Properties

Label 6041.2.a.f.1.11
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.57785 q^{2}\) \(-0.937633 q^{3}\) \(+4.64529 q^{4}\) \(-3.87896 q^{5}\) \(+2.41707 q^{6}\) \(+1.00000 q^{7}\) \(-6.81916 q^{8}\) \(-2.12084 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.57785 q^{2}\) \(-0.937633 q^{3}\) \(+4.64529 q^{4}\) \(-3.87896 q^{5}\) \(+2.41707 q^{6}\) \(+1.00000 q^{7}\) \(-6.81916 q^{8}\) \(-2.12084 q^{9}\) \(+9.99936 q^{10}\) \(+4.77034 q^{11}\) \(-4.35558 q^{12}\) \(-5.45549 q^{13}\) \(-2.57785 q^{14}\) \(+3.63704 q^{15}\) \(+8.28816 q^{16}\) \(-2.70243 q^{17}\) \(+5.46721 q^{18}\) \(-0.0387091 q^{19}\) \(-18.0189 q^{20}\) \(-0.937633 q^{21}\) \(-12.2972 q^{22}\) \(+8.78005 q^{23}\) \(+6.39387 q^{24}\) \(+10.0463 q^{25}\) \(+14.0634 q^{26}\) \(+4.80147 q^{27}\) \(+4.64529 q^{28}\) \(-5.81159 q^{29}\) \(-9.37573 q^{30}\) \(+7.97829 q^{31}\) \(-7.72728 q^{32}\) \(-4.47283 q^{33}\) \(+6.96645 q^{34}\) \(-3.87896 q^{35}\) \(-9.85194 q^{36}\) \(-10.0655 q^{37}\) \(+0.0997860 q^{38}\) \(+5.11525 q^{39}\) \(+26.4512 q^{40}\) \(-1.45641 q^{41}\) \(+2.41707 q^{42}\) \(+6.85876 q^{43}\) \(+22.1596 q^{44}\) \(+8.22667 q^{45}\) \(-22.6336 q^{46}\) \(-7.22348 q^{47}\) \(-7.77125 q^{48}\) \(+1.00000 q^{49}\) \(-25.8979 q^{50}\) \(+2.53389 q^{51}\) \(-25.3424 q^{52}\) \(-8.65850 q^{53}\) \(-12.3775 q^{54}\) \(-18.5040 q^{55}\) \(-6.81916 q^{56}\) \(+0.0362949 q^{57}\) \(+14.9814 q^{58}\) \(-9.38313 q^{59}\) \(+16.8951 q^{60}\) \(+13.2500 q^{61}\) \(-20.5668 q^{62}\) \(-2.12084 q^{63}\) \(+3.34343 q^{64}\) \(+21.1616 q^{65}\) \(+11.5303 q^{66}\) \(-0.538668 q^{67}\) \(-12.5536 q^{68}\) \(-8.23246 q^{69}\) \(+9.99936 q^{70}\) \(+4.14396 q^{71}\) \(+14.4624 q^{72}\) \(+0.785295 q^{73}\) \(+25.9473 q^{74}\) \(-9.41976 q^{75}\) \(-0.179815 q^{76}\) \(+4.77034 q^{77}\) \(-13.1863 q^{78}\) \(+6.77643 q^{79}\) \(-32.1494 q^{80}\) \(+1.86051 q^{81}\) \(+3.75439 q^{82}\) \(-10.7413 q^{83}\) \(-4.35558 q^{84}\) \(+10.4826 q^{85}\) \(-17.6808 q^{86}\) \(+5.44914 q^{87}\) \(-32.5297 q^{88}\) \(-12.2160 q^{89}\) \(-21.2071 q^{90}\) \(-5.45549 q^{91}\) \(+40.7859 q^{92}\) \(-7.48070 q^{93}\) \(+18.6210 q^{94}\) \(+0.150151 q^{95}\) \(+7.24535 q^{96}\) \(+10.1833 q^{97}\) \(-2.57785 q^{98}\) \(-10.1172 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57785 −1.82281 −0.911406 0.411508i \(-0.865002\pi\)
−0.911406 + 0.411508i \(0.865002\pi\)
\(3\) −0.937633 −0.541343 −0.270671 0.962672i \(-0.587246\pi\)
−0.270671 + 0.962672i \(0.587246\pi\)
\(4\) 4.64529 2.32265
\(5\) −3.87896 −1.73472 −0.867362 0.497678i \(-0.834186\pi\)
−0.867362 + 0.497678i \(0.834186\pi\)
\(6\) 2.41707 0.986766
\(7\) 1.00000 0.377964
\(8\) −6.81916 −2.41094
\(9\) −2.12084 −0.706948
\(10\) 9.99936 3.16208
\(11\) 4.77034 1.43831 0.719156 0.694848i \(-0.244529\pi\)
0.719156 + 0.694848i \(0.244529\pi\)
\(12\) −4.35558 −1.25735
\(13\) −5.45549 −1.51308 −0.756541 0.653947i \(-0.773112\pi\)
−0.756541 + 0.653947i \(0.773112\pi\)
\(14\) −2.57785 −0.688958
\(15\) 3.63704 0.939080
\(16\) 8.28816 2.07204
\(17\) −2.70243 −0.655435 −0.327718 0.944776i \(-0.606279\pi\)
−0.327718 + 0.944776i \(0.606279\pi\)
\(18\) 5.46721 1.28863
\(19\) −0.0387091 −0.00888047 −0.00444023 0.999990i \(-0.501413\pi\)
−0.00444023 + 0.999990i \(0.501413\pi\)
\(20\) −18.0189 −4.02915
\(21\) −0.937633 −0.204608
\(22\) −12.2972 −2.62177
\(23\) 8.78005 1.83077 0.915383 0.402583i \(-0.131888\pi\)
0.915383 + 0.402583i \(0.131888\pi\)
\(24\) 6.39387 1.30514
\(25\) 10.0463 2.00926
\(26\) 14.0634 2.75806
\(27\) 4.80147 0.924044
\(28\) 4.64529 0.877878
\(29\) −5.81159 −1.07919 −0.539593 0.841926i \(-0.681422\pi\)
−0.539593 + 0.841926i \(0.681422\pi\)
\(30\) −9.37573 −1.71177
\(31\) 7.97829 1.43294 0.716471 0.697617i \(-0.245756\pi\)
0.716471 + 0.697617i \(0.245756\pi\)
\(32\) −7.72728 −1.36600
\(33\) −4.47283 −0.778620
\(34\) 6.96645 1.19474
\(35\) −3.87896 −0.655664
\(36\) −9.85194 −1.64199
\(37\) −10.0655 −1.65475 −0.827377 0.561646i \(-0.810168\pi\)
−0.827377 + 0.561646i \(0.810168\pi\)
\(38\) 0.0997860 0.0161874
\(39\) 5.11525 0.819095
\(40\) 26.4512 4.18231
\(41\) −1.45641 −0.227453 −0.113726 0.993512i \(-0.536279\pi\)
−0.113726 + 0.993512i \(0.536279\pi\)
\(42\) 2.41707 0.372963
\(43\) 6.85876 1.04595 0.522976 0.852347i \(-0.324822\pi\)
0.522976 + 0.852347i \(0.324822\pi\)
\(44\) 22.1596 3.34069
\(45\) 8.22667 1.22636
\(46\) −22.6336 −3.33714
\(47\) −7.22348 −1.05365 −0.526826 0.849973i \(-0.676618\pi\)
−0.526826 + 0.849973i \(0.676618\pi\)
\(48\) −7.77125 −1.12168
\(49\) 1.00000 0.142857
\(50\) −25.8979 −3.66251
\(51\) 2.53389 0.354815
\(52\) −25.3424 −3.51435
\(53\) −8.65850 −1.18934 −0.594668 0.803971i \(-0.702717\pi\)
−0.594668 + 0.803971i \(0.702717\pi\)
\(54\) −12.3775 −1.68436
\(55\) −18.5040 −2.49507
\(56\) −6.81916 −0.911248
\(57\) 0.0362949 0.00480738
\(58\) 14.9814 1.96715
\(59\) −9.38313 −1.22158 −0.610790 0.791793i \(-0.709148\pi\)
−0.610790 + 0.791793i \(0.709148\pi\)
\(60\) 16.8951 2.18115
\(61\) 13.2500 1.69649 0.848243 0.529607i \(-0.177660\pi\)
0.848243 + 0.529607i \(0.177660\pi\)
\(62\) −20.5668 −2.61199
\(63\) −2.12084 −0.267201
\(64\) 3.34343 0.417929
\(65\) 21.1616 2.62478
\(66\) 11.5303 1.41928
\(67\) −0.538668 −0.0658088 −0.0329044 0.999459i \(-0.510476\pi\)
−0.0329044 + 0.999459i \(0.510476\pi\)
\(68\) −12.5536 −1.52234
\(69\) −8.23246 −0.991072
\(70\) 9.99936 1.19515
\(71\) 4.14396 0.491797 0.245899 0.969296i \(-0.420917\pi\)
0.245899 + 0.969296i \(0.420917\pi\)
\(72\) 14.4624 1.70441
\(73\) 0.785295 0.0919118 0.0459559 0.998943i \(-0.485367\pi\)
0.0459559 + 0.998943i \(0.485367\pi\)
\(74\) 25.9473 3.01631
\(75\) −9.41976 −1.08770
\(76\) −0.179815 −0.0206262
\(77\) 4.77034 0.543631
\(78\) −13.1863 −1.49306
\(79\) 6.77643 0.762408 0.381204 0.924491i \(-0.375510\pi\)
0.381204 + 0.924491i \(0.375510\pi\)
\(80\) −32.1494 −3.59441
\(81\) 1.86051 0.206724
\(82\) 3.75439 0.414603
\(83\) −10.7413 −1.17901 −0.589505 0.807765i \(-0.700677\pi\)
−0.589505 + 0.807765i \(0.700677\pi\)
\(84\) −4.35558 −0.475233
\(85\) 10.4826 1.13700
\(86\) −17.6808 −1.90657
\(87\) 5.44914 0.584209
\(88\) −32.5297 −3.46768
\(89\) −12.2160 −1.29489 −0.647445 0.762113i \(-0.724162\pi\)
−0.647445 + 0.762113i \(0.724162\pi\)
\(90\) −21.2071 −2.23542
\(91\) −5.45549 −0.571891
\(92\) 40.7859 4.25222
\(93\) −7.48070 −0.775713
\(94\) 18.6210 1.92061
\(95\) 0.150151 0.0154052
\(96\) 7.24535 0.739476
\(97\) 10.1833 1.03396 0.516979 0.855998i \(-0.327056\pi\)
0.516979 + 0.855998i \(0.327056\pi\)
\(98\) −2.57785 −0.260402
\(99\) −10.1172 −1.01681
\(100\) 46.6681 4.66681
\(101\) 7.67758 0.763947 0.381974 0.924173i \(-0.375244\pi\)
0.381974 + 0.924173i \(0.375244\pi\)
\(102\) −6.53197 −0.646761
\(103\) −0.915048 −0.0901623 −0.0450812 0.998983i \(-0.514355\pi\)
−0.0450812 + 0.998983i \(0.514355\pi\)
\(104\) 37.2019 3.64794
\(105\) 3.63704 0.354939
\(106\) 22.3203 2.16794
\(107\) 0.196388 0.0189856 0.00949278 0.999955i \(-0.496978\pi\)
0.00949278 + 0.999955i \(0.496978\pi\)
\(108\) 22.3042 2.14623
\(109\) −3.09764 −0.296700 −0.148350 0.988935i \(-0.547396\pi\)
−0.148350 + 0.988935i \(0.547396\pi\)
\(110\) 47.7004 4.54805
\(111\) 9.43773 0.895789
\(112\) 8.28816 0.783157
\(113\) −15.3283 −1.44196 −0.720982 0.692954i \(-0.756309\pi\)
−0.720982 + 0.692954i \(0.756309\pi\)
\(114\) −0.0935627 −0.00876295
\(115\) −34.0574 −3.17587
\(116\) −26.9966 −2.50657
\(117\) 11.5703 1.06967
\(118\) 24.1883 2.22671
\(119\) −2.70243 −0.247731
\(120\) −24.8015 −2.26406
\(121\) 11.7562 1.06874
\(122\) −34.1564 −3.09238
\(123\) 1.36557 0.123130
\(124\) 37.0615 3.32822
\(125\) −19.5745 −1.75079
\(126\) 5.46721 0.487058
\(127\) −17.2937 −1.53457 −0.767284 0.641308i \(-0.778392\pi\)
−0.767284 + 0.641308i \(0.778392\pi\)
\(128\) 6.83571 0.604198
\(129\) −6.43100 −0.566218
\(130\) −54.5514 −4.78448
\(131\) −17.5230 −1.53099 −0.765494 0.643443i \(-0.777505\pi\)
−0.765494 + 0.643443i \(0.777505\pi\)
\(132\) −20.7776 −1.80846
\(133\) −0.0387091 −0.00335650
\(134\) 1.38860 0.119957
\(135\) −18.6247 −1.60296
\(136\) 18.4283 1.58021
\(137\) −4.12588 −0.352498 −0.176249 0.984346i \(-0.556396\pi\)
−0.176249 + 0.984346i \(0.556396\pi\)
\(138\) 21.2220 1.80654
\(139\) −0.708986 −0.0601354 −0.0300677 0.999548i \(-0.509572\pi\)
−0.0300677 + 0.999548i \(0.509572\pi\)
\(140\) −18.0189 −1.52287
\(141\) 6.77297 0.570387
\(142\) −10.6825 −0.896454
\(143\) −26.0246 −2.17628
\(144\) −17.5779 −1.46482
\(145\) 22.5429 1.87209
\(146\) −2.02437 −0.167538
\(147\) −0.937633 −0.0773347
\(148\) −46.7571 −3.84341
\(149\) −10.9216 −0.894736 −0.447368 0.894350i \(-0.647639\pi\)
−0.447368 + 0.894350i \(0.647639\pi\)
\(150\) 24.2827 1.98267
\(151\) 14.3897 1.17101 0.585507 0.810667i \(-0.300895\pi\)
0.585507 + 0.810667i \(0.300895\pi\)
\(152\) 0.263963 0.0214102
\(153\) 5.73143 0.463359
\(154\) −12.2972 −0.990937
\(155\) −30.9474 −2.48576
\(156\) 23.7618 1.90247
\(157\) 5.89056 0.470117 0.235059 0.971981i \(-0.424472\pi\)
0.235059 + 0.971981i \(0.424472\pi\)
\(158\) −17.4686 −1.38973
\(159\) 8.11849 0.643838
\(160\) 29.9738 2.36964
\(161\) 8.78005 0.691965
\(162\) −4.79612 −0.376819
\(163\) 1.22587 0.0960175 0.0480087 0.998847i \(-0.484712\pi\)
0.0480087 + 0.998847i \(0.484712\pi\)
\(164\) −6.76543 −0.528292
\(165\) 17.3499 1.35069
\(166\) 27.6894 2.14911
\(167\) −10.8973 −0.843261 −0.421630 0.906768i \(-0.638542\pi\)
−0.421630 + 0.906768i \(0.638542\pi\)
\(168\) 6.39387 0.493298
\(169\) 16.7624 1.28942
\(170\) −27.0226 −2.07254
\(171\) 0.0820959 0.00627803
\(172\) 31.8610 2.42938
\(173\) 14.7965 1.12496 0.562479 0.826812i \(-0.309848\pi\)
0.562479 + 0.826812i \(0.309848\pi\)
\(174\) −14.0471 −1.06490
\(175\) 10.0463 0.759431
\(176\) 39.5373 2.98024
\(177\) 8.79794 0.661293
\(178\) 31.4909 2.36034
\(179\) −2.18905 −0.163617 −0.0818087 0.996648i \(-0.526070\pi\)
−0.0818087 + 0.996648i \(0.526070\pi\)
\(180\) 38.2153 2.84840
\(181\) −14.1496 −1.05173 −0.525864 0.850568i \(-0.676258\pi\)
−0.525864 + 0.850568i \(0.676258\pi\)
\(182\) 14.0634 1.04245
\(183\) −12.4236 −0.918381
\(184\) −59.8725 −4.41386
\(185\) 39.0436 2.87054
\(186\) 19.2841 1.41398
\(187\) −12.8915 −0.942721
\(188\) −33.5552 −2.44726
\(189\) 4.80147 0.349256
\(190\) −0.387066 −0.0280807
\(191\) 19.3731 1.40179 0.700893 0.713266i \(-0.252785\pi\)
0.700893 + 0.713266i \(0.252785\pi\)
\(192\) −3.13491 −0.226243
\(193\) −21.6103 −1.55554 −0.777772 0.628547i \(-0.783650\pi\)
−0.777772 + 0.628547i \(0.783650\pi\)
\(194\) −26.2510 −1.88471
\(195\) −19.8418 −1.42090
\(196\) 4.64529 0.331807
\(197\) 14.1065 1.00505 0.502523 0.864564i \(-0.332405\pi\)
0.502523 + 0.864564i \(0.332405\pi\)
\(198\) 26.0805 1.85346
\(199\) −9.32295 −0.660886 −0.330443 0.943826i \(-0.607198\pi\)
−0.330443 + 0.943826i \(0.607198\pi\)
\(200\) −68.5075 −4.84421
\(201\) 0.505073 0.0356251
\(202\) −19.7916 −1.39253
\(203\) −5.81159 −0.407894
\(204\) 11.7706 0.824110
\(205\) 5.64934 0.394567
\(206\) 2.35885 0.164349
\(207\) −18.6211 −1.29426
\(208\) −45.2160 −3.13516
\(209\) −0.184656 −0.0127729
\(210\) −9.37573 −0.646987
\(211\) 4.50025 0.309810 0.154905 0.987929i \(-0.450493\pi\)
0.154905 + 0.987929i \(0.450493\pi\)
\(212\) −40.2213 −2.76241
\(213\) −3.88551 −0.266231
\(214\) −0.506259 −0.0346071
\(215\) −26.6049 −1.81444
\(216\) −32.7420 −2.22781
\(217\) 7.97829 0.541601
\(218\) 7.98524 0.540829
\(219\) −0.736319 −0.0497558
\(220\) −85.9563 −5.79517
\(221\) 14.7431 0.991727
\(222\) −24.3290 −1.63286
\(223\) 16.5907 1.11100 0.555498 0.831518i \(-0.312528\pi\)
0.555498 + 0.831518i \(0.312528\pi\)
\(224\) −7.72728 −0.516301
\(225\) −21.3067 −1.42045
\(226\) 39.5140 2.62843
\(227\) −7.84887 −0.520948 −0.260474 0.965481i \(-0.583879\pi\)
−0.260474 + 0.965481i \(0.583879\pi\)
\(228\) 0.168600 0.0111658
\(229\) −20.8885 −1.38035 −0.690177 0.723641i \(-0.742467\pi\)
−0.690177 + 0.723641i \(0.742467\pi\)
\(230\) 87.7949 5.78902
\(231\) −4.47283 −0.294291
\(232\) 39.6302 2.60185
\(233\) 27.4101 1.79569 0.897847 0.440308i \(-0.145131\pi\)
0.897847 + 0.440308i \(0.145131\pi\)
\(234\) −29.8263 −1.94981
\(235\) 28.0196 1.82780
\(236\) −43.5874 −2.83730
\(237\) −6.35380 −0.412724
\(238\) 6.96645 0.451568
\(239\) −4.12394 −0.266756 −0.133378 0.991065i \(-0.542582\pi\)
−0.133378 + 0.991065i \(0.542582\pi\)
\(240\) 30.1444 1.94581
\(241\) 25.6840 1.65445 0.827227 0.561867i \(-0.189917\pi\)
0.827227 + 0.561867i \(0.189917\pi\)
\(242\) −30.3056 −1.94812
\(243\) −16.1489 −1.03595
\(244\) 61.5501 3.94034
\(245\) −3.87896 −0.247818
\(246\) −3.52024 −0.224442
\(247\) 0.211177 0.0134369
\(248\) −54.4052 −3.45473
\(249\) 10.0714 0.638248
\(250\) 50.4600 3.19137
\(251\) −16.1249 −1.01779 −0.508897 0.860827i \(-0.669947\pi\)
−0.508897 + 0.860827i \(0.669947\pi\)
\(252\) −9.85194 −0.620614
\(253\) 41.8838 2.63321
\(254\) 44.5805 2.79723
\(255\) −9.82884 −0.615506
\(256\) −24.3083 −1.51927
\(257\) −11.3156 −0.705847 −0.352924 0.935652i \(-0.614812\pi\)
−0.352924 + 0.935652i \(0.614812\pi\)
\(258\) 16.5781 1.03211
\(259\) −10.0655 −0.625439
\(260\) 98.3020 6.09643
\(261\) 12.3255 0.762928
\(262\) 45.1715 2.79070
\(263\) 13.2993 0.820072 0.410036 0.912069i \(-0.365516\pi\)
0.410036 + 0.912069i \(0.365516\pi\)
\(264\) 30.5009 1.87720
\(265\) 33.5860 2.06317
\(266\) 0.0997860 0.00611827
\(267\) 11.4541 0.700979
\(268\) −2.50227 −0.152850
\(269\) −2.87459 −0.175267 −0.0876336 0.996153i \(-0.527930\pi\)
−0.0876336 + 0.996153i \(0.527930\pi\)
\(270\) 48.0117 2.92190
\(271\) −7.82431 −0.475293 −0.237646 0.971352i \(-0.576376\pi\)
−0.237646 + 0.971352i \(0.576376\pi\)
\(272\) −22.3982 −1.35809
\(273\) 5.11525 0.309589
\(274\) 10.6359 0.642537
\(275\) 47.9244 2.88995
\(276\) −38.2422 −2.30191
\(277\) −30.3783 −1.82525 −0.912627 0.408793i \(-0.865950\pi\)
−0.912627 + 0.408793i \(0.865950\pi\)
\(278\) 1.82766 0.109616
\(279\) −16.9207 −1.01302
\(280\) 26.4512 1.58076
\(281\) −11.1304 −0.663982 −0.331991 0.943282i \(-0.607720\pi\)
−0.331991 + 0.943282i \(0.607720\pi\)
\(282\) −17.4597 −1.03971
\(283\) −12.1409 −0.721699 −0.360849 0.932624i \(-0.617513\pi\)
−0.360849 + 0.932624i \(0.617513\pi\)
\(284\) 19.2499 1.14227
\(285\) −0.140786 −0.00833947
\(286\) 67.0873 3.96696
\(287\) −1.45641 −0.0859690
\(288\) 16.3884 0.965693
\(289\) −9.69688 −0.570405
\(290\) −58.1122 −3.41247
\(291\) −9.54821 −0.559726
\(292\) 3.64793 0.213479
\(293\) −18.9809 −1.10888 −0.554438 0.832225i \(-0.687067\pi\)
−0.554438 + 0.832225i \(0.687067\pi\)
\(294\) 2.41707 0.140967
\(295\) 36.3968 2.11910
\(296\) 68.6381 3.98951
\(297\) 22.9047 1.32906
\(298\) 28.1543 1.63094
\(299\) −47.8995 −2.77010
\(300\) −43.7576 −2.52634
\(301\) 6.85876 0.395333
\(302\) −37.0943 −2.13454
\(303\) −7.19875 −0.413557
\(304\) −0.320827 −0.0184007
\(305\) −51.3962 −2.94293
\(306\) −14.7747 −0.844616
\(307\) −11.4907 −0.655808 −0.327904 0.944711i \(-0.606342\pi\)
−0.327904 + 0.944711i \(0.606342\pi\)
\(308\) 22.1596 1.26266
\(309\) 0.857979 0.0488087
\(310\) 79.7778 4.53107
\(311\) 16.1891 0.918000 0.459000 0.888436i \(-0.348208\pi\)
0.459000 + 0.888436i \(0.348208\pi\)
\(312\) −34.8817 −1.97479
\(313\) −30.0000 −1.69570 −0.847850 0.530237i \(-0.822103\pi\)
−0.847850 + 0.530237i \(0.822103\pi\)
\(314\) −15.1849 −0.856936
\(315\) 8.22667 0.463520
\(316\) 31.4785 1.77080
\(317\) −34.7882 −1.95390 −0.976951 0.213464i \(-0.931525\pi\)
−0.976951 + 0.213464i \(0.931525\pi\)
\(318\) −20.9282 −1.17360
\(319\) −27.7233 −1.55221
\(320\) −12.9690 −0.724990
\(321\) −0.184140 −0.0102777
\(322\) −22.6336 −1.26132
\(323\) 0.104608 0.00582057
\(324\) 8.64263 0.480146
\(325\) −54.8076 −3.04018
\(326\) −3.16010 −0.175022
\(327\) 2.90445 0.160616
\(328\) 9.93147 0.548374
\(329\) −7.22348 −0.398243
\(330\) −44.7254 −2.46205
\(331\) 19.3672 1.06452 0.532258 0.846582i \(-0.321344\pi\)
0.532258 + 0.846582i \(0.321344\pi\)
\(332\) −49.8964 −2.73842
\(333\) 21.3473 1.16983
\(334\) 28.0916 1.53711
\(335\) 2.08947 0.114160
\(336\) −7.77125 −0.423956
\(337\) 24.3052 1.32399 0.661995 0.749508i \(-0.269710\pi\)
0.661995 + 0.749508i \(0.269710\pi\)
\(338\) −43.2109 −2.35036
\(339\) 14.3723 0.780596
\(340\) 48.6948 2.64085
\(341\) 38.0592 2.06102
\(342\) −0.211631 −0.0114437
\(343\) 1.00000 0.0539949
\(344\) −46.7710 −2.52172
\(345\) 31.9334 1.71924
\(346\) −38.1431 −2.05059
\(347\) 16.5127 0.886451 0.443225 0.896410i \(-0.353834\pi\)
0.443225 + 0.896410i \(0.353834\pi\)
\(348\) 25.3129 1.35691
\(349\) −5.48655 −0.293688 −0.146844 0.989160i \(-0.546912\pi\)
−0.146844 + 0.989160i \(0.546912\pi\)
\(350\) −25.8979 −1.38430
\(351\) −26.1944 −1.39815
\(352\) −36.8618 −1.96474
\(353\) 5.20186 0.276867 0.138433 0.990372i \(-0.455793\pi\)
0.138433 + 0.990372i \(0.455793\pi\)
\(354\) −22.6797 −1.20541
\(355\) −16.0742 −0.853132
\(356\) −56.7467 −3.00757
\(357\) 2.53389 0.134107
\(358\) 5.64304 0.298244
\(359\) −1.03219 −0.0544768 −0.0272384 0.999629i \(-0.508671\pi\)
−0.0272384 + 0.999629i \(0.508671\pi\)
\(360\) −56.0989 −2.95667
\(361\) −18.9985 −0.999921
\(362\) 36.4754 1.91710
\(363\) −11.0230 −0.578556
\(364\) −25.3424 −1.32830
\(365\) −3.04613 −0.159442
\(366\) 32.0262 1.67404
\(367\) 2.04562 0.106780 0.0533901 0.998574i \(-0.482997\pi\)
0.0533901 + 0.998574i \(0.482997\pi\)
\(368\) 72.7704 3.79342
\(369\) 3.08881 0.160797
\(370\) −100.648 −5.23246
\(371\) −8.65850 −0.449527
\(372\) −34.7501 −1.80171
\(373\) −6.42788 −0.332823 −0.166412 0.986056i \(-0.553218\pi\)
−0.166412 + 0.986056i \(0.553218\pi\)
\(374\) 33.2323 1.71840
\(375\) 18.3537 0.947780
\(376\) 49.2581 2.54029
\(377\) 31.7051 1.63290
\(378\) −12.3775 −0.636628
\(379\) 22.2017 1.14042 0.570212 0.821497i \(-0.306861\pi\)
0.570212 + 0.821497i \(0.306861\pi\)
\(380\) 0.697495 0.0357807
\(381\) 16.2151 0.830727
\(382\) −49.9408 −2.55519
\(383\) 4.66101 0.238167 0.119083 0.992884i \(-0.462004\pi\)
0.119083 + 0.992884i \(0.462004\pi\)
\(384\) −6.40939 −0.327078
\(385\) −18.5040 −0.943049
\(386\) 55.7081 2.83547
\(387\) −14.5464 −0.739434
\(388\) 47.3045 2.40152
\(389\) 28.6584 1.45304 0.726520 0.687145i \(-0.241136\pi\)
0.726520 + 0.687145i \(0.241136\pi\)
\(390\) 51.1492 2.59004
\(391\) −23.7275 −1.19995
\(392\) −6.81916 −0.344419
\(393\) 16.4301 0.828789
\(394\) −36.3643 −1.83201
\(395\) −26.2855 −1.32257
\(396\) −46.9971 −2.36170
\(397\) 3.57455 0.179402 0.0897008 0.995969i \(-0.471409\pi\)
0.0897008 + 0.995969i \(0.471409\pi\)
\(398\) 24.0331 1.20467
\(399\) 0.0362949 0.00181702
\(400\) 83.2655 4.16327
\(401\) 26.5531 1.32600 0.662998 0.748621i \(-0.269284\pi\)
0.662998 + 0.748621i \(0.269284\pi\)
\(402\) −1.30200 −0.0649379
\(403\) −43.5255 −2.16816
\(404\) 35.6646 1.77438
\(405\) −7.21686 −0.358609
\(406\) 14.9814 0.743514
\(407\) −48.0158 −2.38005
\(408\) −17.2790 −0.855437
\(409\) −14.7280 −0.728252 −0.364126 0.931350i \(-0.618632\pi\)
−0.364126 + 0.931350i \(0.618632\pi\)
\(410\) −14.5631 −0.719222
\(411\) 3.86856 0.190822
\(412\) −4.25066 −0.209415
\(413\) −9.38313 −0.461714
\(414\) 48.0024 2.35919
\(415\) 41.6650 2.04526
\(416\) 42.1561 2.06687
\(417\) 0.664769 0.0325539
\(418\) 0.476014 0.0232826
\(419\) 2.03396 0.0993655 0.0496827 0.998765i \(-0.484179\pi\)
0.0496827 + 0.998765i \(0.484179\pi\)
\(420\) 16.8951 0.824397
\(421\) 17.9581 0.875224 0.437612 0.899164i \(-0.355824\pi\)
0.437612 + 0.899164i \(0.355824\pi\)
\(422\) −11.6010 −0.564726
\(423\) 15.3199 0.744878
\(424\) 59.0437 2.86741
\(425\) −27.1495 −1.31694
\(426\) 10.0162 0.485289
\(427\) 13.2500 0.641212
\(428\) 0.912280 0.0440967
\(429\) 24.4015 1.17812
\(430\) 68.5833 3.30738
\(431\) −26.1554 −1.25986 −0.629931 0.776651i \(-0.716917\pi\)
−0.629931 + 0.776651i \(0.716917\pi\)
\(432\) 39.7954 1.91466
\(433\) −14.0060 −0.673086 −0.336543 0.941668i \(-0.609258\pi\)
−0.336543 + 0.941668i \(0.609258\pi\)
\(434\) −20.5668 −0.987238
\(435\) −21.1370 −1.01344
\(436\) −14.3894 −0.689130
\(437\) −0.339868 −0.0162581
\(438\) 1.89812 0.0906955
\(439\) 40.1642 1.91693 0.958466 0.285207i \(-0.0920623\pi\)
0.958466 + 0.285207i \(0.0920623\pi\)
\(440\) 126.181 6.01546
\(441\) −2.12084 −0.100993
\(442\) −38.0054 −1.80773
\(443\) 26.4561 1.25697 0.628483 0.777823i \(-0.283676\pi\)
0.628483 + 0.777823i \(0.283676\pi\)
\(444\) 43.8410 2.08060
\(445\) 47.3852 2.24627
\(446\) −42.7683 −2.02514
\(447\) 10.2405 0.484359
\(448\) 3.34343 0.157962
\(449\) 22.8507 1.07839 0.539195 0.842181i \(-0.318729\pi\)
0.539195 + 0.842181i \(0.318729\pi\)
\(450\) 54.9254 2.58921
\(451\) −6.94756 −0.327148
\(452\) −71.2044 −3.34917
\(453\) −13.4922 −0.633920
\(454\) 20.2332 0.949590
\(455\) 21.1616 0.992073
\(456\) −0.247501 −0.0115903
\(457\) −5.47242 −0.255989 −0.127995 0.991775i \(-0.540854\pi\)
−0.127995 + 0.991775i \(0.540854\pi\)
\(458\) 53.8475 2.51613
\(459\) −12.9756 −0.605651
\(460\) −158.207 −7.37643
\(461\) 37.7325 1.75738 0.878688 0.477396i \(-0.158419\pi\)
0.878688 + 0.477396i \(0.158419\pi\)
\(462\) 11.5303 0.536437
\(463\) 41.5515 1.93106 0.965532 0.260286i \(-0.0838169\pi\)
0.965532 + 0.260286i \(0.0838169\pi\)
\(464\) −48.1674 −2.23612
\(465\) 29.0173 1.34565
\(466\) −70.6590 −3.27321
\(467\) −22.8757 −1.05856 −0.529280 0.848447i \(-0.677538\pi\)
−0.529280 + 0.848447i \(0.677538\pi\)
\(468\) 53.7472 2.48447
\(469\) −0.538668 −0.0248734
\(470\) −72.2302 −3.33173
\(471\) −5.52318 −0.254495
\(472\) 63.9851 2.94515
\(473\) 32.7187 1.50441
\(474\) 16.3791 0.752318
\(475\) −0.388884 −0.0178432
\(476\) −12.5536 −0.575392
\(477\) 18.3633 0.840799
\(478\) 10.6309 0.486246
\(479\) −13.5084 −0.617214 −0.308607 0.951190i \(-0.599863\pi\)
−0.308607 + 0.951190i \(0.599863\pi\)
\(480\) −28.1044 −1.28279
\(481\) 54.9122 2.50378
\(482\) −66.2095 −3.01576
\(483\) −8.23246 −0.374590
\(484\) 54.6108 2.48231
\(485\) −39.5006 −1.79363
\(486\) 41.6294 1.88835
\(487\) −9.95708 −0.451198 −0.225599 0.974220i \(-0.572434\pi\)
−0.225599 + 0.974220i \(0.572434\pi\)
\(488\) −90.3537 −4.09012
\(489\) −1.14942 −0.0519784
\(490\) 9.99936 0.451725
\(491\) 18.7931 0.848122 0.424061 0.905634i \(-0.360604\pi\)
0.424061 + 0.905634i \(0.360604\pi\)
\(492\) 6.34349 0.285987
\(493\) 15.7054 0.707336
\(494\) −0.544382 −0.0244929
\(495\) 39.2440 1.76389
\(496\) 66.1253 2.96911
\(497\) 4.14396 0.185882
\(498\) −25.9625 −1.16341
\(499\) 5.44976 0.243965 0.121982 0.992532i \(-0.461075\pi\)
0.121982 + 0.992532i \(0.461075\pi\)
\(500\) −90.9292 −4.06648
\(501\) 10.2177 0.456493
\(502\) 41.5675 1.85525
\(503\) 9.54365 0.425530 0.212765 0.977103i \(-0.431753\pi\)
0.212765 + 0.977103i \(0.431753\pi\)
\(504\) 14.4624 0.644205
\(505\) −29.7810 −1.32524
\(506\) −107.970 −4.79986
\(507\) −15.7170 −0.698015
\(508\) −80.3343 −3.56426
\(509\) 5.18384 0.229770 0.114885 0.993379i \(-0.463350\pi\)
0.114885 + 0.993379i \(0.463350\pi\)
\(510\) 25.3372 1.12195
\(511\) 0.785295 0.0347394
\(512\) 48.9916 2.16514
\(513\) −0.185861 −0.00820594
\(514\) 29.1699 1.28663
\(515\) 3.54943 0.156407
\(516\) −29.8739 −1.31512
\(517\) −34.4585 −1.51548
\(518\) 25.9473 1.14006
\(519\) −13.8737 −0.608987
\(520\) −144.304 −6.32817
\(521\) 8.47754 0.371408 0.185704 0.982606i \(-0.440543\pi\)
0.185704 + 0.982606i \(0.440543\pi\)
\(522\) −31.7732 −1.39068
\(523\) −29.0396 −1.26981 −0.634907 0.772589i \(-0.718962\pi\)
−0.634907 + 0.772589i \(0.718962\pi\)
\(524\) −81.3993 −3.55594
\(525\) −9.41976 −0.411112
\(526\) −34.2836 −1.49484
\(527\) −21.5608 −0.939201
\(528\) −37.0715 −1.61333
\(529\) 54.0893 2.35171
\(530\) −86.5795 −3.76077
\(531\) 19.9002 0.863594
\(532\) −0.179815 −0.00779597
\(533\) 7.94542 0.344154
\(534\) −29.5269 −1.27775
\(535\) −0.761782 −0.0329347
\(536\) 3.67326 0.158661
\(537\) 2.05253 0.0885731
\(538\) 7.41026 0.319479
\(539\) 4.77034 0.205473
\(540\) −86.5172 −3.72311
\(541\) −12.0274 −0.517100 −0.258550 0.965998i \(-0.583245\pi\)
−0.258550 + 0.965998i \(0.583245\pi\)
\(542\) 20.1699 0.866370
\(543\) 13.2671 0.569346
\(544\) 20.8824 0.895327
\(545\) 12.0156 0.514693
\(546\) −13.1863 −0.564323
\(547\) 3.77765 0.161520 0.0807602 0.996734i \(-0.474265\pi\)
0.0807602 + 0.996734i \(0.474265\pi\)
\(548\) −19.1659 −0.818728
\(549\) −28.1012 −1.19933
\(550\) −123.542 −5.26784
\(551\) 0.224961 0.00958368
\(552\) 56.1385 2.38941
\(553\) 6.77643 0.288163
\(554\) 78.3105 3.32710
\(555\) −36.6086 −1.55395
\(556\) −3.29345 −0.139673
\(557\) 24.3605 1.03219 0.516093 0.856532i \(-0.327386\pi\)
0.516093 + 0.856532i \(0.327386\pi\)
\(558\) 43.6190 1.84654
\(559\) −37.4179 −1.58261
\(560\) −32.1494 −1.35856
\(561\) 12.0875 0.510335
\(562\) 28.6924 1.21032
\(563\) −29.2307 −1.23193 −0.615963 0.787775i \(-0.711233\pi\)
−0.615963 + 0.787775i \(0.711233\pi\)
\(564\) 31.4624 1.32481
\(565\) 59.4578 2.50141
\(566\) 31.2973 1.31552
\(567\) 1.86051 0.0781343
\(568\) −28.2583 −1.18569
\(569\) −36.8201 −1.54358 −0.771789 0.635879i \(-0.780638\pi\)
−0.771789 + 0.635879i \(0.780638\pi\)
\(570\) 0.362926 0.0152013
\(571\) 2.39605 0.100272 0.0501359 0.998742i \(-0.484035\pi\)
0.0501359 + 0.998742i \(0.484035\pi\)
\(572\) −120.892 −5.05474
\(573\) −18.1648 −0.758847
\(574\) 3.75439 0.156705
\(575\) 88.2072 3.67849
\(576\) −7.09089 −0.295454
\(577\) 29.6014 1.23232 0.616161 0.787620i \(-0.288687\pi\)
0.616161 + 0.787620i \(0.288687\pi\)
\(578\) 24.9971 1.03974
\(579\) 20.2625 0.842082
\(580\) 104.719 4.34820
\(581\) −10.7413 −0.445624
\(582\) 24.6138 1.02028
\(583\) −41.3040 −1.71064
\(584\) −5.35505 −0.221594
\(585\) −44.8805 −1.85558
\(586\) 48.9298 2.02127
\(587\) −2.76761 −0.114232 −0.0571158 0.998368i \(-0.518190\pi\)
−0.0571158 + 0.998368i \(0.518190\pi\)
\(588\) −4.35558 −0.179621
\(589\) −0.308832 −0.0127252
\(590\) −93.8253 −3.86273
\(591\) −13.2267 −0.544074
\(592\) −83.4243 −3.42872
\(593\) −16.7820 −0.689155 −0.344578 0.938758i \(-0.611978\pi\)
−0.344578 + 0.938758i \(0.611978\pi\)
\(594\) −59.0447 −2.42263
\(595\) 10.4826 0.429745
\(596\) −50.7342 −2.07815
\(597\) 8.74150 0.357766
\(598\) 123.478 5.04937
\(599\) 16.2580 0.664282 0.332141 0.943230i \(-0.392229\pi\)
0.332141 + 0.943230i \(0.392229\pi\)
\(600\) 64.2349 2.62238
\(601\) −10.5859 −0.431810 −0.215905 0.976414i \(-0.569270\pi\)
−0.215905 + 0.976414i \(0.569270\pi\)
\(602\) −17.6808 −0.720617
\(603\) 1.14243 0.0465234
\(604\) 66.8442 2.71985
\(605\) −45.6017 −1.85397
\(606\) 18.5573 0.753838
\(607\) 27.1411 1.10162 0.550811 0.834630i \(-0.314318\pi\)
0.550811 + 0.834630i \(0.314318\pi\)
\(608\) 0.299116 0.0121307
\(609\) 5.44914 0.220810
\(610\) 132.491 5.36442
\(611\) 39.4076 1.59426
\(612\) 26.6242 1.07622
\(613\) 26.1294 1.05536 0.527679 0.849444i \(-0.323062\pi\)
0.527679 + 0.849444i \(0.323062\pi\)
\(614\) 29.6212 1.19542
\(615\) −5.29701 −0.213596
\(616\) −32.5297 −1.31066
\(617\) −33.8120 −1.36122 −0.680610 0.732646i \(-0.738285\pi\)
−0.680610 + 0.732646i \(0.738285\pi\)
\(618\) −2.21174 −0.0889691
\(619\) 27.2344 1.09464 0.547322 0.836922i \(-0.315647\pi\)
0.547322 + 0.836922i \(0.315647\pi\)
\(620\) −143.760 −5.77354
\(621\) 42.1572 1.69171
\(622\) −41.7330 −1.67334
\(623\) −12.2160 −0.489422
\(624\) 42.3960 1.69720
\(625\) 25.6970 1.02788
\(626\) 77.3354 3.09094
\(627\) 0.173139 0.00691451
\(628\) 27.3634 1.09192
\(629\) 27.2012 1.08458
\(630\) −21.2071 −0.844911
\(631\) 3.53009 0.140531 0.0702654 0.997528i \(-0.477615\pi\)
0.0702654 + 0.997528i \(0.477615\pi\)
\(632\) −46.2095 −1.83812
\(633\) −4.21958 −0.167713
\(634\) 89.6787 3.56160
\(635\) 67.0815 2.66205
\(636\) 37.7128 1.49541
\(637\) −5.45549 −0.216154
\(638\) 71.4664 2.82938
\(639\) −8.78869 −0.347675
\(640\) −26.5155 −1.04812
\(641\) 19.6280 0.775258 0.387629 0.921815i \(-0.373294\pi\)
0.387629 + 0.921815i \(0.373294\pi\)
\(642\) 0.474685 0.0187343
\(643\) 18.8869 0.744825 0.372413 0.928067i \(-0.378531\pi\)
0.372413 + 0.928067i \(0.378531\pi\)
\(644\) 40.7859 1.60719
\(645\) 24.9456 0.982232
\(646\) −0.269665 −0.0106098
\(647\) −0.274991 −0.0108110 −0.00540551 0.999985i \(-0.501721\pi\)
−0.00540551 + 0.999985i \(0.501721\pi\)
\(648\) −12.6871 −0.498398
\(649\) −44.7608 −1.75701
\(650\) 141.286 5.54168
\(651\) −7.48070 −0.293192
\(652\) 5.69452 0.223015
\(653\) 28.3654 1.11002 0.555012 0.831842i \(-0.312714\pi\)
0.555012 + 0.831842i \(0.312714\pi\)
\(654\) −7.48723 −0.292774
\(655\) 67.9708 2.65584
\(656\) −12.0709 −0.471291
\(657\) −1.66549 −0.0649769
\(658\) 18.6210 0.725923
\(659\) 29.1550 1.13572 0.567859 0.823126i \(-0.307772\pi\)
0.567859 + 0.823126i \(0.307772\pi\)
\(660\) 80.5955 3.13717
\(661\) −45.7238 −1.77845 −0.889224 0.457472i \(-0.848755\pi\)
−0.889224 + 0.457472i \(0.848755\pi\)
\(662\) −49.9256 −1.94041
\(663\) −13.8236 −0.536864
\(664\) 73.2465 2.84252
\(665\) 0.150151 0.00582260
\(666\) −55.0301 −2.13237
\(667\) −51.0261 −1.97574
\(668\) −50.6213 −1.95860
\(669\) −15.5560 −0.601430
\(670\) −5.38633 −0.208092
\(671\) 63.2070 2.44008
\(672\) 7.24535 0.279496
\(673\) −32.1405 −1.23892 −0.619462 0.785026i \(-0.712649\pi\)
−0.619462 + 0.785026i \(0.712649\pi\)
\(674\) −62.6552 −2.41339
\(675\) 48.2371 1.85665
\(676\) 77.8662 2.99486
\(677\) 12.2598 0.471182 0.235591 0.971852i \(-0.424297\pi\)
0.235591 + 0.971852i \(0.424297\pi\)
\(678\) −37.0496 −1.42288
\(679\) 10.1833 0.390800
\(680\) −71.4826 −2.74123
\(681\) 7.35936 0.282011
\(682\) −98.1107 −3.75685
\(683\) 8.27120 0.316489 0.158244 0.987400i \(-0.449417\pi\)
0.158244 + 0.987400i \(0.449417\pi\)
\(684\) 0.381360 0.0145816
\(685\) 16.0041 0.611486
\(686\) −2.57785 −0.0984226
\(687\) 19.5858 0.747244
\(688\) 56.8465 2.16725
\(689\) 47.2364 1.79956
\(690\) −82.3194 −3.13384
\(691\) 6.83587 0.260049 0.130024 0.991511i \(-0.458494\pi\)
0.130024 + 0.991511i \(0.458494\pi\)
\(692\) 68.7341 2.61288
\(693\) −10.1172 −0.384319
\(694\) −42.5673 −1.61583
\(695\) 2.75013 0.104318
\(696\) −37.1586 −1.40849
\(697\) 3.93584 0.149080
\(698\) 14.1435 0.535339
\(699\) −25.7006 −0.972086
\(700\) 46.6681 1.76389
\(701\) 29.0289 1.09641 0.548204 0.836345i \(-0.315312\pi\)
0.548204 + 0.836345i \(0.315312\pi\)
\(702\) 67.5251 2.54857
\(703\) 0.389625 0.0146950
\(704\) 15.9493 0.601112
\(705\) −26.2721 −0.989464
\(706\) −13.4096 −0.504677
\(707\) 7.67758 0.288745
\(708\) 40.8690 1.53595
\(709\) 37.1815 1.39638 0.698190 0.715913i \(-0.253989\pi\)
0.698190 + 0.715913i \(0.253989\pi\)
\(710\) 41.4369 1.55510
\(711\) −14.3718 −0.538983
\(712\) 83.3025 3.12190
\(713\) 70.0497 2.62338
\(714\) −6.53197 −0.244453
\(715\) 100.948 3.77525
\(716\) −10.1688 −0.380025
\(717\) 3.86674 0.144406
\(718\) 2.66082 0.0993010
\(719\) 32.2138 1.20137 0.600685 0.799485i \(-0.294894\pi\)
0.600685 + 0.799485i \(0.294894\pi\)
\(720\) 68.1839 2.54106
\(721\) −0.915048 −0.0340781
\(722\) 48.9752 1.82267
\(723\) −24.0822 −0.895627
\(724\) −65.7289 −2.44279
\(725\) −58.3851 −2.16837
\(726\) 28.4155 1.05460
\(727\) 29.9834 1.11202 0.556011 0.831175i \(-0.312331\pi\)
0.556011 + 0.831175i \(0.312331\pi\)
\(728\) 37.2019 1.37879
\(729\) 9.56020 0.354081
\(730\) 7.85245 0.290632
\(731\) −18.5353 −0.685554
\(732\) −57.7114 −2.13307
\(733\) 15.6602 0.578423 0.289212 0.957265i \(-0.406607\pi\)
0.289212 + 0.957265i \(0.406607\pi\)
\(734\) −5.27328 −0.194640
\(735\) 3.63704 0.134154
\(736\) −67.8459 −2.50083
\(737\) −2.56963 −0.0946535
\(738\) −7.96248 −0.293103
\(739\) 7.31965 0.269258 0.134629 0.990896i \(-0.457016\pi\)
0.134629 + 0.990896i \(0.457016\pi\)
\(740\) 181.369 6.66725
\(741\) −0.198007 −0.00727395
\(742\) 22.3203 0.819403
\(743\) 0.653864 0.0239880 0.0119940 0.999928i \(-0.496182\pi\)
0.0119940 + 0.999928i \(0.496182\pi\)
\(744\) 51.0121 1.87019
\(745\) 42.3646 1.55212
\(746\) 16.5701 0.606674
\(747\) 22.7806 0.833499
\(748\) −59.8848 −2.18961
\(749\) 0.196388 0.00717587
\(750\) −47.3130 −1.72763
\(751\) 41.9202 1.52969 0.764844 0.644215i \(-0.222816\pi\)
0.764844 + 0.644215i \(0.222816\pi\)
\(752\) −59.8693 −2.18321
\(753\) 15.1192 0.550975
\(754\) −81.7309 −2.97646
\(755\) −55.8169 −2.03139
\(756\) 22.3042 0.811198
\(757\) 35.1913 1.27905 0.639524 0.768771i \(-0.279132\pi\)
0.639524 + 0.768771i \(0.279132\pi\)
\(758\) −57.2326 −2.07878
\(759\) −39.2717 −1.42547
\(760\) −1.02390 −0.0371408
\(761\) 18.9471 0.686833 0.343417 0.939183i \(-0.388416\pi\)
0.343417 + 0.939183i \(0.388416\pi\)
\(762\) −41.8001 −1.51426
\(763\) −3.09764 −0.112142
\(764\) 89.9936 3.25585
\(765\) −22.2320 −0.803799
\(766\) −12.0154 −0.434133
\(767\) 51.1896 1.84835
\(768\) 22.7922 0.822444
\(769\) −34.3114 −1.23730 −0.618651 0.785666i \(-0.712320\pi\)
−0.618651 + 0.785666i \(0.712320\pi\)
\(770\) 47.7004 1.71900
\(771\) 10.6099 0.382105
\(772\) −100.386 −3.61298
\(773\) 51.0131 1.83482 0.917408 0.397949i \(-0.130278\pi\)
0.917408 + 0.397949i \(0.130278\pi\)
\(774\) 37.4983 1.34785
\(775\) 80.1524 2.87916
\(776\) −69.4416 −2.49281
\(777\) 9.43773 0.338577
\(778\) −73.8770 −2.64862
\(779\) 0.0563761 0.00201989
\(780\) −92.1712 −3.30026
\(781\) 19.7681 0.707358
\(782\) 61.1657 2.18728
\(783\) −27.9042 −0.997215
\(784\) 8.28816 0.296006
\(785\) −22.8492 −0.815524
\(786\) −42.3543 −1.51073
\(787\) 40.7167 1.45139 0.725696 0.688015i \(-0.241518\pi\)
0.725696 + 0.688015i \(0.241518\pi\)
\(788\) 65.5287 2.33436
\(789\) −12.4699 −0.443940
\(790\) 67.7600 2.41079
\(791\) −15.3283 −0.545011
\(792\) 68.9905 2.45147
\(793\) −72.2852 −2.56692
\(794\) −9.21465 −0.327016
\(795\) −31.4913 −1.11688
\(796\) −43.3078 −1.53500
\(797\) −3.82027 −0.135321 −0.0676604 0.997708i \(-0.521553\pi\)
−0.0676604 + 0.997708i \(0.521553\pi\)
\(798\) −0.0935627 −0.00331208
\(799\) 19.5209 0.690601
\(800\) −77.6308 −2.74466
\(801\) 25.9081 0.915419
\(802\) −68.4497 −2.41704
\(803\) 3.74613 0.132198
\(804\) 2.34621 0.0827445
\(805\) −34.0574 −1.20037
\(806\) 112.202 3.95215
\(807\) 2.69532 0.0948796
\(808\) −52.3546 −1.84183
\(809\) 37.8866 1.33202 0.666011 0.745942i \(-0.268000\pi\)
0.666011 + 0.745942i \(0.268000\pi\)
\(810\) 18.6040 0.653676
\(811\) −36.1885 −1.27075 −0.635375 0.772204i \(-0.719154\pi\)
−0.635375 + 0.772204i \(0.719154\pi\)
\(812\) −26.9966 −0.947393
\(813\) 7.33633 0.257296
\(814\) 123.777 4.33839
\(815\) −4.75510 −0.166564
\(816\) 21.0012 0.735191
\(817\) −0.265496 −0.00928854
\(818\) 37.9665 1.32747
\(819\) 11.5703 0.404297
\(820\) 26.2428 0.916440
\(821\) −12.6712 −0.442226 −0.221113 0.975248i \(-0.570969\pi\)
−0.221113 + 0.975248i \(0.570969\pi\)
\(822\) −9.97256 −0.347833
\(823\) 43.0404 1.50029 0.750146 0.661272i \(-0.229983\pi\)
0.750146 + 0.661272i \(0.229983\pi\)
\(824\) 6.23985 0.217376
\(825\) −44.9355 −1.56445
\(826\) 24.1883 0.841618
\(827\) 23.5051 0.817352 0.408676 0.912680i \(-0.365991\pi\)
0.408676 + 0.912680i \(0.365991\pi\)
\(828\) −86.5005 −3.00610
\(829\) 36.3196 1.26143 0.630716 0.776014i \(-0.282761\pi\)
0.630716 + 0.776014i \(0.282761\pi\)
\(830\) −107.406 −3.72812
\(831\) 28.4837 0.988088
\(832\) −18.2400 −0.632360
\(833\) −2.70243 −0.0936336
\(834\) −1.71367 −0.0593396
\(835\) 42.2703 1.46282
\(836\) −0.857779 −0.0296669
\(837\) 38.3075 1.32410
\(838\) −5.24324 −0.181125
\(839\) −8.78489 −0.303288 −0.151644 0.988435i \(-0.548457\pi\)
−0.151644 + 0.988435i \(0.548457\pi\)
\(840\) −24.8015 −0.855735
\(841\) 4.77462 0.164642
\(842\) −46.2932 −1.59537
\(843\) 10.4362 0.359442
\(844\) 20.9050 0.719579
\(845\) −65.0206 −2.23678
\(846\) −39.4923 −1.35777
\(847\) 11.7562 0.403947
\(848\) −71.7630 −2.46435
\(849\) 11.3837 0.390686
\(850\) 69.9872 2.40054
\(851\) −88.3754 −3.02947
\(852\) −18.0493 −0.618360
\(853\) −43.7324 −1.49737 −0.748685 0.662926i \(-0.769314\pi\)
−0.748685 + 0.662926i \(0.769314\pi\)
\(854\) −34.1564 −1.16881
\(855\) −0.318447 −0.0108906
\(856\) −1.33920 −0.0457730
\(857\) −53.4661 −1.82637 −0.913184 0.407547i \(-0.866384\pi\)
−0.913184 + 0.407547i \(0.866384\pi\)
\(858\) −62.9033 −2.14748
\(859\) 35.8246 1.22232 0.611160 0.791507i \(-0.290703\pi\)
0.611160 + 0.791507i \(0.290703\pi\)
\(860\) −123.587 −4.21429
\(861\) 1.36557 0.0465387
\(862\) 67.4247 2.29649
\(863\) −1.00000 −0.0340404
\(864\) −37.1023 −1.26225
\(865\) −57.3950 −1.95149
\(866\) 36.1053 1.22691
\(867\) 9.09211 0.308784
\(868\) 37.0615 1.25795
\(869\) 32.3259 1.09658
\(870\) 54.4879 1.84731
\(871\) 2.93870 0.0995740
\(872\) 21.1233 0.715325
\(873\) −21.5972 −0.730955
\(874\) 0.876126 0.0296354
\(875\) −19.5745 −0.661738
\(876\) −3.42042 −0.115565
\(877\) 26.8140 0.905446 0.452723 0.891651i \(-0.350453\pi\)
0.452723 + 0.891651i \(0.350453\pi\)
\(878\) −103.537 −3.49421
\(879\) 17.7971 0.600282
\(880\) −153.364 −5.16989
\(881\) −10.3868 −0.349940 −0.174970 0.984574i \(-0.555983\pi\)
−0.174970 + 0.984574i \(0.555983\pi\)
\(882\) 5.46721 0.184091
\(883\) −24.1229 −0.811800 −0.405900 0.913918i \(-0.633042\pi\)
−0.405900 + 0.913918i \(0.633042\pi\)
\(884\) 68.4859 2.30343
\(885\) −34.1268 −1.14716
\(886\) −68.1997 −2.29122
\(887\) 8.97630 0.301395 0.150697 0.988580i \(-0.451848\pi\)
0.150697 + 0.988580i \(0.451848\pi\)
\(888\) −64.3574 −2.15969
\(889\) −17.2937 −0.580012
\(890\) −122.152 −4.09454
\(891\) 8.87529 0.297333
\(892\) 77.0687 2.58045
\(893\) 0.279614 0.00935693
\(894\) −26.3984 −0.882895
\(895\) 8.49124 0.283831
\(896\) 6.83571 0.228365
\(897\) 44.9121 1.49957
\(898\) −58.9055 −1.96570
\(899\) −46.3666 −1.54641
\(900\) −98.9758 −3.29919
\(901\) 23.3990 0.779533
\(902\) 17.9097 0.596329
\(903\) −6.43100 −0.214010
\(904\) 104.526 3.47648
\(905\) 54.8856 1.82446
\(906\) 34.7809 1.15552
\(907\) 23.3138 0.774122 0.387061 0.922054i \(-0.373490\pi\)
0.387061 + 0.922054i \(0.373490\pi\)
\(908\) −36.4603 −1.20998
\(909\) −16.2829 −0.540071
\(910\) −54.5514 −1.80836
\(911\) −48.2761 −1.59946 −0.799729 0.600361i \(-0.795024\pi\)
−0.799729 + 0.600361i \(0.795024\pi\)
\(912\) 0.300818 0.00996107
\(913\) −51.2396 −1.69578
\(914\) 14.1071 0.466620
\(915\) 48.1907 1.59314
\(916\) −97.0334 −3.20607
\(917\) −17.5230 −0.578659
\(918\) 33.4492 1.10399
\(919\) −0.876920 −0.0289269 −0.0144635 0.999895i \(-0.504604\pi\)
−0.0144635 + 0.999895i \(0.504604\pi\)
\(920\) 232.243 7.65683
\(921\) 10.7741 0.355017
\(922\) −97.2685 −3.20337
\(923\) −22.6073 −0.744129
\(924\) −20.7776 −0.683533
\(925\) −101.121 −3.32484
\(926\) −107.113 −3.51997
\(927\) 1.94067 0.0637401
\(928\) 44.9078 1.47417
\(929\) −9.86588 −0.323689 −0.161845 0.986816i \(-0.551744\pi\)
−0.161845 + 0.986816i \(0.551744\pi\)
\(930\) −74.8023 −2.45286
\(931\) −0.0387091 −0.00126864
\(932\) 127.328 4.17076
\(933\) −15.1794 −0.496952
\(934\) 58.9700 1.92956
\(935\) 50.0056 1.63536
\(936\) −78.8994 −2.57891
\(937\) 18.3261 0.598689 0.299344 0.954145i \(-0.403232\pi\)
0.299344 + 0.954145i \(0.403232\pi\)
\(938\) 1.38860 0.0453395
\(939\) 28.1290 0.917954
\(940\) 130.159 4.24532
\(941\) 18.2305 0.594297 0.297149 0.954831i \(-0.403964\pi\)
0.297149 + 0.954831i \(0.403964\pi\)
\(942\) 14.2379 0.463896
\(943\) −12.7873 −0.416412
\(944\) −77.7689 −2.53116
\(945\) −18.6247 −0.605862
\(946\) −84.3437 −2.74225
\(947\) −43.3043 −1.40720 −0.703601 0.710595i \(-0.748426\pi\)
−0.703601 + 0.710595i \(0.748426\pi\)
\(948\) −29.5153 −0.958611
\(949\) −4.28417 −0.139070
\(950\) 1.00248 0.0325248
\(951\) 32.6186 1.05773
\(952\) 18.4283 0.597264
\(953\) 4.98702 0.161545 0.0807727 0.996733i \(-0.474261\pi\)
0.0807727 + 0.996733i \(0.474261\pi\)
\(954\) −47.3378 −1.53262
\(955\) −75.1473 −2.43171
\(956\) −19.1569 −0.619579
\(957\) 25.9943 0.840276
\(958\) 34.8225 1.12506
\(959\) −4.12588 −0.133232
\(960\) 12.1602 0.392468
\(961\) 32.6531 1.05332
\(962\) −141.555 −4.56392
\(963\) −0.416509 −0.0134218
\(964\) 119.310 3.84271
\(965\) 83.8255 2.69844
\(966\) 21.2220 0.682808
\(967\) 6.61202 0.212628 0.106314 0.994333i \(-0.466095\pi\)
0.106314 + 0.994333i \(0.466095\pi\)
\(968\) −80.1671 −2.57667
\(969\) −0.0980844 −0.00315092
\(970\) 101.827 3.26945
\(971\) −35.4704 −1.13830 −0.569150 0.822234i \(-0.692728\pi\)
−0.569150 + 0.822234i \(0.692728\pi\)
\(972\) −75.0163 −2.40615
\(973\) −0.708986 −0.0227291
\(974\) 25.6678 0.822450
\(975\) 51.3894 1.64578
\(976\) 109.818 3.51519
\(977\) 0.708286 0.0226601 0.0113300 0.999936i \(-0.496393\pi\)
0.0113300 + 0.999936i \(0.496393\pi\)
\(978\) 2.96302 0.0947468
\(979\) −58.2743 −1.86245
\(980\) −18.0189 −0.575593
\(981\) 6.56962 0.209752
\(982\) −48.4458 −1.54597
\(983\) 22.7953 0.727057 0.363528 0.931583i \(-0.381572\pi\)
0.363528 + 0.931583i \(0.381572\pi\)
\(984\) −9.31207 −0.296858
\(985\) −54.7185 −1.74347
\(986\) −40.4862 −1.28934
\(987\) 6.77297 0.215586
\(988\) 0.980979 0.0312091
\(989\) 60.2203 1.91489
\(990\) −101.165 −3.21524
\(991\) −51.4319 −1.63379 −0.816895 0.576787i \(-0.804306\pi\)
−0.816895 + 0.576787i \(0.804306\pi\)
\(992\) −61.6505 −1.95740
\(993\) −18.1593 −0.576268
\(994\) −10.6825 −0.338828
\(995\) 36.1633 1.14645
\(996\) 46.7845 1.48242
\(997\) 10.0962 0.319751 0.159875 0.987137i \(-0.448891\pi\)
0.159875 + 0.987137i \(0.448891\pi\)
\(998\) −14.0487 −0.444702
\(999\) −48.3291 −1.52907
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 \(a_p\))