Properties

Label 8013.2.a.d.1.5
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62323 q^{2}\) \(+1.00000 q^{3}\) \(+4.88134 q^{4}\) \(-3.97507 q^{5}\) \(-2.62323 q^{6}\) \(+3.25996 q^{7}\) \(-7.55842 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62323 q^{2}\) \(+1.00000 q^{3}\) \(+4.88134 q^{4}\) \(-3.97507 q^{5}\) \(-2.62323 q^{6}\) \(+3.25996 q^{7}\) \(-7.55842 q^{8}\) \(+1.00000 q^{9}\) \(+10.4275 q^{10}\) \(+3.60022 q^{11}\) \(+4.88134 q^{12}\) \(+2.61007 q^{13}\) \(-8.55162 q^{14}\) \(-3.97507 q^{15}\) \(+10.0648 q^{16}\) \(-5.68631 q^{17}\) \(-2.62323 q^{18}\) \(-4.08358 q^{19}\) \(-19.4037 q^{20}\) \(+3.25996 q^{21}\) \(-9.44421 q^{22}\) \(+5.60639 q^{23}\) \(-7.55842 q^{24}\) \(+10.8012 q^{25}\) \(-6.84681 q^{26}\) \(+1.00000 q^{27}\) \(+15.9130 q^{28}\) \(+8.14243 q^{29}\) \(+10.4275 q^{30}\) \(+4.64738 q^{31}\) \(-11.2855 q^{32}\) \(+3.60022 q^{33}\) \(+14.9165 q^{34}\) \(-12.9586 q^{35}\) \(+4.88134 q^{36}\) \(+8.03456 q^{37}\) \(+10.7122 q^{38}\) \(+2.61007 q^{39}\) \(+30.0452 q^{40}\) \(+0.496116 q^{41}\) \(-8.55162 q^{42}\) \(-7.11924 q^{43}\) \(+17.5739 q^{44}\) \(-3.97507 q^{45}\) \(-14.7068 q^{46}\) \(+2.50556 q^{47}\) \(+10.0648 q^{48}\) \(+3.62733 q^{49}\) \(-28.3340 q^{50}\) \(-5.68631 q^{51}\) \(+12.7406 q^{52}\) \(+2.86690 q^{53}\) \(-2.62323 q^{54}\) \(-14.3111 q^{55}\) \(-24.6401 q^{56}\) \(-4.08358 q^{57}\) \(-21.3595 q^{58}\) \(-12.6429 q^{59}\) \(-19.4037 q^{60}\) \(-6.56251 q^{61}\) \(-12.1911 q^{62}\) \(+3.25996 q^{63}\) \(+9.47476 q^{64}\) \(-10.3752 q^{65}\) \(-9.44421 q^{66}\) \(+8.65278 q^{67}\) \(-27.7568 q^{68}\) \(+5.60639 q^{69}\) \(+33.9933 q^{70}\) \(+10.5356 q^{71}\) \(-7.55842 q^{72}\) \(-0.656707 q^{73}\) \(-21.0765 q^{74}\) \(+10.8012 q^{75}\) \(-19.9333 q^{76}\) \(+11.7366 q^{77}\) \(-6.84681 q^{78}\) \(+11.6684 q^{79}\) \(-40.0083 q^{80}\) \(+1.00000 q^{81}\) \(-1.30143 q^{82}\) \(-5.26568 q^{83}\) \(+15.9130 q^{84}\) \(+22.6035 q^{85}\) \(+18.6754 q^{86}\) \(+8.14243 q^{87}\) \(-27.2120 q^{88}\) \(+0.211415 q^{89}\) \(+10.4275 q^{90}\) \(+8.50871 q^{91}\) \(+27.3667 q^{92}\) \(+4.64738 q^{93}\) \(-6.57266 q^{94}\) \(+16.2325 q^{95}\) \(-11.2855 q^{96}\) \(+1.75190 q^{97}\) \(-9.51531 q^{98}\) \(+3.60022 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62323 −1.85490 −0.927452 0.373942i \(-0.878006\pi\)
−0.927452 + 0.373942i \(0.878006\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.88134 2.44067
\(5\) −3.97507 −1.77770 −0.888852 0.458194i \(-0.848497\pi\)
−0.888852 + 0.458194i \(0.848497\pi\)
\(6\) −2.62323 −1.07093
\(7\) 3.25996 1.23215 0.616074 0.787688i \(-0.288722\pi\)
0.616074 + 0.787688i \(0.288722\pi\)
\(8\) −7.55842 −2.67231
\(9\) 1.00000 0.333333
\(10\) 10.4275 3.29747
\(11\) 3.60022 1.08551 0.542754 0.839892i \(-0.317382\pi\)
0.542754 + 0.839892i \(0.317382\pi\)
\(12\) 4.88134 1.40912
\(13\) 2.61007 0.723903 0.361951 0.932197i \(-0.382111\pi\)
0.361951 + 0.932197i \(0.382111\pi\)
\(14\) −8.55162 −2.28552
\(15\) −3.97507 −1.02636
\(16\) 10.0648 2.51620
\(17\) −5.68631 −1.37913 −0.689566 0.724223i \(-0.742199\pi\)
−0.689566 + 0.724223i \(0.742199\pi\)
\(18\) −2.62323 −0.618301
\(19\) −4.08358 −0.936837 −0.468418 0.883507i \(-0.655176\pi\)
−0.468418 + 0.883507i \(0.655176\pi\)
\(20\) −19.4037 −4.33879
\(21\) 3.25996 0.711381
\(22\) −9.44421 −2.01351
\(23\) 5.60639 1.16901 0.584506 0.811389i \(-0.301288\pi\)
0.584506 + 0.811389i \(0.301288\pi\)
\(24\) −7.55842 −1.54286
\(25\) 10.8012 2.16023
\(26\) −6.84681 −1.34277
\(27\) 1.00000 0.192450
\(28\) 15.9130 3.00727
\(29\) 8.14243 1.51201 0.756006 0.654565i \(-0.227148\pi\)
0.756006 + 0.654565i \(0.227148\pi\)
\(30\) 10.4275 1.90380
\(31\) 4.64738 0.834693 0.417347 0.908747i \(-0.362960\pi\)
0.417347 + 0.908747i \(0.362960\pi\)
\(32\) −11.2855 −1.99501
\(33\) 3.60022 0.626718
\(34\) 14.9165 2.55816
\(35\) −12.9586 −2.19040
\(36\) 4.88134 0.813557
\(37\) 8.03456 1.32087 0.660437 0.750882i \(-0.270371\pi\)
0.660437 + 0.750882i \(0.270371\pi\)
\(38\) 10.7122 1.73774
\(39\) 2.61007 0.417945
\(40\) 30.0452 4.75057
\(41\) 0.496116 0.0774803 0.0387402 0.999249i \(-0.487666\pi\)
0.0387402 + 0.999249i \(0.487666\pi\)
\(42\) −8.55162 −1.31954
\(43\) −7.11924 −1.08567 −0.542837 0.839838i \(-0.682650\pi\)
−0.542837 + 0.839838i \(0.682650\pi\)
\(44\) 17.5739 2.64936
\(45\) −3.97507 −0.592568
\(46\) −14.7068 −2.16841
\(47\) 2.50556 0.365474 0.182737 0.983162i \(-0.441504\pi\)
0.182737 + 0.983162i \(0.441504\pi\)
\(48\) 10.0648 1.45273
\(49\) 3.62733 0.518189
\(50\) −28.3340 −4.00703
\(51\) −5.68631 −0.796242
\(52\) 12.7406 1.76681
\(53\) 2.86690 0.393799 0.196899 0.980424i \(-0.436913\pi\)
0.196899 + 0.980424i \(0.436913\pi\)
\(54\) −2.62323 −0.356977
\(55\) −14.3111 −1.92971
\(56\) −24.6401 −3.29268
\(57\) −4.08358 −0.540883
\(58\) −21.3595 −2.80464
\(59\) −12.6429 −1.64596 −0.822981 0.568069i \(-0.807691\pi\)
−0.822981 + 0.568069i \(0.807691\pi\)
\(60\) −19.4037 −2.50500
\(61\) −6.56251 −0.840244 −0.420122 0.907468i \(-0.638013\pi\)
−0.420122 + 0.907468i \(0.638013\pi\)
\(62\) −12.1911 −1.54828
\(63\) 3.25996 0.410716
\(64\) 9.47476 1.18434
\(65\) −10.3752 −1.28689
\(66\) −9.44421 −1.16250
\(67\) 8.65278 1.05711 0.528553 0.848901i \(-0.322735\pi\)
0.528553 + 0.848901i \(0.322735\pi\)
\(68\) −27.7568 −3.36601
\(69\) 5.60639 0.674930
\(70\) 33.9933 4.06297
\(71\) 10.5356 1.25034 0.625172 0.780487i \(-0.285029\pi\)
0.625172 + 0.780487i \(0.285029\pi\)
\(72\) −7.55842 −0.890768
\(73\) −0.656707 −0.0768617 −0.0384309 0.999261i \(-0.512236\pi\)
−0.0384309 + 0.999261i \(0.512236\pi\)
\(74\) −21.0765 −2.45009
\(75\) 10.8012 1.24721
\(76\) −19.9333 −2.28651
\(77\) 11.7366 1.33751
\(78\) −6.84681 −0.775249
\(79\) 11.6684 1.31280 0.656398 0.754415i \(-0.272079\pi\)
0.656398 + 0.754415i \(0.272079\pi\)
\(80\) −40.0083 −4.47306
\(81\) 1.00000 0.111111
\(82\) −1.30143 −0.143719
\(83\) −5.26568 −0.577984 −0.288992 0.957332i \(-0.593320\pi\)
−0.288992 + 0.957332i \(0.593320\pi\)
\(84\) 15.9130 1.73625
\(85\) 22.6035 2.45169
\(86\) 18.6754 2.01382
\(87\) 8.14243 0.872961
\(88\) −27.2120 −2.90081
\(89\) 0.211415 0.0224100 0.0112050 0.999937i \(-0.496433\pi\)
0.0112050 + 0.999937i \(0.496433\pi\)
\(90\) 10.4275 1.09916
\(91\) 8.50871 0.891956
\(92\) 27.3667 2.85317
\(93\) 4.64738 0.481910
\(94\) −6.57266 −0.677919
\(95\) 16.2325 1.66542
\(96\) −11.2855 −1.15182
\(97\) 1.75190 0.177879 0.0889393 0.996037i \(-0.471652\pi\)
0.0889393 + 0.996037i \(0.471652\pi\)
\(98\) −9.51531 −0.961192
\(99\) 3.60022 0.361836
\(100\) 52.7242 5.27242
\(101\) −13.4362 −1.33695 −0.668475 0.743735i \(-0.733053\pi\)
−0.668475 + 0.743735i \(0.733053\pi\)
\(102\) 14.9165 1.47695
\(103\) −8.46244 −0.833829 −0.416914 0.908946i \(-0.636888\pi\)
−0.416914 + 0.908946i \(0.636888\pi\)
\(104\) −19.7280 −1.93449
\(105\) −12.9586 −1.26463
\(106\) −7.52054 −0.730459
\(107\) 17.4268 1.68471 0.842357 0.538920i \(-0.181167\pi\)
0.842357 + 0.538920i \(0.181167\pi\)
\(108\) 4.88134 0.469707
\(109\) 7.91662 0.758275 0.379138 0.925340i \(-0.376221\pi\)
0.379138 + 0.925340i \(0.376221\pi\)
\(110\) 37.5414 3.57943
\(111\) 8.03456 0.762607
\(112\) 32.8108 3.10033
\(113\) −6.08447 −0.572379 −0.286189 0.958173i \(-0.592389\pi\)
−0.286189 + 0.958173i \(0.592389\pi\)
\(114\) 10.7122 1.00329
\(115\) −22.2858 −2.07816
\(116\) 39.7460 3.69032
\(117\) 2.61007 0.241301
\(118\) 33.1652 3.05310
\(119\) −18.5371 −1.69930
\(120\) 30.0452 2.74274
\(121\) 1.96158 0.178325
\(122\) 17.2150 1.55857
\(123\) 0.496116 0.0447333
\(124\) 22.6854 2.03721
\(125\) −23.0600 −2.06255
\(126\) −8.55162 −0.761839
\(127\) 9.88321 0.876993 0.438497 0.898733i \(-0.355511\pi\)
0.438497 + 0.898733i \(0.355511\pi\)
\(128\) −2.28356 −0.201840
\(129\) −7.11924 −0.626814
\(130\) 27.2165 2.38705
\(131\) 18.6994 1.63378 0.816889 0.576795i \(-0.195697\pi\)
0.816889 + 0.576795i \(0.195697\pi\)
\(132\) 17.5739 1.52961
\(133\) −13.3123 −1.15432
\(134\) −22.6982 −1.96083
\(135\) −3.97507 −0.342119
\(136\) 42.9795 3.68546
\(137\) −20.5954 −1.75959 −0.879793 0.475358i \(-0.842319\pi\)
−0.879793 + 0.475358i \(0.842319\pi\)
\(138\) −14.7068 −1.25193
\(139\) −0.494108 −0.0419097 −0.0209548 0.999780i \(-0.506671\pi\)
−0.0209548 + 0.999780i \(0.506671\pi\)
\(140\) −63.2551 −5.34603
\(141\) 2.50556 0.211006
\(142\) −27.6373 −2.31927
\(143\) 9.39682 0.785802
\(144\) 10.0648 0.838734
\(145\) −32.3667 −2.68791
\(146\) 1.72269 0.142571
\(147\) 3.62733 0.299177
\(148\) 39.2194 3.22382
\(149\) 8.92459 0.731131 0.365566 0.930786i \(-0.380876\pi\)
0.365566 + 0.930786i \(0.380876\pi\)
\(150\) −28.3340 −2.31346
\(151\) 0.767140 0.0624290 0.0312145 0.999513i \(-0.490063\pi\)
0.0312145 + 0.999513i \(0.490063\pi\)
\(152\) 30.8654 2.50351
\(153\) −5.68631 −0.459711
\(154\) −30.7877 −2.48095
\(155\) −18.4736 −1.48384
\(156\) 12.7406 1.02007
\(157\) −7.95890 −0.635190 −0.317595 0.948227i \(-0.602875\pi\)
−0.317595 + 0.948227i \(0.602875\pi\)
\(158\) −30.6089 −2.43511
\(159\) 2.86690 0.227360
\(160\) 44.8605 3.54653
\(161\) 18.2766 1.44040
\(162\) −2.62323 −0.206100
\(163\) 4.63609 0.363126 0.181563 0.983379i \(-0.441884\pi\)
0.181563 + 0.983379i \(0.441884\pi\)
\(164\) 2.42171 0.189104
\(165\) −14.3111 −1.11412
\(166\) 13.8131 1.07210
\(167\) 12.5734 0.972960 0.486480 0.873692i \(-0.338281\pi\)
0.486480 + 0.873692i \(0.338281\pi\)
\(168\) −24.6401 −1.90103
\(169\) −6.18754 −0.475965
\(170\) −59.2941 −4.54765
\(171\) −4.08358 −0.312279
\(172\) −34.7515 −2.64977
\(173\) 14.4053 1.09521 0.547606 0.836736i \(-0.315539\pi\)
0.547606 + 0.836736i \(0.315539\pi\)
\(174\) −21.3595 −1.61926
\(175\) 35.2114 2.66173
\(176\) 36.2355 2.73135
\(177\) −12.6429 −0.950297
\(178\) −0.554591 −0.0415684
\(179\) 1.04264 0.0779308 0.0389654 0.999241i \(-0.487594\pi\)
0.0389654 + 0.999241i \(0.487594\pi\)
\(180\) −19.4037 −1.44626
\(181\) −2.79232 −0.207552 −0.103776 0.994601i \(-0.533092\pi\)
−0.103776 + 0.994601i \(0.533092\pi\)
\(182\) −22.3203 −1.65449
\(183\) −6.56251 −0.485115
\(184\) −42.3754 −3.12396
\(185\) −31.9379 −2.34812
\(186\) −12.1911 −0.893898
\(187\) −20.4720 −1.49706
\(188\) 12.2305 0.892001
\(189\) 3.25996 0.237127
\(190\) −42.5816 −3.08919
\(191\) −21.1704 −1.53184 −0.765918 0.642939i \(-0.777715\pi\)
−0.765918 + 0.642939i \(0.777715\pi\)
\(192\) 9.47476 0.683782
\(193\) −13.3378 −0.960077 −0.480038 0.877248i \(-0.659377\pi\)
−0.480038 + 0.877248i \(0.659377\pi\)
\(194\) −4.59564 −0.329948
\(195\) −10.3752 −0.742984
\(196\) 17.7062 1.26473
\(197\) −3.73769 −0.266300 −0.133150 0.991096i \(-0.542509\pi\)
−0.133150 + 0.991096i \(0.542509\pi\)
\(198\) −9.44421 −0.671171
\(199\) 14.2815 1.01239 0.506195 0.862419i \(-0.331051\pi\)
0.506195 + 0.862419i \(0.331051\pi\)
\(200\) −81.6398 −5.77280
\(201\) 8.65278 0.610320
\(202\) 35.2462 2.47991
\(203\) 26.5440 1.86302
\(204\) −27.7568 −1.94336
\(205\) −1.97210 −0.137737
\(206\) 22.1989 1.54667
\(207\) 5.60639 0.389671
\(208\) 26.2698 1.82148
\(209\) −14.7018 −1.01694
\(210\) 33.9933 2.34576
\(211\) −15.4412 −1.06302 −0.531508 0.847053i \(-0.678375\pi\)
−0.531508 + 0.847053i \(0.678375\pi\)
\(212\) 13.9943 0.961133
\(213\) 10.5356 0.721886
\(214\) −45.7146 −3.12498
\(215\) 28.2995 1.93001
\(216\) −7.55842 −0.514285
\(217\) 15.1502 1.02847
\(218\) −20.7671 −1.40653
\(219\) −0.656707 −0.0443761
\(220\) −69.8574 −4.70979
\(221\) −14.8417 −0.998358
\(222\) −21.0765 −1.41456
\(223\) 24.0196 1.60847 0.804235 0.594312i \(-0.202575\pi\)
0.804235 + 0.594312i \(0.202575\pi\)
\(224\) −36.7901 −2.45814
\(225\) 10.8012 0.720078
\(226\) 15.9610 1.06171
\(227\) 11.1259 0.738453 0.369226 0.929339i \(-0.379623\pi\)
0.369226 + 0.929339i \(0.379623\pi\)
\(228\) −19.9333 −1.32012
\(229\) 26.9584 1.78146 0.890731 0.454532i \(-0.150193\pi\)
0.890731 + 0.454532i \(0.150193\pi\)
\(230\) 58.4607 3.85479
\(231\) 11.7366 0.772209
\(232\) −61.5439 −4.04056
\(233\) 25.1066 1.64479 0.822393 0.568920i \(-0.192638\pi\)
0.822393 + 0.568920i \(0.192638\pi\)
\(234\) −6.84681 −0.447590
\(235\) −9.95978 −0.649704
\(236\) −61.7142 −4.01725
\(237\) 11.6684 0.757943
\(238\) 48.6272 3.15203
\(239\) −25.4136 −1.64387 −0.821935 0.569581i \(-0.807105\pi\)
−0.821935 + 0.569581i \(0.807105\pi\)
\(240\) −40.0083 −2.58252
\(241\) 8.38593 0.540185 0.270093 0.962834i \(-0.412946\pi\)
0.270093 + 0.962834i \(0.412946\pi\)
\(242\) −5.14568 −0.330777
\(243\) 1.00000 0.0641500
\(244\) −32.0339 −2.05076
\(245\) −14.4189 −0.921188
\(246\) −1.30143 −0.0829759
\(247\) −10.6584 −0.678179
\(248\) −35.1268 −2.23056
\(249\) −5.26568 −0.333699
\(250\) 60.4918 3.82584
\(251\) −0.893922 −0.0564238 −0.0282119 0.999602i \(-0.508981\pi\)
−0.0282119 + 0.999602i \(0.508981\pi\)
\(252\) 15.9130 1.00242
\(253\) 20.1842 1.26897
\(254\) −25.9259 −1.62674
\(255\) 22.6035 1.41548
\(256\) −12.9592 −0.809950
\(257\) −28.3274 −1.76702 −0.883508 0.468416i \(-0.844825\pi\)
−0.883508 + 0.468416i \(0.844825\pi\)
\(258\) 18.6754 1.16268
\(259\) 26.1923 1.62751
\(260\) −50.6449 −3.14086
\(261\) 8.14243 0.504004
\(262\) −49.0529 −3.03050
\(263\) 5.75933 0.355136 0.177568 0.984109i \(-0.443177\pi\)
0.177568 + 0.984109i \(0.443177\pi\)
\(264\) −27.2120 −1.67478
\(265\) −11.3961 −0.700058
\(266\) 34.9212 2.14116
\(267\) 0.211415 0.0129384
\(268\) 42.2372 2.58005
\(269\) −5.49747 −0.335187 −0.167593 0.985856i \(-0.553600\pi\)
−0.167593 + 0.985856i \(0.553600\pi\)
\(270\) 10.4275 0.634599
\(271\) −21.7911 −1.32371 −0.661857 0.749631i \(-0.730231\pi\)
−0.661857 + 0.749631i \(0.730231\pi\)
\(272\) −57.2316 −3.47017
\(273\) 8.50871 0.514971
\(274\) 54.0265 3.26386
\(275\) 38.8866 2.34495
\(276\) 27.3667 1.64728
\(277\) −17.4380 −1.04775 −0.523875 0.851795i \(-0.675514\pi\)
−0.523875 + 0.851795i \(0.675514\pi\)
\(278\) 1.29616 0.0777385
\(279\) 4.64738 0.278231
\(280\) 97.9462 5.85341
\(281\) −8.69415 −0.518650 −0.259325 0.965790i \(-0.583500\pi\)
−0.259325 + 0.965790i \(0.583500\pi\)
\(282\) −6.57266 −0.391396
\(283\) −27.9926 −1.66399 −0.831993 0.554787i \(-0.812800\pi\)
−0.831993 + 0.554787i \(0.812800\pi\)
\(284\) 51.4278 3.05168
\(285\) 16.2325 0.961530
\(286\) −24.6500 −1.45759
\(287\) 1.61732 0.0954672
\(288\) −11.2855 −0.665002
\(289\) 15.3341 0.902006
\(290\) 84.9054 4.98582
\(291\) 1.75190 0.102698
\(292\) −3.20561 −0.187594
\(293\) 15.9224 0.930197 0.465099 0.885259i \(-0.346019\pi\)
0.465099 + 0.885259i \(0.346019\pi\)
\(294\) −9.51531 −0.554944
\(295\) 50.2563 2.92603
\(296\) −60.7286 −3.52978
\(297\) 3.60022 0.208906
\(298\) −23.4113 −1.35618
\(299\) 14.6331 0.846251
\(300\) 52.7242 3.04403
\(301\) −23.2084 −1.33771
\(302\) −2.01239 −0.115800
\(303\) −13.4362 −0.771888
\(304\) −41.1004 −2.35727
\(305\) 26.0864 1.49371
\(306\) 14.9165 0.852719
\(307\) 11.0934 0.633136 0.316568 0.948570i \(-0.397469\pi\)
0.316568 + 0.948570i \(0.397469\pi\)
\(308\) 57.2902 3.26441
\(309\) −8.46244 −0.481411
\(310\) 48.4606 2.75238
\(311\) −0.540985 −0.0306764 −0.0153382 0.999882i \(-0.504882\pi\)
−0.0153382 + 0.999882i \(0.504882\pi\)
\(312\) −19.7280 −1.11688
\(313\) −32.7839 −1.85306 −0.926529 0.376224i \(-0.877222\pi\)
−0.926529 + 0.376224i \(0.877222\pi\)
\(314\) 20.8780 1.17822
\(315\) −12.9586 −0.730132
\(316\) 56.9574 3.20410
\(317\) 9.44973 0.530749 0.265375 0.964145i \(-0.414504\pi\)
0.265375 + 0.964145i \(0.414504\pi\)
\(318\) −7.52054 −0.421731
\(319\) 29.3146 1.64130
\(320\) −37.6628 −2.10542
\(321\) 17.4268 0.972670
\(322\) −47.9437 −2.67180
\(323\) 23.2205 1.29202
\(324\) 4.88134 0.271186
\(325\) 28.1918 1.56380
\(326\) −12.1615 −0.673565
\(327\) 7.91662 0.437790
\(328\) −3.74985 −0.207051
\(329\) 8.16802 0.450318
\(330\) 37.5414 2.06658
\(331\) −16.7785 −0.922227 −0.461114 0.887341i \(-0.652550\pi\)
−0.461114 + 0.887341i \(0.652550\pi\)
\(332\) −25.7036 −1.41067
\(333\) 8.03456 0.440291
\(334\) −32.9830 −1.80475
\(335\) −34.3954 −1.87922
\(336\) 32.8108 1.78998
\(337\) −13.0509 −0.710930 −0.355465 0.934690i \(-0.615677\pi\)
−0.355465 + 0.934690i \(0.615677\pi\)
\(338\) 16.2314 0.882869
\(339\) −6.08447 −0.330463
\(340\) 110.335 5.98377
\(341\) 16.7316 0.906065
\(342\) 10.7122 0.579247
\(343\) −10.9948 −0.593662
\(344\) 53.8102 2.90125
\(345\) −22.2858 −1.19983
\(346\) −37.7884 −2.03152
\(347\) 8.46004 0.454159 0.227079 0.973876i \(-0.427082\pi\)
0.227079 + 0.973876i \(0.427082\pi\)
\(348\) 39.7460 2.13061
\(349\) 29.6504 1.58715 0.793574 0.608474i \(-0.208218\pi\)
0.793574 + 0.608474i \(0.208218\pi\)
\(350\) −92.3675 −4.93725
\(351\) 2.61007 0.139315
\(352\) −40.6301 −2.16559
\(353\) 13.6299 0.725447 0.362724 0.931897i \(-0.381847\pi\)
0.362724 + 0.931897i \(0.381847\pi\)
\(354\) 33.1652 1.76271
\(355\) −41.8797 −2.22274
\(356\) 1.03199 0.0546954
\(357\) −18.5371 −0.981089
\(358\) −2.73509 −0.144554
\(359\) −17.7631 −0.937499 −0.468750 0.883331i \(-0.655295\pi\)
−0.468750 + 0.883331i \(0.655295\pi\)
\(360\) 30.0452 1.58352
\(361\) −2.32441 −0.122337
\(362\) 7.32490 0.384988
\(363\) 1.96158 0.102956
\(364\) 41.5339 2.17697
\(365\) 2.61046 0.136637
\(366\) 17.2150 0.899842
\(367\) −28.8068 −1.50370 −0.751851 0.659333i \(-0.770839\pi\)
−0.751851 + 0.659333i \(0.770839\pi\)
\(368\) 56.4272 2.94147
\(369\) 0.496116 0.0258268
\(370\) 83.7806 4.35554
\(371\) 9.34597 0.485218
\(372\) 22.6854 1.17618
\(373\) 34.5972 1.79138 0.895688 0.444683i \(-0.146684\pi\)
0.895688 + 0.444683i \(0.146684\pi\)
\(374\) 53.7027 2.77690
\(375\) −23.0600 −1.19082
\(376\) −18.9381 −0.976657
\(377\) 21.2523 1.09455
\(378\) −8.55162 −0.439848
\(379\) −25.0039 −1.28437 −0.642183 0.766551i \(-0.721971\pi\)
−0.642183 + 0.766551i \(0.721971\pi\)
\(380\) 79.2363 4.06474
\(381\) 9.88321 0.506332
\(382\) 55.5348 2.84141
\(383\) 14.0362 0.717216 0.358608 0.933488i \(-0.383252\pi\)
0.358608 + 0.933488i \(0.383252\pi\)
\(384\) −2.28356 −0.116533
\(385\) −46.6536 −2.37769
\(386\) 34.9882 1.78085
\(387\) −7.11924 −0.361892
\(388\) 8.55163 0.434143
\(389\) 4.82015 0.244391 0.122196 0.992506i \(-0.461006\pi\)
0.122196 + 0.992506i \(0.461006\pi\)
\(390\) 27.2165 1.37816
\(391\) −31.8796 −1.61222
\(392\) −27.4169 −1.38476
\(393\) 18.6994 0.943262
\(394\) 9.80483 0.493960
\(395\) −46.3826 −2.33376
\(396\) 17.5739 0.883122
\(397\) −30.8645 −1.54904 −0.774521 0.632548i \(-0.782009\pi\)
−0.774521 + 0.632548i \(0.782009\pi\)
\(398\) −37.4637 −1.87789
\(399\) −13.3123 −0.666448
\(400\) 108.712 5.43558
\(401\) 14.5006 0.724124 0.362062 0.932154i \(-0.382073\pi\)
0.362062 + 0.932154i \(0.382073\pi\)
\(402\) −22.6982 −1.13209
\(403\) 12.1300 0.604237
\(404\) −65.5866 −3.26305
\(405\) −3.97507 −0.197523
\(406\) −69.6310 −3.45573
\(407\) 28.9262 1.43382
\(408\) 42.9795 2.12780
\(409\) −4.37720 −0.216439 −0.108219 0.994127i \(-0.534515\pi\)
−0.108219 + 0.994127i \(0.534515\pi\)
\(410\) 5.17326 0.255489
\(411\) −20.5954 −1.01590
\(412\) −41.3080 −2.03510
\(413\) −41.2152 −2.02807
\(414\) −14.7068 −0.722802
\(415\) 20.9314 1.02748
\(416\) −29.4558 −1.44419
\(417\) −0.494108 −0.0241966
\(418\) 38.5661 1.88633
\(419\) 2.96627 0.144912 0.0724560 0.997372i \(-0.476916\pi\)
0.0724560 + 0.997372i \(0.476916\pi\)
\(420\) −63.2551 −3.08653
\(421\) −18.2644 −0.890152 −0.445076 0.895493i \(-0.646823\pi\)
−0.445076 + 0.895493i \(0.646823\pi\)
\(422\) 40.5059 1.97179
\(423\) 2.50556 0.121825
\(424\) −21.6692 −1.05235
\(425\) −61.4188 −2.97925
\(426\) −27.6373 −1.33903
\(427\) −21.3935 −1.03530
\(428\) 85.0662 4.11183
\(429\) 9.39682 0.453683
\(430\) −74.2361 −3.57998
\(431\) −4.00652 −0.192987 −0.0964937 0.995334i \(-0.530763\pi\)
−0.0964937 + 0.995334i \(0.530763\pi\)
\(432\) 10.0648 0.484243
\(433\) 22.9215 1.10154 0.550769 0.834658i \(-0.314335\pi\)
0.550769 + 0.834658i \(0.314335\pi\)
\(434\) −39.7426 −1.90771
\(435\) −32.3667 −1.55187
\(436\) 38.6437 1.85070
\(437\) −22.8941 −1.09517
\(438\) 1.72269 0.0823135
\(439\) −3.54741 −0.169309 −0.0846543 0.996410i \(-0.526979\pi\)
−0.0846543 + 0.996410i \(0.526979\pi\)
\(440\) 108.169 5.15678
\(441\) 3.62733 0.172730
\(442\) 38.9331 1.85186
\(443\) 9.88862 0.469822 0.234911 0.972017i \(-0.424520\pi\)
0.234911 + 0.972017i \(0.424520\pi\)
\(444\) 39.2194 1.86127
\(445\) −0.840391 −0.0398383
\(446\) −63.0089 −2.98356
\(447\) 8.92459 0.422119
\(448\) 30.8873 1.45929
\(449\) −35.3243 −1.66706 −0.833529 0.552476i \(-0.813683\pi\)
−0.833529 + 0.552476i \(0.813683\pi\)
\(450\) −28.3340 −1.33568
\(451\) 1.78613 0.0841054
\(452\) −29.7004 −1.39699
\(453\) 0.767140 0.0360434
\(454\) −29.1858 −1.36976
\(455\) −33.8227 −1.58563
\(456\) 30.8654 1.44540
\(457\) 39.1961 1.83352 0.916758 0.399443i \(-0.130796\pi\)
0.916758 + 0.399443i \(0.130796\pi\)
\(458\) −70.7181 −3.30444
\(459\) −5.68631 −0.265414
\(460\) −108.784 −5.07210
\(461\) 5.21627 0.242946 0.121473 0.992595i \(-0.461238\pi\)
0.121473 + 0.992595i \(0.461238\pi\)
\(462\) −30.7877 −1.43237
\(463\) 0.293701 0.0136494 0.00682471 0.999977i \(-0.497828\pi\)
0.00682471 + 0.999977i \(0.497828\pi\)
\(464\) 81.9520 3.80453
\(465\) −18.4736 −0.856694
\(466\) −65.8603 −3.05092
\(467\) −2.40491 −0.111286 −0.0556429 0.998451i \(-0.517721\pi\)
−0.0556429 + 0.998451i \(0.517721\pi\)
\(468\) 12.7406 0.588936
\(469\) 28.2077 1.30251
\(470\) 26.1268 1.20514
\(471\) −7.95890 −0.366727
\(472\) 95.5602 4.39851
\(473\) −25.6308 −1.17851
\(474\) −30.6089 −1.40591
\(475\) −44.1074 −2.02379
\(476\) −90.4860 −4.14742
\(477\) 2.86690 0.131266
\(478\) 66.6658 3.04922
\(479\) 16.0433 0.733038 0.366519 0.930411i \(-0.380550\pi\)
0.366519 + 0.930411i \(0.380550\pi\)
\(480\) 44.8605 2.04759
\(481\) 20.9708 0.956184
\(482\) −21.9982 −1.00199
\(483\) 18.2766 0.831613
\(484\) 9.57514 0.435234
\(485\) −6.96393 −0.316216
\(486\) −2.62323 −0.118992
\(487\) −1.56939 −0.0711158 −0.0355579 0.999368i \(-0.511321\pi\)
−0.0355579 + 0.999368i \(0.511321\pi\)
\(488\) 49.6022 2.24539
\(489\) 4.63609 0.209651
\(490\) 37.8240 1.70872
\(491\) −24.6440 −1.11217 −0.556084 0.831126i \(-0.687697\pi\)
−0.556084 + 0.831126i \(0.687697\pi\)
\(492\) 2.42171 0.109179
\(493\) −46.3004 −2.08526
\(494\) 27.9595 1.25796
\(495\) −14.3111 −0.643237
\(496\) 46.7749 2.10026
\(497\) 34.3456 1.54061
\(498\) 13.8131 0.618980
\(499\) 7.07090 0.316537 0.158268 0.987396i \(-0.449409\pi\)
0.158268 + 0.987396i \(0.449409\pi\)
\(500\) −112.564 −5.03401
\(501\) 12.5734 0.561739
\(502\) 2.34496 0.104661
\(503\) 21.8861 0.975855 0.487927 0.872884i \(-0.337753\pi\)
0.487927 + 0.872884i \(0.337753\pi\)
\(504\) −24.6401 −1.09756
\(505\) 53.4097 2.37670
\(506\) −52.9479 −2.35382
\(507\) −6.18754 −0.274798
\(508\) 48.2433 2.14045
\(509\) 40.8812 1.81203 0.906013 0.423249i \(-0.139110\pi\)
0.906013 + 0.423249i \(0.139110\pi\)
\(510\) −59.2941 −2.62559
\(511\) −2.14084 −0.0947051
\(512\) 38.5621 1.70422
\(513\) −4.08358 −0.180294
\(514\) 74.3094 3.27765
\(515\) 33.6388 1.48230
\(516\) −34.7515 −1.52985
\(517\) 9.02057 0.396724
\(518\) −68.7085 −3.01888
\(519\) 14.4053 0.632321
\(520\) 78.4201 3.43895
\(521\) 39.0153 1.70929 0.854647 0.519210i \(-0.173774\pi\)
0.854647 + 0.519210i \(0.173774\pi\)
\(522\) −21.3595 −0.934879
\(523\) 36.9372 1.61515 0.807576 0.589764i \(-0.200779\pi\)
0.807576 + 0.589764i \(0.200779\pi\)
\(524\) 91.2783 3.98751
\(525\) 35.2114 1.53675
\(526\) −15.1081 −0.658743
\(527\) −26.4264 −1.15115
\(528\) 36.2355 1.57695
\(529\) 8.43156 0.366590
\(530\) 29.8946 1.29854
\(531\) −12.6429 −0.548654
\(532\) −64.9818 −2.81732
\(533\) 1.29490 0.0560882
\(534\) −0.554591 −0.0239995
\(535\) −69.2728 −2.99492
\(536\) −65.4013 −2.82491
\(537\) 1.04264 0.0449934
\(538\) 14.4211 0.621739
\(539\) 13.0592 0.562498
\(540\) −19.4037 −0.835001
\(541\) 18.5185 0.796171 0.398085 0.917348i \(-0.369675\pi\)
0.398085 + 0.917348i \(0.369675\pi\)
\(542\) 57.1630 2.45536
\(543\) −2.79232 −0.119830
\(544\) 64.1726 2.75138
\(545\) −31.4691 −1.34799
\(546\) −22.3203 −0.955222
\(547\) 12.9196 0.552400 0.276200 0.961100i \(-0.410925\pi\)
0.276200 + 0.961100i \(0.410925\pi\)
\(548\) −100.533 −4.29457
\(549\) −6.56251 −0.280081
\(550\) −102.008 −4.34966
\(551\) −33.2502 −1.41651
\(552\) −42.3754 −1.80362
\(553\) 38.0385 1.61756
\(554\) 45.7440 1.94348
\(555\) −31.9379 −1.35569
\(556\) −2.41191 −0.102288
\(557\) 28.3948 1.20313 0.601563 0.798825i \(-0.294545\pi\)
0.601563 + 0.798825i \(0.294545\pi\)
\(558\) −12.1911 −0.516092
\(559\) −18.5817 −0.785923
\(560\) −130.425 −5.51148
\(561\) −20.4720 −0.864327
\(562\) 22.8068 0.962045
\(563\) 6.21438 0.261905 0.130952 0.991389i \(-0.458196\pi\)
0.130952 + 0.991389i \(0.458196\pi\)
\(564\) 12.2305 0.514997
\(565\) 24.1862 1.01752
\(566\) 73.4310 3.08653
\(567\) 3.25996 0.136905
\(568\) −79.6324 −3.34130
\(569\) 2.13913 0.0896768 0.0448384 0.998994i \(-0.485723\pi\)
0.0448384 + 0.998994i \(0.485723\pi\)
\(570\) −42.5816 −1.78355
\(571\) 25.2683 1.05744 0.528722 0.848795i \(-0.322671\pi\)
0.528722 + 0.848795i \(0.322671\pi\)
\(572\) 45.8691 1.91788
\(573\) −21.1704 −0.884406
\(574\) −4.24260 −0.177083
\(575\) 60.5555 2.52534
\(576\) 9.47476 0.394782
\(577\) 21.5626 0.897662 0.448831 0.893617i \(-0.351840\pi\)
0.448831 + 0.893617i \(0.351840\pi\)
\(578\) −40.2249 −1.67313
\(579\) −13.3378 −0.554301
\(580\) −157.993 −6.56030
\(581\) −17.1659 −0.712161
\(582\) −4.59564 −0.190495
\(583\) 10.3215 0.427471
\(584\) 4.96367 0.205398
\(585\) −10.3752 −0.428962
\(586\) −41.7682 −1.72543
\(587\) 21.3769 0.882317 0.441159 0.897429i \(-0.354568\pi\)
0.441159 + 0.897429i \(0.354568\pi\)
\(588\) 17.7062 0.730192
\(589\) −18.9779 −0.781971
\(590\) −131.834 −5.42751
\(591\) −3.73769 −0.153748
\(592\) 80.8663 3.32358
\(593\) 17.5645 0.721290 0.360645 0.932703i \(-0.382557\pi\)
0.360645 + 0.932703i \(0.382557\pi\)
\(594\) −9.44421 −0.387501
\(595\) 73.6863 3.02085
\(596\) 43.5640 1.78445
\(597\) 14.2815 0.584504
\(598\) −38.3859 −1.56971
\(599\) 33.2776 1.35968 0.679842 0.733358i \(-0.262048\pi\)
0.679842 + 0.733358i \(0.262048\pi\)
\(600\) −81.6398 −3.33293
\(601\) 29.8718 1.21849 0.609247 0.792980i \(-0.291472\pi\)
0.609247 + 0.792980i \(0.291472\pi\)
\(602\) 60.8811 2.48133
\(603\) 8.65278 0.352368
\(604\) 3.74467 0.152369
\(605\) −7.79742 −0.317010
\(606\) 35.2462 1.43178
\(607\) −30.8840 −1.25354 −0.626772 0.779203i \(-0.715624\pi\)
−0.626772 + 0.779203i \(0.715624\pi\)
\(608\) 46.0850 1.86899
\(609\) 26.5440 1.07562
\(610\) −68.4308 −2.77068
\(611\) 6.53969 0.264567
\(612\) −27.7568 −1.12200
\(613\) −22.5407 −0.910409 −0.455205 0.890387i \(-0.650434\pi\)
−0.455205 + 0.890387i \(0.650434\pi\)
\(614\) −29.1006 −1.17441
\(615\) −1.97210 −0.0795226
\(616\) −88.7099 −3.57422
\(617\) −10.8898 −0.438406 −0.219203 0.975679i \(-0.570346\pi\)
−0.219203 + 0.975679i \(0.570346\pi\)
\(618\) 22.1989 0.892972
\(619\) −14.9589 −0.601248 −0.300624 0.953743i \(-0.597195\pi\)
−0.300624 + 0.953743i \(0.597195\pi\)
\(620\) −90.1761 −3.62156
\(621\) 5.60639 0.224977
\(622\) 1.41913 0.0569018
\(623\) 0.689205 0.0276124
\(624\) 26.2698 1.05163
\(625\) 37.6594 1.50638
\(626\) 85.9998 3.43724
\(627\) −14.7018 −0.587132
\(628\) −38.8501 −1.55029
\(629\) −45.6870 −1.82166
\(630\) 33.9933 1.35432
\(631\) 26.0306 1.03626 0.518132 0.855301i \(-0.326628\pi\)
0.518132 + 0.855301i \(0.326628\pi\)
\(632\) −88.1946 −3.50819
\(633\) −15.4412 −0.613733
\(634\) −24.7888 −0.984490
\(635\) −39.2864 −1.55904
\(636\) 13.9943 0.554910
\(637\) 9.46757 0.375119
\(638\) −76.8988 −3.04445
\(639\) 10.5356 0.416781
\(640\) 9.07732 0.358813
\(641\) 2.30682 0.0911139 0.0455569 0.998962i \(-0.485494\pi\)
0.0455569 + 0.998962i \(0.485494\pi\)
\(642\) −45.7146 −1.80421
\(643\) −3.39258 −0.133790 −0.0668952 0.997760i \(-0.521309\pi\)
−0.0668952 + 0.997760i \(0.521309\pi\)
\(644\) 89.2142 3.51553
\(645\) 28.2995 1.11429
\(646\) −60.9126 −2.39658
\(647\) −29.5936 −1.16344 −0.581722 0.813388i \(-0.697621\pi\)
−0.581722 + 0.813388i \(0.697621\pi\)
\(648\) −7.55842 −0.296923
\(649\) −45.5171 −1.78670
\(650\) −73.9536 −2.90070
\(651\) 15.1502 0.593785
\(652\) 22.6303 0.886272
\(653\) 18.9272 0.740679 0.370339 0.928897i \(-0.379241\pi\)
0.370339 + 0.928897i \(0.379241\pi\)
\(654\) −20.7671 −0.812059
\(655\) −74.3315 −2.90437
\(656\) 4.99331 0.194956
\(657\) −0.656707 −0.0256206
\(658\) −21.4266 −0.835296
\(659\) −24.0345 −0.936249 −0.468125 0.883662i \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(660\) −69.8574 −2.71920
\(661\) 14.6078 0.568177 0.284088 0.958798i \(-0.408309\pi\)
0.284088 + 0.958798i \(0.408309\pi\)
\(662\) 44.0138 1.71064
\(663\) −14.8417 −0.576402
\(664\) 39.8002 1.54455
\(665\) 52.9172 2.05204
\(666\) −21.0765 −0.816698
\(667\) 45.6496 1.76756
\(668\) 61.3751 2.37467
\(669\) 24.0196 0.928650
\(670\) 90.2270 3.48577
\(671\) −23.6265 −0.912090
\(672\) −36.7901 −1.41921
\(673\) −6.53966 −0.252085 −0.126043 0.992025i \(-0.540228\pi\)
−0.126043 + 0.992025i \(0.540228\pi\)
\(674\) 34.2356 1.31871
\(675\) 10.8012 0.415737
\(676\) −30.2035 −1.16167
\(677\) 33.6985 1.29514 0.647569 0.762007i \(-0.275786\pi\)
0.647569 + 0.762007i \(0.275786\pi\)
\(678\) 15.9610 0.612977
\(679\) 5.71112 0.219173
\(680\) −170.846 −6.55166
\(681\) 11.1259 0.426346
\(682\) −43.8908 −1.68066
\(683\) 32.0658 1.22696 0.613481 0.789709i \(-0.289769\pi\)
0.613481 + 0.789709i \(0.289769\pi\)
\(684\) −19.9333 −0.762170
\(685\) 81.8682 3.12802
\(686\) 28.8418 1.10119
\(687\) 26.9584 1.02853
\(688\) −71.6538 −2.73177
\(689\) 7.48280 0.285072
\(690\) 58.4607 2.22556
\(691\) −5.24430 −0.199503 −0.0997514 0.995012i \(-0.531805\pi\)
−0.0997514 + 0.995012i \(0.531805\pi\)
\(692\) 70.3171 2.67305
\(693\) 11.7366 0.445835
\(694\) −22.1926 −0.842421
\(695\) 1.96411 0.0745030
\(696\) −61.5439 −2.33282
\(697\) −2.82107 −0.106856
\(698\) −77.7798 −2.94401
\(699\) 25.1066 0.949618
\(700\) 171.879 6.49640
\(701\) 32.3513 1.22189 0.610947 0.791672i \(-0.290789\pi\)
0.610947 + 0.791672i \(0.290789\pi\)
\(702\) −6.84681 −0.258416
\(703\) −32.8097 −1.23744
\(704\) 34.1112 1.28561
\(705\) −9.95978 −0.375107
\(706\) −35.7544 −1.34564
\(707\) −43.8014 −1.64732
\(708\) −61.7142 −2.31936
\(709\) 22.8259 0.857243 0.428621 0.903484i \(-0.358999\pi\)
0.428621 + 0.903484i \(0.358999\pi\)
\(710\) 109.860 4.12297
\(711\) 11.6684 0.437599
\(712\) −1.59797 −0.0598863
\(713\) 26.0550 0.975767
\(714\) 48.6272 1.81983
\(715\) −37.3530 −1.39692
\(716\) 5.08949 0.190203
\(717\) −25.4136 −0.949089
\(718\) 46.5966 1.73897
\(719\) −39.7705 −1.48319 −0.741595 0.670848i \(-0.765930\pi\)
−0.741595 + 0.670848i \(0.765930\pi\)
\(720\) −40.0083 −1.49102
\(721\) −27.5872 −1.02740
\(722\) 6.09746 0.226924
\(723\) 8.38593 0.311876
\(724\) −13.6303 −0.506565
\(725\) 87.9478 3.26630
\(726\) −5.14568 −0.190974
\(727\) −9.04489 −0.335456 −0.167728 0.985833i \(-0.553643\pi\)
−0.167728 + 0.985833i \(0.553643\pi\)
\(728\) −64.3124 −2.38358
\(729\) 1.00000 0.0370370
\(730\) −6.84783 −0.253449
\(731\) 40.4822 1.49729
\(732\) −32.0339 −1.18401
\(733\) −2.14807 −0.0793406 −0.0396703 0.999213i \(-0.512631\pi\)
−0.0396703 + 0.999213i \(0.512631\pi\)
\(734\) 75.5668 2.78922
\(735\) −14.4189 −0.531848
\(736\) −63.2706 −2.33219
\(737\) 31.1519 1.14750
\(738\) −1.30143 −0.0479062
\(739\) −0.110901 −0.00407955 −0.00203978 0.999998i \(-0.500649\pi\)
−0.00203978 + 0.999998i \(0.500649\pi\)
\(740\) −155.900 −5.73099
\(741\) −10.6584 −0.391547
\(742\) −24.5166 −0.900034
\(743\) 47.8489 1.75541 0.877703 0.479206i \(-0.159075\pi\)
0.877703 + 0.479206i \(0.159075\pi\)
\(744\) −35.1268 −1.28781
\(745\) −35.4759 −1.29974
\(746\) −90.7565 −3.32283
\(747\) −5.26568 −0.192661
\(748\) −99.9306 −3.65382
\(749\) 56.8107 2.07582
\(750\) 60.4918 2.20885
\(751\) −6.91995 −0.252513 −0.126256 0.991998i \(-0.540296\pi\)
−0.126256 + 0.991998i \(0.540296\pi\)
\(752\) 25.2180 0.919605
\(753\) −0.893922 −0.0325763
\(754\) −55.7497 −2.03029
\(755\) −3.04943 −0.110980
\(756\) 15.9130 0.578749
\(757\) 13.2792 0.482642 0.241321 0.970445i \(-0.422419\pi\)
0.241321 + 0.970445i \(0.422419\pi\)
\(758\) 65.5911 2.38238
\(759\) 20.1842 0.732641
\(760\) −122.692 −4.45051
\(761\) −49.6456 −1.79965 −0.899825 0.436250i \(-0.856306\pi\)
−0.899825 + 0.436250i \(0.856306\pi\)
\(762\) −25.9259 −0.939198
\(763\) 25.8079 0.934307
\(764\) −103.340 −3.73871
\(765\) 22.6035 0.817230
\(766\) −36.8202 −1.33037
\(767\) −32.9988 −1.19152
\(768\) −12.9592 −0.467625
\(769\) 14.0511 0.506696 0.253348 0.967375i \(-0.418468\pi\)
0.253348 + 0.967375i \(0.418468\pi\)
\(770\) 122.383 4.41039
\(771\) −28.3274 −1.02019
\(772\) −65.1064 −2.34323
\(773\) 0.119269 0.00428980 0.00214490 0.999998i \(-0.499317\pi\)
0.00214490 + 0.999998i \(0.499317\pi\)
\(774\) 18.6754 0.671274
\(775\) 50.1971 1.80313
\(776\) −13.2416 −0.475346
\(777\) 26.1923 0.939645
\(778\) −12.6444 −0.453322
\(779\) −2.02593 −0.0725864
\(780\) −50.6449 −1.81338
\(781\) 37.9304 1.35726
\(782\) 83.6276 2.99052
\(783\) 8.14243 0.290987
\(784\) 36.5083 1.30387
\(785\) 31.6372 1.12918
\(786\) −49.0529 −1.74966
\(787\) −38.1910 −1.36136 −0.680681 0.732580i \(-0.738316\pi\)
−0.680681 + 0.732580i \(0.738316\pi\)
\(788\) −18.2450 −0.649950
\(789\) 5.75933 0.205038
\(790\) 121.672 4.32891
\(791\) −19.8351 −0.705255
\(792\) −27.2120 −0.966935
\(793\) −17.1286 −0.608255
\(794\) 80.9646 2.87333
\(795\) −11.3961 −0.404179
\(796\) 69.7130 2.47091
\(797\) −32.5001 −1.15121 −0.575607 0.817726i \(-0.695234\pi\)
−0.575607 + 0.817726i \(0.695234\pi\)
\(798\) 34.9212 1.23620
\(799\) −14.2474 −0.504036
\(800\) −121.896 −4.30968
\(801\) 0.211415 0.00747000
\(802\) −38.0383 −1.34318
\(803\) −2.36429 −0.0834340
\(804\) 42.2372 1.48959
\(805\) −72.6507 −2.56060
\(806\) −31.8197 −1.12080
\(807\) −5.49747 −0.193520
\(808\) 101.556 3.57274
\(809\) −46.7443 −1.64344 −0.821720 0.569891i \(-0.806985\pi\)
−0.821720 + 0.569891i \(0.806985\pi\)
\(810\) 10.4275 0.366386
\(811\) 37.5845 1.31977 0.659885 0.751366i \(-0.270605\pi\)
0.659885 + 0.751366i \(0.270605\pi\)
\(812\) 129.570 4.54702
\(813\) −21.7911 −0.764246
\(814\) −75.8801 −2.65959
\(815\) −18.4288 −0.645531
\(816\) −57.2316 −2.00351
\(817\) 29.0720 1.01710
\(818\) 11.4824 0.401473
\(819\) 8.50871 0.297319
\(820\) −9.62647 −0.336171
\(821\) −8.25043 −0.287942 −0.143971 0.989582i \(-0.545987\pi\)
−0.143971 + 0.989582i \(0.545987\pi\)
\(822\) 54.0265 1.88439
\(823\) 7.04671 0.245633 0.122816 0.992429i \(-0.460807\pi\)
0.122816 + 0.992429i \(0.460807\pi\)
\(824\) 63.9627 2.22824
\(825\) 38.8866 1.35386
\(826\) 108.117 3.76187
\(827\) 31.9885 1.11235 0.556175 0.831065i \(-0.312268\pi\)
0.556175 + 0.831065i \(0.312268\pi\)
\(828\) 27.3667 0.951058
\(829\) −49.5697 −1.72163 −0.860813 0.508921i \(-0.830044\pi\)
−0.860813 + 0.508921i \(0.830044\pi\)
\(830\) −54.9080 −1.90588
\(831\) −17.4380 −0.604919
\(832\) 24.7298 0.857351
\(833\) −20.6261 −0.714652
\(834\) 1.29616 0.0448823
\(835\) −49.9802 −1.72964
\(836\) −71.7643 −2.48202
\(837\) 4.64738 0.160637
\(838\) −7.78122 −0.268798
\(839\) 35.2103 1.21559 0.607797 0.794092i \(-0.292053\pi\)
0.607797 + 0.794092i \(0.292053\pi\)
\(840\) 97.9462 3.37947
\(841\) 37.2992 1.28618
\(842\) 47.9117 1.65115
\(843\) −8.69415 −0.299442
\(844\) −75.3738 −2.59447
\(845\) 24.5959 0.846125
\(846\) −6.57266 −0.225973
\(847\) 6.39467 0.219723
\(848\) 28.8548 0.990877
\(849\) −27.9926 −0.960702
\(850\) 161.116 5.52622
\(851\) 45.0448 1.54412
\(852\) 51.4278 1.76189
\(853\) 19.3039 0.660952 0.330476 0.943814i \(-0.392791\pi\)
0.330476 + 0.943814i \(0.392791\pi\)
\(854\) 56.1201 1.92039
\(855\) 16.2325 0.555140
\(856\) −131.719 −4.50207
\(857\) 22.8919 0.781974 0.390987 0.920396i \(-0.372134\pi\)
0.390987 + 0.920396i \(0.372134\pi\)
\(858\) −24.6500 −0.841538
\(859\) −54.6574 −1.86489 −0.932443 0.361318i \(-0.882327\pi\)
−0.932443 + 0.361318i \(0.882327\pi\)
\(860\) 138.139 4.71051
\(861\) 1.61732 0.0551180
\(862\) 10.5100 0.357973
\(863\) −7.21562 −0.245623 −0.122811 0.992430i \(-0.539191\pi\)
−0.122811 + 0.992430i \(0.539191\pi\)
\(864\) −11.2855 −0.383939
\(865\) −57.2620 −1.94696
\(866\) −60.1284 −2.04325
\(867\) 15.3341 0.520773
\(868\) 73.9535 2.51015
\(869\) 42.0088 1.42505
\(870\) 84.9054 2.87856
\(871\) 22.5843 0.765241
\(872\) −59.8372 −2.02634
\(873\) 1.75190 0.0592929
\(874\) 60.0565 2.03144
\(875\) −75.1748 −2.54137
\(876\) −3.20561 −0.108308
\(877\) 28.4400 0.960351 0.480176 0.877172i \(-0.340573\pi\)
0.480176 + 0.877172i \(0.340573\pi\)
\(878\) 9.30567 0.314051
\(879\) 15.9224 0.537050
\(880\) −144.039 −4.85554
\(881\) 40.8698 1.37694 0.688469 0.725266i \(-0.258283\pi\)
0.688469 + 0.725266i \(0.258283\pi\)
\(882\) −9.51531 −0.320397
\(883\) 22.3021 0.750526 0.375263 0.926918i \(-0.377552\pi\)
0.375263 + 0.926918i \(0.377552\pi\)
\(884\) −72.4472 −2.43666
\(885\) 50.2563 1.68935
\(886\) −25.9401 −0.871476
\(887\) 23.8748 0.801637 0.400819 0.916157i \(-0.368726\pi\)
0.400819 + 0.916157i \(0.368726\pi\)
\(888\) −60.7286 −2.03792
\(889\) 32.2189 1.08059
\(890\) 2.20454 0.0738963
\(891\) 3.60022 0.120612
\(892\) 117.248 3.92574
\(893\) −10.2316 −0.342389
\(894\) −23.4113 −0.782990
\(895\) −4.14458 −0.138538
\(896\) −7.44432 −0.248697
\(897\) 14.6331 0.488583
\(898\) 92.6639 3.09223
\(899\) 37.8409 1.26207
\(900\) 52.7242 1.75747
\(901\) −16.3021 −0.543101
\(902\) −4.68542 −0.156008
\(903\) −23.2084 −0.772328
\(904\) 45.9890 1.52957
\(905\) 11.0997 0.368965
\(906\) −2.01239 −0.0668570
\(907\) −50.9276 −1.69102 −0.845512 0.533956i \(-0.820705\pi\)
−0.845512 + 0.533956i \(0.820705\pi\)
\(908\) 54.3094 1.80232
\(909\) −13.4362 −0.445650
\(910\) 88.7248 2.94120
\(911\) −1.56424 −0.0518255 −0.0259127 0.999664i \(-0.508249\pi\)
−0.0259127 + 0.999664i \(0.508249\pi\)
\(912\) −41.1004 −1.36097
\(913\) −18.9576 −0.627405
\(914\) −102.820 −3.40100
\(915\) 26.0864 0.862391
\(916\) 131.593 4.34796
\(917\) 60.9594 2.01306
\(918\) 14.9165 0.492318
\(919\) 4.66853 0.154001 0.0770004 0.997031i \(-0.475466\pi\)
0.0770004 + 0.997031i \(0.475466\pi\)
\(920\) 168.445 5.55347
\(921\) 11.0934 0.365541
\(922\) −13.6835 −0.450641
\(923\) 27.4986 0.905127
\(924\) 57.2902 1.88471
\(925\) 86.7826 2.85340
\(926\) −0.770445 −0.0253184
\(927\) −8.46244 −0.277943
\(928\) −91.8911 −3.01647
\(929\) −4.23220 −0.138854 −0.0694269 0.997587i \(-0.522117\pi\)
−0.0694269 + 0.997587i \(0.522117\pi\)
\(930\) 48.4606 1.58909
\(931\) −14.8125 −0.485459
\(932\) 122.554 4.01438
\(933\) −0.540985 −0.0177110
\(934\) 6.30863 0.206425
\(935\) 81.3774 2.66133
\(936\) −19.7280 −0.644830
\(937\) 17.1956 0.561756 0.280878 0.959743i \(-0.409374\pi\)
0.280878 + 0.959743i \(0.409374\pi\)
\(938\) −73.9953 −2.41603
\(939\) −32.7839 −1.06986
\(940\) −48.6171 −1.58571
\(941\) −27.0060 −0.880370 −0.440185 0.897907i \(-0.645087\pi\)
−0.440185 + 0.897907i \(0.645087\pi\)
\(942\) 20.8780 0.680243
\(943\) 2.78142 0.0905754
\(944\) −127.248 −4.14157
\(945\) −12.9586 −0.421542
\(946\) 67.2356 2.18602
\(947\) −16.6992 −0.542649 −0.271325 0.962488i \(-0.587462\pi\)
−0.271325 + 0.962488i \(0.587462\pi\)
\(948\) 56.9574 1.84989
\(949\) −1.71405 −0.0556404
\(950\) 115.704 3.75393
\(951\) 9.44973 0.306428
\(952\) 140.111 4.54104
\(953\) −57.2875 −1.85572 −0.927861 0.372925i \(-0.878355\pi\)
−0.927861 + 0.372925i \(0.878355\pi\)
\(954\) −7.52054 −0.243486
\(955\) 84.1537 2.72315
\(956\) −124.053 −4.01215
\(957\) 29.3146 0.947605
\(958\) −42.0853 −1.35971
\(959\) −67.1402 −2.16807
\(960\) −37.6628 −1.21556
\(961\) −9.40190 −0.303287
\(962\) −55.0111 −1.77363
\(963\) 17.4268 0.561571
\(964\) 40.9346 1.31841
\(965\) 53.0187 1.70673
\(966\) −47.9437 −1.54256
\(967\) 3.71914 0.119600 0.0597998 0.998210i \(-0.480954\pi\)
0.0597998 + 0.998210i \(0.480954\pi\)
\(968\) −14.8264 −0.476540
\(969\) 23.2205 0.745949
\(970\) 18.2680 0.586550
\(971\) 46.4666 1.49118 0.745592 0.666403i \(-0.232167\pi\)
0.745592 + 0.666403i \(0.232167\pi\)
\(972\) 4.88134 0.156569
\(973\) −1.61077 −0.0516389
\(974\) 4.11687 0.131913
\(975\) 28.1918 0.902860
\(976\) −66.0504 −2.11422
\(977\) −4.04957 −0.129557 −0.0647786 0.997900i \(-0.520634\pi\)
−0.0647786 + 0.997900i \(0.520634\pi\)
\(978\) −12.1615 −0.388883
\(979\) 0.761142 0.0243262
\(980\) −70.3834 −2.24832
\(981\) 7.91662 0.252758
\(982\) 64.6469 2.06297
\(983\) 43.6692 1.39283 0.696415 0.717639i \(-0.254777\pi\)
0.696415 + 0.717639i \(0.254777\pi\)
\(984\) −3.74985 −0.119541
\(985\) 14.8576 0.473402
\(986\) 121.457 3.86797
\(987\) 8.16802 0.259991
\(988\) −52.0273 −1.65521
\(989\) −39.9132 −1.26917
\(990\) 37.5414 1.19314
\(991\) 41.8688 1.33001 0.665003 0.746841i \(-0.268430\pi\)
0.665003 + 0.746841i \(0.268430\pi\)
\(992\) −52.4478 −1.66522
\(993\) −16.7785 −0.532448
\(994\) −90.0963 −2.85768
\(995\) −56.7701 −1.79973
\(996\) −25.7036 −0.814449
\(997\) 47.9337 1.51808 0.759038 0.651047i \(-0.225670\pi\)
0.759038 + 0.651047i \(0.225670\pi\)
\(998\) −18.5486 −0.587146
\(999\) 8.03456 0.254202
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 \(a_p\))