Properties

Label 6001.2.a.b.1.2
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 1.2
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75915 q^{2}\) \(+3.04798 q^{3}\) \(+5.61289 q^{4}\) \(-2.57270 q^{5}\) \(-8.40983 q^{6}\) \(-0.275912 q^{7}\) \(-9.96848 q^{8}\) \(+6.29019 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75915 q^{2}\) \(+3.04798 q^{3}\) \(+5.61289 q^{4}\) \(-2.57270 q^{5}\) \(-8.40983 q^{6}\) \(-0.275912 q^{7}\) \(-9.96848 q^{8}\) \(+6.29019 q^{9}\) \(+7.09847 q^{10}\) \(+1.07656 q^{11}\) \(+17.1080 q^{12}\) \(+3.84543 q^{13}\) \(+0.761280 q^{14}\) \(-7.84156 q^{15}\) \(+16.2787 q^{16}\) \(+1.00000 q^{17}\) \(-17.3556 q^{18}\) \(-8.39562 q^{19}\) \(-14.4403 q^{20}\) \(-0.840974 q^{21}\) \(-2.97039 q^{22}\) \(-5.83447 q^{23}\) \(-30.3837 q^{24}\) \(+1.61881 q^{25}\) \(-10.6101 q^{26}\) \(+10.0284 q^{27}\) \(-1.54866 q^{28}\) \(+9.83543 q^{29}\) \(+21.6360 q^{30}\) \(-0.683059 q^{31}\) \(-24.9784 q^{32}\) \(+3.28134 q^{33}\) \(-2.75915 q^{34}\) \(+0.709839 q^{35}\) \(+35.3061 q^{36}\) \(+2.82254 q^{37}\) \(+23.1647 q^{38}\) \(+11.7208 q^{39}\) \(+25.6459 q^{40}\) \(-11.8657 q^{41}\) \(+2.32037 q^{42}\) \(+1.63044 q^{43}\) \(+6.04262 q^{44}\) \(-16.1828 q^{45}\) \(+16.0981 q^{46}\) \(-8.40296 q^{47}\) \(+49.6172 q^{48}\) \(-6.92387 q^{49}\) \(-4.46653 q^{50}\) \(+3.04798 q^{51}\) \(+21.5840 q^{52}\) \(-8.09454 q^{53}\) \(-27.6699 q^{54}\) \(-2.76967 q^{55}\) \(+2.75042 q^{56}\) \(-25.5897 q^{57}\) \(-27.1374 q^{58}\) \(-4.19090 q^{59}\) \(-44.0138 q^{60}\) \(+7.21910 q^{61}\) \(+1.88466 q^{62}\) \(-1.73554 q^{63}\) \(+36.3616 q^{64}\) \(-9.89316 q^{65}\) \(-9.05369 q^{66}\) \(-3.59814 q^{67}\) \(+5.61289 q^{68}\) \(-17.7833 q^{69}\) \(-1.95855 q^{70}\) \(-6.33421 q^{71}\) \(-62.7036 q^{72}\) \(+0.910127 q^{73}\) \(-7.78779 q^{74}\) \(+4.93410 q^{75}\) \(-47.1237 q^{76}\) \(-0.297036 q^{77}\) \(-32.3394 q^{78}\) \(-4.28754 q^{79}\) \(-41.8803 q^{80}\) \(+11.6959 q^{81}\) \(+32.7393 q^{82}\) \(-4.00061 q^{83}\) \(-4.72029 q^{84}\) \(-2.57270 q^{85}\) \(-4.49863 q^{86}\) \(+29.9782 q^{87}\) \(-10.7317 q^{88}\) \(+12.2425 q^{89}\) \(+44.6507 q^{90}\) \(-1.06100 q^{91}\) \(-32.7482 q^{92}\) \(-2.08195 q^{93}\) \(+23.1850 q^{94}\) \(+21.5995 q^{95}\) \(-76.1337 q^{96}\) \(+15.4252 q^{97}\) \(+19.1040 q^{98}\) \(+6.77178 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75915 −1.95101 −0.975505 0.219976i \(-0.929402\pi\)
−0.975505 + 0.219976i \(0.929402\pi\)
\(3\) 3.04798 1.75975 0.879876 0.475202i \(-0.157625\pi\)
0.879876 + 0.475202i \(0.157625\pi\)
\(4\) 5.61289 2.80644
\(5\) −2.57270 −1.15055 −0.575274 0.817961i \(-0.695105\pi\)
−0.575274 + 0.817961i \(0.695105\pi\)
\(6\) −8.40983 −3.43330
\(7\) −0.275912 −0.104285 −0.0521424 0.998640i \(-0.516605\pi\)
−0.0521424 + 0.998640i \(0.516605\pi\)
\(8\) −9.96848 −3.52439
\(9\) 6.29019 2.09673
\(10\) 7.09847 2.24473
\(11\) 1.07656 0.324595 0.162298 0.986742i \(-0.448109\pi\)
0.162298 + 0.986742i \(0.448109\pi\)
\(12\) 17.1080 4.93865
\(13\) 3.84543 1.06653 0.533265 0.845948i \(-0.320965\pi\)
0.533265 + 0.845948i \(0.320965\pi\)
\(14\) 0.761280 0.203461
\(15\) −7.84156 −2.02468
\(16\) 16.2787 4.06968
\(17\) 1.00000 0.242536
\(18\) −17.3556 −4.09074
\(19\) −8.39562 −1.92609 −0.963044 0.269345i \(-0.913193\pi\)
−0.963044 + 0.269345i \(0.913193\pi\)
\(20\) −14.4403 −3.22895
\(21\) −0.840974 −0.183515
\(22\) −2.97039 −0.633289
\(23\) −5.83447 −1.21657 −0.608285 0.793719i \(-0.708142\pi\)
−0.608285 + 0.793719i \(0.708142\pi\)
\(24\) −30.3837 −6.20205
\(25\) 1.61881 0.323762
\(26\) −10.6101 −2.08081
\(27\) 10.0284 1.92997
\(28\) −1.54866 −0.292669
\(29\) 9.83543 1.82639 0.913197 0.407519i \(-0.133606\pi\)
0.913197 + 0.407519i \(0.133606\pi\)
\(30\) 21.6360 3.95017
\(31\) −0.683059 −0.122681 −0.0613405 0.998117i \(-0.519538\pi\)
−0.0613405 + 0.998117i \(0.519538\pi\)
\(32\) −24.9784 −4.41560
\(33\) 3.28134 0.571208
\(34\) −2.75915 −0.473190
\(35\) 0.709839 0.119985
\(36\) 35.3061 5.88435
\(37\) 2.82254 0.464022 0.232011 0.972713i \(-0.425469\pi\)
0.232011 + 0.972713i \(0.425469\pi\)
\(38\) 23.1647 3.75782
\(39\) 11.7208 1.87683
\(40\) 25.6459 4.05498
\(41\) −11.8657 −1.85311 −0.926557 0.376154i \(-0.877247\pi\)
−0.926557 + 0.376154i \(0.877247\pi\)
\(42\) 2.32037 0.358041
\(43\) 1.63044 0.248640 0.124320 0.992242i \(-0.460325\pi\)
0.124320 + 0.992242i \(0.460325\pi\)
\(44\) 6.04262 0.910959
\(45\) −16.1828 −2.41239
\(46\) 16.0981 2.37354
\(47\) −8.40296 −1.22570 −0.612849 0.790200i \(-0.709977\pi\)
−0.612849 + 0.790200i \(0.709977\pi\)
\(48\) 49.6172 7.16163
\(49\) −6.92387 −0.989125
\(50\) −4.46653 −0.631663
\(51\) 3.04798 0.426803
\(52\) 21.5840 2.99316
\(53\) −8.09454 −1.11187 −0.555936 0.831225i \(-0.687640\pi\)
−0.555936 + 0.831225i \(0.687640\pi\)
\(54\) −27.6699 −3.76540
\(55\) −2.76967 −0.373463
\(56\) 2.75042 0.367540
\(57\) −25.5897 −3.38944
\(58\) −27.1374 −3.56331
\(59\) −4.19090 −0.545608 −0.272804 0.962070i \(-0.587951\pi\)
−0.272804 + 0.962070i \(0.587951\pi\)
\(60\) −44.0138 −5.68215
\(61\) 7.21910 0.924310 0.462155 0.886799i \(-0.347076\pi\)
0.462155 + 0.886799i \(0.347076\pi\)
\(62\) 1.88466 0.239352
\(63\) −1.73554 −0.218657
\(64\) 36.3616 4.54520
\(65\) −9.89316 −1.22709
\(66\) −9.05369 −1.11443
\(67\) −3.59814 −0.439582 −0.219791 0.975547i \(-0.570538\pi\)
−0.219791 + 0.975547i \(0.570538\pi\)
\(68\) 5.61289 0.680662
\(69\) −17.7833 −2.14086
\(70\) −1.95855 −0.234091
\(71\) −6.33421 −0.751733 −0.375866 0.926674i \(-0.622655\pi\)
−0.375866 + 0.926674i \(0.622655\pi\)
\(72\) −62.7036 −7.38969
\(73\) 0.910127 0.106522 0.0532611 0.998581i \(-0.483038\pi\)
0.0532611 + 0.998581i \(0.483038\pi\)
\(74\) −7.78779 −0.905313
\(75\) 4.93410 0.569741
\(76\) −47.1237 −5.40545
\(77\) −0.297036 −0.0338504
\(78\) −32.3394 −3.66172
\(79\) −4.28754 −0.482386 −0.241193 0.970477i \(-0.577539\pi\)
−0.241193 + 0.970477i \(0.577539\pi\)
\(80\) −41.8803 −4.68236
\(81\) 11.6959 1.29955
\(82\) 32.7393 3.61545
\(83\) −4.00061 −0.439124 −0.219562 0.975599i \(-0.570463\pi\)
−0.219562 + 0.975599i \(0.570463\pi\)
\(84\) −4.72029 −0.515026
\(85\) −2.57270 −0.279049
\(86\) −4.49863 −0.485100
\(87\) 29.9782 3.21400
\(88\) −10.7317 −1.14400
\(89\) 12.2425 1.29771 0.648853 0.760914i \(-0.275249\pi\)
0.648853 + 0.760914i \(0.275249\pi\)
\(90\) 44.6507 4.70660
\(91\) −1.06100 −0.111223
\(92\) −32.7482 −3.41424
\(93\) −2.08195 −0.215888
\(94\) 23.1850 2.39135
\(95\) 21.5995 2.21606
\(96\) −76.1337 −7.77036
\(97\) 15.4252 1.56619 0.783094 0.621904i \(-0.213640\pi\)
0.783094 + 0.621904i \(0.213640\pi\)
\(98\) 19.1040 1.92979
\(99\) 6.77178 0.680589
\(100\) 9.08619 0.908619
\(101\) −18.8474 −1.87539 −0.937695 0.347458i \(-0.887045\pi\)
−0.937695 + 0.347458i \(0.887045\pi\)
\(102\) −8.40983 −0.832697
\(103\) −11.2789 −1.11135 −0.555673 0.831401i \(-0.687539\pi\)
−0.555673 + 0.831401i \(0.687539\pi\)
\(104\) −38.3331 −3.75887
\(105\) 2.16358 0.211143
\(106\) 22.3340 2.16927
\(107\) 4.07973 0.394402 0.197201 0.980363i \(-0.436815\pi\)
0.197201 + 0.980363i \(0.436815\pi\)
\(108\) 56.2885 5.41636
\(109\) 0.691996 0.0662812 0.0331406 0.999451i \(-0.489449\pi\)
0.0331406 + 0.999451i \(0.489449\pi\)
\(110\) 7.64194 0.728630
\(111\) 8.60304 0.816565
\(112\) −4.49149 −0.424406
\(113\) 5.40994 0.508924 0.254462 0.967083i \(-0.418102\pi\)
0.254462 + 0.967083i \(0.418102\pi\)
\(114\) 70.6057 6.61283
\(115\) 15.0104 1.39972
\(116\) 55.2051 5.12567
\(117\) 24.1885 2.23623
\(118\) 11.5633 1.06449
\(119\) −0.275912 −0.0252928
\(120\) 78.1684 7.13576
\(121\) −9.84102 −0.894638
\(122\) −19.9185 −1.80334
\(123\) −36.1665 −3.26102
\(124\) −3.83393 −0.344297
\(125\) 8.69881 0.778045
\(126\) 4.78860 0.426602
\(127\) 10.4288 0.925409 0.462704 0.886513i \(-0.346879\pi\)
0.462704 + 0.886513i \(0.346879\pi\)
\(128\) −50.3701 −4.45213
\(129\) 4.96956 0.437545
\(130\) 27.2967 2.39408
\(131\) −14.4178 −1.25969 −0.629844 0.776722i \(-0.716881\pi\)
−0.629844 + 0.776722i \(0.716881\pi\)
\(132\) 18.4178 1.60306
\(133\) 2.31645 0.200862
\(134\) 9.92778 0.857630
\(135\) −25.8002 −2.22053
\(136\) −9.96848 −0.854790
\(137\) −1.87616 −0.160291 −0.0801455 0.996783i \(-0.525539\pi\)
−0.0801455 + 0.996783i \(0.525539\pi\)
\(138\) 49.0668 4.17685
\(139\) 14.4187 1.22298 0.611489 0.791253i \(-0.290571\pi\)
0.611489 + 0.791253i \(0.290571\pi\)
\(140\) 3.98425 0.336730
\(141\) −25.6121 −2.15693
\(142\) 17.4770 1.46664
\(143\) 4.13984 0.346191
\(144\) 102.396 8.53302
\(145\) −25.3037 −2.10135
\(146\) −2.51117 −0.207826
\(147\) −21.1038 −1.74062
\(148\) 15.8426 1.30225
\(149\) −7.10481 −0.582048 −0.291024 0.956716i \(-0.593996\pi\)
−0.291024 + 0.956716i \(0.593996\pi\)
\(150\) −13.6139 −1.11157
\(151\) 17.7945 1.44809 0.724046 0.689751i \(-0.242280\pi\)
0.724046 + 0.689751i \(0.242280\pi\)
\(152\) 83.6916 6.78828
\(153\) 6.29019 0.508532
\(154\) 0.819565 0.0660424
\(155\) 1.75731 0.141150
\(156\) 65.7875 5.26722
\(157\) −11.4463 −0.913514 −0.456757 0.889591i \(-0.650989\pi\)
−0.456757 + 0.889591i \(0.650989\pi\)
\(158\) 11.8299 0.941140
\(159\) −24.6720 −1.95662
\(160\) 64.2620 5.08036
\(161\) 1.60980 0.126870
\(162\) −32.2708 −2.53543
\(163\) −17.1323 −1.34190 −0.670951 0.741502i \(-0.734114\pi\)
−0.670951 + 0.741502i \(0.734114\pi\)
\(164\) −66.6009 −5.20066
\(165\) −8.44192 −0.657202
\(166\) 11.0383 0.856735
\(167\) −16.1998 −1.25358 −0.626789 0.779189i \(-0.715631\pi\)
−0.626789 + 0.779189i \(0.715631\pi\)
\(168\) 8.38323 0.646780
\(169\) 1.78733 0.137487
\(170\) 7.09847 0.544428
\(171\) −52.8101 −4.03849
\(172\) 9.15149 0.697794
\(173\) −0.995702 −0.0757018 −0.0378509 0.999283i \(-0.512051\pi\)
−0.0378509 + 0.999283i \(0.512051\pi\)
\(174\) −82.7142 −6.27055
\(175\) −0.446648 −0.0337634
\(176\) 17.5250 1.32100
\(177\) −12.7738 −0.960136
\(178\) −33.7789 −2.53184
\(179\) 3.74695 0.280060 0.140030 0.990147i \(-0.455280\pi\)
0.140030 + 0.990147i \(0.455280\pi\)
\(180\) −90.8322 −6.77023
\(181\) 3.00371 0.223264 0.111632 0.993750i \(-0.464392\pi\)
0.111632 + 0.993750i \(0.464392\pi\)
\(182\) 2.92745 0.216997
\(183\) 22.0037 1.62656
\(184\) 58.1608 4.28767
\(185\) −7.26156 −0.533880
\(186\) 5.74440 0.421200
\(187\) 1.07656 0.0787260
\(188\) −47.1649 −3.43985
\(189\) −2.76696 −0.201267
\(190\) −59.5960 −4.32355
\(191\) −11.1324 −0.805515 −0.402757 0.915307i \(-0.631948\pi\)
−0.402757 + 0.915307i \(0.631948\pi\)
\(192\) 110.829 7.99842
\(193\) 22.9052 1.64875 0.824375 0.566045i \(-0.191527\pi\)
0.824375 + 0.566045i \(0.191527\pi\)
\(194\) −42.5603 −3.05565
\(195\) −30.1542 −2.15938
\(196\) −38.8629 −2.77592
\(197\) 16.2607 1.15852 0.579262 0.815141i \(-0.303341\pi\)
0.579262 + 0.815141i \(0.303341\pi\)
\(198\) −18.6843 −1.32784
\(199\) −13.4673 −0.954671 −0.477335 0.878721i \(-0.658397\pi\)
−0.477335 + 0.878721i \(0.658397\pi\)
\(200\) −16.1371 −1.14106
\(201\) −10.9671 −0.773556
\(202\) 52.0029 3.65891
\(203\) −2.71371 −0.190465
\(204\) 17.1080 1.19780
\(205\) 30.5270 2.13210
\(206\) 31.1202 2.16825
\(207\) −36.6999 −2.55082
\(208\) 62.5986 4.34043
\(209\) −9.03840 −0.625199
\(210\) −5.96962 −0.411943
\(211\) 7.68654 0.529164 0.264582 0.964363i \(-0.414766\pi\)
0.264582 + 0.964363i \(0.414766\pi\)
\(212\) −45.4337 −3.12040
\(213\) −19.3066 −1.32286
\(214\) −11.2566 −0.769483
\(215\) −4.19465 −0.286073
\(216\) −99.9683 −6.80198
\(217\) 0.188464 0.0127938
\(218\) −1.90932 −0.129315
\(219\) 2.77405 0.187453
\(220\) −15.5459 −1.04810
\(221\) 3.84543 0.258672
\(222\) −23.7371 −1.59313
\(223\) 11.3649 0.761051 0.380525 0.924770i \(-0.375743\pi\)
0.380525 + 0.924770i \(0.375743\pi\)
\(224\) 6.89183 0.460480
\(225\) 10.1826 0.678841
\(226\) −14.9268 −0.992917
\(227\) 8.68896 0.576706 0.288353 0.957524i \(-0.406892\pi\)
0.288353 + 0.957524i \(0.406892\pi\)
\(228\) −143.632 −9.51226
\(229\) −18.4536 −1.21945 −0.609723 0.792614i \(-0.708720\pi\)
−0.609723 + 0.792614i \(0.708720\pi\)
\(230\) −41.4158 −2.73088
\(231\) −0.905360 −0.0595683
\(232\) −98.0442 −6.43692
\(233\) 3.53003 0.231260 0.115630 0.993292i \(-0.463111\pi\)
0.115630 + 0.993292i \(0.463111\pi\)
\(234\) −66.7396 −4.36290
\(235\) 21.6183 1.41022
\(236\) −23.5230 −1.53122
\(237\) −13.0683 −0.848880
\(238\) 0.761280 0.0493465
\(239\) −21.0528 −1.36179 −0.680896 0.732380i \(-0.738409\pi\)
−0.680896 + 0.732380i \(0.738409\pi\)
\(240\) −127.650 −8.23980
\(241\) 12.1773 0.784411 0.392205 0.919878i \(-0.371712\pi\)
0.392205 + 0.919878i \(0.371712\pi\)
\(242\) 27.1528 1.74545
\(243\) 5.56367 0.356910
\(244\) 40.5200 2.59402
\(245\) 17.8131 1.13804
\(246\) 99.7887 6.36229
\(247\) −32.2848 −2.05423
\(248\) 6.80905 0.432375
\(249\) −12.1938 −0.772749
\(250\) −24.0013 −1.51797
\(251\) 30.0993 1.89985 0.949925 0.312478i \(-0.101159\pi\)
0.949925 + 0.312478i \(0.101159\pi\)
\(252\) −9.74137 −0.613649
\(253\) −6.28116 −0.394893
\(254\) −28.7747 −1.80548
\(255\) −7.84156 −0.491057
\(256\) 66.2554 4.14096
\(257\) 5.68256 0.354469 0.177234 0.984169i \(-0.443285\pi\)
0.177234 + 0.984169i \(0.443285\pi\)
\(258\) −13.7117 −0.853656
\(259\) −0.778771 −0.0483905
\(260\) −55.5291 −3.44377
\(261\) 61.8667 3.82945
\(262\) 39.7808 2.45766
\(263\) −31.4541 −1.93955 −0.969773 0.244010i \(-0.921537\pi\)
−0.969773 + 0.244010i \(0.921537\pi\)
\(264\) −32.7100 −2.01316
\(265\) 20.8249 1.27926
\(266\) −6.39142 −0.391883
\(267\) 37.3150 2.28364
\(268\) −20.1959 −1.23366
\(269\) −0.00307033 −0.000187202 0 −9.36008e−5 1.00000i \(-0.500030\pi\)
−9.36008e−5 1.00000i \(0.500030\pi\)
\(270\) 71.1866 4.33228
\(271\) −21.5107 −1.30668 −0.653342 0.757063i \(-0.726634\pi\)
−0.653342 + 0.757063i \(0.726634\pi\)
\(272\) 16.2787 0.987042
\(273\) −3.23390 −0.195725
\(274\) 5.17659 0.312730
\(275\) 1.74275 0.105092
\(276\) −99.8159 −6.00821
\(277\) −2.50556 −0.150544 −0.0752721 0.997163i \(-0.523983\pi\)
−0.0752721 + 0.997163i \(0.523983\pi\)
\(278\) −39.7833 −2.38604
\(279\) −4.29657 −0.257229
\(280\) −7.07602 −0.422873
\(281\) 4.17035 0.248782 0.124391 0.992233i \(-0.460302\pi\)
0.124391 + 0.992233i \(0.460302\pi\)
\(282\) 70.6674 4.20818
\(283\) −13.9039 −0.826500 −0.413250 0.910618i \(-0.635606\pi\)
−0.413250 + 0.910618i \(0.635606\pi\)
\(284\) −35.5532 −2.10970
\(285\) 65.8347 3.89971
\(286\) −11.4224 −0.675422
\(287\) 3.27389 0.193252
\(288\) −157.119 −9.25832
\(289\) 1.00000 0.0588235
\(290\) 69.8165 4.09976
\(291\) 47.0156 2.75610
\(292\) 5.10844 0.298949
\(293\) 22.9731 1.34210 0.671051 0.741411i \(-0.265843\pi\)
0.671051 + 0.741411i \(0.265843\pi\)
\(294\) 58.2286 3.39596
\(295\) 10.7819 0.627749
\(296\) −28.1364 −1.63540
\(297\) 10.7962 0.626461
\(298\) 19.6032 1.13558
\(299\) −22.4360 −1.29751
\(300\) 27.6945 1.59895
\(301\) −0.449858 −0.0259294
\(302\) −49.0975 −2.82524
\(303\) −57.4467 −3.30022
\(304\) −136.670 −7.83856
\(305\) −18.5726 −1.06346
\(306\) −17.3556 −0.992151
\(307\) −7.31766 −0.417641 −0.208821 0.977954i \(-0.566962\pi\)
−0.208821 + 0.977954i \(0.566962\pi\)
\(308\) −1.66723 −0.0949991
\(309\) −34.3780 −1.95570
\(310\) −4.84867 −0.275386
\(311\) −1.04860 −0.0594606 −0.0297303 0.999558i \(-0.509465\pi\)
−0.0297303 + 0.999558i \(0.509465\pi\)
\(312\) −116.839 −6.61468
\(313\) −9.22256 −0.521290 −0.260645 0.965435i \(-0.583935\pi\)
−0.260645 + 0.965435i \(0.583935\pi\)
\(314\) 31.5820 1.78228
\(315\) 4.46502 0.251576
\(316\) −24.0655 −1.35379
\(317\) 2.43246 0.136621 0.0683104 0.997664i \(-0.478239\pi\)
0.0683104 + 0.997664i \(0.478239\pi\)
\(318\) 68.0737 3.81738
\(319\) 10.5884 0.592839
\(320\) −93.5476 −5.22947
\(321\) 12.4349 0.694050
\(322\) −4.44167 −0.247524
\(323\) −8.39562 −0.467145
\(324\) 65.6480 3.64711
\(325\) 6.22502 0.345302
\(326\) 47.2704 2.61807
\(327\) 2.10919 0.116639
\(328\) 118.283 6.53110
\(329\) 2.31847 0.127822
\(330\) 23.2925 1.28221
\(331\) −17.2043 −0.945636 −0.472818 0.881160i \(-0.656763\pi\)
−0.472818 + 0.881160i \(0.656763\pi\)
\(332\) −22.4549 −1.23238
\(333\) 17.7543 0.972930
\(334\) 44.6976 2.44574
\(335\) 9.25694 0.505761
\(336\) −13.6900 −0.746849
\(337\) −21.2747 −1.15891 −0.579453 0.815005i \(-0.696734\pi\)
−0.579453 + 0.815005i \(0.696734\pi\)
\(338\) −4.93151 −0.268239
\(339\) 16.4894 0.895581
\(340\) −14.4403 −0.783135
\(341\) −0.735355 −0.0398217
\(342\) 145.711 7.87913
\(343\) 3.84176 0.207435
\(344\) −16.2530 −0.876305
\(345\) 45.7513 2.46317
\(346\) 2.74729 0.147695
\(347\) −21.9439 −1.17801 −0.589004 0.808130i \(-0.700480\pi\)
−0.589004 + 0.808130i \(0.700480\pi\)
\(348\) 168.264 9.01991
\(349\) −9.63635 −0.515822 −0.257911 0.966169i \(-0.583034\pi\)
−0.257911 + 0.966169i \(0.583034\pi\)
\(350\) 1.23237 0.0658728
\(351\) 38.5637 2.05838
\(352\) −26.8908 −1.43328
\(353\) 1.00000 0.0532246
\(354\) 35.2447 1.87324
\(355\) 16.2961 0.864905
\(356\) 68.7159 3.64194
\(357\) −0.840974 −0.0445090
\(358\) −10.3384 −0.546401
\(359\) −29.5758 −1.56095 −0.780476 0.625185i \(-0.785023\pi\)
−0.780476 + 0.625185i \(0.785023\pi\)
\(360\) 161.318 8.50220
\(361\) 51.4865 2.70981
\(362\) −8.28768 −0.435591
\(363\) −29.9952 −1.57434
\(364\) −5.95526 −0.312141
\(365\) −2.34149 −0.122559
\(366\) −60.7113 −3.17343
\(367\) −14.3792 −0.750587 −0.375293 0.926906i \(-0.622458\pi\)
−0.375293 + 0.926906i \(0.622458\pi\)
\(368\) −94.9776 −4.95105
\(369\) −74.6377 −3.88548
\(370\) 20.0357 1.04161
\(371\) 2.23338 0.115951
\(372\) −11.6857 −0.605878
\(373\) 23.1709 1.19975 0.599873 0.800095i \(-0.295218\pi\)
0.599873 + 0.800095i \(0.295218\pi\)
\(374\) −2.97039 −0.153595
\(375\) 26.5138 1.36917
\(376\) 83.7647 4.31984
\(377\) 37.8215 1.94790
\(378\) 7.63446 0.392674
\(379\) −34.6024 −1.77741 −0.888703 0.458484i \(-0.848393\pi\)
−0.888703 + 0.458484i \(0.848393\pi\)
\(380\) 121.235 6.21924
\(381\) 31.7869 1.62849
\(382\) 30.7160 1.57157
\(383\) −8.63991 −0.441479 −0.220739 0.975333i \(-0.570847\pi\)
−0.220739 + 0.975333i \(0.570847\pi\)
\(384\) −153.527 −7.83465
\(385\) 0.764185 0.0389465
\(386\) −63.1987 −3.21673
\(387\) 10.2558 0.521331
\(388\) 86.5797 4.39542
\(389\) −22.0077 −1.11584 −0.557918 0.829896i \(-0.688399\pi\)
−0.557918 + 0.829896i \(0.688399\pi\)
\(390\) 83.1997 4.21298
\(391\) −5.83447 −0.295062
\(392\) 69.0205 3.48606
\(393\) −43.9451 −2.21674
\(394\) −44.8655 −2.26029
\(395\) 11.0306 0.555008
\(396\) 38.0092 1.91003
\(397\) −24.9452 −1.25196 −0.625981 0.779838i \(-0.715301\pi\)
−0.625981 + 0.779838i \(0.715301\pi\)
\(398\) 37.1582 1.86257
\(399\) 7.06050 0.353467
\(400\) 26.3521 1.31761
\(401\) 0.955194 0.0477001 0.0238500 0.999716i \(-0.492408\pi\)
0.0238500 + 0.999716i \(0.492408\pi\)
\(402\) 30.2597 1.50922
\(403\) −2.62665 −0.130843
\(404\) −105.789 −5.26318
\(405\) −30.0902 −1.49519
\(406\) 7.48752 0.371599
\(407\) 3.03864 0.150620
\(408\) −30.3837 −1.50422
\(409\) 11.0858 0.548156 0.274078 0.961707i \(-0.411627\pi\)
0.274078 + 0.961707i \(0.411627\pi\)
\(410\) −84.2284 −4.15975
\(411\) −5.71850 −0.282073
\(412\) −63.3074 −3.11893
\(413\) 1.15632 0.0568986
\(414\) 101.260 4.97668
\(415\) 10.2924 0.505233
\(416\) −96.0526 −4.70937
\(417\) 43.9479 2.15214
\(418\) 24.9383 1.21977
\(419\) −34.0109 −1.66154 −0.830771 0.556615i \(-0.812100\pi\)
−0.830771 + 0.556615i \(0.812100\pi\)
\(420\) 12.1439 0.592562
\(421\) −28.5556 −1.39172 −0.695858 0.718179i \(-0.744976\pi\)
−0.695858 + 0.718179i \(0.744976\pi\)
\(422\) −21.2083 −1.03240
\(423\) −52.8562 −2.56996
\(424\) 80.6903 3.91867
\(425\) 1.61881 0.0785238
\(426\) 53.2696 2.58092
\(427\) −1.99183 −0.0963915
\(428\) 22.8990 1.10687
\(429\) 12.6182 0.609211
\(430\) 11.5736 0.558131
\(431\) 0.135371 0.00652058 0.00326029 0.999995i \(-0.498962\pi\)
0.00326029 + 0.999995i \(0.498962\pi\)
\(432\) 163.250 7.85438
\(433\) 5.99029 0.287875 0.143938 0.989587i \(-0.454024\pi\)
0.143938 + 0.989587i \(0.454024\pi\)
\(434\) −0.519999 −0.0249608
\(435\) −77.1251 −3.69786
\(436\) 3.88410 0.186014
\(437\) 48.9840 2.34322
\(438\) −7.65401 −0.365723
\(439\) −0.574794 −0.0274334 −0.0137167 0.999906i \(-0.504366\pi\)
−0.0137167 + 0.999906i \(0.504366\pi\)
\(440\) 27.6094 1.31623
\(441\) −43.5525 −2.07393
\(442\) −10.6101 −0.504671
\(443\) −29.1583 −1.38535 −0.692677 0.721248i \(-0.743569\pi\)
−0.692677 + 0.721248i \(0.743569\pi\)
\(444\) 48.2879 2.29164
\(445\) −31.4964 −1.49307
\(446\) −31.3575 −1.48482
\(447\) −21.6553 −1.02426
\(448\) −10.0326 −0.473995
\(449\) 16.7991 0.792798 0.396399 0.918078i \(-0.370260\pi\)
0.396399 + 0.918078i \(0.370260\pi\)
\(450\) −28.0953 −1.32443
\(451\) −12.7742 −0.601513
\(452\) 30.3654 1.42827
\(453\) 54.2372 2.54829
\(454\) −23.9741 −1.12516
\(455\) 2.72964 0.127967
\(456\) 255.090 11.9457
\(457\) 41.7718 1.95400 0.977001 0.213235i \(-0.0684001\pi\)
0.977001 + 0.213235i \(0.0684001\pi\)
\(458\) 50.9161 2.37915
\(459\) 10.0284 0.468088
\(460\) 84.2514 3.92824
\(461\) −17.5482 −0.817301 −0.408650 0.912691i \(-0.634000\pi\)
−0.408650 + 0.912691i \(0.634000\pi\)
\(462\) 2.49802 0.116218
\(463\) 12.3575 0.574304 0.287152 0.957885i \(-0.407292\pi\)
0.287152 + 0.957885i \(0.407292\pi\)
\(464\) 160.108 7.43283
\(465\) 5.35624 0.248390
\(466\) −9.73987 −0.451191
\(467\) −12.9361 −0.598611 −0.299306 0.954157i \(-0.596755\pi\)
−0.299306 + 0.954157i \(0.596755\pi\)
\(468\) 135.767 6.27584
\(469\) 0.992767 0.0458417
\(470\) −59.6481 −2.75136
\(471\) −34.8881 −1.60756
\(472\) 41.7769 1.92294
\(473\) 1.75527 0.0807075
\(474\) 36.0574 1.65617
\(475\) −13.5909 −0.623594
\(476\) −1.54866 −0.0709827
\(477\) −50.9162 −2.33129
\(478\) 58.0877 2.65687
\(479\) 43.2299 1.97523 0.987613 0.156911i \(-0.0501537\pi\)
0.987613 + 0.156911i \(0.0501537\pi\)
\(480\) 195.869 8.94017
\(481\) 10.8539 0.494894
\(482\) −33.5990 −1.53039
\(483\) 4.90663 0.223260
\(484\) −55.2365 −2.51075
\(485\) −39.6844 −1.80197
\(486\) −15.3510 −0.696334
\(487\) 22.9353 1.03930 0.519649 0.854380i \(-0.326063\pi\)
0.519649 + 0.854380i \(0.326063\pi\)
\(488\) −71.9634 −3.25763
\(489\) −52.2188 −2.36142
\(490\) −49.1489 −2.22032
\(491\) 36.5922 1.65138 0.825690 0.564123i \(-0.190786\pi\)
0.825690 + 0.564123i \(0.190786\pi\)
\(492\) −202.998 −9.15188
\(493\) 9.83543 0.442965
\(494\) 89.0784 4.00783
\(495\) −17.4218 −0.783051
\(496\) −11.1193 −0.499272
\(497\) 1.74768 0.0783943
\(498\) 33.6444 1.50764
\(499\) −4.46293 −0.199788 −0.0998940 0.994998i \(-0.531850\pi\)
−0.0998940 + 0.994998i \(0.531850\pi\)
\(500\) 48.8254 2.18354
\(501\) −49.3767 −2.20599
\(502\) −83.0483 −3.70663
\(503\) 30.0035 1.33779 0.668896 0.743356i \(-0.266767\pi\)
0.668896 + 0.743356i \(0.266767\pi\)
\(504\) 17.3007 0.770633
\(505\) 48.4889 2.15773
\(506\) 17.3306 0.770441
\(507\) 5.44775 0.241943
\(508\) 58.5358 2.59711
\(509\) −7.43252 −0.329440 −0.164720 0.986340i \(-0.552672\pi\)
−0.164720 + 0.986340i \(0.552672\pi\)
\(510\) 21.6360 0.958058
\(511\) −0.251114 −0.0111087
\(512\) −82.0680 −3.62693
\(513\) −84.1950 −3.71730
\(514\) −15.6790 −0.691572
\(515\) 29.0174 1.27866
\(516\) 27.8936 1.22795
\(517\) −9.04630 −0.397856
\(518\) 2.14874 0.0944103
\(519\) −3.03488 −0.133217
\(520\) 98.6197 4.32476
\(521\) 35.6418 1.56150 0.780749 0.624845i \(-0.214838\pi\)
0.780749 + 0.624845i \(0.214838\pi\)
\(522\) −170.699 −7.47131
\(523\) −27.8357 −1.21717 −0.608584 0.793489i \(-0.708262\pi\)
−0.608584 + 0.793489i \(0.708262\pi\)
\(524\) −80.9254 −3.53524
\(525\) −1.36138 −0.0594153
\(526\) 86.7866 3.78407
\(527\) −0.683059 −0.0297545
\(528\) 53.4160 2.32463
\(529\) 11.0410 0.480044
\(530\) −57.4589 −2.49585
\(531\) −26.3615 −1.14399
\(532\) 13.0020 0.563707
\(533\) −45.6288 −1.97640
\(534\) −102.958 −4.45541
\(535\) −10.4959 −0.453779
\(536\) 35.8679 1.54926
\(537\) 11.4206 0.492837
\(538\) 0.00847150 0.000365232 0
\(539\) −7.45397 −0.321065
\(540\) −144.814 −6.23179
\(541\) −11.7582 −0.505526 −0.252763 0.967528i \(-0.581339\pi\)
−0.252763 + 0.967528i \(0.581339\pi\)
\(542\) 59.3513 2.54936
\(543\) 9.15526 0.392890
\(544\) −24.9784 −1.07094
\(545\) −1.78030 −0.0762598
\(546\) 8.92282 0.381861
\(547\) 7.34831 0.314191 0.157095 0.987583i \(-0.449787\pi\)
0.157095 + 0.987583i \(0.449787\pi\)
\(548\) −10.5307 −0.449848
\(549\) 45.4095 1.93803
\(550\) −4.80850 −0.205035
\(551\) −82.5745 −3.51779
\(552\) 177.273 7.54524
\(553\) 1.18298 0.0503055
\(554\) 6.91319 0.293713
\(555\) −22.1331 −0.939497
\(556\) 80.9305 3.43222
\(557\) 20.6326 0.874233 0.437116 0.899405i \(-0.356000\pi\)
0.437116 + 0.899405i \(0.356000\pi\)
\(558\) 11.8549 0.501856
\(559\) 6.26975 0.265182
\(560\) 11.5553 0.488299
\(561\) 3.28134 0.138538
\(562\) −11.5066 −0.485376
\(563\) −8.99049 −0.378904 −0.189452 0.981890i \(-0.560671\pi\)
−0.189452 + 0.981890i \(0.560671\pi\)
\(564\) −143.758 −6.05329
\(565\) −13.9182 −0.585542
\(566\) 38.3628 1.61251
\(567\) −3.22705 −0.135523
\(568\) 63.1425 2.64940
\(569\) 41.9354 1.75802 0.879011 0.476801i \(-0.158204\pi\)
0.879011 + 0.476801i \(0.158204\pi\)
\(570\) −181.648 −7.60838
\(571\) 12.9947 0.543809 0.271905 0.962324i \(-0.412346\pi\)
0.271905 + 0.962324i \(0.412346\pi\)
\(572\) 23.2365 0.971565
\(573\) −33.9315 −1.41751
\(574\) −9.03314 −0.377036
\(575\) −9.44489 −0.393879
\(576\) 228.721 9.53005
\(577\) −22.0443 −0.917715 −0.458858 0.888510i \(-0.651741\pi\)
−0.458858 + 0.888510i \(0.651741\pi\)
\(578\) −2.75915 −0.114765
\(579\) 69.8145 2.90139
\(580\) −142.027 −5.89733
\(581\) 1.10381 0.0457939
\(582\) −129.723 −5.37719
\(583\) −8.71427 −0.360908
\(584\) −9.07258 −0.375426
\(585\) −62.2298 −2.57289
\(586\) −63.3861 −2.61845
\(587\) 14.1701 0.584864 0.292432 0.956286i \(-0.405536\pi\)
0.292432 + 0.956286i \(0.405536\pi\)
\(588\) −118.453 −4.88494
\(589\) 5.73470 0.236294
\(590\) −29.7489 −1.22474
\(591\) 49.5622 2.03872
\(592\) 45.9473 1.88842
\(593\) 9.68032 0.397523 0.198762 0.980048i \(-0.436308\pi\)
0.198762 + 0.980048i \(0.436308\pi\)
\(594\) −29.7884 −1.22223
\(595\) 0.709839 0.0291006
\(596\) −39.8785 −1.63349
\(597\) −41.0480 −1.67998
\(598\) 61.9043 2.53145
\(599\) −17.4311 −0.712215 −0.356108 0.934445i \(-0.615896\pi\)
−0.356108 + 0.934445i \(0.615896\pi\)
\(600\) −49.1855 −2.00799
\(601\) −23.6705 −0.965541 −0.482770 0.875747i \(-0.660369\pi\)
−0.482770 + 0.875747i \(0.660369\pi\)
\(602\) 1.24122 0.0505885
\(603\) −22.6330 −0.921686
\(604\) 99.8783 4.06399
\(605\) 25.3180 1.02932
\(606\) 158.504 6.43877
\(607\) 20.4428 0.829749 0.414874 0.909879i \(-0.363825\pi\)
0.414874 + 0.909879i \(0.363825\pi\)
\(608\) 209.709 8.50482
\(609\) −8.27134 −0.335171
\(610\) 51.2445 2.07483
\(611\) −32.3130 −1.30724
\(612\) 35.3061 1.42717
\(613\) 22.6785 0.915974 0.457987 0.888959i \(-0.348571\pi\)
0.457987 + 0.888959i \(0.348571\pi\)
\(614\) 20.1905 0.814822
\(615\) 93.0457 3.75197
\(616\) 2.96099 0.119302
\(617\) 5.39690 0.217271 0.108636 0.994082i \(-0.465352\pi\)
0.108636 + 0.994082i \(0.465352\pi\)
\(618\) 94.8539 3.81558
\(619\) −15.7245 −0.632020 −0.316010 0.948756i \(-0.602343\pi\)
−0.316010 + 0.948756i \(0.602343\pi\)
\(620\) 9.86357 0.396130
\(621\) −58.5106 −2.34795
\(622\) 2.89324 0.116008
\(623\) −3.37786 −0.135331
\(624\) 190.800 7.63809
\(625\) −30.4735 −1.21894
\(626\) 25.4464 1.01704
\(627\) −27.5489 −1.10020
\(628\) −64.2468 −2.56373
\(629\) 2.82254 0.112542
\(630\) −12.3197 −0.490827
\(631\) −46.7243 −1.86006 −0.930032 0.367478i \(-0.880221\pi\)
−0.930032 + 0.367478i \(0.880221\pi\)
\(632\) 42.7402 1.70011
\(633\) 23.4284 0.931197
\(634\) −6.71152 −0.266549
\(635\) −26.8303 −1.06473
\(636\) −138.481 −5.49114
\(637\) −26.6253 −1.05493
\(638\) −29.2151 −1.15664
\(639\) −39.8434 −1.57618
\(640\) 129.587 5.12239
\(641\) 11.0495 0.436427 0.218214 0.975901i \(-0.429977\pi\)
0.218214 + 0.975901i \(0.429977\pi\)
\(642\) −34.3098 −1.35410
\(643\) −5.23720 −0.206535 −0.103268 0.994654i \(-0.532930\pi\)
−0.103268 + 0.994654i \(0.532930\pi\)
\(644\) 9.03561 0.356053
\(645\) −12.7852 −0.503417
\(646\) 23.1647 0.911405
\(647\) −20.0952 −0.790023 −0.395012 0.918676i \(-0.629259\pi\)
−0.395012 + 0.918676i \(0.629259\pi\)
\(648\) −116.591 −4.58011
\(649\) −4.51176 −0.177102
\(650\) −17.1757 −0.673688
\(651\) 0.574434 0.0225139
\(652\) −96.1614 −3.76597
\(653\) −20.7919 −0.813651 −0.406826 0.913506i \(-0.633364\pi\)
−0.406826 + 0.913506i \(0.633364\pi\)
\(654\) −5.81957 −0.227563
\(655\) 37.0927 1.44933
\(656\) −193.159 −7.54158
\(657\) 5.72487 0.223348
\(658\) −6.39701 −0.249381
\(659\) −29.4240 −1.14620 −0.573099 0.819486i \(-0.694259\pi\)
−0.573099 + 0.819486i \(0.694259\pi\)
\(660\) −47.3835 −1.84440
\(661\) 4.41961 0.171903 0.0859515 0.996299i \(-0.472607\pi\)
0.0859515 + 0.996299i \(0.472607\pi\)
\(662\) 47.4693 1.84495
\(663\) 11.7208 0.455198
\(664\) 39.8800 1.54764
\(665\) −5.95954 −0.231101
\(666\) −48.9867 −1.89820
\(667\) −57.3845 −2.22194
\(668\) −90.9276 −3.51810
\(669\) 34.6400 1.33926
\(670\) −25.5412 −0.986744
\(671\) 7.77180 0.300027
\(672\) 21.0062 0.810330
\(673\) −14.9365 −0.575761 −0.287881 0.957666i \(-0.592951\pi\)
−0.287881 + 0.957666i \(0.592951\pi\)
\(674\) 58.7000 2.26104
\(675\) 16.2341 0.624852
\(676\) 10.0321 0.385849
\(677\) 15.6079 0.599859 0.299929 0.953961i \(-0.403037\pi\)
0.299929 + 0.953961i \(0.403037\pi\)
\(678\) −45.4966 −1.74729
\(679\) −4.25598 −0.163330
\(680\) 25.6459 0.983477
\(681\) 26.4838 1.01486
\(682\) 2.02895 0.0776925
\(683\) 33.0327 1.26396 0.631981 0.774984i \(-0.282242\pi\)
0.631981 + 0.774984i \(0.282242\pi\)
\(684\) −296.417 −11.3338
\(685\) 4.82680 0.184423
\(686\) −10.6000 −0.404709
\(687\) −56.2462 −2.14593
\(688\) 26.5415 1.01189
\(689\) −31.1270 −1.18584
\(690\) −126.235 −4.80567
\(691\) 51.6960 1.96661 0.983303 0.181973i \(-0.0582485\pi\)
0.983303 + 0.181973i \(0.0582485\pi\)
\(692\) −5.58876 −0.212453
\(693\) −1.86841 −0.0709751
\(694\) 60.5463 2.29831
\(695\) −37.0951 −1.40710
\(696\) −298.837 −11.3274
\(697\) −11.8657 −0.449446
\(698\) 26.5881 1.00637
\(699\) 10.7595 0.406960
\(700\) −2.50699 −0.0947552
\(701\) −27.8846 −1.05319 −0.526593 0.850118i \(-0.676531\pi\)
−0.526593 + 0.850118i \(0.676531\pi\)
\(702\) −106.403 −4.01592
\(703\) −23.6970 −0.893748
\(704\) 39.1455 1.47535
\(705\) 65.8923 2.48165
\(706\) −2.75915 −0.103842
\(707\) 5.20023 0.195575
\(708\) −71.6977 −2.69457
\(709\) −8.96482 −0.336681 −0.168340 0.985729i \(-0.553841\pi\)
−0.168340 + 0.985729i \(0.553841\pi\)
\(710\) −44.9632 −1.68744
\(711\) −26.9694 −1.01143
\(712\) −122.039 −4.57362
\(713\) 3.98528 0.149250
\(714\) 2.32037 0.0868376
\(715\) −10.6506 −0.398309
\(716\) 21.0312 0.785973
\(717\) −64.1685 −2.39642
\(718\) 81.6040 3.04544
\(719\) −3.85541 −0.143783 −0.0718913 0.997412i \(-0.522903\pi\)
−0.0718913 + 0.997412i \(0.522903\pi\)
\(720\) −263.435 −9.81765
\(721\) 3.11199 0.115897
\(722\) −142.059 −5.28687
\(723\) 37.1163 1.38037
\(724\) 16.8595 0.626578
\(725\) 15.9217 0.591316
\(726\) 82.7612 3.07156
\(727\) 45.7272 1.69593 0.847965 0.530052i \(-0.177828\pi\)
0.847965 + 0.530052i \(0.177828\pi\)
\(728\) 10.5765 0.391993
\(729\) −18.1298 −0.671476
\(730\) 6.46050 0.239114
\(731\) 1.63044 0.0603041
\(732\) 123.504 4.56484
\(733\) −3.02099 −0.111583 −0.0557915 0.998442i \(-0.517768\pi\)
−0.0557915 + 0.998442i \(0.517768\pi\)
\(734\) 39.6742 1.46440
\(735\) 54.2939 2.00266
\(736\) 145.736 5.37188
\(737\) −3.87361 −0.142686
\(738\) 205.936 7.58062
\(739\) 11.0182 0.405310 0.202655 0.979250i \(-0.435043\pi\)
0.202655 + 0.979250i \(0.435043\pi\)
\(740\) −40.7583 −1.49830
\(741\) −98.4034 −3.61494
\(742\) −6.16222 −0.226222
\(743\) 11.5163 0.422491 0.211246 0.977433i \(-0.432248\pi\)
0.211246 + 0.977433i \(0.432248\pi\)
\(744\) 20.7539 0.760874
\(745\) 18.2786 0.669675
\(746\) −63.9320 −2.34072
\(747\) −25.1646 −0.920724
\(748\) 6.04262 0.220940
\(749\) −1.12564 −0.0411301
\(750\) −73.1554 −2.67126
\(751\) −47.3238 −1.72687 −0.863435 0.504459i \(-0.831692\pi\)
−0.863435 + 0.504459i \(0.831692\pi\)
\(752\) −136.789 −4.98820
\(753\) 91.7421 3.34327
\(754\) −104.355 −3.80038
\(755\) −45.7799 −1.66610
\(756\) −15.5307 −0.564844
\(757\) −16.4081 −0.596363 −0.298181 0.954509i \(-0.596380\pi\)
−0.298181 + 0.954509i \(0.596380\pi\)
\(758\) 95.4730 3.46774
\(759\) −19.1449 −0.694915
\(760\) −215.314 −7.81025
\(761\) 41.4233 1.50159 0.750797 0.660533i \(-0.229670\pi\)
0.750797 + 0.660533i \(0.229670\pi\)
\(762\) −87.7046 −3.17720
\(763\) −0.190930 −0.00691213
\(764\) −62.4851 −2.26063
\(765\) −16.1828 −0.585091
\(766\) 23.8388 0.861330
\(767\) −16.1158 −0.581908
\(768\) 201.945 7.28707
\(769\) −14.4630 −0.521548 −0.260774 0.965400i \(-0.583978\pi\)
−0.260774 + 0.965400i \(0.583978\pi\)
\(770\) −2.10850 −0.0759850
\(771\) 17.3204 0.623777
\(772\) 128.564 4.62712
\(773\) −40.7096 −1.46422 −0.732110 0.681186i \(-0.761465\pi\)
−0.732110 + 0.681186i \(0.761465\pi\)
\(774\) −28.2972 −1.01712
\(775\) −1.10574 −0.0397194
\(776\) −153.765 −5.51985
\(777\) −2.37368 −0.0851553
\(778\) 60.7225 2.17701
\(779\) 99.6201 3.56926
\(780\) −169.252 −6.06019
\(781\) −6.81917 −0.244009
\(782\) 16.0981 0.575668
\(783\) 98.6340 3.52489
\(784\) −112.712 −4.02542
\(785\) 29.4480 1.05104
\(786\) 121.251 4.32488
\(787\) −4.48905 −0.160017 −0.0800087 0.996794i \(-0.525495\pi\)
−0.0800087 + 0.996794i \(0.525495\pi\)
\(788\) 91.2692 3.25133
\(789\) −95.8716 −3.41312
\(790\) −30.4349 −1.08283
\(791\) −1.49266 −0.0530731
\(792\) −67.5043 −2.39866
\(793\) 27.7605 0.985805
\(794\) 68.8274 2.44259
\(795\) 63.4738 2.25118
\(796\) −75.5904 −2.67923
\(797\) 16.3443 0.578943 0.289472 0.957187i \(-0.406520\pi\)
0.289472 + 0.957187i \(0.406520\pi\)
\(798\) −19.4809 −0.689618
\(799\) −8.40296 −0.297275
\(800\) −40.4352 −1.42960
\(801\) 77.0078 2.72094
\(802\) −2.63552 −0.0930634
\(803\) 0.979807 0.0345766
\(804\) −61.5568 −2.17094
\(805\) −4.14153 −0.145970
\(806\) 7.24732 0.255276
\(807\) −0.00935832 −0.000329429 0
\(808\) 187.880 6.60961
\(809\) 12.4977 0.439397 0.219698 0.975568i \(-0.429493\pi\)
0.219698 + 0.975568i \(0.429493\pi\)
\(810\) 83.0232 2.91714
\(811\) −16.3057 −0.572570 −0.286285 0.958144i \(-0.592420\pi\)
−0.286285 + 0.958144i \(0.592420\pi\)
\(812\) −15.2317 −0.534529
\(813\) −65.5643 −2.29944
\(814\) −8.38404 −0.293860
\(815\) 44.0762 1.54392
\(816\) 49.6172 1.73695
\(817\) −13.6886 −0.478903
\(818\) −30.5873 −1.06946
\(819\) −6.67389 −0.233204
\(820\) 171.345 5.98361
\(821\) 15.4545 0.539366 0.269683 0.962949i \(-0.413081\pi\)
0.269683 + 0.962949i \(0.413081\pi\)
\(822\) 15.7782 0.550327
\(823\) −29.9671 −1.04459 −0.522294 0.852766i \(-0.674923\pi\)
−0.522294 + 0.852766i \(0.674923\pi\)
\(824\) 112.434 3.91682
\(825\) 5.31186 0.184935
\(826\) −3.19045 −0.111010
\(827\) 53.3751 1.85604 0.928018 0.372536i \(-0.121512\pi\)
0.928018 + 0.372536i \(0.121512\pi\)
\(828\) −205.992 −7.15873
\(829\) −50.5535 −1.75580 −0.877898 0.478847i \(-0.841055\pi\)
−0.877898 + 0.478847i \(0.841055\pi\)
\(830\) −28.3982 −0.985715
\(831\) −7.63689 −0.264921
\(832\) 139.826 4.84759
\(833\) −6.92387 −0.239898
\(834\) −121.259 −4.19885
\(835\) 41.6773 1.44230
\(836\) −50.7315 −1.75459
\(837\) −6.85002 −0.236771
\(838\) 93.8410 3.24168
\(839\) 24.6800 0.852049 0.426024 0.904712i \(-0.359914\pi\)
0.426024 + 0.904712i \(0.359914\pi\)
\(840\) −21.5676 −0.744152
\(841\) 67.7357 2.33571
\(842\) 78.7892 2.71525
\(843\) 12.7111 0.437795
\(844\) 43.1437 1.48507
\(845\) −4.59827 −0.158185
\(846\) 145.838 5.01402
\(847\) 2.71525 0.0932971
\(848\) −131.769 −4.52496
\(849\) −42.3788 −1.45444
\(850\) −4.46653 −0.153201
\(851\) −16.4680 −0.564516
\(852\) −108.366 −3.71254
\(853\) 2.12450 0.0727414 0.0363707 0.999338i \(-0.488420\pi\)
0.0363707 + 0.999338i \(0.488420\pi\)
\(854\) 5.49576 0.188061
\(855\) 135.865 4.64647
\(856\) −40.6687 −1.39003
\(857\) −5.50448 −0.188029 −0.0940147 0.995571i \(-0.529970\pi\)
−0.0940147 + 0.995571i \(0.529970\pi\)
\(858\) −34.8153 −1.18858
\(859\) −22.9299 −0.782359 −0.391179 0.920314i \(-0.627933\pi\)
−0.391179 + 0.920314i \(0.627933\pi\)
\(860\) −23.5441 −0.802846
\(861\) 9.97876 0.340075
\(862\) −0.373507 −0.0127217
\(863\) 53.4583 1.81974 0.909871 0.414892i \(-0.136180\pi\)
0.909871 + 0.414892i \(0.136180\pi\)
\(864\) −250.494 −8.52199
\(865\) 2.56165 0.0870986
\(866\) −16.5281 −0.561647
\(867\) 3.04798 0.103515
\(868\) 1.05783 0.0359050
\(869\) −4.61580 −0.156580
\(870\) 212.799 7.21457
\(871\) −13.8364 −0.468828
\(872\) −6.89815 −0.233601
\(873\) 97.0272 3.28387
\(874\) −135.154 −4.57165
\(875\) −2.40010 −0.0811382
\(876\) 15.5704 0.526076
\(877\) −55.6896 −1.88050 −0.940252 0.340478i \(-0.889411\pi\)
−0.940252 + 0.340478i \(0.889411\pi\)
\(878\) 1.58594 0.0535229
\(879\) 70.0215 2.36177
\(880\) −45.0867 −1.51987
\(881\) 26.8525 0.904683 0.452342 0.891845i \(-0.350589\pi\)
0.452342 + 0.891845i \(0.350589\pi\)
\(882\) 120.168 4.04626
\(883\) 9.07472 0.305389 0.152694 0.988273i \(-0.451205\pi\)
0.152694 + 0.988273i \(0.451205\pi\)
\(884\) 21.5840 0.725947
\(885\) 32.8631 1.10468
\(886\) 80.4521 2.70284
\(887\) −40.0843 −1.34590 −0.672950 0.739688i \(-0.734973\pi\)
−0.672950 + 0.739688i \(0.734973\pi\)
\(888\) −85.7593 −2.87789
\(889\) −2.87743 −0.0965061
\(890\) 86.9032 2.91300
\(891\) 12.5914 0.421828
\(892\) 63.7900 2.13585
\(893\) 70.5481 2.36080
\(894\) 59.7502 1.99834
\(895\) −9.63980 −0.322223
\(896\) 13.8977 0.464290
\(897\) −68.3846 −2.28330
\(898\) −46.3511 −1.54676
\(899\) −6.71817 −0.224064
\(900\) 57.1539 1.90513
\(901\) −8.09454 −0.269668
\(902\) 35.2458 1.17356
\(903\) −1.37116 −0.0456293
\(904\) −53.9288 −1.79365
\(905\) −7.72767 −0.256876
\(906\) −149.648 −4.97173
\(907\) −13.5350 −0.449421 −0.224710 0.974426i \(-0.572144\pi\)
−0.224710 + 0.974426i \(0.572144\pi\)
\(908\) 48.7701 1.61849
\(909\) −118.554 −3.93219
\(910\) −7.53147 −0.249666
\(911\) −8.64866 −0.286543 −0.143271 0.989683i \(-0.545762\pi\)
−0.143271 + 0.989683i \(0.545762\pi\)
\(912\) −416.567 −13.7939
\(913\) −4.30690 −0.142538
\(914\) −115.254 −3.81228
\(915\) −56.6089 −1.87143
\(916\) −103.578 −3.42231
\(917\) 3.97803 0.131366
\(918\) −27.6699 −0.913244
\(919\) −46.7285 −1.54143 −0.770716 0.637179i \(-0.780101\pi\)
−0.770716 + 0.637179i \(0.780101\pi\)
\(920\) −149.630 −4.93317
\(921\) −22.3041 −0.734945
\(922\) 48.4180 1.59456
\(923\) −24.3578 −0.801746
\(924\) −5.08168 −0.167175
\(925\) 4.56915 0.150233
\(926\) −34.0963 −1.12047
\(927\) −70.9467 −2.33019
\(928\) −245.673 −8.06461
\(929\) 1.55668 0.0510731 0.0255365 0.999674i \(-0.491871\pi\)
0.0255365 + 0.999674i \(0.491871\pi\)
\(930\) −14.7787 −0.484611
\(931\) 58.1302 1.90514
\(932\) 19.8137 0.649018
\(933\) −3.19611 −0.104636
\(934\) 35.6926 1.16790
\(935\) −2.76967 −0.0905780
\(936\) −241.122 −7.88133
\(937\) −56.0835 −1.83217 −0.916084 0.400987i \(-0.868667\pi\)
−0.916084 + 0.400987i \(0.868667\pi\)
\(938\) −2.73919 −0.0894377
\(939\) −28.1102 −0.917341
\(940\) 121.341 3.95772
\(941\) −17.2233 −0.561465 −0.280733 0.959786i \(-0.590577\pi\)
−0.280733 + 0.959786i \(0.590577\pi\)
\(942\) 96.2614 3.13637
\(943\) 69.2302 2.25444
\(944\) −68.2224 −2.22045
\(945\) 7.11858 0.231567
\(946\) −4.84305 −0.157461
\(947\) −23.2500 −0.755522 −0.377761 0.925903i \(-0.623306\pi\)
−0.377761 + 0.925903i \(0.623306\pi\)
\(948\) −73.3511 −2.38233
\(949\) 3.49983 0.113609
\(950\) 37.4993 1.21664
\(951\) 7.41410 0.240419
\(952\) 2.75042 0.0891416
\(953\) 28.5844 0.925938 0.462969 0.886374i \(-0.346784\pi\)
0.462969 + 0.886374i \(0.346784\pi\)
\(954\) 140.485 4.54838
\(955\) 28.6405 0.926784
\(956\) −118.167 −3.82179
\(957\) 32.2734 1.04325
\(958\) −119.278 −3.85369
\(959\) 0.517654 0.0167159
\(960\) −285.131 −9.20257
\(961\) −30.5334 −0.984949
\(962\) −29.9474 −0.965543
\(963\) 25.6623 0.826955
\(964\) 68.3500 2.20140
\(965\) −58.9282 −1.89697
\(966\) −13.5381 −0.435582
\(967\) 49.2918 1.58512 0.792558 0.609797i \(-0.208749\pi\)
0.792558 + 0.609797i \(0.208749\pi\)
\(968\) 98.0999 3.15305
\(969\) −25.5897 −0.822060
\(970\) 109.495 3.51567
\(971\) −41.5039 −1.33192 −0.665962 0.745986i \(-0.731979\pi\)
−0.665962 + 0.745986i \(0.731979\pi\)
\(972\) 31.2282 1.00165
\(973\) −3.97829 −0.127538
\(974\) −63.2819 −2.02768
\(975\) 18.9737 0.607646
\(976\) 117.518 3.76165
\(977\) −0.630180 −0.0201613 −0.0100806 0.999949i \(-0.503209\pi\)
−0.0100806 + 0.999949i \(0.503209\pi\)
\(978\) 144.079 4.60715
\(979\) 13.1798 0.421229
\(980\) 99.9828 3.19383
\(981\) 4.35279 0.138974
\(982\) −100.963 −3.22186
\(983\) 9.70853 0.309654 0.154827 0.987942i \(-0.450518\pi\)
0.154827 + 0.987942i \(0.450518\pi\)
\(984\) 360.525 11.4931
\(985\) −41.8339 −1.33294
\(986\) −27.1374 −0.864230
\(987\) 7.06667 0.224935
\(988\) −181.211 −5.76508
\(989\) −9.51276 −0.302488
\(990\) 48.0692 1.52774
\(991\) 32.8600 1.04383 0.521916 0.852997i \(-0.325217\pi\)
0.521916 + 0.852997i \(0.325217\pi\)
\(992\) 17.0617 0.541710
\(993\) −52.4385 −1.66409
\(994\) −4.82211 −0.152948
\(995\) 34.6474 1.09840
\(996\) −68.4423 −2.16868
\(997\) 8.96902 0.284052 0.142026 0.989863i \(-0.454638\pi\)
0.142026 + 0.989863i \(0.454638\pi\)
\(998\) 12.3139 0.389789
\(999\) 28.3057 0.895552
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 \(a_p\))