Properties

Label 6013.2.a.e.1.15
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 1.15
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.09226 q^{2}\) \(+2.05769 q^{3}\) \(+2.37754 q^{4}\) \(-3.21058 q^{5}\) \(-4.30522 q^{6}\) \(+1.00000 q^{7}\) \(-0.789909 q^{8}\) \(+1.23410 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.09226 q^{2}\) \(+2.05769 q^{3}\) \(+2.37754 q^{4}\) \(-3.21058 q^{5}\) \(-4.30522 q^{6}\) \(+1.00000 q^{7}\) \(-0.789909 q^{8}\) \(+1.23410 q^{9}\) \(+6.71736 q^{10}\) \(-1.05106 q^{11}\) \(+4.89224 q^{12}\) \(-6.03586 q^{13}\) \(-2.09226 q^{14}\) \(-6.60639 q^{15}\) \(-3.10239 q^{16}\) \(-0.303396 q^{17}\) \(-2.58205 q^{18}\) \(-7.88878 q^{19}\) \(-7.63328 q^{20}\) \(+2.05769 q^{21}\) \(+2.19908 q^{22}\) \(-5.99646 q^{23}\) \(-1.62539 q^{24}\) \(+5.30784 q^{25}\) \(+12.6286 q^{26}\) \(-3.63368 q^{27}\) \(+2.37754 q^{28}\) \(-5.87597 q^{29}\) \(+13.8223 q^{30}\) \(-3.70314 q^{31}\) \(+8.07081 q^{32}\) \(-2.16275 q^{33}\) \(+0.634781 q^{34}\) \(-3.21058 q^{35}\) \(+2.93412 q^{36}\) \(+0.931951 q^{37}\) \(+16.5054 q^{38}\) \(-12.4199 q^{39}\) \(+2.53607 q^{40}\) \(-2.50984 q^{41}\) \(-4.30522 q^{42}\) \(+3.08098 q^{43}\) \(-2.49893 q^{44}\) \(-3.96217 q^{45}\) \(+12.5461 q^{46}\) \(-1.55414 q^{47}\) \(-6.38376 q^{48}\) \(+1.00000 q^{49}\) \(-11.1054 q^{50}\) \(-0.624295 q^{51}\) \(-14.3505 q^{52}\) \(+0.950773 q^{53}\) \(+7.60260 q^{54}\) \(+3.37451 q^{55}\) \(-0.789909 q^{56}\) \(-16.2327 q^{57}\) \(+12.2940 q^{58}\) \(+8.70133 q^{59}\) \(-15.7070 q^{60}\) \(-1.10085 q^{61}\) \(+7.74793 q^{62}\) \(+1.23410 q^{63}\) \(-10.6814 q^{64}\) \(+19.3786 q^{65}\) \(+4.52503 q^{66}\) \(-6.34168 q^{67}\) \(-0.721335 q^{68}\) \(-12.3389 q^{69}\) \(+6.71736 q^{70}\) \(+0.621219 q^{71}\) \(-0.974825 q^{72}\) \(-2.68798 q^{73}\) \(-1.94988 q^{74}\) \(+10.9219 q^{75}\) \(-18.7559 q^{76}\) \(-1.05106 q^{77}\) \(+25.9857 q^{78}\) \(+13.4934 q^{79}\) \(+9.96047 q^{80}\) \(-11.1793 q^{81}\) \(+5.25123 q^{82}\) \(+16.1640 q^{83}\) \(+4.89224 q^{84}\) \(+0.974076 q^{85}\) \(-6.44620 q^{86}\) \(-12.0909 q^{87}\) \(+0.830239 q^{88}\) \(+10.0831 q^{89}\) \(+8.28988 q^{90}\) \(-6.03586 q^{91}\) \(-14.2568 q^{92}\) \(-7.61993 q^{93}\) \(+3.25165 q^{94}\) \(+25.3276 q^{95}\) \(+16.6072 q^{96}\) \(+11.8556 q^{97}\) \(-2.09226 q^{98}\) \(-1.29711 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09226 −1.47945 −0.739725 0.672910i \(-0.765044\pi\)
−0.739725 + 0.672910i \(0.765044\pi\)
\(3\) 2.05769 1.18801 0.594005 0.804462i \(-0.297546\pi\)
0.594005 + 0.804462i \(0.297546\pi\)
\(4\) 2.37754 1.18877
\(5\) −3.21058 −1.43582 −0.717908 0.696138i \(-0.754900\pi\)
−0.717908 + 0.696138i \(0.754900\pi\)
\(6\) −4.30522 −1.75760
\(7\) 1.00000 0.377964
\(8\) −0.789909 −0.279275
\(9\) 1.23410 0.411366
\(10\) 6.71736 2.12422
\(11\) −1.05106 −0.316906 −0.158453 0.987367i \(-0.550651\pi\)
−0.158453 + 0.987367i \(0.550651\pi\)
\(12\) 4.89224 1.41227
\(13\) −6.03586 −1.67405 −0.837024 0.547167i \(-0.815706\pi\)
−0.837024 + 0.547167i \(0.815706\pi\)
\(14\) −2.09226 −0.559179
\(15\) −6.60639 −1.70576
\(16\) −3.10239 −0.775597
\(17\) −0.303396 −0.0735842 −0.0367921 0.999323i \(-0.511714\pi\)
−0.0367921 + 0.999323i \(0.511714\pi\)
\(18\) −2.58205 −0.608595
\(19\) −7.88878 −1.80981 −0.904905 0.425613i \(-0.860059\pi\)
−0.904905 + 0.425613i \(0.860059\pi\)
\(20\) −7.63328 −1.70685
\(21\) 2.05769 0.449025
\(22\) 2.19908 0.468846
\(23\) −5.99646 −1.25035 −0.625175 0.780485i \(-0.714972\pi\)
−0.625175 + 0.780485i \(0.714972\pi\)
\(24\) −1.62539 −0.331781
\(25\) 5.30784 1.06157
\(26\) 12.6286 2.47667
\(27\) −3.63368 −0.699303
\(28\) 2.37754 0.449313
\(29\) −5.87597 −1.09114 −0.545570 0.838065i \(-0.683687\pi\)
−0.545570 + 0.838065i \(0.683687\pi\)
\(30\) 13.8223 2.52359
\(31\) −3.70314 −0.665104 −0.332552 0.943085i \(-0.607910\pi\)
−0.332552 + 0.943085i \(0.607910\pi\)
\(32\) 8.07081 1.42673
\(33\) −2.16275 −0.376487
\(34\) 0.634781 0.108864
\(35\) −3.21058 −0.542687
\(36\) 2.93412 0.489019
\(37\) 0.931951 0.153212 0.0766059 0.997061i \(-0.475592\pi\)
0.0766059 + 0.997061i \(0.475592\pi\)
\(38\) 16.5054 2.67752
\(39\) −12.4199 −1.98878
\(40\) 2.53607 0.400987
\(41\) −2.50984 −0.391971 −0.195985 0.980607i \(-0.562791\pi\)
−0.195985 + 0.980607i \(0.562791\pi\)
\(42\) −4.30522 −0.664310
\(43\) 3.08098 0.469845 0.234923 0.972014i \(-0.424516\pi\)
0.234923 + 0.972014i \(0.424516\pi\)
\(44\) −2.49893 −0.376728
\(45\) −3.96217 −0.590646
\(46\) 12.5461 1.84983
\(47\) −1.55414 −0.226694 −0.113347 0.993555i \(-0.536157\pi\)
−0.113347 + 0.993555i \(0.536157\pi\)
\(48\) −6.38376 −0.921416
\(49\) 1.00000 0.142857
\(50\) −11.1054 −1.57053
\(51\) −0.624295 −0.0874187
\(52\) −14.3505 −1.99006
\(53\) 0.950773 0.130599 0.0652994 0.997866i \(-0.479200\pi\)
0.0652994 + 0.997866i \(0.479200\pi\)
\(54\) 7.60260 1.03458
\(55\) 3.37451 0.455018
\(56\) −0.789909 −0.105556
\(57\) −16.2327 −2.15007
\(58\) 12.2940 1.61429
\(59\) 8.70133 1.13282 0.566408 0.824125i \(-0.308332\pi\)
0.566408 + 0.824125i \(0.308332\pi\)
\(60\) −15.7070 −2.02776
\(61\) −1.10085 −0.140949 −0.0704745 0.997514i \(-0.522451\pi\)
−0.0704745 + 0.997514i \(0.522451\pi\)
\(62\) 7.74793 0.983988
\(63\) 1.23410 0.155482
\(64\) −10.6814 −1.33518
\(65\) 19.3786 2.40362
\(66\) 4.52503 0.556993
\(67\) −6.34168 −0.774760 −0.387380 0.921920i \(-0.626620\pi\)
−0.387380 + 0.921920i \(0.626620\pi\)
\(68\) −0.721335 −0.0874747
\(69\) −12.3389 −1.48543
\(70\) 6.71736 0.802878
\(71\) 0.621219 0.0737251 0.0368625 0.999320i \(-0.488264\pi\)
0.0368625 + 0.999320i \(0.488264\pi\)
\(72\) −0.974825 −0.114884
\(73\) −2.68798 −0.314605 −0.157302 0.987550i \(-0.550280\pi\)
−0.157302 + 0.987550i \(0.550280\pi\)
\(74\) −1.94988 −0.226669
\(75\) 10.9219 1.26115
\(76\) −18.7559 −2.15145
\(77\) −1.05106 −0.119779
\(78\) 25.9857 2.94230
\(79\) 13.4934 1.51813 0.759063 0.651017i \(-0.225657\pi\)
0.759063 + 0.651017i \(0.225657\pi\)
\(80\) 9.96047 1.11361
\(81\) −11.1793 −1.24214
\(82\) 5.25123 0.579901
\(83\) 16.1640 1.77423 0.887115 0.461549i \(-0.152706\pi\)
0.887115 + 0.461549i \(0.152706\pi\)
\(84\) 4.89224 0.533788
\(85\) 0.974076 0.105653
\(86\) −6.44620 −0.695112
\(87\) −12.0909 −1.29628
\(88\) 0.830239 0.0885038
\(89\) 10.0831 1.06881 0.534403 0.845230i \(-0.320536\pi\)
0.534403 + 0.845230i \(0.320536\pi\)
\(90\) 8.28988 0.873830
\(91\) −6.03586 −0.632730
\(92\) −14.2568 −1.48638
\(93\) −7.61993 −0.790150
\(94\) 3.25165 0.335382
\(95\) 25.3276 2.59856
\(96\) 16.6072 1.69497
\(97\) 11.8556 1.20375 0.601875 0.798590i \(-0.294421\pi\)
0.601875 + 0.798590i \(0.294421\pi\)
\(98\) −2.09226 −0.211350
\(99\) −1.29711 −0.130364
\(100\) 12.6196 1.26196
\(101\) 15.1082 1.50332 0.751659 0.659552i \(-0.229254\pi\)
0.751659 + 0.659552i \(0.229254\pi\)
\(102\) 1.30618 0.129332
\(103\) −12.9375 −1.27477 −0.637383 0.770547i \(-0.719983\pi\)
−0.637383 + 0.770547i \(0.719983\pi\)
\(104\) 4.76778 0.467519
\(105\) −6.60639 −0.644718
\(106\) −1.98926 −0.193214
\(107\) 18.0641 1.74632 0.873161 0.487431i \(-0.162066\pi\)
0.873161 + 0.487431i \(0.162066\pi\)
\(108\) −8.63922 −0.831310
\(109\) 16.9133 1.62000 0.810001 0.586428i \(-0.199466\pi\)
0.810001 + 0.586428i \(0.199466\pi\)
\(110\) −7.06033 −0.673176
\(111\) 1.91767 0.182017
\(112\) −3.10239 −0.293148
\(113\) 3.86760 0.363833 0.181916 0.983314i \(-0.441770\pi\)
0.181916 + 0.983314i \(0.441770\pi\)
\(114\) 33.9630 3.18092
\(115\) 19.2521 1.79527
\(116\) −13.9704 −1.29711
\(117\) −7.44885 −0.688646
\(118\) −18.2054 −1.67594
\(119\) −0.303396 −0.0278122
\(120\) 5.21844 0.476377
\(121\) −9.89528 −0.899571
\(122\) 2.30325 0.208527
\(123\) −5.16448 −0.465665
\(124\) −8.80437 −0.790656
\(125\) −0.988335 −0.0883994
\(126\) −2.58205 −0.230027
\(127\) −20.9173 −1.85611 −0.928056 0.372442i \(-0.878521\pi\)
−0.928056 + 0.372442i \(0.878521\pi\)
\(128\) 6.20668 0.548598
\(129\) 6.33971 0.558180
\(130\) −40.5451 −3.55604
\(131\) 7.96847 0.696209 0.348104 0.937456i \(-0.386826\pi\)
0.348104 + 0.937456i \(0.386826\pi\)
\(132\) −5.14203 −0.447556
\(133\) −7.88878 −0.684044
\(134\) 13.2684 1.14622
\(135\) 11.6662 1.00407
\(136\) 0.239655 0.0205502
\(137\) −21.3156 −1.82111 −0.910556 0.413385i \(-0.864346\pi\)
−0.910556 + 0.413385i \(0.864346\pi\)
\(138\) 25.8161 2.19761
\(139\) −23.1319 −1.96202 −0.981010 0.193955i \(-0.937868\pi\)
−0.981010 + 0.193955i \(0.937868\pi\)
\(140\) −7.63328 −0.645130
\(141\) −3.19793 −0.269315
\(142\) −1.29975 −0.109073
\(143\) 6.34404 0.530515
\(144\) −3.82865 −0.319054
\(145\) 18.8653 1.56668
\(146\) 5.62395 0.465442
\(147\) 2.05769 0.169716
\(148\) 2.21575 0.182133
\(149\) −14.8882 −1.21969 −0.609844 0.792521i \(-0.708768\pi\)
−0.609844 + 0.792521i \(0.708768\pi\)
\(150\) −22.8514 −1.86581
\(151\) −15.0300 −1.22312 −0.611562 0.791197i \(-0.709459\pi\)
−0.611562 + 0.791197i \(0.709459\pi\)
\(152\) 6.23142 0.505435
\(153\) −0.374420 −0.0302700
\(154\) 2.19908 0.177207
\(155\) 11.8892 0.954967
\(156\) −29.5289 −2.36421
\(157\) 0.373102 0.0297768 0.0148884 0.999889i \(-0.495261\pi\)
0.0148884 + 0.999889i \(0.495261\pi\)
\(158\) −28.2317 −2.24599
\(159\) 1.95640 0.155152
\(160\) −25.9120 −2.04852
\(161\) −5.99646 −0.472588
\(162\) 23.3900 1.83769
\(163\) 12.0449 0.943426 0.471713 0.881752i \(-0.343636\pi\)
0.471713 + 0.881752i \(0.343636\pi\)
\(164\) −5.96724 −0.465963
\(165\) 6.94369 0.540566
\(166\) −33.8192 −2.62488
\(167\) −0.413096 −0.0319663 −0.0159832 0.999872i \(-0.505088\pi\)
−0.0159832 + 0.999872i \(0.505088\pi\)
\(168\) −1.62539 −0.125401
\(169\) 23.4316 1.80243
\(170\) −2.03802 −0.156309
\(171\) −9.73553 −0.744495
\(172\) 7.32515 0.558538
\(173\) 16.6210 1.26367 0.631834 0.775104i \(-0.282303\pi\)
0.631834 + 0.775104i \(0.282303\pi\)
\(174\) 25.2974 1.91779
\(175\) 5.30784 0.401235
\(176\) 3.26079 0.245791
\(177\) 17.9047 1.34580
\(178\) −21.0964 −1.58125
\(179\) −7.34138 −0.548721 −0.274360 0.961627i \(-0.588466\pi\)
−0.274360 + 0.961627i \(0.588466\pi\)
\(180\) −9.42022 −0.702142
\(181\) −6.93257 −0.515294 −0.257647 0.966239i \(-0.582947\pi\)
−0.257647 + 0.966239i \(0.582947\pi\)
\(182\) 12.6286 0.936092
\(183\) −2.26520 −0.167449
\(184\) 4.73666 0.349191
\(185\) −2.99210 −0.219984
\(186\) 15.9429 1.16899
\(187\) 0.318886 0.0233193
\(188\) −3.69502 −0.269487
\(189\) −3.63368 −0.264312
\(190\) −52.9918 −3.84443
\(191\) 12.2337 0.885196 0.442598 0.896720i \(-0.354057\pi\)
0.442598 + 0.896720i \(0.354057\pi\)
\(192\) −21.9791 −1.58620
\(193\) 7.51507 0.540947 0.270473 0.962727i \(-0.412820\pi\)
0.270473 + 0.962727i \(0.412820\pi\)
\(194\) −24.8049 −1.78089
\(195\) 39.8753 2.85553
\(196\) 2.37754 0.169824
\(197\) −20.8935 −1.48860 −0.744300 0.667846i \(-0.767217\pi\)
−0.744300 + 0.667846i \(0.767217\pi\)
\(198\) 2.71388 0.192867
\(199\) 22.3430 1.58386 0.791928 0.610615i \(-0.209078\pi\)
0.791928 + 0.610615i \(0.209078\pi\)
\(200\) −4.19271 −0.296469
\(201\) −13.0492 −0.920422
\(202\) −31.6102 −2.22408
\(203\) −5.87597 −0.412412
\(204\) −1.48428 −0.103921
\(205\) 8.05804 0.562798
\(206\) 27.0685 1.88595
\(207\) −7.40022 −0.514351
\(208\) 18.7256 1.29839
\(209\) 8.29156 0.573539
\(210\) 13.8223 0.953827
\(211\) −2.30648 −0.158784 −0.0793922 0.996843i \(-0.525298\pi\)
−0.0793922 + 0.996843i \(0.525298\pi\)
\(212\) 2.26050 0.155252
\(213\) 1.27828 0.0875861
\(214\) −37.7947 −2.58360
\(215\) −9.89174 −0.674611
\(216\) 2.87028 0.195298
\(217\) −3.70314 −0.251386
\(218\) −35.3870 −2.39671
\(219\) −5.53104 −0.373753
\(220\) 8.02302 0.540912
\(221\) 1.83125 0.123183
\(222\) −4.01225 −0.269285
\(223\) −2.23474 −0.149649 −0.0748246 0.997197i \(-0.523840\pi\)
−0.0748246 + 0.997197i \(0.523840\pi\)
\(224\) 8.07081 0.539253
\(225\) 6.55039 0.436693
\(226\) −8.09200 −0.538272
\(227\) 18.7056 1.24153 0.620767 0.783995i \(-0.286821\pi\)
0.620767 + 0.783995i \(0.286821\pi\)
\(228\) −38.5939 −2.55594
\(229\) −4.34230 −0.286947 −0.143474 0.989654i \(-0.545827\pi\)
−0.143474 + 0.989654i \(0.545827\pi\)
\(230\) −40.2804 −2.65601
\(231\) −2.16275 −0.142299
\(232\) 4.64148 0.304728
\(233\) −5.59457 −0.366512 −0.183256 0.983065i \(-0.558664\pi\)
−0.183256 + 0.983065i \(0.558664\pi\)
\(234\) 15.5849 1.01882
\(235\) 4.98968 0.325491
\(236\) 20.6878 1.34666
\(237\) 27.7653 1.80355
\(238\) 0.634781 0.0411468
\(239\) 6.59741 0.426751 0.213375 0.976970i \(-0.431554\pi\)
0.213375 + 0.976970i \(0.431554\pi\)
\(240\) 20.4956 1.32298
\(241\) −5.67322 −0.365444 −0.182722 0.983165i \(-0.558491\pi\)
−0.182722 + 0.983165i \(0.558491\pi\)
\(242\) 20.7035 1.33087
\(243\) −12.1025 −0.776376
\(244\) −2.61730 −0.167556
\(245\) −3.21058 −0.205117
\(246\) 10.8054 0.688928
\(247\) 47.6156 3.02971
\(248\) 2.92515 0.185747
\(249\) 33.2605 2.10780
\(250\) 2.06785 0.130782
\(251\) −6.54340 −0.413016 −0.206508 0.978445i \(-0.566210\pi\)
−0.206508 + 0.978445i \(0.566210\pi\)
\(252\) 2.93412 0.184832
\(253\) 6.30263 0.396243
\(254\) 43.7644 2.74602
\(255\) 2.00435 0.125517
\(256\) 8.37689 0.523556
\(257\) 5.99910 0.374213 0.187107 0.982340i \(-0.440089\pi\)
0.187107 + 0.982340i \(0.440089\pi\)
\(258\) −13.2643 −0.825800
\(259\) 0.931951 0.0579086
\(260\) 46.0735 2.85735
\(261\) −7.25152 −0.448858
\(262\) −16.6721 −1.03001
\(263\) −31.3468 −1.93293 −0.966463 0.256804i \(-0.917330\pi\)
−0.966463 + 0.256804i \(0.917330\pi\)
\(264\) 1.70838 0.105143
\(265\) −3.05253 −0.187516
\(266\) 16.5054 1.01201
\(267\) 20.7479 1.26975
\(268\) −15.0776 −0.921011
\(269\) −0.857537 −0.0522850 −0.0261425 0.999658i \(-0.508322\pi\)
−0.0261425 + 0.999658i \(0.508322\pi\)
\(270\) −24.4088 −1.48547
\(271\) 14.0768 0.855102 0.427551 0.903991i \(-0.359376\pi\)
0.427551 + 0.903991i \(0.359376\pi\)
\(272\) 0.941250 0.0570717
\(273\) −12.4199 −0.751689
\(274\) 44.5977 2.69424
\(275\) −5.57884 −0.336417
\(276\) −29.3362 −1.76583
\(277\) −20.6830 −1.24272 −0.621362 0.783524i \(-0.713420\pi\)
−0.621362 + 0.783524i \(0.713420\pi\)
\(278\) 48.3978 2.90271
\(279\) −4.57004 −0.273601
\(280\) 2.53607 0.151559
\(281\) −17.6810 −1.05476 −0.527379 0.849630i \(-0.676825\pi\)
−0.527379 + 0.849630i \(0.676825\pi\)
\(282\) 6.69090 0.398437
\(283\) 26.8893 1.59841 0.799203 0.601062i \(-0.205255\pi\)
0.799203 + 0.601062i \(0.205255\pi\)
\(284\) 1.47697 0.0876421
\(285\) 52.1164 3.08711
\(286\) −13.2734 −0.784870
\(287\) −2.50984 −0.148151
\(288\) 9.96017 0.586908
\(289\) −16.9080 −0.994585
\(290\) −39.4710 −2.31782
\(291\) 24.3951 1.43007
\(292\) −6.39079 −0.373993
\(293\) −28.7899 −1.68193 −0.840963 0.541093i \(-0.818011\pi\)
−0.840963 + 0.541093i \(0.818011\pi\)
\(294\) −4.30522 −0.251086
\(295\) −27.9363 −1.62652
\(296\) −0.736156 −0.0427882
\(297\) 3.81921 0.221613
\(298\) 31.1499 1.80447
\(299\) 36.1938 2.09314
\(300\) 25.9672 1.49922
\(301\) 3.08098 0.177585
\(302\) 31.4466 1.80955
\(303\) 31.0880 1.78596
\(304\) 24.4741 1.40368
\(305\) 3.53436 0.202377
\(306\) 0.783382 0.0447830
\(307\) −1.61826 −0.0923587 −0.0461794 0.998933i \(-0.514705\pi\)
−0.0461794 + 0.998933i \(0.514705\pi\)
\(308\) −2.49893 −0.142390
\(309\) −26.6213 −1.51443
\(310\) −24.8754 −1.41283
\(311\) 15.3868 0.872505 0.436252 0.899824i \(-0.356306\pi\)
0.436252 + 0.899824i \(0.356306\pi\)
\(312\) 9.81062 0.555417
\(313\) −32.4562 −1.83453 −0.917266 0.398275i \(-0.869609\pi\)
−0.917266 + 0.398275i \(0.869609\pi\)
\(314\) −0.780625 −0.0440532
\(315\) −3.96217 −0.223243
\(316\) 32.0811 1.80470
\(317\) 4.54123 0.255061 0.127530 0.991835i \(-0.459295\pi\)
0.127530 + 0.991835i \(0.459295\pi\)
\(318\) −4.09329 −0.229540
\(319\) 6.17598 0.345789
\(320\) 34.2936 1.91707
\(321\) 37.1704 2.07465
\(322\) 12.5461 0.699169
\(323\) 2.39342 0.133174
\(324\) −26.5792 −1.47662
\(325\) −32.0374 −1.77711
\(326\) −25.2009 −1.39575
\(327\) 34.8024 1.92458
\(328\) 1.98254 0.109468
\(329\) −1.55414 −0.0856823
\(330\) −14.5280 −0.799740
\(331\) 8.81519 0.484527 0.242263 0.970211i \(-0.422110\pi\)
0.242263 + 0.970211i \(0.422110\pi\)
\(332\) 38.4305 2.10915
\(333\) 1.15012 0.0630261
\(334\) 0.864302 0.0472925
\(335\) 20.3605 1.11241
\(336\) −6.38376 −0.348262
\(337\) −11.0261 −0.600628 −0.300314 0.953840i \(-0.597091\pi\)
−0.300314 + 0.953840i \(0.597091\pi\)
\(338\) −49.0250 −2.66661
\(339\) 7.95832 0.432237
\(340\) 2.31590 0.125598
\(341\) 3.89222 0.210775
\(342\) 20.3692 1.10144
\(343\) 1.00000 0.0539949
\(344\) −2.43369 −0.131216
\(345\) 39.6150 2.13280
\(346\) −34.7753 −1.86953
\(347\) 13.6991 0.735408 0.367704 0.929943i \(-0.380144\pi\)
0.367704 + 0.929943i \(0.380144\pi\)
\(348\) −28.7467 −1.54098
\(349\) −16.5436 −0.885561 −0.442780 0.896630i \(-0.646008\pi\)
−0.442780 + 0.896630i \(0.646008\pi\)
\(350\) −11.1054 −0.593606
\(351\) 21.9324 1.17067
\(352\) −8.48288 −0.452139
\(353\) 21.8507 1.16299 0.581497 0.813548i \(-0.302467\pi\)
0.581497 + 0.813548i \(0.302467\pi\)
\(354\) −37.4612 −1.99104
\(355\) −1.99447 −0.105856
\(356\) 23.9730 1.27057
\(357\) −0.624295 −0.0330412
\(358\) 15.3601 0.811805
\(359\) 23.4410 1.23717 0.618584 0.785719i \(-0.287707\pi\)
0.618584 + 0.785719i \(0.287707\pi\)
\(360\) 3.12975 0.164953
\(361\) 43.2329 2.27542
\(362\) 14.5047 0.762351
\(363\) −20.3614 −1.06870
\(364\) −14.3505 −0.752171
\(365\) 8.62999 0.451715
\(366\) 4.73939 0.247732
\(367\) −16.5785 −0.865391 −0.432695 0.901540i \(-0.642437\pi\)
−0.432695 + 0.901540i \(0.642437\pi\)
\(368\) 18.6033 0.969766
\(369\) −3.09739 −0.161243
\(370\) 6.26025 0.325455
\(371\) 0.950773 0.0493617
\(372\) −18.1167 −0.939306
\(373\) −19.3598 −1.00241 −0.501207 0.865327i \(-0.667111\pi\)
−0.501207 + 0.865327i \(0.667111\pi\)
\(374\) −0.667192 −0.0344997
\(375\) −2.03369 −0.105019
\(376\) 1.22762 0.0633099
\(377\) 35.4666 1.82662
\(378\) 7.60260 0.391035
\(379\) −27.8640 −1.43128 −0.715638 0.698471i \(-0.753864\pi\)
−0.715638 + 0.698471i \(0.753864\pi\)
\(380\) 60.2173 3.08908
\(381\) −43.0414 −2.20508
\(382\) −25.5960 −1.30960
\(383\) −18.0382 −0.921707 −0.460853 0.887476i \(-0.652457\pi\)
−0.460853 + 0.887476i \(0.652457\pi\)
\(384\) 12.7714 0.651740
\(385\) 3.37451 0.171981
\(386\) −15.7235 −0.800303
\(387\) 3.80223 0.193278
\(388\) 28.1871 1.43098
\(389\) −2.27990 −0.115596 −0.0577978 0.998328i \(-0.518408\pi\)
−0.0577978 + 0.998328i \(0.518408\pi\)
\(390\) −83.4293 −4.22461
\(391\) 1.81930 0.0920060
\(392\) −0.789909 −0.0398964
\(393\) 16.3967 0.827102
\(394\) 43.7145 2.20231
\(395\) −43.3217 −2.17975
\(396\) −3.08392 −0.154973
\(397\) 10.6924 0.536637 0.268319 0.963330i \(-0.413532\pi\)
0.268319 + 0.963330i \(0.413532\pi\)
\(398\) −46.7474 −2.34323
\(399\) −16.2327 −0.812651
\(400\) −16.4670 −0.823348
\(401\) −18.5628 −0.926984 −0.463492 0.886101i \(-0.653404\pi\)
−0.463492 + 0.886101i \(0.653404\pi\)
\(402\) 27.3023 1.36172
\(403\) 22.3517 1.11342
\(404\) 35.9203 1.78710
\(405\) 35.8920 1.78349
\(406\) 12.2940 0.610143
\(407\) −0.979534 −0.0485537
\(408\) 0.493136 0.0244139
\(409\) 4.60656 0.227780 0.113890 0.993493i \(-0.463669\pi\)
0.113890 + 0.993493i \(0.463669\pi\)
\(410\) −16.8595 −0.832631
\(411\) −43.8609 −2.16350
\(412\) −30.7593 −1.51540
\(413\) 8.70133 0.428165
\(414\) 15.4832 0.760956
\(415\) −51.8959 −2.54747
\(416\) −48.7143 −2.38841
\(417\) −47.5983 −2.33090
\(418\) −17.3481 −0.848522
\(419\) 34.0273 1.66234 0.831172 0.556016i \(-0.187671\pi\)
0.831172 + 0.556016i \(0.187671\pi\)
\(420\) −15.7070 −0.766421
\(421\) 30.7029 1.49637 0.748185 0.663490i \(-0.230926\pi\)
0.748185 + 0.663490i \(0.230926\pi\)
\(422\) 4.82574 0.234913
\(423\) −1.91796 −0.0932542
\(424\) −0.751024 −0.0364729
\(425\) −1.61037 −0.0781146
\(426\) −2.67448 −0.129579
\(427\) −1.10085 −0.0532737
\(428\) 42.9481 2.07598
\(429\) 13.0541 0.630257
\(430\) 20.6961 0.998053
\(431\) −3.80752 −0.183402 −0.0917008 0.995787i \(-0.529230\pi\)
−0.0917008 + 0.995787i \(0.529230\pi\)
\(432\) 11.2731 0.542377
\(433\) −14.1584 −0.680407 −0.340203 0.940352i \(-0.610496\pi\)
−0.340203 + 0.940352i \(0.610496\pi\)
\(434\) 7.74793 0.371913
\(435\) 38.8190 1.86123
\(436\) 40.2121 1.92581
\(437\) 47.3048 2.26290
\(438\) 11.5724 0.552949
\(439\) −23.6054 −1.12662 −0.563312 0.826244i \(-0.690473\pi\)
−0.563312 + 0.826244i \(0.690473\pi\)
\(440\) −2.66555 −0.127075
\(441\) 1.23410 0.0587666
\(442\) −3.83145 −0.182244
\(443\) 3.43824 0.163356 0.0816778 0.996659i \(-0.473972\pi\)
0.0816778 + 0.996659i \(0.473972\pi\)
\(444\) 4.55933 0.216376
\(445\) −32.3726 −1.53461
\(446\) 4.67565 0.221398
\(447\) −30.6353 −1.44900
\(448\) −10.6814 −0.504650
\(449\) −18.8171 −0.888036 −0.444018 0.896018i \(-0.646447\pi\)
−0.444018 + 0.896018i \(0.646447\pi\)
\(450\) −13.7051 −0.646065
\(451\) 2.63798 0.124218
\(452\) 9.19536 0.432513
\(453\) −30.9271 −1.45308
\(454\) −39.1369 −1.83678
\(455\) 19.3786 0.908484
\(456\) 12.8223 0.600461
\(457\) 18.9213 0.885100 0.442550 0.896744i \(-0.354074\pi\)
0.442550 + 0.896744i \(0.354074\pi\)
\(458\) 9.08521 0.424524
\(459\) 1.10244 0.0514576
\(460\) 45.7727 2.13416
\(461\) 0.871546 0.0405920 0.0202960 0.999794i \(-0.493539\pi\)
0.0202960 + 0.999794i \(0.493539\pi\)
\(462\) 4.52503 0.210524
\(463\) −3.55195 −0.165073 −0.0825365 0.996588i \(-0.526302\pi\)
−0.0825365 + 0.996588i \(0.526302\pi\)
\(464\) 18.2295 0.846285
\(465\) 24.4644 1.13451
\(466\) 11.7053 0.542236
\(467\) −0.750411 −0.0347249 −0.0173624 0.999849i \(-0.505527\pi\)
−0.0173624 + 0.999849i \(0.505527\pi\)
\(468\) −17.7099 −0.818641
\(469\) −6.34168 −0.292832
\(470\) −10.4397 −0.481547
\(471\) 0.767729 0.0353751
\(472\) −6.87326 −0.316367
\(473\) −3.23829 −0.148897
\(474\) −58.0921 −2.66826
\(475\) −41.8724 −1.92124
\(476\) −0.721335 −0.0330623
\(477\) 1.17335 0.0537239
\(478\) −13.8035 −0.631356
\(479\) −10.5208 −0.480707 −0.240354 0.970685i \(-0.577263\pi\)
−0.240354 + 0.970685i \(0.577263\pi\)
\(480\) −53.3189 −2.43366
\(481\) −5.62513 −0.256484
\(482\) 11.8698 0.540656
\(483\) −12.3389 −0.561438
\(484\) −23.5264 −1.06938
\(485\) −38.0633 −1.72836
\(486\) 25.3215 1.14861
\(487\) −36.4341 −1.65098 −0.825492 0.564413i \(-0.809103\pi\)
−0.825492 + 0.564413i \(0.809103\pi\)
\(488\) 0.869568 0.0393635
\(489\) 24.7846 1.12080
\(490\) 6.71736 0.303460
\(491\) −11.4294 −0.515801 −0.257901 0.966171i \(-0.583031\pi\)
−0.257901 + 0.966171i \(0.583031\pi\)
\(492\) −12.2787 −0.553568
\(493\) 1.78274 0.0802907
\(494\) −99.6241 −4.48230
\(495\) 4.16447 0.187179
\(496\) 11.4886 0.515853
\(497\) 0.621219 0.0278655
\(498\) −69.5896 −3.11838
\(499\) −36.1046 −1.61626 −0.808131 0.589003i \(-0.799521\pi\)
−0.808131 + 0.589003i \(0.799521\pi\)
\(500\) −2.34981 −0.105087
\(501\) −0.850024 −0.0379763
\(502\) 13.6905 0.611036
\(503\) 11.3325 0.505289 0.252645 0.967559i \(-0.418700\pi\)
0.252645 + 0.967559i \(0.418700\pi\)
\(504\) −0.974825 −0.0434221
\(505\) −48.5060 −2.15849
\(506\) −13.1867 −0.586221
\(507\) 48.2151 2.14131
\(508\) −49.7317 −2.20649
\(509\) 32.2522 1.42955 0.714777 0.699353i \(-0.246528\pi\)
0.714777 + 0.699353i \(0.246528\pi\)
\(510\) −4.19361 −0.185696
\(511\) −2.68798 −0.118909
\(512\) −29.9400 −1.32317
\(513\) 28.6653 1.26561
\(514\) −12.5517 −0.553630
\(515\) 41.5368 1.83033
\(516\) 15.0729 0.663548
\(517\) 1.63349 0.0718406
\(518\) −1.94988 −0.0856728
\(519\) 34.2008 1.50125
\(520\) −15.3073 −0.671272
\(521\) 28.4147 1.24487 0.622436 0.782671i \(-0.286143\pi\)
0.622436 + 0.782671i \(0.286143\pi\)
\(522\) 15.1721 0.664063
\(523\) 12.2047 0.533672 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(524\) 18.9454 0.827632
\(525\) 10.9219 0.476671
\(526\) 65.5856 2.85967
\(527\) 1.12352 0.0489412
\(528\) 6.70969 0.292002
\(529\) 12.9576 0.563373
\(530\) 6.38669 0.277420
\(531\) 10.7383 0.466002
\(532\) −18.7559 −0.813171
\(533\) 15.1490 0.656178
\(534\) −43.4100 −1.87853
\(535\) −57.9963 −2.50740
\(536\) 5.00935 0.216371
\(537\) −15.1063 −0.651885
\(538\) 1.79419 0.0773530
\(539\) −1.05106 −0.0452722
\(540\) 27.7369 1.19361
\(541\) −21.1480 −0.909225 −0.454612 0.890689i \(-0.650222\pi\)
−0.454612 + 0.890689i \(0.650222\pi\)
\(542\) −29.4522 −1.26508
\(543\) −14.2651 −0.612174
\(544\) −2.44865 −0.104985
\(545\) −54.3016 −2.32603
\(546\) 25.9857 1.11209
\(547\) −22.0675 −0.943540 −0.471770 0.881722i \(-0.656385\pi\)
−0.471770 + 0.881722i \(0.656385\pi\)
\(548\) −50.6786 −2.16488
\(549\) −1.35855 −0.0579816
\(550\) 11.6724 0.497711
\(551\) 46.3543 1.97476
\(552\) 9.74659 0.414842
\(553\) 13.4934 0.573798
\(554\) 43.2742 1.83855
\(555\) −6.15683 −0.261343
\(556\) −54.9970 −2.33239
\(557\) 8.63053 0.365687 0.182844 0.983142i \(-0.441470\pi\)
0.182844 + 0.983142i \(0.441470\pi\)
\(558\) 9.56170 0.404779
\(559\) −18.5964 −0.786543
\(560\) 9.96047 0.420906
\(561\) 0.656170 0.0277035
\(562\) 36.9932 1.56046
\(563\) −35.5158 −1.49681 −0.748406 0.663241i \(-0.769180\pi\)
−0.748406 + 0.663241i \(0.769180\pi\)
\(564\) −7.60321 −0.320153
\(565\) −12.4172 −0.522397
\(566\) −56.2594 −2.36476
\(567\) −11.1793 −0.469486
\(568\) −0.490706 −0.0205896
\(569\) 12.4619 0.522429 0.261214 0.965281i \(-0.415877\pi\)
0.261214 + 0.965281i \(0.415877\pi\)
\(570\) −109.041 −4.56722
\(571\) −31.1268 −1.30262 −0.651309 0.758813i \(-0.725780\pi\)
−0.651309 + 0.758813i \(0.725780\pi\)
\(572\) 15.0832 0.630660
\(573\) 25.1731 1.05162
\(574\) 5.25123 0.219182
\(575\) −31.8282 −1.32733
\(576\) −13.1819 −0.549247
\(577\) 20.2224 0.841868 0.420934 0.907091i \(-0.361702\pi\)
0.420934 + 0.907091i \(0.361702\pi\)
\(578\) 35.3758 1.47144
\(579\) 15.4637 0.642650
\(580\) 44.8530 1.86242
\(581\) 16.1640 0.670596
\(582\) −51.0408 −2.11571
\(583\) −0.999317 −0.0413875
\(584\) 2.12326 0.0878612
\(585\) 23.9151 0.988769
\(586\) 60.2359 2.48832
\(587\) 26.1542 1.07950 0.539749 0.841826i \(-0.318519\pi\)
0.539749 + 0.841826i \(0.318519\pi\)
\(588\) 4.89224 0.201753
\(589\) 29.2133 1.20371
\(590\) 58.4500 2.40635
\(591\) −42.9924 −1.76847
\(592\) −2.89127 −0.118831
\(593\) 24.5242 1.00709 0.503543 0.863970i \(-0.332029\pi\)
0.503543 + 0.863970i \(0.332029\pi\)
\(594\) −7.99077 −0.327865
\(595\) 0.974076 0.0399332
\(596\) −35.3973 −1.44993
\(597\) 45.9751 1.88164
\(598\) −75.7268 −3.09670
\(599\) −37.9591 −1.55096 −0.775482 0.631369i \(-0.782493\pi\)
−0.775482 + 0.631369i \(0.782493\pi\)
\(600\) −8.62730 −0.352208
\(601\) 42.4948 1.73340 0.866699 0.498831i \(-0.166237\pi\)
0.866699 + 0.498831i \(0.166237\pi\)
\(602\) −6.44620 −0.262728
\(603\) −7.82626 −0.318710
\(604\) −35.7344 −1.45401
\(605\) 31.7696 1.29162
\(606\) −65.0440 −2.64223
\(607\) −23.3747 −0.948749 −0.474375 0.880323i \(-0.657326\pi\)
−0.474375 + 0.880323i \(0.657326\pi\)
\(608\) −63.6688 −2.58211
\(609\) −12.0909 −0.489950
\(610\) −7.39478 −0.299406
\(611\) 9.38055 0.379496
\(612\) −0.890198 −0.0359841
\(613\) 36.4687 1.47296 0.736478 0.676461i \(-0.236487\pi\)
0.736478 + 0.676461i \(0.236487\pi\)
\(614\) 3.38581 0.136640
\(615\) 16.5810 0.668609
\(616\) 0.830239 0.0334513
\(617\) 3.98057 0.160252 0.0801258 0.996785i \(-0.474468\pi\)
0.0801258 + 0.996785i \(0.474468\pi\)
\(618\) 55.6986 2.24053
\(619\) −20.5223 −0.824863 −0.412431 0.910989i \(-0.635320\pi\)
−0.412431 + 0.910989i \(0.635320\pi\)
\(620\) 28.2672 1.13524
\(621\) 21.7892 0.874372
\(622\) −32.1931 −1.29083
\(623\) 10.0831 0.403971
\(624\) 38.5315 1.54249
\(625\) −23.3661 −0.934642
\(626\) 67.9067 2.71410
\(627\) 17.0615 0.681370
\(628\) 0.887064 0.0353977
\(629\) −0.282750 −0.0112740
\(630\) 8.28988 0.330277
\(631\) 12.8376 0.511057 0.255528 0.966802i \(-0.417751\pi\)
0.255528 + 0.966802i \(0.417751\pi\)
\(632\) −10.6586 −0.423975
\(633\) −4.74602 −0.188637
\(634\) −9.50141 −0.377349
\(635\) 67.1567 2.66503
\(636\) 4.65141 0.184441
\(637\) −6.03586 −0.239150
\(638\) −12.9217 −0.511577
\(639\) 0.766645 0.0303280
\(640\) −19.9271 −0.787686
\(641\) −10.9318 −0.431778 −0.215889 0.976418i \(-0.569265\pi\)
−0.215889 + 0.976418i \(0.569265\pi\)
\(642\) −77.7700 −3.06934
\(643\) 50.0723 1.97466 0.987330 0.158683i \(-0.0507249\pi\)
0.987330 + 0.158683i \(0.0507249\pi\)
\(644\) −14.2568 −0.561798
\(645\) −20.3542 −0.801444
\(646\) −5.00765 −0.197023
\(647\) −15.4963 −0.609222 −0.304611 0.952477i \(-0.598526\pi\)
−0.304611 + 0.952477i \(0.598526\pi\)
\(648\) 8.83062 0.346900
\(649\) −9.14560 −0.358996
\(650\) 67.0304 2.62915
\(651\) −7.61993 −0.298649
\(652\) 28.6371 1.12152
\(653\) −40.2282 −1.57425 −0.787126 0.616792i \(-0.788432\pi\)
−0.787126 + 0.616792i \(0.788432\pi\)
\(654\) −72.8156 −2.84732
\(655\) −25.5834 −0.999627
\(656\) 7.78649 0.304011
\(657\) −3.31724 −0.129418
\(658\) 3.25165 0.126763
\(659\) −2.38576 −0.0929360 −0.0464680 0.998920i \(-0.514797\pi\)
−0.0464680 + 0.998920i \(0.514797\pi\)
\(660\) 16.5089 0.642608
\(661\) 2.24446 0.0872993 0.0436497 0.999047i \(-0.486101\pi\)
0.0436497 + 0.999047i \(0.486101\pi\)
\(662\) −18.4436 −0.716833
\(663\) 3.76816 0.146343
\(664\) −12.7681 −0.495498
\(665\) 25.3276 0.982162
\(666\) −2.40634 −0.0932439
\(667\) 35.2350 1.36431
\(668\) −0.982151 −0.0380006
\(669\) −4.59840 −0.177785
\(670\) −42.5994 −1.64576
\(671\) 1.15705 0.0446675
\(672\) 16.6072 0.640638
\(673\) −0.310404 −0.0119652 −0.00598260 0.999982i \(-0.501904\pi\)
−0.00598260 + 0.999982i \(0.501904\pi\)
\(674\) 23.0693 0.888598
\(675\) −19.2870 −0.742357
\(676\) 55.7096 2.14268
\(677\) −8.32076 −0.319793 −0.159896 0.987134i \(-0.551116\pi\)
−0.159896 + 0.987134i \(0.551116\pi\)
\(678\) −16.6509 −0.639472
\(679\) 11.8556 0.454975
\(680\) −0.769431 −0.0295063
\(681\) 38.4903 1.47495
\(682\) −8.14352 −0.311831
\(683\) −1.41649 −0.0542005 −0.0271003 0.999633i \(-0.508627\pi\)
−0.0271003 + 0.999633i \(0.508627\pi\)
\(684\) −23.1466 −0.885033
\(685\) 68.4354 2.61478
\(686\) −2.09226 −0.0798827
\(687\) −8.93512 −0.340896
\(688\) −9.55839 −0.364410
\(689\) −5.73873 −0.218628
\(690\) −82.8847 −3.15537
\(691\) 14.6754 0.558279 0.279139 0.960251i \(-0.409951\pi\)
0.279139 + 0.960251i \(0.409951\pi\)
\(692\) 39.5170 1.50221
\(693\) −1.29711 −0.0492730
\(694\) −28.6621 −1.08800
\(695\) 74.2668 2.81710
\(696\) 9.55074 0.362020
\(697\) 0.761474 0.0288429
\(698\) 34.6135 1.31014
\(699\) −11.5119 −0.435420
\(700\) 12.6196 0.476976
\(701\) 38.0423 1.43684 0.718418 0.695612i \(-0.244867\pi\)
0.718418 + 0.695612i \(0.244867\pi\)
\(702\) −45.8882 −1.73194
\(703\) −7.35196 −0.277284
\(704\) 11.2268 0.423126
\(705\) 10.2672 0.386686
\(706\) −45.7173 −1.72059
\(707\) 15.1082 0.568201
\(708\) 42.5690 1.59984
\(709\) −24.6679 −0.926424 −0.463212 0.886248i \(-0.653303\pi\)
−0.463212 + 0.886248i \(0.653303\pi\)
\(710\) 4.17295 0.156608
\(711\) 16.6522 0.624506
\(712\) −7.96473 −0.298491
\(713\) 22.2058 0.831613
\(714\) 1.30618 0.0488827
\(715\) −20.3681 −0.761722
\(716\) −17.4544 −0.652303
\(717\) 13.5754 0.506984
\(718\) −49.0446 −1.83033
\(719\) −19.3021 −0.719847 −0.359923 0.932982i \(-0.617197\pi\)
−0.359923 + 0.932982i \(0.617197\pi\)
\(720\) 12.2922 0.458103
\(721\) −12.9375 −0.481816
\(722\) −90.4543 −3.36636
\(723\) −11.6737 −0.434151
\(724\) −16.4825 −0.612566
\(725\) −31.1887 −1.15832
\(726\) 42.6014 1.58108
\(727\) 22.6204 0.838946 0.419473 0.907768i \(-0.362215\pi\)
0.419473 + 0.907768i \(0.362215\pi\)
\(728\) 4.76778 0.176706
\(729\) 8.63466 0.319802
\(730\) −18.0562 −0.668289
\(731\) −0.934756 −0.0345732
\(732\) −5.38561 −0.199058
\(733\) 13.1730 0.486557 0.243279 0.969956i \(-0.421777\pi\)
0.243279 + 0.969956i \(0.421777\pi\)
\(734\) 34.6865 1.28030
\(735\) −6.60639 −0.243680
\(736\) −48.3963 −1.78391
\(737\) 6.66547 0.245526
\(738\) 6.48053 0.238552
\(739\) −11.2292 −0.413071 −0.206536 0.978439i \(-0.566219\pi\)
−0.206536 + 0.978439i \(0.566219\pi\)
\(740\) −7.11384 −0.261510
\(741\) 97.9783 3.59932
\(742\) −1.98926 −0.0730281
\(743\) 37.3398 1.36987 0.684933 0.728606i \(-0.259832\pi\)
0.684933 + 0.728606i \(0.259832\pi\)
\(744\) 6.01905 0.220669
\(745\) 47.7998 1.75125
\(746\) 40.5058 1.48302
\(747\) 19.9480 0.729858
\(748\) 0.758164 0.0277212
\(749\) 18.0641 0.660048
\(750\) 4.25500 0.155371
\(751\) −16.2709 −0.593733 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(752\) 4.82153 0.175823
\(753\) −13.4643 −0.490666
\(754\) −74.2051 −2.70239
\(755\) 48.2550 1.75618
\(756\) −8.63922 −0.314206
\(757\) −0.162248 −0.00589701 −0.00294851 0.999996i \(-0.500939\pi\)
−0.00294851 + 0.999996i \(0.500939\pi\)
\(758\) 58.2986 2.11750
\(759\) 12.9689 0.470740
\(760\) −20.0065 −0.725711
\(761\) −14.6180 −0.529903 −0.264952 0.964262i \(-0.585356\pi\)
−0.264952 + 0.964262i \(0.585356\pi\)
\(762\) 90.0536 3.26230
\(763\) 16.9133 0.612303
\(764\) 29.0860 1.05229
\(765\) 1.20211 0.0434622
\(766\) 37.7405 1.36362
\(767\) −52.5200 −1.89639
\(768\) 17.2371 0.621989
\(769\) 52.0790 1.87802 0.939008 0.343896i \(-0.111747\pi\)
0.939008 + 0.343896i \(0.111747\pi\)
\(770\) −7.06033 −0.254437
\(771\) 12.3443 0.444569
\(772\) 17.8674 0.643061
\(773\) 48.0473 1.72814 0.864070 0.503371i \(-0.167907\pi\)
0.864070 + 0.503371i \(0.167907\pi\)
\(774\) −7.95525 −0.285945
\(775\) −19.6557 −0.706053
\(776\) −9.36481 −0.336177
\(777\) 1.91767 0.0687960
\(778\) 4.77014 0.171018
\(779\) 19.7996 0.709393
\(780\) 94.8050 3.39456
\(781\) −0.652936 −0.0233639
\(782\) −3.80644 −0.136118
\(783\) 21.3514 0.763037
\(784\) −3.10239 −0.110800
\(785\) −1.19787 −0.0427540
\(786\) −34.3060 −1.22366
\(787\) 51.2322 1.82623 0.913116 0.407701i \(-0.133669\pi\)
0.913116 + 0.407701i \(0.133669\pi\)
\(788\) −49.6751 −1.76960
\(789\) −64.5021 −2.29633
\(790\) 90.6401 3.22483
\(791\) 3.86760 0.137516
\(792\) 1.02460 0.0364075
\(793\) 6.64456 0.235955
\(794\) −22.3713 −0.793928
\(795\) −6.28118 −0.222770
\(796\) 53.1214 1.88284
\(797\) 33.2854 1.17903 0.589515 0.807758i \(-0.299319\pi\)
0.589515 + 0.807758i \(0.299319\pi\)
\(798\) 33.9630 1.20228
\(799\) 0.471518 0.0166811
\(800\) 42.8385 1.51457
\(801\) 12.4435 0.439671
\(802\) 38.8382 1.37143
\(803\) 2.82523 0.0997000
\(804\) −31.0251 −1.09417
\(805\) 19.2521 0.678549
\(806\) −46.7654 −1.64724
\(807\) −1.76455 −0.0621150
\(808\) −11.9341 −0.419839
\(809\) 4.08686 0.143686 0.0718431 0.997416i \(-0.477112\pi\)
0.0718431 + 0.997416i \(0.477112\pi\)
\(810\) −75.0954 −2.63858
\(811\) −20.7905 −0.730053 −0.365027 0.930997i \(-0.618940\pi\)
−0.365027 + 0.930997i \(0.618940\pi\)
\(812\) −13.9704 −0.490263
\(813\) 28.9656 1.01587
\(814\) 2.04944 0.0718327
\(815\) −38.6710 −1.35459
\(816\) 1.93680 0.0678017
\(817\) −24.3052 −0.850331
\(818\) −9.63811 −0.336988
\(819\) −7.44885 −0.260284
\(820\) 19.1583 0.669037
\(821\) 9.67690 0.337726 0.168863 0.985640i \(-0.445990\pi\)
0.168863 + 0.985640i \(0.445990\pi\)
\(822\) 91.7683 3.20079
\(823\) 24.1830 0.842966 0.421483 0.906836i \(-0.361510\pi\)
0.421483 + 0.906836i \(0.361510\pi\)
\(824\) 10.2194 0.356010
\(825\) −11.4795 −0.399666
\(826\) −18.2054 −0.633448
\(827\) −22.6651 −0.788143 −0.394071 0.919080i \(-0.628934\pi\)
−0.394071 + 0.919080i \(0.628934\pi\)
\(828\) −17.5943 −0.611445
\(829\) −28.7050 −0.996967 −0.498484 0.866899i \(-0.666110\pi\)
−0.498484 + 0.866899i \(0.666110\pi\)
\(830\) 108.579 3.76885
\(831\) −42.5593 −1.47637
\(832\) 64.4716 2.23515
\(833\) −0.303396 −0.0105120
\(834\) 99.5879 3.44845
\(835\) 1.32628 0.0458977
\(836\) 19.7135 0.681806
\(837\) 13.4561 0.465109
\(838\) −71.1939 −2.45935
\(839\) −26.8058 −0.925438 −0.462719 0.886505i \(-0.653126\pi\)
−0.462719 + 0.886505i \(0.653126\pi\)
\(840\) 5.21844 0.180053
\(841\) 5.52704 0.190587
\(842\) −64.2384 −2.21380
\(843\) −36.3820 −1.25306
\(844\) −5.48374 −0.188758
\(845\) −75.2292 −2.58796
\(846\) 4.01286 0.137965
\(847\) −9.89528 −0.340006
\(848\) −2.94966 −0.101292
\(849\) 55.3300 1.89892
\(850\) 3.36932 0.115567
\(851\) −5.58841 −0.191568
\(852\) 3.03915 0.104120
\(853\) 4.97057 0.170189 0.0850946 0.996373i \(-0.472881\pi\)
0.0850946 + 0.996373i \(0.472881\pi\)
\(854\) 2.30325 0.0788157
\(855\) 31.2567 1.06896
\(856\) −14.2690 −0.487704
\(857\) 7.34376 0.250858 0.125429 0.992103i \(-0.459969\pi\)
0.125429 + 0.992103i \(0.459969\pi\)
\(858\) −27.3125 −0.932433
\(859\) −1.00000 −0.0341196
\(860\) −23.5180 −0.801957
\(861\) −5.16448 −0.176005
\(862\) 7.96631 0.271333
\(863\) 29.9151 1.01832 0.509161 0.860671i \(-0.329956\pi\)
0.509161 + 0.860671i \(0.329956\pi\)
\(864\) −29.3268 −0.997716
\(865\) −53.3629 −1.81439
\(866\) 29.6229 1.00663
\(867\) −34.7914 −1.18158
\(868\) −8.80437 −0.298840
\(869\) −14.1823 −0.481103
\(870\) −81.2192 −2.75359
\(871\) 38.2775 1.29698
\(872\) −13.3600 −0.452426
\(873\) 14.6309 0.495182
\(874\) −98.9738 −3.34784
\(875\) −0.988335 −0.0334118
\(876\) −13.1503 −0.444307
\(877\) 42.4956 1.43498 0.717488 0.696571i \(-0.245292\pi\)
0.717488 + 0.696571i \(0.245292\pi\)
\(878\) 49.3886 1.66678
\(879\) −59.2408 −1.99814
\(880\) −10.4690 −0.352911
\(881\) 43.1741 1.45457 0.727286 0.686334i \(-0.240781\pi\)
0.727286 + 0.686334i \(0.240781\pi\)
\(882\) −2.58205 −0.0869421
\(883\) −43.4766 −1.46311 −0.731553 0.681785i \(-0.761204\pi\)
−0.731553 + 0.681785i \(0.761204\pi\)
\(884\) 4.35388 0.146437
\(885\) −57.4844 −1.93232
\(886\) −7.19367 −0.241676
\(887\) −57.5739 −1.93314 −0.966571 0.256398i \(-0.917464\pi\)
−0.966571 + 0.256398i \(0.917464\pi\)
\(888\) −1.51478 −0.0508328
\(889\) −20.9173 −0.701544
\(890\) 67.7319 2.27038
\(891\) 11.7501 0.393643
\(892\) −5.31318 −0.177898
\(893\) 12.2602 0.410273
\(894\) 64.0970 2.14372
\(895\) 23.5701 0.787862
\(896\) 6.20668 0.207351
\(897\) 74.4758 2.48667
\(898\) 39.3703 1.31380
\(899\) 21.7596 0.725722
\(900\) 15.5738 0.519127
\(901\) −0.288460 −0.00961000
\(902\) −5.51934 −0.183774
\(903\) 6.33971 0.210972
\(904\) −3.05505 −0.101609
\(905\) 22.2576 0.739867
\(906\) 64.7075 2.14976
\(907\) 14.2605 0.473511 0.236756 0.971569i \(-0.423916\pi\)
0.236756 + 0.971569i \(0.423916\pi\)
\(908\) 44.4732 1.47590
\(909\) 18.6450 0.618414
\(910\) −40.5451 −1.34406
\(911\) 40.6462 1.34667 0.673335 0.739338i \(-0.264861\pi\)
0.673335 + 0.739338i \(0.264861\pi\)
\(912\) 50.3601 1.66759
\(913\) −16.9893 −0.562264
\(914\) −39.5882 −1.30946
\(915\) 7.27262 0.240425
\(916\) −10.3240 −0.341114
\(917\) 7.96847 0.263142
\(918\) −2.30659 −0.0761290
\(919\) −53.0069 −1.74854 −0.874269 0.485443i \(-0.838658\pi\)
−0.874269 + 0.485443i \(0.838658\pi\)
\(920\) −15.2074 −0.501374
\(921\) −3.32987 −0.109723
\(922\) −1.82350 −0.0600537
\(923\) −3.74959 −0.123419
\(924\) −5.14203 −0.169160
\(925\) 4.94664 0.162645
\(926\) 7.43158 0.244217
\(927\) −15.9661 −0.524395
\(928\) −47.4238 −1.55676
\(929\) 53.4740 1.75442 0.877212 0.480103i \(-0.159401\pi\)
0.877212 + 0.480103i \(0.159401\pi\)
\(930\) −51.1858 −1.67845
\(931\) −7.88878 −0.258544
\(932\) −13.3013 −0.435699
\(933\) 31.6613 1.03654
\(934\) 1.57005 0.0513737
\(935\) −1.02381 −0.0334822
\(936\) 5.88391 0.192322
\(937\) −2.90038 −0.0947513 −0.0473756 0.998877i \(-0.515086\pi\)
−0.0473756 + 0.998877i \(0.515086\pi\)
\(938\) 13.2684 0.433230
\(939\) −66.7849 −2.17944
\(940\) 11.8632 0.386934
\(941\) −0.709175 −0.0231184 −0.0115592 0.999933i \(-0.503679\pi\)
−0.0115592 + 0.999933i \(0.503679\pi\)
\(942\) −1.60629 −0.0523356
\(943\) 15.0502 0.490100
\(944\) −26.9949 −0.878609
\(945\) 11.6662 0.379503
\(946\) 6.77533 0.220285
\(947\) 31.4146 1.02084 0.510419 0.859926i \(-0.329490\pi\)
0.510419 + 0.859926i \(0.329490\pi\)
\(948\) 66.0130 2.14400
\(949\) 16.2243 0.526663
\(950\) 87.6078 2.84237
\(951\) 9.34445 0.303014
\(952\) 0.239655 0.00776726
\(953\) 7.77814 0.251959 0.125979 0.992033i \(-0.459793\pi\)
0.125979 + 0.992033i \(0.459793\pi\)
\(954\) −2.45494 −0.0794817
\(955\) −39.2772 −1.27098
\(956\) 15.6856 0.507309
\(957\) 12.7083 0.410800
\(958\) 22.0122 0.711182
\(959\) −21.3156 −0.688316
\(960\) 70.5657 2.27750
\(961\) −17.2867 −0.557636
\(962\) 11.7692 0.379455
\(963\) 22.2929 0.718378
\(964\) −13.4883 −0.434429
\(965\) −24.1278 −0.776700
\(966\) 25.8161 0.830619
\(967\) −31.9037 −1.02595 −0.512977 0.858403i \(-0.671457\pi\)
−0.512977 + 0.858403i \(0.671457\pi\)
\(968\) 7.81637 0.251228
\(969\) 4.92493 0.158211
\(970\) 79.6381 2.55703
\(971\) −18.3994 −0.590464 −0.295232 0.955426i \(-0.595397\pi\)
−0.295232 + 0.955426i \(0.595397\pi\)
\(972\) −28.7742 −0.922932
\(973\) −23.1319 −0.741574
\(974\) 76.2294 2.44255
\(975\) −65.9231 −2.11123
\(976\) 3.41525 0.109319
\(977\) −33.6004 −1.07497 −0.537485 0.843273i \(-0.680626\pi\)
−0.537485 + 0.843273i \(0.680626\pi\)
\(978\) −51.8558 −1.65817
\(979\) −10.5979 −0.338711
\(980\) −7.63328 −0.243836
\(981\) 20.8727 0.666414
\(982\) 23.9132 0.763102
\(983\) 19.3439 0.616974 0.308487 0.951229i \(-0.400177\pi\)
0.308487 + 0.951229i \(0.400177\pi\)
\(984\) 4.07946 0.130049
\(985\) 67.0803 2.13735
\(986\) −3.72996 −0.118786
\(987\) −3.19793 −0.101791
\(988\) 113.208 3.60163
\(989\) −18.4750 −0.587470
\(990\) −8.71314 −0.276922
\(991\) 58.5652 1.86039 0.930193 0.367071i \(-0.119639\pi\)
0.930193 + 0.367071i \(0.119639\pi\)
\(992\) −29.8874 −0.948925
\(993\) 18.1390 0.575622
\(994\) −1.29975 −0.0412255
\(995\) −71.7341 −2.27413
\(996\) 79.0782 2.50569
\(997\) 29.5582 0.936117 0.468059 0.883697i \(-0.344954\pi\)
0.468059 + 0.883697i \(0.344954\pi\)
\(998\) 75.5400 2.39118
\(999\) −3.38641 −0.107141
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 \(a_p\))