Properties

Label 6047.2.a.a.1.13
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54610 q^{2}\) \(-2.31345 q^{3}\) \(+4.48264 q^{4}\) \(-3.02578 q^{5}\) \(+5.89027 q^{6}\) \(-2.15804 q^{7}\) \(-6.32106 q^{8}\) \(+2.35204 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.54610 q^{2}\) \(-2.31345 q^{3}\) \(+4.48264 q^{4}\) \(-3.02578 q^{5}\) \(+5.89027 q^{6}\) \(-2.15804 q^{7}\) \(-6.32106 q^{8}\) \(+2.35204 q^{9}\) \(+7.70396 q^{10}\) \(-1.11866 q^{11}\) \(-10.3704 q^{12}\) \(-5.26486 q^{13}\) \(+5.49458 q^{14}\) \(+6.99999 q^{15}\) \(+7.12878 q^{16}\) \(-6.53216 q^{17}\) \(-5.98853 q^{18}\) \(-6.25317 q^{19}\) \(-13.5635 q^{20}\) \(+4.99250 q^{21}\) \(+2.84823 q^{22}\) \(-1.84125 q^{23}\) \(+14.6234 q^{24}\) \(+4.15537 q^{25}\) \(+13.4049 q^{26}\) \(+1.49903 q^{27}\) \(-9.67370 q^{28}\) \(+1.34606 q^{29}\) \(-17.8227 q^{30}\) \(+0.169506 q^{31}\) \(-5.50850 q^{32}\) \(+2.58797 q^{33}\) \(+16.6315 q^{34}\) \(+6.52975 q^{35}\) \(+10.5433 q^{36}\) \(-9.24432 q^{37}\) \(+15.9212 q^{38}\) \(+12.1800 q^{39}\) \(+19.1262 q^{40}\) \(+11.1562 q^{41}\) \(-12.7114 q^{42}\) \(-1.50820 q^{43}\) \(-5.01456 q^{44}\) \(-7.11676 q^{45}\) \(+4.68802 q^{46}\) \(-4.48501 q^{47}\) \(-16.4921 q^{48}\) \(-2.34288 q^{49}\) \(-10.5800 q^{50}\) \(+15.1118 q^{51}\) \(-23.6005 q^{52}\) \(+6.89328 q^{53}\) \(-3.81668 q^{54}\) \(+3.38483 q^{55}\) \(+13.6411 q^{56}\) \(+14.4664 q^{57}\) \(-3.42721 q^{58}\) \(-2.12259 q^{59}\) \(+31.3784 q^{60}\) \(+8.00933 q^{61}\) \(-0.431580 q^{62}\) \(-5.07578 q^{63}\) \(-0.232355 q^{64}\) \(+15.9303 q^{65}\) \(-6.58923 q^{66}\) \(-13.2349 q^{67}\) \(-29.2813 q^{68}\) \(+4.25964 q^{69}\) \(-16.6254 q^{70}\) \(-0.196267 q^{71}\) \(-14.8674 q^{72}\) \(-9.73800 q^{73}\) \(+23.5370 q^{74}\) \(-9.61323 q^{75}\) \(-28.0307 q^{76}\) \(+2.41411 q^{77}\) \(-31.0115 q^{78}\) \(-7.98632 q^{79}\) \(-21.5702 q^{80}\) \(-10.5240 q^{81}\) \(-28.4048 q^{82}\) \(+14.9679 q^{83}\) \(+22.3796 q^{84}\) \(+19.7649 q^{85}\) \(+3.84003 q^{86}\) \(-3.11404 q^{87}\) \(+7.07113 q^{88}\) \(-4.50608 q^{89}\) \(+18.1200 q^{90}\) \(+11.3617 q^{91}\) \(-8.25368 q^{92}\) \(-0.392143 q^{93}\) \(+11.4193 q^{94}\) \(+18.9208 q^{95}\) \(+12.7436 q^{96}\) \(+2.24387 q^{97}\) \(+5.96522 q^{98}\) \(-2.63114 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54610 −1.80037 −0.900183 0.435511i \(-0.856568\pi\)
−0.900183 + 0.435511i \(0.856568\pi\)
\(3\) −2.31345 −1.33567 −0.667835 0.744310i \(-0.732779\pi\)
−0.667835 + 0.744310i \(0.732779\pi\)
\(4\) 4.48264 2.24132
\(5\) −3.02578 −1.35317 −0.676586 0.736364i \(-0.736541\pi\)
−0.676586 + 0.736364i \(0.736541\pi\)
\(6\) 5.89027 2.40469
\(7\) −2.15804 −0.815661 −0.407830 0.913058i \(-0.633715\pi\)
−0.407830 + 0.913058i \(0.633715\pi\)
\(8\) −6.32106 −2.23483
\(9\) 2.35204 0.784013
\(10\) 7.70396 2.43621
\(11\) −1.11866 −0.337290 −0.168645 0.985677i \(-0.553939\pi\)
−0.168645 + 0.985677i \(0.553939\pi\)
\(12\) −10.3704 −2.99366
\(13\) −5.26486 −1.46021 −0.730104 0.683336i \(-0.760529\pi\)
−0.730104 + 0.683336i \(0.760529\pi\)
\(14\) 5.49458 1.46849
\(15\) 6.99999 1.80739
\(16\) 7.12878 1.78220
\(17\) −6.53216 −1.58428 −0.792140 0.610339i \(-0.791033\pi\)
−0.792140 + 0.610339i \(0.791033\pi\)
\(18\) −5.98853 −1.41151
\(19\) −6.25317 −1.43458 −0.717288 0.696777i \(-0.754617\pi\)
−0.717288 + 0.696777i \(0.754617\pi\)
\(20\) −13.5635 −3.03289
\(21\) 4.99250 1.08945
\(22\) 2.84823 0.607245
\(23\) −1.84125 −0.383928 −0.191964 0.981402i \(-0.561486\pi\)
−0.191964 + 0.981402i \(0.561486\pi\)
\(24\) 14.6234 2.98500
\(25\) 4.15537 0.831074
\(26\) 13.4049 2.62891
\(27\) 1.49903 0.288488
\(28\) −9.67370 −1.82816
\(29\) 1.34606 0.249957 0.124979 0.992159i \(-0.460114\pi\)
0.124979 + 0.992159i \(0.460114\pi\)
\(30\) −17.8227 −3.25397
\(31\) 0.169506 0.0304442 0.0152221 0.999884i \(-0.495154\pi\)
0.0152221 + 0.999884i \(0.495154\pi\)
\(32\) −5.50850 −0.973775
\(33\) 2.58797 0.450507
\(34\) 16.6315 2.85229
\(35\) 6.52975 1.10373
\(36\) 10.5433 1.75722
\(37\) −9.24432 −1.51976 −0.759878 0.650065i \(-0.774741\pi\)
−0.759878 + 0.650065i \(0.774741\pi\)
\(38\) 15.9212 2.58276
\(39\) 12.1800 1.95036
\(40\) 19.1262 3.02411
\(41\) 11.1562 1.74230 0.871152 0.491014i \(-0.163374\pi\)
0.871152 + 0.491014i \(0.163374\pi\)
\(42\) −12.7114 −1.96142
\(43\) −1.50820 −0.229998 −0.114999 0.993366i \(-0.536687\pi\)
−0.114999 + 0.993366i \(0.536687\pi\)
\(44\) −5.01456 −0.755974
\(45\) −7.11676 −1.06090
\(46\) 4.68802 0.691211
\(47\) −4.48501 −0.654206 −0.327103 0.944989i \(-0.606072\pi\)
−0.327103 + 0.944989i \(0.606072\pi\)
\(48\) −16.4921 −2.38042
\(49\) −2.34288 −0.334697
\(50\) −10.5800 −1.49624
\(51\) 15.1118 2.11607
\(52\) −23.6005 −3.27280
\(53\) 6.89328 0.946864 0.473432 0.880830i \(-0.343015\pi\)
0.473432 + 0.880830i \(0.343015\pi\)
\(54\) −3.81668 −0.519384
\(55\) 3.38483 0.456411
\(56\) 13.6411 1.82286
\(57\) 14.4664 1.91612
\(58\) −3.42721 −0.450015
\(59\) −2.12259 −0.276338 −0.138169 0.990409i \(-0.544122\pi\)
−0.138169 + 0.990409i \(0.544122\pi\)
\(60\) 31.3784 4.05094
\(61\) 8.00933 1.02549 0.512745 0.858541i \(-0.328629\pi\)
0.512745 + 0.858541i \(0.328629\pi\)
\(62\) −0.431580 −0.0548107
\(63\) −5.07578 −0.639488
\(64\) −0.232355 −0.0290444
\(65\) 15.9303 1.97591
\(66\) −6.58923 −0.811078
\(67\) −13.2349 −1.61690 −0.808450 0.588564i \(-0.799693\pi\)
−0.808450 + 0.588564i \(0.799693\pi\)
\(68\) −29.2813 −3.55088
\(69\) 4.25964 0.512801
\(70\) −16.6254 −1.98712
\(71\) −0.196267 −0.0232925 −0.0116463 0.999932i \(-0.503707\pi\)
−0.0116463 + 0.999932i \(0.503707\pi\)
\(72\) −14.8674 −1.75214
\(73\) −9.73800 −1.13975 −0.569874 0.821732i \(-0.693008\pi\)
−0.569874 + 0.821732i \(0.693008\pi\)
\(74\) 23.5370 2.73612
\(75\) −9.61323 −1.11004
\(76\) −28.0307 −3.21534
\(77\) 2.41411 0.275114
\(78\) −31.0115 −3.51136
\(79\) −7.98632 −0.898531 −0.449266 0.893398i \(-0.648314\pi\)
−0.449266 + 0.893398i \(0.648314\pi\)
\(80\) −21.5702 −2.41162
\(81\) −10.5240 −1.16934
\(82\) −28.4048 −3.13679
\(83\) 14.9679 1.64295 0.821473 0.570248i \(-0.193153\pi\)
0.821473 + 0.570248i \(0.193153\pi\)
\(84\) 22.3796 2.44181
\(85\) 19.7649 2.14380
\(86\) 3.84003 0.414081
\(87\) −3.11404 −0.333860
\(88\) 7.07113 0.753785
\(89\) −4.50608 −0.477643 −0.238822 0.971063i \(-0.576761\pi\)
−0.238822 + 0.971063i \(0.576761\pi\)
\(90\) 18.1200 1.91002
\(91\) 11.3617 1.19103
\(92\) −8.25368 −0.860506
\(93\) −0.392143 −0.0406633
\(94\) 11.4193 1.17781
\(95\) 18.9208 1.94123
\(96\) 12.7436 1.30064
\(97\) 2.24387 0.227830 0.113915 0.993490i \(-0.463661\pi\)
0.113915 + 0.993490i \(0.463661\pi\)
\(98\) 5.96522 0.602578
\(99\) −2.63114 −0.264439
\(100\) 18.6270 1.86270
\(101\) 1.54808 0.154039 0.0770196 0.997030i \(-0.475460\pi\)
0.0770196 + 0.997030i \(0.475460\pi\)
\(102\) −38.4762 −3.80971
\(103\) 14.8966 1.46781 0.733905 0.679252i \(-0.237696\pi\)
0.733905 + 0.679252i \(0.237696\pi\)
\(104\) 33.2795 3.26332
\(105\) −15.1062 −1.47422
\(106\) −17.5510 −1.70470
\(107\) −4.51998 −0.436963 −0.218482 0.975841i \(-0.570110\pi\)
−0.218482 + 0.975841i \(0.570110\pi\)
\(108\) 6.71960 0.646594
\(109\) 9.46619 0.906696 0.453348 0.891334i \(-0.350229\pi\)
0.453348 + 0.891334i \(0.350229\pi\)
\(110\) −8.61813 −0.821707
\(111\) 21.3862 2.02989
\(112\) −15.3842 −1.45367
\(113\) −3.25496 −0.306200 −0.153100 0.988211i \(-0.548926\pi\)
−0.153100 + 0.988211i \(0.548926\pi\)
\(114\) −36.8329 −3.44972
\(115\) 5.57124 0.519521
\(116\) 6.03391 0.560234
\(117\) −12.3831 −1.14482
\(118\) 5.40434 0.497510
\(119\) 14.0966 1.29224
\(120\) −44.2474 −4.03921
\(121\) −9.74859 −0.886236
\(122\) −20.3926 −1.84626
\(123\) −25.8092 −2.32714
\(124\) 0.759834 0.0682351
\(125\) 2.55566 0.228586
\(126\) 12.9235 1.15131
\(127\) −4.37884 −0.388559 −0.194279 0.980946i \(-0.562237\pi\)
−0.194279 + 0.980946i \(0.562237\pi\)
\(128\) 11.6086 1.02607
\(129\) 3.48914 0.307202
\(130\) −40.5602 −3.55737
\(131\) 2.76271 0.241379 0.120689 0.992690i \(-0.461490\pi\)
0.120689 + 0.992690i \(0.461490\pi\)
\(132\) 11.6009 1.00973
\(133\) 13.4946 1.17013
\(134\) 33.6974 2.91101
\(135\) −4.53573 −0.390374
\(136\) 41.2901 3.54060
\(137\) −11.2697 −0.962839 −0.481419 0.876490i \(-0.659879\pi\)
−0.481419 + 0.876490i \(0.659879\pi\)
\(138\) −10.8455 −0.923230
\(139\) 17.9048 1.51866 0.759331 0.650705i \(-0.225527\pi\)
0.759331 + 0.650705i \(0.225527\pi\)
\(140\) 29.2705 2.47381
\(141\) 10.3758 0.873803
\(142\) 0.499715 0.0419351
\(143\) 5.88960 0.492513
\(144\) 16.7672 1.39726
\(145\) −4.07289 −0.338235
\(146\) 24.7940 2.05196
\(147\) 5.42013 0.447045
\(148\) −41.4390 −3.40626
\(149\) 0.878309 0.0719539 0.0359769 0.999353i \(-0.488546\pi\)
0.0359769 + 0.999353i \(0.488546\pi\)
\(150\) 24.4763 1.99848
\(151\) −21.3497 −1.73741 −0.868707 0.495326i \(-0.835049\pi\)
−0.868707 + 0.495326i \(0.835049\pi\)
\(152\) 39.5267 3.20604
\(153\) −15.3639 −1.24210
\(154\) −6.14658 −0.495306
\(155\) −0.512888 −0.0411962
\(156\) 54.5984 4.37137
\(157\) 11.1660 0.891143 0.445572 0.895246i \(-0.353000\pi\)
0.445572 + 0.895246i \(0.353000\pi\)
\(158\) 20.3340 1.61769
\(159\) −15.9472 −1.26470
\(160\) 16.6675 1.31768
\(161\) 3.97349 0.313155
\(162\) 26.7953 2.10524
\(163\) 12.3511 0.967411 0.483705 0.875231i \(-0.339291\pi\)
0.483705 + 0.875231i \(0.339291\pi\)
\(164\) 50.0092 3.90506
\(165\) −7.83063 −0.609614
\(166\) −38.1099 −2.95790
\(167\) 19.1792 1.48413 0.742067 0.670326i \(-0.233846\pi\)
0.742067 + 0.670326i \(0.233846\pi\)
\(168\) −31.5579 −2.43474
\(169\) 14.7187 1.13221
\(170\) −50.3235 −3.85963
\(171\) −14.7077 −1.12473
\(172\) −6.76072 −0.515500
\(173\) 11.1174 0.845239 0.422619 0.906307i \(-0.361111\pi\)
0.422619 + 0.906307i \(0.361111\pi\)
\(174\) 7.92867 0.601071
\(175\) −8.96744 −0.677875
\(176\) −7.97471 −0.601116
\(177\) 4.91051 0.369097
\(178\) 11.4729 0.859933
\(179\) 17.3640 1.29784 0.648921 0.760855i \(-0.275220\pi\)
0.648921 + 0.760855i \(0.275220\pi\)
\(180\) −31.9019 −2.37783
\(181\) −20.7141 −1.53967 −0.769833 0.638245i \(-0.779661\pi\)
−0.769833 + 0.638245i \(0.779661\pi\)
\(182\) −28.9282 −2.14430
\(183\) −18.5292 −1.36972
\(184\) 11.6387 0.858014
\(185\) 27.9713 2.05649
\(186\) 0.998437 0.0732089
\(187\) 7.30728 0.534361
\(188\) −20.1047 −1.46629
\(189\) −3.23495 −0.235308
\(190\) −48.1742 −3.49492
\(191\) −0.136049 −0.00984415 −0.00492208 0.999988i \(-0.501567\pi\)
−0.00492208 + 0.999988i \(0.501567\pi\)
\(192\) 0.537541 0.0387937
\(193\) −4.33713 −0.312193 −0.156097 0.987742i \(-0.549891\pi\)
−0.156097 + 0.987742i \(0.549891\pi\)
\(194\) −5.71312 −0.410178
\(195\) −36.8540 −2.63917
\(196\) −10.5023 −0.750164
\(197\) −17.8907 −1.27466 −0.637331 0.770590i \(-0.719962\pi\)
−0.637331 + 0.770590i \(0.719962\pi\)
\(198\) 6.69915 0.476088
\(199\) −12.0588 −0.854825 −0.427413 0.904057i \(-0.640575\pi\)
−0.427413 + 0.904057i \(0.640575\pi\)
\(200\) −26.2663 −1.85731
\(201\) 30.6182 2.15964
\(202\) −3.94156 −0.277327
\(203\) −2.90485 −0.203880
\(204\) 67.7408 4.74280
\(205\) −33.7562 −2.35764
\(206\) −37.9284 −2.64260
\(207\) −4.33070 −0.301004
\(208\) −37.5320 −2.60238
\(209\) 6.99519 0.483868
\(210\) 38.4620 2.65413
\(211\) 18.4728 1.27172 0.635859 0.771806i \(-0.280646\pi\)
0.635859 + 0.771806i \(0.280646\pi\)
\(212\) 30.9001 2.12223
\(213\) 0.454052 0.0311111
\(214\) 11.5083 0.786694
\(215\) 4.56349 0.311227
\(216\) −9.47543 −0.644722
\(217\) −0.365800 −0.0248321
\(218\) −24.1019 −1.63239
\(219\) 22.5284 1.52233
\(220\) 15.1730 1.02296
\(221\) 34.3909 2.31338
\(222\) −54.4516 −3.65455
\(223\) 10.1377 0.678870 0.339435 0.940630i \(-0.389764\pi\)
0.339435 + 0.940630i \(0.389764\pi\)
\(224\) 11.8875 0.794270
\(225\) 9.77359 0.651573
\(226\) 8.28745 0.551273
\(227\) −18.9122 −1.25525 −0.627623 0.778517i \(-0.715972\pi\)
−0.627623 + 0.778517i \(0.715972\pi\)
\(228\) 64.8476 4.29464
\(229\) 12.0998 0.799575 0.399787 0.916608i \(-0.369084\pi\)
0.399787 + 0.916608i \(0.369084\pi\)
\(230\) −14.1849 −0.935328
\(231\) −5.58493 −0.367461
\(232\) −8.50853 −0.558612
\(233\) −0.123894 −0.00811658 −0.00405829 0.999992i \(-0.501292\pi\)
−0.00405829 + 0.999992i \(0.501292\pi\)
\(234\) 31.5288 2.06110
\(235\) 13.5707 0.885254
\(236\) −9.51483 −0.619363
\(237\) 18.4759 1.20014
\(238\) −35.8915 −2.32650
\(239\) −4.64682 −0.300578 −0.150289 0.988642i \(-0.548020\pi\)
−0.150289 + 0.988642i \(0.548020\pi\)
\(240\) 49.9014 3.22112
\(241\) 8.69431 0.560049 0.280025 0.959993i \(-0.409657\pi\)
0.280025 + 0.959993i \(0.409657\pi\)
\(242\) 24.8209 1.59555
\(243\) 19.8497 1.27336
\(244\) 35.9029 2.29845
\(245\) 7.08906 0.452903
\(246\) 65.7130 4.18971
\(247\) 32.9221 2.09478
\(248\) −1.07146 −0.0680376
\(249\) −34.6276 −2.19443
\(250\) −6.50698 −0.411538
\(251\) 14.6695 0.925929 0.462965 0.886377i \(-0.346786\pi\)
0.462965 + 0.886377i \(0.346786\pi\)
\(252\) −22.7529 −1.43330
\(253\) 2.05974 0.129495
\(254\) 11.1490 0.699548
\(255\) −45.7250 −2.86341
\(256\) −29.0920 −1.81825
\(257\) 14.2408 0.888319 0.444159 0.895948i \(-0.353502\pi\)
0.444159 + 0.895948i \(0.353502\pi\)
\(258\) −8.88371 −0.553076
\(259\) 19.9496 1.23961
\(260\) 71.4099 4.42865
\(261\) 3.16599 0.195970
\(262\) −7.03413 −0.434570
\(263\) 23.6715 1.45965 0.729823 0.683636i \(-0.239602\pi\)
0.729823 + 0.683636i \(0.239602\pi\)
\(264\) −16.3587 −1.00681
\(265\) −20.8576 −1.28127
\(266\) −34.3586 −2.10666
\(267\) 10.4246 0.637973
\(268\) −59.3273 −3.62399
\(269\) 17.6373 1.07536 0.537681 0.843148i \(-0.319300\pi\)
0.537681 + 0.843148i \(0.319300\pi\)
\(270\) 11.5484 0.702816
\(271\) −21.3323 −1.29584 −0.647922 0.761706i \(-0.724362\pi\)
−0.647922 + 0.761706i \(0.724362\pi\)
\(272\) −46.5663 −2.82350
\(273\) −26.2848 −1.59083
\(274\) 28.6939 1.73346
\(275\) −4.64846 −0.280313
\(276\) 19.0945 1.14935
\(277\) 12.9240 0.776526 0.388263 0.921549i \(-0.373075\pi\)
0.388263 + 0.921549i \(0.373075\pi\)
\(278\) −45.5873 −2.73415
\(279\) 0.398684 0.0238686
\(280\) −41.2749 −2.46665
\(281\) 3.65752 0.218189 0.109095 0.994031i \(-0.465205\pi\)
0.109095 + 0.994031i \(0.465205\pi\)
\(282\) −26.4180 −1.57317
\(283\) 0.0449931 0.00267456 0.00133728 0.999999i \(-0.499574\pi\)
0.00133728 + 0.999999i \(0.499574\pi\)
\(284\) −0.879792 −0.0522061
\(285\) −43.7722 −2.59284
\(286\) −14.9955 −0.886704
\(287\) −24.0754 −1.42113
\(288\) −12.9562 −0.763452
\(289\) 25.6691 1.50994
\(290\) 10.3700 0.608947
\(291\) −5.19107 −0.304306
\(292\) −43.6520 −2.55454
\(293\) 0.922965 0.0539202 0.0269601 0.999637i \(-0.491417\pi\)
0.0269601 + 0.999637i \(0.491417\pi\)
\(294\) −13.8002 −0.804845
\(295\) 6.42251 0.373933
\(296\) 58.4339 3.39640
\(297\) −1.67691 −0.0973039
\(298\) −2.23627 −0.129543
\(299\) 9.69394 0.560615
\(300\) −43.0927 −2.48796
\(301\) 3.25475 0.187601
\(302\) 54.3585 3.12798
\(303\) −3.58139 −0.205745
\(304\) −44.5775 −2.55670
\(305\) −24.2345 −1.38766
\(306\) 39.1180 2.23623
\(307\) −7.64583 −0.436371 −0.218185 0.975907i \(-0.570014\pi\)
−0.218185 + 0.975907i \(0.570014\pi\)
\(308\) 10.8216 0.616618
\(309\) −34.4626 −1.96051
\(310\) 1.30587 0.0741682
\(311\) −27.1648 −1.54037 −0.770187 0.637819i \(-0.779837\pi\)
−0.770187 + 0.637819i \(0.779837\pi\)
\(312\) −76.9903 −4.35872
\(313\) 22.7039 1.28330 0.641651 0.766997i \(-0.278250\pi\)
0.641651 + 0.766997i \(0.278250\pi\)
\(314\) −28.4298 −1.60438
\(315\) 15.3582 0.865338
\(316\) −35.7998 −2.01390
\(317\) −19.8243 −1.11345 −0.556723 0.830698i \(-0.687941\pi\)
−0.556723 + 0.830698i \(0.687941\pi\)
\(318\) 40.6033 2.27692
\(319\) −1.50579 −0.0843080
\(320\) 0.703056 0.0393020
\(321\) 10.4567 0.583638
\(322\) −10.1169 −0.563794
\(323\) 40.8467 2.27277
\(324\) −47.1754 −2.62086
\(325\) −21.8774 −1.21354
\(326\) −31.4471 −1.74169
\(327\) −21.8995 −1.21105
\(328\) −70.5189 −3.89375
\(329\) 9.67882 0.533610
\(330\) 19.9376 1.09753
\(331\) 5.94560 0.326800 0.163400 0.986560i \(-0.447754\pi\)
0.163400 + 0.986560i \(0.447754\pi\)
\(332\) 67.0959 3.68237
\(333\) −21.7430 −1.19151
\(334\) −48.8323 −2.67198
\(335\) 40.0460 2.18794
\(336\) 35.5905 1.94162
\(337\) 11.7125 0.638020 0.319010 0.947751i \(-0.396650\pi\)
0.319010 + 0.947751i \(0.396650\pi\)
\(338\) −37.4754 −2.03839
\(339\) 7.53017 0.408983
\(340\) 88.5989 4.80495
\(341\) −0.189620 −0.0102685
\(342\) 37.4473 2.02492
\(343\) 20.1623 1.08866
\(344\) 9.53342 0.514007
\(345\) −12.8888 −0.693908
\(346\) −28.3060 −1.52174
\(347\) −18.1724 −0.975548 −0.487774 0.872970i \(-0.662191\pi\)
−0.487774 + 0.872970i \(0.662191\pi\)
\(348\) −13.9591 −0.748288
\(349\) −0.0279519 −0.00149623 −0.000748116 1.00000i \(-0.500238\pi\)
−0.000748116 1.00000i \(0.500238\pi\)
\(350\) 22.8320 1.22042
\(351\) −7.89216 −0.421252
\(352\) 6.16216 0.328444
\(353\) 3.52057 0.187381 0.0936905 0.995601i \(-0.470134\pi\)
0.0936905 + 0.995601i \(0.470134\pi\)
\(354\) −12.5027 −0.664509
\(355\) 0.593860 0.0315188
\(356\) −20.1991 −1.07055
\(357\) −32.6118 −1.72600
\(358\) −44.2104 −2.33659
\(359\) −33.3893 −1.76222 −0.881109 0.472914i \(-0.843202\pi\)
−0.881109 + 0.472914i \(0.843202\pi\)
\(360\) 44.9854 2.37094
\(361\) 20.1022 1.05801
\(362\) 52.7402 2.77196
\(363\) 22.5529 1.18372
\(364\) 50.9306 2.66949
\(365\) 29.4651 1.54227
\(366\) 47.1772 2.46599
\(367\) −9.05997 −0.472927 −0.236463 0.971640i \(-0.575988\pi\)
−0.236463 + 0.971640i \(0.575988\pi\)
\(368\) −13.1259 −0.684235
\(369\) 26.2398 1.36599
\(370\) −71.2178 −3.70244
\(371\) −14.8759 −0.772320
\(372\) −1.75784 −0.0911396
\(373\) −22.6728 −1.17396 −0.586978 0.809603i \(-0.699682\pi\)
−0.586978 + 0.809603i \(0.699682\pi\)
\(374\) −18.6051 −0.962046
\(375\) −5.91239 −0.305315
\(376\) 28.3500 1.46204
\(377\) −7.08682 −0.364990
\(378\) 8.23652 0.423641
\(379\) 6.89468 0.354156 0.177078 0.984197i \(-0.443335\pi\)
0.177078 + 0.984197i \(0.443335\pi\)
\(380\) 84.8149 4.35091
\(381\) 10.1302 0.518986
\(382\) 0.346395 0.0177231
\(383\) 28.3483 1.44853 0.724265 0.689521i \(-0.242179\pi\)
0.724265 + 0.689521i \(0.242179\pi\)
\(384\) −26.8559 −1.37048
\(385\) −7.30459 −0.372276
\(386\) 11.0428 0.562062
\(387\) −3.54734 −0.180322
\(388\) 10.0584 0.510640
\(389\) 3.61541 0.183309 0.0916543 0.995791i \(-0.470785\pi\)
0.0916543 + 0.995791i \(0.470785\pi\)
\(390\) 93.8340 4.75147
\(391\) 12.0274 0.608250
\(392\) 14.8095 0.747992
\(393\) −6.39137 −0.322402
\(394\) 45.5517 2.29486
\(395\) 24.1649 1.21587
\(396\) −11.7944 −0.592693
\(397\) 24.5672 1.23299 0.616497 0.787357i \(-0.288551\pi\)
0.616497 + 0.787357i \(0.288551\pi\)
\(398\) 30.7029 1.53900
\(399\) −31.2190 −1.56290
\(400\) 29.6227 1.48114
\(401\) 30.6801 1.53209 0.766045 0.642787i \(-0.222222\pi\)
0.766045 + 0.642787i \(0.222222\pi\)
\(402\) −77.9572 −3.88815
\(403\) −0.892425 −0.0444548
\(404\) 6.93946 0.345251
\(405\) 31.8435 1.58231
\(406\) 7.39604 0.367059
\(407\) 10.3413 0.512598
\(408\) −95.5226 −4.72907
\(409\) 0.984912 0.0487007 0.0243504 0.999703i \(-0.492248\pi\)
0.0243504 + 0.999703i \(0.492248\pi\)
\(410\) 85.9468 4.24461
\(411\) 26.0719 1.28603
\(412\) 66.7763 3.28983
\(413\) 4.58064 0.225398
\(414\) 11.0264 0.541918
\(415\) −45.2898 −2.22319
\(416\) 29.0015 1.42191
\(417\) −41.4217 −2.02843
\(418\) −17.8105 −0.871139
\(419\) −2.30116 −0.112419 −0.0562096 0.998419i \(-0.517902\pi\)
−0.0562096 + 0.998419i \(0.517902\pi\)
\(420\) −67.7158 −3.30419
\(421\) 29.9506 1.45970 0.729851 0.683606i \(-0.239589\pi\)
0.729851 + 0.683606i \(0.239589\pi\)
\(422\) −47.0335 −2.28956
\(423\) −10.5489 −0.512906
\(424\) −43.5728 −2.11608
\(425\) −27.1435 −1.31665
\(426\) −1.15606 −0.0560115
\(427\) −17.2844 −0.836452
\(428\) −20.2615 −0.979374
\(429\) −13.6253 −0.657835
\(430\) −11.6191 −0.560323
\(431\) −20.8300 −1.00335 −0.501673 0.865057i \(-0.667282\pi\)
−0.501673 + 0.865057i \(0.667282\pi\)
\(432\) 10.6862 0.514142
\(433\) −33.8117 −1.62488 −0.812442 0.583042i \(-0.801862\pi\)
−0.812442 + 0.583042i \(0.801862\pi\)
\(434\) 0.931364 0.0447069
\(435\) 9.42242 0.451770
\(436\) 42.4335 2.03220
\(437\) 11.5137 0.550774
\(438\) −57.3595 −2.74074
\(439\) −12.3996 −0.591798 −0.295899 0.955219i \(-0.595619\pi\)
−0.295899 + 0.955219i \(0.595619\pi\)
\(440\) −21.3957 −1.02000
\(441\) −5.51055 −0.262407
\(442\) −87.5627 −4.16493
\(443\) −26.9209 −1.27905 −0.639526 0.768770i \(-0.720869\pi\)
−0.639526 + 0.768770i \(0.720869\pi\)
\(444\) 95.8668 4.54964
\(445\) 13.6344 0.646333
\(446\) −25.8116 −1.22222
\(447\) −2.03192 −0.0961066
\(448\) 0.501430 0.0236903
\(449\) 29.9104 1.41156 0.705779 0.708432i \(-0.250597\pi\)
0.705779 + 0.708432i \(0.250597\pi\)
\(450\) −24.8846 −1.17307
\(451\) −12.4800 −0.587661
\(452\) −14.5908 −0.686293
\(453\) 49.3914 2.32061
\(454\) 48.1524 2.25990
\(455\) −34.3782 −1.61168
\(456\) −91.4429 −4.28220
\(457\) 4.79167 0.224145 0.112072 0.993700i \(-0.464251\pi\)
0.112072 + 0.993700i \(0.464251\pi\)
\(458\) −30.8072 −1.43953
\(459\) −9.79188 −0.457046
\(460\) 24.9739 1.16441
\(461\) 6.91366 0.322001 0.161001 0.986954i \(-0.448528\pi\)
0.161001 + 0.986954i \(0.448528\pi\)
\(462\) 14.2198 0.661565
\(463\) −29.1807 −1.35614 −0.678071 0.734997i \(-0.737184\pi\)
−0.678071 + 0.734997i \(0.737184\pi\)
\(464\) 9.59578 0.445473
\(465\) 1.18654 0.0550245
\(466\) 0.315447 0.0146128
\(467\) −12.0740 −0.558719 −0.279360 0.960187i \(-0.590122\pi\)
−0.279360 + 0.960187i \(0.590122\pi\)
\(468\) −55.5092 −2.56591
\(469\) 28.5614 1.31884
\(470\) −34.5523 −1.59378
\(471\) −25.8319 −1.19027
\(472\) 13.4170 0.617570
\(473\) 1.68717 0.0775760
\(474\) −47.0416 −2.16069
\(475\) −25.9843 −1.19224
\(476\) 63.1901 2.89631
\(477\) 16.2132 0.742354
\(478\) 11.8313 0.541150
\(479\) −25.2183 −1.15225 −0.576127 0.817360i \(-0.695437\pi\)
−0.576127 + 0.817360i \(0.695437\pi\)
\(480\) −38.5595 −1.75999
\(481\) 48.6700 2.21916
\(482\) −22.1366 −1.00829
\(483\) −9.19246 −0.418272
\(484\) −43.6994 −1.98634
\(485\) −6.78946 −0.308293
\(486\) −50.5394 −2.29251
\(487\) 9.99182 0.452772 0.226386 0.974038i \(-0.427309\pi\)
0.226386 + 0.974038i \(0.427309\pi\)
\(488\) −50.6274 −2.29180
\(489\) −28.5736 −1.29214
\(490\) −18.0495 −0.815392
\(491\) 7.59133 0.342592 0.171296 0.985220i \(-0.445205\pi\)
0.171296 + 0.985220i \(0.445205\pi\)
\(492\) −115.694 −5.21587
\(493\) −8.79268 −0.396003
\(494\) −83.8230 −3.77137
\(495\) 7.96125 0.357832
\(496\) 1.20837 0.0542575
\(497\) 0.423550 0.0189988
\(498\) 88.1653 3.95078
\(499\) 8.02626 0.359305 0.179652 0.983730i \(-0.442503\pi\)
0.179652 + 0.983730i \(0.442503\pi\)
\(500\) 11.4561 0.512333
\(501\) −44.3701 −1.98231
\(502\) −37.3500 −1.66701
\(503\) 28.8795 1.28767 0.643836 0.765163i \(-0.277342\pi\)
0.643836 + 0.765163i \(0.277342\pi\)
\(504\) 32.0843 1.42915
\(505\) −4.68414 −0.208442
\(506\) −5.24432 −0.233138
\(507\) −34.0510 −1.51226
\(508\) −19.6287 −0.870885
\(509\) 13.5685 0.601412 0.300706 0.953717i \(-0.402778\pi\)
0.300706 + 0.953717i \(0.402778\pi\)
\(510\) 116.421 5.15519
\(511\) 21.0150 0.929647
\(512\) 50.8540 2.24745
\(513\) −9.37367 −0.413858
\(514\) −36.2586 −1.59930
\(515\) −45.0740 −1.98620
\(516\) 15.6406 0.688537
\(517\) 5.01722 0.220657
\(518\) −50.7937 −2.23174
\(519\) −25.7195 −1.12896
\(520\) −100.696 −4.41583
\(521\) −8.64002 −0.378526 −0.189263 0.981926i \(-0.560610\pi\)
−0.189263 + 0.981926i \(0.560610\pi\)
\(522\) −8.06093 −0.352817
\(523\) 38.3582 1.67729 0.838645 0.544679i \(-0.183349\pi\)
0.838645 + 0.544679i \(0.183349\pi\)
\(524\) 12.3842 0.541007
\(525\) 20.7457 0.905416
\(526\) −60.2701 −2.62790
\(527\) −1.10724 −0.0482321
\(528\) 18.4491 0.802892
\(529\) −19.6098 −0.852599
\(530\) 53.1055 2.30676
\(531\) −4.99242 −0.216653
\(532\) 60.4913 2.62263
\(533\) −58.7357 −2.54413
\(534\) −26.5420 −1.14859
\(535\) 13.6765 0.591286
\(536\) 83.6586 3.61350
\(537\) −40.1706 −1.73349
\(538\) −44.9063 −1.93605
\(539\) 2.62090 0.112890
\(540\) −20.3321 −0.874952
\(541\) −12.0929 −0.519916 −0.259958 0.965620i \(-0.583709\pi\)
−0.259958 + 0.965620i \(0.583709\pi\)
\(542\) 54.3142 2.33300
\(543\) 47.9210 2.05649
\(544\) 35.9824 1.54273
\(545\) −28.6426 −1.22692
\(546\) 66.9238 2.86408
\(547\) 6.79584 0.290569 0.145284 0.989390i \(-0.453590\pi\)
0.145284 + 0.989390i \(0.453590\pi\)
\(548\) −50.5182 −2.15803
\(549\) 18.8382 0.803997
\(550\) 11.8355 0.504666
\(551\) −8.41715 −0.358583
\(552\) −26.9255 −1.14602
\(553\) 17.2348 0.732897
\(554\) −32.9058 −1.39803
\(555\) −64.7102 −2.74679
\(556\) 80.2606 3.40381
\(557\) −5.81733 −0.246488 −0.123244 0.992376i \(-0.539330\pi\)
−0.123244 + 0.992376i \(0.539330\pi\)
\(558\) −1.01509 −0.0429722
\(559\) 7.94045 0.335845
\(560\) 46.5492 1.96706
\(561\) −16.9050 −0.713730
\(562\) −9.31243 −0.392821
\(563\) −27.3558 −1.15291 −0.576456 0.817128i \(-0.695565\pi\)
−0.576456 + 0.817128i \(0.695565\pi\)
\(564\) 46.5112 1.95847
\(565\) 9.84879 0.414342
\(566\) −0.114557 −0.00481519
\(567\) 22.7112 0.953782
\(568\) 1.24061 0.0520549
\(569\) −13.7344 −0.575775 −0.287887 0.957664i \(-0.592953\pi\)
−0.287887 + 0.957664i \(0.592953\pi\)
\(570\) 111.448 4.66806
\(571\) 0.218398 0.00913966 0.00456983 0.999990i \(-0.498545\pi\)
0.00456983 + 0.999990i \(0.498545\pi\)
\(572\) 26.4010 1.10388
\(573\) 0.314742 0.0131485
\(574\) 61.2986 2.55855
\(575\) −7.65109 −0.319073
\(576\) −0.546507 −0.0227711
\(577\) −37.2260 −1.54974 −0.774870 0.632121i \(-0.782185\pi\)
−0.774870 + 0.632121i \(0.782185\pi\)
\(578\) −65.3561 −2.71845
\(579\) 10.0337 0.416987
\(580\) −18.2573 −0.758093
\(581\) −32.3014 −1.34009
\(582\) 13.2170 0.547862
\(583\) −7.71125 −0.319367
\(584\) 61.5545 2.54714
\(585\) 37.4687 1.54914
\(586\) −2.34996 −0.0970761
\(587\) 27.7337 1.14469 0.572346 0.820012i \(-0.306033\pi\)
0.572346 + 0.820012i \(0.306033\pi\)
\(588\) 24.2965 1.00197
\(589\) −1.05995 −0.0436745
\(590\) −16.3524 −0.673217
\(591\) 41.3893 1.70253
\(592\) −65.9007 −2.70850
\(593\) −27.9161 −1.14638 −0.573189 0.819423i \(-0.694294\pi\)
−0.573189 + 0.819423i \(0.694294\pi\)
\(594\) 4.26957 0.175183
\(595\) −42.6533 −1.74862
\(596\) 3.93714 0.161272
\(597\) 27.8974 1.14176
\(598\) −24.6818 −1.00931
\(599\) −4.71962 −0.192838 −0.0964192 0.995341i \(-0.530739\pi\)
−0.0964192 + 0.995341i \(0.530739\pi\)
\(600\) 60.7658 2.48075
\(601\) 3.85608 0.157293 0.0786463 0.996903i \(-0.474940\pi\)
0.0786463 + 0.996903i \(0.474940\pi\)
\(602\) −8.28692 −0.337750
\(603\) −31.1290 −1.26767
\(604\) −95.7030 −3.89410
\(605\) 29.4971 1.19923
\(606\) 9.11859 0.370417
\(607\) 35.6084 1.44530 0.722650 0.691214i \(-0.242924\pi\)
0.722650 + 0.691214i \(0.242924\pi\)
\(608\) 34.4456 1.39695
\(609\) 6.72021 0.272317
\(610\) 61.7036 2.49830
\(611\) 23.6129 0.955278
\(612\) −68.8707 −2.78393
\(613\) −3.38207 −0.136601 −0.0683003 0.997665i \(-0.521758\pi\)
−0.0683003 + 0.997665i \(0.521758\pi\)
\(614\) 19.4671 0.785627
\(615\) 78.0932 3.14902
\(616\) −15.2598 −0.614833
\(617\) −43.2857 −1.74262 −0.871308 0.490737i \(-0.836728\pi\)
−0.871308 + 0.490737i \(0.836728\pi\)
\(618\) 87.7453 3.52963
\(619\) −23.6178 −0.949280 −0.474640 0.880180i \(-0.657422\pi\)
−0.474640 + 0.880180i \(0.657422\pi\)
\(620\) −2.29909 −0.0923338
\(621\) −2.76009 −0.110759
\(622\) 69.1643 2.77324
\(623\) 9.72427 0.389595
\(624\) 86.8284 3.47592
\(625\) −28.5097 −1.14039
\(626\) −57.8065 −2.31041
\(627\) −16.1830 −0.646287
\(628\) 50.0531 1.99734
\(629\) 60.3853 2.40772
\(630\) −39.1036 −1.55792
\(631\) 2.28587 0.0909990 0.0454995 0.998964i \(-0.485512\pi\)
0.0454995 + 0.998964i \(0.485512\pi\)
\(632\) 50.4820 2.00807
\(633\) −42.7358 −1.69859
\(634\) 50.4748 2.00461
\(635\) 13.2494 0.525787
\(636\) −71.4857 −2.83459
\(637\) 12.3349 0.488728
\(638\) 3.83389 0.151785
\(639\) −0.461626 −0.0182617
\(640\) −35.1251 −1.38844
\(641\) −39.0478 −1.54229 −0.771147 0.636657i \(-0.780317\pi\)
−0.771147 + 0.636657i \(0.780317\pi\)
\(642\) −26.6239 −1.05076
\(643\) −3.64472 −0.143734 −0.0718669 0.997414i \(-0.522896\pi\)
−0.0718669 + 0.997414i \(0.522896\pi\)
\(644\) 17.8117 0.701881
\(645\) −10.5574 −0.415697
\(646\) −104.000 −4.09182
\(647\) 2.37465 0.0933571 0.0466785 0.998910i \(-0.485136\pi\)
0.0466785 + 0.998910i \(0.485136\pi\)
\(648\) 66.5230 2.61327
\(649\) 2.37447 0.0932060
\(650\) 55.7022 2.18482
\(651\) 0.846259 0.0331675
\(652\) 55.3654 2.16828
\(653\) −41.9990 −1.64355 −0.821774 0.569814i \(-0.807015\pi\)
−0.821774 + 0.569814i \(0.807015\pi\)
\(654\) 55.7584 2.18033
\(655\) −8.35935 −0.326627
\(656\) 79.5300 3.10513
\(657\) −22.9042 −0.893576
\(658\) −24.6433 −0.960694
\(659\) 41.3762 1.61179 0.805894 0.592059i \(-0.201685\pi\)
0.805894 + 0.592059i \(0.201685\pi\)
\(660\) −35.1019 −1.36634
\(661\) −47.6937 −1.85507 −0.927535 0.373735i \(-0.878077\pi\)
−0.927535 + 0.373735i \(0.878077\pi\)
\(662\) −15.1381 −0.588360
\(663\) −79.5615 −3.08991
\(664\) −94.6133 −3.67171
\(665\) −40.8317 −1.58338
\(666\) 55.3599 2.14515
\(667\) −2.47844 −0.0959656
\(668\) 85.9736 3.32642
\(669\) −23.4530 −0.906746
\(670\) −101.961 −3.93910
\(671\) −8.95974 −0.345887
\(672\) −27.5012 −1.06088
\(673\) −48.6598 −1.87570 −0.937850 0.347042i \(-0.887186\pi\)
−0.937850 + 0.347042i \(0.887186\pi\)
\(674\) −29.8212 −1.14867
\(675\) 6.22901 0.239755
\(676\) 65.9787 2.53764
\(677\) −15.9423 −0.612711 −0.306355 0.951917i \(-0.599110\pi\)
−0.306355 + 0.951917i \(0.599110\pi\)
\(678\) −19.1726 −0.736319
\(679\) −4.84235 −0.185832
\(680\) −124.935 −4.79104
\(681\) 43.7524 1.67659
\(682\) 0.482792 0.0184871
\(683\) 3.83176 0.146618 0.0733092 0.997309i \(-0.476644\pi\)
0.0733092 + 0.997309i \(0.476644\pi\)
\(684\) −65.9293 −2.52087
\(685\) 34.0998 1.30289
\(686\) −51.3352 −1.95999
\(687\) −27.9922 −1.06797
\(688\) −10.7516 −0.409902
\(689\) −36.2921 −1.38262
\(690\) 32.8161 1.24929
\(691\) −11.6515 −0.443245 −0.221622 0.975133i \(-0.571135\pi\)
−0.221622 + 0.975133i \(0.571135\pi\)
\(692\) 49.8352 1.89445
\(693\) 5.67809 0.215693
\(694\) 46.2689 1.75634
\(695\) −54.1759 −2.05501
\(696\) 19.6840 0.746122
\(697\) −72.8739 −2.76030
\(698\) 0.0711685 0.00269377
\(699\) 0.286623 0.0108411
\(700\) −40.1978 −1.51933
\(701\) −31.6364 −1.19489 −0.597445 0.801910i \(-0.703817\pi\)
−0.597445 + 0.801910i \(0.703817\pi\)
\(702\) 20.0943 0.758409
\(703\) 57.8063 2.18021
\(704\) 0.259927 0.00979636
\(705\) −31.3951 −1.18241
\(706\) −8.96374 −0.337355
\(707\) −3.34080 −0.125644
\(708\) 22.0121 0.827264
\(709\) −32.7582 −1.23026 −0.615130 0.788426i \(-0.710897\pi\)
−0.615130 + 0.788426i \(0.710897\pi\)
\(710\) −1.51203 −0.0567454
\(711\) −18.7841 −0.704460
\(712\) 28.4832 1.06745
\(713\) −0.312104 −0.0116884
\(714\) 83.0330 3.10743
\(715\) −17.8207 −0.666455
\(716\) 77.8364 2.90888
\(717\) 10.7502 0.401472
\(718\) 85.0125 3.17264
\(719\) −26.0367 −0.971006 −0.485503 0.874235i \(-0.661363\pi\)
−0.485503 + 0.874235i \(0.661363\pi\)
\(720\) −50.7338 −1.89074
\(721\) −32.1475 −1.19723
\(722\) −51.1822 −1.90480
\(723\) −20.1138 −0.748041
\(724\) −92.8539 −3.45089
\(725\) 5.59338 0.207733
\(726\) −57.4219 −2.13113
\(727\) −20.2033 −0.749298 −0.374649 0.927167i \(-0.622237\pi\)
−0.374649 + 0.927167i \(0.622237\pi\)
\(728\) −71.8183 −2.66176
\(729\) −14.3492 −0.531450
\(730\) −75.0212 −2.77666
\(731\) 9.85179 0.364382
\(732\) −83.0596 −3.06997
\(733\) −26.7064 −0.986423 −0.493212 0.869909i \(-0.664177\pi\)
−0.493212 + 0.869909i \(0.664177\pi\)
\(734\) 23.0676 0.851442
\(735\) −16.4002 −0.604929
\(736\) 10.1426 0.373859
\(737\) 14.8054 0.545364
\(738\) −66.8092 −2.45928
\(739\) −6.02930 −0.221791 −0.110896 0.993832i \(-0.535372\pi\)
−0.110896 + 0.993832i \(0.535372\pi\)
\(740\) 125.385 4.60926
\(741\) −76.1634 −2.79793
\(742\) 37.8757 1.39046
\(743\) 2.64757 0.0971300 0.0485650 0.998820i \(-0.484535\pi\)
0.0485650 + 0.998820i \(0.484535\pi\)
\(744\) 2.47876 0.0908757
\(745\) −2.65757 −0.0973660
\(746\) 57.7274 2.11355
\(747\) 35.2052 1.28809
\(748\) 32.7559 1.19767
\(749\) 9.75428 0.356414
\(750\) 15.0536 0.549678
\(751\) 45.9015 1.67497 0.837485 0.546460i \(-0.184025\pi\)
0.837485 + 0.546460i \(0.184025\pi\)
\(752\) −31.9727 −1.16592
\(753\) −33.9371 −1.23674
\(754\) 18.0438 0.657116
\(755\) 64.5996 2.35102
\(756\) −14.5011 −0.527401
\(757\) 23.7709 0.863966 0.431983 0.901882i \(-0.357814\pi\)
0.431983 + 0.901882i \(0.357814\pi\)
\(758\) −17.5546 −0.637611
\(759\) −4.76511 −0.172962
\(760\) −119.599 −4.33832
\(761\) −14.3488 −0.520144 −0.260072 0.965589i \(-0.583746\pi\)
−0.260072 + 0.965589i \(0.583746\pi\)
\(762\) −25.7925 −0.934365
\(763\) −20.4284 −0.739556
\(764\) −0.609858 −0.0220639
\(765\) 46.4878 1.68077
\(766\) −72.1777 −2.60789
\(767\) 11.1752 0.403512
\(768\) 67.3028 2.42858
\(769\) −15.8726 −0.572382 −0.286191 0.958173i \(-0.592389\pi\)
−0.286191 + 0.958173i \(0.592389\pi\)
\(770\) 18.5982 0.670234
\(771\) −32.9454 −1.18650
\(772\) −19.4418 −0.699725
\(773\) 42.7407 1.53728 0.768639 0.639683i \(-0.220934\pi\)
0.768639 + 0.639683i \(0.220934\pi\)
\(774\) 9.03190 0.324645
\(775\) 0.704360 0.0253014
\(776\) −14.1836 −0.509162
\(777\) −46.1523 −1.65570
\(778\) −9.20521 −0.330023
\(779\) −69.7616 −2.49947
\(780\) −165.203 −5.91522
\(781\) 0.219556 0.00785633
\(782\) −30.6229 −1.09507
\(783\) 2.01778 0.0721096
\(784\) −16.7019 −0.596497
\(785\) −33.7859 −1.20587
\(786\) 16.2731 0.580442
\(787\) 17.0715 0.608533 0.304266 0.952587i \(-0.401589\pi\)
0.304266 + 0.952587i \(0.401589\pi\)
\(788\) −80.1978 −2.85693
\(789\) −54.7627 −1.94961
\(790\) −61.5263 −2.18901
\(791\) 7.02431 0.249756
\(792\) 16.6316 0.590977
\(793\) −42.1680 −1.49743
\(794\) −62.5507 −2.21984
\(795\) 48.2529 1.71135
\(796\) −54.0552 −1.91594
\(797\) 34.1268 1.20883 0.604417 0.796668i \(-0.293406\pi\)
0.604417 + 0.796668i \(0.293406\pi\)
\(798\) 79.4867 2.81380
\(799\) 29.2968 1.03645
\(800\) −22.8899 −0.809279
\(801\) −10.5985 −0.374478
\(802\) −78.1146 −2.75832
\(803\) 10.8935 0.384425
\(804\) 137.251 4.84046
\(805\) −12.0229 −0.423753
\(806\) 2.27220 0.0800350
\(807\) −40.8029 −1.43633
\(808\) −9.78547 −0.344252
\(809\) 43.8724 1.54247 0.771236 0.636549i \(-0.219639\pi\)
0.771236 + 0.636549i \(0.219639\pi\)
\(810\) −81.0767 −2.84875
\(811\) −0.487573 −0.0171210 −0.00856051 0.999963i \(-0.502725\pi\)
−0.00856051 + 0.999963i \(0.502725\pi\)
\(812\) −13.0214 −0.456961
\(813\) 49.3511 1.73082
\(814\) −26.3300 −0.922864
\(815\) −37.3717 −1.30907
\(816\) 107.729 3.77126
\(817\) 9.43103 0.329950
\(818\) −2.50769 −0.0876792
\(819\) 26.7233 0.933786
\(820\) −151.317 −5.28422
\(821\) −3.39195 −0.118380 −0.0591900 0.998247i \(-0.518852\pi\)
−0.0591900 + 0.998247i \(0.518852\pi\)
\(822\) −66.3818 −2.31533
\(823\) 2.28824 0.0797629 0.0398814 0.999204i \(-0.487302\pi\)
0.0398814 + 0.999204i \(0.487302\pi\)
\(824\) −94.1625 −3.28031
\(825\) 10.7540 0.374405
\(826\) −11.6628 −0.405800
\(827\) 14.9974 0.521511 0.260756 0.965405i \(-0.416028\pi\)
0.260756 + 0.965405i \(0.416028\pi\)
\(828\) −19.4130 −0.674647
\(829\) −46.8989 −1.62887 −0.814433 0.580257i \(-0.802952\pi\)
−0.814433 + 0.580257i \(0.802952\pi\)
\(830\) 115.312 4.00255
\(831\) −29.8989 −1.03718
\(832\) 1.22332 0.0424108
\(833\) 15.3041 0.530255
\(834\) 105.464 3.65192
\(835\) −58.0322 −2.00829
\(836\) 31.3569 1.08450
\(837\) 0.254094 0.00878277
\(838\) 5.85900 0.202396
\(839\) 34.0396 1.17518 0.587588 0.809160i \(-0.300078\pi\)
0.587588 + 0.809160i \(0.300078\pi\)
\(840\) 95.4874 3.29463
\(841\) −27.1881 −0.937521
\(842\) −76.2573 −2.62800
\(843\) −8.46148 −0.291429
\(844\) 82.8067 2.85033
\(845\) −44.5357 −1.53207
\(846\) 26.8586 0.923419
\(847\) 21.0378 0.722868
\(848\) 49.1407 1.68750
\(849\) −0.104089 −0.00357233
\(850\) 69.1102 2.37046
\(851\) 17.0211 0.583477
\(852\) 2.03535 0.0697300
\(853\) −5.66104 −0.193830 −0.0969151 0.995293i \(-0.530898\pi\)
−0.0969151 + 0.995293i \(0.530898\pi\)
\(854\) 44.0079 1.50592
\(855\) 44.5023 1.52195
\(856\) 28.5711 0.976539
\(857\) 10.3392 0.353181 0.176590 0.984284i \(-0.443493\pi\)
0.176590 + 0.984284i \(0.443493\pi\)
\(858\) 34.6914 1.18434
\(859\) 51.8642 1.76958 0.884791 0.465988i \(-0.154301\pi\)
0.884791 + 0.465988i \(0.154301\pi\)
\(860\) 20.4565 0.697560
\(861\) 55.6973 1.89816
\(862\) 53.0354 1.80639
\(863\) 15.6714 0.533460 0.266730 0.963771i \(-0.414057\pi\)
0.266730 + 0.963771i \(0.414057\pi\)
\(864\) −8.25739 −0.280922
\(865\) −33.6388 −1.14375
\(866\) 86.0880 2.92539
\(867\) −59.3840 −2.01679
\(868\) −1.63975 −0.0556567
\(869\) 8.93400 0.303065
\(870\) −23.9904 −0.813352
\(871\) 69.6799 2.36101
\(872\) −59.8363 −2.02631
\(873\) 5.27766 0.178622
\(874\) −29.3150 −0.991595
\(875\) −5.51521 −0.186448
\(876\) 100.987 3.41202
\(877\) 41.7811 1.41085 0.705424 0.708786i \(-0.250757\pi\)
0.705424 + 0.708786i \(0.250757\pi\)
\(878\) 31.5705 1.06545
\(879\) −2.13523 −0.0720195
\(880\) 24.1297 0.813413
\(881\) 50.2244 1.69210 0.846052 0.533100i \(-0.178973\pi\)
0.846052 + 0.533100i \(0.178973\pi\)
\(882\) 14.0304 0.472429
\(883\) 33.1248 1.11474 0.557369 0.830265i \(-0.311811\pi\)
0.557369 + 0.830265i \(0.311811\pi\)
\(884\) 154.162 5.18503
\(885\) −14.8581 −0.499451
\(886\) 68.5434 2.30276
\(887\) −32.0100 −1.07479 −0.537396 0.843330i \(-0.680592\pi\)
−0.537396 + 0.843330i \(0.680592\pi\)
\(888\) −135.184 −4.53647
\(889\) 9.44968 0.316932
\(890\) −34.7146 −1.16364
\(891\) 11.7728 0.394405
\(892\) 45.4436 1.52157
\(893\) 28.0456 0.938509
\(894\) 5.17348 0.173027
\(895\) −52.5396 −1.75620
\(896\) −25.0518 −0.836921
\(897\) −22.4264 −0.748796
\(898\) −76.1549 −2.54132
\(899\) 0.228165 0.00760974
\(900\) 43.8115 1.46038
\(901\) −45.0280 −1.50010
\(902\) 31.7754 1.05800
\(903\) −7.52969 −0.250572
\(904\) 20.5748 0.684306
\(905\) 62.6764 2.08343
\(906\) −125.756 −4.17795
\(907\) −51.8138 −1.72045 −0.860225 0.509915i \(-0.829677\pi\)
−0.860225 + 0.509915i \(0.829677\pi\)
\(908\) −84.7766 −2.81341
\(909\) 3.64113 0.120769
\(910\) 87.5304 2.90161
\(911\) −1.01322 −0.0335694 −0.0167847 0.999859i \(-0.505343\pi\)
−0.0167847 + 0.999859i \(0.505343\pi\)
\(912\) 103.128 3.41490
\(913\) −16.7441 −0.554148
\(914\) −12.2001 −0.403543
\(915\) 56.0653 1.85346
\(916\) 54.2389 1.79210
\(917\) −5.96202 −0.196883
\(918\) 24.9311 0.822850
\(919\) 44.4151 1.46512 0.732559 0.680704i \(-0.238326\pi\)
0.732559 + 0.680704i \(0.238326\pi\)
\(920\) −35.2161 −1.16104
\(921\) 17.6882 0.582847
\(922\) −17.6029 −0.579721
\(923\) 1.03332 0.0340120
\(924\) −25.0352 −0.823598
\(925\) −38.4136 −1.26303
\(926\) 74.2970 2.44155
\(927\) 35.0375 1.15078
\(928\) −7.41478 −0.243402
\(929\) −3.62621 −0.118972 −0.0594860 0.998229i \(-0.518946\pi\)
−0.0594860 + 0.998229i \(0.518946\pi\)
\(930\) −3.02105 −0.0990643
\(931\) 14.6504 0.480149
\(932\) −0.555373 −0.0181918
\(933\) 62.8443 2.05743
\(934\) 30.7417 1.00590
\(935\) −22.1103 −0.723083
\(936\) 78.2746 2.55848
\(937\) 13.5578 0.442914 0.221457 0.975170i \(-0.428919\pi\)
0.221457 + 0.975170i \(0.428919\pi\)
\(938\) −72.7202 −2.37440
\(939\) −52.5243 −1.71407
\(940\) 60.8325 1.98414
\(941\) 22.5394 0.734764 0.367382 0.930070i \(-0.380254\pi\)
0.367382 + 0.930070i \(0.380254\pi\)
\(942\) 65.7708 2.14293
\(943\) −20.5414 −0.668919
\(944\) −15.1315 −0.492489
\(945\) 9.78827 0.318412
\(946\) −4.29570 −0.139665
\(947\) 29.0633 0.944429 0.472214 0.881484i \(-0.343455\pi\)
0.472214 + 0.881484i \(0.343455\pi\)
\(948\) 82.8210 2.68990
\(949\) 51.2692 1.66427
\(950\) 66.1586 2.14647
\(951\) 45.8625 1.48719
\(952\) −89.1056 −2.88793
\(953\) −0.340675 −0.0110356 −0.00551778 0.999985i \(-0.501756\pi\)
−0.00551778 + 0.999985i \(0.501756\pi\)
\(954\) −41.2806 −1.33651
\(955\) 0.411655 0.0133208
\(956\) −20.8300 −0.673690
\(957\) 3.48356 0.112608
\(958\) 64.2084 2.07448
\(959\) 24.3205 0.785350
\(960\) −1.62648 −0.0524945
\(961\) −30.9713 −0.999073
\(962\) −123.919 −3.99530
\(963\) −10.6312 −0.342585
\(964\) 38.9734 1.25525
\(965\) 13.1232 0.422451
\(966\) 23.4050 0.753042
\(967\) 0.227348 0.00731102 0.00365551 0.999993i \(-0.498836\pi\)
0.00365551 + 0.999993i \(0.498836\pi\)
\(968\) 61.6214 1.98059
\(969\) −94.4967 −3.03567
\(970\) 17.2867 0.555041
\(971\) 53.3032 1.71058 0.855291 0.518148i \(-0.173378\pi\)
0.855291 + 0.518148i \(0.173378\pi\)
\(972\) 88.9791 2.85401
\(973\) −38.6391 −1.23871
\(974\) −25.4402 −0.815156
\(975\) 50.6123 1.62089
\(976\) 57.0968 1.82762
\(977\) −55.6819 −1.78142 −0.890712 0.454569i \(-0.849793\pi\)
−0.890712 + 0.454569i \(0.849793\pi\)
\(978\) 72.7512 2.32633
\(979\) 5.04078 0.161104
\(980\) 31.7777 1.01510
\(981\) 22.2648 0.710861
\(982\) −19.3283 −0.616791
\(983\) −29.7370 −0.948462 −0.474231 0.880400i \(-0.657274\pi\)
−0.474231 + 0.880400i \(0.657274\pi\)
\(984\) 163.142 5.20077
\(985\) 54.1335 1.72484
\(986\) 22.3871 0.712950
\(987\) −22.3914 −0.712727
\(988\) 147.578 4.69507
\(989\) 2.77698 0.0883028
\(990\) −20.2702 −0.644228
\(991\) 37.0786 1.17784 0.588920 0.808191i \(-0.299553\pi\)
0.588920 + 0.808191i \(0.299553\pi\)
\(992\) −0.933724 −0.0296458
\(993\) −13.7548 −0.436497
\(994\) −1.07840 −0.0342048
\(995\) 36.4873 1.15673
\(996\) −155.223 −4.91842
\(997\) 22.3345 0.707341 0.353671 0.935370i \(-0.384933\pi\)
0.353671 + 0.935370i \(0.384933\pi\)
\(998\) −20.4357 −0.646880
\(999\) −13.8575 −0.438431
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 \(a_p\))