Properties

Label 6026.2.a.h.1.14
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.562960 q^{3}\) \(+1.00000 q^{4}\) \(-3.89005 q^{5}\) \(-0.562960 q^{6}\) \(-0.867650 q^{7}\) \(-1.00000 q^{8}\) \(-2.68308 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.562960 q^{3}\) \(+1.00000 q^{4}\) \(-3.89005 q^{5}\) \(-0.562960 q^{6}\) \(-0.867650 q^{7}\) \(-1.00000 q^{8}\) \(-2.68308 q^{9}\) \(+3.89005 q^{10}\) \(+0.507376 q^{11}\) \(+0.562960 q^{12}\) \(-2.74039 q^{13}\) \(+0.867650 q^{14}\) \(-2.18994 q^{15}\) \(+1.00000 q^{16}\) \(+3.74576 q^{17}\) \(+2.68308 q^{18}\) \(+4.55822 q^{19}\) \(-3.89005 q^{20}\) \(-0.488452 q^{21}\) \(-0.507376 q^{22}\) \(-1.00000 q^{23}\) \(-0.562960 q^{24}\) \(+10.1325 q^{25}\) \(+2.74039 q^{26}\) \(-3.19934 q^{27}\) \(-0.867650 q^{28}\) \(+5.93286 q^{29}\) \(+2.18994 q^{30}\) \(-1.85973 q^{31}\) \(-1.00000 q^{32}\) \(+0.285633 q^{33}\) \(-3.74576 q^{34}\) \(+3.37520 q^{35}\) \(-2.68308 q^{36}\) \(-0.608639 q^{37}\) \(-4.55822 q^{38}\) \(-1.54273 q^{39}\) \(+3.89005 q^{40}\) \(-9.86356 q^{41}\) \(+0.488452 q^{42}\) \(-1.26441 q^{43}\) \(+0.507376 q^{44}\) \(+10.4373 q^{45}\) \(+1.00000 q^{46}\) \(+8.01654 q^{47}\) \(+0.562960 q^{48}\) \(-6.24718 q^{49}\) \(-10.1325 q^{50}\) \(+2.10871 q^{51}\) \(-2.74039 q^{52}\) \(+4.96984 q^{53}\) \(+3.19934 q^{54}\) \(-1.97372 q^{55}\) \(+0.867650 q^{56}\) \(+2.56609 q^{57}\) \(-5.93286 q^{58}\) \(+5.28644 q^{59}\) \(-2.18994 q^{60}\) \(+13.9133 q^{61}\) \(+1.85973 q^{62}\) \(+2.32797 q^{63}\) \(+1.00000 q^{64}\) \(+10.6603 q^{65}\) \(-0.285633 q^{66}\) \(-3.14252 q^{67}\) \(+3.74576 q^{68}\) \(-0.562960 q^{69}\) \(-3.37520 q^{70}\) \(+11.8409 q^{71}\) \(+2.68308 q^{72}\) \(-9.43228 q^{73}\) \(+0.608639 q^{74}\) \(+5.70417 q^{75}\) \(+4.55822 q^{76}\) \(-0.440225 q^{77}\) \(+1.54273 q^{78}\) \(-9.73748 q^{79}\) \(-3.89005 q^{80}\) \(+6.24813 q^{81}\) \(+9.86356 q^{82}\) \(-3.20604 q^{83}\) \(-0.488452 q^{84}\) \(-14.5712 q^{85}\) \(+1.26441 q^{86}\) \(+3.33996 q^{87}\) \(-0.507376 q^{88}\) \(+2.82208 q^{89}\) \(-10.4373 q^{90}\) \(+2.37770 q^{91}\) \(-1.00000 q^{92}\) \(-1.04696 q^{93}\) \(-8.01654 q^{94}\) \(-17.7317 q^{95}\) \(-0.562960 q^{96}\) \(+5.75507 q^{97}\) \(+6.24718 q^{98}\) \(-1.36133 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.562960 0.325025 0.162512 0.986706i \(-0.448040\pi\)
0.162512 + 0.986706i \(0.448040\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.89005 −1.73968 −0.869841 0.493332i \(-0.835779\pi\)
−0.869841 + 0.493332i \(0.835779\pi\)
\(6\) −0.562960 −0.229827
\(7\) −0.867650 −0.327941 −0.163970 0.986465i \(-0.552430\pi\)
−0.163970 + 0.986465i \(0.552430\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.68308 −0.894359
\(10\) 3.89005 1.23014
\(11\) 0.507376 0.152980 0.0764899 0.997070i \(-0.475629\pi\)
0.0764899 + 0.997070i \(0.475629\pi\)
\(12\) 0.562960 0.162512
\(13\) −2.74039 −0.760049 −0.380024 0.924976i \(-0.624084\pi\)
−0.380024 + 0.924976i \(0.624084\pi\)
\(14\) 0.867650 0.231889
\(15\) −2.18994 −0.565440
\(16\) 1.00000 0.250000
\(17\) 3.74576 0.908480 0.454240 0.890879i \(-0.349911\pi\)
0.454240 + 0.890879i \(0.349911\pi\)
\(18\) 2.68308 0.632407
\(19\) 4.55822 1.04573 0.522864 0.852416i \(-0.324864\pi\)
0.522864 + 0.852416i \(0.324864\pi\)
\(20\) −3.89005 −0.869841
\(21\) −0.488452 −0.106589
\(22\) −0.507376 −0.108173
\(23\) −1.00000 −0.208514
\(24\) −0.562960 −0.114914
\(25\) 10.1325 2.02649
\(26\) 2.74039 0.537436
\(27\) −3.19934 −0.615714
\(28\) −0.867650 −0.163970
\(29\) 5.93286 1.10170 0.550852 0.834603i \(-0.314303\pi\)
0.550852 + 0.834603i \(0.314303\pi\)
\(30\) 2.18994 0.399827
\(31\) −1.85973 −0.334018 −0.167009 0.985955i \(-0.553411\pi\)
−0.167009 + 0.985955i \(0.553411\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.285633 0.0497222
\(34\) −3.74576 −0.642392
\(35\) 3.37520 0.570513
\(36\) −2.68308 −0.447179
\(37\) −0.608639 −0.100060 −0.0500298 0.998748i \(-0.515932\pi\)
−0.0500298 + 0.998748i \(0.515932\pi\)
\(38\) −4.55822 −0.739441
\(39\) −1.54273 −0.247035
\(40\) 3.89005 0.615070
\(41\) −9.86356 −1.54043 −0.770214 0.637785i \(-0.779851\pi\)
−0.770214 + 0.637785i \(0.779851\pi\)
\(42\) 0.488452 0.0753698
\(43\) −1.26441 −0.192821 −0.0964104 0.995342i \(-0.530736\pi\)
−0.0964104 + 0.995342i \(0.530736\pi\)
\(44\) 0.507376 0.0764899
\(45\) 10.4373 1.55590
\(46\) 1.00000 0.147442
\(47\) 8.01654 1.16933 0.584667 0.811274i \(-0.301225\pi\)
0.584667 + 0.811274i \(0.301225\pi\)
\(48\) 0.562960 0.0812562
\(49\) −6.24718 −0.892455
\(50\) −10.1325 −1.43295
\(51\) 2.10871 0.295279
\(52\) −2.74039 −0.380024
\(53\) 4.96984 0.682660 0.341330 0.939944i \(-0.389123\pi\)
0.341330 + 0.939944i \(0.389123\pi\)
\(54\) 3.19934 0.435375
\(55\) −1.97372 −0.266136
\(56\) 0.867650 0.115945
\(57\) 2.56609 0.339888
\(58\) −5.93286 −0.779023
\(59\) 5.28644 0.688236 0.344118 0.938926i \(-0.388178\pi\)
0.344118 + 0.938926i \(0.388178\pi\)
\(60\) −2.18994 −0.282720
\(61\) 13.9133 1.78142 0.890708 0.454576i \(-0.150209\pi\)
0.890708 + 0.454576i \(0.150209\pi\)
\(62\) 1.85973 0.236186
\(63\) 2.32797 0.293297
\(64\) 1.00000 0.125000
\(65\) 10.6603 1.32224
\(66\) −0.285633 −0.0351589
\(67\) −3.14252 −0.383919 −0.191960 0.981403i \(-0.561484\pi\)
−0.191960 + 0.981403i \(0.561484\pi\)
\(68\) 3.74576 0.454240
\(69\) −0.562960 −0.0677724
\(70\) −3.37520 −0.403413
\(71\) 11.8409 1.40526 0.702631 0.711554i \(-0.252008\pi\)
0.702631 + 0.711554i \(0.252008\pi\)
\(72\) 2.68308 0.316204
\(73\) −9.43228 −1.10397 −0.551983 0.833856i \(-0.686129\pi\)
−0.551983 + 0.833856i \(0.686129\pi\)
\(74\) 0.608639 0.0707529
\(75\) 5.70417 0.658661
\(76\) 4.55822 0.522864
\(77\) −0.440225 −0.0501683
\(78\) 1.54273 0.174680
\(79\) −9.73748 −1.09555 −0.547776 0.836625i \(-0.684525\pi\)
−0.547776 + 0.836625i \(0.684525\pi\)
\(80\) −3.89005 −0.434920
\(81\) 6.24813 0.694236
\(82\) 9.86356 1.08925
\(83\) −3.20604 −0.351909 −0.175954 0.984398i \(-0.556301\pi\)
−0.175954 + 0.984398i \(0.556301\pi\)
\(84\) −0.488452 −0.0532945
\(85\) −14.5712 −1.58047
\(86\) 1.26441 0.136345
\(87\) 3.33996 0.358081
\(88\) −0.507376 −0.0540865
\(89\) 2.82208 0.299140 0.149570 0.988751i \(-0.452211\pi\)
0.149570 + 0.988751i \(0.452211\pi\)
\(90\) −10.4373 −1.10019
\(91\) 2.37770 0.249251
\(92\) −1.00000 −0.104257
\(93\) −1.04696 −0.108564
\(94\) −8.01654 −0.826843
\(95\) −17.7317 −1.81923
\(96\) −0.562960 −0.0574568
\(97\) 5.75507 0.584339 0.292170 0.956367i \(-0.405623\pi\)
0.292170 + 0.956367i \(0.405623\pi\)
\(98\) 6.24718 0.631061
\(99\) −1.36133 −0.136819
\(100\) 10.1325 1.01325
\(101\) 9.45619 0.940926 0.470463 0.882420i \(-0.344087\pi\)
0.470463 + 0.882420i \(0.344087\pi\)
\(102\) −2.10871 −0.208794
\(103\) 6.08876 0.599943 0.299971 0.953948i \(-0.403023\pi\)
0.299971 + 0.953948i \(0.403023\pi\)
\(104\) 2.74039 0.268718
\(105\) 1.90010 0.185431
\(106\) −4.96984 −0.482713
\(107\) 7.08845 0.685267 0.342633 0.939469i \(-0.388681\pi\)
0.342633 + 0.939469i \(0.388681\pi\)
\(108\) −3.19934 −0.307857
\(109\) −12.7903 −1.22509 −0.612546 0.790435i \(-0.709854\pi\)
−0.612546 + 0.790435i \(0.709854\pi\)
\(110\) 1.97372 0.188187
\(111\) −0.342639 −0.0325219
\(112\) −0.867650 −0.0819852
\(113\) 18.5333 1.74347 0.871734 0.489979i \(-0.162996\pi\)
0.871734 + 0.489979i \(0.162996\pi\)
\(114\) −2.56609 −0.240337
\(115\) 3.89005 0.362749
\(116\) 5.93286 0.550852
\(117\) 7.35269 0.679756
\(118\) −5.28644 −0.486656
\(119\) −3.25001 −0.297928
\(120\) 2.18994 0.199913
\(121\) −10.7426 −0.976597
\(122\) −13.9133 −1.25965
\(123\) −5.55279 −0.500678
\(124\) −1.85973 −0.167009
\(125\) −19.9655 −1.78577
\(126\) −2.32797 −0.207392
\(127\) 8.13209 0.721606 0.360803 0.932642i \(-0.382503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.711812 −0.0626716
\(130\) −10.6603 −0.934967
\(131\) −1.00000 −0.0873704
\(132\) 0.285633 0.0248611
\(133\) −3.95494 −0.342937
\(134\) 3.14252 0.271472
\(135\) 12.4456 1.07115
\(136\) −3.74576 −0.321196
\(137\) −6.54458 −0.559141 −0.279571 0.960125i \(-0.590192\pi\)
−0.279571 + 0.960125i \(0.590192\pi\)
\(138\) 0.562960 0.0479223
\(139\) −9.03391 −0.766246 −0.383123 0.923697i \(-0.625151\pi\)
−0.383123 + 0.923697i \(0.625151\pi\)
\(140\) 3.37520 0.285256
\(141\) 4.51299 0.380062
\(142\) −11.8409 −0.993670
\(143\) −1.39041 −0.116272
\(144\) −2.68308 −0.223590
\(145\) −23.0791 −1.91662
\(146\) 9.43228 0.780621
\(147\) −3.51691 −0.290070
\(148\) −0.608639 −0.0500298
\(149\) −8.90678 −0.729672 −0.364836 0.931072i \(-0.618875\pi\)
−0.364836 + 0.931072i \(0.618875\pi\)
\(150\) −5.70417 −0.465744
\(151\) −10.9588 −0.891813 −0.445907 0.895080i \(-0.647119\pi\)
−0.445907 + 0.895080i \(0.647119\pi\)
\(152\) −4.55822 −0.369721
\(153\) −10.0502 −0.812507
\(154\) 0.440225 0.0354744
\(155\) 7.23445 0.581085
\(156\) −1.54273 −0.123517
\(157\) −1.72106 −0.137356 −0.0686779 0.997639i \(-0.521878\pi\)
−0.0686779 + 0.997639i \(0.521878\pi\)
\(158\) 9.73748 0.774672
\(159\) 2.79782 0.221881
\(160\) 3.89005 0.307535
\(161\) 0.867650 0.0683804
\(162\) −6.24813 −0.490899
\(163\) −16.0234 −1.25505 −0.627526 0.778596i \(-0.715932\pi\)
−0.627526 + 0.778596i \(0.715932\pi\)
\(164\) −9.86356 −0.770214
\(165\) −1.11112 −0.0865009
\(166\) 3.20604 0.248837
\(167\) 0.505553 0.0391209 0.0195604 0.999809i \(-0.493773\pi\)
0.0195604 + 0.999809i \(0.493773\pi\)
\(168\) 0.488452 0.0376849
\(169\) −5.49024 −0.422326
\(170\) 14.5712 1.11756
\(171\) −12.2301 −0.935256
\(172\) −1.26441 −0.0964104
\(173\) −3.02549 −0.230024 −0.115012 0.993364i \(-0.536691\pi\)
−0.115012 + 0.993364i \(0.536691\pi\)
\(174\) −3.33996 −0.253202
\(175\) −8.79143 −0.664570
\(176\) 0.507376 0.0382449
\(177\) 2.97605 0.223694
\(178\) −2.82208 −0.211524
\(179\) −15.7268 −1.17548 −0.587739 0.809050i \(-0.699982\pi\)
−0.587739 + 0.809050i \(0.699982\pi\)
\(180\) 10.4373 0.777950
\(181\) −15.5241 −1.15390 −0.576948 0.816781i \(-0.695757\pi\)
−0.576948 + 0.816781i \(0.695757\pi\)
\(182\) −2.37770 −0.176247
\(183\) 7.83263 0.579005
\(184\) 1.00000 0.0737210
\(185\) 2.36763 0.174072
\(186\) 1.04696 0.0767665
\(187\) 1.90051 0.138979
\(188\) 8.01654 0.584667
\(189\) 2.77591 0.201918
\(190\) 17.7317 1.28639
\(191\) 0.403227 0.0291765 0.0145882 0.999894i \(-0.495356\pi\)
0.0145882 + 0.999894i \(0.495356\pi\)
\(192\) 0.562960 0.0406281
\(193\) −14.3644 −1.03397 −0.516985 0.855994i \(-0.672946\pi\)
−0.516985 + 0.855994i \(0.672946\pi\)
\(194\) −5.75507 −0.413190
\(195\) 6.00130 0.429762
\(196\) −6.24718 −0.446227
\(197\) 6.65067 0.473841 0.236920 0.971529i \(-0.423862\pi\)
0.236920 + 0.971529i \(0.423862\pi\)
\(198\) 1.36133 0.0967455
\(199\) 5.24685 0.371939 0.185970 0.982555i \(-0.440457\pi\)
0.185970 + 0.982555i \(0.440457\pi\)
\(200\) −10.1325 −0.716474
\(201\) −1.76911 −0.124783
\(202\) −9.45619 −0.665335
\(203\) −5.14764 −0.361294
\(204\) 2.10871 0.147639
\(205\) 38.3697 2.67986
\(206\) −6.08876 −0.424224
\(207\) 2.68308 0.186487
\(208\) −2.74039 −0.190012
\(209\) 2.31273 0.159975
\(210\) −1.90010 −0.131119
\(211\) 3.59198 0.247282 0.123641 0.992327i \(-0.460543\pi\)
0.123641 + 0.992327i \(0.460543\pi\)
\(212\) 4.96984 0.341330
\(213\) 6.66598 0.456745
\(214\) −7.08845 −0.484557
\(215\) 4.91862 0.335447
\(216\) 3.19934 0.217688
\(217\) 1.61360 0.109538
\(218\) 12.7903 0.866270
\(219\) −5.31000 −0.358816
\(220\) −1.97372 −0.133068
\(221\) −10.2649 −0.690489
\(222\) 0.342639 0.0229964
\(223\) 24.9469 1.67057 0.835285 0.549817i \(-0.185303\pi\)
0.835285 + 0.549817i \(0.185303\pi\)
\(224\) 0.867650 0.0579723
\(225\) −27.1862 −1.81241
\(226\) −18.5333 −1.23282
\(227\) 3.87747 0.257357 0.128678 0.991686i \(-0.458927\pi\)
0.128678 + 0.991686i \(0.458927\pi\)
\(228\) 2.56609 0.169944
\(229\) 2.35944 0.155916 0.0779579 0.996957i \(-0.475160\pi\)
0.0779579 + 0.996957i \(0.475160\pi\)
\(230\) −3.89005 −0.256502
\(231\) −0.247829 −0.0163060
\(232\) −5.93286 −0.389511
\(233\) 1.47211 0.0964414 0.0482207 0.998837i \(-0.484645\pi\)
0.0482207 + 0.998837i \(0.484645\pi\)
\(234\) −7.35269 −0.480660
\(235\) −31.1847 −2.03427
\(236\) 5.28644 0.344118
\(237\) −5.48181 −0.356082
\(238\) 3.25001 0.210667
\(239\) 18.8116 1.21682 0.608409 0.793623i \(-0.291808\pi\)
0.608409 + 0.793623i \(0.291808\pi\)
\(240\) −2.18994 −0.141360
\(241\) −26.1881 −1.68692 −0.843462 0.537188i \(-0.819486\pi\)
−0.843462 + 0.537188i \(0.819486\pi\)
\(242\) 10.7426 0.690558
\(243\) 13.1155 0.841358
\(244\) 13.9133 0.890708
\(245\) 24.3018 1.55259
\(246\) 5.55279 0.354033
\(247\) −12.4913 −0.794804
\(248\) 1.85973 0.118093
\(249\) −1.80487 −0.114379
\(250\) 19.9655 1.26273
\(251\) 1.24316 0.0784673 0.0392336 0.999230i \(-0.487508\pi\)
0.0392336 + 0.999230i \(0.487508\pi\)
\(252\) 2.32797 0.146648
\(253\) −0.507376 −0.0318985
\(254\) −8.13209 −0.510252
\(255\) −8.20299 −0.513691
\(256\) 1.00000 0.0625000
\(257\) −28.9058 −1.80310 −0.901548 0.432679i \(-0.857568\pi\)
−0.901548 + 0.432679i \(0.857568\pi\)
\(258\) 0.711812 0.0443155
\(259\) 0.528086 0.0328136
\(260\) 10.6603 0.661122
\(261\) −15.9183 −0.985319
\(262\) 1.00000 0.0617802
\(263\) −19.0743 −1.17617 −0.588086 0.808798i \(-0.700118\pi\)
−0.588086 + 0.808798i \(0.700118\pi\)
\(264\) −0.285633 −0.0175795
\(265\) −19.3329 −1.18761
\(266\) 3.95494 0.242493
\(267\) 1.58872 0.0972281
\(268\) −3.14252 −0.191960
\(269\) −29.5171 −1.79969 −0.899846 0.436208i \(-0.856321\pi\)
−0.899846 + 0.436208i \(0.856321\pi\)
\(270\) −12.4456 −0.757415
\(271\) −15.0703 −0.915453 −0.457727 0.889093i \(-0.651336\pi\)
−0.457727 + 0.889093i \(0.651336\pi\)
\(272\) 3.74576 0.227120
\(273\) 1.33855 0.0810128
\(274\) 6.54458 0.395373
\(275\) 5.14098 0.310012
\(276\) −0.562960 −0.0338862
\(277\) 7.02450 0.422061 0.211031 0.977479i \(-0.432318\pi\)
0.211031 + 0.977479i \(0.432318\pi\)
\(278\) 9.03391 0.541818
\(279\) 4.98981 0.298732
\(280\) −3.37520 −0.201707
\(281\) −0.665447 −0.0396972 −0.0198486 0.999803i \(-0.506318\pi\)
−0.0198486 + 0.999803i \(0.506318\pi\)
\(282\) −4.51299 −0.268745
\(283\) −6.65446 −0.395567 −0.197783 0.980246i \(-0.563374\pi\)
−0.197783 + 0.980246i \(0.563374\pi\)
\(284\) 11.8409 0.702631
\(285\) −9.98223 −0.591296
\(286\) 1.39041 0.0822168
\(287\) 8.55811 0.505169
\(288\) 2.68308 0.158102
\(289\) −2.96930 −0.174664
\(290\) 23.0791 1.35525
\(291\) 3.23988 0.189925
\(292\) −9.43228 −0.551983
\(293\) −11.6228 −0.679009 −0.339504 0.940604i \(-0.610259\pi\)
−0.339504 + 0.940604i \(0.610259\pi\)
\(294\) 3.51691 0.205111
\(295\) −20.5645 −1.19731
\(296\) 0.608639 0.0353764
\(297\) −1.62327 −0.0941918
\(298\) 8.90678 0.515956
\(299\) 2.74039 0.158481
\(300\) 5.70417 0.329330
\(301\) 1.09707 0.0632338
\(302\) 10.9588 0.630607
\(303\) 5.32346 0.305825
\(304\) 4.55822 0.261432
\(305\) −54.1234 −3.09910
\(306\) 10.0502 0.574529
\(307\) −22.6431 −1.29231 −0.646154 0.763207i \(-0.723624\pi\)
−0.646154 + 0.763207i \(0.723624\pi\)
\(308\) −0.440225 −0.0250842
\(309\) 3.42772 0.194996
\(310\) −7.23445 −0.410889
\(311\) −20.0523 −1.13706 −0.568531 0.822662i \(-0.692488\pi\)
−0.568531 + 0.822662i \(0.692488\pi\)
\(312\) 1.54273 0.0873400
\(313\) −0.443118 −0.0250465 −0.0125233 0.999922i \(-0.503986\pi\)
−0.0125233 + 0.999922i \(0.503986\pi\)
\(314\) 1.72106 0.0971253
\(315\) −9.05592 −0.510243
\(316\) −9.73748 −0.547776
\(317\) −6.21367 −0.348995 −0.174497 0.984658i \(-0.555830\pi\)
−0.174497 + 0.984658i \(0.555830\pi\)
\(318\) −2.79782 −0.156894
\(319\) 3.01019 0.168538
\(320\) −3.89005 −0.217460
\(321\) 3.99051 0.222729
\(322\) −0.867650 −0.0483522
\(323\) 17.0740 0.950022
\(324\) 6.24813 0.347118
\(325\) −27.7670 −1.54023
\(326\) 16.0234 0.887455
\(327\) −7.20044 −0.398185
\(328\) 9.86356 0.544624
\(329\) −6.95555 −0.383472
\(330\) 1.11112 0.0611654
\(331\) 32.4781 1.78516 0.892579 0.450891i \(-0.148894\pi\)
0.892579 + 0.450891i \(0.148894\pi\)
\(332\) −3.20604 −0.175954
\(333\) 1.63303 0.0894892
\(334\) −0.505553 −0.0276626
\(335\) 12.2245 0.667898
\(336\) −0.488452 −0.0266472
\(337\) 2.43414 0.132596 0.0662979 0.997800i \(-0.478881\pi\)
0.0662979 + 0.997800i \(0.478881\pi\)
\(338\) 5.49024 0.298630
\(339\) 10.4335 0.566671
\(340\) −14.5712 −0.790233
\(341\) −0.943585 −0.0510980
\(342\) 12.2301 0.661326
\(343\) 11.4939 0.620613
\(344\) 1.26441 0.0681725
\(345\) 2.18994 0.117902
\(346\) 3.02549 0.162651
\(347\) −7.34369 −0.394230 −0.197115 0.980380i \(-0.563157\pi\)
−0.197115 + 0.980380i \(0.563157\pi\)
\(348\) 3.33996 0.179041
\(349\) 22.6977 1.21498 0.607491 0.794327i \(-0.292176\pi\)
0.607491 + 0.794327i \(0.292176\pi\)
\(350\) 8.79143 0.469922
\(351\) 8.76746 0.467973
\(352\) −0.507376 −0.0270433
\(353\) 4.70965 0.250670 0.125335 0.992115i \(-0.459999\pi\)
0.125335 + 0.992115i \(0.459999\pi\)
\(354\) −2.97605 −0.158175
\(355\) −46.0618 −2.44471
\(356\) 2.82208 0.149570
\(357\) −1.82962 −0.0968339
\(358\) 15.7268 0.831189
\(359\) −27.9901 −1.47726 −0.738630 0.674111i \(-0.764527\pi\)
−0.738630 + 0.674111i \(0.764527\pi\)
\(360\) −10.4373 −0.550094
\(361\) 1.77738 0.0935462
\(362\) 15.5241 0.815928
\(363\) −6.04763 −0.317418
\(364\) 2.37770 0.124626
\(365\) 36.6920 1.92055
\(366\) −7.83263 −0.409418
\(367\) −10.5595 −0.551199 −0.275599 0.961273i \(-0.588876\pi\)
−0.275599 + 0.961273i \(0.588876\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 26.4647 1.37770
\(370\) −2.36763 −0.123087
\(371\) −4.31208 −0.223872
\(372\) −1.04696 −0.0542821
\(373\) −20.6225 −1.06779 −0.533897 0.845550i \(-0.679273\pi\)
−0.533897 + 0.845550i \(0.679273\pi\)
\(374\) −1.90051 −0.0982730
\(375\) −11.2398 −0.580421
\(376\) −8.01654 −0.413422
\(377\) −16.2584 −0.837349
\(378\) −2.77591 −0.142777
\(379\) −0.843533 −0.0433294 −0.0216647 0.999765i \(-0.506897\pi\)
−0.0216647 + 0.999765i \(0.506897\pi\)
\(380\) −17.7317 −0.909617
\(381\) 4.57804 0.234540
\(382\) −0.403227 −0.0206309
\(383\) 0.943042 0.0481872 0.0240936 0.999710i \(-0.492330\pi\)
0.0240936 + 0.999710i \(0.492330\pi\)
\(384\) −0.562960 −0.0287284
\(385\) 1.71250 0.0872769
\(386\) 14.3644 0.731127
\(387\) 3.39251 0.172451
\(388\) 5.75507 0.292170
\(389\) 7.05035 0.357467 0.178733 0.983898i \(-0.442800\pi\)
0.178733 + 0.983898i \(0.442800\pi\)
\(390\) −6.00130 −0.303888
\(391\) −3.74576 −0.189431
\(392\) 6.24718 0.315530
\(393\) −0.562960 −0.0283976
\(394\) −6.65067 −0.335056
\(395\) 37.8792 1.90591
\(396\) −1.36133 −0.0684094
\(397\) −3.30514 −0.165880 −0.0829402 0.996555i \(-0.526431\pi\)
−0.0829402 + 0.996555i \(0.526431\pi\)
\(398\) −5.24685 −0.263001
\(399\) −2.22647 −0.111463
\(400\) 10.1325 0.506623
\(401\) −17.5817 −0.877988 −0.438994 0.898490i \(-0.644665\pi\)
−0.438994 + 0.898490i \(0.644665\pi\)
\(402\) 1.76911 0.0882352
\(403\) 5.09640 0.253870
\(404\) 9.45619 0.470463
\(405\) −24.3055 −1.20775
\(406\) 5.14764 0.255473
\(407\) −0.308809 −0.0153071
\(408\) −2.10871 −0.104397
\(409\) −6.48197 −0.320513 −0.160256 0.987075i \(-0.551232\pi\)
−0.160256 + 0.987075i \(0.551232\pi\)
\(410\) −38.3697 −1.89494
\(411\) −3.68434 −0.181735
\(412\) 6.08876 0.299971
\(413\) −4.58678 −0.225701
\(414\) −2.68308 −0.131866
\(415\) 12.4716 0.612209
\(416\) 2.74039 0.134359
\(417\) −5.08573 −0.249049
\(418\) −2.31273 −0.113120
\(419\) 21.0811 1.02988 0.514940 0.857226i \(-0.327814\pi\)
0.514940 + 0.857226i \(0.327814\pi\)
\(420\) 1.90010 0.0927154
\(421\) −3.48417 −0.169808 −0.0849041 0.996389i \(-0.527058\pi\)
−0.0849041 + 0.996389i \(0.527058\pi\)
\(422\) −3.59198 −0.174855
\(423\) −21.5090 −1.04580
\(424\) −4.96984 −0.241357
\(425\) 37.9538 1.84103
\(426\) −6.66598 −0.322968
\(427\) −12.0719 −0.584199
\(428\) 7.08845 0.342633
\(429\) −0.782746 −0.0377913
\(430\) −4.91862 −0.237197
\(431\) −15.4716 −0.745243 −0.372621 0.927983i \(-0.621541\pi\)
−0.372621 + 0.927983i \(0.621541\pi\)
\(432\) −3.19934 −0.153928
\(433\) −20.3427 −0.977606 −0.488803 0.872394i \(-0.662566\pi\)
−0.488803 + 0.872394i \(0.662566\pi\)
\(434\) −1.61360 −0.0774552
\(435\) −12.9926 −0.622948
\(436\) −12.7903 −0.612546
\(437\) −4.55822 −0.218049
\(438\) 5.31000 0.253721
\(439\) 17.6676 0.843229 0.421614 0.906775i \(-0.361464\pi\)
0.421614 + 0.906775i \(0.361464\pi\)
\(440\) 1.97372 0.0940933
\(441\) 16.7617 0.798175
\(442\) 10.2649 0.488249
\(443\) 20.9706 0.996346 0.498173 0.867078i \(-0.334005\pi\)
0.498173 + 0.867078i \(0.334005\pi\)
\(444\) −0.342639 −0.0162609
\(445\) −10.9780 −0.520409
\(446\) −24.9469 −1.18127
\(447\) −5.01416 −0.237162
\(448\) −0.867650 −0.0409926
\(449\) 0.184554 0.00870963 0.00435482 0.999991i \(-0.498614\pi\)
0.00435482 + 0.999991i \(0.498614\pi\)
\(450\) 27.1862 1.28157
\(451\) −5.00454 −0.235654
\(452\) 18.5333 0.871734
\(453\) −6.16935 −0.289862
\(454\) −3.87747 −0.181979
\(455\) −9.24938 −0.433618
\(456\) −2.56609 −0.120168
\(457\) 0.149083 0.00697381 0.00348691 0.999994i \(-0.498890\pi\)
0.00348691 + 0.999994i \(0.498890\pi\)
\(458\) −2.35944 −0.110249
\(459\) −11.9840 −0.559364
\(460\) 3.89005 0.181374
\(461\) −16.6132 −0.773756 −0.386878 0.922131i \(-0.626446\pi\)
−0.386878 + 0.922131i \(0.626446\pi\)
\(462\) 0.247829 0.0115300
\(463\) 31.6334 1.47013 0.735065 0.677996i \(-0.237152\pi\)
0.735065 + 0.677996i \(0.237152\pi\)
\(464\) 5.93286 0.275426
\(465\) 4.07271 0.188867
\(466\) −1.47211 −0.0681944
\(467\) −7.99381 −0.369909 −0.184955 0.982747i \(-0.559214\pi\)
−0.184955 + 0.982747i \(0.559214\pi\)
\(468\) 7.35269 0.339878
\(469\) 2.72660 0.125903
\(470\) 31.1847 1.43844
\(471\) −0.968890 −0.0446441
\(472\) −5.28644 −0.243328
\(473\) −0.641532 −0.0294977
\(474\) 5.48181 0.251788
\(475\) 46.1860 2.11916
\(476\) −3.25001 −0.148964
\(477\) −13.3345 −0.610543
\(478\) −18.8116 −0.860421
\(479\) 25.9475 1.18557 0.592786 0.805360i \(-0.298028\pi\)
0.592786 + 0.805360i \(0.298028\pi\)
\(480\) 2.18994 0.0999566
\(481\) 1.66791 0.0760502
\(482\) 26.1881 1.19284
\(483\) 0.488452 0.0222253
\(484\) −10.7426 −0.488299
\(485\) −22.3875 −1.01656
\(486\) −13.1155 −0.594930
\(487\) 29.3717 1.33096 0.665479 0.746417i \(-0.268227\pi\)
0.665479 + 0.746417i \(0.268227\pi\)
\(488\) −13.9133 −0.629826
\(489\) −9.02054 −0.407923
\(490\) −24.3018 −1.09785
\(491\) 28.1115 1.26865 0.634327 0.773065i \(-0.281277\pi\)
0.634327 + 0.773065i \(0.281277\pi\)
\(492\) −5.55279 −0.250339
\(493\) 22.2231 1.00088
\(494\) 12.4913 0.562011
\(495\) 5.29564 0.238021
\(496\) −1.85973 −0.0835045
\(497\) −10.2738 −0.460843
\(498\) 1.80487 0.0808782
\(499\) 14.3639 0.643015 0.321508 0.946907i \(-0.395810\pi\)
0.321508 + 0.946907i \(0.395810\pi\)
\(500\) −19.9655 −0.892886
\(501\) 0.284606 0.0127153
\(502\) −1.24316 −0.0554848
\(503\) 25.9961 1.15911 0.579554 0.814934i \(-0.303227\pi\)
0.579554 + 0.814934i \(0.303227\pi\)
\(504\) −2.32797 −0.103696
\(505\) −36.7850 −1.63691
\(506\) 0.507376 0.0225556
\(507\) −3.09078 −0.137266
\(508\) 8.13209 0.360803
\(509\) 1.10438 0.0489506 0.0244753 0.999700i \(-0.492208\pi\)
0.0244753 + 0.999700i \(0.492208\pi\)
\(510\) 8.20299 0.363234
\(511\) 8.18392 0.362035
\(512\) −1.00000 −0.0441942
\(513\) −14.5833 −0.643869
\(514\) 28.9058 1.27498
\(515\) −23.6855 −1.04371
\(516\) −0.711812 −0.0313358
\(517\) 4.06741 0.178884
\(518\) −0.528086 −0.0232028
\(519\) −1.70323 −0.0747634
\(520\) −10.6603 −0.467484
\(521\) 31.3119 1.37180 0.685900 0.727695i \(-0.259409\pi\)
0.685900 + 0.727695i \(0.259409\pi\)
\(522\) 15.9183 0.696726
\(523\) −4.33176 −0.189415 −0.0947074 0.995505i \(-0.530192\pi\)
−0.0947074 + 0.995505i \(0.530192\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −4.94922 −0.216002
\(526\) 19.0743 0.831680
\(527\) −6.96611 −0.303449
\(528\) 0.285633 0.0124306
\(529\) 1.00000 0.0434783
\(530\) 19.3329 0.839768
\(531\) −14.1839 −0.615530
\(532\) −3.95494 −0.171468
\(533\) 27.0300 1.17080
\(534\) −1.58872 −0.0687506
\(535\) −27.5744 −1.19215
\(536\) 3.14252 0.135736
\(537\) −8.85357 −0.382060
\(538\) 29.5171 1.27257
\(539\) −3.16967 −0.136528
\(540\) 12.4456 0.535573
\(541\) 38.7795 1.66726 0.833630 0.552323i \(-0.186258\pi\)
0.833630 + 0.552323i \(0.186258\pi\)
\(542\) 15.0703 0.647323
\(543\) −8.73944 −0.375045
\(544\) −3.74576 −0.160598
\(545\) 49.7550 2.13127
\(546\) −1.33855 −0.0572847
\(547\) 33.5932 1.43634 0.718171 0.695866i \(-0.244979\pi\)
0.718171 + 0.695866i \(0.244979\pi\)
\(548\) −6.54458 −0.279571
\(549\) −37.3304 −1.59322
\(550\) −5.14098 −0.219212
\(551\) 27.0433 1.15208
\(552\) 0.562960 0.0239612
\(553\) 8.44872 0.359276
\(554\) −7.02450 −0.298443
\(555\) 1.33288 0.0565777
\(556\) −9.03391 −0.383123
\(557\) −36.3397 −1.53976 −0.769881 0.638188i \(-0.779684\pi\)
−0.769881 + 0.638188i \(0.779684\pi\)
\(558\) −4.98981 −0.211235
\(559\) 3.46499 0.146553
\(560\) 3.37520 0.142628
\(561\) 1.06991 0.0451716
\(562\) 0.665447 0.0280702
\(563\) −0.485090 −0.0204441 −0.0102220 0.999948i \(-0.503254\pi\)
−0.0102220 + 0.999948i \(0.503254\pi\)
\(564\) 4.51299 0.190031
\(565\) −72.0955 −3.03308
\(566\) 6.65446 0.279708
\(567\) −5.42119 −0.227668
\(568\) −11.8409 −0.496835
\(569\) −6.11144 −0.256205 −0.128102 0.991761i \(-0.540889\pi\)
−0.128102 + 0.991761i \(0.540889\pi\)
\(570\) 9.98223 0.418110
\(571\) −12.3642 −0.517427 −0.258713 0.965954i \(-0.583299\pi\)
−0.258713 + 0.965954i \(0.583299\pi\)
\(572\) −1.39041 −0.0581360
\(573\) 0.227001 0.00948308
\(574\) −8.55811 −0.357209
\(575\) −10.1325 −0.422553
\(576\) −2.68308 −0.111795
\(577\) 9.10810 0.379175 0.189588 0.981864i \(-0.439285\pi\)
0.189588 + 0.981864i \(0.439285\pi\)
\(578\) 2.96930 0.123506
\(579\) −8.08656 −0.336066
\(580\) −23.0791 −0.958308
\(581\) 2.78172 0.115405
\(582\) −3.23988 −0.134297
\(583\) 2.52158 0.104433
\(584\) 9.43228 0.390311
\(585\) −28.6023 −1.18256
\(586\) 11.6228 0.480132
\(587\) −16.8302 −0.694657 −0.347328 0.937744i \(-0.612911\pi\)
−0.347328 + 0.937744i \(0.612911\pi\)
\(588\) −3.51691 −0.145035
\(589\) −8.47708 −0.349292
\(590\) 20.5645 0.846627
\(591\) 3.74406 0.154010
\(592\) −0.608639 −0.0250149
\(593\) −23.4869 −0.964490 −0.482245 0.876036i \(-0.660178\pi\)
−0.482245 + 0.876036i \(0.660178\pi\)
\(594\) 1.62327 0.0666036
\(595\) 12.6427 0.518299
\(596\) −8.90678 −0.364836
\(597\) 2.95376 0.120890
\(598\) −2.74039 −0.112063
\(599\) −1.53838 −0.0628567 −0.0314284 0.999506i \(-0.510006\pi\)
−0.0314284 + 0.999506i \(0.510006\pi\)
\(600\) −5.70417 −0.232872
\(601\) −36.9377 −1.50672 −0.753359 0.657609i \(-0.771568\pi\)
−0.753359 + 0.657609i \(0.771568\pi\)
\(602\) −1.09707 −0.0447131
\(603\) 8.43161 0.343362
\(604\) −10.9588 −0.445907
\(605\) 41.7891 1.69897
\(606\) −5.32346 −0.216251
\(607\) 42.2010 1.71289 0.856444 0.516240i \(-0.172669\pi\)
0.856444 + 0.516240i \(0.172669\pi\)
\(608\) −4.55822 −0.184860
\(609\) −2.89792 −0.117430
\(610\) 54.1234 2.19139
\(611\) −21.9685 −0.888750
\(612\) −10.0502 −0.406253
\(613\) −11.0111 −0.444734 −0.222367 0.974963i \(-0.571378\pi\)
−0.222367 + 0.974963i \(0.571378\pi\)
\(614\) 22.6431 0.913799
\(615\) 21.6006 0.871020
\(616\) 0.440225 0.0177372
\(617\) −6.45232 −0.259761 −0.129880 0.991530i \(-0.541459\pi\)
−0.129880 + 0.991530i \(0.541459\pi\)
\(618\) −3.42772 −0.137883
\(619\) −31.6631 −1.27265 −0.636323 0.771423i \(-0.719545\pi\)
−0.636323 + 0.771423i \(0.719545\pi\)
\(620\) 7.23445 0.290543
\(621\) 3.19934 0.128385
\(622\) 20.0523 0.804025
\(623\) −2.44858 −0.0981003
\(624\) −1.54273 −0.0617587
\(625\) 27.0046 1.08018
\(626\) 0.443118 0.0177106
\(627\) 1.30198 0.0519959
\(628\) −1.72106 −0.0686779
\(629\) −2.27981 −0.0909022
\(630\) 9.05592 0.360796
\(631\) 11.9404 0.475339 0.237669 0.971346i \(-0.423617\pi\)
0.237669 + 0.971346i \(0.423617\pi\)
\(632\) 9.73748 0.387336
\(633\) 2.02214 0.0803730
\(634\) 6.21367 0.246776
\(635\) −31.6342 −1.25536
\(636\) 2.79782 0.110941
\(637\) 17.1197 0.678309
\(638\) −3.01019 −0.119175
\(639\) −31.7702 −1.25681
\(640\) 3.89005 0.153768
\(641\) −10.4927 −0.414438 −0.207219 0.978295i \(-0.566441\pi\)
−0.207219 + 0.978295i \(0.566441\pi\)
\(642\) −3.99051 −0.157493
\(643\) −31.2591 −1.23274 −0.616370 0.787456i \(-0.711398\pi\)
−0.616370 + 0.787456i \(0.711398\pi\)
\(644\) 0.867650 0.0341902
\(645\) 2.76898 0.109029
\(646\) −17.0740 −0.671767
\(647\) 20.3952 0.801816 0.400908 0.916118i \(-0.368695\pi\)
0.400908 + 0.916118i \(0.368695\pi\)
\(648\) −6.24813 −0.245450
\(649\) 2.68222 0.105286
\(650\) 27.7670 1.08911
\(651\) 0.908391 0.0356026
\(652\) −16.0234 −0.627526
\(653\) 13.1835 0.515911 0.257955 0.966157i \(-0.416951\pi\)
0.257955 + 0.966157i \(0.416951\pi\)
\(654\) 7.20044 0.281559
\(655\) 3.89005 0.151997
\(656\) −9.86356 −0.385107
\(657\) 25.3075 0.987341
\(658\) 6.95555 0.271156
\(659\) −31.6090 −1.23131 −0.615656 0.788015i \(-0.711109\pi\)
−0.615656 + 0.788015i \(0.711109\pi\)
\(660\) −1.11112 −0.0432504
\(661\) −43.5918 −1.69552 −0.847762 0.530377i \(-0.822051\pi\)
−0.847762 + 0.530377i \(0.822051\pi\)
\(662\) −32.4781 −1.26230
\(663\) −5.77870 −0.224426
\(664\) 3.20604 0.124418
\(665\) 15.3849 0.596601
\(666\) −1.63303 −0.0632784
\(667\) −5.93286 −0.229721
\(668\) 0.505553 0.0195604
\(669\) 14.0441 0.542977
\(670\) −12.2245 −0.472275
\(671\) 7.05928 0.272521
\(672\) 0.488452 0.0188424
\(673\) −5.69159 −0.219395 −0.109697 0.993965i \(-0.534988\pi\)
−0.109697 + 0.993965i \(0.534988\pi\)
\(674\) −2.43414 −0.0937595
\(675\) −32.4172 −1.24774
\(676\) −5.49024 −0.211163
\(677\) 27.7504 1.06653 0.533267 0.845947i \(-0.320964\pi\)
0.533267 + 0.845947i \(0.320964\pi\)
\(678\) −10.4335 −0.400697
\(679\) −4.99339 −0.191629
\(680\) 14.5712 0.558779
\(681\) 2.18286 0.0836473
\(682\) 0.943585 0.0361317
\(683\) −11.9064 −0.455584 −0.227792 0.973710i \(-0.573151\pi\)
−0.227792 + 0.973710i \(0.573151\pi\)
\(684\) −12.2301 −0.467628
\(685\) 25.4587 0.972728
\(686\) −11.4939 −0.438840
\(687\) 1.32827 0.0506766
\(688\) −1.26441 −0.0482052
\(689\) −13.6193 −0.518855
\(690\) −2.18994 −0.0833696
\(691\) −36.9998 −1.40754 −0.703769 0.710429i \(-0.748501\pi\)
−0.703769 + 0.710429i \(0.748501\pi\)
\(692\) −3.02549 −0.115012
\(693\) 1.18116 0.0448685
\(694\) 7.34369 0.278763
\(695\) 35.1423 1.33302
\(696\) −3.33996 −0.126601
\(697\) −36.9465 −1.39945
\(698\) −22.6977 −0.859122
\(699\) 0.828741 0.0313459
\(700\) −8.79143 −0.332285
\(701\) 16.4539 0.621456 0.310728 0.950499i \(-0.399427\pi\)
0.310728 + 0.950499i \(0.399427\pi\)
\(702\) −8.76746 −0.330907
\(703\) −2.77431 −0.104635
\(704\) 0.507376 0.0191225
\(705\) −17.5557 −0.661188
\(706\) −4.70965 −0.177250
\(707\) −8.20466 −0.308568
\(708\) 2.97605 0.111847
\(709\) 1.27314 0.0478137 0.0239069 0.999714i \(-0.492389\pi\)
0.0239069 + 0.999714i \(0.492389\pi\)
\(710\) 46.0618 1.72867
\(711\) 26.1264 0.979816
\(712\) −2.82208 −0.105762
\(713\) 1.85973 0.0696476
\(714\) 1.82962 0.0684719
\(715\) 5.40877 0.202276
\(716\) −15.7268 −0.587739
\(717\) 10.5902 0.395496
\(718\) 27.9901 1.04458
\(719\) 25.9542 0.967929 0.483965 0.875088i \(-0.339196\pi\)
0.483965 + 0.875088i \(0.339196\pi\)
\(720\) 10.4373 0.388975
\(721\) −5.28291 −0.196746
\(722\) −1.77738 −0.0661471
\(723\) −14.7429 −0.548293
\(724\) −15.5241 −0.576948
\(725\) 60.1145 2.23260
\(726\) 6.04763 0.224449
\(727\) 35.5548 1.31866 0.659328 0.751856i \(-0.270841\pi\)
0.659328 + 0.751856i \(0.270841\pi\)
\(728\) −2.37770 −0.0881235
\(729\) −11.3609 −0.420774
\(730\) −36.6920 −1.35803
\(731\) −4.73618 −0.175174
\(732\) 7.83263 0.289502
\(733\) 14.2057 0.524699 0.262350 0.964973i \(-0.415503\pi\)
0.262350 + 0.964973i \(0.415503\pi\)
\(734\) 10.5595 0.389757
\(735\) 13.6810 0.504630
\(736\) 1.00000 0.0368605
\(737\) −1.59444 −0.0587319
\(738\) −26.4647 −0.974178
\(739\) −15.6392 −0.575296 −0.287648 0.957736i \(-0.592873\pi\)
−0.287648 + 0.957736i \(0.592873\pi\)
\(740\) 2.36763 0.0870360
\(741\) −7.03211 −0.258331
\(742\) 4.31208 0.158301
\(743\) −32.9894 −1.21026 −0.605132 0.796125i \(-0.706880\pi\)
−0.605132 + 0.796125i \(0.706880\pi\)
\(744\) 1.04696 0.0383832
\(745\) 34.6478 1.26940
\(746\) 20.6225 0.755044
\(747\) 8.60205 0.314733
\(748\) 1.90051 0.0694895
\(749\) −6.15030 −0.224727
\(750\) 11.2398 0.410419
\(751\) −16.6382 −0.607135 −0.303568 0.952810i \(-0.598178\pi\)
−0.303568 + 0.952810i \(0.598178\pi\)
\(752\) 8.01654 0.292333
\(753\) 0.699847 0.0255038
\(754\) 16.2584 0.592095
\(755\) 42.6302 1.55147
\(756\) 2.77591 0.100959
\(757\) −48.4319 −1.76029 −0.880144 0.474707i \(-0.842554\pi\)
−0.880144 + 0.474707i \(0.842554\pi\)
\(758\) 0.843533 0.0306385
\(759\) −0.285633 −0.0103678
\(760\) 17.7317 0.643196
\(761\) 0.666239 0.0241512 0.0120756 0.999927i \(-0.496156\pi\)
0.0120756 + 0.999927i \(0.496156\pi\)
\(762\) −4.57804 −0.165845
\(763\) 11.0975 0.401757
\(764\) 0.403227 0.0145882
\(765\) 39.0956 1.41350
\(766\) −0.943042 −0.0340735
\(767\) −14.4869 −0.523093
\(768\) 0.562960 0.0203141
\(769\) −1.87216 −0.0675117 −0.0337558 0.999430i \(-0.510747\pi\)
−0.0337558 + 0.999430i \(0.510747\pi\)
\(770\) −1.71250 −0.0617141
\(771\) −16.2728 −0.586051
\(772\) −14.3644 −0.516985
\(773\) 7.45580 0.268166 0.134083 0.990970i \(-0.457191\pi\)
0.134083 + 0.990970i \(0.457191\pi\)
\(774\) −3.39251 −0.121941
\(775\) −18.8437 −0.676885
\(776\) −5.75507 −0.206595
\(777\) 0.297291 0.0106653
\(778\) −7.05035 −0.252767
\(779\) −44.9603 −1.61087
\(780\) 6.00130 0.214881
\(781\) 6.00782 0.214977
\(782\) 3.74576 0.133948
\(783\) −18.9813 −0.678335
\(784\) −6.24718 −0.223114
\(785\) 6.69502 0.238955
\(786\) 0.562960 0.0200801
\(787\) −42.1308 −1.50180 −0.750900 0.660416i \(-0.770380\pi\)
−0.750900 + 0.660416i \(0.770380\pi\)
\(788\) 6.65067 0.236920
\(789\) −10.7381 −0.382285
\(790\) −37.8792 −1.34768
\(791\) −16.0804 −0.571754
\(792\) 1.36133 0.0483727
\(793\) −38.1279 −1.35396
\(794\) 3.30514 0.117295
\(795\) −10.8836 −0.386003
\(796\) 5.24685 0.185970
\(797\) 47.4254 1.67989 0.839947 0.542669i \(-0.182586\pi\)
0.839947 + 0.542669i \(0.182586\pi\)
\(798\) 2.22647 0.0788163
\(799\) 30.0280 1.06232
\(800\) −10.1325 −0.358237
\(801\) −7.57187 −0.267539
\(802\) 17.5817 0.620831
\(803\) −4.78572 −0.168884
\(804\) −1.76911 −0.0623917
\(805\) −3.37520 −0.118960
\(806\) −5.09640 −0.179513
\(807\) −16.6170 −0.584945
\(808\) −9.45619 −0.332668
\(809\) 39.7086 1.39608 0.698040 0.716059i \(-0.254056\pi\)
0.698040 + 0.716059i \(0.254056\pi\)
\(810\) 24.3055 0.854009
\(811\) 4.10548 0.144163 0.0720815 0.997399i \(-0.477036\pi\)
0.0720815 + 0.997399i \(0.477036\pi\)
\(812\) −5.14764 −0.180647
\(813\) −8.48395 −0.297545
\(814\) 0.308809 0.0108238
\(815\) 62.3319 2.18339
\(816\) 2.10871 0.0738197
\(817\) −5.76346 −0.201638
\(818\) 6.48197 0.226637
\(819\) −6.37956 −0.222920
\(820\) 38.3697 1.33993
\(821\) −33.9836 −1.18604 −0.593018 0.805189i \(-0.702064\pi\)
−0.593018 + 0.805189i \(0.702064\pi\)
\(822\) 3.68434 0.128506
\(823\) −3.06504 −0.106840 −0.0534202 0.998572i \(-0.517012\pi\)
−0.0534202 + 0.998572i \(0.517012\pi\)
\(824\) −6.08876 −0.212112
\(825\) 2.89416 0.100762
\(826\) 4.58678 0.159594
\(827\) −20.9051 −0.726942 −0.363471 0.931606i \(-0.618408\pi\)
−0.363471 + 0.931606i \(0.618408\pi\)
\(828\) 2.68308 0.0932433
\(829\) −35.1154 −1.21961 −0.609803 0.792553i \(-0.708752\pi\)
−0.609803 + 0.792553i \(0.708752\pi\)
\(830\) −12.4716 −0.432897
\(831\) 3.95451 0.137181
\(832\) −2.74039 −0.0950061
\(833\) −23.4004 −0.810777
\(834\) 5.08573 0.176104
\(835\) −1.96663 −0.0680579
\(836\) 2.31273 0.0799876
\(837\) 5.94993 0.205660
\(838\) −21.0811 −0.728235
\(839\) −35.6940 −1.23229 −0.616147 0.787632i \(-0.711307\pi\)
−0.616147 + 0.787632i \(0.711307\pi\)
\(840\) −1.90010 −0.0655597
\(841\) 6.19881 0.213752
\(842\) 3.48417 0.120073
\(843\) −0.374620 −0.0129026
\(844\) 3.59198 0.123641
\(845\) 21.3573 0.734713
\(846\) 21.5090 0.739495
\(847\) 9.32079 0.320266
\(848\) 4.96984 0.170665
\(849\) −3.74619 −0.128569
\(850\) −37.9538 −1.30180
\(851\) 0.608639 0.0208639
\(852\) 6.66598 0.228373
\(853\) −28.6844 −0.982137 −0.491068 0.871121i \(-0.663393\pi\)
−0.491068 + 0.871121i \(0.663393\pi\)
\(854\) 12.0719 0.413091
\(855\) 47.5755 1.62705
\(856\) −7.08845 −0.242278
\(857\) 51.0458 1.74369 0.871845 0.489782i \(-0.162924\pi\)
0.871845 + 0.489782i \(0.162924\pi\)
\(858\) 0.782746 0.0267225
\(859\) −23.6436 −0.806710 −0.403355 0.915044i \(-0.632156\pi\)
−0.403355 + 0.915044i \(0.632156\pi\)
\(860\) 4.91862 0.167724
\(861\) 4.81787 0.164193
\(862\) 15.4716 0.526966
\(863\) −6.83113 −0.232534 −0.116267 0.993218i \(-0.537093\pi\)
−0.116267 + 0.993218i \(0.537093\pi\)
\(864\) 3.19934 0.108844
\(865\) 11.7693 0.400168
\(866\) 20.3427 0.691272
\(867\) −1.67159 −0.0567703
\(868\) 1.61360 0.0547691
\(869\) −4.94057 −0.167597
\(870\) 12.9926 0.440491
\(871\) 8.61173 0.291797
\(872\) 12.7903 0.433135
\(873\) −15.4413 −0.522609
\(874\) 4.55822 0.154184
\(875\) 17.3231 0.585628
\(876\) −5.31000 −0.179408
\(877\) 30.2626 1.02189 0.510947 0.859612i \(-0.329295\pi\)
0.510947 + 0.859612i \(0.329295\pi\)
\(878\) −17.6676 −0.596253
\(879\) −6.54314 −0.220695
\(880\) −1.97372 −0.0665340
\(881\) 57.0660 1.92260 0.961302 0.275498i \(-0.0888426\pi\)
0.961302 + 0.275498i \(0.0888426\pi\)
\(882\) −16.7617 −0.564395
\(883\) −7.54318 −0.253848 −0.126924 0.991912i \(-0.540510\pi\)
−0.126924 + 0.991912i \(0.540510\pi\)
\(884\) −10.2649 −0.345244
\(885\) −11.5770 −0.389156
\(886\) −20.9706 −0.704523
\(887\) 38.0193 1.27656 0.638281 0.769804i \(-0.279646\pi\)
0.638281 + 0.769804i \(0.279646\pi\)
\(888\) 0.342639 0.0114982
\(889\) −7.05580 −0.236644
\(890\) 10.9780 0.367985
\(891\) 3.17015 0.106204
\(892\) 24.9469 0.835285
\(893\) 36.5412 1.22280
\(894\) 5.01416 0.167699
\(895\) 61.1781 2.04496
\(896\) 0.867650 0.0289861
\(897\) 1.54273 0.0515103
\(898\) −0.184554 −0.00615864
\(899\) −11.0335 −0.367989
\(900\) −27.1862 −0.906206
\(901\) 18.6158 0.620183
\(902\) 5.00454 0.166633
\(903\) 0.617604 0.0205526
\(904\) −18.5333 −0.616409
\(905\) 60.3895 2.00741
\(906\) 6.16935 0.204963
\(907\) −23.1706 −0.769366 −0.384683 0.923049i \(-0.625689\pi\)
−0.384683 + 0.923049i \(0.625689\pi\)
\(908\) 3.87747 0.128678
\(909\) −25.3717 −0.841526
\(910\) 9.24938 0.306614
\(911\) 7.49641 0.248367 0.124184 0.992259i \(-0.460369\pi\)
0.124184 + 0.992259i \(0.460369\pi\)
\(912\) 2.56609 0.0849719
\(913\) −1.62667 −0.0538349
\(914\) −0.149083 −0.00493123
\(915\) −30.4693 −1.00728
\(916\) 2.35944 0.0779579
\(917\) 0.867650 0.0286523
\(918\) 11.9840 0.395530
\(919\) −39.5258 −1.30384 −0.651918 0.758289i \(-0.726035\pi\)
−0.651918 + 0.758289i \(0.726035\pi\)
\(920\) −3.89005 −0.128251
\(921\) −12.7471 −0.420032
\(922\) 16.6132 0.547128
\(923\) −32.4489 −1.06807
\(924\) −0.247829 −0.00815298
\(925\) −6.16702 −0.202770
\(926\) −31.6334 −1.03954
\(927\) −16.3366 −0.536564
\(928\) −5.93286 −0.194756
\(929\) −15.6701 −0.514119 −0.257059 0.966396i \(-0.582754\pi\)
−0.257059 + 0.966396i \(0.582754\pi\)
\(930\) −4.07271 −0.133549
\(931\) −28.4760 −0.933265
\(932\) 1.47211 0.0482207
\(933\) −11.2886 −0.369574
\(934\) 7.99381 0.261565
\(935\) −7.39307 −0.241779
\(936\) −7.35269 −0.240330
\(937\) −36.0191 −1.17669 −0.588346 0.808609i \(-0.700221\pi\)
−0.588346 + 0.808609i \(0.700221\pi\)
\(938\) −2.72660 −0.0890268
\(939\) −0.249458 −0.00814074
\(940\) −31.1847 −1.01713
\(941\) −11.5406 −0.376213 −0.188107 0.982149i \(-0.560235\pi\)
−0.188107 + 0.982149i \(0.560235\pi\)
\(942\) 0.968890 0.0315681
\(943\) 9.86356 0.321202
\(944\) 5.28644 0.172059
\(945\) −10.7984 −0.351273
\(946\) 0.641532 0.0208580
\(947\) −19.4110 −0.630773 −0.315386 0.948963i \(-0.602134\pi\)
−0.315386 + 0.948963i \(0.602134\pi\)
\(948\) −5.48181 −0.178041
\(949\) 25.8482 0.839067
\(950\) −46.1860 −1.49847
\(951\) −3.49805 −0.113432
\(952\) 3.25001 0.105333
\(953\) −20.4627 −0.662852 −0.331426 0.943481i \(-0.607530\pi\)
−0.331426 + 0.943481i \(0.607530\pi\)
\(954\) 13.3345 0.431719
\(955\) −1.56857 −0.0507578
\(956\) 18.8116 0.608409
\(957\) 1.69462 0.0547792
\(958\) −25.9475 −0.838326
\(959\) 5.67841 0.183365
\(960\) −2.18994 −0.0706800
\(961\) −27.5414 −0.888432
\(962\) −1.66791 −0.0537756
\(963\) −19.0189 −0.612874
\(964\) −26.1881 −0.843462
\(965\) 55.8781 1.79878
\(966\) −0.488452 −0.0157157
\(967\) −53.3379 −1.71523 −0.857616 0.514291i \(-0.828055\pi\)
−0.857616 + 0.514291i \(0.828055\pi\)
\(968\) 10.7426 0.345279
\(969\) 9.61197 0.308781
\(970\) 22.3875 0.718820
\(971\) −17.6470 −0.566320 −0.283160 0.959073i \(-0.591383\pi\)
−0.283160 + 0.959073i \(0.591383\pi\)
\(972\) 13.1155 0.420679
\(973\) 7.83827 0.251283
\(974\) −29.3717 −0.941129
\(975\) −15.6317 −0.500614
\(976\) 13.9133 0.445354
\(977\) −22.2704 −0.712492 −0.356246 0.934392i \(-0.615943\pi\)
−0.356246 + 0.934392i \(0.615943\pi\)
\(978\) 9.02054 0.288445
\(979\) 1.43186 0.0457624
\(980\) 24.3018 0.776294
\(981\) 34.3174 1.09567
\(982\) −28.1115 −0.897073
\(983\) 6.23592 0.198895 0.0994474 0.995043i \(-0.468292\pi\)
0.0994474 + 0.995043i \(0.468292\pi\)
\(984\) 5.55279 0.177016
\(985\) −25.8714 −0.824332
\(986\) −22.2231 −0.707726
\(987\) −3.91570 −0.124638
\(988\) −12.4913 −0.397402
\(989\) 1.26441 0.0402059
\(990\) −5.29564 −0.168306
\(991\) −27.1762 −0.863280 −0.431640 0.902046i \(-0.642065\pi\)
−0.431640 + 0.902046i \(0.642065\pi\)
\(992\) 1.85973 0.0590466
\(993\) 18.2839 0.580221
\(994\) 10.2738 0.325865
\(995\) −20.4105 −0.647056
\(996\) −1.80487 −0.0571895
\(997\) 9.21406 0.291812 0.145906 0.989298i \(-0.453390\pi\)
0.145906 + 0.989298i \(0.453390\pi\)
\(998\) −14.3639 −0.454681
\(999\) 1.94725 0.0616081
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 \(a_p\))