i \(-0.461974\pi\)
0.119177 + 0.992873i \(0.461974\pi\)
\(572\) −69.1672 −2.89203
\(573\) −8.99666 −0.375841
\(574\) 14.0541 0.586608
\(575\) 3.87877 0.161756
\(576\) −3.82969 −0.159570
\(577\) 27.9929 1.16536 0.582680 0.812702i \(-0.302004\pi\)
0.582680 + 0.812702i \(0.302004\pi\)
\(578\) −2.56595 −0.106729
\(579\) −5.72123 −0.237766
\(580\) −71.9137 −2.98606
\(581\) −28.9777 −1.20220
\(582\) 1.55127 0.0643024
\(583\) 4.68558 0.194057
\(584\) −13.8850 −0.574567
\(585\) −16.3710 −0.676857
\(586\) −53.6133 −2.21474
\(587\) −23.4527 −0.967996 −0.483998 0.875069i \(-0.660816\pi\)
−0.483998 + 0.875069i \(0.660816\pi\)
\(588\) 15.1083 0.623056
\(589\) −9.37754 −0.386395
\(590\) −67.1439 −2.76427
\(591\) 13.1301 0.540098
\(592\) −7.57267 −0.311235
\(593\) −3.95682 −0.162487 −0.0812436 0.996694i \(-0.525889\pi\)
−0.0812436 + 0.996694i \(0.525889\pi\)
\(594\) −49.3875 −2.02640
\(595\) 6.72164 0.275560
\(596\) 32.8865 1.34709
\(597\) 17.5374 0.717759
\(598\) 65.9904 2.69855
\(599\) 6.19521 0.253129 0.126565 0.991958i \(-0.459605\pi\)
0.126565 + 0.991958i \(0.459605\pi\)
\(600\) 3.99390 0.163050
\(601\) −35.5100 −1.44849 −0.724243 0.689545i \(-0.757810\pi\)
−0.724243 + 0.689545i \(0.757810\pi\)
\(602\) 41.1714 1.67802
\(603\) −20.4811 −0.834053
\(604\) −0.840952 −0.0342178
\(605\) 7.58252 0.308273
\(606\) 19.6261 0.797255
\(607\) −21.2741 −0.863491 −0.431745 0.901996i \(-0.642102\pi\)
−0.431745 + 0.901996i \(0.642102\pi\)
\(608\) 11.4997 0.466374
\(609\) −24.2224 −0.981541
\(610\) 25.6336 1.03787
\(611\) −33.6975 −1.36326
\(612\) −9.05926 −0.366199
\(613\) 48.8542 1.97320 0.986602 0.163147i \(-0.0521646\pi\)
0.986602 + 0.163147i \(0.0521646\pi\)
\(614\) 22.6683 0.914816
\(615\) −3.63159 −0.146440
\(616\) 81.1789 3.27079
\(617\) 22.5379 0.907343 0.453671 0.891169i \(-0.350114\pi\)
0.453671 + 0.891169i \(0.350114\pi\)
\(618\) 0.934752 0.0376012
\(619\) −11.6098 −0.466637 −0.233319 0.972400i \(-0.574959\pi\)
−0.233319 + 0.972400i \(0.574959\pi\)
\(620\) 53.9020 2.16476
\(621\) 32.8062 1.31647
\(622\) 19.9040 0.798076
\(623\) 4.23253 0.169573
\(624\) 31.3339 1.25436
\(625\) −21.6691 −0.866764
\(626\) 43.8096 1.75098
\(627\) 6.47388 0.258542
\(628\) −54.1674 −2.16151
\(629\) −0.965190 −0.0384846
\(630\) 34.0849 1.35797
\(631\) −38.1165 −1.51739 −0.758697 0.651444i \(-0.774163\pi\)
−0.758697 + 0.651444i \(0.774163\pi\)
\(632\) 55.4450 2.20549
\(633\) 11.4472 0.454984
\(634\) −1.96507 −0.0780427
\(635\) −37.1234 −1.47320
\(636\) −5.68525 −0.225435
\(637\) 12.8570 0.509413
\(638\) −73.3189 −2.90272
\(639\) 1.76716 0.0699079
\(640\) 18.4029 0.727439
\(641\) 5.59627 0.221039 0.110520 0.993874i \(-0.464748\pi\)
0.110520 + 0.993874i \(0.464748\pi\)
\(642\) −16.9603 −0.669368
\(643\) −4.21122 −0.166074 −0.0830372 0.996546i \(-0.526462\pi\)
−0.0830372 + 0.996546i \(0.526462\pi\)
\(644\) −95.6590 −3.76949
\(645\) −10.6387 −0.418899
\(646\) 4.29482 0.168977
\(647\) −0.395315 −0.0155414 −0.00777072 0.999970i \(-0.502474\pi\)
−0.00777072 + 0.999970i \(0.502474\pi\)
\(648\) −5.53136 −0.217292
\(649\) −47.6616 −1.87088
\(650\) 6.02928 0.236488
\(651\) 18.1556 0.711573
\(652\) −82.7161 −3.23941
\(653\) 44.0443 1.72359 0.861794 0.507259i \(-0.169341\pi\)
0.861794 + 0.507259i \(0.169341\pi\)
\(654\) −41.0316 −1.60446
\(655\) −11.7061 −0.457396
\(656\) −13.4176 −0.523868
\(657\) −4.13835 −0.161453
\(658\) 70.1593 2.73509
\(659\) 17.2824 0.673225 0.336613 0.941643i \(-0.390719\pi\)
0.336613 + 0.941643i \(0.390719\pi\)
\(660\) −37.2118 −1.44847
\(661\) 21.1771 0.823694 0.411847 0.911253i \(-0.364884\pi\)
0.411847 + 0.911253i \(0.364884\pi\)
\(662\) −59.1818 −2.30017
\(663\) 3.99373 0.155104
\(664\) 59.9935 2.32820
\(665\) −11.2505 −0.436275
\(666\) −4.89440 −0.189654
\(667\) 48.7028 1.88578
\(668\) −91.5114 −3.54068
\(669\) 11.6786 0.451521
\(670\) −55.8111 −2.15617
\(671\) 18.1958 0.702441
\(672\) −22.2642 −0.858861
\(673\) 46.4973 1.79234 0.896169 0.443713i \(-0.146339\pi\)
0.896169 + 0.443713i \(0.146339\pi\)
\(674\) 8.88872 0.342381
\(675\) 2.99737 0.115369
\(676\) 11.8252 0.454814
\(677\) −13.4314 −0.516210 −0.258105 0.966117i \(-0.583098\pi\)
−0.258105 + 0.966117i \(0.583098\pi\)
\(678\) 43.0058 1.65163
\(679\) −1.91363 −0.0734382
\(680\) −13.9160 −0.533656
\(681\) −4.36321 −0.167199
\(682\) 54.9552 2.10434
\(683\) −46.8820 −1.79389 −0.896944 0.442144i \(-0.854218\pi\)
−0.896944 + 0.442144i \(0.854218\pi\)
\(684\) 15.1631 0.579777
\(685\) 21.7922 0.832637
\(686\) 30.7572 1.17432
\(687\) −23.8906 −0.911485
\(688\) −39.3067 −1.49855
\(689\) −4.83809 −0.184316
\(690\) 35.5027 1.35156
\(691\) 25.5103 0.970458 0.485229 0.874387i \(-0.338736\pi\)
0.485229 + 0.874387i \(0.338736\pi\)
\(692\) −98.6866 −3.75150
\(693\) 24.1949 0.919088
\(694\) −71.2295 −2.70384
\(695\) −17.9902 −0.682406
\(696\) 50.1485 1.90087
\(697\) −1.71017 −0.0647771
\(698\) 9.63363 0.364638
\(699\) 17.9154 0.677622
\(700\) −8.73998 −0.330340
\(701\) 34.9380 1.31959 0.659796 0.751445i \(-0.270643\pi\)
0.659796 + 0.751445i \(0.270643\pi\)
\(702\) 50.9950 1.92468
\(703\) 1.61551 0.0609301
\(704\) −7.40787 −0.279195
\(705\) −18.1292 −0.682784
\(706\) −2.56595 −0.0965708
\(707\) −24.2104 −0.910527
\(708\) 57.8302 2.17339
\(709\) −52.2985 −1.96411 −0.982055 0.188593i \(-0.939607\pi\)
−0.982055 + 0.188593i \(0.939607\pi\)
\(710\) 4.81553 0.180724
\(711\) 16.5251 0.619739
\(712\) −8.76276 −0.328398
\(713\) −36.5046 −1.36711
\(714\) −8.31506 −0.311183
\(715\) −31.6668 −1.18427
\(716\) 31.8739 1.19118
\(717\) 6.31862 0.235973
\(718\) −60.4113 −2.25453
\(719\) −34.0384 −1.26942 −0.634709 0.772751i \(-0.718880\pi\)
−0.634709 + 0.772751i \(0.718880\pi\)
\(720\) −32.5411 −1.21274
\(721\) −1.15309 −0.0429435
\(722\) 41.5645 1.54687
\(723\) 18.5316 0.689197
\(724\) −50.3413 −1.87092
\(725\) 4.44979 0.165261
\(726\) −9.38002 −0.348125
\(727\) 21.3031 0.790087 0.395043 0.918662i \(-0.370730\pi\)
0.395043 + 0.918662i \(0.370730\pi\)
\(728\) −83.8210 −3.10661
\(729\) 13.6349 0.504996
\(730\) −11.2770 −0.417382
\(731\) −5.00992 −0.185299
\(732\) −22.0779 −0.816022
\(733\) −11.5023 −0.424846 −0.212423 0.977178i \(-0.568135\pi\)
−0.212423 + 0.977178i \(0.568135\pi\)
\(734\) 6.66499 0.246009
\(735\) 6.91703 0.255139
\(736\) 44.7656 1.65008
\(737\) −39.6171 −1.45931
\(738\) −8.67211 −0.319225
\(739\) 0.486775 0.0179063 0.00895315 0.999960i \(-0.497150\pi\)
0.00895315 + 0.999960i \(0.497150\pi\)
\(740\) −9.28592 −0.341357
\(741\) −6.68459 −0.245565
\(742\) 10.0730 0.369793
\(743\) 50.4185 1.84967 0.924837 0.380363i \(-0.124201\pi\)
0.924837 + 0.380363i \(0.124201\pi\)
\(744\) −37.5881 −1.37805
\(745\) 15.0564 0.551625
\(746\) −34.8198 −1.27484
\(747\) 17.8807 0.654221
\(748\) −17.5236 −0.640725
\(749\) 20.9219 0.764470
\(750\) 30.4881 1.11327
\(751\) 14.6922 0.536126 0.268063 0.963401i \(-0.413616\pi\)
0.268063 + 0.963401i \(0.413616\pi\)
\(752\) −66.9816 −2.44257
\(753\) −18.8022 −0.685191
\(754\) 75.7053 2.75702
\(755\) −0.385013 −0.0140120
\(756\) −73.9218 −2.68851
\(757\) 3.74182 0.135999 0.0679995 0.997685i \(-0.478338\pi\)
0.0679995 + 0.997685i \(0.478338\pi\)
\(758\) −28.8543 −1.04803
\(759\) 25.2013 0.914749
\(760\) 23.2923 0.844900
\(761\) −12.8138 −0.464501 −0.232251 0.972656i \(-0.574609\pi\)
−0.232251 + 0.972656i \(0.574609\pi\)
\(762\) 45.9238 1.66364
\(763\) 50.6160 1.83242
\(764\) −40.7601 −1.47465
\(765\) −4.14760 −0.149957
\(766\) 46.3957 1.67635
\(767\) 49.2129 1.77697
\(768\) −26.6870 −0.962985
\(769\) 36.5460 1.31788 0.658942 0.752194i \(-0.271004\pi\)
0.658942 + 0.752194i \(0.271004\pi\)
\(770\) 65.9313 2.37600
\(771\) 25.9292 0.933819
\(772\) −25.9205 −0.932900
\(773\) 14.1080 0.507429 0.253714 0.967279i \(-0.418348\pi\)
0.253714 + 0.967279i \(0.418348\pi\)
\(774\) −25.4049 −0.913160
\(775\) −3.33528 −0.119807
\(776\) 3.96185 0.142222
\(777\) −3.12774 −0.112207
\(778\) 78.0084 2.79674
\(779\) 2.86243 0.102557
\(780\) 38.4229 1.37576
\(781\) 3.41827 0.122315
\(782\) 16.7187 0.597860
\(783\) 37.6358 1.34499
\(784\) 25.5563 0.912724
\(785\) −24.7994 −0.885130
\(786\) 14.4812 0.516526
\(787\) 4.85838 0.173182 0.0865912 0.996244i \(-0.472403\pi\)
0.0865912 + 0.996244i \(0.472403\pi\)
\(788\) 59.4868 2.11913
\(789\) 6.51752 0.232030
\(790\) 45.0310 1.60213
\(791\) −53.0513 −1.88629
\(792\) −50.0915 −1.77992
\(793\) −18.7880 −0.667182
\(794\) −30.5583 −1.08447
\(795\) −2.60288 −0.0923145
\(796\) 79.4547 2.81620
\(797\) −14.1119 −0.499870 −0.249935 0.968263i \(-0.580409\pi\)
−0.249935 + 0.968263i \(0.580409\pi\)
\(798\) 13.9175 0.492675
\(799\) −8.53728 −0.302027
\(800\) 4.09006 0.144605
\(801\) −2.61169 −0.0922795
\(802\) −68.7342 −2.42709
\(803\) −8.00493 −0.282488
\(804\) 48.0694 1.69528
\(805\) −43.7955 −1.54359
\(806\) −56.7439 −1.99872
\(807\) −4.01045 −0.141174
\(808\) 50.1237 1.76334
\(809\) −19.2807 −0.677875 −0.338937 0.940809i \(-0.610067\pi\)
−0.338937 + 0.940809i \(0.610067\pi\)
\(810\) −4.49242 −0.157847
\(811\) 14.0200 0.492309 0.246154 0.969231i \(-0.420833\pi\)
0.246154 + 0.969231i \(0.420833\pi\)
\(812\) −109.742 −3.85117
\(813\) −1.78403 −0.0625688
\(814\) −9.46737 −0.331831
\(815\) −37.8699 −1.32652
\(816\) 7.93846 0.277902
\(817\) 8.38546 0.293370
\(818\) −52.8270 −1.84705
\(819\) −24.9824 −0.872955
\(820\) −16.4532 −0.574571
\(821\) −26.1915 −0.914091 −0.457046 0.889443i \(-0.651092\pi\)
−0.457046 + 0.889443i \(0.651092\pi\)
\(822\) −26.9583 −0.940277
\(823\) −56.9821 −1.98627 −0.993135 0.116976i \(-0.962680\pi\)
−0.993135 + 0.116976i \(0.962680\pi\)
\(824\) 2.38729 0.0831652
\(825\) 2.30254 0.0801642
\(826\) −102.463 −3.56514
\(827\) 30.3268 1.05457 0.527284 0.849689i \(-0.323210\pi\)
0.527284 + 0.849689i \(0.323210\pi\)
\(828\) 59.0265 2.05131
\(829\) −4.58829 −0.159358 −0.0796789 0.996821i \(-0.525389\pi\)
−0.0796789 + 0.996821i \(0.525389\pi\)
\(830\) 48.7251 1.69127
\(831\) −7.48221 −0.259555
\(832\) 7.64898 0.265181
\(833\) 3.25733 0.112860
\(834\) 22.2549 0.770625
\(835\) −41.8966 −1.44989
\(836\) 29.3304 1.01441
\(837\) −28.2094 −0.975059
\(838\) −24.9697 −0.862565
\(839\) −10.7495 −0.371113 −0.185557 0.982634i \(-0.559409\pi\)
−0.185557 + 0.982634i \(0.559409\pi\)
\(840\) −45.0955 −1.55594
\(841\) 26.8727 0.926645
\(842\) −38.3173 −1.32050
\(843\) 6.25886 0.215567
\(844\) 51.8623 1.78518
\(845\) 5.41391 0.186244
\(846\) −43.2919 −1.48841
\(847\) 11.5710 0.397586
\(848\) −9.61681 −0.330243
\(849\) −19.5216 −0.669980
\(850\) 1.52752 0.0523936
\(851\) 6.28879 0.215577
\(852\) −4.14756 −0.142093
\(853\) −0.997537 −0.0341550 −0.0170775 0.999854i \(-0.505436\pi\)
−0.0170775 + 0.999854i \(0.505436\pi\)
\(854\) 39.1172 1.33856
\(855\) 6.94213 0.237416
\(856\) −43.3153 −1.48049
\(857\) −17.0553 −0.582598 −0.291299 0.956632i \(-0.594088\pi\)
−0.291299 + 0.956632i \(0.594088\pi\)
\(858\) 39.1737 1.33737
\(859\) 39.4260 1.34520 0.672599 0.740007i \(-0.265178\pi\)
0.672599 + 0.740007i \(0.265178\pi\)
\(860\) −48.1995 −1.64359
\(861\) −5.54186 −0.188866
\(862\) 82.6560 2.81527
\(863\) −2.61746 −0.0890994 −0.0445497 0.999007i \(-0.514185\pi\)
−0.0445497 + 0.999007i \(0.514185\pi\)
\(864\) 34.5932 1.17689
\(865\) −45.1816 −1.53622
\(866\) −85.8037 −2.91573
\(867\) 1.01181 0.0343630
\(868\) 82.2553 2.79193
\(869\) 31.9649 1.08433
\(870\) 40.7292 1.38085
\(871\) 40.9065 1.38606
\(872\) −104.792 −3.54870
\(873\) 1.18081 0.0399642
\(874\) −27.9833 −0.946550
\(875\) −37.6096 −1.27144
\(876\) 9.71278 0.328164
\(877\) −42.9635 −1.45077 −0.725386 0.688342i \(-0.758339\pi\)
−0.725386 + 0.688342i \(0.758339\pi\)
\(878\) −3.89055 −0.131300
\(879\) 21.1409 0.713066
\(880\) −62.9451 −2.12188
\(881\) −35.3031 −1.18939 −0.594696 0.803951i \(-0.702727\pi\)
−0.594696 + 0.803951i \(0.702727\pi\)
\(882\) 16.5177 0.556178
\(883\) 48.6272 1.63644 0.818218 0.574908i \(-0.194962\pi\)
0.818218 + 0.574908i \(0.194962\pi\)
\(884\) 18.0939 0.608564
\(885\) 26.4764 0.889994
\(886\) 48.7353 1.63729
\(887\) 52.5407 1.76415 0.882073 0.471113i \(-0.156148\pi\)
0.882073 + 0.471113i \(0.156148\pi\)
\(888\) 6.47546 0.217302
\(889\) −56.6509 −1.90001
\(890\) −7.11687 −0.238558
\(891\) −3.18891 −0.106832
\(892\) 52.9109 1.77159
\(893\) 14.2895 0.478179
\(894\) −18.6257 −0.622936
\(895\) 14.5928 0.487784
\(896\) 28.0831 0.938192
\(897\) −26.0215 −0.868834
\(898\) −55.4280 −1.84966
\(899\) −41.8786 −1.39673
\(900\) 5.39302 0.179767
\(901\) −1.22573 −0.0408350
\(902\) −16.7747 −0.558536
\(903\) −16.2348 −0.540262
\(904\) 109.834 3.65302
\(905\) −23.0477 −0.766133
\(906\) 0.476283 0.0158235
\(907\) −32.6179 −1.08306 −0.541530 0.840681i \(-0.682155\pi\)
−0.541530 + 0.840681i \(0.682155\pi\)
\(908\) −19.7679 −0.656020
\(909\) 14.9391 0.495498
\(910\) −68.0772 −2.25674
\(911\) −36.2740 −1.20181 −0.600906 0.799319i \(-0.705194\pi\)
−0.600906 + 0.799319i \(0.705194\pi\)
\(912\) −13.2872 −0.439982
\(913\) 34.5871 1.14467
\(914\) 5.54229 0.183323
\(915\) −10.1079 −0.334157
\(916\) −108.238 −3.57630
\(917\) −17.8637 −0.589912
\(918\) 12.9196 0.426411
\(919\) 14.4055 0.475192 0.237596 0.971364i \(-0.423641\pi\)
0.237596 + 0.971364i \(0.423641\pi\)
\(920\) 90.6713 2.98935
\(921\) −8.93861 −0.294537
\(922\) 5.59370 0.184219
\(923\) −3.52953 −0.116176
\(924\) −56.7858 −1.86812
\(925\) 0.574582 0.0188921
\(926\) −44.3276 −1.45669
\(927\) 0.711519 0.0233693
\(928\) 51.3558 1.68584
\(929\) −25.8026 −0.846555 −0.423277 0.906000i \(-0.639120\pi\)
−0.423277 + 0.906000i \(0.639120\pi\)
\(930\) −30.5280 −1.00105
\(931\) −5.45203 −0.178683
\(932\) 81.1671 2.65872
\(933\) −7.84859 −0.256951
\(934\) −16.2429 −0.531484
\(935\) −8.02280 −0.262374
\(936\) 51.7219 1.69058
\(937\) −20.1224 −0.657369 −0.328685 0.944440i \(-0.606605\pi\)
−0.328685 + 0.944440i \(0.606605\pi\)
\(938\) −85.1686 −2.78085
\(939\) −17.2751 −0.563752
\(940\) −82.1356 −2.67897
\(941\) 42.7336 1.39308 0.696538 0.717520i \(-0.254723\pi\)
0.696538 + 0.717520i \(0.254723\pi\)
\(942\) 30.6784 0.999555
\(943\) 11.1428 0.362858
\(944\) 97.8220 3.18384
\(945\) −33.8436 −1.10093
\(946\) −49.1413 −1.59772
\(947\) −43.5030 −1.41366 −0.706829 0.707385i \(-0.749875\pi\)
−0.706829 + 0.707385i \(0.749875\pi\)
\(948\) −38.7846 −1.25967
\(949\) 8.26547 0.268308
\(950\) −2.55672 −0.0829511
\(951\) 0.774870 0.0251269
\(952\) −21.2361 −0.688266
\(953\) −30.5250 −0.988803 −0.494401 0.869234i \(-0.664613\pi\)
−0.494401 + 0.869234i \(0.664613\pi\)
\(954\) −6.21559 −0.201237
\(955\) −18.6612 −0.603861
\(956\) 28.6270 0.925864
\(957\) 28.9113 0.934571
\(958\) 26.0611 0.841995
\(959\) 33.2553 1.07387
\(960\) 4.11513 0.132815
\(961\) 0.389568 0.0125667
\(962\) 9.77551 0.315175
\(963\) −12.9099 −0.416015
\(964\) 83.9589 2.70413
\(965\) −11.8672 −0.382018
\(966\) 54.1776 1.74314
\(967\) −0.861347 −0.0276990 −0.0138495 0.999904i \(-0.504409\pi\)
−0.0138495 + 0.999904i \(0.504409\pi\)
\(968\) −23.9559 −0.769973
\(969\) −1.69354 −0.0544045
\(970\) 3.21770 0.103314
\(971\) 19.5290 0.626717 0.313358 0.949635i \(-0.398546\pi\)
0.313358 + 0.949635i \(0.398546\pi\)
\(972\) 73.1124 2.34508
\(973\) −27.4533 −0.880112
\(974\) 37.0932 1.18854
\(975\) −2.37748 −0.0761404
\(976\) −37.3455 −1.19540
\(977\) −35.0890 −1.12260 −0.561298 0.827614i \(-0.689698\pi\)
−0.561298 + 0.827614i \(0.689698\pi\)
\(978\) 46.8473 1.49801
\(979\) −5.05186 −0.161458
\(980\) 31.3382 1.00106
\(981\) −31.2326 −0.997182
\(982\) −33.1547 −1.05801
\(983\) −32.5329 −1.03764 −0.518820 0.854884i \(-0.673628\pi\)
−0.518820 + 0.854884i \(0.673628\pi\)
\(984\) 11.4735 0.365762
\(985\) 27.2348 0.867773
\(986\) 19.1800 0.610815
\(987\) −27.6654 −0.880599
\(988\) −30.2851 −0.963497
\(989\) 32.6426 1.03798
\(990\) −40.6830 −1.29299
\(991\) −17.9653 −0.570688 −0.285344 0.958425i \(-0.592108\pi\)
−0.285344 + 0.958425i \(0.592108\pi\)
\(992\) −38.4931 −1.22216
\(993\) 23.3367 0.740569
\(994\) 7.34858 0.233083
\(995\) 36.3767 1.15322
\(996\) −41.9663 −1.32975
\(997\) 9.94122 0.314841 0.157421 0.987532i \(-0.449682\pi\)
0.157421 + 0.987532i \(0.449682\pi\)
\(998\) 18.6704 0.591001
\(999\) 4.85975 0.153756
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 \(a_p\))