Properties

Label 8023.2.a.c.1.3
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75717 q^{2}\) \(-0.782411 q^{3}\) \(+5.60200 q^{4}\) \(-3.11881 q^{5}\) \(+2.15724 q^{6}\) \(+0.297168 q^{7}\) \(-9.93135 q^{8}\) \(-2.38783 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75717 q^{2}\) \(-0.782411 q^{3}\) \(+5.60200 q^{4}\) \(-3.11881 q^{5}\) \(+2.15724 q^{6}\) \(+0.297168 q^{7}\) \(-9.93135 q^{8}\) \(-2.38783 q^{9}\) \(+8.59909 q^{10}\) \(-5.63230 q^{11}\) \(-4.38307 q^{12}\) \(+6.65009 q^{13}\) \(-0.819343 q^{14}\) \(+2.44019 q^{15}\) \(+16.1784 q^{16}\) \(-7.57293 q^{17}\) \(+6.58367 q^{18}\) \(-2.96394 q^{19}\) \(-17.4716 q^{20}\) \(-0.232507 q^{21}\) \(+15.5292 q^{22}\) \(+6.58625 q^{23}\) \(+7.77040 q^{24}\) \(+4.72695 q^{25}\) \(-18.3354 q^{26}\) \(+4.21550 q^{27}\) \(+1.66474 q^{28}\) \(+3.55881 q^{29}\) \(-6.72802 q^{30}\) \(-2.84059 q^{31}\) \(-24.7441 q^{32}\) \(+4.40678 q^{33}\) \(+20.8799 q^{34}\) \(-0.926809 q^{35}\) \(-13.3767 q^{36}\) \(-9.75146 q^{37}\) \(+8.17209 q^{38}\) \(-5.20310 q^{39}\) \(+30.9740 q^{40}\) \(-8.15833 q^{41}\) \(+0.641063 q^{42}\) \(+2.40358 q^{43}\) \(-31.5522 q^{44}\) \(+7.44719 q^{45}\) \(-18.1594 q^{46}\) \(+9.95062 q^{47}\) \(-12.6582 q^{48}\) \(-6.91169 q^{49}\) \(-13.0330 q^{50}\) \(+5.92515 q^{51}\) \(+37.2538 q^{52}\) \(+7.58554 q^{53}\) \(-11.6229 q^{54}\) \(+17.5661 q^{55}\) \(-2.95128 q^{56}\) \(+2.31902 q^{57}\) \(-9.81225 q^{58}\) \(-5.25491 q^{59}\) \(+13.6699 q^{60}\) \(+4.99706 q^{61}\) \(+7.83201 q^{62}\) \(-0.709587 q^{63}\) \(+35.8668 q^{64}\) \(-20.7403 q^{65}\) \(-12.1502 q^{66}\) \(-13.8137 q^{67}\) \(-42.4236 q^{68}\) \(-5.15315 q^{69}\) \(+2.55537 q^{70}\) \(-1.00000 q^{71}\) \(+23.7144 q^{72}\) \(+1.20986 q^{73}\) \(+26.8865 q^{74}\) \(-3.69842 q^{75}\) \(-16.6040 q^{76}\) \(-1.67374 q^{77}\) \(+14.3459 q^{78}\) \(-0.839614 q^{79}\) \(-50.4574 q^{80}\) \(+3.86525 q^{81}\) \(+22.4939 q^{82}\) \(+14.3039 q^{83}\) \(-1.30251 q^{84}\) \(+23.6185 q^{85}\) \(-6.62709 q^{86}\) \(-2.78445 q^{87}\) \(+55.9364 q^{88}\) \(+9.48423 q^{89}\) \(-20.5332 q^{90}\) \(+1.97619 q^{91}\) \(+36.8962 q^{92}\) \(+2.22251 q^{93}\) \(-27.4356 q^{94}\) \(+9.24395 q^{95}\) \(+19.3600 q^{96}\) \(+2.46458 q^{97}\) \(+19.0567 q^{98}\) \(+13.4490 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75717 −1.94962 −0.974808 0.223046i \(-0.928400\pi\)
−0.974808 + 0.223046i \(0.928400\pi\)
\(3\) −0.782411 −0.451725 −0.225863 0.974159i \(-0.572520\pi\)
−0.225863 + 0.974159i \(0.572520\pi\)
\(4\) 5.60200 2.80100
\(5\) −3.11881 −1.39477 −0.697386 0.716695i \(-0.745654\pi\)
−0.697386 + 0.716695i \(0.745654\pi\)
\(6\) 2.15724 0.880690
\(7\) 0.297168 0.112319 0.0561595 0.998422i \(-0.482114\pi\)
0.0561595 + 0.998422i \(0.482114\pi\)
\(8\) −9.93135 −3.51126
\(9\) −2.38783 −0.795944
\(10\) 8.59909 2.71927
\(11\) −5.63230 −1.69820 −0.849102 0.528229i \(-0.822856\pi\)
−0.849102 + 0.528229i \(0.822856\pi\)
\(12\) −4.38307 −1.26528
\(13\) 6.65009 1.84440 0.922201 0.386710i \(-0.126389\pi\)
0.922201 + 0.386710i \(0.126389\pi\)
\(14\) −0.819343 −0.218979
\(15\) 2.44019 0.630054
\(16\) 16.1784 4.04461
\(17\) −7.57293 −1.83671 −0.918353 0.395762i \(-0.870481\pi\)
−0.918353 + 0.395762i \(0.870481\pi\)
\(18\) 6.58367 1.55179
\(19\) −2.96394 −0.679974 −0.339987 0.940430i \(-0.610423\pi\)
−0.339987 + 0.940430i \(0.610423\pi\)
\(20\) −17.4716 −3.90676
\(21\) −0.232507 −0.0507373
\(22\) 15.5292 3.31084
\(23\) 6.58625 1.37333 0.686664 0.726975i \(-0.259074\pi\)
0.686664 + 0.726975i \(0.259074\pi\)
\(24\) 7.77040 1.58613
\(25\) 4.72695 0.945391
\(26\) −18.3354 −3.59588
\(27\) 4.21550 0.811273
\(28\) 1.66474 0.314606
\(29\) 3.55881 0.660854 0.330427 0.943832i \(-0.392807\pi\)
0.330427 + 0.943832i \(0.392807\pi\)
\(30\) −6.72802 −1.22836
\(31\) −2.84059 −0.510186 −0.255093 0.966917i \(-0.582106\pi\)
−0.255093 + 0.966917i \(0.582106\pi\)
\(32\) −24.7441 −4.37417
\(33\) 4.40678 0.767121
\(34\) 20.8799 3.58087
\(35\) −0.926809 −0.156659
\(36\) −13.3767 −2.22944
\(37\) −9.75146 −1.60313 −0.801565 0.597908i \(-0.795999\pi\)
−0.801565 + 0.597908i \(0.795999\pi\)
\(38\) 8.17209 1.32569
\(39\) −5.20310 −0.833163
\(40\) 30.9740 4.89741
\(41\) −8.15833 −1.27412 −0.637058 0.770816i \(-0.719849\pi\)
−0.637058 + 0.770816i \(0.719849\pi\)
\(42\) 0.641063 0.0989182
\(43\) 2.40358 0.366542 0.183271 0.983062i \(-0.441331\pi\)
0.183271 + 0.983062i \(0.441331\pi\)
\(44\) −31.5522 −4.75667
\(45\) 7.44719 1.11016
\(46\) −18.1594 −2.67746
\(47\) 9.95062 1.45145 0.725724 0.687986i \(-0.241505\pi\)
0.725724 + 0.687986i \(0.241505\pi\)
\(48\) −12.6582 −1.82705
\(49\) −6.91169 −0.987384
\(50\) −13.0330 −1.84315
\(51\) 5.92515 0.829686
\(52\) 37.2538 5.16618
\(53\) 7.58554 1.04195 0.520977 0.853571i \(-0.325568\pi\)
0.520977 + 0.853571i \(0.325568\pi\)
\(54\) −11.6229 −1.58167
\(55\) 17.5661 2.36861
\(56\) −2.95128 −0.394381
\(57\) 2.31902 0.307161
\(58\) −9.81225 −1.28841
\(59\) −5.25491 −0.684131 −0.342066 0.939676i \(-0.611126\pi\)
−0.342066 + 0.939676i \(0.611126\pi\)
\(60\) 13.6699 1.76478
\(61\) 4.99706 0.639808 0.319904 0.947450i \(-0.396349\pi\)
0.319904 + 0.947450i \(0.396349\pi\)
\(62\) 7.83201 0.994666
\(63\) −0.709587 −0.0893996
\(64\) 35.8668 4.48335
\(65\) −20.7403 −2.57252
\(66\) −12.1502 −1.49559
\(67\) −13.8137 −1.68761 −0.843804 0.536652i \(-0.819689\pi\)
−0.843804 + 0.536652i \(0.819689\pi\)
\(68\) −42.4236 −5.14462
\(69\) −5.15315 −0.620367
\(70\) 2.55537 0.305426
\(71\) −1.00000 −0.118678
\(72\) 23.7144 2.79477
\(73\) 1.20986 0.141604 0.0708020 0.997490i \(-0.477444\pi\)
0.0708020 + 0.997490i \(0.477444\pi\)
\(74\) 26.8865 3.12549
\(75\) −3.69842 −0.427057
\(76\) −16.6040 −1.90461
\(77\) −1.67374 −0.190740
\(78\) 14.3459 1.62435
\(79\) −0.839614 −0.0944639 −0.0472320 0.998884i \(-0.515040\pi\)
−0.0472320 + 0.998884i \(0.515040\pi\)
\(80\) −50.4574 −5.64131
\(81\) 3.86525 0.429472
\(82\) 22.4939 2.48404
\(83\) 14.3039 1.57006 0.785029 0.619459i \(-0.212648\pi\)
0.785029 + 0.619459i \(0.212648\pi\)
\(84\) −1.30251 −0.142115
\(85\) 23.6185 2.56179
\(86\) −6.62709 −0.714617
\(87\) −2.78445 −0.298524
\(88\) 55.9364 5.96284
\(89\) 9.48423 1.00533 0.502663 0.864482i \(-0.332354\pi\)
0.502663 + 0.864482i \(0.332354\pi\)
\(90\) −20.5332 −2.16439
\(91\) 1.97619 0.207161
\(92\) 36.8962 3.84669
\(93\) 2.22251 0.230464
\(94\) −27.4356 −2.82977
\(95\) 9.24395 0.948409
\(96\) 19.3600 1.97592
\(97\) 2.46458 0.250241 0.125120 0.992142i \(-0.460068\pi\)
0.125120 + 0.992142i \(0.460068\pi\)
\(98\) 19.0567 1.92502
\(99\) 13.4490 1.35168
\(100\) 26.4804 2.64804
\(101\) 4.56191 0.453927 0.226963 0.973903i \(-0.427120\pi\)
0.226963 + 0.973903i \(0.427120\pi\)
\(102\) −16.3367 −1.61757
\(103\) 0.204277 0.0201281 0.0100640 0.999949i \(-0.496796\pi\)
0.0100640 + 0.999949i \(0.496796\pi\)
\(104\) −66.0443 −6.47618
\(105\) 0.725146 0.0707670
\(106\) −20.9146 −2.03141
\(107\) −10.5970 −1.02445 −0.512223 0.858852i \(-0.671178\pi\)
−0.512223 + 0.858852i \(0.671178\pi\)
\(108\) 23.6152 2.27238
\(109\) 13.2752 1.27153 0.635766 0.771882i \(-0.280684\pi\)
0.635766 + 0.771882i \(0.280684\pi\)
\(110\) −48.4327 −4.61787
\(111\) 7.62965 0.724174
\(112\) 4.80771 0.454286
\(113\) −1.00000 −0.0940721
\(114\) −6.39393 −0.598847
\(115\) −20.5412 −1.91548
\(116\) 19.9365 1.85105
\(117\) −15.8793 −1.46804
\(118\) 14.4887 1.33379
\(119\) −2.25043 −0.206297
\(120\) −24.2344 −2.21228
\(121\) 20.7228 1.88389
\(122\) −13.7778 −1.24738
\(123\) 6.38316 0.575550
\(124\) −15.9130 −1.42903
\(125\) 0.851581 0.0761677
\(126\) 1.95646 0.174295
\(127\) −9.70908 −0.861541 −0.430771 0.902461i \(-0.641758\pi\)
−0.430771 + 0.902461i \(0.641758\pi\)
\(128\) −49.4028 −4.36664
\(129\) −1.88059 −0.165576
\(130\) 57.1847 5.01543
\(131\) 5.59134 0.488517 0.244259 0.969710i \(-0.421455\pi\)
0.244259 + 0.969710i \(0.421455\pi\)
\(132\) 24.6868 2.14871
\(133\) −0.880788 −0.0763740
\(134\) 38.0867 3.29019
\(135\) −13.1473 −1.13154
\(136\) 75.2095 6.44916
\(137\) 11.4113 0.974931 0.487466 0.873142i \(-0.337921\pi\)
0.487466 + 0.873142i \(0.337921\pi\)
\(138\) 14.2081 1.20948
\(139\) 15.9263 1.35085 0.675426 0.737427i \(-0.263960\pi\)
0.675426 + 0.737427i \(0.263960\pi\)
\(140\) −5.19199 −0.438803
\(141\) −7.78548 −0.655655
\(142\) 2.75717 0.231377
\(143\) −37.4553 −3.13217
\(144\) −38.6314 −3.21929
\(145\) −11.0992 −0.921741
\(146\) −3.33581 −0.276073
\(147\) 5.40778 0.446026
\(148\) −54.6277 −4.49037
\(149\) 8.32701 0.682175 0.341087 0.940032i \(-0.389205\pi\)
0.341087 + 0.940032i \(0.389205\pi\)
\(150\) 10.1972 0.832596
\(151\) 8.15113 0.663329 0.331665 0.943397i \(-0.392390\pi\)
0.331665 + 0.943397i \(0.392390\pi\)
\(152\) 29.4359 2.38757
\(153\) 18.0829 1.46192
\(154\) 4.61479 0.371870
\(155\) 8.85926 0.711593
\(156\) −29.1478 −2.33369
\(157\) −7.31229 −0.583584 −0.291792 0.956482i \(-0.594252\pi\)
−0.291792 + 0.956482i \(0.594252\pi\)
\(158\) 2.31496 0.184168
\(159\) −5.93501 −0.470677
\(160\) 77.1720 6.10098
\(161\) 1.95722 0.154251
\(162\) −10.6572 −0.837305
\(163\) −9.24543 −0.724158 −0.362079 0.932147i \(-0.617933\pi\)
−0.362079 + 0.932147i \(0.617933\pi\)
\(164\) −45.7030 −3.56880
\(165\) −13.7439 −1.06996
\(166\) −39.4384 −3.06101
\(167\) 9.29877 0.719560 0.359780 0.933037i \(-0.382852\pi\)
0.359780 + 0.933037i \(0.382852\pi\)
\(168\) 2.30911 0.178152
\(169\) 31.2237 2.40182
\(170\) −65.1203 −4.99450
\(171\) 7.07739 0.541222
\(172\) 13.4649 1.02669
\(173\) 6.52736 0.496266 0.248133 0.968726i \(-0.420183\pi\)
0.248133 + 0.968726i \(0.420183\pi\)
\(174\) 7.67721 0.582008
\(175\) 1.40470 0.106185
\(176\) −91.1219 −6.86857
\(177\) 4.11150 0.309039
\(178\) −26.1497 −1.96000
\(179\) −16.2808 −1.21688 −0.608442 0.793599i \(-0.708205\pi\)
−0.608442 + 0.793599i \(0.708205\pi\)
\(180\) 41.7192 3.10956
\(181\) −7.40722 −0.550575 −0.275287 0.961362i \(-0.588773\pi\)
−0.275287 + 0.961362i \(0.588773\pi\)
\(182\) −5.44871 −0.403885
\(183\) −3.90976 −0.289017
\(184\) −65.4103 −4.82211
\(185\) 30.4129 2.23600
\(186\) −6.12785 −0.449316
\(187\) 42.6531 3.11910
\(188\) 55.7434 4.06551
\(189\) 1.25271 0.0911213
\(190\) −25.4872 −1.84903
\(191\) −2.29571 −0.166112 −0.0830560 0.996545i \(-0.526468\pi\)
−0.0830560 + 0.996545i \(0.526468\pi\)
\(192\) −28.0626 −2.02524
\(193\) −15.3589 −1.10555 −0.552777 0.833329i \(-0.686432\pi\)
−0.552777 + 0.833329i \(0.686432\pi\)
\(194\) −6.79528 −0.487873
\(195\) 16.2275 1.16207
\(196\) −38.7193 −2.76567
\(197\) 3.57093 0.254418 0.127209 0.991876i \(-0.459398\pi\)
0.127209 + 0.991876i \(0.459398\pi\)
\(198\) −37.0812 −2.63525
\(199\) 26.6931 1.89222 0.946111 0.323844i \(-0.104975\pi\)
0.946111 + 0.323844i \(0.104975\pi\)
\(200\) −46.9450 −3.31951
\(201\) 10.8080 0.762335
\(202\) −12.5780 −0.884983
\(203\) 1.05756 0.0742264
\(204\) 33.1927 2.32395
\(205\) 25.4442 1.77710
\(206\) −0.563228 −0.0392420
\(207\) −15.7269 −1.09309
\(208\) 107.588 7.45989
\(209\) 16.6938 1.15473
\(210\) −1.99935 −0.137968
\(211\) −9.61000 −0.661580 −0.330790 0.943704i \(-0.607315\pi\)
−0.330790 + 0.943704i \(0.607315\pi\)
\(212\) 42.4942 2.91851
\(213\) 0.782411 0.0536099
\(214\) 29.2177 1.99728
\(215\) −7.49630 −0.511243
\(216\) −41.8656 −2.84859
\(217\) −0.844133 −0.0573035
\(218\) −36.6020 −2.47900
\(219\) −0.946611 −0.0639660
\(220\) 98.4052 6.63447
\(221\) −50.3607 −3.38763
\(222\) −21.0363 −1.41186
\(223\) −3.27501 −0.219311 −0.109655 0.993970i \(-0.534975\pi\)
−0.109655 + 0.993970i \(0.534975\pi\)
\(224\) −7.35314 −0.491303
\(225\) −11.2872 −0.752478
\(226\) 2.75717 0.183404
\(227\) −0.152049 −0.0100918 −0.00504591 0.999987i \(-0.501606\pi\)
−0.00504591 + 0.999987i \(0.501606\pi\)
\(228\) 12.9911 0.860360
\(229\) 3.54503 0.234262 0.117131 0.993116i \(-0.462630\pi\)
0.117131 + 0.993116i \(0.462630\pi\)
\(230\) 56.6357 3.73445
\(231\) 1.30955 0.0861622
\(232\) −35.3438 −2.32043
\(233\) −23.8614 −1.56321 −0.781605 0.623774i \(-0.785599\pi\)
−0.781605 + 0.623774i \(0.785599\pi\)
\(234\) 43.7820 2.86212
\(235\) −31.0341 −2.02444
\(236\) −29.4380 −1.91625
\(237\) 0.656923 0.0426717
\(238\) 6.20483 0.402200
\(239\) 15.3049 0.989991 0.494996 0.868895i \(-0.335170\pi\)
0.494996 + 0.868895i \(0.335170\pi\)
\(240\) 39.4784 2.54832
\(241\) 10.7640 0.693370 0.346685 0.937982i \(-0.387307\pi\)
0.346685 + 0.937982i \(0.387307\pi\)
\(242\) −57.1365 −3.67287
\(243\) −15.6707 −1.00528
\(244\) 27.9936 1.79210
\(245\) 21.5562 1.37718
\(246\) −17.5995 −1.12210
\(247\) −19.7105 −1.25415
\(248\) 28.2109 1.79140
\(249\) −11.1915 −0.709235
\(250\) −2.34796 −0.148498
\(251\) 5.25145 0.331469 0.165734 0.986170i \(-0.447001\pi\)
0.165734 + 0.986170i \(0.447001\pi\)
\(252\) −3.97511 −0.250409
\(253\) −37.0957 −2.33219
\(254\) 26.7696 1.67967
\(255\) −18.4794 −1.15722
\(256\) 64.4786 4.02991
\(257\) 6.51007 0.406087 0.203044 0.979170i \(-0.434917\pi\)
0.203044 + 0.979170i \(0.434917\pi\)
\(258\) 5.18510 0.322810
\(259\) −2.89782 −0.180062
\(260\) −116.187 −7.20564
\(261\) −8.49784 −0.526003
\(262\) −15.4163 −0.952421
\(263\) 15.8869 0.979629 0.489815 0.871827i \(-0.337064\pi\)
0.489815 + 0.871827i \(0.337064\pi\)
\(264\) −43.7652 −2.69356
\(265\) −23.6578 −1.45329
\(266\) 2.42848 0.148900
\(267\) −7.42057 −0.454131
\(268\) −77.3842 −4.72699
\(269\) 18.9275 1.15403 0.577015 0.816733i \(-0.304217\pi\)
0.577015 + 0.816733i \(0.304217\pi\)
\(270\) 36.2495 2.20607
\(271\) −25.4497 −1.54596 −0.772978 0.634433i \(-0.781234\pi\)
−0.772978 + 0.634433i \(0.781234\pi\)
\(272\) −122.518 −7.42876
\(273\) −1.54619 −0.0935800
\(274\) −31.4629 −1.90074
\(275\) −26.6236 −1.60547
\(276\) −28.8680 −1.73765
\(277\) −4.25098 −0.255417 −0.127708 0.991812i \(-0.540762\pi\)
−0.127708 + 0.991812i \(0.540762\pi\)
\(278\) −43.9116 −2.63364
\(279\) 6.78286 0.406079
\(280\) 9.20447 0.550072
\(281\) −10.6744 −0.636781 −0.318390 0.947960i \(-0.603142\pi\)
−0.318390 + 0.947960i \(0.603142\pi\)
\(282\) 21.4659 1.27828
\(283\) 8.95397 0.532258 0.266129 0.963937i \(-0.414255\pi\)
0.266129 + 0.963937i \(0.414255\pi\)
\(284\) −5.60200 −0.332418
\(285\) −7.23257 −0.428420
\(286\) 103.271 6.10653
\(287\) −2.42439 −0.143107
\(288\) 59.0847 3.48160
\(289\) 40.3493 2.37349
\(290\) 30.6025 1.79704
\(291\) −1.92832 −0.113040
\(292\) 6.77767 0.396633
\(293\) −9.95699 −0.581694 −0.290847 0.956770i \(-0.593937\pi\)
−0.290847 + 0.956770i \(0.593937\pi\)
\(294\) −14.9102 −0.869580
\(295\) 16.3890 0.954207
\(296\) 96.8452 5.62901
\(297\) −23.7430 −1.37771
\(298\) −22.9590 −1.32998
\(299\) 43.7991 2.53297
\(300\) −20.7186 −1.19619
\(301\) 0.714267 0.0411697
\(302\) −22.4741 −1.29324
\(303\) −3.56928 −0.205050
\(304\) −47.9519 −2.75023
\(305\) −15.5849 −0.892387
\(306\) −49.8577 −2.85017
\(307\) 1.19316 0.0680971 0.0340486 0.999420i \(-0.489160\pi\)
0.0340486 + 0.999420i \(0.489160\pi\)
\(308\) −9.37630 −0.534264
\(309\) −0.159829 −0.00909235
\(310\) −24.4265 −1.38733
\(311\) 9.91575 0.562271 0.281135 0.959668i \(-0.409289\pi\)
0.281135 + 0.959668i \(0.409289\pi\)
\(312\) 51.6738 2.92545
\(313\) 8.01406 0.452982 0.226491 0.974013i \(-0.427275\pi\)
0.226491 + 0.974013i \(0.427275\pi\)
\(314\) 20.1613 1.13777
\(315\) 2.21307 0.124692
\(316\) −4.70352 −0.264594
\(317\) −5.64777 −0.317210 −0.158605 0.987342i \(-0.550700\pi\)
−0.158605 + 0.987342i \(0.550700\pi\)
\(318\) 16.3638 0.917639
\(319\) −20.0443 −1.12226
\(320\) −111.862 −6.25325
\(321\) 8.29118 0.462768
\(322\) −5.39640 −0.300730
\(323\) 22.4457 1.24891
\(324\) 21.6531 1.20295
\(325\) 31.4347 1.74368
\(326\) 25.4913 1.41183
\(327\) −10.3866 −0.574383
\(328\) 81.0232 4.47376
\(329\) 2.95701 0.163025
\(330\) 37.8943 2.08601
\(331\) −11.1549 −0.613131 −0.306566 0.951850i \(-0.599180\pi\)
−0.306566 + 0.951850i \(0.599180\pi\)
\(332\) 80.1306 4.39774
\(333\) 23.2849 1.27600
\(334\) −25.6383 −1.40287
\(335\) 43.0821 2.35383
\(336\) −3.76161 −0.205213
\(337\) 31.9195 1.73876 0.869382 0.494140i \(-0.164517\pi\)
0.869382 + 0.494140i \(0.164517\pi\)
\(338\) −86.0891 −4.68263
\(339\) 0.782411 0.0424947
\(340\) 132.311 7.17557
\(341\) 15.9991 0.866399
\(342\) −19.5136 −1.05517
\(343\) −4.13411 −0.223221
\(344\) −23.8708 −1.28703
\(345\) 16.0717 0.865270
\(346\) −17.9971 −0.967528
\(347\) −13.1891 −0.708030 −0.354015 0.935240i \(-0.615184\pi\)
−0.354015 + 0.935240i \(0.615184\pi\)
\(348\) −15.5985 −0.836167
\(349\) −28.7273 −1.53774 −0.768868 0.639408i \(-0.779180\pi\)
−0.768868 + 0.639408i \(0.779180\pi\)
\(350\) −3.87300 −0.207020
\(351\) 28.0334 1.49631
\(352\) 139.366 7.42824
\(353\) −18.1119 −0.964001 −0.482000 0.876171i \(-0.660090\pi\)
−0.482000 + 0.876171i \(0.660090\pi\)
\(354\) −11.3361 −0.602508
\(355\) 3.11881 0.165529
\(356\) 53.1307 2.81592
\(357\) 1.76076 0.0931895
\(358\) 44.8890 2.37245
\(359\) −21.9575 −1.15887 −0.579435 0.815018i \(-0.696727\pi\)
−0.579435 + 0.815018i \(0.696727\pi\)
\(360\) −73.9606 −3.89807
\(361\) −10.2151 −0.537635
\(362\) 20.4230 1.07341
\(363\) −16.2138 −0.851002
\(364\) 11.0706 0.580259
\(365\) −3.77333 −0.197505
\(366\) 10.7799 0.563473
\(367\) −0.403663 −0.0210710 −0.0105355 0.999944i \(-0.503354\pi\)
−0.0105355 + 0.999944i \(0.503354\pi\)
\(368\) 106.555 5.55458
\(369\) 19.4807 1.01413
\(370\) −83.8537 −4.35934
\(371\) 2.25418 0.117031
\(372\) 12.4505 0.645529
\(373\) 24.4449 1.26571 0.632856 0.774270i \(-0.281883\pi\)
0.632856 + 0.774270i \(0.281883\pi\)
\(374\) −117.602 −6.08105
\(375\) −0.666286 −0.0344069
\(376\) −98.8231 −5.09641
\(377\) 23.6664 1.21888
\(378\) −3.45394 −0.177652
\(379\) 37.0498 1.90312 0.951561 0.307460i \(-0.0994792\pi\)
0.951561 + 0.307460i \(0.0994792\pi\)
\(380\) 51.7847 2.65650
\(381\) 7.59649 0.389180
\(382\) 6.32968 0.323855
\(383\) −12.9141 −0.659878 −0.329939 0.944002i \(-0.607028\pi\)
−0.329939 + 0.944002i \(0.607028\pi\)
\(384\) 38.6533 1.97252
\(385\) 5.22007 0.266039
\(386\) 42.3470 2.15541
\(387\) −5.73935 −0.291747
\(388\) 13.8066 0.700924
\(389\) −23.9694 −1.21530 −0.607648 0.794207i \(-0.707887\pi\)
−0.607648 + 0.794207i \(0.707887\pi\)
\(390\) −44.7419 −2.26560
\(391\) −49.8772 −2.52240
\(392\) 68.6424 3.46697
\(393\) −4.37472 −0.220676
\(394\) −9.84568 −0.496018
\(395\) 2.61859 0.131756
\(396\) 75.3414 3.78605
\(397\) −22.8014 −1.14437 −0.572184 0.820125i \(-0.693904\pi\)
−0.572184 + 0.820125i \(0.693904\pi\)
\(398\) −73.5974 −3.68910
\(399\) 0.689138 0.0345000
\(400\) 76.4747 3.82374
\(401\) 36.2381 1.80965 0.904823 0.425789i \(-0.140003\pi\)
0.904823 + 0.425789i \(0.140003\pi\)
\(402\) −29.7994 −1.48626
\(403\) −18.8902 −0.940988
\(404\) 25.5558 1.27145
\(405\) −12.0550 −0.599016
\(406\) −2.91589 −0.144713
\(407\) 54.9232 2.72244
\(408\) −58.8447 −2.91325
\(409\) −4.06412 −0.200958 −0.100479 0.994939i \(-0.532038\pi\)
−0.100479 + 0.994939i \(0.532038\pi\)
\(410\) −70.1542 −3.46467
\(411\) −8.92831 −0.440401
\(412\) 1.14436 0.0563787
\(413\) −1.56159 −0.0768409
\(414\) 43.3617 2.13111
\(415\) −44.6111 −2.18987
\(416\) −164.550 −8.06774
\(417\) −12.4609 −0.610214
\(418\) −46.0277 −2.25129
\(419\) 32.8570 1.60517 0.802585 0.596538i \(-0.203457\pi\)
0.802585 + 0.596538i \(0.203457\pi\)
\(420\) 4.06227 0.198218
\(421\) 14.2195 0.693016 0.346508 0.938047i \(-0.387367\pi\)
0.346508 + 0.938047i \(0.387367\pi\)
\(422\) 26.4964 1.28983
\(423\) −23.7604 −1.15527
\(424\) −75.3346 −3.65857
\(425\) −35.7969 −1.73640
\(426\) −2.15724 −0.104519
\(427\) 1.48497 0.0718626
\(428\) −59.3642 −2.86948
\(429\) 29.3054 1.41488
\(430\) 20.6686 0.996728
\(431\) −21.4224 −1.03188 −0.515940 0.856625i \(-0.672557\pi\)
−0.515940 + 0.856625i \(0.672557\pi\)
\(432\) 68.2002 3.28128
\(433\) −30.7602 −1.47824 −0.739121 0.673573i \(-0.764759\pi\)
−0.739121 + 0.673573i \(0.764759\pi\)
\(434\) 2.32742 0.111720
\(435\) 8.68416 0.416374
\(436\) 74.3676 3.56156
\(437\) −19.5212 −0.933827
\(438\) 2.60997 0.124709
\(439\) 38.1935 1.82288 0.911439 0.411436i \(-0.134973\pi\)
0.911439 + 0.411436i \(0.134973\pi\)
\(440\) −174.455 −8.31680
\(441\) 16.5040 0.785903
\(442\) 138.853 6.60457
\(443\) 37.6101 1.78691 0.893456 0.449151i \(-0.148273\pi\)
0.893456 + 0.449151i \(0.148273\pi\)
\(444\) 42.7413 2.02841
\(445\) −29.5795 −1.40220
\(446\) 9.02976 0.427571
\(447\) −6.51514 −0.308156
\(448\) 10.6585 0.503565
\(449\) 24.0310 1.13409 0.567046 0.823686i \(-0.308086\pi\)
0.567046 + 0.823686i \(0.308086\pi\)
\(450\) 31.1207 1.46704
\(451\) 45.9502 2.16371
\(452\) −5.60200 −0.263496
\(453\) −6.37753 −0.299643
\(454\) 0.419224 0.0196752
\(455\) −6.16336 −0.288943
\(456\) −23.0310 −1.07852
\(457\) 28.1669 1.31759 0.658796 0.752322i \(-0.271066\pi\)
0.658796 + 0.752322i \(0.271066\pi\)
\(458\) −9.77427 −0.456722
\(459\) −31.9237 −1.49007
\(460\) −115.072 −5.36526
\(461\) 2.14843 0.100062 0.0500312 0.998748i \(-0.484068\pi\)
0.0500312 + 0.998748i \(0.484068\pi\)
\(462\) −3.61066 −0.167983
\(463\) 3.20776 0.149077 0.0745387 0.997218i \(-0.476252\pi\)
0.0745387 + 0.997218i \(0.476252\pi\)
\(464\) 57.5760 2.67290
\(465\) −6.93158 −0.321444
\(466\) 65.7899 3.04766
\(467\) 17.8017 0.823763 0.411881 0.911238i \(-0.364872\pi\)
0.411881 + 0.911238i \(0.364872\pi\)
\(468\) −88.9559 −4.11199
\(469\) −4.10498 −0.189550
\(470\) 85.5663 3.94688
\(471\) 5.72122 0.263620
\(472\) 52.1884 2.40216
\(473\) −13.5377 −0.622464
\(474\) −1.81125 −0.0831935
\(475\) −14.0104 −0.642841
\(476\) −12.6069 −0.577838
\(477\) −18.1130 −0.829337
\(478\) −42.1982 −1.93010
\(479\) 10.0196 0.457807 0.228903 0.973449i \(-0.426486\pi\)
0.228903 + 0.973449i \(0.426486\pi\)
\(480\) −60.3802 −2.75597
\(481\) −64.8481 −2.95682
\(482\) −29.6782 −1.35180
\(483\) −1.53135 −0.0696789
\(484\) 116.089 5.27679
\(485\) −7.68656 −0.349029
\(486\) 43.2069 1.95990
\(487\) 17.4777 0.791991 0.395996 0.918252i \(-0.370400\pi\)
0.395996 + 0.918252i \(0.370400\pi\)
\(488\) −49.6276 −2.24653
\(489\) 7.23373 0.327120
\(490\) −59.4342 −2.68497
\(491\) −34.4502 −1.55472 −0.777358 0.629058i \(-0.783441\pi\)
−0.777358 + 0.629058i \(0.783441\pi\)
\(492\) 35.7585 1.61212
\(493\) −26.9506 −1.21379
\(494\) 54.3451 2.44510
\(495\) −41.9448 −1.88528
\(496\) −45.9564 −2.06350
\(497\) −0.297168 −0.0133298
\(498\) 30.8570 1.38274
\(499\) −23.7730 −1.06423 −0.532113 0.846673i \(-0.678602\pi\)
−0.532113 + 0.846673i \(0.678602\pi\)
\(500\) 4.77056 0.213346
\(501\) −7.27546 −0.325043
\(502\) −14.4792 −0.646237
\(503\) 5.95730 0.265623 0.132812 0.991141i \(-0.457600\pi\)
0.132812 + 0.991141i \(0.457600\pi\)
\(504\) 7.04716 0.313905
\(505\) −14.2277 −0.633124
\(506\) 102.279 4.54687
\(507\) −24.4297 −1.08496
\(508\) −54.3903 −2.41318
\(509\) −4.05798 −0.179867 −0.0899334 0.995948i \(-0.528665\pi\)
−0.0899334 + 0.995948i \(0.528665\pi\)
\(510\) 50.9509 2.25614
\(511\) 0.359533 0.0159048
\(512\) −78.9729 −3.49014
\(513\) −12.4945 −0.551645
\(514\) −17.9494 −0.791714
\(515\) −0.637102 −0.0280741
\(516\) −10.5351 −0.463780
\(517\) −56.0449 −2.46485
\(518\) 7.98979 0.351051
\(519\) −5.10708 −0.224176
\(520\) 205.980 9.03280
\(521\) 16.7688 0.734656 0.367328 0.930091i \(-0.380273\pi\)
0.367328 + 0.930091i \(0.380273\pi\)
\(522\) 23.4300 1.02550
\(523\) 17.9611 0.785385 0.392693 0.919670i \(-0.371544\pi\)
0.392693 + 0.919670i \(0.371544\pi\)
\(524\) 31.3227 1.36834
\(525\) −1.09905 −0.0479665
\(526\) −43.8030 −1.90990
\(527\) 21.5116 0.937061
\(528\) 71.2948 3.10271
\(529\) 20.3787 0.886029
\(530\) 65.2287 2.83335
\(531\) 12.5478 0.544530
\(532\) −4.93418 −0.213924
\(533\) −54.2536 −2.34998
\(534\) 20.4598 0.885382
\(535\) 33.0499 1.42887
\(536\) 137.188 5.92563
\(537\) 12.7383 0.549697
\(538\) −52.1864 −2.24992
\(539\) 38.9287 1.67678
\(540\) −73.6514 −3.16945
\(541\) 15.7597 0.677563 0.338782 0.940865i \(-0.389985\pi\)
0.338782 + 0.940865i \(0.389985\pi\)
\(542\) 70.1691 3.01402
\(543\) 5.79549 0.248708
\(544\) 187.385 8.03407
\(545\) −41.4027 −1.77350
\(546\) 4.26313 0.182445
\(547\) −17.2707 −0.738441 −0.369220 0.929342i \(-0.620375\pi\)
−0.369220 + 0.929342i \(0.620375\pi\)
\(548\) 63.9260 2.73078
\(549\) −11.9322 −0.509252
\(550\) 73.4060 3.13004
\(551\) −10.5481 −0.449364
\(552\) 51.1778 2.17827
\(553\) −0.249506 −0.0106101
\(554\) 11.7207 0.497965
\(555\) −23.7954 −1.01006
\(556\) 89.2193 3.78374
\(557\) −19.1217 −0.810212 −0.405106 0.914270i \(-0.632765\pi\)
−0.405106 + 0.914270i \(0.632765\pi\)
\(558\) −18.7015 −0.791699
\(559\) 15.9840 0.676052
\(560\) −14.9943 −0.633626
\(561\) −33.3722 −1.40898
\(562\) 29.4312 1.24148
\(563\) −9.56993 −0.403325 −0.201662 0.979455i \(-0.564634\pi\)
−0.201662 + 0.979455i \(0.564634\pi\)
\(564\) −43.6143 −1.83649
\(565\) 3.11881 0.131209
\(566\) −24.6876 −1.03770
\(567\) 1.14863 0.0482378
\(568\) 9.93135 0.416710
\(569\) 1.79930 0.0754304 0.0377152 0.999289i \(-0.487992\pi\)
0.0377152 + 0.999289i \(0.487992\pi\)
\(570\) 19.9414 0.835255
\(571\) 19.9181 0.833548 0.416774 0.909010i \(-0.363161\pi\)
0.416774 + 0.909010i \(0.363161\pi\)
\(572\) −209.825 −8.77322
\(573\) 1.79619 0.0750370
\(574\) 6.68447 0.279004
\(575\) 31.1329 1.29833
\(576\) −85.6439 −3.56850
\(577\) 23.8184 0.991573 0.495786 0.868444i \(-0.334880\pi\)
0.495786 + 0.868444i \(0.334880\pi\)
\(578\) −111.250 −4.62739
\(579\) 12.0169 0.499407
\(580\) −62.1779 −2.58180
\(581\) 4.25066 0.176347
\(582\) 5.31670 0.220384
\(583\) −42.7240 −1.76945
\(584\) −12.0156 −0.497208
\(585\) 49.5245 2.04758
\(586\) 27.4532 1.13408
\(587\) 3.31009 0.136622 0.0683111 0.997664i \(-0.478239\pi\)
0.0683111 + 0.997664i \(0.478239\pi\)
\(588\) 30.2944 1.24932
\(589\) 8.41934 0.346913
\(590\) −45.1874 −1.86034
\(591\) −2.79394 −0.114927
\(592\) −157.763 −6.48404
\(593\) −19.4542 −0.798889 −0.399445 0.916757i \(-0.630797\pi\)
−0.399445 + 0.916757i \(0.630797\pi\)
\(594\) 65.4635 2.68600
\(595\) 7.01866 0.287737
\(596\) 46.6479 1.91077
\(597\) −20.8849 −0.854764
\(598\) −120.762 −4.93832
\(599\) −37.9356 −1.55001 −0.775003 0.631957i \(-0.782252\pi\)
−0.775003 + 0.631957i \(0.782252\pi\)
\(600\) 36.7303 1.49951
\(601\) −6.22632 −0.253977 −0.126989 0.991904i \(-0.540531\pi\)
−0.126989 + 0.991904i \(0.540531\pi\)
\(602\) −1.96936 −0.0802650
\(603\) 32.9847 1.34324
\(604\) 45.6627 1.85799
\(605\) −64.6305 −2.62760
\(606\) 9.84114 0.399769
\(607\) −27.3757 −1.11115 −0.555573 0.831468i \(-0.687501\pi\)
−0.555573 + 0.831468i \(0.687501\pi\)
\(608\) 73.3399 2.97433
\(609\) −0.827449 −0.0335299
\(610\) 42.9702 1.73981
\(611\) 66.1725 2.67705
\(612\) 101.301 4.09483
\(613\) −24.8765 −1.00475 −0.502376 0.864650i \(-0.667540\pi\)
−0.502376 + 0.864650i \(0.667540\pi\)
\(614\) −3.28974 −0.132763
\(615\) −19.9079 −0.802762
\(616\) 16.6225 0.669739
\(617\) 13.8557 0.557809 0.278905 0.960319i \(-0.410029\pi\)
0.278905 + 0.960319i \(0.410029\pi\)
\(618\) 0.440676 0.0177266
\(619\) −32.7066 −1.31459 −0.657295 0.753633i \(-0.728300\pi\)
−0.657295 + 0.753633i \(0.728300\pi\)
\(620\) 49.6296 1.99317
\(621\) 27.7643 1.11414
\(622\) −27.3395 −1.09621
\(623\) 2.81841 0.112917
\(624\) −84.1781 −3.36982
\(625\) −26.2907 −1.05163
\(626\) −22.0962 −0.883140
\(627\) −13.0614 −0.521623
\(628\) −40.9635 −1.63462
\(629\) 73.8472 2.94448
\(630\) −6.10181 −0.243102
\(631\) −8.04559 −0.320290 −0.160145 0.987094i \(-0.551196\pi\)
−0.160145 + 0.987094i \(0.551196\pi\)
\(632\) 8.33850 0.331688
\(633\) 7.51897 0.298852
\(634\) 15.5719 0.618438
\(635\) 30.2807 1.20165
\(636\) −33.2479 −1.31837
\(637\) −45.9634 −1.82113
\(638\) 55.2656 2.18798
\(639\) 2.38783 0.0944612
\(640\) 154.078 6.09046
\(641\) −16.0524 −0.634030 −0.317015 0.948420i \(-0.602681\pi\)
−0.317015 + 0.948420i \(0.602681\pi\)
\(642\) −22.8602 −0.902221
\(643\) −16.9250 −0.667456 −0.333728 0.942669i \(-0.608307\pi\)
−0.333728 + 0.942669i \(0.608307\pi\)
\(644\) 10.9644 0.432056
\(645\) 5.86519 0.230941
\(646\) −61.8867 −2.43490
\(647\) −42.6738 −1.67768 −0.838840 0.544377i \(-0.816766\pi\)
−0.838840 + 0.544377i \(0.816766\pi\)
\(648\) −38.3871 −1.50799
\(649\) 29.5972 1.16179
\(650\) −86.6708 −3.39951
\(651\) 0.660459 0.0258854
\(652\) −51.7930 −2.02837
\(653\) 37.6729 1.47425 0.737127 0.675754i \(-0.236182\pi\)
0.737127 + 0.675754i \(0.236182\pi\)
\(654\) 28.6378 1.11983
\(655\) −17.4383 −0.681371
\(656\) −131.989 −5.15331
\(657\) −2.88895 −0.112709
\(658\) −8.15298 −0.317836
\(659\) 29.8693 1.16354 0.581771 0.813353i \(-0.302360\pi\)
0.581771 + 0.813353i \(0.302360\pi\)
\(660\) −76.9933 −2.99696
\(661\) −22.9212 −0.891530 −0.445765 0.895150i \(-0.647068\pi\)
−0.445765 + 0.895150i \(0.647068\pi\)
\(662\) 30.7561 1.19537
\(663\) 39.4027 1.53028
\(664\) −142.057 −5.51289
\(665\) 2.74701 0.106524
\(666\) −64.2004 −2.48771
\(667\) 23.4392 0.907569
\(668\) 52.0917 2.01549
\(669\) 2.56240 0.0990681
\(670\) −118.785 −4.58906
\(671\) −28.1450 −1.08652
\(672\) 5.75318 0.221934
\(673\) −16.2700 −0.627163 −0.313581 0.949561i \(-0.601529\pi\)
−0.313581 + 0.949561i \(0.601529\pi\)
\(674\) −88.0075 −3.38992
\(675\) 19.9265 0.766970
\(676\) 174.915 6.72751
\(677\) −34.7188 −1.33435 −0.667176 0.744900i \(-0.732497\pi\)
−0.667176 + 0.744900i \(0.732497\pi\)
\(678\) −2.15724 −0.0828484
\(679\) 0.732395 0.0281068
\(680\) −234.564 −8.99511
\(681\) 0.118964 0.00455873
\(682\) −44.1122 −1.68914
\(683\) 7.98992 0.305726 0.152863 0.988247i \(-0.451151\pi\)
0.152863 + 0.988247i \(0.451151\pi\)
\(684\) 39.6476 1.51596
\(685\) −35.5896 −1.35981
\(686\) 11.3985 0.435195
\(687\) −2.77367 −0.105822
\(688\) 38.8862 1.48252
\(689\) 50.4445 1.92178
\(690\) −44.3124 −1.68694
\(691\) 6.88017 0.261734 0.130867 0.991400i \(-0.458224\pi\)
0.130867 + 0.991400i \(0.458224\pi\)
\(692\) 36.5663 1.39004
\(693\) 3.99661 0.151819
\(694\) 36.3647 1.38039
\(695\) −49.6711 −1.88413
\(696\) 27.6533 1.04820
\(697\) 61.7825 2.34018
\(698\) 79.2061 2.99799
\(699\) 18.6694 0.706141
\(700\) 7.86913 0.297425
\(701\) 11.5530 0.436350 0.218175 0.975910i \(-0.429990\pi\)
0.218175 + 0.975910i \(0.429990\pi\)
\(702\) −77.2931 −2.91724
\(703\) 28.9027 1.09009
\(704\) −202.013 −7.61364
\(705\) 24.2814 0.914490
\(706\) 49.9377 1.87943
\(707\) 1.35565 0.0509845
\(708\) 23.0326 0.865619
\(709\) 34.0414 1.27845 0.639226 0.769019i \(-0.279255\pi\)
0.639226 + 0.769019i \(0.279255\pi\)
\(710\) −8.59909 −0.322718
\(711\) 2.00486 0.0751880
\(712\) −94.1912 −3.52997
\(713\) −18.7088 −0.700652
\(714\) −4.85473 −0.181684
\(715\) 116.816 4.36867
\(716\) −91.2050 −3.40849
\(717\) −11.9747 −0.447204
\(718\) 60.5406 2.25935
\(719\) 23.7192 0.884578 0.442289 0.896873i \(-0.354167\pi\)
0.442289 + 0.896873i \(0.354167\pi\)
\(720\) 120.484 4.49017
\(721\) 0.0607047 0.00226076
\(722\) 28.1647 1.04818
\(723\) −8.42187 −0.313213
\(724\) −41.4953 −1.54216
\(725\) 16.8223 0.624765
\(726\) 44.7042 1.65913
\(727\) 1.96085 0.0727240 0.0363620 0.999339i \(-0.488423\pi\)
0.0363620 + 0.999339i \(0.488423\pi\)
\(728\) −19.6263 −0.727398
\(729\) 0.665190 0.0246367
\(730\) 10.4037 0.385059
\(731\) −18.2022 −0.673231
\(732\) −21.9025 −0.809539
\(733\) 1.98250 0.0732254 0.0366127 0.999330i \(-0.488343\pi\)
0.0366127 + 0.999330i \(0.488343\pi\)
\(734\) 1.11297 0.0410804
\(735\) −16.8658 −0.622105
\(736\) −162.971 −6.00717
\(737\) 77.8027 2.86590
\(738\) −53.7117 −1.97716
\(739\) −28.9271 −1.06410 −0.532051 0.846712i \(-0.678579\pi\)
−0.532051 + 0.846712i \(0.678579\pi\)
\(740\) 170.373 6.26305
\(741\) 15.4217 0.566529
\(742\) −6.21516 −0.228166
\(743\) 8.08169 0.296488 0.148244 0.988951i \(-0.452638\pi\)
0.148244 + 0.988951i \(0.452638\pi\)
\(744\) −22.0725 −0.809218
\(745\) −25.9703 −0.951479
\(746\) −67.3989 −2.46765
\(747\) −34.1554 −1.24968
\(748\) 238.943 8.73661
\(749\) −3.14908 −0.115065
\(750\) 1.83707 0.0670802
\(751\) −47.3577 −1.72811 −0.864053 0.503401i \(-0.832082\pi\)
−0.864053 + 0.503401i \(0.832082\pi\)
\(752\) 160.986 5.87054
\(753\) −4.10879 −0.149733
\(754\) −65.2523 −2.37635
\(755\) −25.4218 −0.925194
\(756\) 7.01769 0.255231
\(757\) −34.5284 −1.25496 −0.627478 0.778634i \(-0.715913\pi\)
−0.627478 + 0.778634i \(0.715913\pi\)
\(758\) −102.153 −3.71036
\(759\) 29.0241 1.05351
\(760\) −91.8049 −3.33011
\(761\) 9.60438 0.348158 0.174079 0.984732i \(-0.444305\pi\)
0.174079 + 0.984732i \(0.444305\pi\)
\(762\) −20.9448 −0.758751
\(763\) 3.94496 0.142817
\(764\) −12.8606 −0.465280
\(765\) −56.3971 −2.03904
\(766\) 35.6063 1.28651
\(767\) −34.9456 −1.26181
\(768\) −50.4487 −1.82041
\(769\) −16.3484 −0.589537 −0.294768 0.955569i \(-0.595243\pi\)
−0.294768 + 0.955569i \(0.595243\pi\)
\(770\) −14.3926 −0.518675
\(771\) −5.09355 −0.183440
\(772\) −86.0404 −3.09666
\(773\) 0.519158 0.0186728 0.00933641 0.999956i \(-0.497028\pi\)
0.00933641 + 0.999956i \(0.497028\pi\)
\(774\) 15.8244 0.568795
\(775\) −13.4273 −0.482325
\(776\) −24.4766 −0.878660
\(777\) 2.26729 0.0813385
\(778\) 66.0877 2.36936
\(779\) 24.1808 0.866367
\(780\) 90.9063 3.25497
\(781\) 5.63230 0.201540
\(782\) 137.520 4.91771
\(783\) 15.0021 0.536133
\(784\) −111.820 −3.99359
\(785\) 22.8056 0.813967
\(786\) 12.0619 0.430232
\(787\) −41.5213 −1.48008 −0.740038 0.672565i \(-0.765193\pi\)
−0.740038 + 0.672565i \(0.765193\pi\)
\(788\) 20.0044 0.712627
\(789\) −12.4301 −0.442523
\(790\) −7.21991 −0.256873
\(791\) −0.297168 −0.0105661
\(792\) −133.567 −4.74609
\(793\) 33.2309 1.18006
\(794\) 62.8673 2.23108
\(795\) 18.5101 0.656487
\(796\) 149.535 5.30012
\(797\) −38.3748 −1.35930 −0.679652 0.733534i \(-0.737869\pi\)
−0.679652 + 0.733534i \(0.737869\pi\)
\(798\) −1.90007 −0.0672618
\(799\) −75.3554 −2.66588
\(800\) −116.964 −4.13530
\(801\) −22.6468 −0.800184
\(802\) −99.9148 −3.52811
\(803\) −6.81432 −0.240472
\(804\) 60.5462 2.13530
\(805\) −6.10420 −0.215145
\(806\) 52.0835 1.83456
\(807\) −14.8091 −0.521305
\(808\) −45.3059 −1.59386
\(809\) −41.5785 −1.46182 −0.730911 0.682473i \(-0.760905\pi\)
−0.730911 + 0.682473i \(0.760905\pi\)
\(810\) 33.2376 1.16785
\(811\) 27.4236 0.962973 0.481486 0.876454i \(-0.340097\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(812\) 5.92447 0.207908
\(813\) 19.9121 0.698347
\(814\) −151.433 −5.30771
\(815\) 28.8347 1.01004
\(816\) 95.8596 3.35576
\(817\) −7.12406 −0.249239
\(818\) 11.2055 0.391791
\(819\) −4.71882 −0.164889
\(820\) 142.539 4.97767
\(821\) −46.4167 −1.61995 −0.809977 0.586461i \(-0.800521\pi\)
−0.809977 + 0.586461i \(0.800521\pi\)
\(822\) 24.6169 0.858612
\(823\) 47.4686 1.65465 0.827326 0.561722i \(-0.189861\pi\)
0.827326 + 0.561722i \(0.189861\pi\)
\(824\) −2.02875 −0.0706749
\(825\) 20.8306 0.725229
\(826\) 4.30558 0.149810
\(827\) −38.3495 −1.33354 −0.666771 0.745263i \(-0.732324\pi\)
−0.666771 + 0.745263i \(0.732324\pi\)
\(828\) −88.1019 −3.06175
\(829\) 14.5194 0.504279 0.252140 0.967691i \(-0.418866\pi\)
0.252140 + 0.967691i \(0.418866\pi\)
\(830\) 123.001 4.26941
\(831\) 3.32601 0.115378
\(832\) 238.517 8.26910
\(833\) 52.3418 1.81354
\(834\) 34.3569 1.18968
\(835\) −29.0011 −1.00362
\(836\) 93.5188 3.23441
\(837\) −11.9745 −0.413900
\(838\) −90.5925 −3.12946
\(839\) −35.0695 −1.21073 −0.605367 0.795947i \(-0.706974\pi\)
−0.605367 + 0.795947i \(0.706974\pi\)
\(840\) −7.20167 −0.248481
\(841\) −16.3349 −0.563272
\(842\) −39.2056 −1.35112
\(843\) 8.35176 0.287650
\(844\) −53.8353 −1.85309
\(845\) −97.3806 −3.34999
\(846\) 65.5116 2.25234
\(847\) 6.15816 0.211597
\(848\) 122.722 4.21430
\(849\) −7.00568 −0.240434
\(850\) 98.6983 3.38532
\(851\) −64.2255 −2.20162
\(852\) 4.38307 0.150161
\(853\) −28.1269 −0.963048 −0.481524 0.876433i \(-0.659917\pi\)
−0.481524 + 0.876433i \(0.659917\pi\)
\(854\) −4.09431 −0.140104
\(855\) −22.0730 −0.754881
\(856\) 105.242 3.59710
\(857\) −47.7875 −1.63239 −0.816194 0.577777i \(-0.803920\pi\)
−0.816194 + 0.577777i \(0.803920\pi\)
\(858\) −80.8002 −2.75847
\(859\) 35.5209 1.21196 0.605979 0.795481i \(-0.292782\pi\)
0.605979 + 0.795481i \(0.292782\pi\)
\(860\) −41.9943 −1.43199
\(861\) 1.89687 0.0646452
\(862\) 59.0653 2.01177
\(863\) −37.7729 −1.28580 −0.642902 0.765948i \(-0.722270\pi\)
−0.642902 + 0.765948i \(0.722270\pi\)
\(864\) −104.309 −3.54865
\(865\) −20.3576 −0.692178
\(866\) 84.8112 2.88200
\(867\) −31.5698 −1.07217
\(868\) −4.72884 −0.160507
\(869\) 4.72896 0.160419
\(870\) −23.9437 −0.811768
\(871\) −91.8621 −3.11263
\(872\) −131.840 −4.46468
\(873\) −5.88502 −0.199178
\(874\) 53.8234 1.82060
\(875\) 0.253063 0.00855508
\(876\) −5.30292 −0.179169
\(877\) 38.2179 1.29053 0.645263 0.763960i \(-0.276748\pi\)
0.645263 + 0.763960i \(0.276748\pi\)
\(878\) −105.306 −3.55391
\(879\) 7.79046 0.262766
\(880\) 284.192 9.58009
\(881\) 9.22324 0.310739 0.155369 0.987856i \(-0.450343\pi\)
0.155369 + 0.987856i \(0.450343\pi\)
\(882\) −45.5043 −1.53221
\(883\) −24.3652 −0.819956 −0.409978 0.912095i \(-0.634464\pi\)
−0.409978 + 0.912095i \(0.634464\pi\)
\(884\) −282.121 −9.48875
\(885\) −12.8230 −0.431039
\(886\) −103.698 −3.48379
\(887\) −28.0237 −0.940945 −0.470473 0.882415i \(-0.655917\pi\)
−0.470473 + 0.882415i \(0.655917\pi\)
\(888\) −75.7727 −2.54277
\(889\) −2.88523 −0.0967674
\(890\) 81.5558 2.73376
\(891\) −21.7702 −0.729331
\(892\) −18.3466 −0.614289
\(893\) −29.4930 −0.986947
\(894\) 17.9634 0.600785
\(895\) 50.7766 1.69728
\(896\) −14.6809 −0.490456
\(897\) −34.2689 −1.14421
\(898\) −66.2575 −2.21104
\(899\) −10.1091 −0.337158
\(900\) −63.2308 −2.10769
\(901\) −57.4448 −1.91376
\(902\) −126.693 −4.21840
\(903\) −0.558850 −0.0185974
\(904\) 9.93135 0.330312
\(905\) 23.1017 0.767926
\(906\) 17.5840 0.584188
\(907\) −43.4622 −1.44314 −0.721569 0.692343i \(-0.756579\pi\)
−0.721569 + 0.692343i \(0.756579\pi\)
\(908\) −0.851777 −0.0282672
\(909\) −10.8931 −0.361300
\(910\) 16.9935 0.563328
\(911\) 39.6579 1.31393 0.656963 0.753923i \(-0.271841\pi\)
0.656963 + 0.753923i \(0.271841\pi\)
\(912\) 37.5181 1.24235
\(913\) −80.5640 −2.66628
\(914\) −77.6610 −2.56880
\(915\) 12.1938 0.403114
\(916\) 19.8593 0.656170
\(917\) 1.66157 0.0548697
\(918\) 88.0192 2.90507
\(919\) 23.0385 0.759970 0.379985 0.924993i \(-0.375929\pi\)
0.379985 + 0.924993i \(0.375929\pi\)
\(920\) 204.002 6.72575
\(921\) −0.933539 −0.0307612
\(922\) −5.92359 −0.195083
\(923\) −6.65009 −0.218890
\(924\) 7.33612 0.241341
\(925\) −46.0947 −1.51558
\(926\) −8.84436 −0.290644
\(927\) −0.487781 −0.0160208
\(928\) −88.0594 −2.89069
\(929\) −19.0999 −0.626648 −0.313324 0.949646i \(-0.601443\pi\)
−0.313324 + 0.949646i \(0.601443\pi\)
\(930\) 19.1116 0.626693
\(931\) 20.4858 0.671396
\(932\) −133.671 −4.37855
\(933\) −7.75819 −0.253992
\(934\) −49.0823 −1.60602
\(935\) −133.027 −4.35044
\(936\) 157.703 5.15468
\(937\) 5.83484 0.190616 0.0953079 0.995448i \(-0.469616\pi\)
0.0953079 + 0.995448i \(0.469616\pi\)
\(938\) 11.3181 0.369550
\(939\) −6.27029 −0.204623
\(940\) −173.853 −5.67046
\(941\) −0.133144 −0.00434038 −0.00217019 0.999998i \(-0.500691\pi\)
−0.00217019 + 0.999998i \(0.500691\pi\)
\(942\) −15.7744 −0.513957
\(943\) −53.7328 −1.74978
\(944\) −85.0163 −2.76704
\(945\) −3.90696 −0.127094
\(946\) 37.3258 1.21356
\(947\) 11.1991 0.363923 0.181961 0.983306i \(-0.441755\pi\)
0.181961 + 0.983306i \(0.441755\pi\)
\(948\) 3.68008 0.119524
\(949\) 8.04571 0.261175
\(950\) 38.6291 1.25329
\(951\) 4.41887 0.143292
\(952\) 22.3498 0.724362
\(953\) 21.9641 0.711487 0.355744 0.934584i \(-0.384228\pi\)
0.355744 + 0.934584i \(0.384228\pi\)
\(954\) 49.9407 1.61689
\(955\) 7.15989 0.231689
\(956\) 85.7381 2.77297
\(957\) 15.6829 0.506955
\(958\) −27.6257 −0.892547
\(959\) 3.39107 0.109503
\(960\) 87.5217 2.82475
\(961\) −22.9310 −0.739711
\(962\) 178.797 5.76466
\(963\) 25.3038 0.815403
\(964\) 60.2999 1.94213
\(965\) 47.9013 1.54200
\(966\) 4.22220 0.135847
\(967\) 5.15613 0.165810 0.0829049 0.996557i \(-0.473580\pi\)
0.0829049 + 0.996557i \(0.473580\pi\)
\(968\) −205.806 −6.61485
\(969\) −17.5618 −0.564165
\(970\) 21.1932 0.680472
\(971\) 55.4784 1.78039 0.890194 0.455582i \(-0.150569\pi\)
0.890194 + 0.455582i \(0.150569\pi\)
\(972\) −87.7874 −2.81578
\(973\) 4.73279 0.151726
\(974\) −48.1891 −1.54408
\(975\) −24.5948 −0.787664
\(976\) 80.8447 2.58778
\(977\) −43.1137 −1.37933 −0.689664 0.724129i \(-0.742242\pi\)
−0.689664 + 0.724129i \(0.742242\pi\)
\(978\) −19.9446 −0.637759
\(979\) −53.4181 −1.70725
\(980\) 120.758 3.85747
\(981\) −31.6989 −1.01207
\(982\) 94.9852 3.03110
\(983\) 28.3694 0.904842 0.452421 0.891804i \(-0.350560\pi\)
0.452421 + 0.891804i \(0.350560\pi\)
\(984\) −63.3934 −2.02091
\(985\) −11.1370 −0.354856
\(986\) 74.3075 2.36643
\(987\) −2.31359 −0.0736425
\(988\) −110.418 −3.51287
\(989\) 15.8306 0.503383
\(990\) 115.649 3.67557
\(991\) −59.2003 −1.88056 −0.940280 0.340403i \(-0.889436\pi\)
−0.940280 + 0.340403i \(0.889436\pi\)
\(992\) 70.2878 2.23164
\(993\) 8.72775 0.276967
\(994\) 0.819343 0.0259880
\(995\) −83.2505 −2.63922
\(996\) −62.6950 −1.98657
\(997\) 27.9110 0.883950 0.441975 0.897027i \(-0.354278\pi\)
0.441975 + 0.897027i \(0.354278\pi\)
\(998\) 65.5463 2.07483
\(999\) −41.1073 −1.30058
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 \(a_p\))