Properties

Label 8003.2.a.c.1.20
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30137 q^{2}\) \(+2.98215 q^{3}\) \(+3.29631 q^{4}\) \(+1.02491 q^{5}\) \(-6.86304 q^{6}\) \(+3.76670 q^{7}\) \(-2.98329 q^{8}\) \(+5.89324 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30137 q^{2}\) \(+2.98215 q^{3}\) \(+3.29631 q^{4}\) \(+1.02491 q^{5}\) \(-6.86304 q^{6}\) \(+3.76670 q^{7}\) \(-2.98329 q^{8}\) \(+5.89324 q^{9}\) \(-2.35871 q^{10}\) \(+0.863524 q^{11}\) \(+9.83010 q^{12}\) \(+4.18568 q^{13}\) \(-8.66858 q^{14}\) \(+3.05645 q^{15}\) \(+0.273033 q^{16}\) \(-6.12712 q^{17}\) \(-13.5625 q^{18}\) \(+6.59089 q^{19}\) \(+3.37843 q^{20}\) \(+11.2329 q^{21}\) \(-1.98729 q^{22}\) \(+0.216673 q^{23}\) \(-8.89662 q^{24}\) \(-3.94955 q^{25}\) \(-9.63280 q^{26}\) \(+8.62809 q^{27}\) \(+12.4162 q^{28}\) \(+9.49709 q^{29}\) \(-7.03402 q^{30}\) \(+7.15623 q^{31}\) \(+5.33822 q^{32}\) \(+2.57516 q^{33}\) \(+14.1008 q^{34}\) \(+3.86054 q^{35}\) \(+19.4259 q^{36}\) \(+4.64001 q^{37}\) \(-15.1681 q^{38}\) \(+12.4823 q^{39}\) \(-3.05761 q^{40}\) \(-7.01617 q^{41}\) \(-25.8510 q^{42}\) \(+7.36862 q^{43}\) \(+2.84644 q^{44}\) \(+6.04006 q^{45}\) \(-0.498644 q^{46}\) \(-8.77056 q^{47}\) \(+0.814225 q^{48}\) \(+7.18804 q^{49}\) \(+9.08939 q^{50}\) \(-18.2720 q^{51}\) \(+13.7973 q^{52}\) \(-1.00000 q^{53}\) \(-19.8564 q^{54}\) \(+0.885038 q^{55}\) \(-11.2372 q^{56}\) \(+19.6550 q^{57}\) \(-21.8563 q^{58}\) \(-4.96831 q^{59}\) \(+10.0750 q^{60}\) \(+3.19614 q^{61}\) \(-16.4691 q^{62}\) \(+22.1981 q^{63}\) \(-12.8313 q^{64}\) \(+4.28996 q^{65}\) \(-5.92640 q^{66}\) \(-7.79211 q^{67}\) \(-20.1969 q^{68}\) \(+0.646151 q^{69}\) \(-8.88454 q^{70}\) \(-14.2155 q^{71}\) \(-17.5812 q^{72}\) \(-8.12270 q^{73}\) \(-10.6784 q^{74}\) \(-11.7782 q^{75}\) \(+21.7256 q^{76}\) \(+3.25264 q^{77}\) \(-28.7265 q^{78}\) \(+1.39950 q^{79}\) \(+0.279835 q^{80}\) \(+8.05056 q^{81}\) \(+16.1468 q^{82}\) \(+8.88774 q^{83}\) \(+37.0270 q^{84}\) \(-6.27977 q^{85}\) \(-16.9579 q^{86}\) \(+28.3218 q^{87}\) \(-2.57614 q^{88}\) \(+0.571882 q^{89}\) \(-13.9004 q^{90}\) \(+15.7662 q^{91}\) \(+0.714220 q^{92}\) \(+21.3410 q^{93}\) \(+20.1843 q^{94}\) \(+6.75509 q^{95}\) \(+15.9194 q^{96}\) \(+16.3787 q^{97}\) \(-16.5423 q^{98}\) \(+5.08896 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30137 −1.62732 −0.813658 0.581345i \(-0.802527\pi\)
−0.813658 + 0.581345i \(0.802527\pi\)
\(3\) 2.98215 1.72175 0.860874 0.508819i \(-0.169918\pi\)
0.860874 + 0.508819i \(0.169918\pi\)
\(4\) 3.29631 1.64815
\(5\) 1.02491 0.458355 0.229178 0.973385i \(-0.426396\pi\)
0.229178 + 0.973385i \(0.426396\pi\)
\(6\) −6.86304 −2.80183
\(7\) 3.76670 1.42368 0.711840 0.702342i \(-0.247862\pi\)
0.711840 + 0.702342i \(0.247862\pi\)
\(8\) −2.98329 −1.05475
\(9\) 5.89324 1.96441
\(10\) −2.35871 −0.745888
\(11\) 0.863524 0.260362 0.130181 0.991490i \(-0.458444\pi\)
0.130181 + 0.991490i \(0.458444\pi\)
\(12\) 9.83010 2.83770
\(13\) 4.18568 1.16090 0.580449 0.814296i \(-0.302877\pi\)
0.580449 + 0.814296i \(0.302877\pi\)
\(14\) −8.66858 −2.31677
\(15\) 3.05645 0.789172
\(16\) 0.273033 0.0682582
\(17\) −6.12712 −1.48605 −0.743023 0.669266i \(-0.766609\pi\)
−0.743023 + 0.669266i \(0.766609\pi\)
\(18\) −13.5625 −3.19672
\(19\) 6.59089 1.51205 0.756026 0.654541i \(-0.227138\pi\)
0.756026 + 0.654541i \(0.227138\pi\)
\(20\) 3.37843 0.755440
\(21\) 11.2329 2.45122
\(22\) −1.98729 −0.423692
\(23\) 0.216673 0.0451794 0.0225897 0.999745i \(-0.492809\pi\)
0.0225897 + 0.999745i \(0.492809\pi\)
\(24\) −8.89662 −1.81601
\(25\) −3.94955 −0.789910
\(26\) −9.63280 −1.88915
\(27\) 8.62809 1.66048
\(28\) 12.4162 2.34644
\(29\) 9.49709 1.76356 0.881782 0.471657i \(-0.156344\pi\)
0.881782 + 0.471657i \(0.156344\pi\)
\(30\) −7.03402 −1.28423
\(31\) 7.15623 1.28530 0.642648 0.766161i \(-0.277836\pi\)
0.642648 + 0.766161i \(0.277836\pi\)
\(32\) 5.33822 0.943674
\(33\) 2.57516 0.448278
\(34\) 14.1008 2.41826
\(35\) 3.86054 0.652551
\(36\) 19.4259 3.23766
\(37\) 4.64001 0.762813 0.381407 0.924407i \(-0.375440\pi\)
0.381407 + 0.924407i \(0.375440\pi\)
\(38\) −15.1681 −2.46059
\(39\) 12.4823 1.99877
\(40\) −3.05761 −0.483451
\(41\) −7.01617 −1.09574 −0.547871 0.836563i \(-0.684561\pi\)
−0.547871 + 0.836563i \(0.684561\pi\)
\(42\) −25.8510 −3.98890
\(43\) 7.36862 1.12370 0.561852 0.827238i \(-0.310089\pi\)
0.561852 + 0.827238i \(0.310089\pi\)
\(44\) 2.84644 0.429117
\(45\) 6.04006 0.900399
\(46\) −0.498644 −0.0735211
\(47\) −8.77056 −1.27932 −0.639659 0.768659i \(-0.720924\pi\)
−0.639659 + 0.768659i \(0.720924\pi\)
\(48\) 0.814225 0.117523
\(49\) 7.18804 1.02686
\(50\) 9.08939 1.28543
\(51\) −18.2720 −2.55859
\(52\) 13.7973 1.91334
\(53\) −1.00000 −0.137361
\(54\) −19.8564 −2.70212
\(55\) 0.885038 0.119338
\(56\) −11.2372 −1.50163
\(57\) 19.6550 2.60337
\(58\) −21.8563 −2.86988
\(59\) −4.96831 −0.646819 −0.323409 0.946259i \(-0.604829\pi\)
−0.323409 + 0.946259i \(0.604829\pi\)
\(60\) 10.0750 1.30068
\(61\) 3.19614 0.409224 0.204612 0.978843i \(-0.434407\pi\)
0.204612 + 0.978843i \(0.434407\pi\)
\(62\) −16.4691 −2.09158
\(63\) 22.1981 2.79669
\(64\) −12.8313 −1.60391
\(65\) 4.28996 0.532104
\(66\) −5.92640 −0.729490
\(67\) −7.79211 −0.951958 −0.475979 0.879457i \(-0.657906\pi\)
−0.475979 + 0.879457i \(0.657906\pi\)
\(68\) −20.1969 −2.44923
\(69\) 0.646151 0.0777875
\(70\) −8.88454 −1.06191
\(71\) −14.2155 −1.68707 −0.843536 0.537072i \(-0.819530\pi\)
−0.843536 + 0.537072i \(0.819530\pi\)
\(72\) −17.5812 −2.07197
\(73\) −8.12270 −0.950690 −0.475345 0.879800i \(-0.657677\pi\)
−0.475345 + 0.879800i \(0.657677\pi\)
\(74\) −10.6784 −1.24134
\(75\) −11.7782 −1.36003
\(76\) 21.7256 2.49210
\(77\) 3.25264 0.370673
\(78\) −28.7265 −3.25264
\(79\) 1.39950 0.157456 0.0787279 0.996896i \(-0.474914\pi\)
0.0787279 + 0.996896i \(0.474914\pi\)
\(80\) 0.279835 0.0312865
\(81\) 8.05056 0.894506
\(82\) 16.1468 1.78312
\(83\) 8.88774 0.975556 0.487778 0.872968i \(-0.337808\pi\)
0.487778 + 0.872968i \(0.337808\pi\)
\(84\) 37.0270 4.03998
\(85\) −6.27977 −0.681137
\(86\) −16.9579 −1.82862
\(87\) 28.3218 3.03641
\(88\) −2.57614 −0.274618
\(89\) 0.571882 0.0606194 0.0303097 0.999541i \(-0.490351\pi\)
0.0303097 + 0.999541i \(0.490351\pi\)
\(90\) −13.9004 −1.46523
\(91\) 15.7662 1.65275
\(92\) 0.714220 0.0744626
\(93\) 21.3410 2.21296
\(94\) 20.1843 2.08185
\(95\) 6.75509 0.693057
\(96\) 15.9194 1.62477
\(97\) 16.3787 1.66300 0.831502 0.555521i \(-0.187481\pi\)
0.831502 + 0.555521i \(0.187481\pi\)
\(98\) −16.5423 −1.67103
\(99\) 5.08896 0.511459
\(100\) −13.0189 −1.30189
\(101\) 12.7568 1.26935 0.634677 0.772778i \(-0.281133\pi\)
0.634677 + 0.772778i \(0.281133\pi\)
\(102\) 42.0507 4.16364
\(103\) −17.8429 −1.75811 −0.879057 0.476716i \(-0.841827\pi\)
−0.879057 + 0.476716i \(0.841827\pi\)
\(104\) −12.4871 −1.22446
\(105\) 11.5127 1.12353
\(106\) 2.30137 0.223529
\(107\) −12.1193 −1.17162 −0.585808 0.810450i \(-0.699223\pi\)
−0.585808 + 0.810450i \(0.699223\pi\)
\(108\) 28.4408 2.73672
\(109\) −15.2640 −1.46202 −0.731011 0.682366i \(-0.760951\pi\)
−0.731011 + 0.682366i \(0.760951\pi\)
\(110\) −2.03680 −0.194201
\(111\) 13.8372 1.31337
\(112\) 1.02843 0.0971777
\(113\) 9.15204 0.860951 0.430476 0.902602i \(-0.358346\pi\)
0.430476 + 0.902602i \(0.358346\pi\)
\(114\) −45.2335 −4.23651
\(115\) 0.222071 0.0207082
\(116\) 31.3053 2.90663
\(117\) 24.6672 2.28049
\(118\) 11.4339 1.05258
\(119\) −23.0790 −2.11565
\(120\) −9.11826 −0.832380
\(121\) −10.2543 −0.932211
\(122\) −7.35551 −0.665937
\(123\) −20.9233 −1.88659
\(124\) 23.5891 2.11837
\(125\) −9.17252 −0.820415
\(126\) −51.0860 −4.55110
\(127\) −10.8226 −0.960350 −0.480175 0.877173i \(-0.659427\pi\)
−0.480175 + 0.877173i \(0.659427\pi\)
\(128\) 18.8531 1.66640
\(129\) 21.9744 1.93473
\(130\) −9.87279 −0.865901
\(131\) −3.51885 −0.307443 −0.153722 0.988114i \(-0.549126\pi\)
−0.153722 + 0.988114i \(0.549126\pi\)
\(132\) 8.48853 0.738832
\(133\) 24.8259 2.15268
\(134\) 17.9325 1.54913
\(135\) 8.84304 0.761088
\(136\) 18.2790 1.56741
\(137\) 1.52226 0.130056 0.0650279 0.997883i \(-0.479286\pi\)
0.0650279 + 0.997883i \(0.479286\pi\)
\(138\) −1.48703 −0.126585
\(139\) 7.96461 0.675550 0.337775 0.941227i \(-0.390326\pi\)
0.337775 + 0.941227i \(0.390326\pi\)
\(140\) 12.7255 1.07550
\(141\) −26.1552 −2.20266
\(142\) 32.7152 2.74540
\(143\) 3.61444 0.302254
\(144\) 1.60905 0.134087
\(145\) 9.73369 0.808339
\(146\) 18.6933 1.54707
\(147\) 21.4358 1.76800
\(148\) 15.2949 1.25723
\(149\) −11.6082 −0.950979 −0.475489 0.879721i \(-0.657729\pi\)
−0.475489 + 0.879721i \(0.657729\pi\)
\(150\) 27.1059 2.21319
\(151\) 1.00000 0.0813788
\(152\) −19.6625 −1.59484
\(153\) −36.1086 −2.91921
\(154\) −7.48553 −0.603201
\(155\) 7.33452 0.589123
\(156\) 41.1457 3.29429
\(157\) 8.42536 0.672417 0.336208 0.941788i \(-0.390855\pi\)
0.336208 + 0.941788i \(0.390855\pi\)
\(158\) −3.22076 −0.256230
\(159\) −2.98215 −0.236500
\(160\) 5.47122 0.432538
\(161\) 0.816141 0.0643210
\(162\) −18.5273 −1.45564
\(163\) 3.67800 0.288084 0.144042 0.989572i \(-0.453990\pi\)
0.144042 + 0.989572i \(0.453990\pi\)
\(164\) −23.1274 −1.80595
\(165\) 2.63932 0.205471
\(166\) −20.4540 −1.58754
\(167\) 7.46285 0.577493 0.288747 0.957406i \(-0.406762\pi\)
0.288747 + 0.957406i \(0.406762\pi\)
\(168\) −33.5109 −2.58542
\(169\) 4.51992 0.347686
\(170\) 14.4521 1.10842
\(171\) 38.8417 2.97030
\(172\) 24.2893 1.85204
\(173\) −11.7681 −0.894710 −0.447355 0.894356i \(-0.647634\pi\)
−0.447355 + 0.894356i \(0.647634\pi\)
\(174\) −65.1789 −4.94120
\(175\) −14.8768 −1.12458
\(176\) 0.235770 0.0177719
\(177\) −14.8163 −1.11366
\(178\) −1.31611 −0.0986468
\(179\) −8.07427 −0.603499 −0.301750 0.953387i \(-0.597571\pi\)
−0.301750 + 0.953387i \(0.597571\pi\)
\(180\) 19.9099 1.48400
\(181\) 15.6685 1.16463 0.582314 0.812964i \(-0.302147\pi\)
0.582314 + 0.812964i \(0.302147\pi\)
\(182\) −36.2839 −2.68954
\(183\) 9.53139 0.704580
\(184\) −0.646397 −0.0476530
\(185\) 4.75561 0.349639
\(186\) −49.1135 −3.60118
\(187\) −5.29092 −0.386910
\(188\) −28.9105 −2.10851
\(189\) 32.4994 2.36399
\(190\) −15.5460 −1.12782
\(191\) 9.20737 0.666222 0.333111 0.942888i \(-0.391902\pi\)
0.333111 + 0.942888i \(0.391902\pi\)
\(192\) −38.2649 −2.76153
\(193\) 21.8627 1.57371 0.786856 0.617137i \(-0.211707\pi\)
0.786856 + 0.617137i \(0.211707\pi\)
\(194\) −37.6935 −2.70623
\(195\) 12.7933 0.916149
\(196\) 23.6940 1.69243
\(197\) −22.2579 −1.58581 −0.792907 0.609343i \(-0.791433\pi\)
−0.792907 + 0.609343i \(0.791433\pi\)
\(198\) −11.7116 −0.832306
\(199\) −19.2109 −1.36182 −0.680911 0.732366i \(-0.738416\pi\)
−0.680911 + 0.732366i \(0.738416\pi\)
\(200\) 11.7826 0.833159
\(201\) −23.2373 −1.63903
\(202\) −29.3582 −2.06564
\(203\) 35.7727 2.51075
\(204\) −60.2302 −4.21696
\(205\) −7.19096 −0.502239
\(206\) 41.0632 2.86101
\(207\) 1.27690 0.0887510
\(208\) 1.14283 0.0792408
\(209\) 5.69139 0.393682
\(210\) −26.4951 −1.82833
\(211\) −7.00867 −0.482496 −0.241248 0.970463i \(-0.577557\pi\)
−0.241248 + 0.970463i \(0.577557\pi\)
\(212\) −3.29631 −0.226391
\(213\) −42.3929 −2.90471
\(214\) 27.8910 1.90659
\(215\) 7.55220 0.515056
\(216\) −25.7401 −1.75139
\(217\) 26.9554 1.82985
\(218\) 35.1280 2.37917
\(219\) −24.2231 −1.63685
\(220\) 2.91736 0.196688
\(221\) −25.6462 −1.72515
\(222\) −31.8446 −2.13727
\(223\) −6.07744 −0.406975 −0.203488 0.979078i \(-0.565228\pi\)
−0.203488 + 0.979078i \(0.565228\pi\)
\(224\) 20.1075 1.34349
\(225\) −23.2757 −1.55171
\(226\) −21.0622 −1.40104
\(227\) 20.1276 1.33591 0.667957 0.744200i \(-0.267169\pi\)
0.667957 + 0.744200i \(0.267169\pi\)
\(228\) 64.7891 4.29076
\(229\) −11.4592 −0.757245 −0.378623 0.925551i \(-0.623602\pi\)
−0.378623 + 0.925551i \(0.623602\pi\)
\(230\) −0.511067 −0.0336988
\(231\) 9.69987 0.638204
\(232\) −28.3325 −1.86012
\(233\) −20.8098 −1.36329 −0.681647 0.731681i \(-0.738736\pi\)
−0.681647 + 0.731681i \(0.738736\pi\)
\(234\) −56.7684 −3.71107
\(235\) −8.98907 −0.586382
\(236\) −16.3771 −1.06606
\(237\) 4.17352 0.271099
\(238\) 53.1134 3.44283
\(239\) 7.05149 0.456123 0.228061 0.973647i \(-0.426761\pi\)
0.228061 + 0.973647i \(0.426761\pi\)
\(240\) 0.834510 0.0538674
\(241\) −4.47295 −0.288128 −0.144064 0.989568i \(-0.546017\pi\)
−0.144064 + 0.989568i \(0.546017\pi\)
\(242\) 23.5990 1.51700
\(243\) −1.87626 −0.120362
\(244\) 10.5355 0.674464
\(245\) 7.36712 0.470668
\(246\) 48.1522 3.07007
\(247\) 27.5873 1.75534
\(248\) −21.3491 −1.35567
\(249\) 26.5046 1.67966
\(250\) 21.1094 1.33507
\(251\) −3.29159 −0.207764 −0.103882 0.994590i \(-0.533126\pi\)
−0.103882 + 0.994590i \(0.533126\pi\)
\(252\) 73.1717 4.60938
\(253\) 0.187102 0.0117630
\(254\) 24.9068 1.56279
\(255\) −18.7272 −1.17275
\(256\) −17.7255 −1.10784
\(257\) 17.2999 1.07914 0.539570 0.841941i \(-0.318587\pi\)
0.539570 + 0.841941i \(0.318587\pi\)
\(258\) −50.5712 −3.14842
\(259\) 17.4775 1.08600
\(260\) 14.1410 0.876990
\(261\) 55.9686 3.46437
\(262\) 8.09818 0.500307
\(263\) 24.6932 1.52265 0.761324 0.648371i \(-0.224549\pi\)
0.761324 + 0.648371i \(0.224549\pi\)
\(264\) −7.68245 −0.472822
\(265\) −1.02491 −0.0629599
\(266\) −57.1336 −3.50309
\(267\) 1.70544 0.104371
\(268\) −25.6852 −1.56897
\(269\) 1.30272 0.0794283 0.0397142 0.999211i \(-0.487355\pi\)
0.0397142 + 0.999211i \(0.487355\pi\)
\(270\) −20.3511 −1.23853
\(271\) −18.8618 −1.14577 −0.572887 0.819634i \(-0.694177\pi\)
−0.572887 + 0.819634i \(0.694177\pi\)
\(272\) −1.67290 −0.101435
\(273\) 47.0173 2.84561
\(274\) −3.50329 −0.211642
\(275\) −3.41054 −0.205663
\(276\) 2.12991 0.128206
\(277\) −25.2993 −1.52009 −0.760044 0.649871i \(-0.774823\pi\)
−0.760044 + 0.649871i \(0.774823\pi\)
\(278\) −18.3295 −1.09933
\(279\) 42.1734 2.52485
\(280\) −11.5171 −0.688279
\(281\) 6.56159 0.391432 0.195716 0.980661i \(-0.437297\pi\)
0.195716 + 0.980661i \(0.437297\pi\)
\(282\) 60.1928 3.58443
\(283\) 4.81080 0.285972 0.142986 0.989725i \(-0.454330\pi\)
0.142986 + 0.989725i \(0.454330\pi\)
\(284\) −46.8588 −2.78056
\(285\) 20.1447 1.19327
\(286\) −8.31816 −0.491863
\(287\) −26.4278 −1.55998
\(288\) 31.4594 1.85377
\(289\) 20.5416 1.20833
\(290\) −22.4008 −1.31542
\(291\) 48.8438 2.86327
\(292\) −26.7749 −1.56688
\(293\) −19.2109 −1.12231 −0.561156 0.827710i \(-0.689643\pi\)
−0.561156 + 0.827710i \(0.689643\pi\)
\(294\) −49.3318 −2.87709
\(295\) −5.09209 −0.296473
\(296\) −13.8425 −0.804578
\(297\) 7.45056 0.432326
\(298\) 26.7147 1.54754
\(299\) 0.906923 0.0524487
\(300\) −38.8245 −2.24153
\(301\) 27.7554 1.59979
\(302\) −2.30137 −0.132429
\(303\) 38.0429 2.18551
\(304\) 1.79953 0.103210
\(305\) 3.27577 0.187570
\(306\) 83.0993 4.75047
\(307\) 8.02995 0.458293 0.229147 0.973392i \(-0.426406\pi\)
0.229147 + 0.973392i \(0.426406\pi\)
\(308\) 10.7217 0.610926
\(309\) −53.2103 −3.02703
\(310\) −16.8794 −0.958688
\(311\) −6.83456 −0.387553 −0.193776 0.981046i \(-0.562074\pi\)
−0.193776 + 0.981046i \(0.562074\pi\)
\(312\) −37.2384 −2.10821
\(313\) −24.0777 −1.36095 −0.680476 0.732770i \(-0.738227\pi\)
−0.680476 + 0.732770i \(0.738227\pi\)
\(314\) −19.3899 −1.09423
\(315\) 22.7511 1.28188
\(316\) 4.61318 0.259511
\(317\) 12.0555 0.677105 0.338553 0.940947i \(-0.390063\pi\)
0.338553 + 0.940947i \(0.390063\pi\)
\(318\) 6.86304 0.384860
\(319\) 8.20097 0.459166
\(320\) −13.1510 −0.735162
\(321\) −36.1416 −2.01723
\(322\) −1.87824 −0.104670
\(323\) −40.3832 −2.24698
\(324\) 26.5371 1.47428
\(325\) −16.5316 −0.917006
\(326\) −8.46445 −0.468803
\(327\) −45.5195 −2.51723
\(328\) 20.9312 1.15573
\(329\) −33.0361 −1.82134
\(330\) −6.07405 −0.334366
\(331\) 21.0996 1.15974 0.579869 0.814709i \(-0.303104\pi\)
0.579869 + 0.814709i \(0.303104\pi\)
\(332\) 29.2967 1.60787
\(333\) 27.3447 1.49848
\(334\) −17.1748 −0.939763
\(335\) −7.98624 −0.436335
\(336\) 3.06694 0.167315
\(337\) 22.0181 1.19940 0.599700 0.800225i \(-0.295287\pi\)
0.599700 + 0.800225i \(0.295287\pi\)
\(338\) −10.4020 −0.565795
\(339\) 27.2928 1.48234
\(340\) −20.7001 −1.12262
\(341\) 6.17958 0.334643
\(342\) −89.3891 −4.83361
\(343\) 0.708285 0.0382438
\(344\) −21.9827 −1.18523
\(345\) 0.662249 0.0356543
\(346\) 27.0827 1.45598
\(347\) 27.0479 1.45201 0.726003 0.687691i \(-0.241376\pi\)
0.726003 + 0.687691i \(0.241376\pi\)
\(348\) 93.3573 5.00448
\(349\) −28.2299 −1.51111 −0.755555 0.655085i \(-0.772633\pi\)
−0.755555 + 0.655085i \(0.772633\pi\)
\(350\) 34.2370 1.83004
\(351\) 36.1144 1.92764
\(352\) 4.60969 0.245697
\(353\) −3.27578 −0.174352 −0.0871761 0.996193i \(-0.527784\pi\)
−0.0871761 + 0.996193i \(0.527784\pi\)
\(354\) 34.0977 1.81227
\(355\) −14.5697 −0.773279
\(356\) 1.88510 0.0999101
\(357\) −68.8252 −3.64262
\(358\) 18.5819 0.982083
\(359\) −9.51743 −0.502311 −0.251156 0.967947i \(-0.580811\pi\)
−0.251156 + 0.967947i \(0.580811\pi\)
\(360\) −18.0192 −0.949697
\(361\) 24.4398 1.28630
\(362\) −36.0590 −1.89522
\(363\) −30.5800 −1.60503
\(364\) 51.9703 2.72398
\(365\) −8.32506 −0.435754
\(366\) −21.9353 −1.14657
\(367\) 0.0106411 0.000555461 0 0.000277730 1.00000i \(-0.499912\pi\)
0.000277730 1.00000i \(0.499912\pi\)
\(368\) 0.0591587 0.00308386
\(369\) −41.3480 −2.15249
\(370\) −10.9444 −0.568973
\(371\) −3.76670 −0.195557
\(372\) 70.3464 3.64729
\(373\) −1.61894 −0.0838256 −0.0419128 0.999121i \(-0.513345\pi\)
−0.0419128 + 0.999121i \(0.513345\pi\)
\(374\) 12.1764 0.629625
\(375\) −27.3539 −1.41255
\(376\) 26.1651 1.34936
\(377\) 39.7518 2.04732
\(378\) −74.7932 −3.84695
\(379\) −18.3501 −0.942582 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(380\) 22.2669 1.14227
\(381\) −32.2746 −1.65348
\(382\) −21.1896 −1.08415
\(383\) −35.0226 −1.78957 −0.894787 0.446494i \(-0.852672\pi\)
−0.894787 + 0.446494i \(0.852672\pi\)
\(384\) 56.2229 2.86911
\(385\) 3.33367 0.169900
\(386\) −50.3142 −2.56093
\(387\) 43.4251 2.20742
\(388\) 53.9892 2.74089
\(389\) 34.5712 1.75283 0.876414 0.481558i \(-0.159929\pi\)
0.876414 + 0.481558i \(0.159929\pi\)
\(390\) −29.4422 −1.49086
\(391\) −1.32758 −0.0671386
\(392\) −21.4440 −1.08308
\(393\) −10.4938 −0.529340
\(394\) 51.2238 2.58062
\(395\) 1.43436 0.0721707
\(396\) 16.7748 0.842964
\(397\) 32.9100 1.65170 0.825852 0.563887i \(-0.190695\pi\)
0.825852 + 0.563887i \(0.190695\pi\)
\(398\) 44.2113 2.21611
\(399\) 74.0346 3.70637
\(400\) −1.07836 −0.0539178
\(401\) −24.4522 −1.22109 −0.610543 0.791983i \(-0.709049\pi\)
−0.610543 + 0.791983i \(0.709049\pi\)
\(402\) 53.4776 2.66722
\(403\) 29.9537 1.49210
\(404\) 42.0505 2.09209
\(405\) 8.25113 0.410002
\(406\) −82.3262 −4.08578
\(407\) 4.00676 0.198608
\(408\) 54.5107 2.69868
\(409\) 10.3637 0.512450 0.256225 0.966617i \(-0.417521\pi\)
0.256225 + 0.966617i \(0.417521\pi\)
\(410\) 16.5491 0.817300
\(411\) 4.53962 0.223923
\(412\) −58.8158 −2.89764
\(413\) −18.7141 −0.920863
\(414\) −2.93863 −0.144426
\(415\) 9.10916 0.447151
\(416\) 22.3441 1.09551
\(417\) 23.7517 1.16313
\(418\) −13.0980 −0.640644
\(419\) 35.6432 1.74128 0.870642 0.491918i \(-0.163704\pi\)
0.870642 + 0.491918i \(0.163704\pi\)
\(420\) 37.9495 1.85175
\(421\) −24.7546 −1.20646 −0.603232 0.797566i \(-0.706121\pi\)
−0.603232 + 0.797566i \(0.706121\pi\)
\(422\) 16.1295 0.785174
\(423\) −51.6870 −2.51311
\(424\) 2.98329 0.144881
\(425\) 24.1994 1.17384
\(426\) 97.5618 4.72688
\(427\) 12.0389 0.582604
\(428\) −39.9489 −1.93100
\(429\) 10.7788 0.520406
\(430\) −17.3804 −0.838158
\(431\) −26.0687 −1.25569 −0.627843 0.778340i \(-0.716062\pi\)
−0.627843 + 0.778340i \(0.716062\pi\)
\(432\) 2.35575 0.113341
\(433\) −25.1886 −1.21049 −0.605243 0.796041i \(-0.706924\pi\)
−0.605243 + 0.796041i \(0.706924\pi\)
\(434\) −62.0343 −2.97774
\(435\) 29.0274 1.39176
\(436\) −50.3147 −2.40964
\(437\) 1.42807 0.0683136
\(438\) 55.7464 2.66367
\(439\) 3.73501 0.178262 0.0891312 0.996020i \(-0.471591\pi\)
0.0891312 + 0.996020i \(0.471591\pi\)
\(440\) −2.64032 −0.125872
\(441\) 42.3608 2.01718
\(442\) 59.0214 2.80736
\(443\) 21.4642 1.01979 0.509896 0.860236i \(-0.329684\pi\)
0.509896 + 0.860236i \(0.329684\pi\)
\(444\) 45.6118 2.16464
\(445\) 0.586129 0.0277852
\(446\) 13.9864 0.662277
\(447\) −34.6174 −1.63734
\(448\) −48.3317 −2.28346
\(449\) −25.4051 −1.19894 −0.599469 0.800398i \(-0.704622\pi\)
−0.599469 + 0.800398i \(0.704622\pi\)
\(450\) 53.5659 2.52512
\(451\) −6.05863 −0.285290
\(452\) 30.1679 1.41898
\(453\) 2.98215 0.140114
\(454\) −46.3210 −2.17395
\(455\) 16.1590 0.757546
\(456\) −58.6366 −2.74591
\(457\) −26.0744 −1.21971 −0.609855 0.792513i \(-0.708772\pi\)
−0.609855 + 0.792513i \(0.708772\pi\)
\(458\) 26.3719 1.23228
\(459\) −52.8653 −2.46754
\(460\) 0.732014 0.0341303
\(461\) 2.95690 0.137717 0.0688583 0.997626i \(-0.478064\pi\)
0.0688583 + 0.997626i \(0.478064\pi\)
\(462\) −22.3230 −1.03856
\(463\) 31.3854 1.45860 0.729302 0.684192i \(-0.239845\pi\)
0.729302 + 0.684192i \(0.239845\pi\)
\(464\) 2.59301 0.120378
\(465\) 21.8727 1.01432
\(466\) 47.8911 2.21851
\(467\) −4.53566 −0.209885 −0.104943 0.994478i \(-0.533466\pi\)
−0.104943 + 0.994478i \(0.533466\pi\)
\(468\) 81.3108 3.75859
\(469\) −29.3505 −1.35528
\(470\) 20.6872 0.954229
\(471\) 25.1257 1.15773
\(472\) 14.8219 0.682233
\(473\) 6.36299 0.292570
\(474\) −9.60481 −0.441164
\(475\) −26.0311 −1.19439
\(476\) −76.0756 −3.48692
\(477\) −5.89324 −0.269833
\(478\) −16.2281 −0.742256
\(479\) −17.4030 −0.795161 −0.397581 0.917567i \(-0.630150\pi\)
−0.397581 + 0.917567i \(0.630150\pi\)
\(480\) 16.3160 0.744721
\(481\) 19.4216 0.885549
\(482\) 10.2939 0.468875
\(483\) 2.43386 0.110744
\(484\) −33.8014 −1.53643
\(485\) 16.7867 0.762247
\(486\) 4.31796 0.195867
\(487\) 30.5766 1.38556 0.692780 0.721149i \(-0.256386\pi\)
0.692780 + 0.721149i \(0.256386\pi\)
\(488\) −9.53501 −0.431630
\(489\) 10.9684 0.496007
\(490\) −16.9545 −0.765925
\(491\) −20.5542 −0.927597 −0.463798 0.885941i \(-0.653514\pi\)
−0.463798 + 0.885941i \(0.653514\pi\)
\(492\) −68.9696 −3.10939
\(493\) −58.1898 −2.62074
\(494\) −63.4887 −2.85649
\(495\) 5.21574 0.234430
\(496\) 1.95388 0.0877320
\(497\) −53.5456 −2.40185
\(498\) −60.9969 −2.73334
\(499\) 30.7657 1.37726 0.688630 0.725113i \(-0.258212\pi\)
0.688630 + 0.725113i \(0.258212\pi\)
\(500\) −30.2354 −1.35217
\(501\) 22.2554 0.994297
\(502\) 7.57518 0.338097
\(503\) 5.88141 0.262239 0.131120 0.991367i \(-0.458143\pi\)
0.131120 + 0.991367i \(0.458143\pi\)
\(504\) −66.2232 −2.94982
\(505\) 13.0747 0.581815
\(506\) −0.430592 −0.0191421
\(507\) 13.4791 0.598628
\(508\) −35.6746 −1.58280
\(509\) −12.3095 −0.545608 −0.272804 0.962070i \(-0.587951\pi\)
−0.272804 + 0.962070i \(0.587951\pi\)
\(510\) 43.0983 1.90843
\(511\) −30.5958 −1.35348
\(512\) 3.08658 0.136409
\(513\) 56.8667 2.51073
\(514\) −39.8136 −1.75610
\(515\) −18.2874 −0.805841
\(516\) 72.4343 3.18874
\(517\) −7.57360 −0.333086
\(518\) −40.2223 −1.76727
\(519\) −35.0942 −1.54047
\(520\) −12.7982 −0.561237
\(521\) 32.1477 1.40842 0.704208 0.709994i \(-0.251302\pi\)
0.704208 + 0.709994i \(0.251302\pi\)
\(522\) −128.805 −5.63762
\(523\) 13.2888 0.581079 0.290540 0.956863i \(-0.406165\pi\)
0.290540 + 0.956863i \(0.406165\pi\)
\(524\) −11.5992 −0.506714
\(525\) −44.3649 −1.93624
\(526\) −56.8282 −2.47783
\(527\) −43.8471 −1.91001
\(528\) 0.703103 0.0305987
\(529\) −22.9531 −0.997959
\(530\) 2.35871 0.102456
\(531\) −29.2794 −1.27062
\(532\) 81.8338 3.54795
\(533\) −29.3674 −1.27204
\(534\) −3.92485 −0.169845
\(535\) −12.4212 −0.537017
\(536\) 23.2461 1.00408
\(537\) −24.0787 −1.03907
\(538\) −2.99804 −0.129255
\(539\) 6.20705 0.267356
\(540\) 29.1494 1.25439
\(541\) 20.9537 0.900869 0.450434 0.892810i \(-0.351269\pi\)
0.450434 + 0.892810i \(0.351269\pi\)
\(542\) 43.4081 1.86454
\(543\) 46.7258 2.00519
\(544\) −32.7080 −1.40234
\(545\) −15.6442 −0.670125
\(546\) −108.204 −4.63071
\(547\) −6.13372 −0.262259 −0.131129 0.991365i \(-0.541860\pi\)
−0.131129 + 0.991365i \(0.541860\pi\)
\(548\) 5.01785 0.214352
\(549\) 18.8356 0.803885
\(550\) 7.84891 0.334679
\(551\) 62.5942 2.66660
\(552\) −1.92765 −0.0820464
\(553\) 5.27149 0.224167
\(554\) 58.2231 2.47366
\(555\) 14.1820 0.601991
\(556\) 26.2538 1.11341
\(557\) −11.6686 −0.494413 −0.247206 0.968963i \(-0.579513\pi\)
−0.247206 + 0.968963i \(0.579513\pi\)
\(558\) −97.0566 −4.10873
\(559\) 30.8427 1.30451
\(560\) 1.05405 0.0445419
\(561\) −15.7783 −0.666162
\(562\) −15.1007 −0.636983
\(563\) −22.4138 −0.944629 −0.472315 0.881430i \(-0.656581\pi\)
−0.472315 + 0.881430i \(0.656581\pi\)
\(564\) −86.2155 −3.63033
\(565\) 9.38005 0.394621
\(566\) −11.0714 −0.465367
\(567\) 30.3240 1.27349
\(568\) 42.4090 1.77944
\(569\) −4.75678 −0.199415 −0.0997073 0.995017i \(-0.531791\pi\)
−0.0997073 + 0.995017i \(0.531791\pi\)
\(570\) −46.3604 −1.94183
\(571\) 8.35497 0.349645 0.174822 0.984600i \(-0.444065\pi\)
0.174822 + 0.984600i \(0.444065\pi\)
\(572\) 11.9143 0.498162
\(573\) 27.4578 1.14707
\(574\) 60.8202 2.53859
\(575\) −0.855760 −0.0356877
\(576\) −75.6179 −3.15075
\(577\) −5.80685 −0.241742 −0.120871 0.992668i \(-0.538569\pi\)
−0.120871 + 0.992668i \(0.538569\pi\)
\(578\) −47.2739 −1.96634
\(579\) 65.1979 2.70953
\(580\) 32.0852 1.33227
\(581\) 33.4775 1.38888
\(582\) −112.408 −4.65945
\(583\) −0.863524 −0.0357635
\(584\) 24.2323 1.00274
\(585\) 25.2818 1.04527
\(586\) 44.2114 1.82636
\(587\) 34.5297 1.42519 0.712597 0.701573i \(-0.247519\pi\)
0.712597 + 0.701573i \(0.247519\pi\)
\(588\) 70.6591 2.91393
\(589\) 47.1659 1.94344
\(590\) 11.7188 0.482455
\(591\) −66.3766 −2.73037
\(592\) 1.26687 0.0520682
\(593\) −2.15064 −0.0883161 −0.0441580 0.999025i \(-0.514061\pi\)
−0.0441580 + 0.999025i \(0.514061\pi\)
\(594\) −17.1465 −0.703530
\(595\) −23.6540 −0.969720
\(596\) −38.2641 −1.56736
\(597\) −57.2897 −2.34471
\(598\) −2.08717 −0.0853506
\(599\) −1.62242 −0.0662901 −0.0331451 0.999451i \(-0.510552\pi\)
−0.0331451 + 0.999451i \(0.510552\pi\)
\(600\) 35.1377 1.43449
\(601\) −8.76684 −0.357607 −0.178803 0.983885i \(-0.557223\pi\)
−0.178803 + 0.983885i \(0.557223\pi\)
\(602\) −63.8755 −2.60337
\(603\) −45.9208 −1.87004
\(604\) 3.29631 0.134125
\(605\) −10.5098 −0.427284
\(606\) −87.5508 −3.55651
\(607\) −25.2819 −1.02616 −0.513081 0.858340i \(-0.671496\pi\)
−0.513081 + 0.858340i \(0.671496\pi\)
\(608\) 35.1836 1.42688
\(609\) 106.680 4.32288
\(610\) −7.53876 −0.305235
\(611\) −36.7108 −1.48516
\(612\) −119.025 −4.81130
\(613\) −8.53372 −0.344674 −0.172337 0.985038i \(-0.555132\pi\)
−0.172337 + 0.985038i \(0.555132\pi\)
\(614\) −18.4799 −0.745788
\(615\) −21.4446 −0.864728
\(616\) −9.70355 −0.390967
\(617\) 25.4705 1.02540 0.512702 0.858566i \(-0.328644\pi\)
0.512702 + 0.858566i \(0.328644\pi\)
\(618\) 122.457 4.92593
\(619\) 8.99297 0.361458 0.180729 0.983533i \(-0.442154\pi\)
0.180729 + 0.983533i \(0.442154\pi\)
\(620\) 24.1768 0.970965
\(621\) 1.86947 0.0750193
\(622\) 15.7289 0.630670
\(623\) 2.15411 0.0863025
\(624\) 3.40809 0.136433
\(625\) 10.3467 0.413869
\(626\) 55.4118 2.21470
\(627\) 16.9726 0.677821
\(628\) 27.7726 1.10825
\(629\) −28.4299 −1.13357
\(630\) −52.3587 −2.08602
\(631\) −19.2999 −0.768316 −0.384158 0.923267i \(-0.625508\pi\)
−0.384158 + 0.923267i \(0.625508\pi\)
\(632\) −4.17510 −0.166077
\(633\) −20.9009 −0.830737
\(634\) −27.7442 −1.10186
\(635\) −11.0922 −0.440181
\(636\) −9.83010 −0.389789
\(637\) 30.0868 1.19208
\(638\) −18.8735 −0.747208
\(639\) −83.7755 −3.31411
\(640\) 19.3228 0.763802
\(641\) −1.48377 −0.0586054 −0.0293027 0.999571i \(-0.509329\pi\)
−0.0293027 + 0.999571i \(0.509329\pi\)
\(642\) 83.1752 3.28266
\(643\) −32.2039 −1.27000 −0.634999 0.772513i \(-0.718999\pi\)
−0.634999 + 0.772513i \(0.718999\pi\)
\(644\) 2.69025 0.106011
\(645\) 22.5218 0.886796
\(646\) 92.9367 3.65654
\(647\) −0.243253 −0.00956326 −0.00478163 0.999989i \(-0.501522\pi\)
−0.00478163 + 0.999989i \(0.501522\pi\)
\(648\) −24.0171 −0.943482
\(649\) −4.29026 −0.168407
\(650\) 38.0453 1.49226
\(651\) 80.3851 3.15054
\(652\) 12.1238 0.474806
\(653\) −41.8638 −1.63826 −0.819128 0.573611i \(-0.805542\pi\)
−0.819128 + 0.573611i \(0.805542\pi\)
\(654\) 104.757 4.09633
\(655\) −3.60652 −0.140918
\(656\) −1.91564 −0.0747933
\(657\) −47.8690 −1.86755
\(658\) 76.0283 2.96389
\(659\) 5.98576 0.233172 0.116586 0.993181i \(-0.462805\pi\)
0.116586 + 0.993181i \(0.462805\pi\)
\(660\) 8.70001 0.338647
\(661\) −23.8982 −0.929533 −0.464767 0.885433i \(-0.653862\pi\)
−0.464767 + 0.885433i \(0.653862\pi\)
\(662\) −48.5580 −1.88726
\(663\) −76.4809 −2.97027
\(664\) −26.5147 −1.02897
\(665\) 25.4444 0.986691
\(666\) −62.9303 −2.43850
\(667\) 2.05776 0.0796768
\(668\) 24.5999 0.951798
\(669\) −18.1239 −0.700709
\(670\) 18.3793 0.710054
\(671\) 2.75995 0.106547
\(672\) 59.9636 2.31315
\(673\) −20.0899 −0.774409 −0.387205 0.921994i \(-0.626559\pi\)
−0.387205 + 0.921994i \(0.626559\pi\)
\(674\) −50.6717 −1.95180
\(675\) −34.0771 −1.31163
\(676\) 14.8991 0.573041
\(677\) −14.8548 −0.570916 −0.285458 0.958391i \(-0.592146\pi\)
−0.285458 + 0.958391i \(0.592146\pi\)
\(678\) −62.8108 −2.41223
\(679\) 61.6937 2.36759
\(680\) 18.7344 0.718430
\(681\) 60.0236 2.30011
\(682\) −14.2215 −0.544570
\(683\) −43.5634 −1.66691 −0.833454 0.552588i \(-0.813640\pi\)
−0.833454 + 0.552588i \(0.813640\pi\)
\(684\) 128.034 4.89551
\(685\) 1.56019 0.0596117
\(686\) −1.63003 −0.0622347
\(687\) −34.1731 −1.30378
\(688\) 2.01187 0.0767020
\(689\) −4.18568 −0.159462
\(690\) −1.52408 −0.0580208
\(691\) −15.7860 −0.600527 −0.300263 0.953856i \(-0.597075\pi\)
−0.300263 + 0.953856i \(0.597075\pi\)
\(692\) −38.7912 −1.47462
\(693\) 19.1686 0.728154
\(694\) −62.2472 −2.36287
\(695\) 8.16304 0.309642
\(696\) −84.4920 −3.20266
\(697\) 42.9889 1.62832
\(698\) 64.9674 2.45905
\(699\) −62.0580 −2.34725
\(700\) −49.0385 −1.85348
\(701\) 28.1957 1.06494 0.532469 0.846450i \(-0.321264\pi\)
0.532469 + 0.846450i \(0.321264\pi\)
\(702\) −83.1127 −3.13689
\(703\) 30.5818 1.15341
\(704\) −11.0801 −0.417599
\(705\) −26.8068 −1.00960
\(706\) 7.53879 0.283726
\(707\) 48.0512 1.80715
\(708\) −48.8390 −1.83548
\(709\) 27.9666 1.05031 0.525153 0.851008i \(-0.324008\pi\)
0.525153 + 0.851008i \(0.324008\pi\)
\(710\) 33.5302 1.25837
\(711\) 8.24757 0.309308
\(712\) −1.70609 −0.0639383
\(713\) 1.55056 0.0580689
\(714\) 158.392 5.92769
\(715\) 3.70449 0.138540
\(716\) −26.6153 −0.994659
\(717\) 21.0286 0.785328
\(718\) 21.9031 0.817418
\(719\) −6.31211 −0.235402 −0.117701 0.993049i \(-0.537552\pi\)
−0.117701 + 0.993049i \(0.537552\pi\)
\(720\) 1.64913 0.0614596
\(721\) −67.2089 −2.50299
\(722\) −56.2450 −2.09322
\(723\) −13.3390 −0.496084
\(724\) 51.6481 1.91949
\(725\) −37.5092 −1.39306
\(726\) 70.3759 2.61189
\(727\) 50.8684 1.88660 0.943302 0.331935i \(-0.107701\pi\)
0.943302 + 0.331935i \(0.107701\pi\)
\(728\) −47.0351 −1.74324
\(729\) −29.7470 −1.10174
\(730\) 19.1591 0.709108
\(731\) −45.1485 −1.66988
\(732\) 31.4184 1.16126
\(733\) 20.6622 0.763177 0.381588 0.924332i \(-0.375377\pi\)
0.381588 + 0.924332i \(0.375377\pi\)
\(734\) −0.0244891 −0.000903910 0
\(735\) 21.9699 0.810371
\(736\) 1.15665 0.0426346
\(737\) −6.72868 −0.247854
\(738\) 95.1570 3.50278
\(739\) −9.64377 −0.354752 −0.177376 0.984143i \(-0.556761\pi\)
−0.177376 + 0.984143i \(0.556761\pi\)
\(740\) 15.6760 0.576260
\(741\) 82.2697 3.02225
\(742\) 8.66858 0.318233
\(743\) 2.22098 0.0814799 0.0407399 0.999170i \(-0.487028\pi\)
0.0407399 + 0.999170i \(0.487028\pi\)
\(744\) −63.6663 −2.33412
\(745\) −11.8974 −0.435886
\(746\) 3.72579 0.136411
\(747\) 52.3776 1.91640
\(748\) −17.4405 −0.637688
\(749\) −45.6498 −1.66801
\(750\) 62.9514 2.29866
\(751\) 13.9140 0.507729 0.253865 0.967240i \(-0.418298\pi\)
0.253865 + 0.967240i \(0.418298\pi\)
\(752\) −2.39465 −0.0873239
\(753\) −9.81604 −0.357716
\(754\) −91.4836 −3.33164
\(755\) 1.02491 0.0373004
\(756\) 107.128 3.89621
\(757\) 17.9477 0.652319 0.326160 0.945315i \(-0.394245\pi\)
0.326160 + 0.945315i \(0.394245\pi\)
\(758\) 42.2304 1.53388
\(759\) 0.557968 0.0202529
\(760\) −20.1524 −0.731003
\(761\) −14.9073 −0.540390 −0.270195 0.962806i \(-0.587088\pi\)
−0.270195 + 0.962806i \(0.587088\pi\)
\(762\) 74.2759 2.69073
\(763\) −57.4948 −2.08145
\(764\) 30.3503 1.09804
\(765\) −37.0082 −1.33803
\(766\) 80.6001 2.91220
\(767\) −20.7958 −0.750891
\(768\) −52.8600 −1.90742
\(769\) −3.55627 −0.128243 −0.0641213 0.997942i \(-0.520424\pi\)
−0.0641213 + 0.997942i \(0.520424\pi\)
\(770\) −7.67202 −0.276480
\(771\) 51.5911 1.85801
\(772\) 72.0662 2.59372
\(773\) 25.7717 0.926943 0.463472 0.886112i \(-0.346604\pi\)
0.463472 + 0.886112i \(0.346604\pi\)
\(774\) −99.9372 −3.59217
\(775\) −28.2639 −1.01527
\(776\) −48.8623 −1.75406
\(777\) 52.1207 1.86982
\(778\) −79.5611 −2.85240
\(779\) −46.2428 −1.65682
\(780\) 42.1707 1.50995
\(781\) −12.2755 −0.439250
\(782\) 3.05526 0.109256
\(783\) 81.9417 2.92836
\(784\) 1.96257 0.0700918
\(785\) 8.63526 0.308206
\(786\) 24.1500 0.861403
\(787\) −18.0928 −0.644938 −0.322469 0.946580i \(-0.604513\pi\)
−0.322469 + 0.946580i \(0.604513\pi\)
\(788\) −73.3691 −2.61366
\(789\) 73.6390 2.62162
\(790\) −3.30100 −0.117444
\(791\) 34.4730 1.22572
\(792\) −15.1818 −0.539462
\(793\) 13.3780 0.475068
\(794\) −75.7381 −2.68784
\(795\) −3.05645 −0.108401
\(796\) −63.3249 −2.24449
\(797\) 55.6917 1.97270 0.986351 0.164655i \(-0.0526510\pi\)
0.986351 + 0.164655i \(0.0526510\pi\)
\(798\) −170.381 −6.03143
\(799\) 53.7383 1.90113
\(800\) −21.0836 −0.745418
\(801\) 3.37024 0.119081
\(802\) 56.2737 1.98709
\(803\) −7.01415 −0.247524
\(804\) −76.5972 −2.70137
\(805\) 0.836474 0.0294818
\(806\) −68.9346 −2.42812
\(807\) 3.88491 0.136755
\(808\) −38.0573 −1.33885
\(809\) −16.9104 −0.594538 −0.297269 0.954794i \(-0.596076\pi\)
−0.297269 + 0.954794i \(0.596076\pi\)
\(810\) −18.9889 −0.667202
\(811\) 23.3920 0.821404 0.410702 0.911770i \(-0.365284\pi\)
0.410702 + 0.911770i \(0.365284\pi\)
\(812\) 117.918 4.13810
\(813\) −56.2489 −1.97273
\(814\) −9.22105 −0.323198
\(815\) 3.76964 0.132045
\(816\) −4.98886 −0.174645
\(817\) 48.5657 1.69910
\(818\) −23.8506 −0.833918
\(819\) 92.9141 3.24668
\(820\) −23.7036 −0.827767
\(821\) 37.5790 1.31152 0.655758 0.754971i \(-0.272349\pi\)
0.655758 + 0.754971i \(0.272349\pi\)
\(822\) −10.4474 −0.364393
\(823\) −20.5585 −0.716625 −0.358312 0.933602i \(-0.616648\pi\)
−0.358312 + 0.933602i \(0.616648\pi\)
\(824\) 53.2305 1.85437
\(825\) −10.1707 −0.354100
\(826\) 43.0682 1.49853
\(827\) −1.54728 −0.0538042 −0.0269021 0.999638i \(-0.508564\pi\)
−0.0269021 + 0.999638i \(0.508564\pi\)
\(828\) 4.20907 0.146275
\(829\) −11.5037 −0.399540 −0.199770 0.979843i \(-0.564019\pi\)
−0.199770 + 0.979843i \(0.564019\pi\)
\(830\) −20.9636 −0.727656
\(831\) −75.4464 −2.61721
\(832\) −53.7077 −1.86198
\(833\) −44.0420 −1.52596
\(834\) −54.6615 −1.89277
\(835\) 7.64878 0.264697
\(836\) 18.7606 0.648848
\(837\) 61.7446 2.13420
\(838\) −82.0282 −2.83362
\(839\) −23.6796 −0.817511 −0.408755 0.912644i \(-0.634037\pi\)
−0.408755 + 0.912644i \(0.634037\pi\)
\(840\) −34.3458 −1.18504
\(841\) 61.1946 2.11016
\(842\) 56.9694 1.96330
\(843\) 19.5677 0.673947
\(844\) −23.1027 −0.795229
\(845\) 4.63253 0.159364
\(846\) 118.951 4.08962
\(847\) −38.6250 −1.32717
\(848\) −0.273033 −0.00937598
\(849\) 14.3465 0.492372
\(850\) −55.6918 −1.91021
\(851\) 1.00536 0.0344634
\(852\) −139.740 −4.78741
\(853\) −27.6271 −0.945933 −0.472966 0.881080i \(-0.656817\pi\)
−0.472966 + 0.881080i \(0.656817\pi\)
\(854\) −27.7060 −0.948080
\(855\) 39.8094 1.36145
\(856\) 36.1553 1.23576
\(857\) −2.20949 −0.0754747 −0.0377373 0.999288i \(-0.512015\pi\)
−0.0377373 + 0.999288i \(0.512015\pi\)
\(858\) −24.8060 −0.846864
\(859\) 18.8250 0.642301 0.321150 0.947028i \(-0.395931\pi\)
0.321150 + 0.947028i \(0.395931\pi\)
\(860\) 24.8944 0.848891
\(861\) −78.8118 −2.68590
\(862\) 59.9937 2.04340
\(863\) 51.1166 1.74003 0.870015 0.493025i \(-0.164109\pi\)
0.870015 + 0.493025i \(0.164109\pi\)
\(864\) 46.0587 1.56695
\(865\) −12.0613 −0.410095
\(866\) 57.9683 1.96984
\(867\) 61.2583 2.08044
\(868\) 88.8533 3.01588
\(869\) 1.20850 0.0409956
\(870\) −66.8027 −2.26482
\(871\) −32.6153 −1.10513
\(872\) 45.5368 1.54207
\(873\) 96.5236 3.26683
\(874\) −3.28651 −0.111168
\(875\) −34.5501 −1.16801
\(876\) −79.8469 −2.69778
\(877\) 13.2566 0.447644 0.223822 0.974630i \(-0.428146\pi\)
0.223822 + 0.974630i \(0.428146\pi\)
\(878\) −8.59565 −0.290089
\(879\) −57.2898 −1.93234
\(880\) 0.241644 0.00814582
\(881\) 47.4575 1.59889 0.799443 0.600742i \(-0.205128\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(882\) −97.4880 −3.28259
\(883\) −22.9651 −0.772836 −0.386418 0.922324i \(-0.626288\pi\)
−0.386418 + 0.922324i \(0.626288\pi\)
\(884\) −84.5377 −2.84331
\(885\) −15.1854 −0.510451
\(886\) −49.3970 −1.65952
\(887\) 15.5718 0.522849 0.261425 0.965224i \(-0.415808\pi\)
0.261425 + 0.965224i \(0.415808\pi\)
\(888\) −41.2804 −1.38528
\(889\) −40.7655 −1.36723
\(890\) −1.34890 −0.0452153
\(891\) 6.95185 0.232896
\(892\) −20.0331 −0.670758
\(893\) −57.8058 −1.93440
\(894\) 79.6674 2.66448
\(895\) −8.27542 −0.276617
\(896\) 71.0141 2.37242
\(897\) 2.70458 0.0903034
\(898\) 58.4665 1.95105
\(899\) 67.9633 2.26670
\(900\) −76.7238 −2.55746
\(901\) 6.12712 0.204124
\(902\) 13.9432 0.464256
\(903\) 82.7709 2.75444
\(904\) −27.3032 −0.908089
\(905\) 16.0588 0.533813
\(906\) −6.86304 −0.228009
\(907\) 47.0825 1.56335 0.781675 0.623686i \(-0.214366\pi\)
0.781675 + 0.623686i \(0.214366\pi\)
\(908\) 66.3467 2.20179
\(909\) 75.1792 2.49354
\(910\) −37.1879 −1.23277
\(911\) 43.7170 1.44841 0.724205 0.689585i \(-0.242207\pi\)
0.724205 + 0.689585i \(0.242207\pi\)
\(912\) 5.36647 0.177701
\(913\) 7.67478 0.253998
\(914\) 60.0069 1.98485
\(915\) 9.76885 0.322948
\(916\) −37.7731 −1.24806
\(917\) −13.2545 −0.437701
\(918\) 121.663 4.01547
\(919\) 39.9549 1.31799 0.658995 0.752147i \(-0.270982\pi\)
0.658995 + 0.752147i \(0.270982\pi\)
\(920\) −0.662501 −0.0218420
\(921\) 23.9465 0.789065
\(922\) −6.80493 −0.224108
\(923\) −59.5017 −1.95852
\(924\) 31.9738 1.05186
\(925\) −18.3260 −0.602554
\(926\) −72.2295 −2.37361
\(927\) −105.153 −3.45366
\(928\) 50.6976 1.66423
\(929\) 38.6007 1.26645 0.633223 0.773969i \(-0.281731\pi\)
0.633223 + 0.773969i \(0.281731\pi\)
\(930\) −50.3371 −1.65062
\(931\) 47.3755 1.55267
\(932\) −68.5955 −2.24692
\(933\) −20.3817 −0.667268
\(934\) 10.4382 0.341549
\(935\) −5.42274 −0.177342
\(936\) −73.5894 −2.40534
\(937\) −56.8786 −1.85814 −0.929071 0.369901i \(-0.879391\pi\)
−0.929071 + 0.369901i \(0.879391\pi\)
\(938\) 67.5465 2.20547
\(939\) −71.8034 −2.34322
\(940\) −29.6307 −0.966448
\(941\) −31.4540 −1.02537 −0.512685 0.858577i \(-0.671349\pi\)
−0.512685 + 0.858577i \(0.671349\pi\)
\(942\) −57.8236 −1.88399
\(943\) −1.52021 −0.0495049
\(944\) −1.35651 −0.0441507
\(945\) 33.3091 1.08354
\(946\) −14.6436 −0.476104
\(947\) −12.2615 −0.398445 −0.199223 0.979954i \(-0.563842\pi\)
−0.199223 + 0.979954i \(0.563842\pi\)
\(948\) 13.7572 0.446813
\(949\) −33.9990 −1.10365
\(950\) 59.9071 1.94364
\(951\) 35.9514 1.16580
\(952\) 68.8514 2.23149
\(953\) 12.0491 0.390308 0.195154 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(954\) 13.5625 0.439103
\(955\) 9.43676 0.305366
\(956\) 23.2439 0.751761
\(957\) 24.4565 0.790568
\(958\) 40.0507 1.29398
\(959\) 5.73391 0.185158
\(960\) −39.2182 −1.26576
\(961\) 20.2116 0.651988
\(962\) −44.6963 −1.44107
\(963\) −71.4219 −2.30154
\(964\) −14.7442 −0.474880
\(965\) 22.4074 0.721319
\(966\) −5.60121 −0.180216
\(967\) 39.4582 1.26889 0.634444 0.772968i \(-0.281229\pi\)
0.634444 + 0.772968i \(0.281229\pi\)
\(968\) 30.5916 0.983251
\(969\) −120.429 −3.86873
\(970\) −38.6325 −1.24042
\(971\) −44.0502 −1.41364 −0.706820 0.707394i \(-0.749871\pi\)
−0.706820 + 0.707394i \(0.749871\pi\)
\(972\) −6.18472 −0.198375
\(973\) 30.0003 0.961766
\(974\) −70.3682 −2.25474
\(975\) −49.2997 −1.57885
\(976\) 0.872651 0.0279329
\(977\) 32.7288 1.04709 0.523544 0.851999i \(-0.324610\pi\)
0.523544 + 0.851999i \(0.324610\pi\)
\(978\) −25.2423 −0.807160
\(979\) 0.493834 0.0157830
\(980\) 24.2843 0.775733
\(981\) −89.9541 −2.87201
\(982\) 47.3028 1.50949
\(983\) 9.28298 0.296081 0.148040 0.988981i \(-0.452703\pi\)
0.148040 + 0.988981i \(0.452703\pi\)
\(984\) 62.4202 1.98988
\(985\) −22.8125 −0.726866
\(986\) 133.916 4.26477
\(987\) −98.5187 −3.13589
\(988\) 90.9364 2.89307
\(989\) 1.59658 0.0507683
\(990\) −12.0034 −0.381492
\(991\) 34.4009 1.09278 0.546390 0.837531i \(-0.316002\pi\)
0.546390 + 0.837531i \(0.316002\pi\)
\(992\) 38.2016 1.21290
\(993\) 62.9222 1.99678
\(994\) 123.228 3.90857
\(995\) −19.6895 −0.624198
\(996\) 87.3673 2.76834
\(997\) −9.71779 −0.307766 −0.153883 0.988089i \(-0.549178\pi\)
−0.153883 + 0.988089i \(0.549178\pi\)
\(998\) −70.8032 −2.24124
\(999\) 40.0344 1.26663
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 \(a_p\))