Properties

Label 6041.2.a.f.1.7
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62362 q^{2}\) \(-1.27143 q^{3}\) \(+4.88340 q^{4}\) \(+1.41870 q^{5}\) \(+3.33576 q^{6}\) \(+1.00000 q^{7}\) \(-7.56495 q^{8}\) \(-1.38346 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62362 q^{2}\) \(-1.27143 q^{3}\) \(+4.88340 q^{4}\) \(+1.41870 q^{5}\) \(+3.33576 q^{6}\) \(+1.00000 q^{7}\) \(-7.56495 q^{8}\) \(-1.38346 q^{9}\) \(-3.72213 q^{10}\) \(+1.00335 q^{11}\) \(-6.20891 q^{12}\) \(+2.84063 q^{13}\) \(-2.62362 q^{14}\) \(-1.80378 q^{15}\) \(+10.0808 q^{16}\) \(-0.358679 q^{17}\) \(+3.62968 q^{18}\) \(+5.52965 q^{19}\) \(+6.92806 q^{20}\) \(-1.27143 q^{21}\) \(-2.63241 q^{22}\) \(-1.69823 q^{23}\) \(+9.61832 q^{24}\) \(-2.98730 q^{25}\) \(-7.45275 q^{26}\) \(+5.57327 q^{27}\) \(+4.88340 q^{28}\) \(+5.52479 q^{29}\) \(+4.73243 q^{30}\) \(+5.40586 q^{31}\) \(-11.3183 q^{32}\) \(-1.27569 q^{33}\) \(+0.941039 q^{34}\) \(+1.41870 q^{35}\) \(-6.75599 q^{36}\) \(+7.60429 q^{37}\) \(-14.5077 q^{38}\) \(-3.61167 q^{39}\) \(-10.7324 q^{40}\) \(+7.89719 q^{41}\) \(+3.33576 q^{42}\) \(-1.43388 q^{43}\) \(+4.89975 q^{44}\) \(-1.96271 q^{45}\) \(+4.45551 q^{46}\) \(-3.18421 q^{47}\) \(-12.8170 q^{48}\) \(+1.00000 q^{49}\) \(+7.83754 q^{50}\) \(+0.456036 q^{51}\) \(+13.8719 q^{52}\) \(-12.9323 q^{53}\) \(-14.6222 q^{54}\) \(+1.42345 q^{55}\) \(-7.56495 q^{56}\) \(-7.03057 q^{57}\) \(-14.4950 q^{58}\) \(+0.388087 q^{59}\) \(-8.80856 q^{60}\) \(+4.85277 q^{61}\) \(-14.1829 q^{62}\) \(-1.38346 q^{63}\) \(+9.53330 q^{64}\) \(+4.03000 q^{65}\) \(+3.34693 q^{66}\) \(-8.67990 q^{67}\) \(-1.75157 q^{68}\) \(+2.15918 q^{69}\) \(-3.72213 q^{70}\) \(-11.8443 q^{71}\) \(+10.4658 q^{72}\) \(+13.4684 q^{73}\) \(-19.9508 q^{74}\) \(+3.79815 q^{75}\) \(+27.0035 q^{76}\) \(+1.00335 q^{77}\) \(+9.47567 q^{78}\) \(+2.15817 q^{79}\) \(+14.3016 q^{80}\) \(-2.93565 q^{81}\) \(-20.7193 q^{82}\) \(+8.98617 q^{83}\) \(-6.20891 q^{84}\) \(-0.508857 q^{85}\) \(+3.76195 q^{86}\) \(-7.02439 q^{87}\) \(-7.59028 q^{88}\) \(+11.1380 q^{89}\) \(+5.14942 q^{90}\) \(+2.84063 q^{91}\) \(-8.29312 q^{92}\) \(-6.87318 q^{93}\) \(+8.35418 q^{94}\) \(+7.84490 q^{95}\) \(+14.3904 q^{96}\) \(-10.7738 q^{97}\) \(-2.62362 q^{98}\) \(-1.38809 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62362 −1.85518 −0.927591 0.373598i \(-0.878124\pi\)
−0.927591 + 0.373598i \(0.878124\pi\)
\(3\) −1.27143 −0.734062 −0.367031 0.930209i \(-0.619626\pi\)
−0.367031 + 0.930209i \(0.619626\pi\)
\(4\) 4.88340 2.44170
\(5\) 1.41870 0.634461 0.317230 0.948348i \(-0.397247\pi\)
0.317230 + 0.948348i \(0.397247\pi\)
\(6\) 3.33576 1.36182
\(7\) 1.00000 0.377964
\(8\) −7.56495 −2.67461
\(9\) −1.38346 −0.461154
\(10\) −3.72213 −1.17704
\(11\) 1.00335 0.302521 0.151261 0.988494i \(-0.451667\pi\)
0.151261 + 0.988494i \(0.451667\pi\)
\(12\) −6.20891 −1.79236
\(13\) 2.84063 0.787850 0.393925 0.919143i \(-0.371117\pi\)
0.393925 + 0.919143i \(0.371117\pi\)
\(14\) −2.62362 −0.701193
\(15\) −1.80378 −0.465733
\(16\) 10.0808 2.52019
\(17\) −0.358679 −0.0869925 −0.0434962 0.999054i \(-0.513850\pi\)
−0.0434962 + 0.999054i \(0.513850\pi\)
\(18\) 3.62968 0.855524
\(19\) 5.52965 1.26859 0.634294 0.773092i \(-0.281291\pi\)
0.634294 + 0.773092i \(0.281291\pi\)
\(20\) 6.92806 1.54916
\(21\) −1.27143 −0.277449
\(22\) −2.63241 −0.561232
\(23\) −1.69823 −0.354105 −0.177052 0.984201i \(-0.556656\pi\)
−0.177052 + 0.984201i \(0.556656\pi\)
\(24\) 9.61832 1.96333
\(25\) −2.98730 −0.597459
\(26\) −7.45275 −1.46160
\(27\) 5.57327 1.07258
\(28\) 4.88340 0.922875
\(29\) 5.52479 1.02593 0.512964 0.858410i \(-0.328548\pi\)
0.512964 + 0.858410i \(0.328548\pi\)
\(30\) 4.73243 0.864020
\(31\) 5.40586 0.970921 0.485460 0.874259i \(-0.338652\pi\)
0.485460 + 0.874259i \(0.338652\pi\)
\(32\) −11.3183 −2.00081
\(33\) −1.27569 −0.222069
\(34\) 0.941039 0.161387
\(35\) 1.41870 0.239804
\(36\) −6.75599 −1.12600
\(37\) 7.60429 1.25014 0.625068 0.780570i \(-0.285071\pi\)
0.625068 + 0.780570i \(0.285071\pi\)
\(38\) −14.5077 −2.35346
\(39\) −3.61167 −0.578330
\(40\) −10.7324 −1.69694
\(41\) 7.89719 1.23333 0.616667 0.787224i \(-0.288482\pi\)
0.616667 + 0.787224i \(0.288482\pi\)
\(42\) 3.33576 0.514719
\(43\) −1.43388 −0.218664 −0.109332 0.994005i \(-0.534871\pi\)
−0.109332 + 0.994005i \(0.534871\pi\)
\(44\) 4.89975 0.738665
\(45\) −1.96271 −0.292584
\(46\) 4.45551 0.656929
\(47\) −3.18421 −0.464465 −0.232233 0.972660i \(-0.574603\pi\)
−0.232233 + 0.972660i \(0.574603\pi\)
\(48\) −12.8170 −1.84998
\(49\) 1.00000 0.142857
\(50\) 7.83754 1.10840
\(51\) 0.456036 0.0638578
\(52\) 13.8719 1.92369
\(53\) −12.9323 −1.77639 −0.888197 0.459462i \(-0.848042\pi\)
−0.888197 + 0.459462i \(0.848042\pi\)
\(54\) −14.6222 −1.98982
\(55\) 1.42345 0.191938
\(56\) −7.56495 −1.01091
\(57\) −7.03057 −0.931222
\(58\) −14.4950 −1.90328
\(59\) 0.388087 0.0505246 0.0252623 0.999681i \(-0.491958\pi\)
0.0252623 + 0.999681i \(0.491958\pi\)
\(60\) −8.80856 −1.13718
\(61\) 4.85277 0.621334 0.310667 0.950519i \(-0.399448\pi\)
0.310667 + 0.950519i \(0.399448\pi\)
\(62\) −14.1829 −1.80123
\(63\) −1.38346 −0.174300
\(64\) 9.53330 1.19166
\(65\) 4.03000 0.499860
\(66\) 3.34693 0.411978
\(67\) −8.67990 −1.06042 −0.530209 0.847867i \(-0.677887\pi\)
−0.530209 + 0.847867i \(0.677887\pi\)
\(68\) −1.75157 −0.212409
\(69\) 2.15918 0.259935
\(70\) −3.72213 −0.444879
\(71\) −11.8443 −1.40566 −0.702831 0.711357i \(-0.748081\pi\)
−0.702831 + 0.711357i \(0.748081\pi\)
\(72\) 10.4658 1.23341
\(73\) 13.4684 1.57635 0.788177 0.615449i \(-0.211025\pi\)
0.788177 + 0.615449i \(0.211025\pi\)
\(74\) −19.9508 −2.31923
\(75\) 3.79815 0.438572
\(76\) 27.0035 3.09751
\(77\) 1.00335 0.114342
\(78\) 9.47567 1.07291
\(79\) 2.15817 0.242813 0.121406 0.992603i \(-0.461260\pi\)
0.121406 + 0.992603i \(0.461260\pi\)
\(80\) 14.3016 1.59896
\(81\) −2.93565 −0.326184
\(82\) −20.7193 −2.28806
\(83\) 8.98617 0.986361 0.493180 0.869927i \(-0.335834\pi\)
0.493180 + 0.869927i \(0.335834\pi\)
\(84\) −6.20891 −0.677447
\(85\) −0.508857 −0.0551933
\(86\) 3.76195 0.405662
\(87\) −7.02439 −0.753094
\(88\) −7.59028 −0.809127
\(89\) 11.1380 1.18063 0.590314 0.807173i \(-0.299004\pi\)
0.590314 + 0.807173i \(0.299004\pi\)
\(90\) 5.14942 0.542796
\(91\) 2.84063 0.297779
\(92\) −8.29312 −0.864617
\(93\) −6.87318 −0.712716
\(94\) 8.35418 0.861668
\(95\) 7.84490 0.804869
\(96\) 14.3904 1.46871
\(97\) −10.7738 −1.09391 −0.546957 0.837161i \(-0.684214\pi\)
−0.546957 + 0.837161i \(0.684214\pi\)
\(98\) −2.62362 −0.265026
\(99\) −1.38809 −0.139509
\(100\) −14.5882 −1.45882
\(101\) 4.40333 0.438147 0.219074 0.975708i \(-0.429697\pi\)
0.219074 + 0.975708i \(0.429697\pi\)
\(102\) −1.19647 −0.118468
\(103\) 8.24817 0.812717 0.406358 0.913714i \(-0.366798\pi\)
0.406358 + 0.913714i \(0.366798\pi\)
\(104\) −21.4892 −2.10719
\(105\) −1.80378 −0.176031
\(106\) 33.9296 3.29554
\(107\) 20.5661 1.98820 0.994098 0.108489i \(-0.0346013\pi\)
0.994098 + 0.108489i \(0.0346013\pi\)
\(108\) 27.2165 2.61891
\(109\) 5.76817 0.552490 0.276245 0.961087i \(-0.410910\pi\)
0.276245 + 0.961087i \(0.410910\pi\)
\(110\) −3.73459 −0.356079
\(111\) −9.66833 −0.917677
\(112\) 10.0808 0.952544
\(113\) −10.4969 −0.987468 −0.493734 0.869613i \(-0.664368\pi\)
−0.493734 + 0.869613i \(0.664368\pi\)
\(114\) 18.4456 1.72759
\(115\) −2.40927 −0.224666
\(116\) 26.9797 2.50501
\(117\) −3.92991 −0.363320
\(118\) −1.01819 −0.0937322
\(119\) −0.358679 −0.0328801
\(120\) 13.6455 1.24566
\(121\) −9.99329 −0.908481
\(122\) −12.7318 −1.15269
\(123\) −10.0407 −0.905343
\(124\) 26.3990 2.37070
\(125\) −11.3316 −1.01353
\(126\) 3.62968 0.323358
\(127\) −7.74654 −0.687394 −0.343697 0.939081i \(-0.611679\pi\)
−0.343697 + 0.939081i \(0.611679\pi\)
\(128\) −2.37526 −0.209945
\(129\) 1.82308 0.160513
\(130\) −10.5732 −0.927331
\(131\) −10.6972 −0.934616 −0.467308 0.884095i \(-0.654776\pi\)
−0.467308 + 0.884095i \(0.654776\pi\)
\(132\) −6.22970 −0.542226
\(133\) 5.52965 0.479481
\(134\) 22.7728 1.96727
\(135\) 7.90679 0.680508
\(136\) 2.71339 0.232671
\(137\) −15.1157 −1.29142 −0.645711 0.763582i \(-0.723439\pi\)
−0.645711 + 0.763582i \(0.723439\pi\)
\(138\) −5.66487 −0.482226
\(139\) 10.2572 0.870008 0.435004 0.900429i \(-0.356747\pi\)
0.435004 + 0.900429i \(0.356747\pi\)
\(140\) 6.92806 0.585528
\(141\) 4.04851 0.340946
\(142\) 31.0750 2.60776
\(143\) 2.85015 0.238341
\(144\) −13.9464 −1.16220
\(145\) 7.83800 0.650911
\(146\) −35.3359 −2.92442
\(147\) −1.27143 −0.104866
\(148\) 37.1347 3.05246
\(149\) −7.02431 −0.575454 −0.287727 0.957713i \(-0.592900\pi\)
−0.287727 + 0.957713i \(0.592900\pi\)
\(150\) −9.96490 −0.813631
\(151\) 14.6847 1.19502 0.597512 0.801860i \(-0.296156\pi\)
0.597512 + 0.801860i \(0.296156\pi\)
\(152\) −41.8315 −3.39298
\(153\) 0.496219 0.0401169
\(154\) −2.63241 −0.212126
\(155\) 7.66928 0.616011
\(156\) −17.6372 −1.41211
\(157\) 16.7482 1.33665 0.668324 0.743870i \(-0.267012\pi\)
0.668324 + 0.743870i \(0.267012\pi\)
\(158\) −5.66222 −0.450462
\(159\) 16.4426 1.30398
\(160\) −16.0572 −1.26943
\(161\) −1.69823 −0.133839
\(162\) 7.70205 0.605130
\(163\) 21.2624 1.66540 0.832698 0.553727i \(-0.186795\pi\)
0.832698 + 0.553727i \(0.186795\pi\)
\(164\) 38.5651 3.01143
\(165\) −1.80982 −0.140894
\(166\) −23.5763 −1.82988
\(167\) 14.3356 1.10932 0.554661 0.832077i \(-0.312848\pi\)
0.554661 + 0.832077i \(0.312848\pi\)
\(168\) 9.61832 0.742069
\(169\) −4.93080 −0.379292
\(170\) 1.33505 0.102394
\(171\) −7.65005 −0.585014
\(172\) −7.00219 −0.533912
\(173\) 13.5304 1.02870 0.514350 0.857580i \(-0.328033\pi\)
0.514350 + 0.857580i \(0.328033\pi\)
\(174\) 18.4294 1.39713
\(175\) −2.98730 −0.225818
\(176\) 10.1145 0.762412
\(177\) −0.493426 −0.0370881
\(178\) −29.2220 −2.19028
\(179\) −12.8676 −0.961771 −0.480886 0.876783i \(-0.659685\pi\)
−0.480886 + 0.876783i \(0.659685\pi\)
\(180\) −9.58471 −0.714402
\(181\) −12.1559 −0.903540 −0.451770 0.892134i \(-0.649207\pi\)
−0.451770 + 0.892134i \(0.649207\pi\)
\(182\) −7.45275 −0.552435
\(183\) −6.16997 −0.456097
\(184\) 12.8470 0.947093
\(185\) 10.7882 0.793163
\(186\) 18.0326 1.32222
\(187\) −0.359880 −0.0263171
\(188\) −15.5498 −1.13408
\(189\) 5.57327 0.405396
\(190\) −20.5821 −1.49318
\(191\) 4.58823 0.331993 0.165996 0.986126i \(-0.446916\pi\)
0.165996 + 0.986126i \(0.446916\pi\)
\(192\) −12.1209 −0.874754
\(193\) −12.2706 −0.883254 −0.441627 0.897199i \(-0.645599\pi\)
−0.441627 + 0.897199i \(0.645599\pi\)
\(194\) 28.2664 2.02941
\(195\) −5.12387 −0.366928
\(196\) 4.88340 0.348814
\(197\) 1.99005 0.141785 0.0708926 0.997484i \(-0.477415\pi\)
0.0708926 + 0.997484i \(0.477415\pi\)
\(198\) 3.64184 0.258814
\(199\) −7.22899 −0.512449 −0.256225 0.966617i \(-0.582479\pi\)
−0.256225 + 0.966617i \(0.582479\pi\)
\(200\) 22.5988 1.59797
\(201\) 11.0359 0.778412
\(202\) −11.5527 −0.812843
\(203\) 5.52479 0.387764
\(204\) 2.22701 0.155922
\(205\) 11.2037 0.782502
\(206\) −21.6401 −1.50774
\(207\) 2.34943 0.163297
\(208\) 28.6358 1.98554
\(209\) 5.54817 0.383775
\(210\) 4.73243 0.326569
\(211\) 12.7426 0.877234 0.438617 0.898674i \(-0.355469\pi\)
0.438617 + 0.898674i \(0.355469\pi\)
\(212\) −63.1538 −4.33742
\(213\) 15.0592 1.03184
\(214\) −53.9576 −3.68846
\(215\) −2.03424 −0.138734
\(216\) −42.1615 −2.86873
\(217\) 5.40586 0.366974
\(218\) −15.1335 −1.02497
\(219\) −17.1241 −1.15714
\(220\) 6.95127 0.468654
\(221\) −1.01888 −0.0685370
\(222\) 25.3661 1.70246
\(223\) −25.5811 −1.71303 −0.856517 0.516119i \(-0.827376\pi\)
−0.856517 + 0.516119i \(0.827376\pi\)
\(224\) −11.3183 −0.756233
\(225\) 4.13281 0.275521
\(226\) 27.5400 1.83193
\(227\) −0.774330 −0.0513941 −0.0256970 0.999670i \(-0.508181\pi\)
−0.0256970 + 0.999670i \(0.508181\pi\)
\(228\) −34.3331 −2.27376
\(229\) 20.2797 1.34012 0.670061 0.742306i \(-0.266268\pi\)
0.670061 + 0.742306i \(0.266268\pi\)
\(230\) 6.32102 0.416796
\(231\) −1.27569 −0.0839342
\(232\) −41.7947 −2.74396
\(233\) −3.89638 −0.255260 −0.127630 0.991822i \(-0.540737\pi\)
−0.127630 + 0.991822i \(0.540737\pi\)
\(234\) 10.3106 0.674024
\(235\) −4.51744 −0.294685
\(236\) 1.89518 0.123366
\(237\) −2.74396 −0.178240
\(238\) 0.941039 0.0609985
\(239\) 11.2504 0.727727 0.363864 0.931452i \(-0.381457\pi\)
0.363864 + 0.931452i \(0.381457\pi\)
\(240\) −18.1835 −1.17374
\(241\) 13.1433 0.846637 0.423318 0.905981i \(-0.360865\pi\)
0.423318 + 0.905981i \(0.360865\pi\)
\(242\) 26.2186 1.68540
\(243\) −12.9873 −0.833138
\(244\) 23.6980 1.51711
\(245\) 1.41870 0.0906373
\(246\) 26.3431 1.67958
\(247\) 15.7077 0.999457
\(248\) −40.8950 −2.59684
\(249\) −11.4253 −0.724049
\(250\) 29.7297 1.88027
\(251\) 20.4839 1.29293 0.646465 0.762944i \(-0.276247\pi\)
0.646465 + 0.762944i \(0.276247\pi\)
\(252\) −6.75599 −0.425587
\(253\) −1.70391 −0.107124
\(254\) 20.3240 1.27524
\(255\) 0.646977 0.0405153
\(256\) −12.8348 −0.802176
\(257\) −29.4392 −1.83637 −0.918185 0.396152i \(-0.870345\pi\)
−0.918185 + 0.396152i \(0.870345\pi\)
\(258\) −4.78306 −0.297781
\(259\) 7.60429 0.472507
\(260\) 19.6801 1.22051
\(261\) −7.64333 −0.473110
\(262\) 28.0653 1.73388
\(263\) −30.4121 −1.87529 −0.937644 0.347597i \(-0.886998\pi\)
−0.937644 + 0.347597i \(0.886998\pi\)
\(264\) 9.65053 0.593949
\(265\) −18.3471 −1.12705
\(266\) −14.5077 −0.889525
\(267\) −14.1612 −0.866654
\(268\) −42.3874 −2.58922
\(269\) 1.92312 0.117254 0.0586272 0.998280i \(-0.481328\pi\)
0.0586272 + 0.998280i \(0.481328\pi\)
\(270\) −20.7444 −1.26247
\(271\) −8.56791 −0.520463 −0.260232 0.965546i \(-0.583799\pi\)
−0.260232 + 0.965546i \(0.583799\pi\)
\(272\) −3.61576 −0.219238
\(273\) −3.61167 −0.218588
\(274\) 39.6579 2.39582
\(275\) −2.99730 −0.180744
\(276\) 10.5441 0.634682
\(277\) −12.0706 −0.725249 −0.362625 0.931935i \(-0.618119\pi\)
−0.362625 + 0.931935i \(0.618119\pi\)
\(278\) −26.9111 −1.61402
\(279\) −7.47880 −0.447744
\(280\) −10.7324 −0.641382
\(281\) −24.4139 −1.45641 −0.728206 0.685359i \(-0.759645\pi\)
−0.728206 + 0.685359i \(0.759645\pi\)
\(282\) −10.6218 −0.632517
\(283\) 1.38787 0.0825001 0.0412501 0.999149i \(-0.486866\pi\)
0.0412501 + 0.999149i \(0.486866\pi\)
\(284\) −57.8405 −3.43220
\(285\) −9.97425 −0.590824
\(286\) −7.47771 −0.442166
\(287\) 7.89719 0.466157
\(288\) 15.6584 0.922679
\(289\) −16.8713 −0.992432
\(290\) −20.5640 −1.20756
\(291\) 13.6982 0.803000
\(292\) 65.7714 3.84898
\(293\) −14.5443 −0.849688 −0.424844 0.905267i \(-0.639671\pi\)
−0.424844 + 0.905267i \(0.639671\pi\)
\(294\) 3.33576 0.194545
\(295\) 0.550577 0.0320559
\(296\) −57.5260 −3.34363
\(297\) 5.59194 0.324477
\(298\) 18.4291 1.06757
\(299\) −4.82404 −0.278982
\(300\) 18.5479 1.07086
\(301\) −1.43388 −0.0826473
\(302\) −38.5271 −2.21699
\(303\) −5.59853 −0.321627
\(304\) 55.7431 3.19709
\(305\) 6.88461 0.394212
\(306\) −1.30189 −0.0744241
\(307\) −9.31668 −0.531731 −0.265866 0.964010i \(-0.585658\pi\)
−0.265866 + 0.964010i \(0.585658\pi\)
\(308\) 4.89975 0.279189
\(309\) −10.4870 −0.596584
\(310\) −20.1213 −1.14281
\(311\) −19.4038 −1.10029 −0.550145 0.835069i \(-0.685428\pi\)
−0.550145 + 0.835069i \(0.685428\pi\)
\(312\) 27.3221 1.54681
\(313\) 7.37349 0.416774 0.208387 0.978046i \(-0.433179\pi\)
0.208387 + 0.978046i \(0.433179\pi\)
\(314\) −43.9409 −2.47973
\(315\) −1.96271 −0.110586
\(316\) 10.5392 0.592876
\(317\) 13.4956 0.757990 0.378995 0.925399i \(-0.376270\pi\)
0.378995 + 0.925399i \(0.376270\pi\)
\(318\) −43.1392 −2.41913
\(319\) 5.54329 0.310365
\(320\) 13.5249 0.756063
\(321\) −26.1483 −1.45946
\(322\) 4.45551 0.248296
\(323\) −1.98337 −0.110358
\(324\) −14.3360 −0.796442
\(325\) −8.48582 −0.470708
\(326\) −55.7844 −3.08961
\(327\) −7.33383 −0.405562
\(328\) −59.7419 −3.29869
\(329\) −3.18421 −0.175551
\(330\) 4.74828 0.261384
\(331\) 28.7446 1.57994 0.789972 0.613143i \(-0.210095\pi\)
0.789972 + 0.613143i \(0.210095\pi\)
\(332\) 43.8831 2.40840
\(333\) −10.5202 −0.576505
\(334\) −37.6112 −2.05799
\(335\) −12.3142 −0.672794
\(336\) −12.8170 −0.699226
\(337\) −10.8952 −0.593502 −0.296751 0.954955i \(-0.595903\pi\)
−0.296751 + 0.954955i \(0.595903\pi\)
\(338\) 12.9366 0.703656
\(339\) 13.3461 0.724863
\(340\) −2.48495 −0.134765
\(341\) 5.42396 0.293724
\(342\) 20.0709 1.08531
\(343\) 1.00000 0.0539949
\(344\) 10.8472 0.584842
\(345\) 3.06322 0.164918
\(346\) −35.4988 −1.90843
\(347\) −36.3110 −1.94927 −0.974637 0.223790i \(-0.928157\pi\)
−0.974637 + 0.223790i \(0.928157\pi\)
\(348\) −34.3029 −1.83883
\(349\) 4.74346 0.253912 0.126956 0.991908i \(-0.459479\pi\)
0.126956 + 0.991908i \(0.459479\pi\)
\(350\) 7.83754 0.418934
\(351\) 15.8316 0.845030
\(352\) −11.3562 −0.605286
\(353\) 24.8401 1.32210 0.661052 0.750340i \(-0.270110\pi\)
0.661052 + 0.750340i \(0.270110\pi\)
\(354\) 1.29456 0.0688052
\(355\) −16.8035 −0.891837
\(356\) 54.3914 2.88274
\(357\) 0.456036 0.0241360
\(358\) 33.7598 1.78426
\(359\) −0.364763 −0.0192514 −0.00962572 0.999954i \(-0.503064\pi\)
−0.00962572 + 0.999954i \(0.503064\pi\)
\(360\) 14.8478 0.782549
\(361\) 11.5770 0.609316
\(362\) 31.8925 1.67623
\(363\) 12.7058 0.666881
\(364\) 13.8719 0.727087
\(365\) 19.1075 1.00013
\(366\) 16.1877 0.846143
\(367\) −16.7597 −0.874848 −0.437424 0.899255i \(-0.644109\pi\)
−0.437424 + 0.899255i \(0.644109\pi\)
\(368\) −17.1195 −0.892413
\(369\) −10.9255 −0.568757
\(370\) −28.3041 −1.47146
\(371\) −12.9323 −0.671414
\(372\) −33.5645 −1.74024
\(373\) 4.97701 0.257700 0.128850 0.991664i \(-0.458871\pi\)
0.128850 + 0.991664i \(0.458871\pi\)
\(374\) 0.944190 0.0488229
\(375\) 14.4073 0.743990
\(376\) 24.0884 1.24227
\(377\) 15.6939 0.808277
\(378\) −14.6222 −0.752083
\(379\) −4.43273 −0.227694 −0.113847 0.993498i \(-0.536317\pi\)
−0.113847 + 0.993498i \(0.536317\pi\)
\(380\) 38.3097 1.96525
\(381\) 9.84920 0.504590
\(382\) −12.0378 −0.615907
\(383\) 0.741365 0.0378820 0.0189410 0.999821i \(-0.493971\pi\)
0.0189410 + 0.999821i \(0.493971\pi\)
\(384\) 3.01998 0.154113
\(385\) 1.42345 0.0725457
\(386\) 32.1933 1.63860
\(387\) 1.98371 0.100838
\(388\) −52.6128 −2.67101
\(389\) 19.8357 1.00571 0.502854 0.864371i \(-0.332283\pi\)
0.502854 + 0.864371i \(0.332283\pi\)
\(390\) 13.4431 0.680718
\(391\) 0.609119 0.0308045
\(392\) −7.56495 −0.382088
\(393\) 13.6007 0.686066
\(394\) −5.22114 −0.263037
\(395\) 3.06179 0.154055
\(396\) −6.77862 −0.340638
\(397\) −0.940959 −0.0472254 −0.0236127 0.999721i \(-0.507517\pi\)
−0.0236127 + 0.999721i \(0.507517\pi\)
\(398\) 18.9661 0.950686
\(399\) −7.03057 −0.351969
\(400\) −30.1143 −1.50571
\(401\) 27.1068 1.35365 0.676825 0.736144i \(-0.263355\pi\)
0.676825 + 0.736144i \(0.263355\pi\)
\(402\) −28.9540 −1.44410
\(403\) 15.3561 0.764940
\(404\) 21.5032 1.06982
\(405\) −4.16480 −0.206951
\(406\) −14.4950 −0.719373
\(407\) 7.62975 0.378193
\(408\) −3.44989 −0.170795
\(409\) 6.45681 0.319268 0.159634 0.987176i \(-0.448969\pi\)
0.159634 + 0.987176i \(0.448969\pi\)
\(410\) −29.3944 −1.45168
\(411\) 19.2186 0.947984
\(412\) 40.2791 1.98441
\(413\) 0.388087 0.0190965
\(414\) −6.16402 −0.302945
\(415\) 12.7487 0.625807
\(416\) −32.1510 −1.57633
\(417\) −13.0414 −0.638639
\(418\) −14.5563 −0.711972
\(419\) 0.669887 0.0327261 0.0163631 0.999866i \(-0.494791\pi\)
0.0163631 + 0.999866i \(0.494791\pi\)
\(420\) −8.80856 −0.429814
\(421\) 7.71126 0.375824 0.187912 0.982186i \(-0.439828\pi\)
0.187912 + 0.982186i \(0.439828\pi\)
\(422\) −33.4317 −1.62743
\(423\) 4.40524 0.214190
\(424\) 97.8326 4.75117
\(425\) 1.07148 0.0519745
\(426\) −39.5098 −1.91426
\(427\) 4.85277 0.234842
\(428\) 100.432 4.85457
\(429\) −3.62377 −0.174957
\(430\) 5.33707 0.257376
\(431\) −6.20495 −0.298882 −0.149441 0.988771i \(-0.547747\pi\)
−0.149441 + 0.988771i \(0.547747\pi\)
\(432\) 56.1829 2.70310
\(433\) 27.0266 1.29882 0.649409 0.760440i \(-0.275017\pi\)
0.649409 + 0.760440i \(0.275017\pi\)
\(434\) −14.1829 −0.680803
\(435\) −9.96549 −0.477809
\(436\) 28.1683 1.34901
\(437\) −9.39060 −0.449213
\(438\) 44.9272 2.14671
\(439\) 7.68565 0.366816 0.183408 0.983037i \(-0.441287\pi\)
0.183408 + 0.983037i \(0.441287\pi\)
\(440\) −10.7683 −0.513359
\(441\) −1.38346 −0.0658791
\(442\) 2.67315 0.127149
\(443\) −3.68603 −0.175128 −0.0875642 0.996159i \(-0.527908\pi\)
−0.0875642 + 0.996159i \(0.527908\pi\)
\(444\) −47.2143 −2.24069
\(445\) 15.8015 0.749063
\(446\) 67.1150 3.17799
\(447\) 8.93093 0.422418
\(448\) 9.53330 0.450406
\(449\) 8.92995 0.421431 0.210715 0.977547i \(-0.432421\pi\)
0.210715 + 0.977547i \(0.432421\pi\)
\(450\) −10.8429 −0.511141
\(451\) 7.92364 0.373110
\(452\) −51.2607 −2.41110
\(453\) −18.6706 −0.877221
\(454\) 2.03155 0.0953453
\(455\) 4.03000 0.188929
\(456\) 53.1859 2.49066
\(457\) 16.5931 0.776190 0.388095 0.921619i \(-0.373133\pi\)
0.388095 + 0.921619i \(0.373133\pi\)
\(458\) −53.2064 −2.48617
\(459\) −1.99902 −0.0933061
\(460\) −11.7654 −0.548566
\(461\) 31.7615 1.47928 0.739640 0.673003i \(-0.234996\pi\)
0.739640 + 0.673003i \(0.234996\pi\)
\(462\) 3.34693 0.155713
\(463\) −9.40780 −0.437218 −0.218609 0.975813i \(-0.570152\pi\)
−0.218609 + 0.975813i \(0.570152\pi\)
\(464\) 55.6942 2.58554
\(465\) −9.75096 −0.452190
\(466\) 10.2226 0.473554
\(467\) −34.8129 −1.61095 −0.805475 0.592629i \(-0.798090\pi\)
−0.805475 + 0.592629i \(0.798090\pi\)
\(468\) −19.1913 −0.887118
\(469\) −8.67990 −0.400801
\(470\) 11.8521 0.546694
\(471\) −21.2941 −0.981182
\(472\) −2.93585 −0.135134
\(473\) −1.43868 −0.0661505
\(474\) 7.19913 0.330667
\(475\) −16.5187 −0.757930
\(476\) −1.75157 −0.0802832
\(477\) 17.8914 0.819191
\(478\) −29.5168 −1.35007
\(479\) 21.8378 0.997796 0.498898 0.866661i \(-0.333738\pi\)
0.498898 + 0.866661i \(0.333738\pi\)
\(480\) 20.4156 0.931841
\(481\) 21.6010 0.984920
\(482\) −34.4832 −1.57066
\(483\) 2.15918 0.0982461
\(484\) −48.8012 −2.21824
\(485\) −15.2848 −0.694046
\(486\) 34.0739 1.54562
\(487\) 37.6515 1.70615 0.853077 0.521785i \(-0.174734\pi\)
0.853077 + 0.521785i \(0.174734\pi\)
\(488\) −36.7110 −1.66183
\(489\) −27.0336 −1.22250
\(490\) −3.72213 −0.168149
\(491\) −10.1391 −0.457571 −0.228785 0.973477i \(-0.573475\pi\)
−0.228785 + 0.973477i \(0.573475\pi\)
\(492\) −49.0329 −2.21058
\(493\) −1.98163 −0.0892480
\(494\) −41.2111 −1.85417
\(495\) −1.96929 −0.0885128
\(496\) 54.4953 2.44691
\(497\) −11.8443 −0.531290
\(498\) 29.9757 1.34324
\(499\) −5.93453 −0.265666 −0.132833 0.991138i \(-0.542407\pi\)
−0.132833 + 0.991138i \(0.542407\pi\)
\(500\) −55.3365 −2.47472
\(501\) −18.2267 −0.814310
\(502\) −53.7419 −2.39862
\(503\) −4.78204 −0.213221 −0.106610 0.994301i \(-0.534000\pi\)
−0.106610 + 0.994301i \(0.534000\pi\)
\(504\) 10.4658 0.466184
\(505\) 6.24699 0.277987
\(506\) 4.47043 0.198735
\(507\) 6.26918 0.278424
\(508\) −37.8294 −1.67841
\(509\) 41.8774 1.85618 0.928092 0.372350i \(-0.121448\pi\)
0.928092 + 0.372350i \(0.121448\pi\)
\(510\) −1.69742 −0.0751632
\(511\) 13.4684 0.595806
\(512\) 38.4242 1.69813
\(513\) 30.8182 1.36066
\(514\) 77.2375 3.40680
\(515\) 11.7017 0.515637
\(516\) 8.90280 0.391924
\(517\) −3.19488 −0.140511
\(518\) −19.9508 −0.876587
\(519\) −17.2030 −0.755129
\(520\) −30.4867 −1.33693
\(521\) −16.9223 −0.741381 −0.370691 0.928756i \(-0.620879\pi\)
−0.370691 + 0.928756i \(0.620879\pi\)
\(522\) 20.0532 0.877705
\(523\) 1.70053 0.0743589 0.0371794 0.999309i \(-0.488163\pi\)
0.0371794 + 0.999309i \(0.488163\pi\)
\(524\) −52.2385 −2.28205
\(525\) 3.79815 0.165765
\(526\) 79.7898 3.47900
\(527\) −1.93897 −0.0844628
\(528\) −12.8599 −0.559657
\(529\) −20.1160 −0.874610
\(530\) 48.1359 2.09089
\(531\) −0.536903 −0.0232996
\(532\) 27.0035 1.17075
\(533\) 22.4330 0.971683
\(534\) 37.1538 1.60780
\(535\) 29.1770 1.26143
\(536\) 65.6630 2.83621
\(537\) 16.3603 0.705999
\(538\) −5.04553 −0.217528
\(539\) 1.00335 0.0432173
\(540\) 38.6120 1.66160
\(541\) 24.6674 1.06053 0.530267 0.847831i \(-0.322092\pi\)
0.530267 + 0.847831i \(0.322092\pi\)
\(542\) 22.4790 0.965554
\(543\) 15.4554 0.663254
\(544\) 4.05962 0.174055
\(545\) 8.18328 0.350533
\(546\) 9.47567 0.405521
\(547\) −36.5380 −1.56225 −0.781125 0.624374i \(-0.785354\pi\)
−0.781125 + 0.624374i \(0.785354\pi\)
\(548\) −73.8160 −3.15326
\(549\) −6.71362 −0.286530
\(550\) 7.86379 0.335313
\(551\) 30.5501 1.30148
\(552\) −16.3341 −0.695225
\(553\) 2.15817 0.0917747
\(554\) 31.6686 1.34547
\(555\) −13.7164 −0.582230
\(556\) 50.0902 2.12430
\(557\) −12.5265 −0.530763 −0.265381 0.964144i \(-0.585498\pi\)
−0.265381 + 0.964144i \(0.585498\pi\)
\(558\) 19.6215 0.830646
\(559\) −4.07312 −0.172274
\(560\) 14.3016 0.604352
\(561\) 0.457563 0.0193183
\(562\) 64.0529 2.70191
\(563\) 41.0593 1.73044 0.865221 0.501391i \(-0.167178\pi\)
0.865221 + 0.501391i \(0.167178\pi\)
\(564\) 19.7705 0.832488
\(565\) −14.8920 −0.626510
\(566\) −3.64124 −0.153053
\(567\) −2.93565 −0.123286
\(568\) 89.6017 3.75960
\(569\) 10.7698 0.451495 0.225747 0.974186i \(-0.427518\pi\)
0.225747 + 0.974186i \(0.427518\pi\)
\(570\) 26.1687 1.09609
\(571\) 12.5226 0.524055 0.262028 0.965060i \(-0.415609\pi\)
0.262028 + 0.965060i \(0.415609\pi\)
\(572\) 13.9184 0.581958
\(573\) −5.83362 −0.243703
\(574\) −20.7193 −0.864805
\(575\) 5.07311 0.211563
\(576\) −13.1889 −0.549540
\(577\) −6.88690 −0.286705 −0.143353 0.989672i \(-0.545788\pi\)
−0.143353 + 0.989672i \(0.545788\pi\)
\(578\) 44.2641 1.84114
\(579\) 15.6012 0.648363
\(580\) 38.2761 1.58933
\(581\) 8.98617 0.372809
\(582\) −35.9388 −1.48971
\(583\) −12.9757 −0.537397
\(584\) −101.888 −4.21614
\(585\) −5.57535 −0.230512
\(586\) 38.1588 1.57633
\(587\) 39.2707 1.62087 0.810437 0.585826i \(-0.199230\pi\)
0.810437 + 0.585826i \(0.199230\pi\)
\(588\) −6.20891 −0.256051
\(589\) 29.8925 1.23170
\(590\) −1.44451 −0.0594694
\(591\) −2.53021 −0.104079
\(592\) 76.6571 3.15059
\(593\) −15.6776 −0.643803 −0.321901 0.946773i \(-0.604322\pi\)
−0.321901 + 0.946773i \(0.604322\pi\)
\(594\) −14.6711 −0.601964
\(595\) −0.508857 −0.0208611
\(596\) −34.3025 −1.40508
\(597\) 9.19116 0.376169
\(598\) 12.6565 0.517561
\(599\) −45.7991 −1.87130 −0.935650 0.352929i \(-0.885186\pi\)
−0.935650 + 0.352929i \(0.885186\pi\)
\(600\) −28.7328 −1.17301
\(601\) −6.99513 −0.285337 −0.142669 0.989771i \(-0.545568\pi\)
−0.142669 + 0.989771i \(0.545568\pi\)
\(602\) 3.76195 0.153326
\(603\) 12.0083 0.489016
\(604\) 71.7112 2.91789
\(605\) −14.1775 −0.576396
\(606\) 14.6884 0.596677
\(607\) 26.5766 1.07871 0.539356 0.842078i \(-0.318668\pi\)
0.539356 + 0.842078i \(0.318668\pi\)
\(608\) −62.5860 −2.53820
\(609\) −7.02439 −0.284643
\(610\) −18.0626 −0.731335
\(611\) −9.04519 −0.365929
\(612\) 2.42323 0.0979534
\(613\) 38.4416 1.55264 0.776322 0.630337i \(-0.217083\pi\)
0.776322 + 0.630337i \(0.217083\pi\)
\(614\) 24.4435 0.986458
\(615\) −14.2448 −0.574405
\(616\) −7.59028 −0.305821
\(617\) −31.4730 −1.26705 −0.633527 0.773721i \(-0.718393\pi\)
−0.633527 + 0.773721i \(0.718393\pi\)
\(618\) 27.5139 1.10677
\(619\) 39.5958 1.59149 0.795745 0.605631i \(-0.207079\pi\)
0.795745 + 0.605631i \(0.207079\pi\)
\(620\) 37.4521 1.50411
\(621\) −9.46468 −0.379805
\(622\) 50.9083 2.04124
\(623\) 11.1380 0.446236
\(624\) −36.4085 −1.45751
\(625\) −1.13957 −0.0455827
\(626\) −19.3452 −0.773192
\(627\) −7.05411 −0.281714
\(628\) 81.7879 3.26369
\(629\) −2.72750 −0.108752
\(630\) 5.14942 0.205158
\(631\) 43.3957 1.72755 0.863777 0.503875i \(-0.168093\pi\)
0.863777 + 0.503875i \(0.168093\pi\)
\(632\) −16.3264 −0.649431
\(633\) −16.2013 −0.643944
\(634\) −35.4075 −1.40621
\(635\) −10.9900 −0.436125
\(636\) 80.2958 3.18393
\(637\) 2.84063 0.112550
\(638\) −14.5435 −0.575783
\(639\) 16.3862 0.648226
\(640\) −3.36977 −0.133202
\(641\) −33.7650 −1.33364 −0.666818 0.745220i \(-0.732344\pi\)
−0.666818 + 0.745220i \(0.732344\pi\)
\(642\) 68.6034 2.70756
\(643\) 37.5203 1.47966 0.739829 0.672795i \(-0.234906\pi\)
0.739829 + 0.672795i \(0.234906\pi\)
\(644\) −8.29312 −0.326795
\(645\) 2.58639 0.101839
\(646\) 5.20361 0.204733
\(647\) −0.762837 −0.0299902 −0.0149951 0.999888i \(-0.504773\pi\)
−0.0149951 + 0.999888i \(0.504773\pi\)
\(648\) 22.2081 0.872415
\(649\) 0.389386 0.0152847
\(650\) 22.2636 0.873250
\(651\) −6.87318 −0.269381
\(652\) 103.833 4.06640
\(653\) −24.0453 −0.940963 −0.470482 0.882410i \(-0.655920\pi\)
−0.470482 + 0.882410i \(0.655920\pi\)
\(654\) 19.2412 0.752391
\(655\) −15.1760 −0.592977
\(656\) 79.6099 3.10824
\(657\) −18.6330 −0.726941
\(658\) 8.35418 0.325680
\(659\) 10.7830 0.420046 0.210023 0.977696i \(-0.432646\pi\)
0.210023 + 0.977696i \(0.432646\pi\)
\(660\) −8.83806 −0.344021
\(661\) −27.0293 −1.05132 −0.525660 0.850695i \(-0.676181\pi\)
−0.525660 + 0.850695i \(0.676181\pi\)
\(662\) −75.4149 −2.93108
\(663\) 1.29543 0.0503104
\(664\) −67.9799 −2.63813
\(665\) 7.84490 0.304212
\(666\) 27.6011 1.06952
\(667\) −9.38235 −0.363286
\(668\) 70.0064 2.70863
\(669\) 32.5246 1.25747
\(670\) 32.3077 1.24815
\(671\) 4.86902 0.187967
\(672\) 14.3904 0.555122
\(673\) −23.2270 −0.895336 −0.447668 0.894200i \(-0.647745\pi\)
−0.447668 + 0.894200i \(0.647745\pi\)
\(674\) 28.5850 1.10105
\(675\) −16.6490 −0.640821
\(676\) −24.0791 −0.926118
\(677\) 21.5465 0.828098 0.414049 0.910255i \(-0.364114\pi\)
0.414049 + 0.910255i \(0.364114\pi\)
\(678\) −35.0152 −1.34475
\(679\) −10.7738 −0.413461
\(680\) 3.84948 0.147621
\(681\) 0.984507 0.0377264
\(682\) −14.2304 −0.544911
\(683\) 36.8466 1.40990 0.704948 0.709259i \(-0.250970\pi\)
0.704948 + 0.709259i \(0.250970\pi\)
\(684\) −37.3582 −1.42843
\(685\) −21.4446 −0.819357
\(686\) −2.62362 −0.100170
\(687\) −25.7843 −0.983732
\(688\) −14.4546 −0.551076
\(689\) −36.7361 −1.39953
\(690\) −8.03674 −0.305954
\(691\) 32.3596 1.23102 0.615508 0.788131i \(-0.288951\pi\)
0.615508 + 0.788131i \(0.288951\pi\)
\(692\) 66.0745 2.51178
\(693\) −1.38809 −0.0527293
\(694\) 95.2663 3.61626
\(695\) 14.5519 0.551986
\(696\) 53.1392 2.01423
\(697\) −2.83256 −0.107291
\(698\) −12.4451 −0.471052
\(699\) 4.95398 0.187377
\(700\) −14.5882 −0.551381
\(701\) −10.2804 −0.388286 −0.194143 0.980973i \(-0.562193\pi\)
−0.194143 + 0.980973i \(0.562193\pi\)
\(702\) −41.5362 −1.56768
\(703\) 42.0490 1.58591
\(704\) 9.56523 0.360503
\(705\) 5.74361 0.216317
\(706\) −65.1710 −2.45274
\(707\) 4.40333 0.165604
\(708\) −2.40959 −0.0905581
\(709\) −2.01430 −0.0756488 −0.0378244 0.999284i \(-0.512043\pi\)
−0.0378244 + 0.999284i \(0.512043\pi\)
\(710\) 44.0861 1.65452
\(711\) −2.98574 −0.111974
\(712\) −84.2586 −3.15773
\(713\) −9.18038 −0.343808
\(714\) −1.19647 −0.0447766
\(715\) 4.04350 0.151218
\(716\) −62.8377 −2.34836
\(717\) −14.3041 −0.534197
\(718\) 0.957000 0.0357149
\(719\) 6.09844 0.227433 0.113717 0.993513i \(-0.463724\pi\)
0.113717 + 0.993513i \(0.463724\pi\)
\(720\) −19.7857 −0.737368
\(721\) 8.24817 0.307178
\(722\) −30.3737 −1.13039
\(723\) −16.7109 −0.621483
\(724\) −59.3620 −2.20617
\(725\) −16.5042 −0.612950
\(726\) −33.3352 −1.23719
\(727\) 16.2330 0.602049 0.301024 0.953616i \(-0.402671\pi\)
0.301024 + 0.953616i \(0.402671\pi\)
\(728\) −21.4892 −0.796445
\(729\) 25.3195 0.937758
\(730\) −50.1310 −1.85543
\(731\) 0.514301 0.0190221
\(732\) −30.1304 −1.11365
\(733\) −29.7793 −1.09992 −0.549961 0.835190i \(-0.685357\pi\)
−0.549961 + 0.835190i \(0.685357\pi\)
\(734\) 43.9711 1.62300
\(735\) −1.80378 −0.0665333
\(736\) 19.2210 0.708495
\(737\) −8.70897 −0.320799
\(738\) 28.6643 1.05515
\(739\) 24.2669 0.892671 0.446335 0.894866i \(-0.352729\pi\)
0.446335 + 0.894866i \(0.352729\pi\)
\(740\) 52.6830 1.93666
\(741\) −19.9713 −0.733663
\(742\) 33.9296 1.24560
\(743\) −12.6911 −0.465593 −0.232797 0.972525i \(-0.574788\pi\)
−0.232797 + 0.972525i \(0.574788\pi\)
\(744\) 51.9953 1.90624
\(745\) −9.96537 −0.365103
\(746\) −13.0578 −0.478080
\(747\) −12.4320 −0.454864
\(748\) −1.75744 −0.0642583
\(749\) 20.5661 0.751467
\(750\) −37.7993 −1.38024
\(751\) 0.551230 0.0201147 0.0100573 0.999949i \(-0.496799\pi\)
0.0100573 + 0.999949i \(0.496799\pi\)
\(752\) −32.0994 −1.17054
\(753\) −26.0438 −0.949090
\(754\) −41.1749 −1.49950
\(755\) 20.8331 0.758196
\(756\) 27.2165 0.989855
\(757\) 14.1085 0.512784 0.256392 0.966573i \(-0.417466\pi\)
0.256392 + 0.966573i \(0.417466\pi\)
\(758\) 11.6298 0.422414
\(759\) 2.16641 0.0786357
\(760\) −59.3462 −2.15271
\(761\) 7.29511 0.264448 0.132224 0.991220i \(-0.457788\pi\)
0.132224 + 0.991220i \(0.457788\pi\)
\(762\) −25.8406 −0.936106
\(763\) 5.76817 0.208822
\(764\) 22.4062 0.810626
\(765\) 0.703984 0.0254526
\(766\) −1.94506 −0.0702779
\(767\) 1.10241 0.0398058
\(768\) 16.3186 0.588846
\(769\) 38.3516 1.38300 0.691498 0.722379i \(-0.256951\pi\)
0.691498 + 0.722379i \(0.256951\pi\)
\(770\) −3.73459 −0.134585
\(771\) 37.4300 1.34801
\(772\) −59.9220 −2.15664
\(773\) −7.46079 −0.268346 −0.134173 0.990958i \(-0.542838\pi\)
−0.134173 + 0.990958i \(0.542838\pi\)
\(774\) −5.20451 −0.187072
\(775\) −16.1489 −0.580086
\(776\) 81.5033 2.92580
\(777\) −9.66833 −0.346849
\(778\) −52.0413 −1.86577
\(779\) 43.6687 1.56459
\(780\) −25.0219 −0.895928
\(781\) −11.8840 −0.425242
\(782\) −1.59810 −0.0571479
\(783\) 30.7911 1.10039
\(784\) 10.0808 0.360028
\(785\) 23.7606 0.848051
\(786\) −35.6832 −1.27278
\(787\) −42.7412 −1.52356 −0.761779 0.647837i \(-0.775674\pi\)
−0.761779 + 0.647837i \(0.775674\pi\)
\(788\) 9.71821 0.346197
\(789\) 38.6669 1.37658
\(790\) −8.03298 −0.285801
\(791\) −10.4969 −0.373228
\(792\) 10.5009 0.373132
\(793\) 13.7849 0.489518
\(794\) 2.46872 0.0876117
\(795\) 23.3271 0.827326
\(796\) −35.3020 −1.25125
\(797\) 24.8675 0.880852 0.440426 0.897789i \(-0.354827\pi\)
0.440426 + 0.897789i \(0.354827\pi\)
\(798\) 18.4456 0.652966
\(799\) 1.14211 0.0404050
\(800\) 33.8110 1.19540
\(801\) −15.4090 −0.544451
\(802\) −71.1181 −2.51127
\(803\) 13.5135 0.476880
\(804\) 53.8927 1.90065
\(805\) −2.40927 −0.0849156
\(806\) −40.2885 −1.41910
\(807\) −2.44511 −0.0860720
\(808\) −33.3109 −1.17187
\(809\) −35.2861 −1.24059 −0.620296 0.784368i \(-0.712988\pi\)
−0.620296 + 0.784368i \(0.712988\pi\)
\(810\) 10.9269 0.383931
\(811\) 52.0766 1.82866 0.914329 0.404972i \(-0.132719\pi\)
0.914329 + 0.404972i \(0.132719\pi\)
\(812\) 26.9797 0.946803
\(813\) 10.8935 0.382052
\(814\) −20.0176 −0.701616
\(815\) 30.1649 1.05663
\(816\) 4.59720 0.160934
\(817\) −7.92883 −0.277395
\(818\) −16.9402 −0.592301
\(819\) −3.92991 −0.137322
\(820\) 54.7123 1.91064
\(821\) 27.5507 0.961526 0.480763 0.876851i \(-0.340360\pi\)
0.480763 + 0.876851i \(0.340360\pi\)
\(822\) −50.4224 −1.75868
\(823\) −18.6228 −0.649149 −0.324574 0.945860i \(-0.605221\pi\)
−0.324574 + 0.945860i \(0.605221\pi\)
\(824\) −62.3970 −2.17370
\(825\) 3.81086 0.132677
\(826\) −1.01819 −0.0354275
\(827\) −41.2752 −1.43528 −0.717639 0.696415i \(-0.754777\pi\)
−0.717639 + 0.696415i \(0.754777\pi\)
\(828\) 11.4732 0.398721
\(829\) −41.5670 −1.44368 −0.721841 0.692059i \(-0.756704\pi\)
−0.721841 + 0.692059i \(0.756704\pi\)
\(830\) −33.4477 −1.16099
\(831\) 15.3469 0.532378
\(832\) 27.0806 0.938851
\(833\) −0.358679 −0.0124275
\(834\) 34.2157 1.18479
\(835\) 20.3379 0.703821
\(836\) 27.0939 0.937062
\(837\) 30.1283 1.04139
\(838\) −1.75753 −0.0607129
\(839\) 25.6470 0.885434 0.442717 0.896661i \(-0.354015\pi\)
0.442717 + 0.896661i \(0.354015\pi\)
\(840\) 13.6455 0.470814
\(841\) 1.52329 0.0525272
\(842\) −20.2314 −0.697221
\(843\) 31.0406 1.06910
\(844\) 62.2270 2.14194
\(845\) −6.99531 −0.240646
\(846\) −11.5577 −0.397361
\(847\) −9.99329 −0.343374
\(848\) −130.368 −4.47686
\(849\) −1.76458 −0.0605602
\(850\) −2.81116 −0.0964221
\(851\) −12.9138 −0.442679
\(852\) 73.5403 2.51945
\(853\) 26.0641 0.892416 0.446208 0.894929i \(-0.352774\pi\)
0.446208 + 0.894929i \(0.352774\pi\)
\(854\) −12.7318 −0.435675
\(855\) −10.8531 −0.371168
\(856\) −155.581 −5.31765
\(857\) −36.3613 −1.24208 −0.621039 0.783780i \(-0.713289\pi\)
−0.621039 + 0.783780i \(0.713289\pi\)
\(858\) 9.50740 0.324577
\(859\) −30.8138 −1.05135 −0.525677 0.850684i \(-0.676188\pi\)
−0.525677 + 0.850684i \(0.676188\pi\)
\(860\) −9.93399 −0.338746
\(861\) −10.0407 −0.342188
\(862\) 16.2794 0.554480
\(863\) −1.00000 −0.0340404
\(864\) −63.0798 −2.14602
\(865\) 19.1956 0.652670
\(866\) −70.9077 −2.40954
\(867\) 21.4508 0.728506
\(868\) 26.3990 0.896039
\(869\) 2.16540 0.0734560
\(870\) 26.1457 0.886422
\(871\) −24.6564 −0.835451
\(872\) −43.6359 −1.47770
\(873\) 14.9051 0.504463
\(874\) 24.6374 0.833372
\(875\) −11.3316 −0.383077
\(876\) −83.6239 −2.82539
\(877\) −23.5148 −0.794037 −0.397019 0.917811i \(-0.629955\pi\)
−0.397019 + 0.917811i \(0.629955\pi\)
\(878\) −20.1642 −0.680510
\(879\) 18.4921 0.623723
\(880\) 14.3495 0.483720
\(881\) 43.2880 1.45841 0.729206 0.684295i \(-0.239890\pi\)
0.729206 + 0.684295i \(0.239890\pi\)
\(882\) 3.62968 0.122218
\(883\) 53.1004 1.78697 0.893485 0.449092i \(-0.148253\pi\)
0.893485 + 0.449092i \(0.148253\pi\)
\(884\) −4.97558 −0.167347
\(885\) −0.700022 −0.0235310
\(886\) 9.67074 0.324895
\(887\) 15.4190 0.517719 0.258859 0.965915i \(-0.416653\pi\)
0.258859 + 0.965915i \(0.416653\pi\)
\(888\) 73.1404 2.45443
\(889\) −7.74654 −0.259811
\(890\) −41.4572 −1.38965
\(891\) −2.94548 −0.0986774
\(892\) −124.922 −4.18271
\(893\) −17.6076 −0.589215
\(894\) −23.4314 −0.783663
\(895\) −18.2553 −0.610206
\(896\) −2.37526 −0.0793518
\(897\) 6.13344 0.204790
\(898\) −23.4288 −0.781830
\(899\) 29.8662 0.996094
\(900\) 20.1822 0.672738
\(901\) 4.63856 0.154533
\(902\) −20.7886 −0.692186
\(903\) 1.82308 0.0606682
\(904\) 79.4088 2.64110
\(905\) −17.2455 −0.573261
\(906\) 48.9846 1.62740
\(907\) 33.3959 1.10889 0.554447 0.832219i \(-0.312930\pi\)
0.554447 + 0.832219i \(0.312930\pi\)
\(908\) −3.78136 −0.125489
\(909\) −6.09183 −0.202053
\(910\) −10.5732 −0.350498
\(911\) 46.6324 1.54500 0.772501 0.635014i \(-0.219006\pi\)
0.772501 + 0.635014i \(0.219006\pi\)
\(912\) −70.8736 −2.34686
\(913\) 9.01627 0.298395
\(914\) −43.5339 −1.43997
\(915\) −8.75332 −0.289376
\(916\) 99.0340 3.27218
\(917\) −10.6972 −0.353252
\(918\) 5.24466 0.173100
\(919\) −1.44613 −0.0477035 −0.0238518 0.999716i \(-0.507593\pi\)
−0.0238518 + 0.999716i \(0.507593\pi\)
\(920\) 18.2260 0.600894
\(921\) 11.8455 0.390323
\(922\) −83.3302 −2.74433
\(923\) −33.6454 −1.10745
\(924\) −6.22970 −0.204942
\(925\) −22.7163 −0.746906
\(926\) 24.6825 0.811118
\(927\) −11.4110 −0.374787
\(928\) −62.5310 −2.05268
\(929\) −2.65734 −0.0871846 −0.0435923 0.999049i \(-0.513880\pi\)
−0.0435923 + 0.999049i \(0.513880\pi\)
\(930\) 25.5829 0.838895
\(931\) 5.52965 0.181227
\(932\) −19.0276 −0.623269
\(933\) 24.6707 0.807681
\(934\) 91.3360 2.98861
\(935\) −0.510561 −0.0166971
\(936\) 29.7295 0.971740
\(937\) 0.769474 0.0251376 0.0125688 0.999921i \(-0.495999\pi\)
0.0125688 + 0.999921i \(0.495999\pi\)
\(938\) 22.7728 0.743558
\(939\) −9.37489 −0.305938
\(940\) −22.0604 −0.719532
\(941\) −37.8046 −1.23239 −0.616197 0.787592i \(-0.711328\pi\)
−0.616197 + 0.787592i \(0.711328\pi\)
\(942\) 55.8678 1.82027
\(943\) −13.4112 −0.436730
\(944\) 3.91221 0.127332
\(945\) 7.90679 0.257208
\(946\) 3.77455 0.122721
\(947\) 0.244560 0.00794712 0.00397356 0.999992i \(-0.498735\pi\)
0.00397356 + 0.999992i \(0.498735\pi\)
\(948\) −13.3999 −0.435208
\(949\) 38.2587 1.24193
\(950\) 43.3388 1.40610
\(951\) −17.1588 −0.556412
\(952\) 2.71339 0.0879414
\(953\) −37.9064 −1.22791 −0.613955 0.789341i \(-0.710422\pi\)
−0.613955 + 0.789341i \(0.710422\pi\)
\(954\) −46.9403 −1.51975
\(955\) 6.50931 0.210636
\(956\) 54.9401 1.77689
\(957\) −7.04792 −0.227827
\(958\) −57.2943 −1.85109
\(959\) −15.1157 −0.488112
\(960\) −17.1959 −0.554997
\(961\) −1.77669 −0.0573126
\(962\) −56.6729 −1.82721
\(963\) −28.4523 −0.916864
\(964\) 64.1841 2.06723
\(965\) −17.4082 −0.560390
\(966\) −5.66487 −0.182264
\(967\) −4.93632 −0.158741 −0.0793707 0.996845i \(-0.525291\pi\)
−0.0793707 + 0.996845i \(0.525291\pi\)
\(968\) 75.5987 2.42984
\(969\) 2.52172 0.0810093
\(970\) 40.1015 1.28758
\(971\) 46.5158 1.49276 0.746381 0.665519i \(-0.231790\pi\)
0.746381 + 0.665519i \(0.231790\pi\)
\(972\) −63.4223 −2.03427
\(973\) 10.2572 0.328832
\(974\) −98.7835 −3.16523
\(975\) 10.7891 0.345529
\(976\) 48.9197 1.56588
\(977\) 23.0833 0.738499 0.369250 0.929330i \(-0.379615\pi\)
0.369250 + 0.929330i \(0.379615\pi\)
\(978\) 70.9261 2.26797
\(979\) 11.1753 0.357165
\(980\) 6.92806 0.221309
\(981\) −7.98003 −0.254783
\(982\) 26.6011 0.848877
\(983\) 4.63684 0.147892 0.0739461 0.997262i \(-0.476441\pi\)
0.0739461 + 0.997262i \(0.476441\pi\)
\(984\) 75.9577 2.42144
\(985\) 2.82328 0.0899572
\(986\) 5.19904 0.165571
\(987\) 4.04851 0.128866
\(988\) 76.7070 2.44037
\(989\) 2.43505 0.0774300
\(990\) 5.16666 0.164207
\(991\) −49.5792 −1.57494 −0.787468 0.616356i \(-0.788608\pi\)
−0.787468 + 0.616356i \(0.788608\pi\)
\(992\) −61.1849 −1.94262
\(993\) −36.5468 −1.15978
\(994\) 31.0750 0.985640
\(995\) −10.2557 −0.325129
\(996\) −55.7943 −1.76791
\(997\) −38.6510 −1.22409 −0.612045 0.790823i \(-0.709653\pi\)
−0.612045 + 0.790823i \(0.709653\pi\)
\(998\) 15.5700 0.492859
\(999\) 42.3808 1.34087
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 \(a_p\))