Properties

Label 6013.2.a.e.1.6
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 1.6
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53104 q^{2}\) \(+0.289125 q^{3}\) \(+4.40615 q^{4}\) \(-2.52674 q^{5}\) \(-0.731786 q^{6}\) \(+1.00000 q^{7}\) \(-6.09005 q^{8}\) \(-2.91641 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53104 q^{2}\) \(+0.289125 q^{3}\) \(+4.40615 q^{4}\) \(-2.52674 q^{5}\) \(-0.731786 q^{6}\) \(+1.00000 q^{7}\) \(-6.09005 q^{8}\) \(-2.91641 q^{9}\) \(+6.39527 q^{10}\) \(+3.22310 q^{11}\) \(+1.27393 q^{12}\) \(+0.295446 q^{13}\) \(-2.53104 q^{14}\) \(-0.730544 q^{15}\) \(+6.60184 q^{16}\) \(-1.30810 q^{17}\) \(+7.38153 q^{18}\) \(-5.37595 q^{19}\) \(-11.1332 q^{20}\) \(+0.289125 q^{21}\) \(-8.15777 q^{22}\) \(+6.32217 q^{23}\) \(-1.76079 q^{24}\) \(+1.38441 q^{25}\) \(-0.747786 q^{26}\) \(-1.71058 q^{27}\) \(+4.40615 q^{28}\) \(-1.72339 q^{29}\) \(+1.84903 q^{30}\) \(+5.03594 q^{31}\) \(-4.52940 q^{32}\) \(+0.931878 q^{33}\) \(+3.31085 q^{34}\) \(-2.52674 q^{35}\) \(-12.8501 q^{36}\) \(-10.0376 q^{37}\) \(+13.6067 q^{38}\) \(+0.0854210 q^{39}\) \(+15.3880 q^{40}\) \(-6.07216 q^{41}\) \(-0.731786 q^{42}\) \(-7.48467 q^{43}\) \(+14.2014 q^{44}\) \(+7.36900 q^{45}\) \(-16.0016 q^{46}\) \(+10.8622 q^{47}\) \(+1.90876 q^{48}\) \(+1.00000 q^{49}\) \(-3.50399 q^{50}\) \(-0.378205 q^{51}\) \(+1.30178 q^{52}\) \(+3.83827 q^{53}\) \(+4.32955 q^{54}\) \(-8.14392 q^{55}\) \(-6.09005 q^{56}\) \(-1.55432 q^{57}\) \(+4.36196 q^{58}\) \(+1.17293 q^{59}\) \(-3.21888 q^{60}\) \(+14.4379 q^{61}\) \(-12.7461 q^{62}\) \(-2.91641 q^{63}\) \(-1.73959 q^{64}\) \(-0.746516 q^{65}\) \(-2.35862 q^{66}\) \(-8.85743 q^{67}\) \(-5.76369 q^{68}\) \(+1.82790 q^{69}\) \(+6.39527 q^{70}\) \(+11.0535 q^{71}\) \(+17.7611 q^{72}\) \(-12.7184 q^{73}\) \(+25.4055 q^{74}\) \(+0.400268 q^{75}\) \(-23.6872 q^{76}\) \(+3.22310 q^{77}\) \(-0.216204 q^{78}\) \(-13.1112 q^{79}\) \(-16.6811 q^{80}\) \(+8.25465 q^{81}\) \(+15.3689 q^{82}\) \(+1.56809 q^{83}\) \(+1.27393 q^{84}\) \(+3.30523 q^{85}\) \(+18.9440 q^{86}\) \(-0.498275 q^{87}\) \(-19.6288 q^{88}\) \(+0.986945 q^{89}\) \(-18.6512 q^{90}\) \(+0.295446 q^{91}\) \(+27.8564 q^{92}\) \(+1.45602 q^{93}\) \(-27.4926 q^{94}\) \(+13.5836 q^{95}\) \(-1.30956 q^{96}\) \(-1.18449 q^{97}\) \(-2.53104 q^{98}\) \(-9.39986 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53104 −1.78971 −0.894857 0.446354i \(-0.852722\pi\)
−0.894857 + 0.446354i \(0.852722\pi\)
\(3\) 0.289125 0.166926 0.0834632 0.996511i \(-0.473402\pi\)
0.0834632 + 0.996511i \(0.473402\pi\)
\(4\) 4.40615 2.20307
\(5\) −2.52674 −1.12999 −0.564996 0.825094i \(-0.691122\pi\)
−0.564996 + 0.825094i \(0.691122\pi\)
\(6\) −0.731786 −0.298750
\(7\) 1.00000 0.377964
\(8\) −6.09005 −2.15316
\(9\) −2.91641 −0.972136
\(10\) 6.39527 2.02236
\(11\) 3.22310 0.971800 0.485900 0.874014i \(-0.338492\pi\)
0.485900 + 0.874014i \(0.338492\pi\)
\(12\) 1.27393 0.367751
\(13\) 0.295446 0.0819421 0.0409710 0.999160i \(-0.486955\pi\)
0.0409710 + 0.999160i \(0.486955\pi\)
\(14\) −2.53104 −0.676448
\(15\) −0.730544 −0.188626
\(16\) 6.60184 1.65046
\(17\) −1.30810 −0.317261 −0.158631 0.987338i \(-0.550708\pi\)
−0.158631 + 0.987338i \(0.550708\pi\)
\(18\) 7.38153 1.73984
\(19\) −5.37595 −1.23333 −0.616664 0.787227i \(-0.711516\pi\)
−0.616664 + 0.787227i \(0.711516\pi\)
\(20\) −11.1332 −2.48946
\(21\) 0.289125 0.0630923
\(22\) −8.15777 −1.73924
\(23\) 6.32217 1.31826 0.659131 0.752028i \(-0.270924\pi\)
0.659131 + 0.752028i \(0.270924\pi\)
\(24\) −1.76079 −0.359419
\(25\) 1.38441 0.276882
\(26\) −0.747786 −0.146653
\(27\) −1.71058 −0.329202
\(28\) 4.40615 0.832684
\(29\) −1.72339 −0.320026 −0.160013 0.987115i \(-0.551154\pi\)
−0.160013 + 0.987115i \(0.551154\pi\)
\(30\) 1.84903 0.337586
\(31\) 5.03594 0.904481 0.452241 0.891896i \(-0.350625\pi\)
0.452241 + 0.891896i \(0.350625\pi\)
\(32\) −4.52940 −0.800693
\(33\) 0.931878 0.162219
\(34\) 3.31085 0.567806
\(35\) −2.52674 −0.427097
\(36\) −12.8501 −2.14169
\(37\) −10.0376 −1.65017 −0.825084 0.565011i \(-0.808872\pi\)
−0.825084 + 0.565011i \(0.808872\pi\)
\(38\) 13.6067 2.20730
\(39\) 0.0854210 0.0136783
\(40\) 15.3880 2.43305
\(41\) −6.07216 −0.948312 −0.474156 0.880441i \(-0.657247\pi\)
−0.474156 + 0.880441i \(0.657247\pi\)
\(42\) −0.731786 −0.112917
\(43\) −7.48467 −1.14140 −0.570701 0.821158i \(-0.693328\pi\)
−0.570701 + 0.821158i \(0.693328\pi\)
\(44\) 14.2014 2.14095
\(45\) 7.36900 1.09851
\(46\) −16.0016 −2.35931
\(47\) 10.8622 1.58441 0.792206 0.610253i \(-0.208932\pi\)
0.792206 + 0.610253i \(0.208932\pi\)
\(48\) 1.90876 0.275505
\(49\) 1.00000 0.142857
\(50\) −3.50399 −0.495540
\(51\) −0.378205 −0.0529593
\(52\) 1.30178 0.180524
\(53\) 3.83827 0.527227 0.263613 0.964628i \(-0.415086\pi\)
0.263613 + 0.964628i \(0.415086\pi\)
\(54\) 4.32955 0.589176
\(55\) −8.14392 −1.09813
\(56\) −6.09005 −0.813817
\(57\) −1.55432 −0.205875
\(58\) 4.36196 0.572754
\(59\) 1.17293 0.152703 0.0763514 0.997081i \(-0.475673\pi\)
0.0763514 + 0.997081i \(0.475673\pi\)
\(60\) −3.21888 −0.415556
\(61\) 14.4379 1.84859 0.924293 0.381684i \(-0.124656\pi\)
0.924293 + 0.381684i \(0.124656\pi\)
\(62\) −12.7461 −1.61876
\(63\) −2.91641 −0.367433
\(64\) −1.73959 −0.217449
\(65\) −0.746516 −0.0925939
\(66\) −2.35862 −0.290326
\(67\) −8.85743 −1.08211 −0.541054 0.840988i \(-0.681974\pi\)
−0.541054 + 0.840988i \(0.681974\pi\)
\(68\) −5.76369 −0.698950
\(69\) 1.82790 0.220053
\(70\) 6.39527 0.764381
\(71\) 11.0535 1.31181 0.655907 0.754842i \(-0.272286\pi\)
0.655907 + 0.754842i \(0.272286\pi\)
\(72\) 17.7611 2.09316
\(73\) −12.7184 −1.48858 −0.744288 0.667859i \(-0.767211\pi\)
−0.744288 + 0.667859i \(0.767211\pi\)
\(74\) 25.4055 2.95333
\(75\) 0.400268 0.0462189
\(76\) −23.6872 −2.71711
\(77\) 3.22310 0.367306
\(78\) −0.216204 −0.0244802
\(79\) −13.1112 −1.47513 −0.737564 0.675278i \(-0.764024\pi\)
−0.737564 + 0.675278i \(0.764024\pi\)
\(80\) −16.6811 −1.86501
\(81\) 8.25465 0.917183
\(82\) 15.3689 1.69721
\(83\) 1.56809 0.172121 0.0860603 0.996290i \(-0.472572\pi\)
0.0860603 + 0.996290i \(0.472572\pi\)
\(84\) 1.27393 0.138997
\(85\) 3.30523 0.358503
\(86\) 18.9440 2.04278
\(87\) −0.498275 −0.0534207
\(88\) −19.6288 −2.09244
\(89\) 0.986945 0.104616 0.0523080 0.998631i \(-0.483342\pi\)
0.0523080 + 0.998631i \(0.483342\pi\)
\(90\) −18.6512 −1.96601
\(91\) 0.295446 0.0309712
\(92\) 27.8564 2.90423
\(93\) 1.45602 0.150982
\(94\) −27.4926 −2.83564
\(95\) 13.5836 1.39365
\(96\) −1.30956 −0.133657
\(97\) −1.18449 −0.120266 −0.0601332 0.998190i \(-0.519153\pi\)
−0.0601332 + 0.998190i \(0.519153\pi\)
\(98\) −2.53104 −0.255673
\(99\) −9.39986 −0.944721
\(100\) 6.09992 0.609992
\(101\) −6.41675 −0.638490 −0.319245 0.947672i \(-0.603429\pi\)
−0.319245 + 0.947672i \(0.603429\pi\)
\(102\) 0.957250 0.0947819
\(103\) 1.18530 0.116792 0.0583958 0.998294i \(-0.481401\pi\)
0.0583958 + 0.998294i \(0.481401\pi\)
\(104\) −1.79928 −0.176434
\(105\) −0.730544 −0.0712938
\(106\) −9.71480 −0.943585
\(107\) 12.1543 1.17500 0.587501 0.809223i \(-0.300112\pi\)
0.587501 + 0.809223i \(0.300112\pi\)
\(108\) −7.53707 −0.725255
\(109\) −3.19686 −0.306204 −0.153102 0.988210i \(-0.548926\pi\)
−0.153102 + 0.988210i \(0.548926\pi\)
\(110\) 20.6126 1.96533
\(111\) −2.90211 −0.275457
\(112\) 6.60184 0.623815
\(113\) 1.38759 0.130533 0.0652667 0.997868i \(-0.479210\pi\)
0.0652667 + 0.997868i \(0.479210\pi\)
\(114\) 3.93405 0.368457
\(115\) −15.9745 −1.48963
\(116\) −7.59351 −0.705040
\(117\) −0.861642 −0.0796588
\(118\) −2.96873 −0.273294
\(119\) −1.30810 −0.119913
\(120\) 4.44905 0.406140
\(121\) −0.611653 −0.0556048
\(122\) −36.5429 −3.30844
\(123\) −1.75561 −0.158298
\(124\) 22.1891 1.99264
\(125\) 9.13565 0.817118
\(126\) 7.38153 0.657599
\(127\) −3.11282 −0.276218 −0.138109 0.990417i \(-0.544102\pi\)
−0.138109 + 0.990417i \(0.544102\pi\)
\(128\) 13.4618 1.18986
\(129\) −2.16401 −0.190530
\(130\) 1.88946 0.165717
\(131\) −21.9862 −1.92094 −0.960471 0.278381i \(-0.910202\pi\)
−0.960471 + 0.278381i \(0.910202\pi\)
\(132\) 4.10599 0.357381
\(133\) −5.37595 −0.466154
\(134\) 22.4185 1.93666
\(135\) 4.32219 0.371995
\(136\) 7.96640 0.683113
\(137\) −6.38763 −0.545732 −0.272866 0.962052i \(-0.587972\pi\)
−0.272866 + 0.962052i \(0.587972\pi\)
\(138\) −4.62647 −0.393832
\(139\) −8.41355 −0.713628 −0.356814 0.934175i \(-0.616137\pi\)
−0.356814 + 0.934175i \(0.616137\pi\)
\(140\) −11.1332 −0.940926
\(141\) 3.14053 0.264480
\(142\) −27.9769 −2.34777
\(143\) 0.952252 0.0796313
\(144\) −19.2536 −1.60447
\(145\) 4.35456 0.361626
\(146\) 32.1907 2.66412
\(147\) 0.289125 0.0238466
\(148\) −44.2270 −3.63544
\(149\) 12.1403 0.994573 0.497287 0.867586i \(-0.334330\pi\)
0.497287 + 0.867586i \(0.334330\pi\)
\(150\) −1.01309 −0.0827187
\(151\) 2.18738 0.178006 0.0890031 0.996031i \(-0.471632\pi\)
0.0890031 + 0.996031i \(0.471632\pi\)
\(152\) 32.7398 2.65555
\(153\) 3.81496 0.308421
\(154\) −8.15777 −0.657372
\(155\) −12.7245 −1.02206
\(156\) 0.376377 0.0301343
\(157\) 3.01375 0.240524 0.120262 0.992742i \(-0.461627\pi\)
0.120262 + 0.992742i \(0.461627\pi\)
\(158\) 33.1850 2.64005
\(159\) 1.10974 0.0880081
\(160\) 11.4446 0.904776
\(161\) 6.32217 0.498256
\(162\) −20.8928 −1.64149
\(163\) 21.4132 1.67721 0.838607 0.544737i \(-0.183371\pi\)
0.838607 + 0.544737i \(0.183371\pi\)
\(164\) −26.7548 −2.08920
\(165\) −2.35461 −0.183306
\(166\) −3.96890 −0.308047
\(167\) −16.1730 −1.25150 −0.625752 0.780022i \(-0.715208\pi\)
−0.625752 + 0.780022i \(0.715208\pi\)
\(168\) −1.76079 −0.135848
\(169\) −12.9127 −0.993285
\(170\) −8.36566 −0.641617
\(171\) 15.6785 1.19896
\(172\) −32.9785 −2.51459
\(173\) 2.75549 0.209496 0.104748 0.994499i \(-0.466596\pi\)
0.104748 + 0.994499i \(0.466596\pi\)
\(174\) 1.26115 0.0956078
\(175\) 1.38441 0.104652
\(176\) 21.2784 1.60392
\(177\) 0.339124 0.0254901
\(178\) −2.49800 −0.187233
\(179\) 21.0117 1.57049 0.785244 0.619187i \(-0.212538\pi\)
0.785244 + 0.619187i \(0.212538\pi\)
\(180\) 32.4689 2.42009
\(181\) −0.0902325 −0.00670693 −0.00335347 0.999994i \(-0.501067\pi\)
−0.00335347 + 0.999994i \(0.501067\pi\)
\(182\) −0.747786 −0.0554296
\(183\) 4.17436 0.308578
\(184\) −38.5023 −2.83843
\(185\) 25.3623 1.86468
\(186\) −3.68523 −0.270214
\(187\) −4.21614 −0.308314
\(188\) 47.8604 3.49058
\(189\) −1.71058 −0.124427
\(190\) −34.3806 −2.49423
\(191\) −22.4058 −1.62123 −0.810613 0.585582i \(-0.800866\pi\)
−0.810613 + 0.585582i \(0.800866\pi\)
\(192\) −0.502960 −0.0362980
\(193\) 20.6089 1.48346 0.741731 0.670698i \(-0.234005\pi\)
0.741731 + 0.670698i \(0.234005\pi\)
\(194\) 2.99798 0.215242
\(195\) −0.215836 −0.0154564
\(196\) 4.40615 0.314725
\(197\) −8.09990 −0.577094 −0.288547 0.957466i \(-0.593172\pi\)
−0.288547 + 0.957466i \(0.593172\pi\)
\(198\) 23.7914 1.69078
\(199\) 13.8692 0.983164 0.491582 0.870831i \(-0.336419\pi\)
0.491582 + 0.870831i \(0.336419\pi\)
\(200\) −8.43112 −0.596170
\(201\) −2.56091 −0.180632
\(202\) 16.2410 1.14271
\(203\) −1.72339 −0.120958
\(204\) −1.66643 −0.116673
\(205\) 15.3428 1.07158
\(206\) −3.00005 −0.209023
\(207\) −18.4380 −1.28153
\(208\) 1.95049 0.135242
\(209\) −17.3272 −1.19855
\(210\) 1.84903 0.127595
\(211\) −5.08346 −0.349960 −0.174980 0.984572i \(-0.555986\pi\)
−0.174980 + 0.984572i \(0.555986\pi\)
\(212\) 16.9120 1.16152
\(213\) 3.19586 0.218976
\(214\) −30.7630 −2.10292
\(215\) 18.9118 1.28977
\(216\) 10.4175 0.708823
\(217\) 5.03594 0.341862
\(218\) 8.09137 0.548017
\(219\) −3.67721 −0.248483
\(220\) −35.8833 −2.41925
\(221\) −0.386474 −0.0259970
\(222\) 7.34536 0.492988
\(223\) 7.85607 0.526082 0.263041 0.964785i \(-0.415275\pi\)
0.263041 + 0.964785i \(0.415275\pi\)
\(224\) −4.52940 −0.302633
\(225\) −4.03750 −0.269167
\(226\) −3.51204 −0.233617
\(227\) 5.19582 0.344859 0.172429 0.985022i \(-0.444838\pi\)
0.172429 + 0.985022i \(0.444838\pi\)
\(228\) −6.84857 −0.453558
\(229\) 24.5104 1.61969 0.809847 0.586641i \(-0.199550\pi\)
0.809847 + 0.586641i \(0.199550\pi\)
\(230\) 40.4320 2.66600
\(231\) 0.931878 0.0613131
\(232\) 10.4955 0.689065
\(233\) 4.12455 0.270209 0.135104 0.990831i \(-0.456863\pi\)
0.135104 + 0.990831i \(0.456863\pi\)
\(234\) 2.18085 0.142566
\(235\) −27.4459 −1.79037
\(236\) 5.16811 0.336415
\(237\) −3.79078 −0.246238
\(238\) 3.31085 0.214611
\(239\) −6.63821 −0.429390 −0.214695 0.976681i \(-0.568876\pi\)
−0.214695 + 0.976681i \(0.568876\pi\)
\(240\) −4.82293 −0.311319
\(241\) 20.3477 1.31071 0.655354 0.755322i \(-0.272519\pi\)
0.655354 + 0.755322i \(0.272519\pi\)
\(242\) 1.54812 0.0995167
\(243\) 7.51837 0.482304
\(244\) 63.6156 4.07257
\(245\) −2.52674 −0.161427
\(246\) 4.44352 0.283309
\(247\) −1.58830 −0.101061
\(248\) −30.6691 −1.94749
\(249\) 0.453375 0.0287315
\(250\) −23.1227 −1.46241
\(251\) 29.0224 1.83188 0.915940 0.401314i \(-0.131447\pi\)
0.915940 + 0.401314i \(0.131447\pi\)
\(252\) −12.8501 −0.809481
\(253\) 20.3769 1.28109
\(254\) 7.87867 0.494352
\(255\) 0.955625 0.0598436
\(256\) −30.5931 −1.91207
\(257\) −18.8010 −1.17277 −0.586387 0.810031i \(-0.699450\pi\)
−0.586387 + 0.810031i \(0.699450\pi\)
\(258\) 5.47718 0.340994
\(259\) −10.0376 −0.623705
\(260\) −3.28926 −0.203991
\(261\) 5.02611 0.311108
\(262\) 55.6478 3.43793
\(263\) −8.14012 −0.501941 −0.250971 0.967995i \(-0.580750\pi\)
−0.250971 + 0.967995i \(0.580750\pi\)
\(264\) −5.67518 −0.349283
\(265\) −9.69831 −0.595762
\(266\) 13.6067 0.834282
\(267\) 0.285351 0.0174632
\(268\) −39.0271 −2.38396
\(269\) 6.07112 0.370163 0.185081 0.982723i \(-0.440745\pi\)
0.185081 + 0.982723i \(0.440745\pi\)
\(270\) −10.9396 −0.665765
\(271\) −4.17241 −0.253456 −0.126728 0.991938i \(-0.540448\pi\)
−0.126728 + 0.991938i \(0.540448\pi\)
\(272\) −8.63587 −0.523627
\(273\) 0.0854210 0.00516991
\(274\) 16.1673 0.976704
\(275\) 4.46209 0.269074
\(276\) 8.05398 0.484793
\(277\) 14.1861 0.852360 0.426180 0.904638i \(-0.359859\pi\)
0.426180 + 0.904638i \(0.359859\pi\)
\(278\) 21.2950 1.27719
\(279\) −14.6868 −0.879278
\(280\) 15.3880 0.919606
\(281\) −26.6996 −1.59276 −0.796382 0.604794i \(-0.793256\pi\)
−0.796382 + 0.604794i \(0.793256\pi\)
\(282\) −7.94880 −0.473344
\(283\) −8.97698 −0.533626 −0.266813 0.963748i \(-0.585971\pi\)
−0.266813 + 0.963748i \(0.585971\pi\)
\(284\) 48.7035 2.89002
\(285\) 3.92737 0.232637
\(286\) −2.41018 −0.142517
\(287\) −6.07216 −0.358428
\(288\) 13.2096 0.778382
\(289\) −15.2889 −0.899345
\(290\) −11.0215 −0.647207
\(291\) −0.342465 −0.0200756
\(292\) −56.0391 −3.27944
\(293\) 21.1130 1.23343 0.616717 0.787185i \(-0.288462\pi\)
0.616717 + 0.787185i \(0.288462\pi\)
\(294\) −0.731786 −0.0426786
\(295\) −2.96369 −0.172553
\(296\) 61.1293 3.55307
\(297\) −5.51337 −0.319918
\(298\) −30.7276 −1.78000
\(299\) 1.86786 0.108021
\(300\) 1.76364 0.101824
\(301\) −7.48467 −0.431409
\(302\) −5.53633 −0.318580
\(303\) −1.85524 −0.106581
\(304\) −35.4911 −2.03556
\(305\) −36.4808 −2.08889
\(306\) −9.65579 −0.551985
\(307\) 1.31237 0.0749010 0.0374505 0.999298i \(-0.488076\pi\)
0.0374505 + 0.999298i \(0.488076\pi\)
\(308\) 14.2014 0.809202
\(309\) 0.342701 0.0194956
\(310\) 32.2062 1.82919
\(311\) −5.01181 −0.284193 −0.142097 0.989853i \(-0.545384\pi\)
−0.142097 + 0.989853i \(0.545384\pi\)
\(312\) −0.520218 −0.0294515
\(313\) 11.7713 0.665351 0.332676 0.943041i \(-0.392049\pi\)
0.332676 + 0.943041i \(0.392049\pi\)
\(314\) −7.62792 −0.430469
\(315\) 7.36900 0.415196
\(316\) −57.7700 −3.24981
\(317\) 5.71465 0.320967 0.160483 0.987039i \(-0.448695\pi\)
0.160483 + 0.987039i \(0.448695\pi\)
\(318\) −2.80879 −0.157509
\(319\) −5.55465 −0.311001
\(320\) 4.39550 0.245716
\(321\) 3.51412 0.196139
\(322\) −16.0016 −0.891736
\(323\) 7.03228 0.391287
\(324\) 36.3712 2.02062
\(325\) 0.409019 0.0226883
\(326\) −54.1977 −3.00173
\(327\) −0.924292 −0.0511135
\(328\) 36.9797 2.04186
\(329\) 10.8622 0.598852
\(330\) 5.95961 0.328066
\(331\) −13.3725 −0.735017 −0.367508 0.930020i \(-0.619789\pi\)
−0.367508 + 0.930020i \(0.619789\pi\)
\(332\) 6.90925 0.379194
\(333\) 29.2736 1.60419
\(334\) 40.9345 2.23983
\(335\) 22.3804 1.22277
\(336\) 1.90876 0.104131
\(337\) −4.98328 −0.271456 −0.135728 0.990746i \(-0.543337\pi\)
−0.135728 + 0.990746i \(0.543337\pi\)
\(338\) 32.6825 1.77770
\(339\) 0.401187 0.0217895
\(340\) 14.5633 0.789808
\(341\) 16.2313 0.878975
\(342\) −39.6827 −2.14580
\(343\) 1.00000 0.0539949
\(344\) 45.5820 2.45762
\(345\) −4.61862 −0.248658
\(346\) −6.97424 −0.374938
\(347\) −36.0836 −1.93707 −0.968535 0.248878i \(-0.919938\pi\)
−0.968535 + 0.248878i \(0.919938\pi\)
\(348\) −2.19547 −0.117690
\(349\) −18.3720 −0.983431 −0.491715 0.870756i \(-0.663630\pi\)
−0.491715 + 0.870756i \(0.663630\pi\)
\(350\) −3.50399 −0.187296
\(351\) −0.505385 −0.0269755
\(352\) −14.5987 −0.778113
\(353\) −26.5619 −1.41375 −0.706873 0.707341i \(-0.749895\pi\)
−0.706873 + 0.707341i \(0.749895\pi\)
\(354\) −0.858336 −0.0456200
\(355\) −27.9294 −1.48234
\(356\) 4.34863 0.230477
\(357\) −0.378205 −0.0200167
\(358\) −53.1814 −2.81072
\(359\) −9.00294 −0.475157 −0.237579 0.971368i \(-0.576354\pi\)
−0.237579 + 0.971368i \(0.576354\pi\)
\(360\) −44.8775 −2.36525
\(361\) 9.90082 0.521096
\(362\) 0.228382 0.0120035
\(363\) −0.176844 −0.00928192
\(364\) 1.30178 0.0682318
\(365\) 32.1361 1.68208
\(366\) −10.5655 −0.552266
\(367\) 13.8384 0.722357 0.361179 0.932497i \(-0.382374\pi\)
0.361179 + 0.932497i \(0.382374\pi\)
\(368\) 41.7379 2.17574
\(369\) 17.7089 0.921888
\(370\) −64.1930 −3.33723
\(371\) 3.83827 0.199273
\(372\) 6.41542 0.332624
\(373\) 34.3713 1.77968 0.889840 0.456272i \(-0.150816\pi\)
0.889840 + 0.456272i \(0.150816\pi\)
\(374\) 10.6712 0.551794
\(375\) 2.64135 0.136399
\(376\) −66.1512 −3.41149
\(377\) −0.509169 −0.0262236
\(378\) 4.32955 0.222688
\(379\) −8.74453 −0.449176 −0.224588 0.974454i \(-0.572104\pi\)
−0.224588 + 0.974454i \(0.572104\pi\)
\(380\) 59.8514 3.07031
\(381\) −0.899996 −0.0461082
\(382\) 56.7099 2.90153
\(383\) 15.1599 0.774635 0.387317 0.921946i \(-0.373402\pi\)
0.387317 + 0.921946i \(0.373402\pi\)
\(384\) 3.89214 0.198620
\(385\) −8.14392 −0.415053
\(386\) −52.1619 −2.65497
\(387\) 21.8283 1.10960
\(388\) −5.21902 −0.264956
\(389\) 14.8276 0.751788 0.375894 0.926663i \(-0.377336\pi\)
0.375894 + 0.926663i \(0.377336\pi\)
\(390\) 0.546290 0.0276625
\(391\) −8.27003 −0.418234
\(392\) −6.09005 −0.307594
\(393\) −6.35676 −0.320656
\(394\) 20.5011 1.03283
\(395\) 33.1286 1.66688
\(396\) −41.4172 −2.08129
\(397\) 16.8209 0.844215 0.422108 0.906546i \(-0.361290\pi\)
0.422108 + 0.906546i \(0.361290\pi\)
\(398\) −35.1036 −1.75958
\(399\) −1.55432 −0.0778134
\(400\) 9.13965 0.456983
\(401\) −18.1018 −0.903958 −0.451979 0.892029i \(-0.649282\pi\)
−0.451979 + 0.892029i \(0.649282\pi\)
\(402\) 6.48174 0.323280
\(403\) 1.48785 0.0741151
\(404\) −28.2731 −1.40664
\(405\) −20.8573 −1.03641
\(406\) 4.36196 0.216481
\(407\) −32.3521 −1.60363
\(408\) 2.30329 0.114030
\(409\) −1.37063 −0.0677731 −0.0338865 0.999426i \(-0.510788\pi\)
−0.0338865 + 0.999426i \(0.510788\pi\)
\(410\) −38.8331 −1.91783
\(411\) −1.84682 −0.0910971
\(412\) 5.22263 0.257300
\(413\) 1.17293 0.0577162
\(414\) 46.6673 2.29357
\(415\) −3.96216 −0.194495
\(416\) −1.33820 −0.0656104
\(417\) −2.43257 −0.119123
\(418\) 43.8558 2.14506
\(419\) 20.8605 1.01910 0.509552 0.860440i \(-0.329811\pi\)
0.509552 + 0.860440i \(0.329811\pi\)
\(420\) −3.21888 −0.157065
\(421\) −11.7759 −0.573921 −0.286960 0.957942i \(-0.592645\pi\)
−0.286960 + 0.957942i \(0.592645\pi\)
\(422\) 12.8664 0.626328
\(423\) −31.6786 −1.54026
\(424\) −23.3752 −1.13520
\(425\) −1.81095 −0.0878439
\(426\) −8.08883 −0.391905
\(427\) 14.4379 0.698700
\(428\) 53.5537 2.58862
\(429\) 0.275320 0.0132926
\(430\) −47.8665 −2.30833
\(431\) −7.08570 −0.341306 −0.170653 0.985331i \(-0.554588\pi\)
−0.170653 + 0.985331i \(0.554588\pi\)
\(432\) −11.2930 −0.543334
\(433\) 6.21534 0.298690 0.149345 0.988785i \(-0.452283\pi\)
0.149345 + 0.988785i \(0.452283\pi\)
\(434\) −12.7461 −0.611835
\(435\) 1.25901 0.0603650
\(436\) −14.0858 −0.674589
\(437\) −33.9876 −1.62585
\(438\) 9.30715 0.444713
\(439\) 10.9523 0.522723 0.261362 0.965241i \(-0.415828\pi\)
0.261362 + 0.965241i \(0.415828\pi\)
\(440\) 49.5969 2.36444
\(441\) −2.91641 −0.138877
\(442\) 0.978179 0.0465272
\(443\) −5.51650 −0.262097 −0.131048 0.991376i \(-0.541834\pi\)
−0.131048 + 0.991376i \(0.541834\pi\)
\(444\) −12.7871 −0.606851
\(445\) −2.49375 −0.118215
\(446\) −19.8840 −0.941535
\(447\) 3.51007 0.166021
\(448\) −1.73959 −0.0821881
\(449\) 22.4565 1.05979 0.529895 0.848063i \(-0.322231\pi\)
0.529895 + 0.848063i \(0.322231\pi\)
\(450\) 10.2191 0.481732
\(451\) −19.5711 −0.921569
\(452\) 6.11392 0.287575
\(453\) 0.632426 0.0297140
\(454\) −13.1508 −0.617199
\(455\) −0.746516 −0.0349972
\(456\) 9.46589 0.443281
\(457\) 39.0414 1.82628 0.913139 0.407648i \(-0.133651\pi\)
0.913139 + 0.407648i \(0.133651\pi\)
\(458\) −62.0368 −2.89879
\(459\) 2.23761 0.104443
\(460\) −70.3858 −3.28176
\(461\) 17.0595 0.794542 0.397271 0.917701i \(-0.369957\pi\)
0.397271 + 0.917701i \(0.369957\pi\)
\(462\) −2.35862 −0.109733
\(463\) 30.2558 1.40611 0.703054 0.711136i \(-0.251819\pi\)
0.703054 + 0.711136i \(0.251819\pi\)
\(464\) −11.3775 −0.528189
\(465\) −3.67897 −0.170608
\(466\) −10.4394 −0.483596
\(467\) 6.28049 0.290627 0.145313 0.989386i \(-0.453581\pi\)
0.145313 + 0.989386i \(0.453581\pi\)
\(468\) −3.79652 −0.175494
\(469\) −8.85743 −0.408998
\(470\) 69.4666 3.20426
\(471\) 0.871352 0.0401498
\(472\) −7.14321 −0.328793
\(473\) −24.1238 −1.10921
\(474\) 9.59461 0.440695
\(475\) −7.44252 −0.341486
\(476\) −5.76369 −0.264178
\(477\) −11.1940 −0.512536
\(478\) 16.8016 0.768485
\(479\) 5.01403 0.229097 0.114548 0.993418i \(-0.463458\pi\)
0.114548 + 0.993418i \(0.463458\pi\)
\(480\) 3.30893 0.151031
\(481\) −2.96556 −0.135218
\(482\) −51.5007 −2.34579
\(483\) 1.82790 0.0831722
\(484\) −2.69503 −0.122502
\(485\) 2.99289 0.135900
\(486\) −19.0293 −0.863185
\(487\) −8.45019 −0.382915 −0.191457 0.981501i \(-0.561321\pi\)
−0.191457 + 0.981501i \(0.561321\pi\)
\(488\) −87.9276 −3.98029
\(489\) 6.19110 0.279971
\(490\) 6.39527 0.288909
\(491\) −14.0934 −0.636026 −0.318013 0.948086i \(-0.603016\pi\)
−0.318013 + 0.948086i \(0.603016\pi\)
\(492\) −7.73549 −0.348743
\(493\) 2.25437 0.101532
\(494\) 4.02006 0.180871
\(495\) 23.7510 1.06753
\(496\) 33.2465 1.49281
\(497\) 11.0535 0.495819
\(498\) −1.14751 −0.0514211
\(499\) −6.62850 −0.296732 −0.148366 0.988932i \(-0.547401\pi\)
−0.148366 + 0.988932i \(0.547401\pi\)
\(500\) 40.2530 1.80017
\(501\) −4.67602 −0.208909
\(502\) −73.4569 −3.27854
\(503\) 38.1438 1.70075 0.850374 0.526179i \(-0.176376\pi\)
0.850374 + 0.526179i \(0.176376\pi\)
\(504\) 17.7611 0.791140
\(505\) 16.2135 0.721489
\(506\) −51.5748 −2.29278
\(507\) −3.73339 −0.165806
\(508\) −13.7156 −0.608530
\(509\) 25.0132 1.10869 0.554346 0.832287i \(-0.312969\pi\)
0.554346 + 0.832287i \(0.312969\pi\)
\(510\) −2.41872 −0.107103
\(511\) −12.7184 −0.562629
\(512\) 50.5086 2.23219
\(513\) 9.19600 0.406013
\(514\) 47.5860 2.09893
\(515\) −2.99496 −0.131974
\(516\) −9.53493 −0.419752
\(517\) 35.0099 1.53973
\(518\) 25.4055 1.11625
\(519\) 0.796681 0.0349704
\(520\) 4.54632 0.199369
\(521\) −20.8270 −0.912448 −0.456224 0.889865i \(-0.650799\pi\)
−0.456224 + 0.889865i \(0.650799\pi\)
\(522\) −12.7213 −0.556795
\(523\) −29.2822 −1.28042 −0.640211 0.768199i \(-0.721153\pi\)
−0.640211 + 0.768199i \(0.721153\pi\)
\(524\) −96.8744 −4.23198
\(525\) 0.400268 0.0174691
\(526\) 20.6029 0.898331
\(527\) −6.58752 −0.286957
\(528\) 6.15211 0.267736
\(529\) 16.9698 0.737817
\(530\) 24.5468 1.06624
\(531\) −3.42075 −0.148448
\(532\) −23.6872 −1.02697
\(533\) −1.79400 −0.0777066
\(534\) −0.722233 −0.0312541
\(535\) −30.7108 −1.32774
\(536\) 53.9422 2.32995
\(537\) 6.07501 0.262156
\(538\) −15.3662 −0.662485
\(539\) 3.22310 0.138829
\(540\) 19.0442 0.819533
\(541\) 23.3158 1.00242 0.501212 0.865324i \(-0.332888\pi\)
0.501212 + 0.865324i \(0.332888\pi\)
\(542\) 10.5605 0.453613
\(543\) −0.0260885 −0.00111956
\(544\) 5.92492 0.254029
\(545\) 8.07763 0.346008
\(546\) −0.216204 −0.00925266
\(547\) −24.3738 −1.04215 −0.521073 0.853512i \(-0.674468\pi\)
−0.521073 + 0.853512i \(0.674468\pi\)
\(548\) −28.1448 −1.20229
\(549\) −42.1068 −1.79708
\(550\) −11.2937 −0.481565
\(551\) 9.26486 0.394696
\(552\) −11.1320 −0.473808
\(553\) −13.1112 −0.557546
\(554\) −35.9055 −1.52548
\(555\) 7.33289 0.311264
\(556\) −37.0713 −1.57218
\(557\) 28.2930 1.19881 0.599407 0.800445i \(-0.295403\pi\)
0.599407 + 0.800445i \(0.295403\pi\)
\(558\) 37.1729 1.57366
\(559\) −2.21132 −0.0935288
\(560\) −16.6811 −0.704906
\(561\) −1.21899 −0.0514658
\(562\) 67.5777 2.85059
\(563\) 45.8567 1.93263 0.966315 0.257364i \(-0.0828538\pi\)
0.966315 + 0.257364i \(0.0828538\pi\)
\(564\) 13.8376 0.582670
\(565\) −3.50607 −0.147502
\(566\) 22.7211 0.955038
\(567\) 8.25465 0.346663
\(568\) −67.3166 −2.82454
\(569\) 40.2347 1.68673 0.843363 0.537344i \(-0.180572\pi\)
0.843363 + 0.537344i \(0.180572\pi\)
\(570\) −9.94031 −0.416354
\(571\) 31.9257 1.33605 0.668025 0.744139i \(-0.267140\pi\)
0.668025 + 0.744139i \(0.267140\pi\)
\(572\) 4.19576 0.175434
\(573\) −6.47808 −0.270626
\(574\) 15.3689 0.641484
\(575\) 8.75247 0.365003
\(576\) 5.07337 0.211390
\(577\) 5.13806 0.213900 0.106950 0.994264i \(-0.465891\pi\)
0.106950 + 0.994264i \(0.465891\pi\)
\(578\) 38.6967 1.60957
\(579\) 5.95855 0.247629
\(580\) 19.1868 0.796689
\(581\) 1.56809 0.0650555
\(582\) 0.866790 0.0359296
\(583\) 12.3711 0.512359
\(584\) 77.4556 3.20514
\(585\) 2.17714 0.0900138
\(586\) −53.4377 −2.20749
\(587\) −17.6558 −0.728734 −0.364367 0.931255i \(-0.618715\pi\)
−0.364367 + 0.931255i \(0.618715\pi\)
\(588\) 1.27393 0.0525359
\(589\) −27.0730 −1.11552
\(590\) 7.50122 0.308820
\(591\) −2.34188 −0.0963323
\(592\) −66.2664 −2.72353
\(593\) 22.5350 0.925402 0.462701 0.886514i \(-0.346880\pi\)
0.462701 + 0.886514i \(0.346880\pi\)
\(594\) 13.9545 0.572562
\(595\) 3.30523 0.135501
\(596\) 53.4920 2.19112
\(597\) 4.00994 0.164116
\(598\) −4.72762 −0.193327
\(599\) 21.5029 0.878585 0.439293 0.898344i \(-0.355229\pi\)
0.439293 + 0.898344i \(0.355229\pi\)
\(600\) −2.43765 −0.0995166
\(601\) 6.88847 0.280986 0.140493 0.990082i \(-0.455131\pi\)
0.140493 + 0.990082i \(0.455131\pi\)
\(602\) 18.9440 0.772099
\(603\) 25.8319 1.05195
\(604\) 9.63791 0.392161
\(605\) 1.54549 0.0628330
\(606\) 4.69569 0.190749
\(607\) −7.80968 −0.316985 −0.158493 0.987360i \(-0.550663\pi\)
−0.158493 + 0.987360i \(0.550663\pi\)
\(608\) 24.3498 0.987516
\(609\) −0.498275 −0.0201911
\(610\) 92.3343 3.73851
\(611\) 3.20919 0.129830
\(612\) 16.8093 0.679474
\(613\) −10.1103 −0.408353 −0.204176 0.978934i \(-0.565452\pi\)
−0.204176 + 0.978934i \(0.565452\pi\)
\(614\) −3.32166 −0.134051
\(615\) 4.43598 0.178876
\(616\) −19.6288 −0.790867
\(617\) −30.6342 −1.23329 −0.616643 0.787243i \(-0.711508\pi\)
−0.616643 + 0.787243i \(0.711508\pi\)
\(618\) −0.867390 −0.0348915
\(619\) 25.4695 1.02370 0.511852 0.859074i \(-0.328960\pi\)
0.511852 + 0.859074i \(0.328960\pi\)
\(620\) −56.0660 −2.25167
\(621\) −10.8146 −0.433974
\(622\) 12.6851 0.508625
\(623\) 0.986945 0.0395411
\(624\) 0.563935 0.0225755
\(625\) −30.0055 −1.20022
\(626\) −29.7935 −1.19079
\(627\) −5.00973 −0.200069
\(628\) 13.2790 0.529892
\(629\) 13.1302 0.523534
\(630\) −18.6512 −0.743082
\(631\) −3.20776 −0.127699 −0.0638495 0.997960i \(-0.520338\pi\)
−0.0638495 + 0.997960i \(0.520338\pi\)
\(632\) 79.8479 3.17618
\(633\) −1.46976 −0.0584176
\(634\) −14.4640 −0.574439
\(635\) 7.86529 0.312125
\(636\) 4.88968 0.193888
\(637\) 0.295446 0.0117060
\(638\) 14.0590 0.556602
\(639\) −32.2366 −1.27526
\(640\) −34.0144 −1.34454
\(641\) 37.3692 1.47599 0.737997 0.674804i \(-0.235772\pi\)
0.737997 + 0.674804i \(0.235772\pi\)
\(642\) −8.89436 −0.351033
\(643\) 34.5691 1.36327 0.681636 0.731692i \(-0.261269\pi\)
0.681636 + 0.731692i \(0.261269\pi\)
\(644\) 27.8564 1.09770
\(645\) 5.46788 0.215297
\(646\) −17.7990 −0.700291
\(647\) 39.5573 1.55516 0.777579 0.628785i \(-0.216447\pi\)
0.777579 + 0.628785i \(0.216447\pi\)
\(648\) −50.2712 −1.97484
\(649\) 3.78047 0.148397
\(650\) −1.03524 −0.0406055
\(651\) 1.45602 0.0570658
\(652\) 94.3499 3.69503
\(653\) 47.7365 1.86807 0.934036 0.357178i \(-0.116261\pi\)
0.934036 + 0.357178i \(0.116261\pi\)
\(654\) 2.33942 0.0914785
\(655\) 55.5533 2.17065
\(656\) −40.0874 −1.56515
\(657\) 37.0920 1.44710
\(658\) −27.4926 −1.07177
\(659\) −49.4866 −1.92772 −0.963862 0.266402i \(-0.914165\pi\)
−0.963862 + 0.266402i \(0.914165\pi\)
\(660\) −10.3748 −0.403837
\(661\) 44.6284 1.73584 0.867922 0.496700i \(-0.165455\pi\)
0.867922 + 0.496700i \(0.165455\pi\)
\(662\) 33.8462 1.31547
\(663\) −0.111739 −0.00433959
\(664\) −9.54976 −0.370603
\(665\) 13.5836 0.526750
\(666\) −74.0927 −2.87103
\(667\) −10.8956 −0.421878
\(668\) −71.2606 −2.75716
\(669\) 2.27139 0.0878169
\(670\) −56.6456 −2.18841
\(671\) 46.5348 1.79646
\(672\) −1.30956 −0.0505175
\(673\) 35.5597 1.37072 0.685362 0.728202i \(-0.259644\pi\)
0.685362 + 0.728202i \(0.259644\pi\)
\(674\) 12.6129 0.485829
\(675\) −2.36815 −0.0911500
\(676\) −56.8953 −2.18828
\(677\) 47.1000 1.81020 0.905101 0.425197i \(-0.139795\pi\)
0.905101 + 0.425197i \(0.139795\pi\)
\(678\) −1.01542 −0.0389969
\(679\) −1.18449 −0.0454564
\(680\) −20.1290 −0.771912
\(681\) 1.50224 0.0575661
\(682\) −41.0821 −1.57311
\(683\) 31.7202 1.21374 0.606870 0.794801i \(-0.292425\pi\)
0.606870 + 0.794801i \(0.292425\pi\)
\(684\) 69.0816 2.64140
\(685\) 16.1399 0.616673
\(686\) −2.53104 −0.0966354
\(687\) 7.08658 0.270370
\(688\) −49.4126 −1.88384
\(689\) 1.13400 0.0432021
\(690\) 11.6899 0.445027
\(691\) −11.8878 −0.452233 −0.226116 0.974100i \(-0.572603\pi\)
−0.226116 + 0.974100i \(0.572603\pi\)
\(692\) 12.1411 0.461535
\(693\) −9.39986 −0.357071
\(694\) 91.3290 3.46680
\(695\) 21.2589 0.806394
\(696\) 3.03452 0.115023
\(697\) 7.94300 0.300862
\(698\) 46.5002 1.76006
\(699\) 1.19251 0.0451050
\(700\) 6.09992 0.230555
\(701\) 33.1635 1.25257 0.626285 0.779594i \(-0.284575\pi\)
0.626285 + 0.779594i \(0.284575\pi\)
\(702\) 1.27915 0.0482783
\(703\) 53.9615 2.03520
\(704\) −5.60688 −0.211317
\(705\) −7.93530 −0.298861
\(706\) 67.2290 2.53020
\(707\) −6.41675 −0.241327
\(708\) 1.49423 0.0561566
\(709\) −8.84896 −0.332330 −0.166165 0.986098i \(-0.553138\pi\)
−0.166165 + 0.986098i \(0.553138\pi\)
\(710\) 70.6904 2.65296
\(711\) 38.2376 1.43402
\(712\) −6.01054 −0.225255
\(713\) 31.8380 1.19234
\(714\) 0.957250 0.0358242
\(715\) −2.40609 −0.0899827
\(716\) 92.5806 3.45990
\(717\) −1.91927 −0.0716766
\(718\) 22.7868 0.850395
\(719\) −48.6385 −1.81391 −0.906956 0.421226i \(-0.861600\pi\)
−0.906956 + 0.421226i \(0.861600\pi\)
\(720\) 48.6489 1.81304
\(721\) 1.18530 0.0441431
\(722\) −25.0593 −0.932612
\(723\) 5.88302 0.218792
\(724\) −0.397578 −0.0147759
\(725\) −2.38588 −0.0886093
\(726\) 0.447599 0.0166120
\(727\) 38.1262 1.41402 0.707012 0.707202i \(-0.250043\pi\)
0.707012 + 0.707202i \(0.250043\pi\)
\(728\) −1.79928 −0.0666858
\(729\) −22.5902 −0.836674
\(730\) −81.3376 −3.01044
\(731\) 9.79070 0.362122
\(732\) 18.3929 0.679820
\(733\) 10.4874 0.387360 0.193680 0.981065i \(-0.437958\pi\)
0.193680 + 0.981065i \(0.437958\pi\)
\(734\) −35.0254 −1.29281
\(735\) −0.730544 −0.0269465
\(736\) −28.6356 −1.05552
\(737\) −28.5483 −1.05159
\(738\) −44.8218 −1.64991
\(739\) −51.2896 −1.88672 −0.943359 0.331773i \(-0.892353\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(740\) 111.750 4.10802
\(741\) −0.459219 −0.0168698
\(742\) −9.71480 −0.356642
\(743\) −6.44101 −0.236298 −0.118149 0.992996i \(-0.537696\pi\)
−0.118149 + 0.992996i \(0.537696\pi\)
\(744\) −8.86721 −0.325088
\(745\) −30.6754 −1.12386
\(746\) −86.9951 −3.18512
\(747\) −4.57320 −0.167325
\(748\) −18.5769 −0.679239
\(749\) 12.1543 0.444109
\(750\) −6.68534 −0.244114
\(751\) 23.0230 0.840120 0.420060 0.907496i \(-0.362009\pi\)
0.420060 + 0.907496i \(0.362009\pi\)
\(752\) 71.7104 2.61501
\(753\) 8.39112 0.305789
\(754\) 1.28873 0.0469327
\(755\) −5.52693 −0.201146
\(756\) −7.53707 −0.274121
\(757\) −22.1852 −0.806333 −0.403167 0.915127i \(-0.632090\pi\)
−0.403167 + 0.915127i \(0.632090\pi\)
\(758\) 22.1327 0.803897
\(759\) 5.89149 0.213847
\(760\) −82.7249 −3.00075
\(761\) −36.3675 −1.31832 −0.659161 0.752002i \(-0.729088\pi\)
−0.659161 + 0.752002i \(0.729088\pi\)
\(762\) 2.27792 0.0825204
\(763\) −3.19686 −0.115734
\(764\) −98.7232 −3.57168
\(765\) −9.63940 −0.348513
\(766\) −38.3703 −1.38637
\(767\) 0.346539 0.0125128
\(768\) −8.84523 −0.319175
\(769\) 7.87740 0.284066 0.142033 0.989862i \(-0.454636\pi\)
0.142033 + 0.989862i \(0.454636\pi\)
\(770\) 20.6126 0.742825
\(771\) −5.43584 −0.195767
\(772\) 90.8059 3.26817
\(773\) 43.2792 1.55665 0.778323 0.627864i \(-0.216071\pi\)
0.778323 + 0.627864i \(0.216071\pi\)
\(774\) −55.2483 −1.98586
\(775\) 6.97181 0.250435
\(776\) 7.21357 0.258952
\(777\) −2.90211 −0.104113
\(778\) −37.5291 −1.34548
\(779\) 32.6436 1.16958
\(780\) −0.951007 −0.0340515
\(781\) 35.6266 1.27482
\(782\) 20.9318 0.748518
\(783\) 2.94800 0.105353
\(784\) 6.60184 0.235780
\(785\) −7.61497 −0.271790
\(786\) 16.0892 0.573882
\(787\) 9.95463 0.354844 0.177422 0.984135i \(-0.443224\pi\)
0.177422 + 0.984135i \(0.443224\pi\)
\(788\) −35.6894 −1.27138
\(789\) −2.35351 −0.0837873
\(790\) −83.8498 −2.98324
\(791\) 1.38759 0.0493370
\(792\) 57.2456 2.03413
\(793\) 4.26563 0.151477
\(794\) −42.5742 −1.51090
\(795\) −2.80402 −0.0994485
\(796\) 61.1099 2.16598
\(797\) 10.5031 0.372037 0.186019 0.982546i \(-0.440442\pi\)
0.186019 + 0.982546i \(0.440442\pi\)
\(798\) 3.93405 0.139264
\(799\) −14.2088 −0.502673
\(800\) −6.27055 −0.221697
\(801\) −2.87833 −0.101701
\(802\) 45.8162 1.61783
\(803\) −40.9926 −1.44660
\(804\) −11.2837 −0.397946
\(805\) −15.9745 −0.563026
\(806\) −3.76580 −0.132645
\(807\) 1.75531 0.0617900
\(808\) 39.0783 1.37477
\(809\) −4.58616 −0.161241 −0.0806204 0.996745i \(-0.525690\pi\)
−0.0806204 + 0.996745i \(0.525690\pi\)
\(810\) 52.7907 1.85488
\(811\) 31.9442 1.12171 0.560856 0.827913i \(-0.310472\pi\)
0.560856 + 0.827913i \(0.310472\pi\)
\(812\) −7.59351 −0.266480
\(813\) −1.20635 −0.0423085
\(814\) 81.8843 2.87004
\(815\) −54.1057 −1.89524
\(816\) −2.49685 −0.0874071
\(817\) 40.2372 1.40772
\(818\) 3.46910 0.121294
\(819\) −0.861642 −0.0301082
\(820\) 67.6025 2.36078
\(821\) −10.6343 −0.371139 −0.185570 0.982631i \(-0.559413\pi\)
−0.185570 + 0.982631i \(0.559413\pi\)
\(822\) 4.67438 0.163038
\(823\) 19.2072 0.669520 0.334760 0.942303i \(-0.391345\pi\)
0.334760 + 0.942303i \(0.391345\pi\)
\(824\) −7.21856 −0.251470
\(825\) 1.29010 0.0449156
\(826\) −2.96873 −0.103295
\(827\) 55.5387 1.93127 0.965635 0.259902i \(-0.0836902\pi\)
0.965635 + 0.259902i \(0.0836902\pi\)
\(828\) −81.2406 −2.82331
\(829\) 28.2653 0.981693 0.490846 0.871246i \(-0.336688\pi\)
0.490846 + 0.871246i \(0.336688\pi\)
\(830\) 10.0284 0.348090
\(831\) 4.10156 0.142281
\(832\) −0.513957 −0.0178182
\(833\) −1.30810 −0.0453230
\(834\) 6.15692 0.213197
\(835\) 40.8650 1.41419
\(836\) −76.3462 −2.64049
\(837\) −8.61439 −0.297757
\(838\) −52.7988 −1.82390
\(839\) 11.8970 0.410730 0.205365 0.978685i \(-0.434162\pi\)
0.205365 + 0.978685i \(0.434162\pi\)
\(840\) 4.44905 0.153507
\(841\) −26.0299 −0.897584
\(842\) 29.8052 1.02715
\(843\) −7.71952 −0.265875
\(844\) −22.3985 −0.770987
\(845\) 32.6271 1.12240
\(846\) 80.1796 2.75663
\(847\) −0.611653 −0.0210166
\(848\) 25.3396 0.870167
\(849\) −2.59547 −0.0890763
\(850\) 4.58358 0.157215
\(851\) −63.4592 −2.17535
\(852\) 14.0814 0.482421
\(853\) −18.6623 −0.638986 −0.319493 0.947589i \(-0.603513\pi\)
−0.319493 + 0.947589i \(0.603513\pi\)
\(854\) −36.5429 −1.25047
\(855\) −39.6154 −1.35482
\(856\) −74.0204 −2.52996
\(857\) 1.59377 0.0544420 0.0272210 0.999629i \(-0.491334\pi\)
0.0272210 + 0.999629i \(0.491334\pi\)
\(858\) −0.696845 −0.0237899
\(859\) −1.00000 −0.0341196
\(860\) 83.3282 2.84147
\(861\) −1.75561 −0.0598311
\(862\) 17.9342 0.610840
\(863\) 12.1094 0.412210 0.206105 0.978530i \(-0.433921\pi\)
0.206105 + 0.978530i \(0.433921\pi\)
\(864\) 7.74791 0.263589
\(865\) −6.96240 −0.236729
\(866\) −15.7313 −0.534570
\(867\) −4.42040 −0.150125
\(868\) 22.1891 0.753147
\(869\) −42.2587 −1.43353
\(870\) −3.18661 −0.108036
\(871\) −2.61690 −0.0886701
\(872\) 19.4690 0.659304
\(873\) 3.45444 0.116915
\(874\) 86.0240 2.90980
\(875\) 9.13565 0.308841
\(876\) −16.2023 −0.547426
\(877\) −14.7202 −0.497065 −0.248532 0.968624i \(-0.579948\pi\)
−0.248532 + 0.968624i \(0.579948\pi\)
\(878\) −27.7206 −0.935525
\(879\) 6.10429 0.205893
\(880\) −53.7649 −1.81241
\(881\) −11.7035 −0.394301 −0.197151 0.980373i \(-0.563169\pi\)
−0.197151 + 0.980373i \(0.563169\pi\)
\(882\) 7.38153 0.248549
\(883\) −8.03627 −0.270442 −0.135221 0.990815i \(-0.543174\pi\)
−0.135221 + 0.990815i \(0.543174\pi\)
\(884\) −1.70286 −0.0572734
\(885\) −0.856878 −0.0288036
\(886\) 13.9625 0.469078
\(887\) 42.5424 1.42843 0.714217 0.699925i \(-0.246783\pi\)
0.714217 + 0.699925i \(0.246783\pi\)
\(888\) 17.6740 0.593101
\(889\) −3.11282 −0.104401
\(890\) 6.31178 0.211571
\(891\) 26.6055 0.891319
\(892\) 34.6150 1.15900
\(893\) −58.3946 −1.95410
\(894\) −8.88411 −0.297129
\(895\) −53.0911 −1.77464
\(896\) 13.4618 0.449727
\(897\) 0.540045 0.0180316
\(898\) −56.8383 −1.89672
\(899\) −8.67889 −0.289457
\(900\) −17.7898 −0.592995
\(901\) −5.02085 −0.167269
\(902\) 49.5353 1.64934
\(903\) −2.16401 −0.0720136
\(904\) −8.45048 −0.281059
\(905\) 0.227994 0.00757878
\(906\) −1.60069 −0.0531795
\(907\) 5.90337 0.196018 0.0980091 0.995186i \(-0.468753\pi\)
0.0980091 + 0.995186i \(0.468753\pi\)
\(908\) 22.8936 0.759750
\(909\) 18.7139 0.620699
\(910\) 1.88946 0.0626350
\(911\) −10.0983 −0.334571 −0.167285 0.985908i \(-0.553500\pi\)
−0.167285 + 0.985908i \(0.553500\pi\)
\(912\) −10.2614 −0.339788
\(913\) 5.05412 0.167267
\(914\) −98.8151 −3.26851
\(915\) −10.5475 −0.348690
\(916\) 107.997 3.56831
\(917\) −21.9862 −0.726048
\(918\) −5.66348 −0.186923
\(919\) −51.8165 −1.70927 −0.854634 0.519231i \(-0.826218\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(920\) 97.2852 3.20740
\(921\) 0.379440 0.0125030
\(922\) −43.1783 −1.42200
\(923\) 3.26573 0.107493
\(924\) 4.10599 0.135077
\(925\) −13.8961 −0.456902
\(926\) −76.5786 −2.51653
\(927\) −3.45683 −0.113537
\(928\) 7.80593 0.256242
\(929\) −45.3911 −1.48923 −0.744616 0.667493i \(-0.767367\pi\)
−0.744616 + 0.667493i \(0.767367\pi\)
\(930\) 9.31162 0.305340
\(931\) −5.37595 −0.176190
\(932\) 18.1734 0.595289
\(933\) −1.44904 −0.0474394
\(934\) −15.8962 −0.520138
\(935\) 10.6531 0.348393
\(936\) 5.24744 0.171518
\(937\) 43.2934 1.41433 0.707167 0.707047i \(-0.249973\pi\)
0.707167 + 0.707047i \(0.249973\pi\)
\(938\) 22.4185 0.731989
\(939\) 3.40337 0.111065
\(940\) −120.931 −3.94433
\(941\) 33.2694 1.08455 0.542276 0.840200i \(-0.317563\pi\)
0.542276 + 0.840200i \(0.317563\pi\)
\(942\) −2.20542 −0.0718566
\(943\) −38.3892 −1.25012
\(944\) 7.74351 0.252030
\(945\) 4.32219 0.140601
\(946\) 61.0582 1.98517
\(947\) 58.9688 1.91623 0.958114 0.286388i \(-0.0924547\pi\)
0.958114 + 0.286388i \(0.0924547\pi\)
\(948\) −16.7027 −0.542480
\(949\) −3.75760 −0.121977
\(950\) 18.8373 0.611162
\(951\) 1.65225 0.0535778
\(952\) 7.96640 0.258192
\(953\) −18.5706 −0.601560 −0.300780 0.953694i \(-0.597247\pi\)
−0.300780 + 0.953694i \(0.597247\pi\)
\(954\) 28.3323 0.917293
\(955\) 56.6136 1.83197
\(956\) −29.2489 −0.945978
\(957\) −1.60599 −0.0519143
\(958\) −12.6907 −0.410017
\(959\) −6.38763 −0.206267
\(960\) 1.27085 0.0410165
\(961\) −5.63932 −0.181913
\(962\) 7.50595 0.242002
\(963\) −35.4469 −1.14226
\(964\) 89.6548 2.88759
\(965\) −52.0733 −1.67630
\(966\) −4.62647 −0.148854
\(967\) 5.30714 0.170666 0.0853330 0.996352i \(-0.472805\pi\)
0.0853330 + 0.996352i \(0.472805\pi\)
\(968\) 3.72500 0.119726
\(969\) 2.03321 0.0653161
\(970\) −7.57511 −0.243222
\(971\) −22.3661 −0.717763 −0.358881 0.933383i \(-0.616842\pi\)
−0.358881 + 0.933383i \(0.616842\pi\)
\(972\) 33.1270 1.06255
\(973\) −8.41355 −0.269726
\(974\) 21.3877 0.685308
\(975\) 0.118258 0.00378728
\(976\) 95.3168 3.05102
\(977\) 35.4689 1.13475 0.567375 0.823459i \(-0.307959\pi\)
0.567375 + 0.823459i \(0.307959\pi\)
\(978\) −15.6699 −0.501068
\(979\) 3.18102 0.101666
\(980\) −11.1332 −0.355637
\(981\) 9.32334 0.297671
\(982\) 35.6709 1.13830
\(983\) −2.38518 −0.0760753 −0.0380377 0.999276i \(-0.512111\pi\)
−0.0380377 + 0.999276i \(0.512111\pi\)
\(984\) 10.6918 0.340841
\(985\) 20.4663 0.652112
\(986\) −5.70589 −0.181713
\(987\) 3.14053 0.0999642
\(988\) −6.99830 −0.222646
\(989\) −47.3193 −1.50467
\(990\) −60.1146 −1.91057
\(991\) −35.2261 −1.11899 −0.559497 0.828833i \(-0.689005\pi\)
−0.559497 + 0.828833i \(0.689005\pi\)
\(992\) −22.8098 −0.724212
\(993\) −3.86631 −0.122694
\(994\) −27.9769 −0.887374
\(995\) −35.0439 −1.11097
\(996\) 1.99764 0.0632976
\(997\) 3.91260 0.123913 0.0619567 0.998079i \(-0.480266\pi\)
0.0619567 + 0.998079i \(0.480266\pi\)
\(998\) 16.7770 0.531066
\(999\) 17.1701 0.543238
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 \(a_p\))