Properties

Label 8003.2.a.c.1.5
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 1.5
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.68534 q^{2}\) \(-1.17289 q^{3}\) \(+5.21107 q^{4}\) \(+0.884422 q^{5}\) \(+3.14961 q^{6}\) \(-0.361098 q^{7}\) \(-8.62282 q^{8}\) \(-1.62433 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.68534 q^{2}\) \(-1.17289 q^{3}\) \(+5.21107 q^{4}\) \(+0.884422 q^{5}\) \(+3.14961 q^{6}\) \(-0.361098 q^{7}\) \(-8.62282 q^{8}\) \(-1.62433 q^{9}\) \(-2.37498 q^{10}\) \(-0.487997 q^{11}\) \(-6.11201 q^{12}\) \(+3.81664 q^{13}\) \(+0.969672 q^{14}\) \(-1.03733 q^{15}\) \(+12.7331 q^{16}\) \(+1.24710 q^{17}\) \(+4.36188 q^{18}\) \(+2.14182 q^{19}\) \(+4.60878 q^{20}\) \(+0.423529 q^{21}\) \(+1.31044 q^{22}\) \(-8.74394 q^{23}\) \(+10.1136 q^{24}\) \(-4.21780 q^{25}\) \(-10.2490 q^{26}\) \(+5.42383 q^{27}\) \(-1.88171 q^{28}\) \(-1.05174 q^{29}\) \(+2.78559 q^{30}\) \(+1.50367 q^{31}\) \(-16.9471 q^{32}\) \(+0.572367 q^{33}\) \(-3.34889 q^{34}\) \(-0.319363 q^{35}\) \(-8.46448 q^{36}\) \(+8.49233 q^{37}\) \(-5.75152 q^{38}\) \(-4.47650 q^{39}\) \(-7.62621 q^{40}\) \(+9.25630 q^{41}\) \(-1.13732 q^{42}\) \(+7.47251 q^{43}\) \(-2.54298 q^{44}\) \(-1.43659 q^{45}\) \(+23.4805 q^{46}\) \(-1.75620 q^{47}\) \(-14.9345 q^{48}\) \(-6.86961 q^{49}\) \(+11.3262 q^{50}\) \(-1.46271 q^{51}\) \(+19.8887 q^{52}\) \(-1.00000 q^{53}\) \(-14.5648 q^{54}\) \(-0.431595 q^{55}\) \(+3.11368 q^{56}\) \(-2.51212 q^{57}\) \(+2.82428 q^{58}\) \(-4.21030 q^{59}\) \(-5.40559 q^{60}\) \(+6.49096 q^{61}\) \(-4.03787 q^{62}\) \(+0.586542 q^{63}\) \(+20.0425 q^{64}\) \(+3.37552 q^{65}\) \(-1.53700 q^{66}\) \(-15.1703 q^{67}\) \(+6.49872 q^{68}\) \(+10.2557 q^{69}\) \(+0.857599 q^{70}\) \(-11.2902 q^{71}\) \(+14.0063 q^{72}\) \(+15.6610 q^{73}\) \(-22.8048 q^{74}\) \(+4.94701 q^{75}\) \(+11.1612 q^{76}\) \(+0.176215 q^{77}\) \(+12.0209 q^{78}\) \(-7.81059 q^{79}\) \(+11.2614 q^{80}\) \(-1.48857 q^{81}\) \(-24.8564 q^{82}\) \(+12.9474 q^{83}\) \(+2.20704 q^{84}\) \(+1.10296 q^{85}\) \(-20.0663 q^{86}\) \(+1.23358 q^{87}\) \(+4.20791 q^{88}\) \(-7.41778 q^{89}\) \(+3.85774 q^{90}\) \(-1.37818 q^{91}\) \(-45.5653 q^{92}\) \(-1.76364 q^{93}\) \(+4.71600 q^{94}\) \(+1.89427 q^{95}\) \(+19.8771 q^{96}\) \(-12.2137 q^{97}\) \(+18.4473 q^{98}\) \(+0.792667 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68534 −1.89882 −0.949412 0.314033i \(-0.898320\pi\)
−0.949412 + 0.314033i \(0.898320\pi\)
\(3\) −1.17289 −0.677169 −0.338584 0.940936i \(-0.609948\pi\)
−0.338584 + 0.940936i \(0.609948\pi\)
\(4\) 5.21107 2.60553
\(5\) 0.884422 0.395525 0.197763 0.980250i \(-0.436632\pi\)
0.197763 + 0.980250i \(0.436632\pi\)
\(6\) 3.14961 1.28582
\(7\) −0.361098 −0.136482 −0.0682411 0.997669i \(-0.521739\pi\)
−0.0682411 + 0.997669i \(0.521739\pi\)
\(8\) −8.62282 −3.04863
\(9\) −1.62433 −0.541443
\(10\) −2.37498 −0.751033
\(11\) −0.487997 −0.147137 −0.0735683 0.997290i \(-0.523439\pi\)
−0.0735683 + 0.997290i \(0.523439\pi\)
\(12\) −6.11201 −1.76439
\(13\) 3.81664 1.05854 0.529272 0.848452i \(-0.322465\pi\)
0.529272 + 0.848452i \(0.322465\pi\)
\(14\) 0.969672 0.259156
\(15\) −1.03733 −0.267837
\(16\) 12.7331 3.18327
\(17\) 1.24710 0.302466 0.151233 0.988498i \(-0.451676\pi\)
0.151233 + 0.988498i \(0.451676\pi\)
\(18\) 4.36188 1.02810
\(19\) 2.14182 0.491367 0.245684 0.969350i \(-0.420988\pi\)
0.245684 + 0.969350i \(0.420988\pi\)
\(20\) 4.60878 1.03055
\(21\) 0.423529 0.0924215
\(22\) 1.31044 0.279386
\(23\) −8.74394 −1.82324 −0.911619 0.411036i \(-0.865167\pi\)
−0.911619 + 0.411036i \(0.865167\pi\)
\(24\) 10.1136 2.06443
\(25\) −4.21780 −0.843560
\(26\) −10.2490 −2.00999
\(27\) 5.42383 1.04382
\(28\) −1.88171 −0.355609
\(29\) −1.05174 −0.195303 −0.0976517 0.995221i \(-0.531133\pi\)
−0.0976517 + 0.995221i \(0.531133\pi\)
\(30\) 2.78559 0.508576
\(31\) 1.50367 0.270067 0.135034 0.990841i \(-0.456886\pi\)
0.135034 + 0.990841i \(0.456886\pi\)
\(32\) −16.9471 −2.99585
\(33\) 0.572367 0.0996362
\(34\) −3.34889 −0.574330
\(35\) −0.319363 −0.0539822
\(36\) −8.46448 −1.41075
\(37\) 8.49233 1.39613 0.698065 0.716034i \(-0.254045\pi\)
0.698065 + 0.716034i \(0.254045\pi\)
\(38\) −5.75152 −0.933020
\(39\) −4.47650 −0.716813
\(40\) −7.62621 −1.20581
\(41\) 9.25630 1.44559 0.722796 0.691062i \(-0.242857\pi\)
0.722796 + 0.691062i \(0.242857\pi\)
\(42\) −1.13732 −0.175492
\(43\) 7.47251 1.13955 0.569774 0.821802i \(-0.307031\pi\)
0.569774 + 0.821802i \(0.307031\pi\)
\(44\) −2.54298 −0.383369
\(45\) −1.43659 −0.214154
\(46\) 23.4805 3.46201
\(47\) −1.75620 −0.256168 −0.128084 0.991763i \(-0.540883\pi\)
−0.128084 + 0.991763i \(0.540883\pi\)
\(48\) −14.9345 −2.15561
\(49\) −6.86961 −0.981373
\(50\) 11.3262 1.60177
\(51\) −1.46271 −0.204820
\(52\) 19.8887 2.75807
\(53\) −1.00000 −0.137361
\(54\) −14.5648 −1.98202
\(55\) −0.431595 −0.0581962
\(56\) 3.11368 0.416084
\(57\) −2.51212 −0.332738
\(58\) 2.82428 0.370847
\(59\) −4.21030 −0.548134 −0.274067 0.961711i \(-0.588369\pi\)
−0.274067 + 0.961711i \(0.588369\pi\)
\(60\) −5.40559 −0.697859
\(61\) 6.49096 0.831083 0.415541 0.909574i \(-0.363592\pi\)
0.415541 + 0.909574i \(0.363592\pi\)
\(62\) −4.03787 −0.512811
\(63\) 0.586542 0.0738973
\(64\) 20.0425 2.50532
\(65\) 3.37552 0.418681
\(66\) −1.53700 −0.189192
\(67\) −15.1703 −1.85334 −0.926671 0.375874i \(-0.877342\pi\)
−0.926671 + 0.375874i \(0.877342\pi\)
\(68\) 6.49872 0.788086
\(69\) 10.2557 1.23464
\(70\) 0.857599 0.102503
\(71\) −11.2902 −1.33990 −0.669949 0.742407i \(-0.733684\pi\)
−0.669949 + 0.742407i \(0.733684\pi\)
\(72\) 14.0063 1.65066
\(73\) 15.6610 1.83298 0.916492 0.400052i \(-0.131008\pi\)
0.916492 + 0.400052i \(0.131008\pi\)
\(74\) −22.8048 −2.65101
\(75\) 4.94701 0.571232
\(76\) 11.1612 1.28027
\(77\) 0.176215 0.0200815
\(78\) 12.0209 1.36110
\(79\) −7.81059 −0.878760 −0.439380 0.898301i \(-0.644802\pi\)
−0.439380 + 0.898301i \(0.644802\pi\)
\(80\) 11.2614 1.25907
\(81\) −1.48857 −0.165397
\(82\) −24.8564 −2.74492
\(83\) 12.9474 1.42117 0.710583 0.703613i \(-0.248431\pi\)
0.710583 + 0.703613i \(0.248431\pi\)
\(84\) 2.20704 0.240807
\(85\) 1.10296 0.119633
\(86\) −20.0663 −2.16380
\(87\) 1.23358 0.132253
\(88\) 4.20791 0.448564
\(89\) −7.41778 −0.786284 −0.393142 0.919478i \(-0.628612\pi\)
−0.393142 + 0.919478i \(0.628612\pi\)
\(90\) 3.85774 0.406642
\(91\) −1.37818 −0.144473
\(92\) −45.5653 −4.75051
\(93\) −1.76364 −0.182881
\(94\) 4.71600 0.486418
\(95\) 1.89427 0.194348
\(96\) 19.8771 2.02869
\(97\) −12.2137 −1.24011 −0.620055 0.784558i \(-0.712890\pi\)
−0.620055 + 0.784558i \(0.712890\pi\)
\(98\) 18.4473 1.86345
\(99\) 0.792667 0.0796660
\(100\) −21.9792 −2.19792
\(101\) −10.0030 −0.995334 −0.497667 0.867368i \(-0.665810\pi\)
−0.497667 + 0.867368i \(0.665810\pi\)
\(102\) 3.92788 0.388918
\(103\) 10.0840 0.993608 0.496804 0.867863i \(-0.334507\pi\)
0.496804 + 0.867863i \(0.334507\pi\)
\(104\) −32.9102 −3.22711
\(105\) 0.374578 0.0365551
\(106\) 2.68534 0.260824
\(107\) −2.87826 −0.278252 −0.139126 0.990275i \(-0.544429\pi\)
−0.139126 + 0.990275i \(0.544429\pi\)
\(108\) 28.2639 2.71970
\(109\) 3.78290 0.362337 0.181168 0.983452i \(-0.442012\pi\)
0.181168 + 0.983452i \(0.442012\pi\)
\(110\) 1.15898 0.110504
\(111\) −9.96057 −0.945416
\(112\) −4.59790 −0.434460
\(113\) −0.945287 −0.0889251 −0.0444626 0.999011i \(-0.514158\pi\)
−0.0444626 + 0.999011i \(0.514158\pi\)
\(114\) 6.74590 0.631812
\(115\) −7.73333 −0.721137
\(116\) −5.48069 −0.508870
\(117\) −6.19947 −0.573141
\(118\) 11.3061 1.04081
\(119\) −0.450325 −0.0412813
\(120\) 8.94471 0.816536
\(121\) −10.7619 −0.978351
\(122\) −17.4305 −1.57808
\(123\) −10.8566 −0.978909
\(124\) 7.83573 0.703670
\(125\) −8.15242 −0.729175
\(126\) −1.57507 −0.140318
\(127\) 14.4738 1.28434 0.642171 0.766562i \(-0.278034\pi\)
0.642171 + 0.766562i \(0.278034\pi\)
\(128\) −19.9269 −1.76131
\(129\) −8.76443 −0.771665
\(130\) −9.06442 −0.795002
\(131\) 1.81293 0.158396 0.0791980 0.996859i \(-0.474764\pi\)
0.0791980 + 0.996859i \(0.474764\pi\)
\(132\) 2.98264 0.259606
\(133\) −0.773407 −0.0670629
\(134\) 40.7373 3.51917
\(135\) 4.79695 0.412856
\(136\) −10.7535 −0.922106
\(137\) 20.2414 1.72934 0.864671 0.502339i \(-0.167527\pi\)
0.864671 + 0.502339i \(0.167527\pi\)
\(138\) −27.5400 −2.34436
\(139\) 5.02638 0.426332 0.213166 0.977016i \(-0.431622\pi\)
0.213166 + 0.977016i \(0.431622\pi\)
\(140\) −1.66422 −0.140652
\(141\) 2.05983 0.173469
\(142\) 30.3180 2.54423
\(143\) −1.86251 −0.155751
\(144\) −20.6827 −1.72356
\(145\) −0.930182 −0.0772474
\(146\) −42.0552 −3.48052
\(147\) 8.05730 0.664555
\(148\) 44.2541 3.63767
\(149\) 11.8723 0.972618 0.486309 0.873787i \(-0.338343\pi\)
0.486309 + 0.873787i \(0.338343\pi\)
\(150\) −13.2844 −1.08467
\(151\) 1.00000 0.0813788
\(152\) −18.4685 −1.49800
\(153\) −2.02570 −0.163768
\(154\) −0.473197 −0.0381313
\(155\) 1.32988 0.106819
\(156\) −23.3273 −1.86768
\(157\) −1.16809 −0.0932236 −0.0466118 0.998913i \(-0.514842\pi\)
−0.0466118 + 0.998913i \(0.514842\pi\)
\(158\) 20.9741 1.66861
\(159\) 1.17289 0.0930163
\(160\) −14.9884 −1.18493
\(161\) 3.15742 0.248840
\(162\) 3.99733 0.314060
\(163\) −6.12530 −0.479770 −0.239885 0.970801i \(-0.577110\pi\)
−0.239885 + 0.970801i \(0.577110\pi\)
\(164\) 48.2352 3.76654
\(165\) 0.506213 0.0394087
\(166\) −34.7683 −2.69855
\(167\) −5.90499 −0.456942 −0.228471 0.973551i \(-0.573373\pi\)
−0.228471 + 0.973551i \(0.573373\pi\)
\(168\) −3.65201 −0.281759
\(169\) 1.56671 0.120516
\(170\) −2.96183 −0.227162
\(171\) −3.47902 −0.266047
\(172\) 38.9398 2.96913
\(173\) 16.5708 1.25985 0.629926 0.776655i \(-0.283085\pi\)
0.629926 + 0.776655i \(0.283085\pi\)
\(174\) −3.31258 −0.251126
\(175\) 1.52304 0.115131
\(176\) −6.21371 −0.468376
\(177\) 4.93822 0.371179
\(178\) 19.9193 1.49301
\(179\) −4.28985 −0.320639 −0.160319 0.987065i \(-0.551252\pi\)
−0.160319 + 0.987065i \(0.551252\pi\)
\(180\) −7.48617 −0.557986
\(181\) −7.42026 −0.551543 −0.275772 0.961223i \(-0.588933\pi\)
−0.275772 + 0.961223i \(0.588933\pi\)
\(182\) 3.70089 0.274328
\(183\) −7.61319 −0.562783
\(184\) 75.3974 5.55837
\(185\) 7.51080 0.552205
\(186\) 4.73598 0.347259
\(187\) −0.608580 −0.0445038
\(188\) −9.15168 −0.667455
\(189\) −1.95853 −0.142462
\(190\) −5.08677 −0.369033
\(191\) 13.2090 0.955766 0.477883 0.878423i \(-0.341404\pi\)
0.477883 + 0.878423i \(0.341404\pi\)
\(192\) −23.5077 −1.69652
\(193\) 12.0278 0.865778 0.432889 0.901447i \(-0.357494\pi\)
0.432889 + 0.901447i \(0.357494\pi\)
\(194\) 32.7979 2.35475
\(195\) −3.95911 −0.283518
\(196\) −35.7980 −2.55700
\(197\) −22.8987 −1.63146 −0.815732 0.578430i \(-0.803666\pi\)
−0.815732 + 0.578430i \(0.803666\pi\)
\(198\) −2.12858 −0.151272
\(199\) 8.38940 0.594709 0.297355 0.954767i \(-0.403896\pi\)
0.297355 + 0.954767i \(0.403896\pi\)
\(200\) 36.3693 2.57170
\(201\) 17.7930 1.25502
\(202\) 26.8614 1.88996
\(203\) 0.379782 0.0266554
\(204\) −7.62229 −0.533667
\(205\) 8.18648 0.571768
\(206\) −27.0790 −1.88669
\(207\) 14.2030 0.987179
\(208\) 48.5976 3.36964
\(209\) −1.04520 −0.0722981
\(210\) −1.00587 −0.0694116
\(211\) 8.92553 0.614459 0.307229 0.951636i \(-0.400598\pi\)
0.307229 + 0.951636i \(0.400598\pi\)
\(212\) −5.21107 −0.357898
\(213\) 13.2422 0.907337
\(214\) 7.72911 0.528351
\(215\) 6.60885 0.450720
\(216\) −46.7687 −3.18221
\(217\) −0.542973 −0.0368594
\(218\) −10.1584 −0.688013
\(219\) −18.3687 −1.24124
\(220\) −2.24907 −0.151632
\(221\) 4.75972 0.320174
\(222\) 26.7476 1.79518
\(223\) −15.7402 −1.05404 −0.527022 0.849852i \(-0.676691\pi\)
−0.527022 + 0.849852i \(0.676691\pi\)
\(224\) 6.11956 0.408880
\(225\) 6.85109 0.456739
\(226\) 2.53842 0.168853
\(227\) −14.5190 −0.963659 −0.481829 0.876265i \(-0.660028\pi\)
−0.481829 + 0.876265i \(0.660028\pi\)
\(228\) −13.0908 −0.866961
\(229\) 10.6816 0.705858 0.352929 0.935650i \(-0.385186\pi\)
0.352929 + 0.935650i \(0.385186\pi\)
\(230\) 20.7667 1.36931
\(231\) −0.206681 −0.0135986
\(232\) 9.06897 0.595407
\(233\) 9.25329 0.606203 0.303101 0.952958i \(-0.401978\pi\)
0.303101 + 0.952958i \(0.401978\pi\)
\(234\) 16.6477 1.08829
\(235\) −1.55322 −0.101321
\(236\) −21.9402 −1.42818
\(237\) 9.16096 0.595069
\(238\) 1.20928 0.0783858
\(239\) −14.2837 −0.923939 −0.461969 0.886896i \(-0.652857\pi\)
−0.461969 + 0.886896i \(0.652857\pi\)
\(240\) −13.2084 −0.852599
\(241\) 13.1156 0.844851 0.422426 0.906398i \(-0.361179\pi\)
0.422426 + 0.906398i \(0.361179\pi\)
\(242\) 28.8993 1.85772
\(243\) −14.5256 −0.931815
\(244\) 33.8248 2.16541
\(245\) −6.07563 −0.388158
\(246\) 29.1538 1.85878
\(247\) 8.17455 0.520134
\(248\) −12.9659 −0.823335
\(249\) −15.1859 −0.962369
\(250\) 21.8920 1.38457
\(251\) −22.1267 −1.39662 −0.698312 0.715794i \(-0.746065\pi\)
−0.698312 + 0.715794i \(0.746065\pi\)
\(252\) 3.05651 0.192542
\(253\) 4.26702 0.268265
\(254\) −38.8671 −2.43874
\(255\) −1.29365 −0.0810117
\(256\) 13.4256 0.839100
\(257\) 20.1509 1.25698 0.628490 0.777818i \(-0.283673\pi\)
0.628490 + 0.777818i \(0.283673\pi\)
\(258\) 23.5355 1.46526
\(259\) −3.06657 −0.190547
\(260\) 17.5900 1.09089
\(261\) 1.70837 0.105746
\(262\) −4.86833 −0.300766
\(263\) 16.1841 0.997957 0.498978 0.866614i \(-0.333709\pi\)
0.498978 + 0.866614i \(0.333709\pi\)
\(264\) −4.93541 −0.303754
\(265\) −0.884422 −0.0543296
\(266\) 2.07686 0.127341
\(267\) 8.70025 0.532446
\(268\) −79.0532 −4.82894
\(269\) 22.3131 1.36045 0.680227 0.733001i \(-0.261881\pi\)
0.680227 + 0.733001i \(0.261881\pi\)
\(270\) −12.8815 −0.783941
\(271\) −7.62998 −0.463488 −0.231744 0.972777i \(-0.574443\pi\)
−0.231744 + 0.972777i \(0.574443\pi\)
\(272\) 15.8794 0.962832
\(273\) 1.61645 0.0978323
\(274\) −54.3552 −3.28372
\(275\) 2.05827 0.124118
\(276\) 53.4431 3.21689
\(277\) −8.61319 −0.517516 −0.258758 0.965942i \(-0.583313\pi\)
−0.258758 + 0.965942i \(0.583313\pi\)
\(278\) −13.4976 −0.809530
\(279\) −2.44246 −0.146226
\(280\) 2.75381 0.164572
\(281\) 13.4241 0.800815 0.400408 0.916337i \(-0.368869\pi\)
0.400408 + 0.916337i \(0.368869\pi\)
\(282\) −5.53135 −0.329387
\(283\) 24.0622 1.43035 0.715176 0.698945i \(-0.246347\pi\)
0.715176 + 0.698945i \(0.246347\pi\)
\(284\) −58.8339 −3.49115
\(285\) −2.22177 −0.131606
\(286\) 5.00147 0.295743
\(287\) −3.34243 −0.197298
\(288\) 27.5276 1.62208
\(289\) −15.4447 −0.908514
\(290\) 2.49786 0.146679
\(291\) 14.3253 0.839764
\(292\) 81.6107 4.77590
\(293\) −30.3761 −1.77459 −0.887294 0.461204i \(-0.847418\pi\)
−0.887294 + 0.461204i \(0.847418\pi\)
\(294\) −21.6366 −1.26187
\(295\) −3.72368 −0.216801
\(296\) −73.2278 −4.25628
\(297\) −2.64681 −0.153584
\(298\) −31.8812 −1.84683
\(299\) −33.3724 −1.92998
\(300\) 25.7792 1.48836
\(301\) −2.69831 −0.155528
\(302\) −2.68534 −0.154524
\(303\) 11.7324 0.674009
\(304\) 27.2720 1.56416
\(305\) 5.74075 0.328714
\(306\) 5.43970 0.310967
\(307\) 2.56443 0.146360 0.0731800 0.997319i \(-0.476685\pi\)
0.0731800 + 0.997319i \(0.476685\pi\)
\(308\) 0.918267 0.0523231
\(309\) −11.8274 −0.672840
\(310\) −3.57118 −0.202830
\(311\) 9.57297 0.542833 0.271417 0.962462i \(-0.412508\pi\)
0.271417 + 0.962462i \(0.412508\pi\)
\(312\) 38.6000 2.18530
\(313\) 33.9493 1.91893 0.959465 0.281829i \(-0.0909411\pi\)
0.959465 + 0.281829i \(0.0909411\pi\)
\(314\) 3.13672 0.177015
\(315\) 0.518750 0.0292283
\(316\) −40.7015 −2.28964
\(317\) 16.7272 0.939492 0.469746 0.882802i \(-0.344346\pi\)
0.469746 + 0.882802i \(0.344346\pi\)
\(318\) −3.14961 −0.176622
\(319\) 0.513246 0.0287363
\(320\) 17.7261 0.990917
\(321\) 3.37588 0.188423
\(322\) −8.47876 −0.472503
\(323\) 2.67106 0.148622
\(324\) −7.75705 −0.430947
\(325\) −16.0978 −0.892945
\(326\) 16.4485 0.910999
\(327\) −4.43693 −0.245363
\(328\) −79.8154 −4.40707
\(329\) 0.634161 0.0349624
\(330\) −1.35936 −0.0748301
\(331\) −29.1574 −1.60264 −0.801319 0.598238i \(-0.795868\pi\)
−0.801319 + 0.598238i \(0.795868\pi\)
\(332\) 67.4700 3.70290
\(333\) −13.7943 −0.755925
\(334\) 15.8569 0.867652
\(335\) −13.4169 −0.733044
\(336\) 5.39283 0.294203
\(337\) 27.6815 1.50791 0.753955 0.656926i \(-0.228144\pi\)
0.753955 + 0.656926i \(0.228144\pi\)
\(338\) −4.20716 −0.228839
\(339\) 1.10872 0.0602173
\(340\) 5.74761 0.311708
\(341\) −0.733787 −0.0397368
\(342\) 9.34236 0.505177
\(343\) 5.00829 0.270422
\(344\) −64.4341 −3.47405
\(345\) 9.07035 0.488331
\(346\) −44.4982 −2.39224
\(347\) −6.39575 −0.343342 −0.171671 0.985154i \(-0.554917\pi\)
−0.171671 + 0.985154i \(0.554917\pi\)
\(348\) 6.42825 0.344590
\(349\) −17.7946 −0.952521 −0.476261 0.879304i \(-0.658008\pi\)
−0.476261 + 0.879304i \(0.658008\pi\)
\(350\) −4.08988 −0.218613
\(351\) 20.7008 1.10493
\(352\) 8.27012 0.440799
\(353\) 2.17367 0.115693 0.0578465 0.998325i \(-0.481577\pi\)
0.0578465 + 0.998325i \(0.481577\pi\)
\(354\) −13.2608 −0.704804
\(355\) −9.98529 −0.529964
\(356\) −38.6546 −2.04869
\(357\) 0.528182 0.0279544
\(358\) 11.5197 0.608837
\(359\) −31.3541 −1.65481 −0.827404 0.561607i \(-0.810183\pi\)
−0.827404 + 0.561607i \(0.810183\pi\)
\(360\) 12.3875 0.652877
\(361\) −14.4126 −0.758558
\(362\) 19.9259 1.04728
\(363\) 12.6225 0.662508
\(364\) −7.18179 −0.376428
\(365\) 13.8510 0.724992
\(366\) 20.4440 1.06863
\(367\) 20.1479 1.05171 0.525856 0.850574i \(-0.323745\pi\)
0.525856 + 0.850574i \(0.323745\pi\)
\(368\) −111.337 −5.80386
\(369\) −15.0353 −0.782705
\(370\) −20.1691 −1.04854
\(371\) 0.361098 0.0187473
\(372\) −9.19046 −0.476503
\(373\) −23.9812 −1.24170 −0.620849 0.783930i \(-0.713212\pi\)
−0.620849 + 0.783930i \(0.713212\pi\)
\(374\) 1.63425 0.0845049
\(375\) 9.56190 0.493774
\(376\) 15.1434 0.780961
\(377\) −4.01411 −0.206737
\(378\) 5.25934 0.270511
\(379\) 16.6262 0.854030 0.427015 0.904244i \(-0.359565\pi\)
0.427015 + 0.904244i \(0.359565\pi\)
\(380\) 9.87118 0.506381
\(381\) −16.9762 −0.869716
\(382\) −35.4706 −1.81483
\(383\) −26.8236 −1.37062 −0.685310 0.728251i \(-0.740333\pi\)
−0.685310 + 0.728251i \(0.740333\pi\)
\(384\) 23.3721 1.19270
\(385\) 0.155848 0.00794276
\(386\) −32.2987 −1.64396
\(387\) −12.1378 −0.617000
\(388\) −63.6463 −3.23115
\(389\) 34.1360 1.73077 0.865383 0.501111i \(-0.167075\pi\)
0.865383 + 0.501111i \(0.167075\pi\)
\(390\) 10.6316 0.538350
\(391\) −10.9046 −0.551468
\(392\) 59.2354 2.99184
\(393\) −2.12636 −0.107261
\(394\) 61.4908 3.09786
\(395\) −6.90785 −0.347572
\(396\) 4.13064 0.207573
\(397\) −25.8571 −1.29773 −0.648867 0.760902i \(-0.724757\pi\)
−0.648867 + 0.760902i \(0.724757\pi\)
\(398\) −22.5284 −1.12925
\(399\) 0.907122 0.0454129
\(400\) −53.7056 −2.68528
\(401\) −29.5208 −1.47420 −0.737100 0.675784i \(-0.763805\pi\)
−0.737100 + 0.675784i \(0.763805\pi\)
\(402\) −47.7804 −2.38307
\(403\) 5.73897 0.285878
\(404\) −52.1262 −2.59338
\(405\) −1.31653 −0.0654187
\(406\) −1.01984 −0.0506140
\(407\) −4.14423 −0.205422
\(408\) 12.6127 0.624421
\(409\) −8.24400 −0.407640 −0.203820 0.979008i \(-0.565336\pi\)
−0.203820 + 0.979008i \(0.565336\pi\)
\(410\) −21.9835 −1.08569
\(411\) −23.7410 −1.17106
\(412\) 52.5485 2.58888
\(413\) 1.52033 0.0748106
\(414\) −38.1400 −1.87448
\(415\) 11.4510 0.562108
\(416\) −64.6808 −3.17124
\(417\) −5.89540 −0.288699
\(418\) 2.80672 0.137281
\(419\) −3.03519 −0.148279 −0.0741393 0.997248i \(-0.523621\pi\)
−0.0741393 + 0.997248i \(0.523621\pi\)
\(420\) 1.95195 0.0952454
\(421\) 1.82390 0.0888913 0.0444457 0.999012i \(-0.485848\pi\)
0.0444457 + 0.999012i \(0.485848\pi\)
\(422\) −23.9681 −1.16675
\(423\) 2.85265 0.138700
\(424\) 8.62282 0.418761
\(425\) −5.26001 −0.255148
\(426\) −35.5597 −1.72287
\(427\) −2.34387 −0.113428
\(428\) −14.9988 −0.724995
\(429\) 2.18452 0.105469
\(430\) −17.7470 −0.855838
\(431\) 12.1740 0.586401 0.293201 0.956051i \(-0.405280\pi\)
0.293201 + 0.956051i \(0.405280\pi\)
\(432\) 69.0621 3.32275
\(433\) −16.4391 −0.790015 −0.395008 0.918678i \(-0.629258\pi\)
−0.395008 + 0.918678i \(0.629258\pi\)
\(434\) 1.45807 0.0699896
\(435\) 1.09100 0.0523095
\(436\) 19.7130 0.944080
\(437\) −18.7280 −0.895879
\(438\) 49.3262 2.35690
\(439\) 12.2301 0.583709 0.291854 0.956463i \(-0.405728\pi\)
0.291854 + 0.956463i \(0.405728\pi\)
\(440\) 3.72156 0.177419
\(441\) 11.1585 0.531357
\(442\) −12.7815 −0.607954
\(443\) −37.1334 −1.76426 −0.882130 0.471007i \(-0.843891\pi\)
−0.882130 + 0.471007i \(0.843891\pi\)
\(444\) −51.9052 −2.46331
\(445\) −6.56045 −0.310995
\(446\) 42.2679 2.00144
\(447\) −13.9249 −0.658626
\(448\) −7.23733 −0.341932
\(449\) 3.29013 0.155271 0.0776354 0.996982i \(-0.475263\pi\)
0.0776354 + 0.996982i \(0.475263\pi\)
\(450\) −18.3975 −0.867268
\(451\) −4.51705 −0.212699
\(452\) −4.92596 −0.231697
\(453\) −1.17289 −0.0551072
\(454\) 38.9885 1.82982
\(455\) −1.21889 −0.0571426
\(456\) 21.6616 1.01440
\(457\) −6.13031 −0.286764 −0.143382 0.989667i \(-0.545798\pi\)
−0.143382 + 0.989667i \(0.545798\pi\)
\(458\) −28.6837 −1.34030
\(459\) 6.76406 0.315719
\(460\) −40.2989 −1.87895
\(461\) 1.04742 0.0487831 0.0243915 0.999702i \(-0.492235\pi\)
0.0243915 + 0.999702i \(0.492235\pi\)
\(462\) 0.555008 0.0258213
\(463\) 20.6117 0.957906 0.478953 0.877841i \(-0.341016\pi\)
0.478953 + 0.877841i \(0.341016\pi\)
\(464\) −13.3919 −0.621704
\(465\) −1.55980 −0.0723341
\(466\) −24.8482 −1.15107
\(467\) 2.59284 0.119982 0.0599911 0.998199i \(-0.480893\pi\)
0.0599911 + 0.998199i \(0.480893\pi\)
\(468\) −32.3059 −1.49334
\(469\) 5.47795 0.252948
\(470\) 4.17093 0.192391
\(471\) 1.37004 0.0631281
\(472\) 36.3047 1.67106
\(473\) −3.64656 −0.167669
\(474\) −24.6003 −1.12993
\(475\) −9.03376 −0.414498
\(476\) −2.34668 −0.107560
\(477\) 1.62433 0.0743729
\(478\) 38.3568 1.75440
\(479\) 31.3486 1.43236 0.716178 0.697918i \(-0.245890\pi\)
0.716178 + 0.697918i \(0.245890\pi\)
\(480\) 17.5797 0.802400
\(481\) 32.4121 1.47787
\(482\) −35.2199 −1.60422
\(483\) −3.70331 −0.168506
\(484\) −56.0808 −2.54913
\(485\) −10.8020 −0.490495
\(486\) 39.0061 1.76935
\(487\) −18.2798 −0.828336 −0.414168 0.910201i \(-0.635927\pi\)
−0.414168 + 0.910201i \(0.635927\pi\)
\(488\) −55.9704 −2.53366
\(489\) 7.18430 0.324885
\(490\) 16.3152 0.737043
\(491\) 4.95438 0.223588 0.111794 0.993731i \(-0.464340\pi\)
0.111794 + 0.993731i \(0.464340\pi\)
\(492\) −56.5746 −2.55058
\(493\) −1.31163 −0.0590726
\(494\) −21.9515 −0.987643
\(495\) 0.701052 0.0315099
\(496\) 19.1464 0.859698
\(497\) 4.07687 0.182872
\(498\) 40.7794 1.82737
\(499\) 1.73032 0.0774596 0.0387298 0.999250i \(-0.487669\pi\)
0.0387298 + 0.999250i \(0.487669\pi\)
\(500\) −42.4828 −1.89989
\(501\) 6.92591 0.309427
\(502\) 59.4177 2.65194
\(503\) 26.5135 1.18218 0.591088 0.806607i \(-0.298698\pi\)
0.591088 + 0.806607i \(0.298698\pi\)
\(504\) −5.05764 −0.225285
\(505\) −8.84685 −0.393680
\(506\) −11.4584 −0.509388
\(507\) −1.83758 −0.0816098
\(508\) 75.4239 3.34640
\(509\) −22.0325 −0.976573 −0.488286 0.872684i \(-0.662378\pi\)
−0.488286 + 0.872684i \(0.662378\pi\)
\(510\) 3.47390 0.153827
\(511\) −5.65517 −0.250170
\(512\) 3.80154 0.168006
\(513\) 11.6169 0.512897
\(514\) −54.1121 −2.38678
\(515\) 8.91852 0.392997
\(516\) −45.6721 −2.01060
\(517\) 0.857020 0.0376917
\(518\) 8.23478 0.361815
\(519\) −19.4357 −0.853133
\(520\) −29.1065 −1.27640
\(521\) −24.3157 −1.06529 −0.532646 0.846338i \(-0.678802\pi\)
−0.532646 + 0.846338i \(0.678802\pi\)
\(522\) −4.58757 −0.200792
\(523\) −18.7224 −0.818674 −0.409337 0.912383i \(-0.634240\pi\)
−0.409337 + 0.912383i \(0.634240\pi\)
\(524\) 9.44728 0.412706
\(525\) −1.78636 −0.0779630
\(526\) −43.4600 −1.89494
\(527\) 1.87523 0.0816862
\(528\) 7.28800 0.317169
\(529\) 53.4565 2.32420
\(530\) 2.37498 0.103162
\(531\) 6.83891 0.296783
\(532\) −4.03028 −0.174735
\(533\) 35.3279 1.53022
\(534\) −23.3631 −1.01102
\(535\) −2.54560 −0.110056
\(536\) 130.810 5.65015
\(537\) 5.03153 0.217126
\(538\) −59.9184 −2.58326
\(539\) 3.35235 0.144396
\(540\) 24.9972 1.07571
\(541\) 30.8987 1.32844 0.664219 0.747538i \(-0.268764\pi\)
0.664219 + 0.747538i \(0.268764\pi\)
\(542\) 20.4891 0.880083
\(543\) 8.70315 0.373488
\(544\) −21.1347 −0.906143
\(545\) 3.34568 0.143313
\(546\) −4.34073 −0.185766
\(547\) 18.2914 0.782082 0.391041 0.920373i \(-0.372115\pi\)
0.391041 + 0.920373i \(0.372115\pi\)
\(548\) 105.479 4.50586
\(549\) −10.5435 −0.449984
\(550\) −5.52717 −0.235679
\(551\) −2.25264 −0.0959657
\(552\) −88.4329 −3.76395
\(553\) 2.82039 0.119935
\(554\) 23.1294 0.982673
\(555\) −8.80935 −0.373936
\(556\) 26.1928 1.11082
\(557\) −34.9434 −1.48060 −0.740299 0.672278i \(-0.765316\pi\)
−0.740299 + 0.672278i \(0.765316\pi\)
\(558\) 6.55883 0.277658
\(559\) 28.5199 1.20626
\(560\) −4.06648 −0.171840
\(561\) 0.713798 0.0301366
\(562\) −36.0483 −1.52061
\(563\) 9.92320 0.418213 0.209107 0.977893i \(-0.432944\pi\)
0.209107 + 0.977893i \(0.432944\pi\)
\(564\) 10.7339 0.451980
\(565\) −0.836032 −0.0351721
\(566\) −64.6154 −2.71599
\(567\) 0.537521 0.0225737
\(568\) 97.3532 4.08485
\(569\) −0.327086 −0.0137121 −0.00685607 0.999976i \(-0.502182\pi\)
−0.00685607 + 0.999976i \(0.502182\pi\)
\(570\) 5.96622 0.249898
\(571\) 27.0523 1.13211 0.566053 0.824369i \(-0.308470\pi\)
0.566053 + 0.824369i \(0.308470\pi\)
\(572\) −9.70564 −0.405813
\(573\) −15.4927 −0.647215
\(574\) 8.97558 0.374634
\(575\) 36.8802 1.53801
\(576\) −32.5557 −1.35649
\(577\) 31.8857 1.32742 0.663709 0.747991i \(-0.268981\pi\)
0.663709 + 0.747991i \(0.268981\pi\)
\(578\) 41.4744 1.72511
\(579\) −14.1072 −0.586277
\(580\) −4.84724 −0.201271
\(581\) −4.67530 −0.193964
\(582\) −38.4683 −1.59456
\(583\) 0.487997 0.0202108
\(584\) −135.042 −5.58809
\(585\) −5.48295 −0.226692
\(586\) 81.5702 3.36963
\(587\) 42.6627 1.76088 0.880439 0.474160i \(-0.157248\pi\)
0.880439 + 0.474160i \(0.157248\pi\)
\(588\) 41.9871 1.73152
\(589\) 3.22059 0.132702
\(590\) 9.99936 0.411667
\(591\) 26.8576 1.10478
\(592\) 108.134 4.44426
\(593\) −17.0411 −0.699792 −0.349896 0.936788i \(-0.613783\pi\)
−0.349896 + 0.936788i \(0.613783\pi\)
\(594\) 7.10760 0.291628
\(595\) −0.398277 −0.0163278
\(596\) 61.8674 2.53419
\(597\) −9.83985 −0.402718
\(598\) 89.6165 3.66469
\(599\) 30.2852 1.23742 0.618710 0.785620i \(-0.287656\pi\)
0.618710 + 0.785620i \(0.287656\pi\)
\(600\) −42.6572 −1.74147
\(601\) −14.5319 −0.592770 −0.296385 0.955069i \(-0.595781\pi\)
−0.296385 + 0.955069i \(0.595781\pi\)
\(602\) 7.24589 0.295320
\(603\) 24.6415 1.00348
\(604\) 5.21107 0.212035
\(605\) −9.51802 −0.386963
\(606\) −31.5055 −1.27982
\(607\) 36.4525 1.47956 0.739781 0.672848i \(-0.234929\pi\)
0.739781 + 0.672848i \(0.234929\pi\)
\(608\) −36.2976 −1.47206
\(609\) −0.445442 −0.0180502
\(610\) −15.4159 −0.624171
\(611\) −6.70278 −0.271165
\(612\) −10.5561 −0.426703
\(613\) 41.6822 1.68353 0.841765 0.539844i \(-0.181517\pi\)
0.841765 + 0.539844i \(0.181517\pi\)
\(614\) −6.88638 −0.277912
\(615\) −9.60184 −0.387184
\(616\) −1.51947 −0.0612211
\(617\) 36.0920 1.45301 0.726504 0.687162i \(-0.241144\pi\)
0.726504 + 0.687162i \(0.241144\pi\)
\(618\) 31.7608 1.27760
\(619\) −10.3980 −0.417930 −0.208965 0.977923i \(-0.567009\pi\)
−0.208965 + 0.977923i \(0.567009\pi\)
\(620\) 6.93009 0.278319
\(621\) −47.4257 −1.90313
\(622\) −25.7067 −1.03074
\(623\) 2.67855 0.107314
\(624\) −56.9996 −2.28181
\(625\) 13.8788 0.555153
\(626\) −91.1656 −3.64371
\(627\) 1.22591 0.0489580
\(628\) −6.08698 −0.242897
\(629\) 10.5908 0.422282
\(630\) −1.39302 −0.0554994
\(631\) 37.3536 1.48702 0.743511 0.668723i \(-0.233159\pi\)
0.743511 + 0.668723i \(0.233159\pi\)
\(632\) 67.3493 2.67901
\(633\) −10.4687 −0.416092
\(634\) −44.9182 −1.78393
\(635\) 12.8009 0.507990
\(636\) 6.11201 0.242357
\(637\) −26.2188 −1.03883
\(638\) −1.37824 −0.0545651
\(639\) 18.3390 0.725479
\(640\) −17.6238 −0.696643
\(641\) −4.30166 −0.169905 −0.0849527 0.996385i \(-0.527074\pi\)
−0.0849527 + 0.996385i \(0.527074\pi\)
\(642\) −9.06540 −0.357783
\(643\) 2.21238 0.0872476 0.0436238 0.999048i \(-0.486110\pi\)
0.0436238 + 0.999048i \(0.486110\pi\)
\(644\) 16.4535 0.648360
\(645\) −7.75146 −0.305213
\(646\) −7.17272 −0.282207
\(647\) −30.0019 −1.17950 −0.589749 0.807587i \(-0.700773\pi\)
−0.589749 + 0.807587i \(0.700773\pi\)
\(648\) 12.8357 0.504233
\(649\) 2.05461 0.0806506
\(650\) 43.2281 1.69555
\(651\) 0.636848 0.0249600
\(652\) −31.9193 −1.25006
\(653\) 30.8115 1.20575 0.602874 0.797836i \(-0.294022\pi\)
0.602874 + 0.797836i \(0.294022\pi\)
\(654\) 11.9147 0.465901
\(655\) 1.60339 0.0626497
\(656\) 117.861 4.60171
\(657\) −25.4386 −0.992456
\(658\) −1.70294 −0.0663875
\(659\) −28.4467 −1.10813 −0.554063 0.832475i \(-0.686923\pi\)
−0.554063 + 0.832475i \(0.686923\pi\)
\(660\) 2.63791 0.102681
\(661\) 2.48366 0.0966033 0.0483017 0.998833i \(-0.484619\pi\)
0.0483017 + 0.998833i \(0.484619\pi\)
\(662\) 78.2977 3.04313
\(663\) −5.58263 −0.216812
\(664\) −111.643 −4.33261
\(665\) −0.684018 −0.0265251
\(666\) 37.0425 1.43537
\(667\) 9.19636 0.356085
\(668\) −30.7713 −1.19058
\(669\) 18.4616 0.713765
\(670\) 36.0290 1.39192
\(671\) −3.16757 −0.122283
\(672\) −7.17757 −0.276881
\(673\) 12.8091 0.493756 0.246878 0.969047i \(-0.420595\pi\)
0.246878 + 0.969047i \(0.420595\pi\)
\(674\) −74.3345 −2.86326
\(675\) −22.8766 −0.880522
\(676\) 8.16423 0.314009
\(677\) 39.2090 1.50692 0.753462 0.657492i \(-0.228383\pi\)
0.753462 + 0.657492i \(0.228383\pi\)
\(678\) −2.97729 −0.114342
\(679\) 4.41033 0.169253
\(680\) −9.51064 −0.364716
\(681\) 17.0292 0.652559
\(682\) 1.97047 0.0754532
\(683\) −22.1384 −0.847101 −0.423550 0.905873i \(-0.639216\pi\)
−0.423550 + 0.905873i \(0.639216\pi\)
\(684\) −18.1294 −0.693195
\(685\) 17.9020 0.683999
\(686\) −13.4490 −0.513484
\(687\) −12.5283 −0.477985
\(688\) 95.1482 3.62749
\(689\) −3.81664 −0.145402
\(690\) −24.3570 −0.927255
\(691\) −16.9735 −0.645704 −0.322852 0.946449i \(-0.604642\pi\)
−0.322852 + 0.946449i \(0.604642\pi\)
\(692\) 86.3514 3.28259
\(693\) −0.286231 −0.0108730
\(694\) 17.1748 0.651946
\(695\) 4.44544 0.168625
\(696\) −10.6369 −0.403191
\(697\) 11.5435 0.437242
\(698\) 47.7845 1.80867
\(699\) −10.8531 −0.410501
\(700\) 7.93666 0.299978
\(701\) 1.86972 0.0706183 0.0353092 0.999376i \(-0.488758\pi\)
0.0353092 + 0.999376i \(0.488758\pi\)
\(702\) −55.5887 −2.09806
\(703\) 18.1890 0.686013
\(704\) −9.78070 −0.368624
\(705\) 1.82176 0.0686114
\(706\) −5.83706 −0.219681
\(707\) 3.61206 0.135845
\(708\) 25.7334 0.967120
\(709\) −41.4439 −1.55646 −0.778230 0.627980i \(-0.783882\pi\)
−0.778230 + 0.627980i \(0.783882\pi\)
\(710\) 26.8139 1.00631
\(711\) 12.6870 0.475798
\(712\) 63.9622 2.39708
\(713\) −13.1480 −0.492397
\(714\) −1.41835 −0.0530804
\(715\) −1.64724 −0.0616033
\(716\) −22.3547 −0.835435
\(717\) 16.7533 0.625662
\(718\) 84.1966 3.14219
\(719\) −5.41599 −0.201982 −0.100991 0.994887i \(-0.532201\pi\)
−0.100991 + 0.994887i \(0.532201\pi\)
\(720\) −18.2922 −0.681712
\(721\) −3.64132 −0.135610
\(722\) 38.7028 1.44037
\(723\) −15.3832 −0.572107
\(724\) −38.6675 −1.43706
\(725\) 4.43603 0.164750
\(726\) −33.8957 −1.25799
\(727\) −22.7235 −0.842770 −0.421385 0.906882i \(-0.638456\pi\)
−0.421385 + 0.906882i \(0.638456\pi\)
\(728\) 11.8838 0.440443
\(729\) 21.5026 0.796393
\(730\) −37.1946 −1.37663
\(731\) 9.31896 0.344674
\(732\) −39.6728 −1.46635
\(733\) 34.8033 1.28549 0.642744 0.766081i \(-0.277796\pi\)
0.642744 + 0.766081i \(0.277796\pi\)
\(734\) −54.1040 −1.99702
\(735\) 7.12605 0.262848
\(736\) 148.184 5.46215
\(737\) 7.40303 0.272694
\(738\) 40.3749 1.48622
\(739\) 1.86685 0.0686732 0.0343366 0.999410i \(-0.489068\pi\)
0.0343366 + 0.999410i \(0.489068\pi\)
\(740\) 39.1393 1.43879
\(741\) −9.58785 −0.352218
\(742\) −0.969672 −0.0355978
\(743\) 42.3785 1.55472 0.777359 0.629057i \(-0.216559\pi\)
0.777359 + 0.629057i \(0.216559\pi\)
\(744\) 15.2076 0.557536
\(745\) 10.5001 0.384695
\(746\) 64.3977 2.35777
\(747\) −21.0309 −0.769481
\(748\) −3.17135 −0.115956
\(749\) 1.03933 0.0379764
\(750\) −25.6770 −0.937590
\(751\) −19.2375 −0.701985 −0.350993 0.936378i \(-0.614156\pi\)
−0.350993 + 0.936378i \(0.614156\pi\)
\(752\) −22.3619 −0.815453
\(753\) 25.9522 0.945749
\(754\) 10.7793 0.392558
\(755\) 0.884422 0.0321874
\(756\) −10.2061 −0.371191
\(757\) 13.1138 0.476631 0.238315 0.971188i \(-0.423405\pi\)
0.238315 + 0.971188i \(0.423405\pi\)
\(758\) −44.6470 −1.62165
\(759\) −5.00474 −0.181661
\(760\) −16.3340 −0.592495
\(761\) −35.9168 −1.30198 −0.650992 0.759085i \(-0.725647\pi\)
−0.650992 + 0.759085i \(0.725647\pi\)
\(762\) 45.5868 1.65144
\(763\) −1.36600 −0.0494525
\(764\) 68.8328 2.49028
\(765\) −1.79157 −0.0647744
\(766\) 72.0305 2.60257
\(767\) −16.0692 −0.580225
\(768\) −15.7468 −0.568212
\(769\) −9.59014 −0.345829 −0.172915 0.984937i \(-0.555318\pi\)
−0.172915 + 0.984937i \(0.555318\pi\)
\(770\) −0.418506 −0.0150819
\(771\) −23.6348 −0.851187
\(772\) 62.6775 2.25581
\(773\) 40.3150 1.45003 0.725015 0.688733i \(-0.241833\pi\)
0.725015 + 0.688733i \(0.241833\pi\)
\(774\) 32.5942 1.17157
\(775\) −6.34218 −0.227818
\(776\) 105.316 3.78063
\(777\) 3.59674 0.129032
\(778\) −91.6670 −3.28642
\(779\) 19.8253 0.710316
\(780\) −20.6312 −0.738715
\(781\) 5.50958 0.197148
\(782\) 29.2825 1.04714
\(783\) −5.70446 −0.203861
\(784\) −87.4713 −3.12398
\(785\) −1.03308 −0.0368723
\(786\) 5.71001 0.203669
\(787\) 4.79720 0.171002 0.0855009 0.996338i \(-0.472751\pi\)
0.0855009 + 0.996338i \(0.472751\pi\)
\(788\) −119.327 −4.25083
\(789\) −18.9822 −0.675785
\(790\) 18.5500 0.659978
\(791\) 0.341341 0.0121367
\(792\) −6.83502 −0.242872
\(793\) 24.7736 0.879738
\(794\) 69.4353 2.46417
\(795\) 1.03733 0.0367903
\(796\) 43.7178 1.54953
\(797\) −47.4236 −1.67983 −0.839915 0.542719i \(-0.817395\pi\)
−0.839915 + 0.542719i \(0.817395\pi\)
\(798\) −2.43593 −0.0862311
\(799\) −2.19016 −0.0774822
\(800\) 71.4794 2.52718
\(801\) 12.0489 0.425728
\(802\) 79.2736 2.79925
\(803\) −7.64253 −0.269699
\(804\) 92.7207 3.27001
\(805\) 2.79249 0.0984224
\(806\) −15.4111 −0.542833
\(807\) −26.1708 −0.921257
\(808\) 86.2539 3.03440
\(809\) 28.1963 0.991329 0.495665 0.868514i \(-0.334925\pi\)
0.495665 + 0.868514i \(0.334925\pi\)
\(810\) 3.53532 0.124219
\(811\) 42.8750 1.50554 0.752772 0.658281i \(-0.228716\pi\)
0.752772 + 0.658281i \(0.228716\pi\)
\(812\) 1.97907 0.0694517
\(813\) 8.94913 0.313860
\(814\) 11.1287 0.390060
\(815\) −5.41734 −0.189761
\(816\) −18.6248 −0.651999
\(817\) 16.0048 0.559936
\(818\) 22.1380 0.774036
\(819\) 2.23862 0.0782236
\(820\) 42.6603 1.48976
\(821\) 7.52722 0.262702 0.131351 0.991336i \(-0.458069\pi\)
0.131351 + 0.991336i \(0.458069\pi\)
\(822\) 63.7526 2.22363
\(823\) −14.1945 −0.494788 −0.247394 0.968915i \(-0.579574\pi\)
−0.247394 + 0.968915i \(0.579574\pi\)
\(824\) −86.9527 −3.02914
\(825\) −2.41413 −0.0840491
\(826\) −4.08261 −0.142052
\(827\) 29.4427 1.02382 0.511911 0.859039i \(-0.328938\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(828\) 74.0130 2.57213
\(829\) 30.6806 1.06558 0.532791 0.846247i \(-0.321143\pi\)
0.532791 + 0.846247i \(0.321143\pi\)
\(830\) −30.7499 −1.06734
\(831\) 10.1023 0.350446
\(832\) 76.4951 2.65199
\(833\) −8.56708 −0.296832
\(834\) 15.8312 0.548188
\(835\) −5.22250 −0.180732
\(836\) −5.44661 −0.188375
\(837\) 8.15566 0.281901
\(838\) 8.15052 0.281555
\(839\) 11.2298 0.387694 0.193847 0.981032i \(-0.437903\pi\)
0.193847 + 0.981032i \(0.437903\pi\)
\(840\) −3.22992 −0.111443
\(841\) −27.8938 −0.961857
\(842\) −4.89779 −0.168789
\(843\) −15.7450 −0.542287
\(844\) 46.5115 1.60099
\(845\) 1.38563 0.0476672
\(846\) −7.66034 −0.263368
\(847\) 3.88609 0.133528
\(848\) −12.7331 −0.437256
\(849\) −28.2224 −0.968589
\(850\) 14.1249 0.484482
\(851\) −74.2565 −2.54548
\(852\) 69.0058 2.36410
\(853\) 27.2043 0.931458 0.465729 0.884927i \(-0.345792\pi\)
0.465729 + 0.884927i \(0.345792\pi\)
\(854\) 6.29411 0.215380
\(855\) −3.07692 −0.105228
\(856\) 24.8187 0.848286
\(857\) −3.25762 −0.111278 −0.0556391 0.998451i \(-0.517720\pi\)
−0.0556391 + 0.998451i \(0.517720\pi\)
\(858\) −5.86617 −0.200268
\(859\) −44.2838 −1.51094 −0.755472 0.655181i \(-0.772592\pi\)
−0.755472 + 0.655181i \(0.772592\pi\)
\(860\) 34.4392 1.17437
\(861\) 3.92031 0.133604
\(862\) −32.6914 −1.11347
\(863\) 54.8601 1.86746 0.933731 0.357977i \(-0.116533\pi\)
0.933731 + 0.357977i \(0.116533\pi\)
\(864\) −91.9181 −3.12712
\(865\) 14.6556 0.498304
\(866\) 44.1448 1.50010
\(867\) 18.1150 0.615217
\(868\) −2.82947 −0.0960385
\(869\) 3.81154 0.129298
\(870\) −2.92971 −0.0993266
\(871\) −57.8993 −1.96184
\(872\) −32.6193 −1.10463
\(873\) 19.8390 0.671449
\(874\) 50.2910 1.70112
\(875\) 2.94382 0.0995194
\(876\) −95.7204 −3.23409
\(877\) 14.0994 0.476104 0.238052 0.971252i \(-0.423491\pi\)
0.238052 + 0.971252i \(0.423491\pi\)
\(878\) −32.8419 −1.10836
\(879\) 35.6278 1.20170
\(880\) −5.49554 −0.185255
\(881\) −0.786599 −0.0265012 −0.0132506 0.999912i \(-0.504218\pi\)
−0.0132506 + 0.999912i \(0.504218\pi\)
\(882\) −29.9644 −1.00895
\(883\) 25.1514 0.846413 0.423207 0.906033i \(-0.360904\pi\)
0.423207 + 0.906033i \(0.360904\pi\)
\(884\) 24.8032 0.834223
\(885\) 4.36747 0.146811
\(886\) 99.7158 3.35002
\(887\) −30.0873 −1.01023 −0.505117 0.863051i \(-0.668551\pi\)
−0.505117 + 0.863051i \(0.668551\pi\)
\(888\) 85.8882 2.88222
\(889\) −5.22646 −0.175290
\(890\) 17.6171 0.590525
\(891\) 0.726418 0.0243359
\(892\) −82.0234 −2.74635
\(893\) −3.76147 −0.125873
\(894\) 37.3932 1.25062
\(895\) −3.79404 −0.126821
\(896\) 7.19558 0.240388
\(897\) 39.1422 1.30692
\(898\) −8.83512 −0.294832
\(899\) −1.58147 −0.0527451
\(900\) 35.7015 1.19005
\(901\) −1.24710 −0.0415469
\(902\) 12.1298 0.403879
\(903\) 3.16482 0.105319
\(904\) 8.15104 0.271100
\(905\) −6.56264 −0.218149
\(906\) 3.14961 0.104639
\(907\) −24.1132 −0.800666 −0.400333 0.916370i \(-0.631106\pi\)
−0.400333 + 0.916370i \(0.631106\pi\)
\(908\) −75.6594 −2.51085
\(909\) 16.2481 0.538916
\(910\) 3.27314 0.108504
\(911\) 10.7343 0.355645 0.177822 0.984063i \(-0.443095\pi\)
0.177822 + 0.984063i \(0.443095\pi\)
\(912\) −31.9870 −1.05920
\(913\) −6.31831 −0.209106
\(914\) 16.4620 0.544514
\(915\) −6.73327 −0.222595
\(916\) 55.6624 1.83914
\(917\) −0.654644 −0.0216182
\(918\) −18.1638 −0.599495
\(919\) 31.9719 1.05466 0.527328 0.849662i \(-0.323194\pi\)
0.527328 + 0.849662i \(0.323194\pi\)
\(920\) 66.6831 2.19848
\(921\) −3.00780 −0.0991103
\(922\) −2.81267 −0.0926305
\(923\) −43.0905 −1.41834
\(924\) −1.07703 −0.0354316
\(925\) −35.8189 −1.17772
\(926\) −55.3494 −1.81889
\(927\) −16.3798 −0.537982
\(928\) 17.8239 0.585099
\(929\) −21.2448 −0.697018 −0.348509 0.937305i \(-0.613312\pi\)
−0.348509 + 0.937305i \(0.613312\pi\)
\(930\) 4.18861 0.137350
\(931\) −14.7135 −0.482214
\(932\) 48.2195 1.57948
\(933\) −11.2280 −0.367589
\(934\) −6.96266 −0.227825
\(935\) −0.538242 −0.0176024
\(936\) 53.4569 1.74729
\(937\) 48.1485 1.57294 0.786471 0.617627i \(-0.211906\pi\)
0.786471 + 0.617627i \(0.211906\pi\)
\(938\) −14.7102 −0.480304
\(939\) −39.8188 −1.29944
\(940\) −8.09395 −0.263995
\(941\) 24.2579 0.790785 0.395393 0.918512i \(-0.370608\pi\)
0.395393 + 0.918512i \(0.370608\pi\)
\(942\) −3.67902 −0.119869
\(943\) −80.9366 −2.63566
\(944\) −53.6101 −1.74486
\(945\) −1.73217 −0.0563475
\(946\) 9.79227 0.318374
\(947\) 30.4608 0.989841 0.494921 0.868938i \(-0.335197\pi\)
0.494921 + 0.868938i \(0.335197\pi\)
\(948\) 47.7384 1.55047
\(949\) 59.7724 1.94030
\(950\) 24.2588 0.787058
\(951\) −19.6191 −0.636194
\(952\) 3.88307 0.125851
\(953\) 46.5873 1.50911 0.754555 0.656236i \(-0.227853\pi\)
0.754555 + 0.656236i \(0.227853\pi\)
\(954\) −4.36188 −0.141221
\(955\) 11.6823 0.378030
\(956\) −74.4336 −2.40735
\(957\) −0.601981 −0.0194593
\(958\) −84.1819 −2.71979
\(959\) −7.30914 −0.236024
\(960\) −20.7907 −0.671018
\(961\) −28.7390 −0.927064
\(962\) −87.0377 −2.80621
\(963\) 4.67524 0.150657
\(964\) 68.3464 2.20129
\(965\) 10.6376 0.342437
\(966\) 9.94466 0.319964
\(967\) −13.5693 −0.436360 −0.218180 0.975909i \(-0.570012\pi\)
−0.218180 + 0.975909i \(0.570012\pi\)
\(968\) 92.7976 2.98263
\(969\) −3.13286 −0.100642
\(970\) 29.0072 0.931364
\(971\) −4.24439 −0.136209 −0.0681045 0.997678i \(-0.521695\pi\)
−0.0681045 + 0.997678i \(0.521695\pi\)
\(972\) −75.6937 −2.42788
\(973\) −1.81502 −0.0581868
\(974\) 49.0875 1.57286
\(975\) 18.8810 0.604674
\(976\) 82.6500 2.64556
\(977\) 37.1885 1.18976 0.594882 0.803813i \(-0.297199\pi\)
0.594882 + 0.803813i \(0.297199\pi\)
\(978\) −19.2923 −0.616900
\(979\) 3.61985 0.115691
\(980\) −31.6605 −1.01136
\(981\) −6.14468 −0.196185
\(982\) −13.3042 −0.424555
\(983\) −37.3592 −1.19157 −0.595786 0.803143i \(-0.703160\pi\)
−0.595786 + 0.803143i \(0.703160\pi\)
\(984\) 93.6147 2.98433
\(985\) −20.2521 −0.645285
\(986\) 3.52216 0.112169
\(987\) −0.743801 −0.0236755
\(988\) 42.5981 1.35523
\(989\) −65.3392 −2.07767
\(990\) −1.88256 −0.0598318
\(991\) 41.3444 1.31335 0.656674 0.754175i \(-0.271963\pi\)
0.656674 + 0.754175i \(0.271963\pi\)
\(992\) −25.4828 −0.809081
\(993\) 34.1985 1.08526
\(994\) −10.9478 −0.347243
\(995\) 7.41977 0.235223
\(996\) −79.1349 −2.50749
\(997\) −48.2596 −1.52840 −0.764199 0.644981i \(-0.776865\pi\)
−0.764199 + 0.644981i \(0.776865\pi\)
\(998\) −4.64649 −0.147082
\(999\) 46.0610 1.45730
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 \(a_p\))