Properties

Label 8003.2.a.c.1.19
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 1.19
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30956 q^{2}\) \(-1.91926 q^{3}\) \(+3.33407 q^{4}\) \(+3.27349 q^{5}\) \(+4.43265 q^{6}\) \(-1.87972 q^{7}\) \(-3.08112 q^{8}\) \(+0.683571 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30956 q^{2}\) \(-1.91926 q^{3}\) \(+3.33407 q^{4}\) \(+3.27349 q^{5}\) \(+4.43265 q^{6}\) \(-1.87972 q^{7}\) \(-3.08112 q^{8}\) \(+0.683571 q^{9}\) \(-7.56031 q^{10}\) \(-2.21776 q^{11}\) \(-6.39896 q^{12}\) \(-3.64849 q^{13}\) \(+4.34132 q^{14}\) \(-6.28268 q^{15}\) \(+0.447889 q^{16}\) \(+3.59852 q^{17}\) \(-1.57875 q^{18}\) \(+1.47965 q^{19}\) \(+10.9140 q^{20}\) \(+3.60767 q^{21}\) \(+5.12206 q^{22}\) \(+7.78404 q^{23}\) \(+5.91348 q^{24}\) \(+5.71571 q^{25}\) \(+8.42641 q^{26}\) \(+4.44584 q^{27}\) \(-6.26711 q^{28}\) \(+2.80949 q^{29}\) \(+14.5102 q^{30}\) \(+4.86111 q^{31}\) \(+5.12781 q^{32}\) \(+4.25647 q^{33}\) \(-8.31100 q^{34}\) \(-6.15322 q^{35}\) \(+2.27907 q^{36}\) \(-4.38957 q^{37}\) \(-3.41735 q^{38}\) \(+7.00241 q^{39}\) \(-10.0860 q^{40}\) \(+10.2889 q^{41}\) \(-8.33213 q^{42}\) \(+7.72765 q^{43}\) \(-7.39418 q^{44}\) \(+2.23766 q^{45}\) \(-17.9777 q^{46}\) \(+10.9635 q^{47}\) \(-0.859617 q^{48}\) \(-3.46667 q^{49}\) \(-13.2008 q^{50}\) \(-6.90651 q^{51}\) \(-12.1643 q^{52}\) \(-1.00000 q^{53}\) \(-10.2679 q^{54}\) \(-7.25981 q^{55}\) \(+5.79163 q^{56}\) \(-2.83985 q^{57}\) \(-6.48869 q^{58}\) \(+3.58544 q^{59}\) \(-20.9469 q^{60}\) \(-0.904674 q^{61}\) \(-11.2270 q^{62}\) \(-1.28492 q^{63}\) \(-12.7388 q^{64}\) \(-11.9433 q^{65}\) \(-9.83057 q^{66}\) \(-8.44392 q^{67}\) \(+11.9977 q^{68}\) \(-14.9396 q^{69}\) \(+14.2112 q^{70}\) \(-13.6198 q^{71}\) \(-2.10616 q^{72}\) \(-3.01943 q^{73}\) \(+10.1380 q^{74}\) \(-10.9699 q^{75}\) \(+4.93327 q^{76}\) \(+4.16876 q^{77}\) \(-16.1725 q^{78}\) \(-2.84607 q^{79}\) \(+1.46616 q^{80}\) \(-10.5834 q^{81}\) \(-23.7628 q^{82}\) \(-5.76261 q^{83}\) \(+12.0282 q^{84}\) \(+11.7797 q^{85}\) \(-17.8475 q^{86}\) \(-5.39215 q^{87}\) \(+6.83319 q^{88}\) \(+12.5944 q^{89}\) \(-5.16801 q^{90}\) \(+6.85812 q^{91}\) \(+25.9526 q^{92}\) \(-9.32974 q^{93}\) \(-25.3209 q^{94}\) \(+4.84363 q^{95}\) \(-9.84162 q^{96}\) \(+18.1031 q^{97}\) \(+8.00649 q^{98}\) \(-1.51600 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30956 −1.63311 −0.816553 0.577270i \(-0.804118\pi\)
−0.816553 + 0.577270i \(0.804118\pi\)
\(3\) −1.91926 −1.10809 −0.554044 0.832488i \(-0.686916\pi\)
−0.554044 + 0.832488i \(0.686916\pi\)
\(4\) 3.33407 1.66704
\(5\) 3.27349 1.46395 0.731974 0.681333i \(-0.238599\pi\)
0.731974 + 0.681333i \(0.238599\pi\)
\(6\) 4.43265 1.80962
\(7\) −1.87972 −0.710466 −0.355233 0.934778i \(-0.615598\pi\)
−0.355233 + 0.934778i \(0.615598\pi\)
\(8\) −3.08112 −1.08934
\(9\) 0.683571 0.227857
\(10\) −7.56031 −2.39078
\(11\) −2.21776 −0.668680 −0.334340 0.942452i \(-0.608513\pi\)
−0.334340 + 0.942452i \(0.608513\pi\)
\(12\) −6.39896 −1.84722
\(13\) −3.64849 −1.01191 −0.505955 0.862560i \(-0.668860\pi\)
−0.505955 + 0.862560i \(0.668860\pi\)
\(14\) 4.34132 1.16027
\(15\) −6.28268 −1.62218
\(16\) 0.447889 0.111972
\(17\) 3.59852 0.872769 0.436385 0.899760i \(-0.356259\pi\)
0.436385 + 0.899760i \(0.356259\pi\)
\(18\) −1.57875 −0.372114
\(19\) 1.47965 0.339456 0.169728 0.985491i \(-0.445711\pi\)
0.169728 + 0.985491i \(0.445711\pi\)
\(20\) 10.9140 2.44045
\(21\) 3.60767 0.787258
\(22\) 5.12206 1.09203
\(23\) 7.78404 1.62309 0.811543 0.584293i \(-0.198628\pi\)
0.811543 + 0.584293i \(0.198628\pi\)
\(24\) 5.91348 1.20708
\(25\) 5.71571 1.14314
\(26\) 8.42641 1.65256
\(27\) 4.44584 0.855602
\(28\) −6.26711 −1.18437
\(29\) 2.80949 0.521709 0.260855 0.965378i \(-0.415996\pi\)
0.260855 + 0.965378i \(0.415996\pi\)
\(30\) 14.5102 2.64919
\(31\) 4.86111 0.873080 0.436540 0.899685i \(-0.356204\pi\)
0.436540 + 0.899685i \(0.356204\pi\)
\(32\) 5.12781 0.906477
\(33\) 4.25647 0.740956
\(34\) −8.31100 −1.42532
\(35\) −6.15322 −1.04008
\(36\) 2.27907 0.379845
\(37\) −4.38957 −0.721641 −0.360820 0.932635i \(-0.617503\pi\)
−0.360820 + 0.932635i \(0.617503\pi\)
\(38\) −3.41735 −0.554368
\(39\) 7.00241 1.12128
\(40\) −10.0860 −1.59474
\(41\) 10.2889 1.60686 0.803428 0.595402i \(-0.203007\pi\)
0.803428 + 0.595402i \(0.203007\pi\)
\(42\) −8.33213 −1.28568
\(43\) 7.72765 1.17846 0.589228 0.807967i \(-0.299432\pi\)
0.589228 + 0.807967i \(0.299432\pi\)
\(44\) −7.39418 −1.11471
\(45\) 2.23766 0.333570
\(46\) −17.9777 −2.65067
\(47\) 10.9635 1.59919 0.799596 0.600538i \(-0.205047\pi\)
0.799596 + 0.600538i \(0.205047\pi\)
\(48\) −0.859617 −0.124075
\(49\) −3.46667 −0.495239
\(50\) −13.2008 −1.86687
\(51\) −6.90651 −0.967104
\(52\) −12.1643 −1.68689
\(53\) −1.00000 −0.137361
\(54\) −10.2679 −1.39729
\(55\) −7.25981 −0.978913
\(56\) 5.79163 0.773939
\(57\) −2.83985 −0.376147
\(58\) −6.48869 −0.852006
\(59\) 3.58544 0.466785 0.233392 0.972383i \(-0.425017\pi\)
0.233392 + 0.972383i \(0.425017\pi\)
\(60\) −20.9469 −2.70423
\(61\) −0.904674 −0.115832 −0.0579158 0.998321i \(-0.518445\pi\)
−0.0579158 + 0.998321i \(0.518445\pi\)
\(62\) −11.2270 −1.42583
\(63\) −1.28492 −0.161884
\(64\) −12.7388 −1.59235
\(65\) −11.9433 −1.48138
\(66\) −9.83057 −1.21006
\(67\) −8.44392 −1.03159 −0.515795 0.856712i \(-0.672503\pi\)
−0.515795 + 0.856712i \(0.672503\pi\)
\(68\) 11.9977 1.45494
\(69\) −14.9396 −1.79852
\(70\) 14.2112 1.69857
\(71\) −13.6198 −1.61638 −0.808188 0.588925i \(-0.799551\pi\)
−0.808188 + 0.588925i \(0.799551\pi\)
\(72\) −2.10616 −0.248214
\(73\) −3.01943 −0.353398 −0.176699 0.984265i \(-0.556542\pi\)
−0.176699 + 0.984265i \(0.556542\pi\)
\(74\) 10.1380 1.17852
\(75\) −10.9699 −1.26670
\(76\) 4.93327 0.565885
\(77\) 4.16876 0.475074
\(78\) −16.1725 −1.83117
\(79\) −2.84607 −0.320208 −0.160104 0.987100i \(-0.551183\pi\)
−0.160104 + 0.987100i \(0.551183\pi\)
\(80\) 1.46616 0.163922
\(81\) −10.5834 −1.17594
\(82\) −23.7628 −2.62417
\(83\) −5.76261 −0.632528 −0.316264 0.948671i \(-0.602429\pi\)
−0.316264 + 0.948671i \(0.602429\pi\)
\(84\) 12.0282 1.31239
\(85\) 11.7797 1.27769
\(86\) −17.8475 −1.92454
\(87\) −5.39215 −0.578099
\(88\) 6.83319 0.728420
\(89\) 12.5944 1.33500 0.667501 0.744609i \(-0.267364\pi\)
0.667501 + 0.744609i \(0.267364\pi\)
\(90\) −5.16801 −0.544756
\(91\) 6.85812 0.718927
\(92\) 25.9526 2.70574
\(93\) −9.32974 −0.967449
\(94\) −25.3209 −2.61165
\(95\) 4.84363 0.496946
\(96\) −9.84162 −1.00446
\(97\) 18.1031 1.83809 0.919045 0.394153i \(-0.128962\pi\)
0.919045 + 0.394153i \(0.128962\pi\)
\(98\) 8.00649 0.808777
\(99\) −1.51600 −0.152363
\(100\) 19.0566 1.90566
\(101\) 3.92619 0.390671 0.195335 0.980736i \(-0.437420\pi\)
0.195335 + 0.980736i \(0.437420\pi\)
\(102\) 15.9510 1.57938
\(103\) −13.3680 −1.31718 −0.658592 0.752501i \(-0.728848\pi\)
−0.658592 + 0.752501i \(0.728848\pi\)
\(104\) 11.2414 1.10231
\(105\) 11.8096 1.15250
\(106\) 2.30956 0.224324
\(107\) −1.64347 −0.158880 −0.0794399 0.996840i \(-0.525313\pi\)
−0.0794399 + 0.996840i \(0.525313\pi\)
\(108\) 14.8227 1.42632
\(109\) 4.02805 0.385817 0.192909 0.981217i \(-0.438208\pi\)
0.192909 + 0.981217i \(0.438208\pi\)
\(110\) 16.7670 1.59867
\(111\) 8.42474 0.799641
\(112\) −0.841904 −0.0795525
\(113\) 7.43035 0.698989 0.349494 0.936938i \(-0.386353\pi\)
0.349494 + 0.936938i \(0.386353\pi\)
\(114\) 6.55880 0.614288
\(115\) 25.4810 2.37611
\(116\) 9.36704 0.869708
\(117\) −2.49400 −0.230570
\(118\) −8.28080 −0.762309
\(119\) −6.76419 −0.620073
\(120\) 19.3577 1.76711
\(121\) −6.08153 −0.552867
\(122\) 2.08940 0.189165
\(123\) −19.7471 −1.78054
\(124\) 16.2073 1.45546
\(125\) 2.34286 0.209552
\(126\) 2.96760 0.264375
\(127\) −15.2184 −1.35042 −0.675208 0.737627i \(-0.735946\pi\)
−0.675208 + 0.737627i \(0.735946\pi\)
\(128\) 19.1653 1.69399
\(129\) −14.8314 −1.30583
\(130\) 27.5837 2.41925
\(131\) −3.66294 −0.320032 −0.160016 0.987114i \(-0.551155\pi\)
−0.160016 + 0.987114i \(0.551155\pi\)
\(132\) 14.1914 1.23520
\(133\) −2.78133 −0.241172
\(134\) 19.5018 1.68470
\(135\) 14.5534 1.25256
\(136\) −11.0875 −0.950742
\(137\) 3.47664 0.297029 0.148515 0.988910i \(-0.452551\pi\)
0.148515 + 0.988910i \(0.452551\pi\)
\(138\) 34.5040 2.93717
\(139\) −12.9927 −1.10202 −0.551011 0.834498i \(-0.685758\pi\)
−0.551011 + 0.834498i \(0.685758\pi\)
\(140\) −20.5153 −1.73386
\(141\) −21.0419 −1.77204
\(142\) 31.4558 2.63971
\(143\) 8.09148 0.676644
\(144\) 0.306164 0.0255137
\(145\) 9.19682 0.763755
\(146\) 6.97357 0.577136
\(147\) 6.65345 0.548767
\(148\) −14.6351 −1.20300
\(149\) −9.82114 −0.804579 −0.402290 0.915512i \(-0.631785\pi\)
−0.402290 + 0.915512i \(0.631785\pi\)
\(150\) 25.3358 2.06866
\(151\) 1.00000 0.0813788
\(152\) −4.55899 −0.369783
\(153\) 2.45984 0.198866
\(154\) −9.62801 −0.775847
\(155\) 15.9128 1.27814
\(156\) 23.3465 1.86922
\(157\) −1.49729 −0.119496 −0.0597482 0.998213i \(-0.519030\pi\)
−0.0597482 + 0.998213i \(0.519030\pi\)
\(158\) 6.57318 0.522934
\(159\) 1.91926 0.152207
\(160\) 16.7858 1.32704
\(161\) −14.6318 −1.15315
\(162\) 24.4431 1.92043
\(163\) −13.1307 −1.02848 −0.514238 0.857647i \(-0.671925\pi\)
−0.514238 + 0.857647i \(0.671925\pi\)
\(164\) 34.3039 2.67869
\(165\) 13.9335 1.08472
\(166\) 13.3091 1.03299
\(167\) −15.5508 −1.20336 −0.601680 0.798737i \(-0.705502\pi\)
−0.601680 + 0.798737i \(0.705502\pi\)
\(168\) −11.1157 −0.857591
\(169\) 0.311484 0.0239603
\(170\) −27.2059 −2.08660
\(171\) 1.01145 0.0773474
\(172\) 25.7645 1.96453
\(173\) 4.19065 0.318609 0.159305 0.987229i \(-0.449075\pi\)
0.159305 + 0.987229i \(0.449075\pi\)
\(174\) 12.4535 0.944097
\(175\) −10.7439 −0.812163
\(176\) −0.993311 −0.0748737
\(177\) −6.88141 −0.517238
\(178\) −29.0875 −2.18020
\(179\) 17.5057 1.30844 0.654218 0.756306i \(-0.272998\pi\)
0.654218 + 0.756306i \(0.272998\pi\)
\(180\) 7.46051 0.556074
\(181\) 19.1505 1.42344 0.711721 0.702462i \(-0.247916\pi\)
0.711721 + 0.702462i \(0.247916\pi\)
\(182\) −15.8393 −1.17408
\(183\) 1.73631 0.128352
\(184\) −23.9836 −1.76809
\(185\) −14.3692 −1.05644
\(186\) 21.5476 1.57995
\(187\) −7.98066 −0.583604
\(188\) 36.5531 2.66591
\(189\) −8.35691 −0.607876
\(190\) −11.1867 −0.811565
\(191\) 11.0182 0.797250 0.398625 0.917114i \(-0.369488\pi\)
0.398625 + 0.917114i \(0.369488\pi\)
\(192\) 24.4490 1.76446
\(193\) −1.58339 −0.113975 −0.0569874 0.998375i \(-0.518149\pi\)
−0.0569874 + 0.998375i \(0.518149\pi\)
\(194\) −41.8102 −3.00180
\(195\) 22.9223 1.64150
\(196\) −11.5581 −0.825580
\(197\) 15.4228 1.09883 0.549414 0.835550i \(-0.314851\pi\)
0.549414 + 0.835550i \(0.314851\pi\)
\(198\) 3.50129 0.248826
\(199\) −21.9639 −1.55698 −0.778490 0.627657i \(-0.784014\pi\)
−0.778490 + 0.627657i \(0.784014\pi\)
\(200\) −17.6108 −1.24527
\(201\) 16.2061 1.14309
\(202\) −9.06779 −0.638007
\(203\) −5.28104 −0.370656
\(204\) −23.0268 −1.61220
\(205\) 33.6806 2.35235
\(206\) 30.8741 2.15110
\(207\) 5.32094 0.369831
\(208\) −1.63412 −0.113306
\(209\) −3.28152 −0.226988
\(210\) −27.2751 −1.88216
\(211\) −1.00415 −0.0691283 −0.0345641 0.999402i \(-0.511004\pi\)
−0.0345641 + 0.999402i \(0.511004\pi\)
\(212\) −3.33407 −0.228985
\(213\) 26.1400 1.79108
\(214\) 3.79569 0.259468
\(215\) 25.2964 1.72520
\(216\) −13.6982 −0.932041
\(217\) −9.13750 −0.620294
\(218\) −9.30303 −0.630081
\(219\) 5.79509 0.391596
\(220\) −24.2047 −1.63188
\(221\) −13.1292 −0.883163
\(222\) −19.4575 −1.30590
\(223\) 23.3504 1.56366 0.781830 0.623492i \(-0.214287\pi\)
0.781830 + 0.623492i \(0.214287\pi\)
\(224\) −9.63882 −0.644021
\(225\) 3.90709 0.260473
\(226\) −17.1609 −1.14152
\(227\) 8.81313 0.584948 0.292474 0.956273i \(-0.405521\pi\)
0.292474 + 0.956273i \(0.405521\pi\)
\(228\) −9.46825 −0.627050
\(229\) 20.4097 1.34871 0.674357 0.738406i \(-0.264421\pi\)
0.674357 + 0.738406i \(0.264421\pi\)
\(230\) −58.8498 −3.88044
\(231\) −8.00095 −0.526424
\(232\) −8.65637 −0.568319
\(233\) 28.9327 1.89544 0.947721 0.319101i \(-0.103381\pi\)
0.947721 + 0.319101i \(0.103381\pi\)
\(234\) 5.76005 0.376546
\(235\) 35.8889 2.34113
\(236\) 11.9541 0.778147
\(237\) 5.46236 0.354819
\(238\) 15.6223 1.01264
\(239\) −8.18888 −0.529695 −0.264847 0.964290i \(-0.585322\pi\)
−0.264847 + 0.964290i \(0.585322\pi\)
\(240\) −2.81394 −0.181639
\(241\) −21.8283 −1.40609 −0.703043 0.711147i \(-0.748176\pi\)
−0.703043 + 0.711147i \(0.748176\pi\)
\(242\) 14.0457 0.902890
\(243\) 6.97490 0.447440
\(244\) −3.01625 −0.193095
\(245\) −11.3481 −0.725003
\(246\) 45.6071 2.90781
\(247\) −5.39850 −0.343499
\(248\) −14.9776 −0.951082
\(249\) 11.0600 0.700896
\(250\) −5.41097 −0.342220
\(251\) −28.5648 −1.80299 −0.901497 0.432785i \(-0.857531\pi\)
−0.901497 + 0.432785i \(0.857531\pi\)
\(252\) −4.28401 −0.269867
\(253\) −17.2632 −1.08533
\(254\) 35.1479 2.20537
\(255\) −22.6083 −1.41579
\(256\) −18.7860 −1.17412
\(257\) −12.0070 −0.748975 −0.374487 0.927232i \(-0.622181\pi\)
−0.374487 + 0.927232i \(0.622181\pi\)
\(258\) 34.2540 2.13256
\(259\) 8.25114 0.512701
\(260\) −39.8198 −2.46952
\(261\) 1.92048 0.118875
\(262\) 8.45978 0.522647
\(263\) −15.7180 −0.969214 −0.484607 0.874732i \(-0.661037\pi\)
−0.484607 + 0.874732i \(0.661037\pi\)
\(264\) −13.1147 −0.807153
\(265\) −3.27349 −0.201089
\(266\) 6.42365 0.393859
\(267\) −24.1719 −1.47930
\(268\) −28.1526 −1.71970
\(269\) 21.7690 1.32728 0.663641 0.748052i \(-0.269010\pi\)
0.663641 + 0.748052i \(0.269010\pi\)
\(270\) −33.6119 −2.04556
\(271\) −29.4138 −1.78676 −0.893380 0.449301i \(-0.851673\pi\)
−0.893380 + 0.449301i \(0.851673\pi\)
\(272\) 1.61174 0.0977260
\(273\) −13.1625 −0.796633
\(274\) −8.02950 −0.485080
\(275\) −12.6761 −0.764396
\(276\) −49.8098 −2.99820
\(277\) 10.3320 0.620787 0.310393 0.950608i \(-0.399539\pi\)
0.310393 + 0.950608i \(0.399539\pi\)
\(278\) 30.0073 1.79972
\(279\) 3.32291 0.198937
\(280\) 18.9588 1.13301
\(281\) 20.8017 1.24092 0.620462 0.784237i \(-0.286945\pi\)
0.620462 + 0.784237i \(0.286945\pi\)
\(282\) 48.5974 2.89394
\(283\) 16.2866 0.968138 0.484069 0.875030i \(-0.339158\pi\)
0.484069 + 0.875030i \(0.339158\pi\)
\(284\) −45.4095 −2.69456
\(285\) −9.29619 −0.550659
\(286\) −18.6878 −1.10503
\(287\) −19.3402 −1.14162
\(288\) 3.50522 0.206547
\(289\) −4.05066 −0.238274
\(290\) −21.2406 −1.24729
\(291\) −34.7446 −2.03676
\(292\) −10.0670 −0.589127
\(293\) −19.9458 −1.16525 −0.582624 0.812742i \(-0.697974\pi\)
−0.582624 + 0.812742i \(0.697974\pi\)
\(294\) −15.3666 −0.896196
\(295\) 11.7369 0.683348
\(296\) 13.5248 0.786112
\(297\) −9.85981 −0.572124
\(298\) 22.6825 1.31396
\(299\) −28.4000 −1.64242
\(300\) −36.5746 −2.11163
\(301\) −14.5258 −0.837252
\(302\) −2.30956 −0.132900
\(303\) −7.53540 −0.432897
\(304\) 0.662721 0.0380097
\(305\) −2.96144 −0.169571
\(306\) −5.68115 −0.324770
\(307\) −16.9915 −0.969755 −0.484878 0.874582i \(-0.661136\pi\)
−0.484878 + 0.874582i \(0.661136\pi\)
\(308\) 13.8989 0.791966
\(309\) 25.6566 1.45955
\(310\) −36.7515 −2.08734
\(311\) 8.81642 0.499933 0.249967 0.968254i \(-0.419580\pi\)
0.249967 + 0.968254i \(0.419580\pi\)
\(312\) −21.5753 −1.22146
\(313\) 16.4759 0.931271 0.465635 0.884977i \(-0.345826\pi\)
0.465635 + 0.884977i \(0.345826\pi\)
\(314\) 3.45807 0.195150
\(315\) −4.20616 −0.236990
\(316\) −9.48901 −0.533799
\(317\) 24.3009 1.36487 0.682437 0.730945i \(-0.260920\pi\)
0.682437 + 0.730945i \(0.260920\pi\)
\(318\) −4.43265 −0.248571
\(319\) −6.23078 −0.348857
\(320\) −41.7002 −2.33111
\(321\) 3.15424 0.176053
\(322\) 33.7930 1.88321
\(323\) 5.32456 0.296267
\(324\) −35.2860 −1.96033
\(325\) −20.8537 −1.15676
\(326\) 30.3262 1.67961
\(327\) −7.73089 −0.427519
\(328\) −31.7013 −1.75041
\(329\) −20.6083 −1.13617
\(330\) −32.1802 −1.77146
\(331\) −13.8721 −0.762481 −0.381241 0.924476i \(-0.624503\pi\)
−0.381241 + 0.924476i \(0.624503\pi\)
\(332\) −19.2129 −1.05445
\(333\) −3.00058 −0.164431
\(334\) 35.9156 1.96522
\(335\) −27.6411 −1.51019
\(336\) 1.61584 0.0881510
\(337\) 33.2050 1.80879 0.904396 0.426694i \(-0.140322\pi\)
0.904396 + 0.426694i \(0.140322\pi\)
\(338\) −0.719391 −0.0391297
\(339\) −14.2608 −0.774540
\(340\) 39.2744 2.12995
\(341\) −10.7808 −0.583812
\(342\) −2.33600 −0.126316
\(343\) 19.6744 1.06232
\(344\) −23.8098 −1.28374
\(345\) −48.9047 −2.63294
\(346\) −9.67856 −0.520322
\(347\) 12.3421 0.662559 0.331280 0.943533i \(-0.392520\pi\)
0.331280 + 0.943533i \(0.392520\pi\)
\(348\) −17.9778 −0.963712
\(349\) −19.5434 −1.04614 −0.523068 0.852291i \(-0.675213\pi\)
−0.523068 + 0.852291i \(0.675213\pi\)
\(350\) 24.8137 1.32635
\(351\) −16.2206 −0.865791
\(352\) −11.3723 −0.606144
\(353\) −36.7985 −1.95859 −0.979295 0.202441i \(-0.935113\pi\)
−0.979295 + 0.202441i \(0.935113\pi\)
\(354\) 15.8930 0.844705
\(355\) −44.5843 −2.36629
\(356\) 41.9906 2.22550
\(357\) 12.9823 0.687094
\(358\) −40.4305 −2.13682
\(359\) 23.7785 1.25498 0.627490 0.778625i \(-0.284082\pi\)
0.627490 + 0.778625i \(0.284082\pi\)
\(360\) −6.89449 −0.363372
\(361\) −16.8106 −0.884770
\(362\) −44.2291 −2.32463
\(363\) 11.6721 0.612624
\(364\) 22.8655 1.19848
\(365\) −9.88407 −0.517356
\(366\) −4.01011 −0.209612
\(367\) 29.9281 1.56224 0.781118 0.624384i \(-0.214650\pi\)
0.781118 + 0.624384i \(0.214650\pi\)
\(368\) 3.48639 0.181741
\(369\) 7.03319 0.366133
\(370\) 33.1865 1.72529
\(371\) 1.87972 0.0975900
\(372\) −31.1060 −1.61277
\(373\) 32.5622 1.68601 0.843003 0.537909i \(-0.180786\pi\)
0.843003 + 0.537909i \(0.180786\pi\)
\(374\) 18.4318 0.953087
\(375\) −4.49656 −0.232201
\(376\) −33.7799 −1.74206
\(377\) −10.2504 −0.527922
\(378\) 19.3008 0.992725
\(379\) 29.8578 1.53369 0.766846 0.641831i \(-0.221825\pi\)
0.766846 + 0.641831i \(0.221825\pi\)
\(380\) 16.1490 0.828426
\(381\) 29.2081 1.49638
\(382\) −25.4472 −1.30199
\(383\) 1.66611 0.0851343 0.0425672 0.999094i \(-0.486446\pi\)
0.0425672 + 0.999094i \(0.486446\pi\)
\(384\) −36.7833 −1.87709
\(385\) 13.6464 0.695484
\(386\) 3.65693 0.186133
\(387\) 5.28239 0.268519
\(388\) 60.3570 3.06416
\(389\) −5.04024 −0.255550 −0.127775 0.991803i \(-0.540784\pi\)
−0.127775 + 0.991803i \(0.540784\pi\)
\(390\) −52.9404 −2.68074
\(391\) 28.0110 1.41658
\(392\) 10.6812 0.539483
\(393\) 7.03014 0.354624
\(394\) −35.6198 −1.79450
\(395\) −9.31658 −0.468768
\(396\) −5.05444 −0.253995
\(397\) 27.0756 1.35888 0.679442 0.733729i \(-0.262222\pi\)
0.679442 + 0.733729i \(0.262222\pi\)
\(398\) 50.7270 2.54271
\(399\) 5.33810 0.267239
\(400\) 2.56000 0.128000
\(401\) −26.7171 −1.33419 −0.667094 0.744973i \(-0.732462\pi\)
−0.667094 + 0.744973i \(0.732462\pi\)
\(402\) −37.4290 −1.86679
\(403\) −17.7357 −0.883478
\(404\) 13.0902 0.651262
\(405\) −34.6447 −1.72151
\(406\) 12.1969 0.605321
\(407\) 9.73502 0.482547
\(408\) 21.2798 1.05351
\(409\) −18.0560 −0.892810 −0.446405 0.894831i \(-0.647296\pi\)
−0.446405 + 0.894831i \(0.647296\pi\)
\(410\) −77.7873 −3.84164
\(411\) −6.67258 −0.329134
\(412\) −44.5697 −2.19579
\(413\) −6.73961 −0.331635
\(414\) −12.2890 −0.603973
\(415\) −18.8638 −0.925988
\(416\) −18.7088 −0.917273
\(417\) 24.9363 1.22114
\(418\) 7.57887 0.370695
\(419\) −30.6121 −1.49550 −0.747749 0.663981i \(-0.768865\pi\)
−0.747749 + 0.663981i \(0.768865\pi\)
\(420\) 39.3742 1.92126
\(421\) −1.17832 −0.0574280 −0.0287140 0.999588i \(-0.509141\pi\)
−0.0287140 + 0.999588i \(0.509141\pi\)
\(422\) 2.31914 0.112894
\(423\) 7.49433 0.364387
\(424\) 3.08112 0.149632
\(425\) 20.5681 0.997699
\(426\) −60.3720 −2.92503
\(427\) 1.70053 0.0822944
\(428\) −5.47943 −0.264858
\(429\) −15.5297 −0.749780
\(430\) −58.4235 −2.81743
\(431\) 2.85372 0.137459 0.0687294 0.997635i \(-0.478105\pi\)
0.0687294 + 0.997635i \(0.478105\pi\)
\(432\) 1.99124 0.0958037
\(433\) 33.2602 1.59839 0.799193 0.601075i \(-0.205261\pi\)
0.799193 + 0.601075i \(0.205261\pi\)
\(434\) 21.1036 1.01301
\(435\) −17.6511 −0.846307
\(436\) 13.4298 0.643171
\(437\) 11.5177 0.550966
\(438\) −13.3841 −0.639517
\(439\) 8.26120 0.394286 0.197143 0.980375i \(-0.436834\pi\)
0.197143 + 0.980375i \(0.436834\pi\)
\(440\) 22.3683 1.06637
\(441\) −2.36971 −0.112844
\(442\) 30.3226 1.44230
\(443\) 29.1001 1.38259 0.691294 0.722574i \(-0.257041\pi\)
0.691294 + 0.722574i \(0.257041\pi\)
\(444\) 28.0887 1.33303
\(445\) 41.2276 1.95437
\(446\) −53.9292 −2.55362
\(447\) 18.8494 0.891544
\(448\) 23.9453 1.13131
\(449\) 23.5257 1.11025 0.555123 0.831768i \(-0.312671\pi\)
0.555123 + 0.831768i \(0.312671\pi\)
\(450\) −9.02366 −0.425379
\(451\) −22.8183 −1.07447
\(452\) 24.7733 1.16524
\(453\) −1.91926 −0.0901748
\(454\) −20.3545 −0.955283
\(455\) 22.4500 1.05247
\(456\) 8.74990 0.409752
\(457\) −34.0547 −1.59301 −0.796505 0.604632i \(-0.793320\pi\)
−0.796505 + 0.604632i \(0.793320\pi\)
\(458\) −47.1375 −2.20259
\(459\) 15.9984 0.746743
\(460\) 84.9553 3.96106
\(461\) 9.89205 0.460719 0.230359 0.973106i \(-0.426010\pi\)
0.230359 + 0.973106i \(0.426010\pi\)
\(462\) 18.4787 0.859706
\(463\) 10.1614 0.472238 0.236119 0.971724i \(-0.424124\pi\)
0.236119 + 0.971724i \(0.424124\pi\)
\(464\) 1.25834 0.0584170
\(465\) −30.5408 −1.41629
\(466\) −66.8217 −3.09546
\(467\) 37.1208 1.71775 0.858873 0.512189i \(-0.171165\pi\)
0.858873 + 0.512189i \(0.171165\pi\)
\(468\) −8.31518 −0.384369
\(469\) 15.8722 0.732909
\(470\) −82.8876 −3.82332
\(471\) 2.87368 0.132412
\(472\) −11.0472 −0.508487
\(473\) −17.1381 −0.788010
\(474\) −12.6157 −0.579456
\(475\) 8.45727 0.388046
\(476\) −22.5523 −1.03368
\(477\) −0.683571 −0.0312985
\(478\) 18.9127 0.865048
\(479\) −42.1038 −1.92377 −0.961886 0.273452i \(-0.911835\pi\)
−0.961886 + 0.273452i \(0.911835\pi\)
\(480\) −32.2164 −1.47047
\(481\) 16.0153 0.730235
\(482\) 50.4139 2.29629
\(483\) 28.0822 1.27779
\(484\) −20.2763 −0.921648
\(485\) 59.2602 2.69087
\(486\) −16.1090 −0.730717
\(487\) 22.9855 1.04157 0.520786 0.853687i \(-0.325639\pi\)
0.520786 + 0.853687i \(0.325639\pi\)
\(488\) 2.78741 0.126180
\(489\) 25.2013 1.13964
\(490\) 26.2091 1.18401
\(491\) 25.3716 1.14500 0.572502 0.819903i \(-0.305973\pi\)
0.572502 + 0.819903i \(0.305973\pi\)
\(492\) −65.8383 −2.96822
\(493\) 10.1100 0.455332
\(494\) 12.4682 0.560970
\(495\) −4.96259 −0.223052
\(496\) 2.17724 0.0977608
\(497\) 25.6014 1.14838
\(498\) −25.5436 −1.14464
\(499\) 10.4864 0.469437 0.234719 0.972063i \(-0.424583\pi\)
0.234719 + 0.972063i \(0.424583\pi\)
\(500\) 7.81126 0.349330
\(501\) 29.8462 1.33343
\(502\) 65.9721 2.94448
\(503\) −38.2463 −1.70532 −0.852658 0.522469i \(-0.825011\pi\)
−0.852658 + 0.522469i \(0.825011\pi\)
\(504\) 3.95899 0.176347
\(505\) 12.8523 0.571922
\(506\) 39.8703 1.77245
\(507\) −0.597819 −0.0265501
\(508\) −50.7393 −2.25119
\(509\) −5.55991 −0.246439 −0.123219 0.992379i \(-0.539322\pi\)
−0.123219 + 0.992379i \(0.539322\pi\)
\(510\) 52.2154 2.31213
\(511\) 5.67568 0.251077
\(512\) 5.05669 0.223476
\(513\) 6.57830 0.290439
\(514\) 27.7309 1.22316
\(515\) −43.7598 −1.92829
\(516\) −49.4489 −2.17687
\(517\) −24.3144 −1.06935
\(518\) −19.0565 −0.837295
\(519\) −8.04296 −0.353047
\(520\) 36.7987 1.61373
\(521\) −14.3266 −0.627659 −0.313829 0.949479i \(-0.601612\pi\)
−0.313829 + 0.949479i \(0.601612\pi\)
\(522\) −4.43548 −0.194135
\(523\) 37.0173 1.61865 0.809327 0.587358i \(-0.199832\pi\)
0.809327 + 0.587358i \(0.199832\pi\)
\(524\) −12.2125 −0.533505
\(525\) 20.6204 0.899947
\(526\) 36.3017 1.58283
\(527\) 17.4928 0.761998
\(528\) 1.90643 0.0829665
\(529\) 37.5913 1.63441
\(530\) 7.56031 0.328399
\(531\) 2.45090 0.106360
\(532\) −9.27315 −0.402042
\(533\) −37.5390 −1.62599
\(534\) 55.8266 2.41585
\(535\) −5.37986 −0.232592
\(536\) 26.0167 1.12375
\(537\) −33.5980 −1.44986
\(538\) −50.2769 −2.16759
\(539\) 7.68825 0.331156
\(540\) 48.5220 2.08806
\(541\) −8.13669 −0.349824 −0.174912 0.984584i \(-0.555964\pi\)
−0.174912 + 0.984584i \(0.555964\pi\)
\(542\) 67.9329 2.91797
\(543\) −36.7548 −1.57730
\(544\) 18.4525 0.791146
\(545\) 13.1858 0.564816
\(546\) 30.3997 1.30099
\(547\) −37.8013 −1.61627 −0.808133 0.589001i \(-0.799522\pi\)
−0.808133 + 0.589001i \(0.799522\pi\)
\(548\) 11.5914 0.495158
\(549\) −0.618408 −0.0263930
\(550\) 29.2762 1.24834
\(551\) 4.15707 0.177097
\(552\) 46.0308 1.95920
\(553\) 5.34981 0.227497
\(554\) −23.8623 −1.01381
\(555\) 27.5783 1.17063
\(556\) −43.3184 −1.83711
\(557\) 32.2145 1.36497 0.682486 0.730899i \(-0.260899\pi\)
0.682486 + 0.730899i \(0.260899\pi\)
\(558\) −7.67446 −0.324886
\(559\) −28.1943 −1.19249
\(560\) −2.75596 −0.116461
\(561\) 15.3170 0.646684
\(562\) −48.0427 −2.02656
\(563\) 13.4393 0.566398 0.283199 0.959061i \(-0.408604\pi\)
0.283199 + 0.959061i \(0.408604\pi\)
\(564\) −70.1550 −2.95406
\(565\) 24.3232 1.02328
\(566\) −37.6149 −1.58107
\(567\) 19.8939 0.835464
\(568\) 41.9643 1.76078
\(569\) −27.0179 −1.13265 −0.566325 0.824182i \(-0.691635\pi\)
−0.566325 + 0.824182i \(0.691635\pi\)
\(570\) 21.4701 0.899285
\(571\) 19.8098 0.829015 0.414507 0.910046i \(-0.363954\pi\)
0.414507 + 0.910046i \(0.363954\pi\)
\(572\) 26.9776 1.12799
\(573\) −21.1468 −0.883422
\(574\) 44.6674 1.86438
\(575\) 44.4913 1.85542
\(576\) −8.70785 −0.362827
\(577\) 15.6485 0.651458 0.325729 0.945463i \(-0.394390\pi\)
0.325729 + 0.945463i \(0.394390\pi\)
\(578\) 9.35524 0.389127
\(579\) 3.03894 0.126294
\(580\) 30.6629 1.27321
\(581\) 10.8321 0.449390
\(582\) 80.2447 3.32625
\(583\) 2.21776 0.0918503
\(584\) 9.30324 0.384971
\(585\) −8.16408 −0.337543
\(586\) 46.0661 1.90297
\(587\) 16.3338 0.674166 0.337083 0.941475i \(-0.390560\pi\)
0.337083 + 0.941475i \(0.390560\pi\)
\(588\) 22.1831 0.914815
\(589\) 7.19276 0.296372
\(590\) −27.1071 −1.11598
\(591\) −29.6004 −1.21760
\(592\) −1.96604 −0.0808038
\(593\) 16.3928 0.673172 0.336586 0.941653i \(-0.390728\pi\)
0.336586 + 0.941653i \(0.390728\pi\)
\(594\) 22.7718 0.934339
\(595\) −22.1425 −0.907753
\(596\) −32.7444 −1.34126
\(597\) 42.1545 1.72527
\(598\) 65.5916 2.68224
\(599\) −22.8961 −0.935509 −0.467754 0.883858i \(-0.654937\pi\)
−0.467754 + 0.883858i \(0.654937\pi\)
\(600\) 33.7997 1.37987
\(601\) 23.0659 0.940879 0.470439 0.882432i \(-0.344095\pi\)
0.470439 + 0.882432i \(0.344095\pi\)
\(602\) 33.5482 1.36732
\(603\) −5.77202 −0.235055
\(604\) 3.33407 0.135661
\(605\) −19.9078 −0.809367
\(606\) 17.4035 0.706967
\(607\) 11.1633 0.453102 0.226551 0.973999i \(-0.427255\pi\)
0.226551 + 0.973999i \(0.427255\pi\)
\(608\) 7.58739 0.307709
\(609\) 10.1357 0.410720
\(610\) 6.83962 0.276928
\(611\) −40.0003 −1.61824
\(612\) 8.20129 0.331517
\(613\) 44.3273 1.79036 0.895182 0.445701i \(-0.147046\pi\)
0.895182 + 0.445701i \(0.147046\pi\)
\(614\) 39.2429 1.58371
\(615\) −64.6419 −2.60661
\(616\) −12.8444 −0.517518
\(617\) 35.7813 1.44050 0.720250 0.693714i \(-0.244027\pi\)
0.720250 + 0.693714i \(0.244027\pi\)
\(618\) −59.2555 −2.38361
\(619\) −15.7385 −0.632584 −0.316292 0.948662i \(-0.602438\pi\)
−0.316292 + 0.948662i \(0.602438\pi\)
\(620\) 53.0543 2.13071
\(621\) 34.6066 1.38871
\(622\) −20.3621 −0.816444
\(623\) −23.6739 −0.948474
\(624\) 3.13630 0.125553
\(625\) −20.9092 −0.836369
\(626\) −38.0520 −1.52086
\(627\) 6.29810 0.251522
\(628\) −4.99206 −0.199205
\(629\) −15.7960 −0.629826
\(630\) 9.71438 0.387030
\(631\) −38.1728 −1.51964 −0.759818 0.650136i \(-0.774712\pi\)
−0.759818 + 0.650136i \(0.774712\pi\)
\(632\) 8.76909 0.348816
\(633\) 1.92722 0.0766001
\(634\) −56.1244 −2.22898
\(635\) −49.8173 −1.97694
\(636\) 6.39896 0.253735
\(637\) 12.6481 0.501137
\(638\) 14.3904 0.569720
\(639\) −9.31011 −0.368302
\(640\) 62.7375 2.47992
\(641\) 1.02145 0.0403449 0.0201725 0.999797i \(-0.493578\pi\)
0.0201725 + 0.999797i \(0.493578\pi\)
\(642\) −7.28492 −0.287513
\(643\) 10.0459 0.396171 0.198085 0.980185i \(-0.436528\pi\)
0.198085 + 0.980185i \(0.436528\pi\)
\(644\) −48.7834 −1.92234
\(645\) −48.5504 −1.91167
\(646\) −12.2974 −0.483835
\(647\) −47.4236 −1.86442 −0.932208 0.361924i \(-0.882120\pi\)
−0.932208 + 0.361924i \(0.882120\pi\)
\(648\) 32.6088 1.28100
\(649\) −7.95166 −0.312130
\(650\) 48.1629 1.88910
\(651\) 17.5373 0.687339
\(652\) −43.7787 −1.71451
\(653\) 23.8511 0.933366 0.466683 0.884425i \(-0.345449\pi\)
0.466683 + 0.884425i \(0.345449\pi\)
\(654\) 17.8550 0.698184
\(655\) −11.9906 −0.468510
\(656\) 4.60829 0.179923
\(657\) −2.06400 −0.0805242
\(658\) 47.5961 1.85549
\(659\) −6.02906 −0.234859 −0.117429 0.993081i \(-0.537465\pi\)
−0.117429 + 0.993081i \(0.537465\pi\)
\(660\) 46.4552 1.80827
\(661\) −12.4097 −0.482680 −0.241340 0.970441i \(-0.577587\pi\)
−0.241340 + 0.970441i \(0.577587\pi\)
\(662\) 32.0385 1.24521
\(663\) 25.1983 0.978622
\(664\) 17.7553 0.689038
\(665\) −9.10464 −0.353063
\(666\) 6.93003 0.268533
\(667\) 21.8692 0.846778
\(668\) −51.8476 −2.00605
\(669\) −44.8156 −1.73267
\(670\) 63.8387 2.46631
\(671\) 2.00635 0.0774543
\(672\) 18.4994 0.713631
\(673\) −3.96652 −0.152898 −0.0764490 0.997073i \(-0.524358\pi\)
−0.0764490 + 0.997073i \(0.524358\pi\)
\(674\) −76.6890 −2.95395
\(675\) 25.4111 0.978074
\(676\) 1.03851 0.0399427
\(677\) 30.6803 1.17914 0.589570 0.807717i \(-0.299297\pi\)
0.589570 + 0.807717i \(0.299297\pi\)
\(678\) 32.9362 1.26491
\(679\) −34.0286 −1.30590
\(680\) −36.2947 −1.39184
\(681\) −16.9147 −0.648174
\(682\) 24.8989 0.953427
\(683\) 33.9964 1.30083 0.650417 0.759577i \(-0.274594\pi\)
0.650417 + 0.759577i \(0.274594\pi\)
\(684\) 3.37224 0.128941
\(685\) 11.3807 0.434835
\(686\) −45.4391 −1.73487
\(687\) −39.1716 −1.49449
\(688\) 3.46113 0.131954
\(689\) 3.64849 0.138996
\(690\) 112.948 4.29987
\(691\) −6.44366 −0.245128 −0.122564 0.992461i \(-0.539112\pi\)
−0.122564 + 0.992461i \(0.539112\pi\)
\(692\) 13.9719 0.531133
\(693\) 2.84964 0.108249
\(694\) −28.5049 −1.08203
\(695\) −42.5313 −1.61330
\(696\) 16.6139 0.629747
\(697\) 37.0248 1.40241
\(698\) 45.1368 1.70845
\(699\) −55.5294 −2.10031
\(700\) −35.8209 −1.35390
\(701\) 23.4318 0.885009 0.442504 0.896766i \(-0.354090\pi\)
0.442504 + 0.896766i \(0.354090\pi\)
\(702\) 37.4625 1.41393
\(703\) −6.49505 −0.244965
\(704\) 28.2516 1.06477
\(705\) −68.8802 −2.59418
\(706\) 84.9885 3.19858
\(707\) −7.38013 −0.277558
\(708\) −22.9431 −0.862255
\(709\) 9.46196 0.355351 0.177676 0.984089i \(-0.443142\pi\)
0.177676 + 0.984089i \(0.443142\pi\)
\(710\) 102.970 3.86440
\(711\) −1.94549 −0.0729616
\(712\) −38.8048 −1.45427
\(713\) 37.8391 1.41708
\(714\) −29.9833 −1.12210
\(715\) 26.4874 0.990571
\(716\) 58.3652 2.18121
\(717\) 15.7166 0.586948
\(718\) −54.9178 −2.04952
\(719\) −10.6941 −0.398823 −0.199412 0.979916i \(-0.563903\pi\)
−0.199412 + 0.979916i \(0.563903\pi\)
\(720\) 1.00222 0.0373506
\(721\) 25.1279 0.935813
\(722\) 38.8252 1.44492
\(723\) 41.8943 1.55807
\(724\) 63.8490 2.37293
\(725\) 16.0582 0.596387
\(726\) −26.9573 −1.00048
\(727\) −44.6229 −1.65497 −0.827485 0.561487i \(-0.810229\pi\)
−0.827485 + 0.561487i \(0.810229\pi\)
\(728\) −21.1307 −0.783156
\(729\) 18.3637 0.680136
\(730\) 22.8279 0.844897
\(731\) 27.8081 1.02852
\(732\) 5.78897 0.213967
\(733\) 9.32718 0.344507 0.172254 0.985053i \(-0.444895\pi\)
0.172254 + 0.985053i \(0.444895\pi\)
\(734\) −69.1208 −2.55130
\(735\) 21.7800 0.803367
\(736\) 39.9151 1.47129
\(737\) 18.7266 0.689804
\(738\) −16.2436 −0.597934
\(739\) 5.90595 0.217254 0.108627 0.994083i \(-0.465355\pi\)
0.108627 + 0.994083i \(0.465355\pi\)
\(740\) −47.9079 −1.76113
\(741\) 10.3611 0.380626
\(742\) −4.34132 −0.159375
\(743\) −34.7745 −1.27575 −0.637876 0.770139i \(-0.720187\pi\)
−0.637876 + 0.770139i \(0.720187\pi\)
\(744\) 28.7460 1.05388
\(745\) −32.1494 −1.17786
\(746\) −75.2043 −2.75343
\(747\) −3.93915 −0.144126
\(748\) −26.6081 −0.972888
\(749\) 3.08925 0.112879
\(750\) 10.3851 0.379210
\(751\) 49.1285 1.79273 0.896363 0.443321i \(-0.146200\pi\)
0.896363 + 0.443321i \(0.146200\pi\)
\(752\) 4.91044 0.179065
\(753\) 54.8234 1.99787
\(754\) 23.6739 0.862153
\(755\) 3.27349 0.119134
\(756\) −27.8625 −1.01335
\(757\) −6.20659 −0.225582 −0.112791 0.993619i \(-0.535979\pi\)
−0.112791 + 0.993619i \(0.535979\pi\)
\(758\) −68.9584 −2.50468
\(759\) 33.1325 1.20263
\(760\) −14.9238 −0.541343
\(761\) 33.8891 1.22848 0.614239 0.789120i \(-0.289463\pi\)
0.614239 + 0.789120i \(0.289463\pi\)
\(762\) −67.4580 −2.44374
\(763\) −7.57159 −0.274110
\(764\) 36.7355 1.32904
\(765\) 8.05226 0.291130
\(766\) −3.84799 −0.139033
\(767\) −13.0815 −0.472344
\(768\) 36.0552 1.30103
\(769\) 36.0049 1.29837 0.649186 0.760630i \(-0.275110\pi\)
0.649186 + 0.760630i \(0.275110\pi\)
\(770\) −31.5171 −1.13580
\(771\) 23.0446 0.829929
\(772\) −5.27913 −0.190000
\(773\) 4.75472 0.171016 0.0855078 0.996338i \(-0.472749\pi\)
0.0855078 + 0.996338i \(0.472749\pi\)
\(774\) −12.2000 −0.438520
\(775\) 27.7847 0.998055
\(776\) −55.7778 −2.00230
\(777\) −15.8361 −0.568117
\(778\) 11.6407 0.417341
\(779\) 15.2240 0.545457
\(780\) 76.4246 2.73644
\(781\) 30.2055 1.08084
\(782\) −64.6932 −2.31342
\(783\) 12.4905 0.446375
\(784\) −1.55268 −0.0554530
\(785\) −4.90134 −0.174936
\(786\) −16.2365 −0.579138
\(787\) −20.5082 −0.731039 −0.365519 0.930804i \(-0.619109\pi\)
−0.365519 + 0.930804i \(0.619109\pi\)
\(788\) 51.4207 1.83178
\(789\) 30.1670 1.07397
\(790\) 21.5172 0.765548
\(791\) −13.9669 −0.496608
\(792\) 4.67097 0.165976
\(793\) 3.30069 0.117211
\(794\) −62.5327 −2.21920
\(795\) 6.28268 0.222824
\(796\) −73.2292 −2.59554
\(797\) 11.7873 0.417527 0.208763 0.977966i \(-0.433056\pi\)
0.208763 + 0.977966i \(0.433056\pi\)
\(798\) −12.3287 −0.436430
\(799\) 39.4524 1.39573
\(800\) 29.3091 1.03623
\(801\) 8.60915 0.304190
\(802\) 61.7048 2.17887
\(803\) 6.69639 0.236310
\(804\) 54.0323 1.90557
\(805\) −47.8969 −1.68815
\(806\) 40.9617 1.44281
\(807\) −41.7805 −1.47074
\(808\) −12.0971 −0.425574
\(809\) 19.2214 0.675787 0.337894 0.941184i \(-0.390286\pi\)
0.337894 + 0.941184i \(0.390286\pi\)
\(810\) 80.0142 2.81141
\(811\) 27.7705 0.975153 0.487577 0.873080i \(-0.337881\pi\)
0.487577 + 0.873080i \(0.337881\pi\)
\(812\) −17.6074 −0.617897
\(813\) 56.4528 1.97989
\(814\) −22.4836 −0.788051
\(815\) −42.9832 −1.50564
\(816\) −3.09335 −0.108289
\(817\) 11.4343 0.400034
\(818\) 41.7013 1.45805
\(819\) 4.68801 0.163812
\(820\) 112.293 3.92146
\(821\) 8.56562 0.298942 0.149471 0.988766i \(-0.452243\pi\)
0.149471 + 0.988766i \(0.452243\pi\)
\(822\) 15.4107 0.537511
\(823\) −40.6392 −1.41659 −0.708297 0.705914i \(-0.750536\pi\)
−0.708297 + 0.705914i \(0.750536\pi\)
\(824\) 41.1882 1.43486
\(825\) 24.3287 0.847018
\(826\) 15.5655 0.541594
\(827\) 7.78134 0.270584 0.135292 0.990806i \(-0.456803\pi\)
0.135292 + 0.990806i \(0.456803\pi\)
\(828\) 17.7404 0.616522
\(829\) −10.8179 −0.375721 −0.187861 0.982196i \(-0.560155\pi\)
−0.187861 + 0.982196i \(0.560155\pi\)
\(830\) 43.5671 1.51224
\(831\) −19.8297 −0.687886
\(832\) 46.4773 1.61131
\(833\) −12.4749 −0.432229
\(834\) −57.5920 −1.99425
\(835\) −50.9055 −1.76166
\(836\) −10.9408 −0.378396
\(837\) 21.6117 0.747009
\(838\) 70.7005 2.44231
\(839\) 17.1284 0.591336 0.295668 0.955291i \(-0.404458\pi\)
0.295668 + 0.955291i \(0.404458\pi\)
\(840\) −36.3869 −1.25547
\(841\) −21.1068 −0.727820
\(842\) 2.72141 0.0937860
\(843\) −39.9239 −1.37505
\(844\) −3.34789 −0.115239
\(845\) 1.01964 0.0350766
\(846\) −17.3086 −0.595082
\(847\) 11.4315 0.392793
\(848\) −0.447889 −0.0153806
\(849\) −31.2583 −1.07278
\(850\) −47.5032 −1.62935
\(851\) −34.1686 −1.17128
\(852\) 87.1527 2.98580
\(853\) −11.5163 −0.394312 −0.197156 0.980372i \(-0.563170\pi\)
−0.197156 + 0.980372i \(0.563170\pi\)
\(854\) −3.92748 −0.134395
\(855\) 3.31096 0.113232
\(856\) 5.06372 0.173074
\(857\) 7.93496 0.271053 0.135527 0.990774i \(-0.456727\pi\)
0.135527 + 0.990774i \(0.456727\pi\)
\(858\) 35.8668 1.22447
\(859\) −49.3300 −1.68312 −0.841558 0.540166i \(-0.818361\pi\)
−0.841558 + 0.540166i \(0.818361\pi\)
\(860\) 84.3398 2.87596
\(861\) 37.1189 1.26501
\(862\) −6.59084 −0.224485
\(863\) −31.2389 −1.06338 −0.531692 0.846938i \(-0.678443\pi\)
−0.531692 + 0.846938i \(0.678443\pi\)
\(864\) 22.7974 0.775584
\(865\) 13.7180 0.466427
\(866\) −76.8166 −2.61033
\(867\) 7.77427 0.264028
\(868\) −30.4651 −1.03405
\(869\) 6.31191 0.214117
\(870\) 40.7663 1.38211
\(871\) 30.8076 1.04388
\(872\) −12.4109 −0.420286
\(873\) 12.3747 0.418821
\(874\) −26.6008 −0.899786
\(875\) −4.40391 −0.148879
\(876\) 19.3212 0.652804
\(877\) −7.40098 −0.249913 −0.124957 0.992162i \(-0.539879\pi\)
−0.124957 + 0.992162i \(0.539879\pi\)
\(878\) −19.0797 −0.643910
\(879\) 38.2813 1.29120
\(880\) −3.25159 −0.109611
\(881\) −45.5784 −1.53557 −0.767787 0.640705i \(-0.778642\pi\)
−0.767787 + 0.640705i \(0.778642\pi\)
\(882\) 5.47300 0.184285
\(883\) 32.6686 1.09939 0.549693 0.835367i \(-0.314745\pi\)
0.549693 + 0.835367i \(0.314745\pi\)
\(884\) −43.7736 −1.47226
\(885\) −22.5262 −0.757209
\(886\) −67.2085 −2.25791
\(887\) 9.07105 0.304576 0.152288 0.988336i \(-0.451336\pi\)
0.152288 + 0.988336i \(0.451336\pi\)
\(888\) −25.9576 −0.871081
\(889\) 28.6063 0.959424
\(890\) −95.2175 −3.19170
\(891\) 23.4716 0.786327
\(892\) 77.8520 2.60668
\(893\) 16.2222 0.542855
\(894\) −43.5337 −1.45599
\(895\) 57.3046 1.91548
\(896\) −36.0254 −1.20352
\(897\) 54.5071 1.81994
\(898\) −54.3340 −1.81315
\(899\) 13.6572 0.455494
\(900\) 13.0265 0.434217
\(901\) −3.59852 −0.119884
\(902\) 52.7003 1.75473
\(903\) 27.8788 0.927748
\(904\) −22.8938 −0.761437
\(905\) 62.6887 2.08384
\(906\) 4.43265 0.147265
\(907\) 31.4090 1.04292 0.521459 0.853276i \(-0.325388\pi\)
0.521459 + 0.853276i \(0.325388\pi\)
\(908\) 29.3836 0.975130
\(909\) 2.68383 0.0890171
\(910\) −51.8496 −1.71880
\(911\) −15.9759 −0.529306 −0.264653 0.964344i \(-0.585257\pi\)
−0.264653 + 0.964344i \(0.585257\pi\)
\(912\) −1.27194 −0.0421180
\(913\) 12.7801 0.422959
\(914\) 78.6513 2.60155
\(915\) 5.68378 0.187900
\(916\) 68.0475 2.24835
\(917\) 6.88528 0.227372
\(918\) −36.9494 −1.21951
\(919\) −23.1449 −0.763480 −0.381740 0.924270i \(-0.624675\pi\)
−0.381740 + 0.924270i \(0.624675\pi\)
\(920\) −78.5099 −2.58839
\(921\) 32.6111 1.07457
\(922\) −22.8463 −0.752403
\(923\) 49.6918 1.63563
\(924\) −26.6757 −0.877567
\(925\) −25.0895 −0.824938
\(926\) −23.4683 −0.771215
\(927\) −9.13794 −0.300129
\(928\) 14.4065 0.472918
\(929\) −0.134367 −0.00440844 −0.00220422 0.999998i \(-0.500702\pi\)
−0.00220422 + 0.999998i \(0.500702\pi\)
\(930\) 70.5358 2.31296
\(931\) −5.12947 −0.168112
\(932\) 96.4635 3.15977
\(933\) −16.9210 −0.553970
\(934\) −85.7327 −2.80526
\(935\) −26.1246 −0.854365
\(936\) 7.68431 0.251170
\(937\) −58.4414 −1.90920 −0.954599 0.297894i \(-0.903716\pi\)
−0.954599 + 0.297894i \(0.903716\pi\)
\(938\) −36.6578 −1.19692
\(939\) −31.6215 −1.03193
\(940\) 119.656 3.90275
\(941\) 58.1044 1.89415 0.947074 0.321014i \(-0.104024\pi\)
0.947074 + 0.321014i \(0.104024\pi\)
\(942\) −6.63695 −0.216243
\(943\) 80.0893 2.60806
\(944\) 1.60588 0.0522670
\(945\) −27.3562 −0.889898
\(946\) 39.5815 1.28690
\(947\) 40.0725 1.30218 0.651090 0.759000i \(-0.274312\pi\)
0.651090 + 0.759000i \(0.274312\pi\)
\(948\) 18.2119 0.591495
\(949\) 11.0164 0.357607
\(950\) −19.5326 −0.633721
\(951\) −46.6398 −1.51240
\(952\) 20.8413 0.675470
\(953\) 17.5718 0.569207 0.284603 0.958645i \(-0.408138\pi\)
0.284603 + 0.958645i \(0.408138\pi\)
\(954\) 1.57875 0.0511138
\(955\) 36.0680 1.16713
\(956\) −27.3023 −0.883020
\(957\) 11.9585 0.386564
\(958\) 97.2413 3.14172
\(959\) −6.53509 −0.211029
\(960\) 80.0336 2.58307
\(961\) −7.36965 −0.237731
\(962\) −36.9883 −1.19255
\(963\) −1.12343 −0.0362019
\(964\) −72.7772 −2.34400
\(965\) −5.18320 −0.166853
\(966\) −64.8577 −2.08676
\(967\) 4.12595 0.132682 0.0663408 0.997797i \(-0.478868\pi\)
0.0663408 + 0.997797i \(0.478868\pi\)
\(968\) 18.7379 0.602260
\(969\) −10.2192 −0.328289
\(970\) −136.865 −4.39447
\(971\) 12.3135 0.395159 0.197579 0.980287i \(-0.436692\pi\)
0.197579 + 0.980287i \(0.436692\pi\)
\(972\) 23.2548 0.745898
\(973\) 24.4225 0.782949
\(974\) −53.0864 −1.70100
\(975\) 40.0237 1.28179
\(976\) −0.405194 −0.0129699
\(977\) −55.6143 −1.77926 −0.889630 0.456683i \(-0.849038\pi\)
−0.889630 + 0.456683i \(0.849038\pi\)
\(978\) −58.2039 −1.86116
\(979\) −27.9314 −0.892690
\(980\) −37.8354 −1.20861
\(981\) 2.75346 0.0879111
\(982\) −58.5972 −1.86991
\(983\) −3.71278 −0.118419 −0.0592096 0.998246i \(-0.518858\pi\)
−0.0592096 + 0.998246i \(0.518858\pi\)
\(984\) 60.8432 1.93961
\(985\) 50.4862 1.60863
\(986\) −23.3497 −0.743605
\(987\) 39.5527 1.25898
\(988\) −17.9990 −0.572624
\(989\) 60.1524 1.91273
\(990\) 11.4614 0.364268
\(991\) 33.0253 1.04908 0.524542 0.851385i \(-0.324237\pi\)
0.524542 + 0.851385i \(0.324237\pi\)
\(992\) 24.9268 0.791428
\(993\) 26.6243 0.844895
\(994\) −59.1280 −1.87543
\(995\) −71.8985 −2.27934
\(996\) 36.8747 1.16842
\(997\) −16.2510 −0.514674 −0.257337 0.966322i \(-0.582845\pi\)
−0.257337 + 0.966322i \(0.582845\pi\)
\(998\) −24.2191 −0.766641
\(999\) −19.5153 −0.617437
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 \(a_p\))