Properties

Label 6013.2.a.e.1.7
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.44055 q^{2}\) \(+1.60583 q^{3}\) \(+3.95629 q^{4}\) \(+4.05418 q^{5}\) \(-3.91911 q^{6}\) \(+1.00000 q^{7}\) \(-4.77442 q^{8}\) \(-0.421314 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.44055 q^{2}\) \(+1.60583 q^{3}\) \(+3.95629 q^{4}\) \(+4.05418 q^{5}\) \(-3.91911 q^{6}\) \(+1.00000 q^{7}\) \(-4.77442 q^{8}\) \(-0.421314 q^{9}\) \(-9.89444 q^{10}\) \(+5.61936 q^{11}\) \(+6.35312 q^{12}\) \(+3.03148 q^{13}\) \(-2.44055 q^{14}\) \(+6.51032 q^{15}\) \(+3.73964 q^{16}\) \(-1.73615 q^{17}\) \(+1.02824 q^{18}\) \(+4.70704 q^{19}\) \(+16.0395 q^{20}\) \(+1.60583 q^{21}\) \(-13.7143 q^{22}\) \(+1.98175 q^{23}\) \(-7.66690 q^{24}\) \(+11.4364 q^{25}\) \(-7.39847 q^{26}\) \(-5.49404 q^{27}\) \(+3.95629 q^{28}\) \(-0.147179 q^{29}\) \(-15.8888 q^{30}\) \(+8.30517 q^{31}\) \(+0.422066 q^{32}\) \(+9.02374 q^{33}\) \(+4.23717 q^{34}\) \(+4.05418 q^{35}\) \(-1.66684 q^{36}\) \(-5.25613 q^{37}\) \(-11.4878 q^{38}\) \(+4.86803 q^{39}\) \(-19.3564 q^{40}\) \(+5.32712 q^{41}\) \(-3.91911 q^{42}\) \(-1.76833 q^{43}\) \(+22.2318 q^{44}\) \(-1.70808 q^{45}\) \(-4.83657 q^{46}\) \(+11.9709 q^{47}\) \(+6.00522 q^{48}\) \(+1.00000 q^{49}\) \(-27.9111 q^{50}\) \(-2.78796 q^{51}\) \(+11.9934 q^{52}\) \(-0.255700 q^{53}\) \(+13.4085 q^{54}\) \(+22.7819 q^{55}\) \(-4.77442 q^{56}\) \(+7.55871 q^{57}\) \(+0.359198 q^{58}\) \(-8.52605 q^{59}\) \(+25.7567 q^{60}\) \(-12.0498 q^{61}\) \(-20.2692 q^{62}\) \(-0.421314 q^{63}\) \(-8.50935 q^{64}\) \(+12.2902 q^{65}\) \(-22.0229 q^{66}\) \(+7.20097 q^{67}\) \(-6.86872 q^{68}\) \(+3.18236 q^{69}\) \(-9.89444 q^{70}\) \(-7.61283 q^{71}\) \(+2.01153 q^{72}\) \(+2.22604 q^{73}\) \(+12.8278 q^{74}\) \(+18.3649 q^{75}\) \(+18.6224 q^{76}\) \(+5.61936 q^{77}\) \(-11.8807 q^{78}\) \(-15.9297 q^{79}\) \(+15.1612 q^{80}\) \(-7.55855 q^{81}\) \(-13.0011 q^{82}\) \(-14.6721 q^{83}\) \(+6.35312 q^{84}\) \(-7.03868 q^{85}\) \(+4.31571 q^{86}\) \(-0.236345 q^{87}\) \(-26.8292 q^{88}\) \(-12.5202 q^{89}\) \(+4.16866 q^{90}\) \(+3.03148 q^{91}\) \(+7.84039 q^{92}\) \(+13.3367 q^{93}\) \(-29.2156 q^{94}\) \(+19.0832 q^{95}\) \(+0.677766 q^{96}\) \(-3.70267 q^{97}\) \(-2.44055 q^{98}\) \(-2.36752 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44055 −1.72573 −0.862865 0.505435i \(-0.831332\pi\)
−0.862865 + 0.505435i \(0.831332\pi\)
\(3\) 1.60583 0.927126 0.463563 0.886064i \(-0.346571\pi\)
0.463563 + 0.886064i \(0.346571\pi\)
\(4\) 3.95629 1.97814
\(5\) 4.05418 1.81309 0.906543 0.422114i \(-0.138712\pi\)
0.906543 + 0.422114i \(0.138712\pi\)
\(6\) −3.91911 −1.59997
\(7\) 1.00000 0.377964
\(8\) −4.77442 −1.68801
\(9\) −0.421314 −0.140438
\(10\) −9.89444 −3.12890
\(11\) 5.61936 1.69430 0.847151 0.531352i \(-0.178316\pi\)
0.847151 + 0.531352i \(0.178316\pi\)
\(12\) 6.35312 1.83399
\(13\) 3.03148 0.840780 0.420390 0.907343i \(-0.361893\pi\)
0.420390 + 0.907343i \(0.361893\pi\)
\(14\) −2.44055 −0.652265
\(15\) 6.51032 1.68096
\(16\) 3.73964 0.934909
\(17\) −1.73615 −0.421079 −0.210539 0.977585i \(-0.567522\pi\)
−0.210539 + 0.977585i \(0.567522\pi\)
\(18\) 1.02824 0.242358
\(19\) 4.70704 1.07987 0.539935 0.841707i \(-0.318449\pi\)
0.539935 + 0.841707i \(0.318449\pi\)
\(20\) 16.0395 3.58654
\(21\) 1.60583 0.350421
\(22\) −13.7143 −2.92391
\(23\) 1.98175 0.413224 0.206612 0.978423i \(-0.433756\pi\)
0.206612 + 0.978423i \(0.433756\pi\)
\(24\) −7.66690 −1.56500
\(25\) 11.4364 2.28728
\(26\) −7.39847 −1.45096
\(27\) −5.49404 −1.05733
\(28\) 3.95629 0.747668
\(29\) −0.147179 −0.0273305 −0.0136652 0.999907i \(-0.504350\pi\)
−0.0136652 + 0.999907i \(0.504350\pi\)
\(30\) −15.8888 −2.90088
\(31\) 8.30517 1.49165 0.745826 0.666141i \(-0.232055\pi\)
0.745826 + 0.666141i \(0.232055\pi\)
\(32\) 0.422066 0.0746114
\(33\) 9.02374 1.57083
\(34\) 4.23717 0.726669
\(35\) 4.05418 0.685282
\(36\) −1.66684 −0.277807
\(37\) −5.25613 −0.864102 −0.432051 0.901849i \(-0.642210\pi\)
−0.432051 + 0.901849i \(0.642210\pi\)
\(38\) −11.4878 −1.86356
\(39\) 4.86803 0.779509
\(40\) −19.3564 −3.06051
\(41\) 5.32712 0.831956 0.415978 0.909375i \(-0.363439\pi\)
0.415978 + 0.909375i \(0.363439\pi\)
\(42\) −3.91911 −0.604731
\(43\) −1.76833 −0.269668 −0.134834 0.990868i \(-0.543050\pi\)
−0.134834 + 0.990868i \(0.543050\pi\)
\(44\) 22.2318 3.35157
\(45\) −1.70808 −0.254626
\(46\) −4.83657 −0.713114
\(47\) 11.9709 1.74613 0.873067 0.487600i \(-0.162127\pi\)
0.873067 + 0.487600i \(0.162127\pi\)
\(48\) 6.00522 0.866778
\(49\) 1.00000 0.142857
\(50\) −27.9111 −3.94723
\(51\) −2.78796 −0.390393
\(52\) 11.9934 1.66318
\(53\) −0.255700 −0.0351231 −0.0175615 0.999846i \(-0.505590\pi\)
−0.0175615 + 0.999846i \(0.505590\pi\)
\(54\) 13.4085 1.82466
\(55\) 22.7819 3.07191
\(56\) −4.77442 −0.638009
\(57\) 7.55871 1.00118
\(58\) 0.359198 0.0471650
\(59\) −8.52605 −1.11000 −0.554998 0.831851i \(-0.687281\pi\)
−0.554998 + 0.831851i \(0.687281\pi\)
\(60\) 25.7567 3.32518
\(61\) −12.0498 −1.54282 −0.771411 0.636338i \(-0.780449\pi\)
−0.771411 + 0.636338i \(0.780449\pi\)
\(62\) −20.2692 −2.57419
\(63\) −0.421314 −0.0530806
\(64\) −8.50935 −1.06367
\(65\) 12.2902 1.52441
\(66\) −22.0229 −2.71083
\(67\) 7.20097 0.879739 0.439869 0.898062i \(-0.355025\pi\)
0.439869 + 0.898062i \(0.355025\pi\)
\(68\) −6.86872 −0.832955
\(69\) 3.18236 0.383111
\(70\) −9.89444 −1.18261
\(71\) −7.61283 −0.903477 −0.451739 0.892150i \(-0.649196\pi\)
−0.451739 + 0.892150i \(0.649196\pi\)
\(72\) 2.01153 0.237061
\(73\) 2.22604 0.260538 0.130269 0.991479i \(-0.458416\pi\)
0.130269 + 0.991479i \(0.458416\pi\)
\(74\) 12.8278 1.49121
\(75\) 18.3649 2.12060
\(76\) 18.6224 2.13614
\(77\) 5.61936 0.640386
\(78\) −11.8807 −1.34522
\(79\) −15.9297 −1.79223 −0.896116 0.443820i \(-0.853623\pi\)
−0.896116 + 0.443820i \(0.853623\pi\)
\(80\) 15.1612 1.69507
\(81\) −7.55855 −0.839839
\(82\) −13.0011 −1.43573
\(83\) −14.6721 −1.61047 −0.805237 0.592953i \(-0.797962\pi\)
−0.805237 + 0.592953i \(0.797962\pi\)
\(84\) 6.35312 0.693182
\(85\) −7.03868 −0.763452
\(86\) 4.31571 0.465375
\(87\) −0.236345 −0.0253388
\(88\) −26.8292 −2.86000
\(89\) −12.5202 −1.32714 −0.663571 0.748113i \(-0.730960\pi\)
−0.663571 + 0.748113i \(0.730960\pi\)
\(90\) 4.16866 0.439416
\(91\) 3.03148 0.317785
\(92\) 7.84039 0.817417
\(93\) 13.3367 1.38295
\(94\) −29.2156 −3.01336
\(95\) 19.0832 1.95790
\(96\) 0.677766 0.0691742
\(97\) −3.70267 −0.375949 −0.187975 0.982174i \(-0.560192\pi\)
−0.187975 + 0.982174i \(0.560192\pi\)
\(98\) −2.44055 −0.246533
\(99\) −2.36752 −0.237944
\(100\) 45.2457 4.52457
\(101\) 3.97789 0.395815 0.197907 0.980221i \(-0.436585\pi\)
0.197907 + 0.980221i \(0.436585\pi\)
\(102\) 6.80417 0.673713
\(103\) −7.90372 −0.778777 −0.389388 0.921074i \(-0.627314\pi\)
−0.389388 + 0.921074i \(0.627314\pi\)
\(104\) −14.4735 −1.41925
\(105\) 6.51032 0.635342
\(106\) 0.624048 0.0606129
\(107\) −13.1151 −1.26788 −0.633940 0.773382i \(-0.718564\pi\)
−0.633940 + 0.773382i \(0.718564\pi\)
\(108\) −21.7360 −2.09155
\(109\) 9.17631 0.878931 0.439465 0.898260i \(-0.355168\pi\)
0.439465 + 0.898260i \(0.355168\pi\)
\(110\) −55.6004 −5.30129
\(111\) −8.44044 −0.801131
\(112\) 3.73964 0.353362
\(113\) 11.5599 1.08746 0.543732 0.839259i \(-0.317011\pi\)
0.543732 + 0.839259i \(0.317011\pi\)
\(114\) −18.4474 −1.72776
\(115\) 8.03440 0.749211
\(116\) −0.582283 −0.0540636
\(117\) −1.27720 −0.118077
\(118\) 20.8082 1.91555
\(119\) −1.73615 −0.159153
\(120\) −31.0830 −2.83748
\(121\) 20.5772 1.87066
\(122\) 29.4082 2.66249
\(123\) 8.55444 0.771328
\(124\) 32.8576 2.95070
\(125\) 26.0943 2.33395
\(126\) 1.02824 0.0916027
\(127\) 9.77573 0.867455 0.433728 0.901044i \(-0.357198\pi\)
0.433728 + 0.901044i \(0.357198\pi\)
\(128\) 19.9234 1.76099
\(129\) −2.83964 −0.250016
\(130\) −29.9947 −2.63071
\(131\) −10.8149 −0.944903 −0.472451 0.881357i \(-0.656631\pi\)
−0.472451 + 0.881357i \(0.656631\pi\)
\(132\) 35.7005 3.10733
\(133\) 4.70704 0.408152
\(134\) −17.5743 −1.51819
\(135\) −22.2739 −1.91703
\(136\) 8.28912 0.710786
\(137\) −11.8746 −1.01451 −0.507256 0.861795i \(-0.669340\pi\)
−0.507256 + 0.861795i \(0.669340\pi\)
\(138\) −7.76671 −0.661146
\(139\) −18.2040 −1.54405 −0.772024 0.635594i \(-0.780755\pi\)
−0.772024 + 0.635594i \(0.780755\pi\)
\(140\) 16.0395 1.35559
\(141\) 19.2232 1.61889
\(142\) 18.5795 1.55916
\(143\) 17.0350 1.42454
\(144\) −1.57556 −0.131297
\(145\) −0.596691 −0.0495525
\(146\) −5.43276 −0.449618
\(147\) 1.60583 0.132447
\(148\) −20.7947 −1.70932
\(149\) −14.5101 −1.18872 −0.594359 0.804200i \(-0.702594\pi\)
−0.594359 + 0.804200i \(0.702594\pi\)
\(150\) −44.8204 −3.65957
\(151\) −1.80705 −0.147056 −0.0735278 0.997293i \(-0.523426\pi\)
−0.0735278 + 0.997293i \(0.523426\pi\)
\(152\) −22.4734 −1.82283
\(153\) 0.731465 0.0591355
\(154\) −13.7143 −1.10513
\(155\) 33.6707 2.70449
\(156\) 19.2593 1.54198
\(157\) 6.75914 0.539438 0.269719 0.962939i \(-0.413069\pi\)
0.269719 + 0.962939i \(0.413069\pi\)
\(158\) 38.8773 3.09291
\(159\) −0.410610 −0.0325635
\(160\) 1.71113 0.135277
\(161\) 1.98175 0.156184
\(162\) 18.4470 1.44934
\(163\) −9.12240 −0.714521 −0.357261 0.934005i \(-0.616289\pi\)
−0.357261 + 0.934005i \(0.616289\pi\)
\(164\) 21.0756 1.64573
\(165\) 36.5839 2.84805
\(166\) 35.8080 2.77924
\(167\) −4.60013 −0.355969 −0.177984 0.984033i \(-0.556958\pi\)
−0.177984 + 0.984033i \(0.556958\pi\)
\(168\) −7.66690 −0.591514
\(169\) −3.81015 −0.293089
\(170\) 17.1783 1.31751
\(171\) −1.98314 −0.151655
\(172\) −6.99604 −0.533443
\(173\) 22.6611 1.72289 0.861446 0.507849i \(-0.169559\pi\)
0.861446 + 0.507849i \(0.169559\pi\)
\(174\) 0.576811 0.0437279
\(175\) 11.4364 0.864510
\(176\) 21.0144 1.58402
\(177\) −13.6914 −1.02911
\(178\) 30.5563 2.29029
\(179\) 8.88782 0.664307 0.332153 0.943225i \(-0.392225\pi\)
0.332153 + 0.943225i \(0.392225\pi\)
\(180\) −6.75767 −0.503687
\(181\) 20.6924 1.53805 0.769026 0.639218i \(-0.220742\pi\)
0.769026 + 0.639218i \(0.220742\pi\)
\(182\) −7.39847 −0.548411
\(183\) −19.3499 −1.43039
\(184\) −9.46173 −0.697528
\(185\) −21.3093 −1.56669
\(186\) −32.5488 −2.38660
\(187\) −9.75607 −0.713435
\(188\) 47.3603 3.45411
\(189\) −5.49404 −0.399633
\(190\) −46.5735 −3.37880
\(191\) −4.63599 −0.335449 −0.167724 0.985834i \(-0.553642\pi\)
−0.167724 + 0.985834i \(0.553642\pi\)
\(192\) −13.6646 −0.986154
\(193\) −7.66220 −0.551537 −0.275769 0.961224i \(-0.588932\pi\)
−0.275769 + 0.961224i \(0.588932\pi\)
\(194\) 9.03655 0.648787
\(195\) 19.7359 1.41332
\(196\) 3.95629 0.282592
\(197\) 0.587802 0.0418792 0.0209396 0.999781i \(-0.493334\pi\)
0.0209396 + 0.999781i \(0.493334\pi\)
\(198\) 5.77804 0.410628
\(199\) −1.46974 −0.104187 −0.0520936 0.998642i \(-0.516589\pi\)
−0.0520936 + 0.998642i \(0.516589\pi\)
\(200\) −54.6021 −3.86095
\(201\) 11.5635 0.815628
\(202\) −9.70824 −0.683070
\(203\) −0.147179 −0.0103300
\(204\) −11.0300 −0.772254
\(205\) 21.5971 1.50841
\(206\) 19.2894 1.34396
\(207\) −0.834941 −0.0580324
\(208\) 11.3366 0.786053
\(209\) 26.4506 1.82963
\(210\) −15.8888 −1.09643
\(211\) −9.30602 −0.640653 −0.320326 0.947307i \(-0.603793\pi\)
−0.320326 + 0.947307i \(0.603793\pi\)
\(212\) −1.01162 −0.0694785
\(213\) −12.2249 −0.837637
\(214\) 32.0080 2.18802
\(215\) −7.16915 −0.488932
\(216\) 26.2309 1.78478
\(217\) 8.30517 0.563792
\(218\) −22.3952 −1.51680
\(219\) 3.57464 0.241551
\(220\) 90.1318 6.07669
\(221\) −5.26311 −0.354035
\(222\) 20.5993 1.38254
\(223\) −11.7599 −0.787503 −0.393751 0.919217i \(-0.628823\pi\)
−0.393751 + 0.919217i \(0.628823\pi\)
\(224\) 0.422066 0.0282005
\(225\) −4.81831 −0.321221
\(226\) −28.2125 −1.87667
\(227\) 5.14725 0.341635 0.170817 0.985303i \(-0.445359\pi\)
0.170817 + 0.985303i \(0.445359\pi\)
\(228\) 29.9044 1.98047
\(229\) −18.9903 −1.25492 −0.627458 0.778650i \(-0.715905\pi\)
−0.627458 + 0.778650i \(0.715905\pi\)
\(230\) −19.6084 −1.29294
\(231\) 9.02374 0.593718
\(232\) 0.702695 0.0461342
\(233\) 25.2766 1.65593 0.827963 0.560783i \(-0.189500\pi\)
0.827963 + 0.560783i \(0.189500\pi\)
\(234\) 3.11708 0.203770
\(235\) 48.5322 3.16589
\(236\) −33.7315 −2.19573
\(237\) −25.5804 −1.66162
\(238\) 4.23717 0.274655
\(239\) −19.9839 −1.29265 −0.646324 0.763063i \(-0.723695\pi\)
−0.646324 + 0.763063i \(0.723695\pi\)
\(240\) 24.3462 1.57154
\(241\) 11.3576 0.731609 0.365804 0.930692i \(-0.380794\pi\)
0.365804 + 0.930692i \(0.380794\pi\)
\(242\) −50.2198 −3.22825
\(243\) 4.34439 0.278693
\(244\) −47.6726 −3.05192
\(245\) 4.05418 0.259012
\(246\) −20.8775 −1.33110
\(247\) 14.2693 0.907933
\(248\) −39.6524 −2.51793
\(249\) −23.5609 −1.49311
\(250\) −63.6845 −4.02776
\(251\) −14.4867 −0.914390 −0.457195 0.889367i \(-0.651146\pi\)
−0.457195 + 0.889367i \(0.651146\pi\)
\(252\) −1.66684 −0.105001
\(253\) 11.1362 0.700127
\(254\) −23.8582 −1.49699
\(255\) −11.3029 −0.707816
\(256\) −31.6053 −1.97533
\(257\) 27.0966 1.69024 0.845119 0.534578i \(-0.179529\pi\)
0.845119 + 0.534578i \(0.179529\pi\)
\(258\) 6.93029 0.431461
\(259\) −5.25613 −0.326600
\(260\) 48.6234 3.01549
\(261\) 0.0620086 0.00383824
\(262\) 26.3943 1.63065
\(263\) −5.58167 −0.344180 −0.172090 0.985081i \(-0.555052\pi\)
−0.172090 + 0.985081i \(0.555052\pi\)
\(264\) −43.0831 −2.65158
\(265\) −1.03665 −0.0636811
\(266\) −11.4878 −0.704361
\(267\) −20.1054 −1.23043
\(268\) 28.4891 1.74025
\(269\) 8.84328 0.539185 0.269592 0.962975i \(-0.413111\pi\)
0.269592 + 0.962975i \(0.413111\pi\)
\(270\) 54.3605 3.30827
\(271\) 0.0306869 0.00186410 0.000932049 1.00000i \(-0.499703\pi\)
0.000932049 1.00000i \(0.499703\pi\)
\(272\) −6.49258 −0.393671
\(273\) 4.86803 0.294627
\(274\) 28.9805 1.75077
\(275\) 64.2653 3.87534
\(276\) 12.5903 0.757849
\(277\) −16.9180 −1.01650 −0.508252 0.861208i \(-0.669708\pi\)
−0.508252 + 0.861208i \(0.669708\pi\)
\(278\) 44.4279 2.66461
\(279\) −3.49908 −0.209485
\(280\) −19.3564 −1.15676
\(281\) −30.8942 −1.84299 −0.921497 0.388386i \(-0.873033\pi\)
−0.921497 + 0.388386i \(0.873033\pi\)
\(282\) −46.9152 −2.79376
\(283\) −15.3016 −0.909586 −0.454793 0.890597i \(-0.650287\pi\)
−0.454793 + 0.890597i \(0.650287\pi\)
\(284\) −30.1186 −1.78721
\(285\) 30.6444 1.81522
\(286\) −41.5747 −2.45836
\(287\) 5.32712 0.314450
\(288\) −0.177822 −0.0104783
\(289\) −13.9858 −0.822693
\(290\) 1.45626 0.0855142
\(291\) −5.94585 −0.348552
\(292\) 8.80685 0.515382
\(293\) −19.7498 −1.15380 −0.576899 0.816816i \(-0.695737\pi\)
−0.576899 + 0.816816i \(0.695737\pi\)
\(294\) −3.91911 −0.228567
\(295\) −34.5661 −2.01252
\(296\) 25.0949 1.45861
\(297\) −30.8730 −1.79143
\(298\) 35.4127 2.05140
\(299\) 6.00764 0.347431
\(300\) 72.6568 4.19484
\(301\) −1.76833 −0.101925
\(302\) 4.41020 0.253778
\(303\) 6.38781 0.366970
\(304\) 17.6026 1.00958
\(305\) −48.8522 −2.79727
\(306\) −1.78518 −0.102052
\(307\) 9.43508 0.538488 0.269244 0.963072i \(-0.413226\pi\)
0.269244 + 0.963072i \(0.413226\pi\)
\(308\) 22.2318 1.26678
\(309\) −12.6920 −0.722024
\(310\) −82.1750 −4.66723
\(311\) 6.10976 0.346453 0.173226 0.984882i \(-0.444581\pi\)
0.173226 + 0.984882i \(0.444581\pi\)
\(312\) −23.2420 −1.31582
\(313\) −8.89970 −0.503041 −0.251520 0.967852i \(-0.580931\pi\)
−0.251520 + 0.967852i \(0.580931\pi\)
\(314\) −16.4960 −0.930925
\(315\) −1.70808 −0.0962396
\(316\) −63.0225 −3.54529
\(317\) −3.97682 −0.223360 −0.111680 0.993744i \(-0.535623\pi\)
−0.111680 + 0.993744i \(0.535623\pi\)
\(318\) 1.00211 0.0561958
\(319\) −0.827053 −0.0463061
\(320\) −34.4984 −1.92852
\(321\) −21.0605 −1.17548
\(322\) −4.83657 −0.269532
\(323\) −8.17215 −0.454710
\(324\) −29.9038 −1.66132
\(325\) 34.6692 1.92310
\(326\) 22.2637 1.23307
\(327\) 14.7356 0.814879
\(328\) −25.4339 −1.40435
\(329\) 11.9709 0.659977
\(330\) −89.2848 −4.91497
\(331\) 14.4699 0.795336 0.397668 0.917529i \(-0.369820\pi\)
0.397668 + 0.917529i \(0.369820\pi\)
\(332\) −58.0471 −3.18575
\(333\) 2.21448 0.121353
\(334\) 11.2269 0.614306
\(335\) 29.1940 1.59504
\(336\) 6.00522 0.327611
\(337\) 12.5830 0.685442 0.342721 0.939437i \(-0.388652\pi\)
0.342721 + 0.939437i \(0.388652\pi\)
\(338\) 9.29888 0.505792
\(339\) 18.5632 1.00822
\(340\) −27.8470 −1.51022
\(341\) 46.6698 2.52731
\(342\) 4.83996 0.261715
\(343\) 1.00000 0.0539949
\(344\) 8.44277 0.455203
\(345\) 12.9019 0.694613
\(346\) −55.3056 −2.97325
\(347\) 3.30124 0.177220 0.0886100 0.996066i \(-0.471758\pi\)
0.0886100 + 0.996066i \(0.471758\pi\)
\(348\) −0.935047 −0.0501238
\(349\) −3.61199 −0.193345 −0.0966726 0.995316i \(-0.530820\pi\)
−0.0966726 + 0.995316i \(0.530820\pi\)
\(350\) −27.9111 −1.49191
\(351\) −16.6551 −0.888981
\(352\) 2.37174 0.126414
\(353\) 5.65269 0.300862 0.150431 0.988620i \(-0.451934\pi\)
0.150431 + 0.988620i \(0.451934\pi\)
\(354\) 33.4145 1.77596
\(355\) −30.8638 −1.63808
\(356\) −49.5337 −2.62528
\(357\) −2.78796 −0.147555
\(358\) −21.6912 −1.14641
\(359\) 17.4037 0.918531 0.459265 0.888299i \(-0.348113\pi\)
0.459265 + 0.888299i \(0.348113\pi\)
\(360\) 8.15511 0.429812
\(361\) 3.15626 0.166119
\(362\) −50.5008 −2.65426
\(363\) 33.0435 1.73434
\(364\) 11.9934 0.628624
\(365\) 9.02476 0.472378
\(366\) 47.2245 2.46847
\(367\) −15.8799 −0.828924 −0.414462 0.910067i \(-0.636030\pi\)
−0.414462 + 0.910067i \(0.636030\pi\)
\(368\) 7.41104 0.386327
\(369\) −2.24439 −0.116838
\(370\) 52.0064 2.70368
\(371\) −0.255700 −0.0132753
\(372\) 52.7637 2.73567
\(373\) −26.8938 −1.39251 −0.696254 0.717795i \(-0.745151\pi\)
−0.696254 + 0.717795i \(0.745151\pi\)
\(374\) 23.8102 1.23120
\(375\) 41.9030 2.16386
\(376\) −57.1541 −2.94750
\(377\) −0.446170 −0.0229789
\(378\) 13.4085 0.689659
\(379\) −21.7543 −1.11744 −0.558722 0.829355i \(-0.688708\pi\)
−0.558722 + 0.829355i \(0.688708\pi\)
\(380\) 75.4987 3.87300
\(381\) 15.6981 0.804240
\(382\) 11.3144 0.578894
\(383\) 4.06617 0.207772 0.103886 0.994589i \(-0.466872\pi\)
0.103886 + 0.994589i \(0.466872\pi\)
\(384\) 31.9935 1.63266
\(385\) 22.7819 1.16107
\(386\) 18.7000 0.951804
\(387\) 0.745024 0.0378717
\(388\) −14.6488 −0.743682
\(389\) −8.17657 −0.414569 −0.207284 0.978281i \(-0.566463\pi\)
−0.207284 + 0.978281i \(0.566463\pi\)
\(390\) −48.1664 −2.43900
\(391\) −3.44063 −0.174000
\(392\) −4.77442 −0.241145
\(393\) −17.3669 −0.876044
\(394\) −1.43456 −0.0722721
\(395\) −64.5819 −3.24947
\(396\) −9.36658 −0.470688
\(397\) −34.1595 −1.71442 −0.857208 0.514970i \(-0.827803\pi\)
−0.857208 + 0.514970i \(0.827803\pi\)
\(398\) 3.58698 0.179799
\(399\) 7.55871 0.378409
\(400\) 42.7680 2.13840
\(401\) 29.7200 1.48415 0.742073 0.670320i \(-0.233843\pi\)
0.742073 + 0.670320i \(0.233843\pi\)
\(402\) −28.2214 −1.40755
\(403\) 25.1769 1.25415
\(404\) 15.7377 0.782979
\(405\) −30.6438 −1.52270
\(406\) 0.359198 0.0178267
\(407\) −29.5361 −1.46405
\(408\) 13.3109 0.658988
\(409\) −17.3535 −0.858073 −0.429037 0.903287i \(-0.641147\pi\)
−0.429037 + 0.903287i \(0.641147\pi\)
\(410\) −52.7088 −2.60310
\(411\) −19.0685 −0.940580
\(412\) −31.2694 −1.54053
\(413\) −8.52605 −0.419539
\(414\) 2.03772 0.100148
\(415\) −59.4834 −2.91993
\(416\) 1.27948 0.0627318
\(417\) −29.2326 −1.43153
\(418\) −64.5540 −3.15744
\(419\) 8.70836 0.425431 0.212716 0.977114i \(-0.431769\pi\)
0.212716 + 0.977114i \(0.431769\pi\)
\(420\) 25.7567 1.25680
\(421\) 13.3328 0.649802 0.324901 0.945748i \(-0.394669\pi\)
0.324901 + 0.945748i \(0.394669\pi\)
\(422\) 22.7118 1.10559
\(423\) −5.04351 −0.245224
\(424\) 1.22082 0.0592882
\(425\) −19.8553 −0.963125
\(426\) 29.8355 1.44553
\(427\) −12.0498 −0.583132
\(428\) −51.8870 −2.50805
\(429\) 27.3552 1.32072
\(430\) 17.4967 0.843764
\(431\) −21.4699 −1.03417 −0.517084 0.855934i \(-0.672983\pi\)
−0.517084 + 0.855934i \(0.672983\pi\)
\(432\) −20.5457 −0.988507
\(433\) −29.6160 −1.42325 −0.711626 0.702559i \(-0.752041\pi\)
−0.711626 + 0.702559i \(0.752041\pi\)
\(434\) −20.2692 −0.972952
\(435\) −0.958184 −0.0459414
\(436\) 36.3041 1.73865
\(437\) 9.32821 0.446229
\(438\) −8.72408 −0.416853
\(439\) 0.394740 0.0188399 0.00941995 0.999956i \(-0.497001\pi\)
0.00941995 + 0.999956i \(0.497001\pi\)
\(440\) −108.770 −5.18543
\(441\) −0.421314 −0.0200626
\(442\) 12.8449 0.610968
\(443\) −4.66698 −0.221735 −0.110868 0.993835i \(-0.535363\pi\)
−0.110868 + 0.993835i \(0.535363\pi\)
\(444\) −33.3928 −1.58475
\(445\) −50.7593 −2.40622
\(446\) 28.7007 1.35902
\(447\) −23.3008 −1.10209
\(448\) −8.50935 −0.402029
\(449\) −8.10122 −0.382320 −0.191160 0.981559i \(-0.561225\pi\)
−0.191160 + 0.981559i \(0.561225\pi\)
\(450\) 11.7593 0.554340
\(451\) 29.9350 1.40958
\(452\) 45.7343 2.15116
\(453\) −2.90181 −0.136339
\(454\) −12.5621 −0.589570
\(455\) 12.2902 0.576171
\(456\) −36.0884 −1.69000
\(457\) −1.73849 −0.0813233 −0.0406616 0.999173i \(-0.512947\pi\)
−0.0406616 + 0.999173i \(0.512947\pi\)
\(458\) 46.3469 2.16565
\(459\) 9.53850 0.445219
\(460\) 31.7864 1.48205
\(461\) −12.3136 −0.573503 −0.286751 0.958005i \(-0.592575\pi\)
−0.286751 + 0.958005i \(0.592575\pi\)
\(462\) −22.0229 −1.02460
\(463\) 18.6885 0.868528 0.434264 0.900786i \(-0.357008\pi\)
0.434264 + 0.900786i \(0.357008\pi\)
\(464\) −0.550397 −0.0255515
\(465\) 54.0693 2.50741
\(466\) −61.6888 −2.85768
\(467\) 34.7687 1.60890 0.804452 0.594018i \(-0.202459\pi\)
0.804452 + 0.594018i \(0.202459\pi\)
\(468\) −5.05298 −0.233574
\(469\) 7.20097 0.332510
\(470\) −118.445 −5.46347
\(471\) 10.8540 0.500127
\(472\) 40.7069 1.87369
\(473\) −9.93691 −0.456900
\(474\) 62.4302 2.86751
\(475\) 53.8316 2.46996
\(476\) −6.86872 −0.314827
\(477\) 0.107730 0.00493261
\(478\) 48.7716 2.23076
\(479\) 6.58647 0.300943 0.150472 0.988614i \(-0.451921\pi\)
0.150472 + 0.988614i \(0.451921\pi\)
\(480\) 2.74779 0.125419
\(481\) −15.9338 −0.726520
\(482\) −27.7189 −1.26256
\(483\) 3.18236 0.144802
\(484\) 81.4095 3.70043
\(485\) −15.0113 −0.681628
\(486\) −10.6027 −0.480949
\(487\) 27.9890 1.26830 0.634151 0.773209i \(-0.281350\pi\)
0.634151 + 0.773209i \(0.281350\pi\)
\(488\) 57.5309 2.60430
\(489\) −14.6490 −0.662451
\(490\) −9.89444 −0.446985
\(491\) 20.0508 0.904879 0.452439 0.891795i \(-0.350554\pi\)
0.452439 + 0.891795i \(0.350554\pi\)
\(492\) 33.8438 1.52580
\(493\) 0.255526 0.0115083
\(494\) −34.8249 −1.56685
\(495\) −9.59834 −0.431413
\(496\) 31.0583 1.39456
\(497\) −7.61283 −0.341482
\(498\) 57.5016 2.57671
\(499\) 26.2190 1.17372 0.586862 0.809687i \(-0.300363\pi\)
0.586862 + 0.809687i \(0.300363\pi\)
\(500\) 103.237 4.61688
\(501\) −7.38702 −0.330028
\(502\) 35.3554 1.57799
\(503\) 9.09643 0.405590 0.202795 0.979221i \(-0.434998\pi\)
0.202795 + 0.979221i \(0.434998\pi\)
\(504\) 2.01153 0.0896006
\(505\) 16.1271 0.717646
\(506\) −27.1785 −1.20823
\(507\) −6.11846 −0.271730
\(508\) 38.6756 1.71595
\(509\) 41.2330 1.82762 0.913811 0.406140i \(-0.133126\pi\)
0.913811 + 0.406140i \(0.133126\pi\)
\(510\) 27.5853 1.22150
\(511\) 2.22604 0.0984741
\(512\) 37.2876 1.64789
\(513\) −25.8607 −1.14178
\(514\) −66.1306 −2.91690
\(515\) −32.0431 −1.41199
\(516\) −11.2344 −0.494569
\(517\) 67.2688 2.95848
\(518\) 12.8278 0.563623
\(519\) 36.3899 1.59734
\(520\) −58.6784 −2.57322
\(521\) 12.1497 0.532288 0.266144 0.963933i \(-0.414250\pi\)
0.266144 + 0.963933i \(0.414250\pi\)
\(522\) −0.151335 −0.00662376
\(523\) 26.9739 1.17948 0.589742 0.807591i \(-0.299229\pi\)
0.589742 + 0.807591i \(0.299229\pi\)
\(524\) −42.7869 −1.86915
\(525\) 18.3649 0.801510
\(526\) 13.6223 0.593962
\(527\) −14.4190 −0.628103
\(528\) 33.7455 1.46858
\(529\) −19.0726 −0.829246
\(530\) 2.53001 0.109896
\(531\) 3.59214 0.155886
\(532\) 18.6224 0.807384
\(533\) 16.1490 0.699492
\(534\) 49.0681 2.12339
\(535\) −53.1709 −2.29878
\(536\) −34.3805 −1.48501
\(537\) 14.2723 0.615896
\(538\) −21.5825 −0.930487
\(539\) 5.61936 0.242043
\(540\) −88.1218 −3.79216
\(541\) −1.52981 −0.0657715 −0.0328858 0.999459i \(-0.510470\pi\)
−0.0328858 + 0.999459i \(0.510470\pi\)
\(542\) −0.0748930 −0.00321693
\(543\) 33.2284 1.42597
\(544\) −0.732771 −0.0314173
\(545\) 37.2024 1.59358
\(546\) −11.8807 −0.508446
\(547\) 14.3993 0.615669 0.307835 0.951440i \(-0.400396\pi\)
0.307835 + 0.951440i \(0.400396\pi\)
\(548\) −46.9792 −2.00685
\(549\) 5.07676 0.216671
\(550\) −156.843 −6.68779
\(551\) −0.692779 −0.0295134
\(552\) −15.1939 −0.646696
\(553\) −15.9297 −0.677400
\(554\) 41.2892 1.75421
\(555\) −34.2191 −1.45252
\(556\) −72.0205 −3.05435
\(557\) 33.3037 1.41112 0.705562 0.708648i \(-0.250695\pi\)
0.705562 + 0.708648i \(0.250695\pi\)
\(558\) 8.53969 0.361514
\(559\) −5.36066 −0.226732
\(560\) 15.1612 0.640676
\(561\) −15.6666 −0.661444
\(562\) 75.3989 3.18051
\(563\) 37.7490 1.59093 0.795464 0.606000i \(-0.207227\pi\)
0.795464 + 0.606000i \(0.207227\pi\)
\(564\) 76.0525 3.20239
\(565\) 46.8660 1.97167
\(566\) 37.3444 1.56970
\(567\) −7.55855 −0.317429
\(568\) 36.3469 1.52508
\(569\) −18.4976 −0.775459 −0.387730 0.921773i \(-0.626741\pi\)
−0.387730 + 0.921773i \(0.626741\pi\)
\(570\) −74.7891 −3.13257
\(571\) −43.4542 −1.81850 −0.909251 0.416249i \(-0.863344\pi\)
−0.909251 + 0.416249i \(0.863344\pi\)
\(572\) 67.3952 2.81794
\(573\) −7.44461 −0.311003
\(574\) −13.0011 −0.542656
\(575\) 22.6641 0.945160
\(576\) 3.58511 0.149379
\(577\) −10.6079 −0.441612 −0.220806 0.975318i \(-0.570869\pi\)
−0.220806 + 0.975318i \(0.570869\pi\)
\(578\) 34.1330 1.41975
\(579\) −12.3042 −0.511344
\(580\) −2.36068 −0.0980220
\(581\) −14.6721 −0.608702
\(582\) 14.5112 0.601507
\(583\) −1.43687 −0.0595091
\(584\) −10.6280 −0.439791
\(585\) −5.17801 −0.214085
\(586\) 48.2005 1.99114
\(587\) −19.0583 −0.786620 −0.393310 0.919406i \(-0.628670\pi\)
−0.393310 + 0.919406i \(0.628670\pi\)
\(588\) 6.35312 0.261998
\(589\) 39.0928 1.61079
\(590\) 84.3604 3.47306
\(591\) 0.943909 0.0388272
\(592\) −19.6560 −0.807857
\(593\) −5.81928 −0.238969 −0.119485 0.992836i \(-0.538124\pi\)
−0.119485 + 0.992836i \(0.538124\pi\)
\(594\) 75.3472 3.09153
\(595\) −7.03868 −0.288558
\(596\) −57.4063 −2.35145
\(597\) −2.36015 −0.0965946
\(598\) −14.6620 −0.599572
\(599\) −26.4097 −1.07907 −0.539535 0.841963i \(-0.681400\pi\)
−0.539535 + 0.841963i \(0.681400\pi\)
\(600\) −87.6817 −3.57959
\(601\) −42.5034 −1.73375 −0.866876 0.498525i \(-0.833875\pi\)
−0.866876 + 0.498525i \(0.833875\pi\)
\(602\) 4.31571 0.175895
\(603\) −3.03387 −0.123549
\(604\) −7.14921 −0.290897
\(605\) 83.4239 3.39166
\(606\) −15.5898 −0.633291
\(607\) −39.8934 −1.61923 −0.809613 0.586965i \(-0.800323\pi\)
−0.809613 + 0.586965i \(0.800323\pi\)
\(608\) 1.98668 0.0805706
\(609\) −0.236345 −0.00957716
\(610\) 119.226 4.82733
\(611\) 36.2895 1.46812
\(612\) 2.89389 0.116978
\(613\) 11.3211 0.457256 0.228628 0.973514i \(-0.426576\pi\)
0.228628 + 0.973514i \(0.426576\pi\)
\(614\) −23.0268 −0.929285
\(615\) 34.6813 1.39848
\(616\) −26.8292 −1.08098
\(617\) 33.5516 1.35074 0.675369 0.737480i \(-0.263984\pi\)
0.675369 + 0.737480i \(0.263984\pi\)
\(618\) 30.9755 1.24602
\(619\) −6.65515 −0.267493 −0.133747 0.991016i \(-0.542701\pi\)
−0.133747 + 0.991016i \(0.542701\pi\)
\(620\) 133.211 5.34988
\(621\) −10.8878 −0.436914
\(622\) −14.9112 −0.597884
\(623\) −12.5202 −0.501613
\(624\) 18.2047 0.728770
\(625\) 48.6092 1.94437
\(626\) 21.7202 0.868112
\(627\) 42.4751 1.69629
\(628\) 26.7411 1.06709
\(629\) 9.12544 0.363855
\(630\) 4.16866 0.166084
\(631\) 21.3981 0.851846 0.425923 0.904759i \(-0.359949\pi\)
0.425923 + 0.904759i \(0.359949\pi\)
\(632\) 76.0551 3.02531
\(633\) −14.9439 −0.593966
\(634\) 9.70562 0.385460
\(635\) 39.6326 1.57277
\(636\) −1.62449 −0.0644153
\(637\) 3.03148 0.120111
\(638\) 2.01847 0.0799118
\(639\) 3.20739 0.126883
\(640\) 80.7729 3.19283
\(641\) 38.6480 1.52650 0.763251 0.646102i \(-0.223602\pi\)
0.763251 + 0.646102i \(0.223602\pi\)
\(642\) 51.3993 2.02857
\(643\) 9.46299 0.373184 0.186592 0.982438i \(-0.440256\pi\)
0.186592 + 0.982438i \(0.440256\pi\)
\(644\) 7.84039 0.308955
\(645\) −11.5124 −0.453301
\(646\) 19.9445 0.784707
\(647\) 34.8896 1.37165 0.685825 0.727766i \(-0.259441\pi\)
0.685825 + 0.727766i \(0.259441\pi\)
\(648\) 36.0877 1.41766
\(649\) −47.9109 −1.88067
\(650\) −84.6118 −3.31875
\(651\) 13.3367 0.522706
\(652\) −36.0908 −1.41343
\(653\) −11.0205 −0.431264 −0.215632 0.976475i \(-0.569181\pi\)
−0.215632 + 0.976475i \(0.569181\pi\)
\(654\) −35.9629 −1.40626
\(655\) −43.8456 −1.71319
\(656\) 19.9215 0.777803
\(657\) −0.937861 −0.0365894
\(658\) −29.2156 −1.13894
\(659\) 25.0437 0.975562 0.487781 0.872966i \(-0.337806\pi\)
0.487781 + 0.872966i \(0.337806\pi\)
\(660\) 144.736 5.63385
\(661\) 46.6718 1.81532 0.907662 0.419701i \(-0.137865\pi\)
0.907662 + 0.419701i \(0.137865\pi\)
\(662\) −35.3145 −1.37254
\(663\) −8.45165 −0.328235
\(664\) 70.0508 2.71850
\(665\) 19.0832 0.740015
\(666\) −5.40455 −0.209422
\(667\) −0.291673 −0.0112936
\(668\) −18.1994 −0.704158
\(669\) −18.8844 −0.730114
\(670\) −71.2496 −2.75261
\(671\) −67.7123 −2.61400
\(672\) 0.677766 0.0261454
\(673\) −37.9417 −1.46255 −0.731273 0.682085i \(-0.761073\pi\)
−0.731273 + 0.682085i \(0.761073\pi\)
\(674\) −30.7095 −1.18289
\(675\) −62.8321 −2.41841
\(676\) −15.0741 −0.579772
\(677\) −4.47977 −0.172171 −0.0860857 0.996288i \(-0.527436\pi\)
−0.0860857 + 0.996288i \(0.527436\pi\)
\(678\) −45.3045 −1.73991
\(679\) −3.70267 −0.142095
\(680\) 33.6056 1.28872
\(681\) 8.26560 0.316738
\(682\) −113.900 −4.36145
\(683\) 15.3383 0.586905 0.293452 0.955974i \(-0.405196\pi\)
0.293452 + 0.955974i \(0.405196\pi\)
\(684\) −7.84588 −0.299995
\(685\) −48.1416 −1.83940
\(686\) −2.44055 −0.0931807
\(687\) −30.4952 −1.16347
\(688\) −6.61292 −0.252115
\(689\) −0.775148 −0.0295308
\(690\) −31.4877 −1.19871
\(691\) 30.9027 1.17560 0.587798 0.809008i \(-0.299995\pi\)
0.587798 + 0.809008i \(0.299995\pi\)
\(692\) 89.6539 3.40813
\(693\) −2.36752 −0.0899345
\(694\) −8.05685 −0.305834
\(695\) −73.8025 −2.79949
\(696\) 1.12841 0.0427722
\(697\) −9.24869 −0.350319
\(698\) 8.81524 0.333662
\(699\) 40.5899 1.53525
\(700\) 45.2457 1.71013
\(701\) 27.2746 1.03015 0.515074 0.857146i \(-0.327764\pi\)
0.515074 + 0.857146i \(0.327764\pi\)
\(702\) 40.6475 1.53414
\(703\) −24.7408 −0.933118
\(704\) −47.8171 −1.80218
\(705\) 77.9344 2.93518
\(706\) −13.7957 −0.519207
\(707\) 3.97789 0.149604
\(708\) −54.1670 −2.03572
\(709\) −7.72825 −0.290240 −0.145120 0.989414i \(-0.546357\pi\)
−0.145120 + 0.989414i \(0.546357\pi\)
\(710\) 75.3247 2.82689
\(711\) 6.71141 0.251697
\(712\) 59.7769 2.24023
\(713\) 16.4588 0.616387
\(714\) 6.80417 0.254640
\(715\) 69.0628 2.58280
\(716\) 35.1628 1.31409
\(717\) −32.0907 −1.19845
\(718\) −42.4746 −1.58514
\(719\) 1.76981 0.0660027 0.0330013 0.999455i \(-0.489493\pi\)
0.0330013 + 0.999455i \(0.489493\pi\)
\(720\) −6.38761 −0.238052
\(721\) −7.90372 −0.294350
\(722\) −7.70301 −0.286676
\(723\) 18.2384 0.678293
\(724\) 81.8650 3.04249
\(725\) −1.68320 −0.0625124
\(726\) −80.6444 −2.99299
\(727\) −12.2925 −0.455903 −0.227951 0.973673i \(-0.573203\pi\)
−0.227951 + 0.973673i \(0.573203\pi\)
\(728\) −14.4735 −0.536425
\(729\) 29.6520 1.09822
\(730\) −22.0254 −0.815196
\(731\) 3.07010 0.113552
\(732\) −76.5540 −2.82952
\(733\) −44.0270 −1.62618 −0.813088 0.582141i \(-0.802215\pi\)
−0.813088 + 0.582141i \(0.802215\pi\)
\(734\) 38.7557 1.43050
\(735\) 6.51032 0.240137
\(736\) 0.836431 0.0308313
\(737\) 40.4649 1.49054
\(738\) 5.47755 0.201631
\(739\) −7.22370 −0.265728 −0.132864 0.991134i \(-0.542417\pi\)
−0.132864 + 0.991134i \(0.542417\pi\)
\(740\) −84.3057 −3.09914
\(741\) 22.9140 0.841768
\(742\) 0.624048 0.0229095
\(743\) 12.2947 0.451048 0.225524 0.974238i \(-0.427591\pi\)
0.225524 + 0.974238i \(0.427591\pi\)
\(744\) −63.6749 −2.33443
\(745\) −58.8268 −2.15525
\(746\) 65.6357 2.40309
\(747\) 6.18157 0.226172
\(748\) −38.5978 −1.41128
\(749\) −13.1151 −0.479214
\(750\) −102.266 −3.73424
\(751\) 29.7606 1.08598 0.542990 0.839739i \(-0.317292\pi\)
0.542990 + 0.839739i \(0.317292\pi\)
\(752\) 44.7668 1.63248
\(753\) −23.2631 −0.847754
\(754\) 1.08890 0.0396554
\(755\) −7.32611 −0.266624
\(756\) −21.7360 −0.790531
\(757\) 48.9921 1.78065 0.890324 0.455327i \(-0.150478\pi\)
0.890324 + 0.455327i \(0.150478\pi\)
\(758\) 53.0925 1.92841
\(759\) 17.8828 0.649106
\(760\) −91.1113 −3.30495
\(761\) 17.4016 0.630806 0.315403 0.948958i \(-0.397860\pi\)
0.315403 + 0.948958i \(0.397860\pi\)
\(762\) −38.3121 −1.38790
\(763\) 9.17631 0.332205
\(764\) −18.3413 −0.663566
\(765\) 2.96549 0.107218
\(766\) −9.92370 −0.358558
\(767\) −25.8465 −0.933263
\(768\) −50.7527 −1.83138
\(769\) −47.1929 −1.70182 −0.850909 0.525312i \(-0.823948\pi\)
−0.850909 + 0.525312i \(0.823948\pi\)
\(770\) −55.6004 −2.00370
\(771\) 43.5125 1.56706
\(772\) −30.3139 −1.09102
\(773\) −49.9860 −1.79787 −0.898936 0.438080i \(-0.855659\pi\)
−0.898936 + 0.438080i \(0.855659\pi\)
\(774\) −1.81827 −0.0653563
\(775\) 94.9812 3.41183
\(776\) 17.6781 0.634607
\(777\) −8.44044 −0.302799
\(778\) 19.9553 0.715434
\(779\) 25.0750 0.898404
\(780\) 78.0808 2.79574
\(781\) −42.7793 −1.53076
\(782\) 8.39703 0.300277
\(783\) 0.808609 0.0288973
\(784\) 3.73964 0.133558
\(785\) 27.4028 0.978048
\(786\) 42.3848 1.51181
\(787\) −46.4030 −1.65409 −0.827044 0.562136i \(-0.809980\pi\)
−0.827044 + 0.562136i \(0.809980\pi\)
\(788\) 2.32551 0.0828430
\(789\) −8.96320 −0.319099
\(790\) 157.615 5.60771
\(791\) 11.5599 0.411023
\(792\) 11.3035 0.401653
\(793\) −36.5287 −1.29717
\(794\) 83.3680 2.95862
\(795\) −1.66469 −0.0590404
\(796\) −5.81472 −0.206097
\(797\) 54.7396 1.93898 0.969488 0.245140i \(-0.0788338\pi\)
0.969488 + 0.245140i \(0.0788338\pi\)
\(798\) −18.4474 −0.653031
\(799\) −20.7833 −0.735261
\(800\) 4.82691 0.170657
\(801\) 5.27495 0.186381
\(802\) −72.5331 −2.56123
\(803\) 12.5089 0.441430
\(804\) 45.7486 1.61343
\(805\) 8.03440 0.283175
\(806\) −61.4455 −2.16433
\(807\) 14.2008 0.499892
\(808\) −18.9921 −0.668140
\(809\) −18.8141 −0.661469 −0.330735 0.943724i \(-0.607296\pi\)
−0.330735 + 0.943724i \(0.607296\pi\)
\(810\) 74.7876 2.62777
\(811\) −13.1392 −0.461379 −0.230689 0.973027i \(-0.574098\pi\)
−0.230689 + 0.973027i \(0.574098\pi\)
\(812\) −0.582283 −0.0204341
\(813\) 0.0492779 0.00172825
\(814\) 72.0843 2.52655
\(815\) −36.9839 −1.29549
\(816\) −10.4260 −0.364982
\(817\) −8.32362 −0.291207
\(818\) 42.3520 1.48080
\(819\) −1.27720 −0.0446291
\(820\) 85.4444 2.98385
\(821\) −17.6974 −0.617644 −0.308822 0.951120i \(-0.599935\pi\)
−0.308822 + 0.951120i \(0.599935\pi\)
\(822\) 46.5377 1.62319
\(823\) −13.8177 −0.481655 −0.240827 0.970568i \(-0.577419\pi\)
−0.240827 + 0.970568i \(0.577419\pi\)
\(824\) 37.7357 1.31458
\(825\) 103.199 3.59293
\(826\) 20.8082 0.724012
\(827\) −2.30044 −0.0799943 −0.0399971 0.999200i \(-0.512735\pi\)
−0.0399971 + 0.999200i \(0.512735\pi\)
\(828\) −3.30327 −0.114796
\(829\) 14.8132 0.514482 0.257241 0.966347i \(-0.417187\pi\)
0.257241 + 0.966347i \(0.417187\pi\)
\(830\) 145.172 5.03900
\(831\) −27.1674 −0.942427
\(832\) −25.7959 −0.894311
\(833\) −1.73615 −0.0601541
\(834\) 71.3436 2.47043
\(835\) −18.6498 −0.645402
\(836\) 104.646 3.61926
\(837\) −45.6290 −1.57717
\(838\) −21.2532 −0.734179
\(839\) 2.15298 0.0743292 0.0371646 0.999309i \(-0.488167\pi\)
0.0371646 + 0.999309i \(0.488167\pi\)
\(840\) −31.0830 −1.07247
\(841\) −28.9783 −0.999253
\(842\) −32.5394 −1.12138
\(843\) −49.6108 −1.70869
\(844\) −36.8173 −1.26730
\(845\) −15.4471 −0.531395
\(846\) 12.3089 0.423190
\(847\) 20.5772 0.707042
\(848\) −0.956224 −0.0328369
\(849\) −24.5718 −0.843301
\(850\) 48.4579 1.66209
\(851\) −10.4164 −0.357068
\(852\) −48.3652 −1.65697
\(853\) 32.7125 1.12006 0.560028 0.828474i \(-0.310791\pi\)
0.560028 + 0.828474i \(0.310791\pi\)
\(854\) 29.4082 1.00633
\(855\) −8.04002 −0.274963
\(856\) 62.6168 2.14020
\(857\) −28.9878 −0.990204 −0.495102 0.868835i \(-0.664869\pi\)
−0.495102 + 0.868835i \(0.664869\pi\)
\(858\) −66.7618 −2.27921
\(859\) −1.00000 −0.0341196
\(860\) −28.3632 −0.967177
\(861\) 8.55444 0.291535
\(862\) 52.3984 1.78470
\(863\) 46.8259 1.59397 0.796985 0.603999i \(-0.206427\pi\)
0.796985 + 0.603999i \(0.206427\pi\)
\(864\) −2.31885 −0.0788889
\(865\) 91.8723 3.12375
\(866\) 72.2792 2.45615
\(867\) −22.4588 −0.762739
\(868\) 32.8576 1.11526
\(869\) −89.5148 −3.03658
\(870\) 2.33850 0.0792824
\(871\) 21.8296 0.739667
\(872\) −43.8115 −1.48365
\(873\) 1.55999 0.0527975
\(874\) −22.7660 −0.770070
\(875\) 26.0943 0.882149
\(876\) 14.1423 0.477824
\(877\) 39.4096 1.33077 0.665384 0.746501i \(-0.268268\pi\)
0.665384 + 0.746501i \(0.268268\pi\)
\(878\) −0.963382 −0.0325126
\(879\) −31.7149 −1.06972
\(880\) 85.1961 2.87196
\(881\) 57.8516 1.94907 0.974536 0.224232i \(-0.0719873\pi\)
0.974536 + 0.224232i \(0.0719873\pi\)
\(882\) 1.02824 0.0346226
\(883\) 36.5295 1.22932 0.614659 0.788793i \(-0.289294\pi\)
0.614659 + 0.788793i \(0.289294\pi\)
\(884\) −20.8224 −0.700332
\(885\) −55.5073 −1.86586
\(886\) 11.3900 0.382655
\(887\) 16.4771 0.553247 0.276623 0.960978i \(-0.410785\pi\)
0.276623 + 0.960978i \(0.410785\pi\)
\(888\) 40.2982 1.35232
\(889\) 9.77573 0.327867
\(890\) 123.881 4.15249
\(891\) −42.4743 −1.42294
\(892\) −46.5257 −1.55779
\(893\) 56.3475 1.88560
\(894\) 56.8668 1.90191
\(895\) 36.0329 1.20445
\(896\) 19.9234 0.665593
\(897\) 9.64724 0.322112
\(898\) 19.7714 0.659782
\(899\) −1.22235 −0.0407676
\(900\) −19.0626 −0.635421
\(901\) 0.443934 0.0147896
\(902\) −73.0579 −2.43256
\(903\) −2.83964 −0.0944973
\(904\) −55.1918 −1.83565
\(905\) 83.8906 2.78862
\(906\) 7.08202 0.235284
\(907\) −44.2731 −1.47006 −0.735031 0.678033i \(-0.762833\pi\)
−0.735031 + 0.678033i \(0.762833\pi\)
\(908\) 20.3640 0.675803
\(909\) −1.67594 −0.0555874
\(910\) −29.9947 −0.994316
\(911\) −33.7779 −1.11911 −0.559555 0.828793i \(-0.689028\pi\)
−0.559555 + 0.828793i \(0.689028\pi\)
\(912\) 28.2668 0.936008
\(913\) −82.4479 −2.72863
\(914\) 4.24288 0.140342
\(915\) −78.4482 −2.59342
\(916\) −75.1312 −2.48241
\(917\) −10.8149 −0.357140
\(918\) −23.2792 −0.768328
\(919\) 58.3753 1.92562 0.962811 0.270175i \(-0.0870816\pi\)
0.962811 + 0.270175i \(0.0870816\pi\)
\(920\) −38.3596 −1.26468
\(921\) 15.1511 0.499246
\(922\) 30.0520 0.989711
\(923\) −23.0781 −0.759626
\(924\) 35.7005 1.17446
\(925\) −60.1111 −1.97644
\(926\) −45.6102 −1.49885
\(927\) 3.32995 0.109370
\(928\) −0.0621193 −0.00203917
\(929\) −25.5947 −0.839735 −0.419868 0.907585i \(-0.637923\pi\)
−0.419868 + 0.907585i \(0.637923\pi\)
\(930\) −131.959 −4.32710
\(931\) 4.70704 0.154267
\(932\) 100.002 3.27566
\(933\) 9.81123 0.321205
\(934\) −84.8548 −2.77653
\(935\) −39.5529 −1.29352
\(936\) 6.09790 0.199316
\(937\) 41.0242 1.34020 0.670101 0.742270i \(-0.266251\pi\)
0.670101 + 0.742270i \(0.266251\pi\)
\(938\) −17.5743 −0.573822
\(939\) −14.2914 −0.466382
\(940\) 192.007 6.26259
\(941\) −3.27021 −0.106606 −0.0533028 0.998578i \(-0.516975\pi\)
−0.0533028 + 0.998578i \(0.516975\pi\)
\(942\) −26.4898 −0.863085
\(943\) 10.5570 0.343785
\(944\) −31.8843 −1.03775
\(945\) −22.2739 −0.724569
\(946\) 24.2515 0.788485
\(947\) 7.62585 0.247807 0.123903 0.992294i \(-0.460459\pi\)
0.123903 + 0.992294i \(0.460459\pi\)
\(948\) −101.203 −3.28693
\(949\) 6.74818 0.219055
\(950\) −131.379 −4.26249
\(951\) −6.38609 −0.207083
\(952\) 8.28912 0.268652
\(953\) −15.5860 −0.504880 −0.252440 0.967613i \(-0.581233\pi\)
−0.252440 + 0.967613i \(0.581233\pi\)
\(954\) −0.262920 −0.00851236
\(955\) −18.7952 −0.608197
\(956\) −79.0619 −2.55704
\(957\) −1.32811 −0.0429316
\(958\) −16.0746 −0.519347
\(959\) −11.8746 −0.383449
\(960\) −55.3986 −1.78798
\(961\) 37.9758 1.22503
\(962\) 38.8873 1.25378
\(963\) 5.52556 0.178059
\(964\) 44.9340 1.44723
\(965\) −31.0639 −0.999984
\(966\) −7.76671 −0.249890
\(967\) −8.39129 −0.269846 −0.134923 0.990856i \(-0.543079\pi\)
−0.134923 + 0.990856i \(0.543079\pi\)
\(968\) −98.2444 −3.15769
\(969\) −13.1231 −0.421574
\(970\) 36.6358 1.17631
\(971\) 19.2995 0.619351 0.309675 0.950842i \(-0.399780\pi\)
0.309675 + 0.950842i \(0.399780\pi\)
\(972\) 17.1877 0.551295
\(973\) −18.2040 −0.583595
\(974\) −68.3086 −2.18875
\(975\) 55.6727 1.78295
\(976\) −45.0619 −1.44240
\(977\) 40.3448 1.29075 0.645373 0.763868i \(-0.276702\pi\)
0.645373 + 0.763868i \(0.276702\pi\)
\(978\) 35.7516 1.14321
\(979\) −70.3558 −2.24858
\(980\) 16.0395 0.512363
\(981\) −3.86611 −0.123435
\(982\) −48.9349 −1.56158
\(983\) −10.1453 −0.323585 −0.161792 0.986825i \(-0.551727\pi\)
−0.161792 + 0.986825i \(0.551727\pi\)
\(984\) −40.8425 −1.30201
\(985\) 2.38306 0.0759305
\(986\) −0.623623 −0.0198602
\(987\) 19.2232 0.611881
\(988\) 56.4534 1.79602
\(989\) −3.50440 −0.111434
\(990\) 23.4252 0.744503
\(991\) 45.5718 1.44764 0.723818 0.689991i \(-0.242386\pi\)
0.723818 + 0.689991i \(0.242386\pi\)
\(992\) 3.50533 0.111294
\(993\) 23.2361 0.737377
\(994\) 18.5795 0.589306
\(995\) −5.95860 −0.188900
\(996\) −93.2137 −2.95359
\(997\) −30.8439 −0.976837 −0.488419 0.872609i \(-0.662426\pi\)
−0.488419 + 0.872609i \(0.662426\pi\)
\(998\) −63.9888 −2.02553
\(999\) 28.8774 0.913640
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 \(a_p\))