Properties

Label 8011.2.a.b.1.12
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62246 q^{2}\) \(-2.12328 q^{3}\) \(+4.87729 q^{4}\) \(+2.57436 q^{5}\) \(+5.56822 q^{6}\) \(-3.69406 q^{7}\) \(-7.54557 q^{8}\) \(+1.50833 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62246 q^{2}\) \(-2.12328 q^{3}\) \(+4.87729 q^{4}\) \(+2.57436 q^{5}\) \(+5.56822 q^{6}\) \(-3.69406 q^{7}\) \(-7.54557 q^{8}\) \(+1.50833 q^{9}\) \(-6.75115 q^{10}\) \(-0.495298 q^{11}\) \(-10.3559 q^{12}\) \(+5.97668 q^{13}\) \(+9.68751 q^{14}\) \(-5.46609 q^{15}\) \(+10.0334 q^{16}\) \(-3.51722 q^{17}\) \(-3.95553 q^{18}\) \(-8.34345 q^{19}\) \(+12.5559 q^{20}\) \(+7.84353 q^{21}\) \(+1.29890 q^{22}\) \(-5.47494 q^{23}\) \(+16.0214 q^{24}\) \(+1.62732 q^{25}\) \(-15.6736 q^{26}\) \(+3.16724 q^{27}\) \(-18.0170 q^{28}\) \(+6.95494 q^{29}\) \(+14.3346 q^{30}\) \(+1.64309 q^{31}\) \(-11.2210 q^{32}\) \(+1.05166 q^{33}\) \(+9.22377 q^{34}\) \(-9.50983 q^{35}\) \(+7.35656 q^{36}\) \(+0.114816 q^{37}\) \(+21.8803 q^{38}\) \(-12.6902 q^{39}\) \(-19.4250 q^{40}\) \(-7.14150 q^{41}\) \(-20.5693 q^{42}\) \(-4.66431 q^{43}\) \(-2.41571 q^{44}\) \(+3.88298 q^{45}\) \(+14.3578 q^{46}\) \(-3.97553 q^{47}\) \(-21.3037 q^{48}\) \(+6.64605 q^{49}\) \(-4.26759 q^{50}\) \(+7.46806 q^{51}\) \(+29.1500 q^{52}\) \(+4.37021 q^{53}\) \(-8.30595 q^{54}\) \(-1.27508 q^{55}\) \(+27.8738 q^{56}\) \(+17.7155 q^{57}\) \(-18.2390 q^{58}\) \(-6.50881 q^{59}\) \(-26.6597 q^{60}\) \(-1.38885 q^{61}\) \(-4.30893 q^{62}\) \(-5.57185 q^{63}\) \(+9.35975 q^{64}\) \(+15.3861 q^{65}\) \(-2.75793 q^{66}\) \(-5.99388 q^{67}\) \(-17.1545 q^{68}\) \(+11.6248 q^{69}\) \(+24.9391 q^{70}\) \(+16.5048 q^{71}\) \(-11.3812 q^{72}\) \(-12.4975 q^{73}\) \(-0.301100 q^{74}\) \(-3.45527 q^{75}\) \(-40.6934 q^{76}\) \(+1.82966 q^{77}\) \(+33.2795 q^{78}\) \(+0.963915 q^{79}\) \(+25.8295 q^{80}\) \(-11.2499 q^{81}\) \(+18.7283 q^{82}\) \(-8.20641 q^{83}\) \(+38.2551 q^{84}\) \(-9.05459 q^{85}\) \(+12.2320 q^{86}\) \(-14.7673 q^{87}\) \(+3.73731 q^{88}\) \(-1.76787 q^{89}\) \(-10.1830 q^{90}\) \(-22.0782 q^{91}\) \(-26.7028 q^{92}\) \(-3.48874 q^{93}\) \(+10.4257 q^{94}\) \(-21.4790 q^{95}\) \(+23.8253 q^{96}\) \(-1.36444 q^{97}\) \(-17.4290 q^{98}\) \(-0.747073 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62246 −1.85436 −0.927179 0.374618i \(-0.877774\pi\)
−0.927179 + 0.374618i \(0.877774\pi\)
\(3\) −2.12328 −1.22588 −0.612939 0.790130i \(-0.710013\pi\)
−0.612939 + 0.790130i \(0.710013\pi\)
\(4\) 4.87729 2.43864
\(5\) 2.57436 1.15129 0.575644 0.817700i \(-0.304751\pi\)
0.575644 + 0.817700i \(0.304751\pi\)
\(6\) 5.56822 2.27322
\(7\) −3.69406 −1.39622 −0.698111 0.715990i \(-0.745976\pi\)
−0.698111 + 0.715990i \(0.745976\pi\)
\(8\) −7.54557 −2.66776
\(9\) 1.50833 0.502777
\(10\) −6.75115 −2.13490
\(11\) −0.495298 −0.149338 −0.0746691 0.997208i \(-0.523790\pi\)
−0.0746691 + 0.997208i \(0.523790\pi\)
\(12\) −10.3559 −2.98948
\(13\) 5.97668 1.65763 0.828816 0.559521i \(-0.189015\pi\)
0.828816 + 0.559521i \(0.189015\pi\)
\(14\) 9.68751 2.58910
\(15\) −5.46609 −1.41134
\(16\) 10.0334 2.50834
\(17\) −3.51722 −0.853052 −0.426526 0.904475i \(-0.640263\pi\)
−0.426526 + 0.904475i \(0.640263\pi\)
\(18\) −3.95553 −0.932328
\(19\) −8.34345 −1.91412 −0.957059 0.289892i \(-0.906380\pi\)
−0.957059 + 0.289892i \(0.906380\pi\)
\(20\) 12.5559 2.80758
\(21\) 7.84353 1.71160
\(22\) 1.29890 0.276926
\(23\) −5.47494 −1.14160 −0.570802 0.821088i \(-0.693367\pi\)
−0.570802 + 0.821088i \(0.693367\pi\)
\(24\) 16.0214 3.27035
\(25\) 1.62732 0.325465
\(26\) −15.6736 −3.07384
\(27\) 3.16724 0.609535
\(28\) −18.0170 −3.40489
\(29\) 6.95494 1.29150 0.645750 0.763549i \(-0.276545\pi\)
0.645750 + 0.763549i \(0.276545\pi\)
\(30\) 14.3346 2.61713
\(31\) 1.64309 0.295107 0.147554 0.989054i \(-0.452860\pi\)
0.147554 + 0.989054i \(0.452860\pi\)
\(32\) −11.2210 −1.98360
\(33\) 1.05166 0.183070
\(34\) 9.22377 1.58186
\(35\) −9.50983 −1.60745
\(36\) 7.35656 1.22609
\(37\) 0.114816 0.0188756 0.00943781 0.999955i \(-0.496996\pi\)
0.00943781 + 0.999955i \(0.496996\pi\)
\(38\) 21.8803 3.54946
\(39\) −12.6902 −2.03205
\(40\) −19.4250 −3.07136
\(41\) −7.14150 −1.11531 −0.557657 0.830071i \(-0.688300\pi\)
−0.557657 + 0.830071i \(0.688300\pi\)
\(42\) −20.5693 −3.17392
\(43\) −4.66431 −0.711301 −0.355650 0.934619i \(-0.615741\pi\)
−0.355650 + 0.934619i \(0.615741\pi\)
\(44\) −2.41571 −0.364183
\(45\) 3.88298 0.578841
\(46\) 14.3578 2.11694
\(47\) −3.97553 −0.579891 −0.289946 0.957043i \(-0.593637\pi\)
−0.289946 + 0.957043i \(0.593637\pi\)
\(48\) −21.3037 −3.07492
\(49\) 6.64605 0.949436
\(50\) −4.26759 −0.603529
\(51\) 7.46806 1.04574
\(52\) 29.1500 4.04237
\(53\) 4.37021 0.600294 0.300147 0.953893i \(-0.402964\pi\)
0.300147 + 0.953893i \(0.402964\pi\)
\(54\) −8.30595 −1.13030
\(55\) −1.27508 −0.171931
\(56\) 27.8738 3.72479
\(57\) 17.7155 2.34648
\(58\) −18.2390 −2.39490
\(59\) −6.50881 −0.847375 −0.423687 0.905809i \(-0.639264\pi\)
−0.423687 + 0.905809i \(0.639264\pi\)
\(60\) −26.6597 −3.44175
\(61\) −1.38885 −0.177824 −0.0889119 0.996039i \(-0.528339\pi\)
−0.0889119 + 0.996039i \(0.528339\pi\)
\(62\) −4.30893 −0.547235
\(63\) −5.57185 −0.701988
\(64\) 9.35975 1.16997
\(65\) 15.3861 1.90841
\(66\) −2.75793 −0.339478
\(67\) −5.99388 −0.732269 −0.366135 0.930562i \(-0.619319\pi\)
−0.366135 + 0.930562i \(0.619319\pi\)
\(68\) −17.1545 −2.08029
\(69\) 11.6248 1.39947
\(70\) 24.9391 2.98080
\(71\) 16.5048 1.95876 0.979380 0.202027i \(-0.0647528\pi\)
0.979380 + 0.202027i \(0.0647528\pi\)
\(72\) −11.3812 −1.34129
\(73\) −12.4975 −1.46272 −0.731360 0.681991i \(-0.761114\pi\)
−0.731360 + 0.681991i \(0.761114\pi\)
\(74\) −0.301100 −0.0350022
\(75\) −3.45527 −0.398980
\(76\) −40.6934 −4.66785
\(77\) 1.82966 0.208509
\(78\) 33.2795 3.76816
\(79\) 0.963915 0.108449 0.0542245 0.998529i \(-0.482731\pi\)
0.0542245 + 0.998529i \(0.482731\pi\)
\(80\) 25.8295 2.88783
\(81\) −11.2499 −1.24999
\(82\) 18.7283 2.06819
\(83\) −8.20641 −0.900770 −0.450385 0.892834i \(-0.648713\pi\)
−0.450385 + 0.892834i \(0.648713\pi\)
\(84\) 38.2551 4.17398
\(85\) −9.05459 −0.982108
\(86\) 12.2320 1.31901
\(87\) −14.7673 −1.58322
\(88\) 3.73731 0.398399
\(89\) −1.76787 −0.187394 −0.0936969 0.995601i \(-0.529868\pi\)
−0.0936969 + 0.995601i \(0.529868\pi\)
\(90\) −10.1830 −1.07338
\(91\) −22.0782 −2.31442
\(92\) −26.7028 −2.78396
\(93\) −3.48874 −0.361765
\(94\) 10.4257 1.07533
\(95\) −21.4790 −2.20370
\(96\) 23.8253 2.43166
\(97\) −1.36444 −0.138538 −0.0692691 0.997598i \(-0.522067\pi\)
−0.0692691 + 0.997598i \(0.522067\pi\)
\(98\) −17.4290 −1.76059
\(99\) −0.747073 −0.0750837
\(100\) 7.93693 0.793693
\(101\) 8.06225 0.802223 0.401112 0.916029i \(-0.368624\pi\)
0.401112 + 0.916029i \(0.368624\pi\)
\(102\) −19.5847 −1.93917
\(103\) −5.00940 −0.493591 −0.246795 0.969068i \(-0.579378\pi\)
−0.246795 + 0.969068i \(0.579378\pi\)
\(104\) −45.0974 −4.42217
\(105\) 20.1921 1.97054
\(106\) −11.4607 −1.11316
\(107\) −10.7604 −1.04024 −0.520122 0.854092i \(-0.674114\pi\)
−0.520122 + 0.854092i \(0.674114\pi\)
\(108\) 15.4475 1.48644
\(109\) 17.7083 1.69615 0.848073 0.529880i \(-0.177763\pi\)
0.848073 + 0.529880i \(0.177763\pi\)
\(110\) 3.34383 0.318822
\(111\) −0.243787 −0.0231392
\(112\) −37.0638 −3.50220
\(113\) −18.8603 −1.77422 −0.887112 0.461554i \(-0.847292\pi\)
−0.887112 + 0.461554i \(0.847292\pi\)
\(114\) −46.4582 −4.35121
\(115\) −14.0945 −1.31431
\(116\) 33.9213 3.14951
\(117\) 9.01480 0.833418
\(118\) 17.0691 1.57134
\(119\) 12.9928 1.19105
\(120\) 41.2448 3.76512
\(121\) −10.7547 −0.977698
\(122\) 3.64220 0.329749
\(123\) 15.1634 1.36724
\(124\) 8.01381 0.719662
\(125\) −8.68248 −0.776584
\(126\) 14.6120 1.30174
\(127\) 13.8862 1.23220 0.616100 0.787668i \(-0.288712\pi\)
0.616100 + 0.787668i \(0.288712\pi\)
\(128\) −2.10365 −0.185938
\(129\) 9.90365 0.871968
\(130\) −40.3494 −3.53888
\(131\) 14.7953 1.29267 0.646337 0.763052i \(-0.276300\pi\)
0.646337 + 0.763052i \(0.276300\pi\)
\(132\) 5.12924 0.446443
\(133\) 30.8212 2.67253
\(134\) 15.7187 1.35789
\(135\) 8.15361 0.701751
\(136\) 26.5394 2.27574
\(137\) −18.2090 −1.55570 −0.777849 0.628451i \(-0.783689\pi\)
−0.777849 + 0.628451i \(0.783689\pi\)
\(138\) −30.4857 −2.59511
\(139\) −0.751610 −0.0637507 −0.0318754 0.999492i \(-0.510148\pi\)
−0.0318754 + 0.999492i \(0.510148\pi\)
\(140\) −46.3822 −3.92001
\(141\) 8.44118 0.710876
\(142\) −43.2832 −3.63224
\(143\) −2.96024 −0.247548
\(144\) 15.1336 1.26114
\(145\) 17.9045 1.48689
\(146\) 32.7741 2.71241
\(147\) −14.1114 −1.16389
\(148\) 0.559990 0.0460309
\(149\) 9.02651 0.739481 0.369740 0.929135i \(-0.379447\pi\)
0.369740 + 0.929135i \(0.379447\pi\)
\(150\) 9.06130 0.739852
\(151\) 10.5635 0.859649 0.429825 0.902912i \(-0.358575\pi\)
0.429825 + 0.902912i \(0.358575\pi\)
\(152\) 62.9561 5.10641
\(153\) −5.30513 −0.428894
\(154\) −4.79821 −0.386651
\(155\) 4.22990 0.339754
\(156\) −61.8937 −4.95546
\(157\) −6.66893 −0.532239 −0.266119 0.963940i \(-0.585742\pi\)
−0.266119 + 0.963940i \(0.585742\pi\)
\(158\) −2.52783 −0.201103
\(159\) −9.27918 −0.735887
\(160\) −28.8868 −2.28370
\(161\) 20.2247 1.59393
\(162\) 29.5025 2.31793
\(163\) 6.19594 0.485303 0.242652 0.970113i \(-0.421983\pi\)
0.242652 + 0.970113i \(0.421983\pi\)
\(164\) −34.8312 −2.71986
\(165\) 2.70735 0.210767
\(166\) 21.5210 1.67035
\(167\) 8.85709 0.685383 0.342691 0.939448i \(-0.388662\pi\)
0.342691 + 0.939448i \(0.388662\pi\)
\(168\) −59.1839 −4.56614
\(169\) 22.7207 1.74774
\(170\) 23.7453 1.82118
\(171\) −12.5847 −0.962374
\(172\) −22.7492 −1.73461
\(173\) 6.87287 0.522535 0.261267 0.965266i \(-0.415860\pi\)
0.261267 + 0.965266i \(0.415860\pi\)
\(174\) 38.7267 2.93586
\(175\) −6.01143 −0.454421
\(176\) −4.96951 −0.374591
\(177\) 13.8200 1.03878
\(178\) 4.63617 0.347495
\(179\) 4.94169 0.369359 0.184679 0.982799i \(-0.440875\pi\)
0.184679 + 0.982799i \(0.440875\pi\)
\(180\) 18.9384 1.41159
\(181\) −6.80310 −0.505671 −0.252835 0.967509i \(-0.581363\pi\)
−0.252835 + 0.967509i \(0.581363\pi\)
\(182\) 57.8991 4.29177
\(183\) 2.94892 0.217990
\(184\) 41.3115 3.04553
\(185\) 0.295577 0.0217313
\(186\) 9.14908 0.670843
\(187\) 1.74207 0.127393
\(188\) −19.3898 −1.41415
\(189\) −11.7000 −0.851046
\(190\) 56.3279 4.08645
\(191\) 5.60597 0.405633 0.202817 0.979217i \(-0.434990\pi\)
0.202817 + 0.979217i \(0.434990\pi\)
\(192\) −19.8734 −1.43424
\(193\) 19.9563 1.43649 0.718243 0.695792i \(-0.244947\pi\)
0.718243 + 0.695792i \(0.244947\pi\)
\(194\) 3.57820 0.256900
\(195\) −32.6691 −2.33948
\(196\) 32.4147 2.31534
\(197\) 20.8896 1.48832 0.744160 0.668001i \(-0.232850\pi\)
0.744160 + 0.668001i \(0.232850\pi\)
\(198\) 1.95917 0.139232
\(199\) −5.19715 −0.368416 −0.184208 0.982887i \(-0.558972\pi\)
−0.184208 + 0.982887i \(0.558972\pi\)
\(200\) −12.2791 −0.868263
\(201\) 12.7267 0.897672
\(202\) −21.1429 −1.48761
\(203\) −25.6919 −1.80322
\(204\) 36.4239 2.55018
\(205\) −18.3848 −1.28405
\(206\) 13.1369 0.915294
\(207\) −8.25801 −0.573971
\(208\) 59.9662 4.15791
\(209\) 4.13250 0.285851
\(210\) −52.9528 −3.65409
\(211\) 20.4682 1.40909 0.704546 0.709658i \(-0.251151\pi\)
0.704546 + 0.709658i \(0.251151\pi\)
\(212\) 21.3148 1.46390
\(213\) −35.0444 −2.40120
\(214\) 28.2186 1.92899
\(215\) −12.0076 −0.818912
\(216\) −23.8986 −1.62610
\(217\) −6.06966 −0.412035
\(218\) −46.4392 −3.14526
\(219\) 26.5357 1.79312
\(220\) −6.21892 −0.419279
\(221\) −21.0213 −1.41405
\(222\) 0.639320 0.0429084
\(223\) −25.2565 −1.69130 −0.845650 0.533739i \(-0.820787\pi\)
−0.845650 + 0.533739i \(0.820787\pi\)
\(224\) 41.4508 2.76955
\(225\) 2.45454 0.163636
\(226\) 49.4603 3.29005
\(227\) −14.5384 −0.964950 −0.482475 0.875910i \(-0.660262\pi\)
−0.482475 + 0.875910i \(0.660262\pi\)
\(228\) 86.4036 5.72222
\(229\) −8.14567 −0.538281 −0.269141 0.963101i \(-0.586740\pi\)
−0.269141 + 0.963101i \(0.586740\pi\)
\(230\) 36.9621 2.43721
\(231\) −3.88489 −0.255607
\(232\) −52.4790 −3.44542
\(233\) 16.4477 1.07752 0.538762 0.842458i \(-0.318892\pi\)
0.538762 + 0.842458i \(0.318892\pi\)
\(234\) −23.6409 −1.54546
\(235\) −10.2344 −0.667622
\(236\) −31.7453 −2.06645
\(237\) −2.04666 −0.132945
\(238\) −34.0731 −2.20863
\(239\) 9.99532 0.646543 0.323272 0.946306i \(-0.395217\pi\)
0.323272 + 0.946306i \(0.395217\pi\)
\(240\) −54.8433 −3.54012
\(241\) −24.0020 −1.54610 −0.773052 0.634342i \(-0.781271\pi\)
−0.773052 + 0.634342i \(0.781271\pi\)
\(242\) 28.2037 1.81300
\(243\) 14.3851 0.922803
\(244\) −6.77381 −0.433649
\(245\) 17.1093 1.09307
\(246\) −39.7655 −2.53535
\(247\) −49.8661 −3.17290
\(248\) −12.3980 −0.787276
\(249\) 17.4245 1.10423
\(250\) 22.7694 1.44007
\(251\) −17.3855 −1.09736 −0.548681 0.836032i \(-0.684870\pi\)
−0.548681 + 0.836032i \(0.684870\pi\)
\(252\) −27.1755 −1.71190
\(253\) 2.71173 0.170485
\(254\) −36.4160 −2.28494
\(255\) 19.2255 1.20394
\(256\) −13.2028 −0.825173
\(257\) 25.8083 1.60987 0.804937 0.593360i \(-0.202199\pi\)
0.804937 + 0.593360i \(0.202199\pi\)
\(258\) −25.9719 −1.61694
\(259\) −0.424137 −0.0263546
\(260\) 75.0425 4.65394
\(261\) 10.4903 0.649336
\(262\) −38.8001 −2.39708
\(263\) −21.8763 −1.34895 −0.674475 0.738297i \(-0.735630\pi\)
−0.674475 + 0.738297i \(0.735630\pi\)
\(264\) −7.93537 −0.488388
\(265\) 11.2505 0.691111
\(266\) −80.8272 −4.95584
\(267\) 3.75369 0.229722
\(268\) −29.2339 −1.78574
\(269\) 2.17383 0.132541 0.0662705 0.997802i \(-0.478890\pi\)
0.0662705 + 0.997802i \(0.478890\pi\)
\(270\) −21.3825 −1.30130
\(271\) −27.7046 −1.68293 −0.841467 0.540308i \(-0.818308\pi\)
−0.841467 + 0.540308i \(0.818308\pi\)
\(272\) −35.2896 −2.13975
\(273\) 46.8782 2.83720
\(274\) 47.7523 2.88482
\(275\) −0.806011 −0.0486043
\(276\) 56.6977 3.41280
\(277\) −12.2117 −0.733730 −0.366865 0.930274i \(-0.619569\pi\)
−0.366865 + 0.930274i \(0.619569\pi\)
\(278\) 1.97107 0.118217
\(279\) 2.47832 0.148373
\(280\) 71.7571 4.28831
\(281\) 29.9597 1.78725 0.893624 0.448817i \(-0.148154\pi\)
0.893624 + 0.448817i \(0.148154\pi\)
\(282\) −22.1366 −1.31822
\(283\) −17.7801 −1.05692 −0.528460 0.848958i \(-0.677230\pi\)
−0.528460 + 0.848958i \(0.677230\pi\)
\(284\) 80.4987 4.77672
\(285\) 45.6061 2.70147
\(286\) 7.76310 0.459042
\(287\) 26.3811 1.55723
\(288\) −16.9249 −0.997309
\(289\) −4.62915 −0.272303
\(290\) −46.9539 −2.75723
\(291\) 2.89710 0.169831
\(292\) −60.9539 −3.56706
\(293\) −8.28073 −0.483766 −0.241883 0.970305i \(-0.577765\pi\)
−0.241883 + 0.970305i \(0.577765\pi\)
\(294\) 37.0067 2.15827
\(295\) −16.7560 −0.975573
\(296\) −0.866352 −0.0503557
\(297\) −1.56873 −0.0910268
\(298\) −23.6716 −1.37126
\(299\) −32.7219 −1.89236
\(300\) −16.8524 −0.972971
\(301\) 17.2302 0.993133
\(302\) −27.7025 −1.59410
\(303\) −17.1184 −0.983428
\(304\) −83.7129 −4.80126
\(305\) −3.57539 −0.204726
\(306\) 13.9125 0.795324
\(307\) 12.7718 0.728926 0.364463 0.931218i \(-0.381253\pi\)
0.364463 + 0.931218i \(0.381253\pi\)
\(308\) 8.92378 0.508480
\(309\) 10.6364 0.605082
\(310\) −11.0927 −0.630025
\(311\) −24.2820 −1.37691 −0.688453 0.725281i \(-0.741710\pi\)
−0.688453 + 0.725281i \(0.741710\pi\)
\(312\) 95.7546 5.42104
\(313\) 14.4328 0.815790 0.407895 0.913029i \(-0.366263\pi\)
0.407895 + 0.913029i \(0.366263\pi\)
\(314\) 17.4890 0.986962
\(315\) −14.3440 −0.808190
\(316\) 4.70129 0.264468
\(317\) 5.31540 0.298542 0.149271 0.988796i \(-0.452307\pi\)
0.149271 + 0.988796i \(0.452307\pi\)
\(318\) 24.3343 1.36460
\(319\) −3.44477 −0.192870
\(320\) 24.0954 1.34697
\(321\) 22.8473 1.27521
\(322\) −53.0385 −2.95572
\(323\) 29.3458 1.63284
\(324\) −54.8692 −3.04829
\(325\) 9.72599 0.539501
\(326\) −16.2486 −0.899926
\(327\) −37.5997 −2.07927
\(328\) 53.8867 2.97540
\(329\) 14.6858 0.809657
\(330\) −7.09991 −0.390837
\(331\) −11.8664 −0.652237 −0.326119 0.945329i \(-0.605741\pi\)
−0.326119 + 0.945329i \(0.605741\pi\)
\(332\) −40.0250 −2.19666
\(333\) 0.173180 0.00949022
\(334\) −23.2274 −1.27094
\(335\) −15.4304 −0.843053
\(336\) 78.6970 4.29327
\(337\) −11.1479 −0.607265 −0.303632 0.952789i \(-0.598199\pi\)
−0.303632 + 0.952789i \(0.598199\pi\)
\(338\) −59.5840 −3.24094
\(339\) 40.0457 2.17498
\(340\) −44.1619 −2.39501
\(341\) −0.813819 −0.0440708
\(342\) 33.0028 1.78459
\(343\) 1.30751 0.0705987
\(344\) 35.1949 1.89758
\(345\) 29.9265 1.61119
\(346\) −18.0238 −0.968967
\(347\) 11.6908 0.627595 0.313798 0.949490i \(-0.398399\pi\)
0.313798 + 0.949490i \(0.398399\pi\)
\(348\) −72.0244 −3.86091
\(349\) −9.79573 −0.524353 −0.262177 0.965020i \(-0.584440\pi\)
−0.262177 + 0.965020i \(0.584440\pi\)
\(350\) 15.7647 0.842660
\(351\) 18.9296 1.01039
\(352\) 5.55772 0.296228
\(353\) −21.0312 −1.11938 −0.559689 0.828703i \(-0.689079\pi\)
−0.559689 + 0.828703i \(0.689079\pi\)
\(354\) −36.2425 −1.92627
\(355\) 42.4893 2.25510
\(356\) −8.62241 −0.456987
\(357\) −27.5874 −1.46008
\(358\) −12.9594 −0.684924
\(359\) −23.6567 −1.24855 −0.624277 0.781203i \(-0.714606\pi\)
−0.624277 + 0.781203i \(0.714606\pi\)
\(360\) −29.2993 −1.54421
\(361\) 50.6131 2.66385
\(362\) 17.8409 0.937695
\(363\) 22.8352 1.19854
\(364\) −107.682 −5.64405
\(365\) −32.1730 −1.68401
\(366\) −7.73341 −0.404232
\(367\) 1.30702 0.0682259 0.0341130 0.999418i \(-0.489139\pi\)
0.0341130 + 0.999418i \(0.489139\pi\)
\(368\) −54.9321 −2.86353
\(369\) −10.7717 −0.560754
\(370\) −0.775140 −0.0402976
\(371\) −16.1438 −0.838144
\(372\) −17.0156 −0.882217
\(373\) −27.2531 −1.41111 −0.705555 0.708655i \(-0.749302\pi\)
−0.705555 + 0.708655i \(0.749302\pi\)
\(374\) −4.56852 −0.236232
\(375\) 18.4354 0.951998
\(376\) 29.9977 1.54701
\(377\) 41.5674 2.14083
\(378\) 30.6826 1.57815
\(379\) 12.3670 0.635250 0.317625 0.948216i \(-0.397115\pi\)
0.317625 + 0.948216i \(0.397115\pi\)
\(380\) −104.759 −5.37405
\(381\) −29.4843 −1.51053
\(382\) −14.7014 −0.752190
\(383\) 21.6502 1.10628 0.553138 0.833090i \(-0.313430\pi\)
0.553138 + 0.833090i \(0.313430\pi\)
\(384\) 4.46664 0.227937
\(385\) 4.71020 0.240054
\(386\) −52.3346 −2.66376
\(387\) −7.03532 −0.357625
\(388\) −6.65478 −0.337845
\(389\) −33.1177 −1.67913 −0.839567 0.543256i \(-0.817191\pi\)
−0.839567 + 0.543256i \(0.817191\pi\)
\(390\) 85.6733 4.33823
\(391\) 19.2566 0.973846
\(392\) −50.1483 −2.53287
\(393\) −31.4147 −1.58466
\(394\) −54.7820 −2.75988
\(395\) 2.48146 0.124856
\(396\) −3.64369 −0.183102
\(397\) −10.8938 −0.546743 −0.273371 0.961909i \(-0.588139\pi\)
−0.273371 + 0.961909i \(0.588139\pi\)
\(398\) 13.6293 0.683176
\(399\) −65.4421 −3.27620
\(400\) 16.3276 0.816378
\(401\) 0.640899 0.0320050 0.0160025 0.999872i \(-0.494906\pi\)
0.0160025 + 0.999872i \(0.494906\pi\)
\(402\) −33.3753 −1.66461
\(403\) 9.82020 0.489179
\(404\) 39.3219 1.95634
\(405\) −28.9614 −1.43910
\(406\) 67.3761 3.34382
\(407\) −0.0568682 −0.00281885
\(408\) −56.3507 −2.78978
\(409\) −20.6544 −1.02129 −0.510646 0.859791i \(-0.670594\pi\)
−0.510646 + 0.859791i \(0.670594\pi\)
\(410\) 48.2133 2.38109
\(411\) 38.6628 1.90710
\(412\) −24.4323 −1.20369
\(413\) 24.0439 1.18312
\(414\) 21.6563 1.06435
\(415\) −21.1262 −1.03705
\(416\) −67.0640 −3.28808
\(417\) 1.59588 0.0781506
\(418\) −10.8373 −0.530070
\(419\) 11.8486 0.578842 0.289421 0.957202i \(-0.406537\pi\)
0.289421 + 0.957202i \(0.406537\pi\)
\(420\) 98.4825 4.80545
\(421\) −7.66252 −0.373448 −0.186724 0.982412i \(-0.559787\pi\)
−0.186724 + 0.982412i \(0.559787\pi\)
\(422\) −53.6771 −2.61296
\(423\) −5.99641 −0.291556
\(424\) −32.9757 −1.60144
\(425\) −5.72366 −0.277638
\(426\) 91.9024 4.45269
\(427\) 5.13048 0.248281
\(428\) −52.4814 −2.53679
\(429\) 6.28542 0.303463
\(430\) 31.4895 1.51856
\(431\) 13.5323 0.651826 0.325913 0.945400i \(-0.394328\pi\)
0.325913 + 0.945400i \(0.394328\pi\)
\(432\) 31.7781 1.52892
\(433\) −6.82557 −0.328016 −0.164008 0.986459i \(-0.552442\pi\)
−0.164008 + 0.986459i \(0.552442\pi\)
\(434\) 15.9174 0.764061
\(435\) −38.0164 −1.82274
\(436\) 86.3684 4.13630
\(437\) 45.6799 2.18516
\(438\) −69.5888 −3.32508
\(439\) 14.1805 0.676799 0.338400 0.941003i \(-0.390114\pi\)
0.338400 + 0.941003i \(0.390114\pi\)
\(440\) 9.62118 0.458672
\(441\) 10.0244 0.477354
\(442\) 55.1275 2.62215
\(443\) 38.2677 1.81816 0.909078 0.416627i \(-0.136788\pi\)
0.909078 + 0.416627i \(0.136788\pi\)
\(444\) −1.18902 −0.0564283
\(445\) −4.55113 −0.215744
\(446\) 66.2341 3.13627
\(447\) −19.1658 −0.906513
\(448\) −34.5754 −1.63354
\(449\) 22.4203 1.05808 0.529040 0.848597i \(-0.322552\pi\)
0.529040 + 0.848597i \(0.322552\pi\)
\(450\) −6.43694 −0.303440
\(451\) 3.53717 0.166559
\(452\) −91.9869 −4.32670
\(453\) −22.4294 −1.05383
\(454\) 38.1265 1.78936
\(455\) −56.8372 −2.66457
\(456\) −133.674 −6.25984
\(457\) −12.0090 −0.561757 −0.280879 0.959743i \(-0.590626\pi\)
−0.280879 + 0.959743i \(0.590626\pi\)
\(458\) 21.3617 0.998166
\(459\) −11.1399 −0.519965
\(460\) −68.7427 −3.20515
\(461\) 12.8426 0.598141 0.299070 0.954231i \(-0.403323\pi\)
0.299070 + 0.954231i \(0.403323\pi\)
\(462\) 10.1880 0.473987
\(463\) −25.5790 −1.18876 −0.594379 0.804185i \(-0.702602\pi\)
−0.594379 + 0.804185i \(0.702602\pi\)
\(464\) 69.7815 3.23952
\(465\) −8.98127 −0.416496
\(466\) −43.1334 −1.99812
\(467\) −30.1067 −1.39317 −0.696586 0.717473i \(-0.745299\pi\)
−0.696586 + 0.717473i \(0.745299\pi\)
\(468\) 43.9678 2.03241
\(469\) 22.1417 1.02241
\(470\) 26.8394 1.23801
\(471\) 14.1600 0.652460
\(472\) 49.1127 2.26059
\(473\) 2.31023 0.106224
\(474\) 5.36729 0.246528
\(475\) −13.5775 −0.622978
\(476\) 63.3697 2.90455
\(477\) 6.59171 0.301814
\(478\) −26.2123 −1.19892
\(479\) 22.1949 1.01411 0.507055 0.861914i \(-0.330734\pi\)
0.507055 + 0.861914i \(0.330734\pi\)
\(480\) 61.3348 2.79954
\(481\) 0.686218 0.0312888
\(482\) 62.9442 2.86703
\(483\) −42.9428 −1.95397
\(484\) −52.4537 −2.38426
\(485\) −3.51257 −0.159497
\(486\) −37.7243 −1.71121
\(487\) −10.3416 −0.468625 −0.234312 0.972161i \(-0.575284\pi\)
−0.234312 + 0.972161i \(0.575284\pi\)
\(488\) 10.4796 0.474391
\(489\) −13.1557 −0.594923
\(490\) −44.8685 −2.02695
\(491\) 28.4685 1.28476 0.642382 0.766385i \(-0.277946\pi\)
0.642382 + 0.766385i \(0.277946\pi\)
\(492\) 73.9564 3.33421
\(493\) −24.4621 −1.10172
\(494\) 130.772 5.88370
\(495\) −1.92324 −0.0864430
\(496\) 16.4857 0.740230
\(497\) −60.9697 −2.73486
\(498\) −45.6951 −2.04765
\(499\) −29.2362 −1.30879 −0.654395 0.756153i \(-0.727077\pi\)
−0.654395 + 0.756153i \(0.727077\pi\)
\(500\) −42.3470 −1.89381
\(501\) −18.8061 −0.840195
\(502\) 45.5927 2.03490
\(503\) 34.1701 1.52357 0.761784 0.647831i \(-0.224324\pi\)
0.761784 + 0.647831i \(0.224324\pi\)
\(504\) 42.0428 1.87274
\(505\) 20.7551 0.923591
\(506\) −7.11139 −0.316140
\(507\) −48.2424 −2.14252
\(508\) 67.7270 3.00490
\(509\) −15.3626 −0.680937 −0.340469 0.940256i \(-0.610586\pi\)
−0.340469 + 0.940256i \(0.610586\pi\)
\(510\) −50.4180 −2.23255
\(511\) 46.1664 2.04228
\(512\) 38.8310 1.71610
\(513\) −26.4257 −1.16672
\(514\) −67.6811 −2.98528
\(515\) −12.8960 −0.568266
\(516\) 48.3030 2.12642
\(517\) 1.96908 0.0865998
\(518\) 1.11228 0.0488708
\(519\) −14.5931 −0.640564
\(520\) −116.097 −5.09119
\(521\) −21.3254 −0.934282 −0.467141 0.884183i \(-0.654716\pi\)
−0.467141 + 0.884183i \(0.654716\pi\)
\(522\) −27.5105 −1.20410
\(523\) 39.0138 1.70596 0.852978 0.521948i \(-0.174794\pi\)
0.852978 + 0.521948i \(0.174794\pi\)
\(524\) 72.1611 3.15237
\(525\) 12.7640 0.557065
\(526\) 57.3697 2.50144
\(527\) −5.77910 −0.251742
\(528\) 10.5517 0.459203
\(529\) 6.97493 0.303258
\(530\) −29.5039 −1.28157
\(531\) −9.81743 −0.426040
\(532\) 150.324 6.51736
\(533\) −42.6824 −1.84878
\(534\) −9.84389 −0.425987
\(535\) −27.7011 −1.19762
\(536\) 45.2273 1.95352
\(537\) −10.4926 −0.452789
\(538\) −5.70079 −0.245779
\(539\) −3.29178 −0.141787
\(540\) 39.7675 1.71132
\(541\) 30.5151 1.31195 0.655973 0.754785i \(-0.272259\pi\)
0.655973 + 0.754785i \(0.272259\pi\)
\(542\) 72.6542 3.12076
\(543\) 14.4449 0.619890
\(544\) 39.4666 1.69212
\(545\) 45.5875 1.95275
\(546\) −122.936 −5.26118
\(547\) 15.6078 0.667343 0.333671 0.942689i \(-0.391712\pi\)
0.333671 + 0.942689i \(0.391712\pi\)
\(548\) −88.8105 −3.79379
\(549\) −2.09484 −0.0894056
\(550\) 2.11373 0.0901298
\(551\) −58.0282 −2.47208
\(552\) −87.7160 −3.73344
\(553\) −3.56076 −0.151419
\(554\) 32.0247 1.36060
\(555\) −0.627594 −0.0266399
\(556\) −3.66582 −0.155465
\(557\) −7.65266 −0.324254 −0.162127 0.986770i \(-0.551835\pi\)
−0.162127 + 0.986770i \(0.551835\pi\)
\(558\) −6.49929 −0.275137
\(559\) −27.8771 −1.17907
\(560\) −95.4156 −4.03205
\(561\) −3.69892 −0.156168
\(562\) −78.5681 −3.31420
\(563\) −43.7816 −1.84518 −0.922588 0.385787i \(-0.873930\pi\)
−0.922588 + 0.385787i \(0.873930\pi\)
\(564\) 41.1701 1.73357
\(565\) −48.5531 −2.04264
\(566\) 46.6277 1.95991
\(567\) 41.5579 1.74527
\(568\) −124.538 −5.22551
\(569\) −4.26891 −0.178962 −0.0894810 0.995989i \(-0.528521\pi\)
−0.0894810 + 0.995989i \(0.528521\pi\)
\(570\) −119.600 −5.00949
\(571\) −36.3894 −1.52285 −0.761424 0.648255i \(-0.775499\pi\)
−0.761424 + 0.648255i \(0.775499\pi\)
\(572\) −14.4379 −0.603681
\(573\) −11.9030 −0.497257
\(574\) −69.1834 −2.88766
\(575\) −8.90950 −0.371552
\(576\) 14.1176 0.588233
\(577\) 5.30055 0.220665 0.110332 0.993895i \(-0.464808\pi\)
0.110332 + 0.993895i \(0.464808\pi\)
\(578\) 12.1398 0.504948
\(579\) −42.3729 −1.76096
\(580\) 87.3255 3.62599
\(581\) 30.3149 1.25768
\(582\) −7.59752 −0.314927
\(583\) −2.16456 −0.0896468
\(584\) 94.3007 3.90219
\(585\) 23.2073 0.959505
\(586\) 21.7159 0.897075
\(587\) −40.2217 −1.66013 −0.830064 0.557668i \(-0.811696\pi\)
−0.830064 + 0.557668i \(0.811696\pi\)
\(588\) −68.8256 −2.83832
\(589\) −13.7090 −0.564870
\(590\) 43.9419 1.80906
\(591\) −44.3545 −1.82450
\(592\) 1.15199 0.0473465
\(593\) 23.9449 0.983298 0.491649 0.870793i \(-0.336394\pi\)
0.491649 + 0.870793i \(0.336394\pi\)
\(594\) 4.11392 0.168796
\(595\) 33.4482 1.37124
\(596\) 44.0249 1.80333
\(597\) 11.0350 0.451633
\(598\) 85.8119 3.50911
\(599\) 28.4448 1.16222 0.581111 0.813825i \(-0.302618\pi\)
0.581111 + 0.813825i \(0.302618\pi\)
\(600\) 26.0720 1.06438
\(601\) 16.5880 0.676640 0.338320 0.941031i \(-0.390141\pi\)
0.338320 + 0.941031i \(0.390141\pi\)
\(602\) −45.1855 −1.84163
\(603\) −9.04075 −0.368168
\(604\) 51.5215 2.09638
\(605\) −27.6864 −1.12561
\(606\) 44.8924 1.82363
\(607\) 10.2001 0.414009 0.207004 0.978340i \(-0.433629\pi\)
0.207004 + 0.978340i \(0.433629\pi\)
\(608\) 93.6215 3.79685
\(609\) 54.5513 2.21053
\(610\) 9.37632 0.379636
\(611\) −23.7605 −0.961246
\(612\) −25.8747 −1.04592
\(613\) −3.26789 −0.131989 −0.0659945 0.997820i \(-0.521022\pi\)
−0.0659945 + 0.997820i \(0.521022\pi\)
\(614\) −33.4935 −1.35169
\(615\) 39.0361 1.57409
\(616\) −13.8058 −0.556253
\(617\) 26.3219 1.05968 0.529841 0.848097i \(-0.322252\pi\)
0.529841 + 0.848097i \(0.322252\pi\)
\(618\) −27.8935 −1.12204
\(619\) 7.61212 0.305957 0.152978 0.988230i \(-0.451113\pi\)
0.152978 + 0.988230i \(0.451113\pi\)
\(620\) 20.6304 0.828538
\(621\) −17.3404 −0.695847
\(622\) 63.6785 2.55328
\(623\) 6.53061 0.261643
\(624\) −127.325 −5.09709
\(625\) −30.4884 −1.21954
\(626\) −37.8494 −1.51277
\(627\) −8.77446 −0.350418
\(628\) −32.5263 −1.29794
\(629\) −0.403833 −0.0161019
\(630\) 37.6164 1.49867
\(631\) 34.9343 1.39071 0.695355 0.718666i \(-0.255247\pi\)
0.695355 + 0.718666i \(0.255247\pi\)
\(632\) −7.27329 −0.289316
\(633\) −43.4599 −1.72737
\(634\) −13.9394 −0.553605
\(635\) 35.7480 1.41862
\(636\) −45.2573 −1.79457
\(637\) 39.7213 1.57382
\(638\) 9.03377 0.357650
\(639\) 24.8947 0.984819
\(640\) −5.41554 −0.214068
\(641\) 39.1496 1.54632 0.773158 0.634214i \(-0.218676\pi\)
0.773158 + 0.634214i \(0.218676\pi\)
\(642\) −59.9161 −2.36470
\(643\) −28.6390 −1.12941 −0.564705 0.825293i \(-0.691010\pi\)
−0.564705 + 0.825293i \(0.691010\pi\)
\(644\) 98.6418 3.88703
\(645\) 25.4955 1.00389
\(646\) −76.9580 −3.02787
\(647\) 11.7241 0.460920 0.230460 0.973082i \(-0.425977\pi\)
0.230460 + 0.973082i \(0.425977\pi\)
\(648\) 84.8872 3.33468
\(649\) 3.22380 0.126545
\(650\) −25.5060 −1.00043
\(651\) 12.8876 0.505105
\(652\) 30.2194 1.18348
\(653\) −13.7044 −0.536296 −0.268148 0.963378i \(-0.586412\pi\)
−0.268148 + 0.963378i \(0.586412\pi\)
\(654\) 98.6036 3.85571
\(655\) 38.0885 1.48824
\(656\) −71.6533 −2.79759
\(657\) −18.8503 −0.735422
\(658\) −38.5130 −1.50139
\(659\) 35.6349 1.38814 0.694069 0.719909i \(-0.255816\pi\)
0.694069 + 0.719909i \(0.255816\pi\)
\(660\) 13.2045 0.513985
\(661\) 26.3826 1.02616 0.513082 0.858340i \(-0.328504\pi\)
0.513082 + 0.858340i \(0.328504\pi\)
\(662\) 31.1192 1.20948
\(663\) 44.6342 1.73345
\(664\) 61.9220 2.40304
\(665\) 79.3448 3.07686
\(666\) −0.454158 −0.0175983
\(667\) −38.0779 −1.47438
\(668\) 43.1986 1.67140
\(669\) 53.6267 2.07333
\(670\) 40.4656 1.56332
\(671\) 0.687894 0.0265559
\(672\) −88.0119 −3.39513
\(673\) 11.6934 0.450747 0.225373 0.974272i \(-0.427640\pi\)
0.225373 + 0.974272i \(0.427640\pi\)
\(674\) 29.2349 1.12609
\(675\) 5.15412 0.198382
\(676\) 110.815 4.26213
\(677\) 20.1776 0.775487 0.387744 0.921767i \(-0.373255\pi\)
0.387744 + 0.921767i \(0.373255\pi\)
\(678\) −105.018 −4.03320
\(679\) 5.04033 0.193430
\(680\) 68.3221 2.62003
\(681\) 30.8692 1.18291
\(682\) 2.13421 0.0817230
\(683\) −10.6885 −0.408984 −0.204492 0.978868i \(-0.565554\pi\)
−0.204492 + 0.978868i \(0.565554\pi\)
\(684\) −61.3791 −2.34689
\(685\) −46.8765 −1.79106
\(686\) −3.42888 −0.130915
\(687\) 17.2956 0.659867
\(688\) −46.7987 −1.78419
\(689\) 26.1193 0.995066
\(690\) −78.4810 −2.98772
\(691\) 30.8960 1.17534 0.587669 0.809101i \(-0.300046\pi\)
0.587669 + 0.809101i \(0.300046\pi\)
\(692\) 33.5210 1.27428
\(693\) 2.75973 0.104834
\(694\) −30.6587 −1.16379
\(695\) −1.93491 −0.0733955
\(696\) 111.428 4.22366
\(697\) 25.1182 0.951421
\(698\) 25.6889 0.972339
\(699\) −34.9231 −1.32091
\(700\) −29.3195 −1.10817
\(701\) 50.2952 1.89962 0.949812 0.312822i \(-0.101274\pi\)
0.949812 + 0.312822i \(0.101274\pi\)
\(702\) −49.6420 −1.87362
\(703\) −0.957961 −0.0361302
\(704\) −4.63587 −0.174721
\(705\) 21.7306 0.818423
\(706\) 55.1534 2.07573
\(707\) −29.7824 −1.12008
\(708\) 67.4043 2.53321
\(709\) −3.11713 −0.117066 −0.0585332 0.998285i \(-0.518642\pi\)
−0.0585332 + 0.998285i \(0.518642\pi\)
\(710\) −111.426 −4.18176
\(711\) 1.45390 0.0545256
\(712\) 13.3396 0.499922
\(713\) −8.99580 −0.336895
\(714\) 72.3469 2.70751
\(715\) −7.62072 −0.284999
\(716\) 24.1020 0.900735
\(717\) −21.2229 −0.792583
\(718\) 62.0388 2.31527
\(719\) −8.87317 −0.330913 −0.165457 0.986217i \(-0.552910\pi\)
−0.165457 + 0.986217i \(0.552910\pi\)
\(720\) 38.9594 1.45193
\(721\) 18.5050 0.689163
\(722\) −132.731 −4.93973
\(723\) 50.9630 1.89534
\(724\) −33.1807 −1.23315
\(725\) 11.3179 0.420338
\(726\) −59.8844 −2.22252
\(727\) 19.5032 0.723334 0.361667 0.932307i \(-0.382208\pi\)
0.361667 + 0.932307i \(0.382208\pi\)
\(728\) 166.592 6.17433
\(729\) 3.20622 0.118749
\(730\) 84.3724 3.12276
\(731\) 16.4054 0.606776
\(732\) 14.3827 0.531600
\(733\) −0.853618 −0.0315291 −0.0157646 0.999876i \(-0.505018\pi\)
−0.0157646 + 0.999876i \(0.505018\pi\)
\(734\) −3.42761 −0.126515
\(735\) −36.3279 −1.33998
\(736\) 61.4340 2.26449
\(737\) 2.96876 0.109356
\(738\) 28.2484 1.03984
\(739\) −25.1255 −0.924258 −0.462129 0.886813i \(-0.652914\pi\)
−0.462129 + 0.886813i \(0.652914\pi\)
\(740\) 1.44162 0.0529949
\(741\) 105.880 3.88959
\(742\) 42.3364 1.55422
\(743\) −14.7403 −0.540769 −0.270384 0.962752i \(-0.587151\pi\)
−0.270384 + 0.962752i \(0.587151\pi\)
\(744\) 26.3245 0.965104
\(745\) 23.2375 0.851355
\(746\) 71.4700 2.61670
\(747\) −12.3780 −0.452886
\(748\) 8.49660 0.310666
\(749\) 39.7494 1.45241
\(750\) −48.3460 −1.76534
\(751\) 17.1548 0.625989 0.312995 0.949755i \(-0.398668\pi\)
0.312995 + 0.949755i \(0.398668\pi\)
\(752\) −39.8880 −1.45457
\(753\) 36.9143 1.34523
\(754\) −109.009 −3.96987
\(755\) 27.1944 0.989704
\(756\) −57.0641 −2.07540
\(757\) 4.46359 0.162232 0.0811159 0.996705i \(-0.474152\pi\)
0.0811159 + 0.996705i \(0.474152\pi\)
\(758\) −32.4319 −1.17798
\(759\) −5.75777 −0.208994
\(760\) 162.072 5.87895
\(761\) 1.40186 0.0508175 0.0254087 0.999677i \(-0.491911\pi\)
0.0254087 + 0.999677i \(0.491911\pi\)
\(762\) 77.3214 2.80106
\(763\) −65.4154 −2.36820
\(764\) 27.3419 0.989196
\(765\) −13.6573 −0.493781
\(766\) −56.7769 −2.05143
\(767\) −38.9010 −1.40464
\(768\) 28.0332 1.01156
\(769\) 22.6490 0.816743 0.408372 0.912816i \(-0.366097\pi\)
0.408372 + 0.912816i \(0.366097\pi\)
\(770\) −12.3523 −0.445146
\(771\) −54.7982 −1.97351
\(772\) 97.3326 3.50308
\(773\) −24.6865 −0.887910 −0.443955 0.896049i \(-0.646425\pi\)
−0.443955 + 0.896049i \(0.646425\pi\)
\(774\) 18.4498 0.663165
\(775\) 2.67384 0.0960471
\(776\) 10.2955 0.369587
\(777\) 0.900562 0.0323075
\(778\) 86.8498 3.11372
\(779\) 59.5847 2.13485
\(780\) −159.336 −5.70516
\(781\) −8.17481 −0.292518
\(782\) −50.4995 −1.80586
\(783\) 22.0280 0.787215
\(784\) 66.6823 2.38151
\(785\) −17.1682 −0.612760
\(786\) 82.3836 2.93853
\(787\) 36.9055 1.31554 0.657770 0.753219i \(-0.271500\pi\)
0.657770 + 0.753219i \(0.271500\pi\)
\(788\) 101.884 3.62948
\(789\) 46.4496 1.65365
\(790\) −6.50754 −0.231528
\(791\) 69.6709 2.47721
\(792\) 5.63710 0.200305
\(793\) −8.30069 −0.294766
\(794\) 28.5685 1.01386
\(795\) −23.8879 −0.847218
\(796\) −25.3480 −0.898436
\(797\) −4.79724 −0.169927 −0.0849634 0.996384i \(-0.527077\pi\)
−0.0849634 + 0.996384i \(0.527077\pi\)
\(798\) 171.619 6.07525
\(799\) 13.9828 0.494677
\(800\) −18.2601 −0.645593
\(801\) −2.66653 −0.0942172
\(802\) −1.68073 −0.0593487
\(803\) 6.18999 0.218440
\(804\) 62.0718 2.18910
\(805\) 52.0657 1.83507
\(806\) −25.7531 −0.907114
\(807\) −4.61567 −0.162479
\(808\) −60.8343 −2.14014
\(809\) −29.9285 −1.05223 −0.526116 0.850413i \(-0.676352\pi\)
−0.526116 + 0.850413i \(0.676352\pi\)
\(810\) 75.9500 2.66861
\(811\) 14.4777 0.508381 0.254191 0.967154i \(-0.418191\pi\)
0.254191 + 0.967154i \(0.418191\pi\)
\(812\) −125.307 −4.39741
\(813\) 58.8247 2.06307
\(814\) 0.149134 0.00522716
\(815\) 15.9506 0.558724
\(816\) 74.9298 2.62307
\(817\) 38.9164 1.36151
\(818\) 54.1652 1.89384
\(819\) −33.3012 −1.16364
\(820\) −89.6679 −3.13134
\(821\) −21.4614 −0.749009 −0.374505 0.927225i \(-0.622187\pi\)
−0.374505 + 0.927225i \(0.622187\pi\)
\(822\) −101.392 −3.53644
\(823\) 30.7576 1.07214 0.536071 0.844173i \(-0.319908\pi\)
0.536071 + 0.844173i \(0.319908\pi\)
\(824\) 37.7988 1.31678
\(825\) 1.71139 0.0595830
\(826\) −63.0541 −2.19393
\(827\) −13.3096 −0.462820 −0.231410 0.972856i \(-0.574334\pi\)
−0.231410 + 0.972856i \(0.574334\pi\)
\(828\) −40.2767 −1.39971
\(829\) −49.0060 −1.70205 −0.851024 0.525127i \(-0.824018\pi\)
−0.851024 + 0.525127i \(0.824018\pi\)
\(830\) 55.4027 1.92306
\(831\) 25.9289 0.899463
\(832\) 55.9402 1.93938
\(833\) −23.3756 −0.809918
\(834\) −4.18513 −0.144919
\(835\) 22.8013 0.789073
\(836\) 20.1554 0.697089
\(837\) 5.20405 0.179878
\(838\) −31.0725 −1.07338
\(839\) −10.5379 −0.363810 −0.181905 0.983316i \(-0.558226\pi\)
−0.181905 + 0.983316i \(0.558226\pi\)
\(840\) −152.361 −5.25694
\(841\) 19.3712 0.667973
\(842\) 20.0946 0.692507
\(843\) −63.6130 −2.19095
\(844\) 99.8295 3.43627
\(845\) 58.4912 2.01216
\(846\) 15.7253 0.540649
\(847\) 39.7284 1.36508
\(848\) 43.8479 1.50574
\(849\) 37.7523 1.29565
\(850\) 15.0101 0.514841
\(851\) −0.628610 −0.0215485
\(852\) −170.922 −5.85567
\(853\) −12.5306 −0.429039 −0.214520 0.976720i \(-0.568819\pi\)
−0.214520 + 0.976720i \(0.568819\pi\)
\(854\) −13.4545 −0.460403
\(855\) −32.3975 −1.10797
\(856\) 81.1931 2.77512
\(857\) 47.6658 1.62823 0.814117 0.580701i \(-0.197221\pi\)
0.814117 + 0.580701i \(0.197221\pi\)
\(858\) −16.4833 −0.562729
\(859\) −36.1047 −1.23188 −0.615939 0.787794i \(-0.711223\pi\)
−0.615939 + 0.787794i \(0.711223\pi\)
\(860\) −58.5646 −1.99704
\(861\) −56.0145 −1.90897
\(862\) −35.4878 −1.20872
\(863\) 50.2612 1.71091 0.855456 0.517875i \(-0.173277\pi\)
0.855456 + 0.517875i \(0.173277\pi\)
\(864\) −35.5394 −1.20908
\(865\) 17.6932 0.601588
\(866\) 17.8998 0.608259
\(867\) 9.82900 0.333810
\(868\) −29.6035 −1.00481
\(869\) −0.477426 −0.0161956
\(870\) 99.6963 3.38002
\(871\) −35.8235 −1.21383
\(872\) −133.619 −4.52491
\(873\) −2.05803 −0.0696538
\(874\) −119.794 −4.05208
\(875\) 32.0736 1.08428
\(876\) 129.422 4.37277
\(877\) −50.4153 −1.70240 −0.851202 0.524838i \(-0.824126\pi\)
−0.851202 + 0.524838i \(0.824126\pi\)
\(878\) −37.1878 −1.25503
\(879\) 17.5823 0.593038
\(880\) −12.7933 −0.431262
\(881\) −20.8921 −0.703872 −0.351936 0.936024i \(-0.614477\pi\)
−0.351936 + 0.936024i \(0.614477\pi\)
\(882\) −26.2887 −0.885186
\(883\) 12.0556 0.405703 0.202851 0.979210i \(-0.434979\pi\)
0.202851 + 0.979210i \(0.434979\pi\)
\(884\) −102.527 −3.44835
\(885\) 35.5777 1.19593
\(886\) −100.356 −3.37151
\(887\) 42.0475 1.41182 0.705908 0.708304i \(-0.250539\pi\)
0.705908 + 0.708304i \(0.250539\pi\)
\(888\) 1.83951 0.0617299
\(889\) −51.2964 −1.72042
\(890\) 11.9352 0.400067
\(891\) 5.57207 0.186671
\(892\) −123.183 −4.12448
\(893\) 33.1697 1.10998
\(894\) 50.2616 1.68100
\(895\) 12.7217 0.425239
\(896\) 7.77099 0.259610
\(897\) 69.4779 2.31980
\(898\) −58.7964 −1.96206
\(899\) 11.4276 0.381131
\(900\) 11.9715 0.399050
\(901\) −15.3710 −0.512082
\(902\) −9.27609 −0.308860
\(903\) −36.5846 −1.21746
\(904\) 142.311 4.73321
\(905\) −17.5136 −0.582173
\(906\) 58.8202 1.95417
\(907\) −29.0309 −0.963955 −0.481978 0.876183i \(-0.660081\pi\)
−0.481978 + 0.876183i \(0.660081\pi\)
\(908\) −70.9082 −2.35317
\(909\) 12.1605 0.403339
\(910\) 149.053 4.94106
\(911\) −2.69669 −0.0893453 −0.0446727 0.999002i \(-0.514224\pi\)
−0.0446727 + 0.999002i \(0.514224\pi\)
\(912\) 177.746 5.88576
\(913\) 4.06462 0.134519
\(914\) 31.4931 1.04170
\(915\) 7.59157 0.250970
\(916\) −39.7288 −1.31268
\(917\) −54.6548 −1.80486
\(918\) 29.2139 0.964201
\(919\) 38.4948 1.26983 0.634913 0.772584i \(-0.281036\pi\)
0.634913 + 0.772584i \(0.281036\pi\)
\(920\) 106.351 3.50628
\(921\) −27.1182 −0.893574
\(922\) −33.6792 −1.10917
\(923\) 98.6439 3.24690
\(924\) −18.9477 −0.623334
\(925\) 0.186843 0.00614335
\(926\) 67.0800 2.20438
\(927\) −7.55583 −0.248166
\(928\) −78.0411 −2.56182
\(929\) −10.3990 −0.341180 −0.170590 0.985342i \(-0.554567\pi\)
−0.170590 + 0.985342i \(0.554567\pi\)
\(930\) 23.5530 0.772334
\(931\) −55.4510 −1.81733
\(932\) 80.2202 2.62770
\(933\) 51.5575 1.68792
\(934\) 78.9536 2.58344
\(935\) 4.48473 0.146666
\(936\) −68.0218 −2.22336
\(937\) 6.69629 0.218758 0.109379 0.994000i \(-0.465114\pi\)
0.109379 + 0.994000i \(0.465114\pi\)
\(938\) −58.0658 −1.89591
\(939\) −30.6449 −1.00006
\(940\) −49.9164 −1.62809
\(941\) 19.9735 0.651119 0.325559 0.945522i \(-0.394447\pi\)
0.325559 + 0.945522i \(0.394447\pi\)
\(942\) −37.1341 −1.20989
\(943\) 39.0993 1.27325
\(944\) −65.3053 −2.12551
\(945\) −30.1199 −0.979800
\(946\) −6.05847 −0.196978
\(947\) 49.1728 1.59790 0.798951 0.601397i \(-0.205389\pi\)
0.798951 + 0.601397i \(0.205389\pi\)
\(948\) −9.98218 −0.324206
\(949\) −74.6934 −2.42465
\(950\) 35.6064 1.15523
\(951\) −11.2861 −0.365976
\(952\) −98.0382 −3.17744
\(953\) 39.8727 1.29160 0.645801 0.763506i \(-0.276524\pi\)
0.645801 + 0.763506i \(0.276524\pi\)
\(954\) −17.2865 −0.559671
\(955\) 14.4318 0.467001
\(956\) 48.7501 1.57669
\(957\) 7.31422 0.236435
\(958\) −58.2051 −1.88052
\(959\) 67.2650 2.17210
\(960\) −51.1613 −1.65122
\(961\) −28.3003 −0.912912
\(962\) −1.79958 −0.0580207
\(963\) −16.2302 −0.523010
\(964\) −117.065 −3.77040
\(965\) 51.3747 1.65381
\(966\) 112.616 3.62335
\(967\) −24.2306 −0.779203 −0.389601 0.920984i \(-0.627387\pi\)
−0.389601 + 0.920984i \(0.627387\pi\)
\(968\) 81.1502 2.60827
\(969\) −62.3093 −2.00166
\(970\) 9.21156 0.295765
\(971\) 52.7038 1.69134 0.845672 0.533702i \(-0.179200\pi\)
0.845672 + 0.533702i \(0.179200\pi\)
\(972\) 70.1601 2.25039
\(973\) 2.77649 0.0890102
\(974\) 27.1205 0.868998
\(975\) −20.6510 −0.661362
\(976\) −13.9348 −0.446043
\(977\) 60.8726 1.94749 0.973744 0.227648i \(-0.0731035\pi\)
0.973744 + 0.227648i \(0.0731035\pi\)
\(978\) 34.5003 1.10320
\(979\) 0.875623 0.0279850
\(980\) 83.4471 2.66562
\(981\) 26.7099 0.852782
\(982\) −74.6574 −2.38241
\(983\) −51.3243 −1.63699 −0.818495 0.574514i \(-0.805191\pi\)
−0.818495 + 0.574514i \(0.805191\pi\)
\(984\) −114.417 −3.64747
\(985\) 53.7773 1.71349
\(986\) 64.1508 2.04298
\(987\) −31.1822 −0.992540
\(988\) −243.211 −7.73758
\(989\) 25.5368 0.812023
\(990\) 5.04360 0.160296
\(991\) 48.3760 1.53671 0.768357 0.640022i \(-0.221075\pi\)
0.768357 + 0.640022i \(0.221075\pi\)
\(992\) −18.4370 −0.585376
\(993\) 25.1958 0.799563
\(994\) 159.890 5.07142
\(995\) −13.3793 −0.424153
\(996\) 84.9844 2.69283
\(997\) 29.2455 0.926213 0.463106 0.886303i \(-0.346735\pi\)
0.463106 + 0.886303i \(0.346735\pi\)
\(998\) 76.6706 2.42697
\(999\) 0.363649 0.0115054
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 \(a_p\))