Properties

Label 8011.2.a.b.1.5
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70980 q^{2}\) \(-2.88951 q^{3}\) \(+5.34304 q^{4}\) \(-1.42877 q^{5}\) \(+7.83002 q^{6}\) \(-3.83323 q^{7}\) \(-9.05899 q^{8}\) \(+5.34929 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70980 q^{2}\) \(-2.88951 q^{3}\) \(+5.34304 q^{4}\) \(-1.42877 q^{5}\) \(+7.83002 q^{6}\) \(-3.83323 q^{7}\) \(-9.05899 q^{8}\) \(+5.34929 q^{9}\) \(+3.87170 q^{10}\) \(-1.77195 q^{11}\) \(-15.4388 q^{12}\) \(-2.78462 q^{13}\) \(+10.3873 q^{14}\) \(+4.12846 q^{15}\) \(+13.8620 q^{16}\) \(+5.22233 q^{17}\) \(-14.4955 q^{18}\) \(+1.32291 q^{19}\) \(-7.63400 q^{20}\) \(+11.0762 q^{21}\) \(+4.80165 q^{22}\) \(-7.98809 q^{23}\) \(+26.1761 q^{24}\) \(-2.95860 q^{25}\) \(+7.54577 q^{26}\) \(-6.78830 q^{27}\) \(-20.4811 q^{28}\) \(+8.30704 q^{29}\) \(-11.1873 q^{30}\) \(+4.90753 q^{31}\) \(-19.4454 q^{32}\) \(+5.12008 q^{33}\) \(-14.1515 q^{34}\) \(+5.47683 q^{35}\) \(+28.5815 q^{36}\) \(+9.12496 q^{37}\) \(-3.58483 q^{38}\) \(+8.04619 q^{39}\) \(+12.9433 q^{40}\) \(+11.9978 q^{41}\) \(-30.0143 q^{42}\) \(-7.89656 q^{43}\) \(-9.46762 q^{44}\) \(-7.64293 q^{45}\) \(+21.6462 q^{46}\) \(-3.43126 q^{47}\) \(-40.0545 q^{48}\) \(+7.69368 q^{49}\) \(+8.01724 q^{50}\) \(-15.0900 q^{51}\) \(-14.8783 q^{52}\) \(+5.91825 q^{53}\) \(+18.3950 q^{54}\) \(+2.53172 q^{55}\) \(+34.7252 q^{56}\) \(-3.82256 q^{57}\) \(-22.5105 q^{58}\) \(-0.635113 q^{59}\) \(+22.0586 q^{60}\) \(-3.47084 q^{61}\) \(-13.2984 q^{62}\) \(-20.5051 q^{63}\) \(+24.9691 q^{64}\) \(+3.97859 q^{65}\) \(-13.8744 q^{66}\) \(-3.67411 q^{67}\) \(+27.9031 q^{68}\) \(+23.0817 q^{69}\) \(-14.8411 q^{70}\) \(+2.70307 q^{71}\) \(-48.4591 q^{72}\) \(-2.67837 q^{73}\) \(-24.7269 q^{74}\) \(+8.54892 q^{75}\) \(+7.06836 q^{76}\) \(+6.79231 q^{77}\) \(-21.8036 q^{78}\) \(+9.08912 q^{79}\) \(-19.8057 q^{80}\) \(+3.56701 q^{81}\) \(-32.5117 q^{82}\) \(+9.99796 q^{83}\) \(+59.1805 q^{84}\) \(-7.46154 q^{85}\) \(+21.3981 q^{86}\) \(-24.0033 q^{87}\) \(+16.0521 q^{88}\) \(-16.7217 q^{89}\) \(+20.7108 q^{90}\) \(+10.6741 q^{91}\) \(-42.6807 q^{92}\) \(-14.1804 q^{93}\) \(+9.29804 q^{94}\) \(-1.89014 q^{95}\) \(+56.1876 q^{96}\) \(+10.2160 q^{97}\) \(-20.8484 q^{98}\) \(-9.47869 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70980 −1.91612 −0.958061 0.286566i \(-0.907486\pi\)
−0.958061 + 0.286566i \(0.907486\pi\)
\(3\) −2.88951 −1.66826 −0.834131 0.551567i \(-0.814030\pi\)
−0.834131 + 0.551567i \(0.814030\pi\)
\(4\) 5.34304 2.67152
\(5\) −1.42877 −0.638967 −0.319484 0.947592i \(-0.603509\pi\)
−0.319484 + 0.947592i \(0.603509\pi\)
\(6\) 7.83002 3.19659
\(7\) −3.83323 −1.44883 −0.724413 0.689366i \(-0.757889\pi\)
−0.724413 + 0.689366i \(0.757889\pi\)
\(8\) −9.05899 −3.20284
\(9\) 5.34929 1.78310
\(10\) 3.87170 1.22434
\(11\) −1.77195 −0.534264 −0.267132 0.963660i \(-0.586076\pi\)
−0.267132 + 0.963660i \(0.586076\pi\)
\(12\) −15.4388 −4.45679
\(13\) −2.78462 −0.772314 −0.386157 0.922433i \(-0.626198\pi\)
−0.386157 + 0.922433i \(0.626198\pi\)
\(14\) 10.3873 2.77613
\(15\) 4.12846 1.06596
\(16\) 13.8620 3.46550
\(17\) 5.22233 1.26660 0.633301 0.773906i \(-0.281700\pi\)
0.633301 + 0.773906i \(0.281700\pi\)
\(18\) −14.4955 −3.41663
\(19\) 1.32291 0.303496 0.151748 0.988419i \(-0.451510\pi\)
0.151748 + 0.988419i \(0.451510\pi\)
\(20\) −7.63400 −1.70701
\(21\) 11.0762 2.41702
\(22\) 4.80165 1.02371
\(23\) −7.98809 −1.66563 −0.832816 0.553550i \(-0.813273\pi\)
−0.832816 + 0.553550i \(0.813273\pi\)
\(24\) 26.1761 5.34317
\(25\) −2.95860 −0.591721
\(26\) 7.54577 1.47985
\(27\) −6.78830 −1.30641
\(28\) −20.4811 −3.87057
\(29\) 8.30704 1.54258 0.771290 0.636484i \(-0.219612\pi\)
0.771290 + 0.636484i \(0.219612\pi\)
\(30\) −11.1873 −2.04252
\(31\) 4.90753 0.881418 0.440709 0.897650i \(-0.354727\pi\)
0.440709 + 0.897650i \(0.354727\pi\)
\(32\) −19.4454 −3.43749
\(33\) 5.12008 0.891292
\(34\) −14.1515 −2.42696
\(35\) 5.47683 0.925753
\(36\) 28.5815 4.76358
\(37\) 9.12496 1.50013 0.750067 0.661361i \(-0.230021\pi\)
0.750067 + 0.661361i \(0.230021\pi\)
\(38\) −3.58483 −0.581536
\(39\) 8.04619 1.28842
\(40\) 12.9433 2.04651
\(41\) 11.9978 1.87374 0.936871 0.349675i \(-0.113708\pi\)
0.936871 + 0.349675i \(0.113708\pi\)
\(42\) −30.0143 −4.63130
\(43\) −7.89656 −1.20421 −0.602107 0.798415i \(-0.705672\pi\)
−0.602107 + 0.798415i \(0.705672\pi\)
\(44\) −9.46762 −1.42730
\(45\) −7.64293 −1.13934
\(46\) 21.6462 3.19155
\(47\) −3.43126 −0.500501 −0.250250 0.968181i \(-0.580513\pi\)
−0.250250 + 0.968181i \(0.580513\pi\)
\(48\) −40.0545 −5.78136
\(49\) 7.69368 1.09910
\(50\) 8.01724 1.13381
\(51\) −15.0900 −2.11302
\(52\) −14.8783 −2.06325
\(53\) 5.91825 0.812934 0.406467 0.913666i \(-0.366761\pi\)
0.406467 + 0.913666i \(0.366761\pi\)
\(54\) 18.3950 2.50324
\(55\) 2.53172 0.341377
\(56\) 34.7252 4.64035
\(57\) −3.82256 −0.506311
\(58\) −22.5105 −2.95577
\(59\) −0.635113 −0.0826847 −0.0413423 0.999145i \(-0.513163\pi\)
−0.0413423 + 0.999145i \(0.513163\pi\)
\(60\) 22.0586 2.84775
\(61\) −3.47084 −0.444395 −0.222198 0.975002i \(-0.571323\pi\)
−0.222198 + 0.975002i \(0.571323\pi\)
\(62\) −13.2984 −1.68890
\(63\) −20.5051 −2.58340
\(64\) 24.9691 3.12114
\(65\) 3.97859 0.493484
\(66\) −13.8744 −1.70782
\(67\) −3.67411 −0.448863 −0.224432 0.974490i \(-0.572053\pi\)
−0.224432 + 0.974490i \(0.572053\pi\)
\(68\) 27.9031 3.38375
\(69\) 23.0817 2.77871
\(70\) −14.8411 −1.77385
\(71\) 2.70307 0.320796 0.160398 0.987052i \(-0.448722\pi\)
0.160398 + 0.987052i \(0.448722\pi\)
\(72\) −48.4591 −5.71096
\(73\) −2.67837 −0.313479 −0.156740 0.987640i \(-0.550098\pi\)
−0.156740 + 0.987640i \(0.550098\pi\)
\(74\) −24.7269 −2.87444
\(75\) 8.54892 0.987144
\(76\) 7.06836 0.810796
\(77\) 6.79231 0.774056
\(78\) −21.8036 −2.46877
\(79\) 9.08912 1.02261 0.511303 0.859400i \(-0.329163\pi\)
0.511303 + 0.859400i \(0.329163\pi\)
\(80\) −19.8057 −2.21434
\(81\) 3.56701 0.396335
\(82\) −32.5117 −3.59032
\(83\) 9.99796 1.09742 0.548709 0.836013i \(-0.315119\pi\)
0.548709 + 0.836013i \(0.315119\pi\)
\(84\) 59.1805 6.45712
\(85\) −7.46154 −0.809317
\(86\) 21.3981 2.30742
\(87\) −24.0033 −2.57342
\(88\) 16.0521 1.71116
\(89\) −16.7217 −1.77250 −0.886250 0.463207i \(-0.846699\pi\)
−0.886250 + 0.463207i \(0.846699\pi\)
\(90\) 20.7108 2.18311
\(91\) 10.6741 1.11895
\(92\) −42.6807 −4.44977
\(93\) −14.1804 −1.47044
\(94\) 9.29804 0.959020
\(95\) −1.89014 −0.193924
\(96\) 56.1876 5.73462
\(97\) 10.2160 1.03728 0.518640 0.854992i \(-0.326438\pi\)
0.518640 + 0.854992i \(0.326438\pi\)
\(98\) −20.8484 −2.10600
\(99\) −9.47869 −0.952644
\(100\) −15.8079 −1.58079
\(101\) −15.1185 −1.50434 −0.752172 0.658967i \(-0.770994\pi\)
−0.752172 + 0.658967i \(0.770994\pi\)
\(102\) 40.8909 4.04881
\(103\) 2.59956 0.256142 0.128071 0.991765i \(-0.459121\pi\)
0.128071 + 0.991765i \(0.459121\pi\)
\(104\) 25.2258 2.47360
\(105\) −15.8254 −1.54440
\(106\) −16.0373 −1.55768
\(107\) 15.3589 1.48480 0.742400 0.669956i \(-0.233687\pi\)
0.742400 + 0.669956i \(0.233687\pi\)
\(108\) −36.2701 −3.49010
\(109\) −6.72982 −0.644600 −0.322300 0.946638i \(-0.604456\pi\)
−0.322300 + 0.946638i \(0.604456\pi\)
\(110\) −6.86047 −0.654120
\(111\) −26.3667 −2.50262
\(112\) −53.1363 −5.02091
\(113\) 18.8419 1.77249 0.886247 0.463213i \(-0.153304\pi\)
0.886247 + 0.463213i \(0.153304\pi\)
\(114\) 10.3584 0.970153
\(115\) 11.4132 1.06428
\(116\) 44.3849 4.12103
\(117\) −14.8957 −1.37711
\(118\) 1.72103 0.158434
\(119\) −20.0184 −1.83509
\(120\) −37.3997 −3.41411
\(121\) −7.86018 −0.714562
\(122\) 9.40529 0.851515
\(123\) −34.6678 −3.12589
\(124\) 26.2211 2.35473
\(125\) 11.3711 1.01706
\(126\) 55.5647 4.95010
\(127\) −10.5252 −0.933961 −0.466981 0.884268i \(-0.654658\pi\)
−0.466981 + 0.884268i \(0.654658\pi\)
\(128\) −28.7707 −2.54299
\(129\) 22.8172 2.00894
\(130\) −10.7812 −0.945575
\(131\) −1.53735 −0.134319 −0.0671594 0.997742i \(-0.521394\pi\)
−0.0671594 + 0.997742i \(0.521394\pi\)
\(132\) 27.3568 2.38110
\(133\) −5.07102 −0.439713
\(134\) 9.95611 0.860077
\(135\) 9.69895 0.834752
\(136\) −47.3090 −4.05672
\(137\) 1.27855 0.109234 0.0546169 0.998507i \(-0.482606\pi\)
0.0546169 + 0.998507i \(0.482606\pi\)
\(138\) −62.5469 −5.32434
\(139\) −10.5073 −0.891217 −0.445609 0.895228i \(-0.647013\pi\)
−0.445609 + 0.895228i \(0.647013\pi\)
\(140\) 29.2629 2.47317
\(141\) 9.91467 0.834966
\(142\) −7.32480 −0.614684
\(143\) 4.93421 0.412620
\(144\) 74.1519 6.17932
\(145\) −11.8689 −0.985658
\(146\) 7.25786 0.600664
\(147\) −22.2310 −1.83358
\(148\) 48.7551 4.00764
\(149\) 10.8544 0.889229 0.444614 0.895722i \(-0.353341\pi\)
0.444614 + 0.895722i \(0.353341\pi\)
\(150\) −23.1659 −1.89149
\(151\) −8.07195 −0.656886 −0.328443 0.944524i \(-0.606524\pi\)
−0.328443 + 0.944524i \(0.606524\pi\)
\(152\) −11.9842 −0.972049
\(153\) 27.9358 2.25847
\(154\) −18.4058 −1.48318
\(155\) −7.01175 −0.563197
\(156\) 42.9911 3.44205
\(157\) 23.6772 1.88964 0.944822 0.327583i \(-0.106234\pi\)
0.944822 + 0.327583i \(0.106234\pi\)
\(158\) −24.6297 −1.95944
\(159\) −17.1009 −1.35619
\(160\) 27.7830 2.19644
\(161\) 30.6202 2.41321
\(162\) −9.66590 −0.759425
\(163\) 5.34506 0.418658 0.209329 0.977845i \(-0.432872\pi\)
0.209329 + 0.977845i \(0.432872\pi\)
\(164\) 64.1048 5.00574
\(165\) −7.31544 −0.569507
\(166\) −27.0925 −2.10279
\(167\) −4.26388 −0.329949 −0.164975 0.986298i \(-0.552754\pi\)
−0.164975 + 0.986298i \(0.552754\pi\)
\(168\) −100.339 −7.74132
\(169\) −5.24590 −0.403531
\(170\) 20.2193 1.55075
\(171\) 7.07662 0.541163
\(172\) −42.1917 −3.21708
\(173\) 10.0473 0.763881 0.381941 0.924187i \(-0.375256\pi\)
0.381941 + 0.924187i \(0.375256\pi\)
\(174\) 65.0443 4.93099
\(175\) 11.3410 0.857300
\(176\) −24.5628 −1.85149
\(177\) 1.83517 0.137940
\(178\) 45.3126 3.39633
\(179\) −18.7289 −1.39986 −0.699931 0.714210i \(-0.746786\pi\)
−0.699931 + 0.714210i \(0.746786\pi\)
\(180\) −40.8365 −3.04377
\(181\) −22.8576 −1.69899 −0.849496 0.527595i \(-0.823094\pi\)
−0.849496 + 0.527595i \(0.823094\pi\)
\(182\) −28.9247 −2.14404
\(183\) 10.0290 0.741368
\(184\) 72.3640 5.33475
\(185\) −13.0375 −0.958537
\(186\) 38.4260 2.81753
\(187\) −9.25373 −0.676700
\(188\) −18.3334 −1.33710
\(189\) 26.0211 1.89276
\(190\) 5.12191 0.371582
\(191\) 11.1641 0.807804 0.403902 0.914802i \(-0.367654\pi\)
0.403902 + 0.914802i \(0.367654\pi\)
\(192\) −72.1485 −5.20687
\(193\) 6.38782 0.459805 0.229903 0.973214i \(-0.426159\pi\)
0.229903 + 0.973214i \(0.426159\pi\)
\(194\) −27.6835 −1.98756
\(195\) −11.4962 −0.823260
\(196\) 41.1077 2.93626
\(197\) −13.1387 −0.936096 −0.468048 0.883703i \(-0.655043\pi\)
−0.468048 + 0.883703i \(0.655043\pi\)
\(198\) 25.6854 1.82538
\(199\) −7.96614 −0.564705 −0.282352 0.959311i \(-0.591115\pi\)
−0.282352 + 0.959311i \(0.591115\pi\)
\(200\) 26.8019 1.89518
\(201\) 10.6164 0.748821
\(202\) 40.9681 2.88251
\(203\) −31.8428 −2.23493
\(204\) −80.6265 −5.64498
\(205\) −17.1422 −1.19726
\(206\) −7.04429 −0.490799
\(207\) −42.7306 −2.96998
\(208\) −38.6004 −2.67646
\(209\) −2.34413 −0.162147
\(210\) 42.8837 2.95925
\(211\) −10.6888 −0.735850 −0.367925 0.929855i \(-0.619932\pi\)
−0.367925 + 0.929855i \(0.619932\pi\)
\(212\) 31.6214 2.17177
\(213\) −7.81057 −0.535171
\(214\) −41.6196 −2.84506
\(215\) 11.2824 0.769454
\(216\) 61.4951 4.18421
\(217\) −18.8117 −1.27702
\(218\) 18.2365 1.23513
\(219\) 7.73918 0.522965
\(220\) 13.5271 0.911997
\(221\) −14.5422 −0.978214
\(222\) 71.4486 4.79532
\(223\) 12.2530 0.820519 0.410260 0.911969i \(-0.365438\pi\)
0.410260 + 0.911969i \(0.365438\pi\)
\(224\) 74.5386 4.98032
\(225\) −15.8264 −1.05509
\(226\) −51.0578 −3.39631
\(227\) −1.64371 −0.109097 −0.0545484 0.998511i \(-0.517372\pi\)
−0.0545484 + 0.998511i \(0.517372\pi\)
\(228\) −20.4241 −1.35262
\(229\) 13.4902 0.891456 0.445728 0.895168i \(-0.352945\pi\)
0.445728 + 0.895168i \(0.352945\pi\)
\(230\) −30.9275 −2.03930
\(231\) −19.6265 −1.29133
\(232\) −75.2534 −4.94063
\(233\) −9.84455 −0.644938 −0.322469 0.946580i \(-0.604513\pi\)
−0.322469 + 0.946580i \(0.604513\pi\)
\(234\) 40.3645 2.63871
\(235\) 4.90250 0.319804
\(236\) −3.39344 −0.220894
\(237\) −26.2631 −1.70597
\(238\) 54.2460 3.51625
\(239\) 12.0164 0.777279 0.388640 0.921390i \(-0.372945\pi\)
0.388640 + 0.921390i \(0.372945\pi\)
\(240\) 57.2288 3.69410
\(241\) 12.1346 0.781661 0.390830 0.920463i \(-0.372188\pi\)
0.390830 + 0.920463i \(0.372188\pi\)
\(242\) 21.2996 1.36919
\(243\) 10.0580 0.645219
\(244\) −18.5448 −1.18721
\(245\) −10.9925 −0.702288
\(246\) 93.9430 5.98959
\(247\) −3.68380 −0.234394
\(248\) −44.4572 −2.82304
\(249\) −28.8892 −1.83078
\(250\) −30.8133 −1.94881
\(251\) 19.6871 1.24264 0.621318 0.783559i \(-0.286598\pi\)
0.621318 + 0.783559i \(0.286598\pi\)
\(252\) −109.559 −6.90160
\(253\) 14.1545 0.889887
\(254\) 28.5213 1.78958
\(255\) 21.5602 1.35015
\(256\) 28.0247 1.75154
\(257\) 20.9205 1.30498 0.652492 0.757796i \(-0.273724\pi\)
0.652492 + 0.757796i \(0.273724\pi\)
\(258\) −61.8302 −3.84938
\(259\) −34.9781 −2.17343
\(260\) 21.2578 1.31835
\(261\) 44.4368 2.75057
\(262\) 4.16591 0.257371
\(263\) 23.3252 1.43829 0.719147 0.694858i \(-0.244533\pi\)
0.719147 + 0.694858i \(0.244533\pi\)
\(264\) −46.3828 −2.85466
\(265\) −8.45584 −0.519438
\(266\) 13.7415 0.842544
\(267\) 48.3177 2.95699
\(268\) −19.6309 −1.19915
\(269\) 21.1677 1.29062 0.645309 0.763922i \(-0.276729\pi\)
0.645309 + 0.763922i \(0.276729\pi\)
\(270\) −26.2823 −1.59949
\(271\) −16.4478 −0.999132 −0.499566 0.866276i \(-0.666507\pi\)
−0.499566 + 0.866276i \(0.666507\pi\)
\(272\) 72.3920 4.38941
\(273\) −30.8429 −1.86670
\(274\) −3.46462 −0.209305
\(275\) 5.24251 0.316135
\(276\) 123.326 7.42338
\(277\) −9.92574 −0.596380 −0.298190 0.954507i \(-0.596383\pi\)
−0.298190 + 0.954507i \(0.596383\pi\)
\(278\) 28.4727 1.70768
\(279\) 26.2518 1.57165
\(280\) −49.6145 −2.96503
\(281\) −26.1765 −1.56156 −0.780779 0.624808i \(-0.785177\pi\)
−0.780779 + 0.624808i \(0.785177\pi\)
\(282\) −26.8668 −1.59990
\(283\) −25.3553 −1.50722 −0.753608 0.657324i \(-0.771688\pi\)
−0.753608 + 0.657324i \(0.771688\pi\)
\(284\) 14.4426 0.857013
\(285\) 5.46158 0.323516
\(286\) −13.3708 −0.790629
\(287\) −45.9904 −2.71473
\(288\) −104.019 −6.12937
\(289\) 10.2727 0.604279
\(290\) 32.1624 1.88864
\(291\) −29.5194 −1.73046
\(292\) −14.3106 −0.837466
\(293\) 4.49282 0.262474 0.131237 0.991351i \(-0.458105\pi\)
0.131237 + 0.991351i \(0.458105\pi\)
\(294\) 60.2417 3.51337
\(295\) 0.907434 0.0528328
\(296\) −82.6629 −4.80469
\(297\) 12.0285 0.697967
\(298\) −29.4134 −1.70387
\(299\) 22.2438 1.28639
\(300\) 45.6772 2.63718
\(301\) 30.2694 1.74470
\(302\) 21.8734 1.25867
\(303\) 43.6850 2.50964
\(304\) 18.3382 1.05177
\(305\) 4.95905 0.283954
\(306\) −75.7004 −4.32751
\(307\) −5.42538 −0.309643 −0.154821 0.987942i \(-0.549480\pi\)
−0.154821 + 0.987942i \(0.549480\pi\)
\(308\) 36.2916 2.06791
\(309\) −7.51146 −0.427312
\(310\) 19.0005 1.07915
\(311\) −23.7292 −1.34556 −0.672781 0.739842i \(-0.734900\pi\)
−0.672781 + 0.739842i \(0.734900\pi\)
\(312\) −72.8904 −4.12660
\(313\) −20.8533 −1.17870 −0.589349 0.807879i \(-0.700616\pi\)
−0.589349 + 0.807879i \(0.700616\pi\)
\(314\) −64.1605 −3.62079
\(315\) 29.2971 1.65071
\(316\) 48.5636 2.73191
\(317\) −28.0023 −1.57277 −0.786383 0.617739i \(-0.788049\pi\)
−0.786383 + 0.617739i \(0.788049\pi\)
\(318\) 46.3400 2.59862
\(319\) −14.7197 −0.824145
\(320\) −35.6752 −1.99431
\(321\) −44.3797 −2.47704
\(322\) −82.9748 −4.62401
\(323\) 6.90867 0.384409
\(324\) 19.0587 1.05882
\(325\) 8.23858 0.456994
\(326\) −14.4841 −0.802199
\(327\) 19.4459 1.07536
\(328\) −108.688 −6.00129
\(329\) 13.1528 0.725138
\(330\) 19.8234 1.09124
\(331\) −27.0060 −1.48438 −0.742192 0.670187i \(-0.766214\pi\)
−0.742192 + 0.670187i \(0.766214\pi\)
\(332\) 53.4195 2.93178
\(333\) 48.8121 2.67488
\(334\) 11.5543 0.632223
\(335\) 5.24947 0.286809
\(336\) 153.538 8.37619
\(337\) −0.285512 −0.0155528 −0.00777641 0.999970i \(-0.502475\pi\)
−0.00777641 + 0.999970i \(0.502475\pi\)
\(338\) 14.2154 0.773214
\(339\) −54.4438 −2.95698
\(340\) −39.8673 −2.16211
\(341\) −8.69591 −0.470910
\(342\) −19.1763 −1.03693
\(343\) −2.65905 −0.143575
\(344\) 71.5349 3.85690
\(345\) −32.9785 −1.77551
\(346\) −27.2262 −1.46369
\(347\) −12.5188 −0.672046 −0.336023 0.941854i \(-0.609082\pi\)
−0.336023 + 0.941854i \(0.609082\pi\)
\(348\) −128.251 −6.87496
\(349\) −17.1667 −0.918912 −0.459456 0.888200i \(-0.651956\pi\)
−0.459456 + 0.888200i \(0.651956\pi\)
\(350\) −30.7319 −1.64269
\(351\) 18.9028 1.00896
\(352\) 34.4563 1.83652
\(353\) −29.8553 −1.58904 −0.794520 0.607238i \(-0.792277\pi\)
−0.794520 + 0.607238i \(0.792277\pi\)
\(354\) −4.97295 −0.264309
\(355\) −3.86208 −0.204978
\(356\) −89.3449 −4.73527
\(357\) 57.8435 3.06140
\(358\) 50.7516 2.68231
\(359\) −4.71127 −0.248651 −0.124326 0.992241i \(-0.539677\pi\)
−0.124326 + 0.992241i \(0.539677\pi\)
\(360\) 69.2372 3.64912
\(361\) −17.2499 −0.907890
\(362\) 61.9396 3.25547
\(363\) 22.7121 1.19208
\(364\) 57.0321 2.98930
\(365\) 3.82679 0.200303
\(366\) −27.1767 −1.42055
\(367\) 6.67163 0.348256 0.174128 0.984723i \(-0.444289\pi\)
0.174128 + 0.984723i \(0.444289\pi\)
\(368\) −110.731 −5.77225
\(369\) 64.1797 3.34106
\(370\) 35.3291 1.83667
\(371\) −22.6860 −1.17780
\(372\) −75.7663 −3.92830
\(373\) 17.9752 0.930723 0.465362 0.885121i \(-0.345924\pi\)
0.465362 + 0.885121i \(0.345924\pi\)
\(374\) 25.0758 1.29664
\(375\) −32.8568 −1.69672
\(376\) 31.0837 1.60302
\(377\) −23.1319 −1.19136
\(378\) −70.5122 −3.62675
\(379\) −22.2881 −1.14486 −0.572432 0.819952i \(-0.694000\pi\)
−0.572432 + 0.819952i \(0.694000\pi\)
\(380\) −10.0991 −0.518073
\(381\) 30.4127 1.55809
\(382\) −30.2524 −1.54785
\(383\) −24.0199 −1.22736 −0.613680 0.789555i \(-0.710311\pi\)
−0.613680 + 0.789555i \(0.710311\pi\)
\(384\) 83.1332 4.24237
\(385\) −9.70468 −0.494596
\(386\) −17.3097 −0.881043
\(387\) −42.2410 −2.14723
\(388\) 54.5847 2.77112
\(389\) 24.3599 1.23510 0.617548 0.786533i \(-0.288126\pi\)
0.617548 + 0.786533i \(0.288126\pi\)
\(390\) 31.1524 1.57747
\(391\) −41.7165 −2.10969
\(392\) −69.6970 −3.52023
\(393\) 4.44219 0.224079
\(394\) 35.6034 1.79367
\(395\) −12.9863 −0.653412
\(396\) −50.6450 −2.54501
\(397\) −18.6209 −0.934558 −0.467279 0.884110i \(-0.654766\pi\)
−0.467279 + 0.884110i \(0.654766\pi\)
\(398\) 21.5867 1.08204
\(399\) 14.6528 0.733557
\(400\) −41.0122 −2.05061
\(401\) −15.9682 −0.797413 −0.398706 0.917079i \(-0.630541\pi\)
−0.398706 + 0.917079i \(0.630541\pi\)
\(402\) −28.7683 −1.43483
\(403\) −13.6656 −0.680732
\(404\) −80.7786 −4.01889
\(405\) −5.09646 −0.253245
\(406\) 86.2879 4.28239
\(407\) −16.1690 −0.801468
\(408\) 136.700 6.76766
\(409\) 4.77904 0.236308 0.118154 0.992995i \(-0.462302\pi\)
0.118154 + 0.992995i \(0.462302\pi\)
\(410\) 46.4519 2.29410
\(411\) −3.69438 −0.182230
\(412\) 13.8895 0.684289
\(413\) 2.43454 0.119796
\(414\) 115.792 5.69084
\(415\) −14.2848 −0.701215
\(416\) 54.1479 2.65482
\(417\) 30.3610 1.48678
\(418\) 6.35214 0.310694
\(419\) 16.1191 0.787468 0.393734 0.919224i \(-0.371183\pi\)
0.393734 + 0.919224i \(0.371183\pi\)
\(420\) −84.5556 −4.12589
\(421\) 1.45900 0.0711072 0.0355536 0.999368i \(-0.488681\pi\)
0.0355536 + 0.999368i \(0.488681\pi\)
\(422\) 28.9647 1.40998
\(423\) −18.3548 −0.892440
\(424\) −53.6133 −2.60369
\(425\) −15.4508 −0.749474
\(426\) 21.1651 1.02545
\(427\) 13.3045 0.643852
\(428\) 82.0632 3.96668
\(429\) −14.2575 −0.688357
\(430\) −30.5731 −1.47437
\(431\) −15.2265 −0.733433 −0.366717 0.930333i \(-0.619518\pi\)
−0.366717 + 0.930333i \(0.619518\pi\)
\(432\) −94.0994 −4.52736
\(433\) −25.2105 −1.21154 −0.605769 0.795641i \(-0.707134\pi\)
−0.605769 + 0.795641i \(0.707134\pi\)
\(434\) 50.9760 2.44693
\(435\) 34.2953 1.64433
\(436\) −35.9577 −1.72206
\(437\) −10.5675 −0.505513
\(438\) −20.9717 −1.00207
\(439\) −13.0209 −0.621455 −0.310727 0.950499i \(-0.600573\pi\)
−0.310727 + 0.950499i \(0.600573\pi\)
\(440\) −22.9348 −1.09338
\(441\) 41.1557 1.95980
\(442\) 39.4065 1.87438
\(443\) 8.69065 0.412905 0.206453 0.978457i \(-0.433808\pi\)
0.206453 + 0.978457i \(0.433808\pi\)
\(444\) −140.878 −6.68579
\(445\) 23.8916 1.13257
\(446\) −33.2031 −1.57221
\(447\) −31.3640 −1.48347
\(448\) −95.7124 −4.52199
\(449\) −6.14292 −0.289902 −0.144951 0.989439i \(-0.546303\pi\)
−0.144951 + 0.989439i \(0.546303\pi\)
\(450\) 42.8865 2.02169
\(451\) −21.2595 −1.00107
\(452\) 100.673 4.73525
\(453\) 23.3240 1.09586
\(454\) 4.45413 0.209043
\(455\) −15.2509 −0.714972
\(456\) 34.6286 1.62163
\(457\) −5.64994 −0.264293 −0.132147 0.991230i \(-0.542187\pi\)
−0.132147 + 0.991230i \(0.542187\pi\)
\(458\) −36.5558 −1.70814
\(459\) −35.4507 −1.65470
\(460\) 60.9811 2.84326
\(461\) −34.9341 −1.62704 −0.813522 0.581534i \(-0.802453\pi\)
−0.813522 + 0.581534i \(0.802453\pi\)
\(462\) 53.1839 2.47434
\(463\) −5.10015 −0.237024 −0.118512 0.992953i \(-0.537812\pi\)
−0.118512 + 0.992953i \(0.537812\pi\)
\(464\) 115.152 5.34581
\(465\) 20.2605 0.939560
\(466\) 26.6768 1.23578
\(467\) 18.7010 0.865380 0.432690 0.901543i \(-0.357565\pi\)
0.432690 + 0.901543i \(0.357565\pi\)
\(468\) −79.5885 −3.67898
\(469\) 14.0837 0.650325
\(470\) −13.2848 −0.612782
\(471\) −68.4155 −3.15242
\(472\) 5.75348 0.264826
\(473\) 13.9923 0.643369
\(474\) 71.1680 3.26885
\(475\) −3.91396 −0.179585
\(476\) −106.959 −4.90247
\(477\) 31.6584 1.44954
\(478\) −32.5622 −1.48936
\(479\) 32.1391 1.46847 0.734237 0.678894i \(-0.237540\pi\)
0.734237 + 0.678894i \(0.237540\pi\)
\(480\) −80.2794 −3.66424
\(481\) −25.4095 −1.15858
\(482\) −32.8825 −1.49776
\(483\) −88.4775 −4.02587
\(484\) −41.9973 −1.90897
\(485\) −14.5964 −0.662789
\(486\) −27.2551 −1.23632
\(487\) −35.7644 −1.62064 −0.810320 0.585988i \(-0.800706\pi\)
−0.810320 + 0.585988i \(0.800706\pi\)
\(488\) 31.4423 1.42333
\(489\) −15.4446 −0.698430
\(490\) 29.7876 1.34567
\(491\) 26.6334 1.20195 0.600973 0.799269i \(-0.294780\pi\)
0.600973 + 0.799269i \(0.294780\pi\)
\(492\) −185.232 −8.35088
\(493\) 43.3821 1.95383
\(494\) 9.98237 0.449128
\(495\) 13.5429 0.608708
\(496\) 68.0282 3.05456
\(497\) −10.3615 −0.464777
\(498\) 78.2842 3.50800
\(499\) −11.7764 −0.527183 −0.263592 0.964634i \(-0.584907\pi\)
−0.263592 + 0.964634i \(0.584907\pi\)
\(500\) 60.7560 2.71709
\(501\) 12.3205 0.550441
\(502\) −53.3481 −2.38104
\(503\) 7.25854 0.323642 0.161821 0.986820i \(-0.448263\pi\)
0.161821 + 0.986820i \(0.448263\pi\)
\(504\) 185.755 8.27419
\(505\) 21.6009 0.961227
\(506\) −38.3560 −1.70513
\(507\) 15.1581 0.673195
\(508\) −56.2366 −2.49510
\(509\) 30.6817 1.35994 0.679971 0.733239i \(-0.261992\pi\)
0.679971 + 0.733239i \(0.261992\pi\)
\(510\) −58.4239 −2.58706
\(511\) 10.2668 0.454177
\(512\) −18.4001 −0.813177
\(513\) −8.98030 −0.396490
\(514\) −56.6904 −2.50051
\(515\) −3.71418 −0.163666
\(516\) 121.913 5.36694
\(517\) 6.08003 0.267399
\(518\) 94.7839 4.16456
\(519\) −29.0318 −1.27435
\(520\) −36.0420 −1.58055
\(521\) 0.510460 0.0223636 0.0111818 0.999937i \(-0.496441\pi\)
0.0111818 + 0.999937i \(0.496441\pi\)
\(522\) −120.415 −5.27042
\(523\) 27.1358 1.18657 0.593283 0.804994i \(-0.297832\pi\)
0.593283 + 0.804994i \(0.297832\pi\)
\(524\) −8.21411 −0.358835
\(525\) −32.7700 −1.43020
\(526\) −63.2068 −2.75595
\(527\) 25.6287 1.11641
\(528\) 70.9746 3.08877
\(529\) 40.8096 1.77433
\(530\) 22.9137 0.995307
\(531\) −3.39740 −0.147435
\(532\) −27.0947 −1.17470
\(533\) −33.4093 −1.44712
\(534\) −130.931 −5.66596
\(535\) −21.9444 −0.948739
\(536\) 33.2837 1.43764
\(537\) 54.1174 2.33534
\(538\) −57.3603 −2.47298
\(539\) −13.6328 −0.587208
\(540\) 51.8219 2.23006
\(541\) 41.8205 1.79800 0.899002 0.437945i \(-0.144294\pi\)
0.899002 + 0.437945i \(0.144294\pi\)
\(542\) 44.5703 1.91446
\(543\) 66.0473 2.83436
\(544\) −101.550 −4.35392
\(545\) 9.61540 0.411878
\(546\) 83.5783 3.57682
\(547\) −13.6772 −0.584797 −0.292398 0.956297i \(-0.594453\pi\)
−0.292398 + 0.956297i \(0.594453\pi\)
\(548\) 6.83134 0.291820
\(549\) −18.5665 −0.792399
\(550\) −14.2062 −0.605753
\(551\) 10.9895 0.468167
\(552\) −209.097 −8.89975
\(553\) −34.8407 −1.48158
\(554\) 26.8968 1.14274
\(555\) 37.6721 1.59909
\(556\) −56.1409 −2.38091
\(557\) −43.6478 −1.84942 −0.924709 0.380675i \(-0.875692\pi\)
−0.924709 + 0.380675i \(0.875692\pi\)
\(558\) −71.1372 −3.01148
\(559\) 21.9889 0.930032
\(560\) 75.9198 3.20820
\(561\) 26.7388 1.12891
\(562\) 70.9331 2.99213
\(563\) 33.9721 1.43175 0.715876 0.698227i \(-0.246027\pi\)
0.715876 + 0.698227i \(0.246027\pi\)
\(564\) 52.9745 2.23063
\(565\) −26.9208 −1.13257
\(566\) 68.7079 2.88801
\(567\) −13.6732 −0.574220
\(568\) −24.4871 −1.02746
\(569\) 3.86187 0.161898 0.0809491 0.996718i \(-0.474205\pi\)
0.0809491 + 0.996718i \(0.474205\pi\)
\(570\) −14.7998 −0.619896
\(571\) −18.2804 −0.765010 −0.382505 0.923954i \(-0.624938\pi\)
−0.382505 + 0.923954i \(0.624938\pi\)
\(572\) 26.3637 1.10232
\(573\) −32.2587 −1.34763
\(574\) 124.625 5.20175
\(575\) 23.6336 0.985589
\(576\) 133.567 5.56529
\(577\) −23.1337 −0.963069 −0.481534 0.876427i \(-0.659920\pi\)
−0.481534 + 0.876427i \(0.659920\pi\)
\(578\) −27.8371 −1.15787
\(579\) −18.4577 −0.767075
\(580\) −63.4160 −2.63321
\(581\) −38.3245 −1.58997
\(582\) 79.9917 3.31576
\(583\) −10.4869 −0.434321
\(584\) 24.2633 1.00402
\(585\) 21.2826 0.879929
\(586\) −12.1747 −0.502931
\(587\) 28.5251 1.17736 0.588679 0.808367i \(-0.299648\pi\)
0.588679 + 0.808367i \(0.299648\pi\)
\(588\) −118.781 −4.89845
\(589\) 6.49221 0.267507
\(590\) −2.45897 −0.101234
\(591\) 37.9646 1.56165
\(592\) 126.490 5.19872
\(593\) −36.8277 −1.51233 −0.756166 0.654380i \(-0.772930\pi\)
−0.756166 + 0.654380i \(0.772930\pi\)
\(594\) −32.5950 −1.33739
\(595\) 28.6018 1.17256
\(596\) 57.9956 2.37559
\(597\) 23.0183 0.942075
\(598\) −60.2763 −2.46488
\(599\) −29.1279 −1.19013 −0.595067 0.803676i \(-0.702874\pi\)
−0.595067 + 0.803676i \(0.702874\pi\)
\(600\) −77.4446 −3.16166
\(601\) 35.4979 1.44799 0.723994 0.689806i \(-0.242304\pi\)
0.723994 + 0.689806i \(0.242304\pi\)
\(602\) −82.0241 −3.34305
\(603\) −19.6538 −0.800366
\(604\) −43.1288 −1.75489
\(605\) 11.2304 0.456582
\(606\) −118.378 −4.80877
\(607\) 41.2155 1.67288 0.836442 0.548056i \(-0.184632\pi\)
0.836442 + 0.548056i \(0.184632\pi\)
\(608\) −25.7244 −1.04326
\(609\) 92.0103 3.72845
\(610\) −13.4380 −0.544091
\(611\) 9.55475 0.386544
\(612\) 149.262 6.03355
\(613\) 32.0359 1.29392 0.646960 0.762524i \(-0.276040\pi\)
0.646960 + 0.762524i \(0.276040\pi\)
\(614\) 14.7017 0.593313
\(615\) 49.5325 1.99734
\(616\) −61.5315 −2.47917
\(617\) 18.5640 0.747358 0.373679 0.927558i \(-0.378096\pi\)
0.373679 + 0.927558i \(0.378096\pi\)
\(618\) 20.3546 0.818781
\(619\) 13.1283 0.527672 0.263836 0.964568i \(-0.415012\pi\)
0.263836 + 0.964568i \(0.415012\pi\)
\(620\) −37.4641 −1.50459
\(621\) 54.2255 2.17600
\(622\) 64.3016 2.57826
\(623\) 64.0983 2.56804
\(624\) 111.536 4.46503
\(625\) −1.45366 −0.0581463
\(626\) 56.5083 2.25853
\(627\) 6.77341 0.270504
\(628\) 126.508 5.04822
\(629\) 47.6536 1.90007
\(630\) −79.3895 −3.16295
\(631\) −0.843975 −0.0335981 −0.0167991 0.999859i \(-0.505348\pi\)
−0.0167991 + 0.999859i \(0.505348\pi\)
\(632\) −82.3382 −3.27524
\(633\) 30.8856 1.22759
\(634\) 75.8808 3.01361
\(635\) 15.0382 0.596771
\(636\) −91.3706 −3.62308
\(637\) −21.4240 −0.848849
\(638\) 39.8875 1.57916
\(639\) 14.4595 0.572010
\(640\) 41.1068 1.62489
\(641\) 1.83299 0.0723989 0.0361995 0.999345i \(-0.488475\pi\)
0.0361995 + 0.999345i \(0.488475\pi\)
\(642\) 120.260 4.74630
\(643\) 11.8871 0.468780 0.234390 0.972143i \(-0.424691\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(644\) 163.605 6.44694
\(645\) −32.6007 −1.28365
\(646\) −18.7212 −0.736574
\(647\) 9.15698 0.359998 0.179999 0.983667i \(-0.442391\pi\)
0.179999 + 0.983667i \(0.442391\pi\)
\(648\) −32.3135 −1.26939
\(649\) 1.12539 0.0441755
\(650\) −22.3249 −0.875656
\(651\) 54.3567 2.13041
\(652\) 28.5589 1.11845
\(653\) 8.93522 0.349662 0.174831 0.984598i \(-0.444062\pi\)
0.174831 + 0.984598i \(0.444062\pi\)
\(654\) −52.6946 −2.06052
\(655\) 2.19652 0.0858253
\(656\) 166.314 6.49346
\(657\) −14.3274 −0.558964
\(658\) −35.6416 −1.38945
\(659\) 49.3492 1.92237 0.961185 0.275904i \(-0.0889773\pi\)
0.961185 + 0.275904i \(0.0889773\pi\)
\(660\) −39.0867 −1.52145
\(661\) −35.6402 −1.38624 −0.693121 0.720821i \(-0.743765\pi\)
−0.693121 + 0.720821i \(0.743765\pi\)
\(662\) 73.1810 2.84426
\(663\) 42.0199 1.63192
\(664\) −90.5714 −3.51485
\(665\) 7.24535 0.280963
\(666\) −132.271 −5.12540
\(667\) −66.3574 −2.56937
\(668\) −22.7821 −0.881466
\(669\) −35.4051 −1.36884
\(670\) −14.2250 −0.549561
\(671\) 6.15016 0.237424
\(672\) −215.380 −8.30847
\(673\) 36.8833 1.42175 0.710873 0.703320i \(-0.248300\pi\)
0.710873 + 0.703320i \(0.248300\pi\)
\(674\) 0.773682 0.0298011
\(675\) 20.0839 0.773029
\(676\) −28.0291 −1.07804
\(677\) −22.7248 −0.873386 −0.436693 0.899611i \(-0.643850\pi\)
−0.436693 + 0.899611i \(0.643850\pi\)
\(678\) 147.532 5.66594
\(679\) −39.1604 −1.50284
\(680\) 67.5940 2.59211
\(681\) 4.74952 0.182002
\(682\) 23.5642 0.902320
\(683\) 27.6502 1.05801 0.529003 0.848620i \(-0.322566\pi\)
0.529003 + 0.848620i \(0.322566\pi\)
\(684\) 37.8107 1.44573
\(685\) −1.82676 −0.0697968
\(686\) 7.20550 0.275107
\(687\) −38.9801 −1.48718
\(688\) −109.462 −4.17321
\(689\) −16.4801 −0.627840
\(690\) 89.3654 3.40208
\(691\) 37.6609 1.43269 0.716344 0.697747i \(-0.245814\pi\)
0.716344 + 0.697747i \(0.245814\pi\)
\(692\) 53.6831 2.04072
\(693\) 36.3340 1.38022
\(694\) 33.9236 1.28772
\(695\) 15.0126 0.569459
\(696\) 217.446 8.24226
\(697\) 62.6565 2.37328
\(698\) 46.5184 1.76075
\(699\) 28.4460 1.07592
\(700\) 60.5955 2.29030
\(701\) 22.1947 0.838281 0.419141 0.907921i \(-0.362331\pi\)
0.419141 + 0.907921i \(0.362331\pi\)
\(702\) −51.2229 −1.93329
\(703\) 12.0715 0.455285
\(704\) −44.2441 −1.66751
\(705\) −14.1658 −0.533516
\(706\) 80.9022 3.04479
\(707\) 57.9526 2.17953
\(708\) 9.80538 0.368509
\(709\) 30.7035 1.15309 0.576547 0.817064i \(-0.304400\pi\)
0.576547 + 0.817064i \(0.304400\pi\)
\(710\) 10.4655 0.392763
\(711\) 48.6203 1.82340
\(712\) 151.482 5.67703
\(713\) −39.2018 −1.46812
\(714\) −156.745 −5.86602
\(715\) −7.04988 −0.263651
\(716\) −100.069 −3.73976
\(717\) −34.7217 −1.29670
\(718\) 12.7666 0.476446
\(719\) 3.56573 0.132979 0.0664897 0.997787i \(-0.478820\pi\)
0.0664897 + 0.997787i \(0.478820\pi\)
\(720\) −105.946 −3.94839
\(721\) −9.96471 −0.371105
\(722\) 46.7439 1.73963
\(723\) −35.0632 −1.30401
\(724\) −122.129 −4.53889
\(725\) −24.5772 −0.912776
\(726\) −61.5454 −2.28416
\(727\) 28.7650 1.06683 0.533417 0.845852i \(-0.320908\pi\)
0.533417 + 0.845852i \(0.320908\pi\)
\(728\) −96.6965 −3.58381
\(729\) −39.7637 −1.47273
\(730\) −10.3698 −0.383805
\(731\) −41.2385 −1.52526
\(732\) 53.5855 1.98058
\(733\) −13.3095 −0.491596 −0.245798 0.969321i \(-0.579050\pi\)
−0.245798 + 0.969321i \(0.579050\pi\)
\(734\) −18.0788 −0.667301
\(735\) 31.7631 1.17160
\(736\) 155.331 5.72559
\(737\) 6.51034 0.239812
\(738\) −173.914 −6.40188
\(739\) −19.2829 −0.709333 −0.354666 0.934993i \(-0.615406\pi\)
−0.354666 + 0.934993i \(0.615406\pi\)
\(740\) −69.6600 −2.56075
\(741\) 10.6444 0.391031
\(742\) 61.4747 2.25681
\(743\) −2.19734 −0.0806124 −0.0403062 0.999187i \(-0.512833\pi\)
−0.0403062 + 0.999187i \(0.512833\pi\)
\(744\) 128.460 4.70956
\(745\) −15.5085 −0.568188
\(746\) −48.7094 −1.78338
\(747\) 53.4820 1.95680
\(748\) −49.4430 −1.80782
\(749\) −58.8743 −2.15122
\(750\) 89.0355 3.25112
\(751\) 49.0429 1.78960 0.894800 0.446468i \(-0.147318\pi\)
0.894800 + 0.446468i \(0.147318\pi\)
\(752\) −47.5641 −1.73449
\(753\) −56.8860 −2.07304
\(754\) 62.6830 2.28278
\(755\) 11.5330 0.419729
\(756\) 139.032 5.05654
\(757\) 8.64068 0.314051 0.157025 0.987595i \(-0.449810\pi\)
0.157025 + 0.987595i \(0.449810\pi\)
\(758\) 60.3965 2.19370
\(759\) −40.8997 −1.48456
\(760\) 17.1228 0.621108
\(761\) 31.4275 1.13924 0.569622 0.821906i \(-0.307089\pi\)
0.569622 + 0.821906i \(0.307089\pi\)
\(762\) −82.4126 −2.98549
\(763\) 25.7970 0.933913
\(764\) 59.6501 2.15806
\(765\) −39.9139 −1.44309
\(766\) 65.0892 2.35177
\(767\) 1.76855 0.0638586
\(768\) −80.9777 −2.92203
\(769\) −0.0262640 −0.000947103 0 −0.000473551 1.00000i \(-0.500151\pi\)
−0.000473551 1.00000i \(0.500151\pi\)
\(770\) 26.2978 0.947707
\(771\) −60.4500 −2.17705
\(772\) 34.1304 1.22838
\(773\) −38.3693 −1.38005 −0.690023 0.723787i \(-0.742400\pi\)
−0.690023 + 0.723787i \(0.742400\pi\)
\(774\) 114.465 4.11435
\(775\) −14.5194 −0.521553
\(776\) −92.5469 −3.32224
\(777\) 101.070 3.62586
\(778\) −66.0106 −2.36660
\(779\) 15.8720 0.568674
\(780\) −61.4247 −2.19936
\(781\) −4.78972 −0.171390
\(782\) 113.043 4.04243
\(783\) −56.3907 −2.01524
\(784\) 106.650 3.80892
\(785\) −33.8294 −1.20742
\(786\) −12.0375 −0.429362
\(787\) −48.5157 −1.72940 −0.864699 0.502290i \(-0.832491\pi\)
−0.864699 + 0.502290i \(0.832491\pi\)
\(788\) −70.2008 −2.50080
\(789\) −67.3985 −2.39945
\(790\) 35.1904 1.25202
\(791\) −72.2253 −2.56804
\(792\) 85.8673 3.05116
\(793\) 9.66496 0.343213
\(794\) 50.4591 1.79073
\(795\) 24.4333 0.866559
\(796\) −42.5634 −1.50862
\(797\) 16.5500 0.586231 0.293116 0.956077i \(-0.405308\pi\)
0.293116 + 0.956077i \(0.405308\pi\)
\(798\) −39.7062 −1.40558
\(799\) −17.9192 −0.633935
\(800\) 57.5311 2.03403
\(801\) −89.4494 −3.16054
\(802\) 43.2706 1.52794
\(803\) 4.74594 0.167481
\(804\) 56.7237 2.00049
\(805\) −43.7494 −1.54196
\(806\) 37.0311 1.30436
\(807\) −61.1643 −2.15309
\(808\) 136.958 4.81817
\(809\) 22.4985 0.791005 0.395502 0.918465i \(-0.370570\pi\)
0.395502 + 0.918465i \(0.370570\pi\)
\(810\) 13.8104 0.485248
\(811\) −21.7528 −0.763843 −0.381921 0.924195i \(-0.624737\pi\)
−0.381921 + 0.924195i \(0.624737\pi\)
\(812\) −170.138 −5.97066
\(813\) 47.5261 1.66681
\(814\) 43.8149 1.53571
\(815\) −7.63689 −0.267509
\(816\) −209.178 −7.32268
\(817\) −10.4464 −0.365475
\(818\) −12.9503 −0.452795
\(819\) 57.0988 1.99519
\(820\) −91.5913 −3.19851
\(821\) −11.4291 −0.398878 −0.199439 0.979910i \(-0.563912\pi\)
−0.199439 + 0.979910i \(0.563912\pi\)
\(822\) 10.0111 0.349176
\(823\) 10.0768 0.351257 0.175628 0.984457i \(-0.443804\pi\)
0.175628 + 0.984457i \(0.443804\pi\)
\(824\) −23.5494 −0.820381
\(825\) −15.1483 −0.527396
\(826\) −6.59712 −0.229543
\(827\) 5.79378 0.201470 0.100735 0.994913i \(-0.467881\pi\)
0.100735 + 0.994913i \(0.467881\pi\)
\(828\) −228.311 −7.93437
\(829\) 8.17338 0.283873 0.141937 0.989876i \(-0.454667\pi\)
0.141937 + 0.989876i \(0.454667\pi\)
\(830\) 38.7091 1.34361
\(831\) 28.6806 0.994918
\(832\) −69.5294 −2.41050
\(833\) 40.1790 1.39212
\(834\) −82.2723 −2.84886
\(835\) 6.09213 0.210827
\(836\) −12.5248 −0.433179
\(837\) −33.3138 −1.15149
\(838\) −43.6795 −1.50888
\(839\) −31.7323 −1.09552 −0.547760 0.836635i \(-0.684519\pi\)
−0.547760 + 0.836635i \(0.684519\pi\)
\(840\) 143.362 4.94645
\(841\) 40.0070 1.37955
\(842\) −3.95360 −0.136250
\(843\) 75.6373 2.60509
\(844\) −57.1109 −1.96584
\(845\) 7.49521 0.257843
\(846\) 49.7379 1.71002
\(847\) 30.1299 1.03528
\(848\) 82.0388 2.81722
\(849\) 73.2644 2.51443
\(850\) 41.8687 1.43608
\(851\) −72.8910 −2.49867
\(852\) −41.7322 −1.42972
\(853\) −38.3474 −1.31299 −0.656496 0.754330i \(-0.727962\pi\)
−0.656496 + 0.754330i \(0.727962\pi\)
\(854\) −36.0527 −1.23370
\(855\) −10.1109 −0.345785
\(856\) −139.136 −4.75557
\(857\) −48.0678 −1.64196 −0.820982 0.570954i \(-0.806574\pi\)
−0.820982 + 0.570954i \(0.806574\pi\)
\(858\) 38.6350 1.31898
\(859\) 40.6676 1.38756 0.693780 0.720187i \(-0.255944\pi\)
0.693780 + 0.720187i \(0.255944\pi\)
\(860\) 60.2824 2.05561
\(861\) 132.890 4.52887
\(862\) 41.2607 1.40535
\(863\) −23.9701 −0.815953 −0.407977 0.912992i \(-0.633766\pi\)
−0.407977 + 0.912992i \(0.633766\pi\)
\(864\) 132.001 4.49076
\(865\) −14.3553 −0.488095
\(866\) 68.3155 2.32145
\(867\) −29.6832 −1.00810
\(868\) −100.512 −3.41159
\(869\) −16.1055 −0.546342
\(870\) −92.9336 −3.15074
\(871\) 10.2310 0.346664
\(872\) 60.9654 2.06455
\(873\) 54.6485 1.84957
\(874\) 28.6359 0.968624
\(875\) −43.5879 −1.47354
\(876\) 41.3508 1.39711
\(877\) 14.0601 0.474777 0.237388 0.971415i \(-0.423709\pi\)
0.237388 + 0.971415i \(0.423709\pi\)
\(878\) 35.2842 1.19078
\(879\) −12.9821 −0.437875
\(880\) 35.0948 1.18304
\(881\) −26.0723 −0.878398 −0.439199 0.898390i \(-0.644738\pi\)
−0.439199 + 0.898390i \(0.644738\pi\)
\(882\) −111.524 −3.75521
\(883\) −11.0266 −0.371074 −0.185537 0.982637i \(-0.559402\pi\)
−0.185537 + 0.982637i \(0.559402\pi\)
\(884\) −77.6996 −2.61332
\(885\) −2.62204 −0.0881390
\(886\) −23.5500 −0.791177
\(887\) 13.2068 0.443440 0.221720 0.975110i \(-0.428833\pi\)
0.221720 + 0.975110i \(0.428833\pi\)
\(888\) 238.856 8.01547
\(889\) 40.3456 1.35315
\(890\) −64.7415 −2.17014
\(891\) −6.32058 −0.211747
\(892\) 65.4681 2.19203
\(893\) −4.53925 −0.151900
\(894\) 84.9903 2.84250
\(895\) 26.7594 0.894467
\(896\) 110.285 3.68435
\(897\) −64.2737 −2.14604
\(898\) 16.6461 0.555488
\(899\) 40.7670 1.35966
\(900\) −84.5612 −2.81871
\(901\) 30.9070 1.02966
\(902\) 57.6092 1.91818
\(903\) −87.4638 −2.91061
\(904\) −170.688 −5.67701
\(905\) 32.6584 1.08560
\(906\) −63.2035 −2.09980
\(907\) 9.09509 0.301998 0.150999 0.988534i \(-0.451751\pi\)
0.150999 + 0.988534i \(0.451751\pi\)
\(908\) −8.78241 −0.291454
\(909\) −80.8730 −2.68239
\(910\) 41.3269 1.36997
\(911\) 44.2686 1.46668 0.733342 0.679859i \(-0.237959\pi\)
0.733342 + 0.679859i \(0.237959\pi\)
\(912\) −52.9884 −1.75462
\(913\) −17.7159 −0.586311
\(914\) 15.3102 0.506418
\(915\) −14.3292 −0.473710
\(916\) 72.0786 2.38154
\(917\) 5.89302 0.194605
\(918\) 96.0646 3.17060
\(919\) 53.1699 1.75391 0.876957 0.480569i \(-0.159570\pi\)
0.876957 + 0.480569i \(0.159570\pi\)
\(920\) −103.392 −3.40873
\(921\) 15.6767 0.516565
\(922\) 94.6646 3.11761
\(923\) −7.52703 −0.247755
\(924\) −104.865 −3.44981
\(925\) −26.9971 −0.887661
\(926\) 13.8204 0.454166
\(927\) 13.9058 0.456726
\(928\) −161.533 −5.30259
\(929\) −17.3158 −0.568112 −0.284056 0.958808i \(-0.591680\pi\)
−0.284056 + 0.958808i \(0.591680\pi\)
\(930\) −54.9021 −1.80031
\(931\) 10.1780 0.333572
\(932\) −52.5998 −1.72296
\(933\) 68.5659 2.24475
\(934\) −50.6761 −1.65817
\(935\) 13.2215 0.432389
\(936\) 134.940 4.41066
\(937\) −27.4506 −0.896771 −0.448386 0.893840i \(-0.648001\pi\)
−0.448386 + 0.893840i \(0.648001\pi\)
\(938\) −38.1641 −1.24610
\(939\) 60.2558 1.96637
\(940\) 26.1942 0.854362
\(941\) 15.1633 0.494310 0.247155 0.968976i \(-0.420504\pi\)
0.247155 + 0.968976i \(0.420504\pi\)
\(942\) 185.393 6.04042
\(943\) −95.8395 −3.12096
\(944\) −8.80394 −0.286544
\(945\) −37.1783 −1.20941
\(946\) −37.9165 −1.23277
\(947\) 23.2061 0.754098 0.377049 0.926193i \(-0.376939\pi\)
0.377049 + 0.926193i \(0.376939\pi\)
\(948\) −140.325 −4.55755
\(949\) 7.45823 0.242105
\(950\) 10.6061 0.344107
\(951\) 80.9130 2.62378
\(952\) 181.347 5.87748
\(953\) 20.3035 0.657695 0.328847 0.944383i \(-0.393340\pi\)
0.328847 + 0.944383i \(0.393340\pi\)
\(954\) −85.7881 −2.77749
\(955\) −15.9509 −0.516160
\(956\) 64.2044 2.07652
\(957\) 42.5327 1.37489
\(958\) −87.0907 −2.81377
\(959\) −4.90098 −0.158261
\(960\) 103.084 3.32702
\(961\) −6.91617 −0.223102
\(962\) 68.8549 2.21997
\(963\) 82.1592 2.64754
\(964\) 64.8359 2.08822
\(965\) −9.12676 −0.293801
\(966\) 239.757 7.71405
\(967\) 21.7092 0.698121 0.349061 0.937100i \(-0.386501\pi\)
0.349061 + 0.937100i \(0.386501\pi\)
\(968\) 71.2053 2.28862
\(969\) −19.9627 −0.641294
\(970\) 39.5534 1.26998
\(971\) −2.33267 −0.0748590 −0.0374295 0.999299i \(-0.511917\pi\)
−0.0374295 + 0.999299i \(0.511917\pi\)
\(972\) 53.7401 1.72371
\(973\) 40.2769 1.29122
\(974\) 96.9145 3.10534
\(975\) −23.8055 −0.762386
\(976\) −48.1128 −1.54005
\(977\) 45.6936 1.46187 0.730933 0.682449i \(-0.239085\pi\)
0.730933 + 0.682449i \(0.239085\pi\)
\(978\) 41.8519 1.33828
\(979\) 29.6301 0.946983
\(980\) −58.7336 −1.87618
\(981\) −35.9997 −1.14938
\(982\) −72.1712 −2.30307
\(983\) −15.4750 −0.493574 −0.246787 0.969070i \(-0.579375\pi\)
−0.246787 + 0.969070i \(0.579375\pi\)
\(984\) 314.055 10.0117
\(985\) 18.7723 0.598135
\(986\) −117.557 −3.74378
\(987\) −38.0052 −1.20972
\(988\) −19.6827 −0.626190
\(989\) 63.0785 2.00578
\(990\) −36.6986 −1.16636
\(991\) 37.3148 1.18534 0.592672 0.805444i \(-0.298073\pi\)
0.592672 + 0.805444i \(0.298073\pi\)
\(992\) −95.4286 −3.02986
\(993\) 78.0342 2.47634
\(994\) 28.0777 0.890570
\(995\) 11.3818 0.360828
\(996\) −154.356 −4.89097
\(997\) −21.0858 −0.667792 −0.333896 0.942610i \(-0.608364\pi\)
−0.333896 + 0.942610i \(0.608364\pi\)
\(998\) 31.9117 1.01015
\(999\) −61.9430 −1.95979
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 \(a_p\))