Properties

Label 8042.2.a.c.1.1
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.40447 q^{3}\) \(+1.00000 q^{4}\) \(-1.12046 q^{5}\) \(+3.40447 q^{6}\) \(+3.83806 q^{7}\) \(-1.00000 q^{8}\) \(+8.59041 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.40447 q^{3}\) \(+1.00000 q^{4}\) \(-1.12046 q^{5}\) \(+3.40447 q^{6}\) \(+3.83806 q^{7}\) \(-1.00000 q^{8}\) \(+8.59041 q^{9}\) \(+1.12046 q^{10}\) \(+0.103454 q^{11}\) \(-3.40447 q^{12}\) \(+3.82445 q^{13}\) \(-3.83806 q^{14}\) \(+3.81458 q^{15}\) \(+1.00000 q^{16}\) \(-3.12423 q^{17}\) \(-8.59041 q^{18}\) \(-1.69585 q^{19}\) \(-1.12046 q^{20}\) \(-13.0666 q^{21}\) \(-0.103454 q^{22}\) \(-1.75653 q^{23}\) \(+3.40447 q^{24}\) \(-3.74456 q^{25}\) \(-3.82445 q^{26}\) \(-19.0324 q^{27}\) \(+3.83806 q^{28}\) \(+1.73082 q^{29}\) \(-3.81458 q^{30}\) \(+1.88344 q^{31}\) \(-1.00000 q^{32}\) \(-0.352205 q^{33}\) \(+3.12423 q^{34}\) \(-4.30040 q^{35}\) \(+8.59041 q^{36}\) \(+5.06635 q^{37}\) \(+1.69585 q^{38}\) \(-13.0202 q^{39}\) \(+1.12046 q^{40}\) \(-1.44472 q^{41}\) \(+13.0666 q^{42}\) \(+11.9263 q^{43}\) \(+0.103454 q^{44}\) \(-9.62524 q^{45}\) \(+1.75653 q^{46}\) \(-1.12399 q^{47}\) \(-3.40447 q^{48}\) \(+7.73070 q^{49}\) \(+3.74456 q^{50}\) \(+10.6363 q^{51}\) \(+3.82445 q^{52}\) \(-0.556433 q^{53}\) \(+19.0324 q^{54}\) \(-0.115916 q^{55}\) \(-3.83806 q^{56}\) \(+5.77347 q^{57}\) \(-1.73082 q^{58}\) \(-6.44203 q^{59}\) \(+3.81458 q^{60}\) \(+11.3879 q^{61}\) \(-1.88344 q^{62}\) \(+32.9705 q^{63}\) \(+1.00000 q^{64}\) \(-4.28516 q^{65}\) \(+0.352205 q^{66}\) \(+14.5779 q^{67}\) \(-3.12423 q^{68}\) \(+5.98007 q^{69}\) \(+4.30040 q^{70}\) \(+11.9703 q^{71}\) \(-8.59041 q^{72}\) \(-9.36331 q^{73}\) \(-5.06635 q^{74}\) \(+12.7482 q^{75}\) \(-1.69585 q^{76}\) \(+0.397061 q^{77}\) \(+13.0202 q^{78}\) \(-4.17319 q^{79}\) \(-1.12046 q^{80}\) \(+39.0240 q^{81}\) \(+1.44472 q^{82}\) \(+9.41280 q^{83}\) \(-13.0666 q^{84}\) \(+3.50058 q^{85}\) \(-11.9263 q^{86}\) \(-5.89254 q^{87}\) \(-0.103454 q^{88}\) \(+0.195299 q^{89}\) \(+9.62524 q^{90}\) \(+14.6785 q^{91}\) \(-1.75653 q^{92}\) \(-6.41211 q^{93}\) \(+1.12399 q^{94}\) \(+1.90014 q^{95}\) \(+3.40447 q^{96}\) \(-11.2817 q^{97}\) \(-7.73070 q^{98}\) \(+0.888709 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.40447 −1.96557 −0.982786 0.184749i \(-0.940853\pi\)
−0.982786 + 0.184749i \(0.940853\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.12046 −0.501086 −0.250543 0.968105i \(-0.580609\pi\)
−0.250543 + 0.968105i \(0.580609\pi\)
\(6\) 3.40447 1.38987
\(7\) 3.83806 1.45065 0.725325 0.688407i \(-0.241689\pi\)
0.725325 + 0.688407i \(0.241689\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.59041 2.86347
\(10\) 1.12046 0.354322
\(11\) 0.103454 0.0311924 0.0155962 0.999878i \(-0.495035\pi\)
0.0155962 + 0.999878i \(0.495035\pi\)
\(12\) −3.40447 −0.982786
\(13\) 3.82445 1.06071 0.530356 0.847775i \(-0.322058\pi\)
0.530356 + 0.847775i \(0.322058\pi\)
\(14\) −3.83806 −1.02576
\(15\) 3.81458 0.984921
\(16\) 1.00000 0.250000
\(17\) −3.12423 −0.757736 −0.378868 0.925451i \(-0.623687\pi\)
−0.378868 + 0.925451i \(0.623687\pi\)
\(18\) −8.59041 −2.02478
\(19\) −1.69585 −0.389055 −0.194527 0.980897i \(-0.562317\pi\)
−0.194527 + 0.980897i \(0.562317\pi\)
\(20\) −1.12046 −0.250543
\(21\) −13.0666 −2.85136
\(22\) −0.103454 −0.0220564
\(23\) −1.75653 −0.366263 −0.183131 0.983088i \(-0.558623\pi\)
−0.183131 + 0.983088i \(0.558623\pi\)
\(24\) 3.40447 0.694934
\(25\) −3.74456 −0.748912
\(26\) −3.82445 −0.750037
\(27\) −19.0324 −3.66279
\(28\) 3.83806 0.725325
\(29\) 1.73082 0.321406 0.160703 0.987003i \(-0.448624\pi\)
0.160703 + 0.987003i \(0.448624\pi\)
\(30\) −3.81458 −0.696445
\(31\) 1.88344 0.338276 0.169138 0.985592i \(-0.445902\pi\)
0.169138 + 0.985592i \(0.445902\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.352205 −0.0613110
\(34\) 3.12423 0.535800
\(35\) −4.30040 −0.726901
\(36\) 8.59041 1.43174
\(37\) 5.06635 0.832903 0.416451 0.909158i \(-0.363274\pi\)
0.416451 + 0.909158i \(0.363274\pi\)
\(38\) 1.69585 0.275103
\(39\) −13.0202 −2.08491
\(40\) 1.12046 0.177161
\(41\) −1.44472 −0.225627 −0.112814 0.993616i \(-0.535986\pi\)
−0.112814 + 0.993616i \(0.535986\pi\)
\(42\) 13.0666 2.01621
\(43\) 11.9263 1.81875 0.909373 0.415981i \(-0.136562\pi\)
0.909373 + 0.415981i \(0.136562\pi\)
\(44\) 0.103454 0.0155962
\(45\) −9.62524 −1.43485
\(46\) 1.75653 0.258987
\(47\) −1.12399 −0.163950 −0.0819751 0.996634i \(-0.526123\pi\)
−0.0819751 + 0.996634i \(0.526123\pi\)
\(48\) −3.40447 −0.491393
\(49\) 7.73070 1.10439
\(50\) 3.74456 0.529561
\(51\) 10.6363 1.48938
\(52\) 3.82445 0.530356
\(53\) −0.556433 −0.0764319 −0.0382160 0.999270i \(-0.512167\pi\)
−0.0382160 + 0.999270i \(0.512167\pi\)
\(54\) 19.0324 2.58998
\(55\) −0.115916 −0.0156301
\(56\) −3.83806 −0.512882
\(57\) 5.77347 0.764715
\(58\) −1.73082 −0.227268
\(59\) −6.44203 −0.838681 −0.419340 0.907829i \(-0.637739\pi\)
−0.419340 + 0.907829i \(0.637739\pi\)
\(60\) 3.81458 0.492461
\(61\) 11.3879 1.45807 0.729034 0.684477i \(-0.239969\pi\)
0.729034 + 0.684477i \(0.239969\pi\)
\(62\) −1.88344 −0.239197
\(63\) 32.9705 4.15389
\(64\) 1.00000 0.125000
\(65\) −4.28516 −0.531509
\(66\) 0.352205 0.0433534
\(67\) 14.5779 1.78097 0.890485 0.455012i \(-0.150365\pi\)
0.890485 + 0.455012i \(0.150365\pi\)
\(68\) −3.12423 −0.378868
\(69\) 5.98007 0.719915
\(70\) 4.30040 0.513997
\(71\) 11.9703 1.42062 0.710309 0.703890i \(-0.248555\pi\)
0.710309 + 0.703890i \(0.248555\pi\)
\(72\) −8.59041 −1.01239
\(73\) −9.36331 −1.09589 −0.547946 0.836514i \(-0.684590\pi\)
−0.547946 + 0.836514i \(0.684590\pi\)
\(74\) −5.06635 −0.588951
\(75\) 12.7482 1.47204
\(76\) −1.69585 −0.194527
\(77\) 0.397061 0.0452493
\(78\) 13.0202 1.47425
\(79\) −4.17319 −0.469520 −0.234760 0.972053i \(-0.575430\pi\)
−0.234760 + 0.972053i \(0.575430\pi\)
\(80\) −1.12046 −0.125272
\(81\) 39.0240 4.33600
\(82\) 1.44472 0.159543
\(83\) 9.41280 1.03319 0.516594 0.856230i \(-0.327200\pi\)
0.516594 + 0.856230i \(0.327200\pi\)
\(84\) −13.0666 −1.42568
\(85\) 3.50058 0.379691
\(86\) −11.9263 −1.28605
\(87\) −5.89254 −0.631746
\(88\) −0.103454 −0.0110282
\(89\) 0.195299 0.0207016 0.0103508 0.999946i \(-0.496705\pi\)
0.0103508 + 0.999946i \(0.496705\pi\)
\(90\) 9.62524 1.01459
\(91\) 14.6785 1.53872
\(92\) −1.75653 −0.183131
\(93\) −6.41211 −0.664905
\(94\) 1.12399 0.115930
\(95\) 1.90014 0.194950
\(96\) 3.40447 0.347467
\(97\) −11.2817 −1.14548 −0.572741 0.819736i \(-0.694120\pi\)
−0.572741 + 0.819736i \(0.694120\pi\)
\(98\) −7.73070 −0.780918
\(99\) 0.888709 0.0893186
\(100\) −3.74456 −0.374456
\(101\) −16.3651 −1.62838 −0.814192 0.580595i \(-0.802820\pi\)
−0.814192 + 0.580595i \(0.802820\pi\)
\(102\) −10.6363 −1.05315
\(103\) −2.72133 −0.268140 −0.134070 0.990972i \(-0.542805\pi\)
−0.134070 + 0.990972i \(0.542805\pi\)
\(104\) −3.82445 −0.375018
\(105\) 14.6406 1.42878
\(106\) 0.556433 0.0540455
\(107\) −0.571223 −0.0552222 −0.0276111 0.999619i \(-0.508790\pi\)
−0.0276111 + 0.999619i \(0.508790\pi\)
\(108\) −19.0324 −1.83139
\(109\) 1.32179 0.126605 0.0633024 0.997994i \(-0.479837\pi\)
0.0633024 + 0.997994i \(0.479837\pi\)
\(110\) 0.115916 0.0110522
\(111\) −17.2482 −1.63713
\(112\) 3.83806 0.362662
\(113\) −4.40607 −0.414488 −0.207244 0.978289i \(-0.566449\pi\)
−0.207244 + 0.978289i \(0.566449\pi\)
\(114\) −5.77347 −0.540735
\(115\) 1.96813 0.183529
\(116\) 1.73082 0.160703
\(117\) 32.8536 3.03732
\(118\) 6.44203 0.593037
\(119\) −11.9910 −1.09921
\(120\) −3.81458 −0.348222
\(121\) −10.9893 −0.999027
\(122\) −11.3879 −1.03101
\(123\) 4.91851 0.443487
\(124\) 1.88344 0.169138
\(125\) 9.79796 0.876356
\(126\) −32.9705 −2.93725
\(127\) 12.5153 1.11055 0.555276 0.831666i \(-0.312612\pi\)
0.555276 + 0.831666i \(0.312612\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −40.6028 −3.57488
\(130\) 4.28516 0.375833
\(131\) −16.9230 −1.47857 −0.739283 0.673395i \(-0.764836\pi\)
−0.739283 + 0.673395i \(0.764836\pi\)
\(132\) −0.352205 −0.0306555
\(133\) −6.50877 −0.564382
\(134\) −14.5779 −1.25934
\(135\) 21.3251 1.83537
\(136\) 3.12423 0.267900
\(137\) 14.6461 1.25130 0.625651 0.780103i \(-0.284833\pi\)
0.625651 + 0.780103i \(0.284833\pi\)
\(138\) −5.98007 −0.509057
\(139\) 18.4316 1.56335 0.781675 0.623686i \(-0.214365\pi\)
0.781675 + 0.623686i \(0.214365\pi\)
\(140\) −4.30040 −0.363451
\(141\) 3.82658 0.322256
\(142\) −11.9703 −1.00453
\(143\) 0.395653 0.0330862
\(144\) 8.59041 0.715868
\(145\) −1.93932 −0.161052
\(146\) 9.36331 0.774913
\(147\) −26.3189 −2.17075
\(148\) 5.06635 0.416451
\(149\) −8.36090 −0.684951 −0.342476 0.939527i \(-0.611265\pi\)
−0.342476 + 0.939527i \(0.611265\pi\)
\(150\) −12.7482 −1.04089
\(151\) −11.7406 −0.955440 −0.477720 0.878512i \(-0.658537\pi\)
−0.477720 + 0.878512i \(0.658537\pi\)
\(152\) 1.69585 0.137552
\(153\) −26.8384 −2.16976
\(154\) −0.397061 −0.0319961
\(155\) −2.11033 −0.169505
\(156\) −13.0202 −1.04245
\(157\) 5.57613 0.445024 0.222512 0.974930i \(-0.428574\pi\)
0.222512 + 0.974930i \(0.428574\pi\)
\(158\) 4.17319 0.332001
\(159\) 1.89436 0.150232
\(160\) 1.12046 0.0885804
\(161\) −6.74168 −0.531319
\(162\) −39.0240 −3.06601
\(163\) 0.689524 0.0540077 0.0270038 0.999635i \(-0.491403\pi\)
0.0270038 + 0.999635i \(0.491403\pi\)
\(164\) −1.44472 −0.112814
\(165\) 0.394632 0.0307221
\(166\) −9.41280 −0.730575
\(167\) 6.56375 0.507918 0.253959 0.967215i \(-0.418267\pi\)
0.253959 + 0.967215i \(0.418267\pi\)
\(168\) 13.0666 1.00811
\(169\) 1.62644 0.125110
\(170\) −3.50058 −0.268482
\(171\) −14.5681 −1.11405
\(172\) 11.9263 0.909373
\(173\) 6.91163 0.525482 0.262741 0.964866i \(-0.415374\pi\)
0.262741 + 0.964866i \(0.415374\pi\)
\(174\) 5.89254 0.446712
\(175\) −14.3718 −1.08641
\(176\) 0.103454 0.00779811
\(177\) 21.9317 1.64849
\(178\) −0.195299 −0.0146383
\(179\) 14.6092 1.09194 0.545972 0.837803i \(-0.316160\pi\)
0.545972 + 0.837803i \(0.316160\pi\)
\(180\) −9.62524 −0.717423
\(181\) 0.464401 0.0345187 0.0172593 0.999851i \(-0.494506\pi\)
0.0172593 + 0.999851i \(0.494506\pi\)
\(182\) −14.6785 −1.08804
\(183\) −38.7697 −2.86594
\(184\) 1.75653 0.129493
\(185\) −5.67666 −0.417356
\(186\) 6.41211 0.470159
\(187\) −0.323213 −0.0236356
\(188\) −1.12399 −0.0819751
\(189\) −73.0475 −5.31342
\(190\) −1.90014 −0.137851
\(191\) 0.0538546 0.00389678 0.00194839 0.999998i \(-0.499380\pi\)
0.00194839 + 0.999998i \(0.499380\pi\)
\(192\) −3.40447 −0.245696
\(193\) 7.36228 0.529949 0.264974 0.964255i \(-0.414637\pi\)
0.264974 + 0.964255i \(0.414637\pi\)
\(194\) 11.2817 0.809978
\(195\) 14.5887 1.04472
\(196\) 7.73070 0.552193
\(197\) 19.1876 1.36706 0.683528 0.729924i \(-0.260445\pi\)
0.683528 + 0.729924i \(0.260445\pi\)
\(198\) −0.888709 −0.0631578
\(199\) −10.0373 −0.711523 −0.355761 0.934577i \(-0.615778\pi\)
−0.355761 + 0.934577i \(0.615778\pi\)
\(200\) 3.74456 0.264780
\(201\) −49.6299 −3.50063
\(202\) 16.3651 1.15144
\(203\) 6.64300 0.466247
\(204\) 10.6363 0.744692
\(205\) 1.61876 0.113059
\(206\) 2.72133 0.189604
\(207\) −15.0894 −1.04878
\(208\) 3.82445 0.265178
\(209\) −0.175442 −0.0121356
\(210\) −14.6406 −1.01030
\(211\) 0.217298 0.0149594 0.00747972 0.999972i \(-0.497619\pi\)
0.00747972 + 0.999972i \(0.497619\pi\)
\(212\) −0.556433 −0.0382160
\(213\) −40.7527 −2.79233
\(214\) 0.571223 0.0390480
\(215\) −13.3630 −0.911349
\(216\) 19.0324 1.29499
\(217\) 7.22875 0.490720
\(218\) −1.32179 −0.0895232
\(219\) 31.8771 2.15405
\(220\) −0.115916 −0.00781505
\(221\) −11.9485 −0.803740
\(222\) 17.2482 1.15763
\(223\) 8.46482 0.566847 0.283423 0.958995i \(-0.408530\pi\)
0.283423 + 0.958995i \(0.408530\pi\)
\(224\) −3.83806 −0.256441
\(225\) −32.1673 −2.14449
\(226\) 4.40607 0.293088
\(227\) −13.6199 −0.903986 −0.451993 0.892022i \(-0.649287\pi\)
−0.451993 + 0.892022i \(0.649287\pi\)
\(228\) 5.77347 0.382357
\(229\) −16.8844 −1.11575 −0.557876 0.829924i \(-0.688383\pi\)
−0.557876 + 0.829924i \(0.688383\pi\)
\(230\) −1.96813 −0.129775
\(231\) −1.35178 −0.0889408
\(232\) −1.73082 −0.113634
\(233\) −10.1780 −0.666783 −0.333392 0.942788i \(-0.608193\pi\)
−0.333392 + 0.942788i \(0.608193\pi\)
\(234\) −32.8536 −2.14771
\(235\) 1.25939 0.0821532
\(236\) −6.44203 −0.419340
\(237\) 14.2075 0.922875
\(238\) 11.9910 0.777259
\(239\) 5.56786 0.360155 0.180077 0.983652i \(-0.442365\pi\)
0.180077 + 0.983652i \(0.442365\pi\)
\(240\) 3.81458 0.246230
\(241\) 17.7321 1.14223 0.571114 0.820871i \(-0.306512\pi\)
0.571114 + 0.820871i \(0.306512\pi\)
\(242\) 10.9893 0.706419
\(243\) −75.7587 −4.85992
\(244\) 11.3879 0.729034
\(245\) −8.66196 −0.553393
\(246\) −4.91851 −0.313593
\(247\) −6.48570 −0.412675
\(248\) −1.88344 −0.119599
\(249\) −32.0456 −2.03081
\(250\) −9.79796 −0.619678
\(251\) 7.39420 0.466717 0.233359 0.972391i \(-0.425028\pi\)
0.233359 + 0.972391i \(0.425028\pi\)
\(252\) 32.9705 2.07695
\(253\) −0.181720 −0.0114246
\(254\) −12.5153 −0.785279
\(255\) −11.9176 −0.746311
\(256\) 1.00000 0.0625000
\(257\) −16.0060 −0.998427 −0.499214 0.866479i \(-0.666378\pi\)
−0.499214 + 0.866479i \(0.666378\pi\)
\(258\) 40.6028 2.52782
\(259\) 19.4450 1.20825
\(260\) −4.28516 −0.265754
\(261\) 14.8685 0.920336
\(262\) 16.9230 1.04550
\(263\) 15.5834 0.960916 0.480458 0.877018i \(-0.340470\pi\)
0.480458 + 0.877018i \(0.340470\pi\)
\(264\) 0.352205 0.0216767
\(265\) 0.623463 0.0382990
\(266\) 6.50877 0.399078
\(267\) −0.664889 −0.0406905
\(268\) 14.5779 0.890485
\(269\) 15.9836 0.974535 0.487267 0.873253i \(-0.337994\pi\)
0.487267 + 0.873253i \(0.337994\pi\)
\(270\) −21.3251 −1.29780
\(271\) −12.1165 −0.736023 −0.368011 0.929821i \(-0.619961\pi\)
−0.368011 + 0.929821i \(0.619961\pi\)
\(272\) −3.12423 −0.189434
\(273\) −49.9724 −3.02447
\(274\) −14.6461 −0.884804
\(275\) −0.387388 −0.0233604
\(276\) 5.98007 0.359958
\(277\) −17.9231 −1.07689 −0.538447 0.842659i \(-0.680989\pi\)
−0.538447 + 0.842659i \(0.680989\pi\)
\(278\) −18.4316 −1.10546
\(279\) 16.1795 0.968643
\(280\) 4.30040 0.256998
\(281\) 20.3334 1.21299 0.606495 0.795087i \(-0.292575\pi\)
0.606495 + 0.795087i \(0.292575\pi\)
\(282\) −3.82658 −0.227869
\(283\) 1.61413 0.0959504 0.0479752 0.998849i \(-0.484723\pi\)
0.0479752 + 0.998849i \(0.484723\pi\)
\(284\) 11.9703 0.710309
\(285\) −6.46896 −0.383188
\(286\) −0.395653 −0.0233955
\(287\) −5.54492 −0.327307
\(288\) −8.59041 −0.506195
\(289\) −7.23921 −0.425836
\(290\) 1.93932 0.113881
\(291\) 38.4082 2.25153
\(292\) −9.36331 −0.547946
\(293\) 0.643565 0.0375975 0.0187987 0.999823i \(-0.494016\pi\)
0.0187987 + 0.999823i \(0.494016\pi\)
\(294\) 26.3189 1.53495
\(295\) 7.21806 0.420252
\(296\) −5.06635 −0.294476
\(297\) −1.96897 −0.114251
\(298\) 8.36090 0.484334
\(299\) −6.71778 −0.388499
\(300\) 12.7482 0.736020
\(301\) 45.7739 2.63836
\(302\) 11.7406 0.675598
\(303\) 55.7144 3.20071
\(304\) −1.69585 −0.0972637
\(305\) −12.7597 −0.730618
\(306\) 26.8384 1.53425
\(307\) 5.29202 0.302031 0.151016 0.988531i \(-0.451746\pi\)
0.151016 + 0.988531i \(0.451746\pi\)
\(308\) 0.397061 0.0226247
\(309\) 9.26468 0.527049
\(310\) 2.11033 0.119858
\(311\) 13.1005 0.742863 0.371431 0.928460i \(-0.378867\pi\)
0.371431 + 0.928460i \(0.378867\pi\)
\(312\) 13.0202 0.737125
\(313\) −10.9173 −0.617080 −0.308540 0.951211i \(-0.599840\pi\)
−0.308540 + 0.951211i \(0.599840\pi\)
\(314\) −5.57613 −0.314679
\(315\) −36.9423 −2.08146
\(316\) −4.17319 −0.234760
\(317\) −26.7093 −1.50015 −0.750073 0.661355i \(-0.769982\pi\)
−0.750073 + 0.661355i \(0.769982\pi\)
\(318\) −1.89436 −0.106230
\(319\) 0.179060 0.0100254
\(320\) −1.12046 −0.0626358
\(321\) 1.94471 0.108543
\(322\) 6.74168 0.375699
\(323\) 5.29822 0.294801
\(324\) 39.0240 2.16800
\(325\) −14.3209 −0.794380
\(326\) −0.689524 −0.0381892
\(327\) −4.50001 −0.248851
\(328\) 1.44472 0.0797714
\(329\) −4.31392 −0.237834
\(330\) −0.394632 −0.0217238
\(331\) −17.9560 −0.986949 −0.493474 0.869760i \(-0.664273\pi\)
−0.493474 + 0.869760i \(0.664273\pi\)
\(332\) 9.41280 0.516594
\(333\) 43.5220 2.38499
\(334\) −6.56375 −0.359152
\(335\) −16.3340 −0.892420
\(336\) −13.0666 −0.712839
\(337\) 17.0461 0.928563 0.464281 0.885688i \(-0.346313\pi\)
0.464281 + 0.885688i \(0.346313\pi\)
\(338\) −1.62644 −0.0884665
\(339\) 15.0003 0.814707
\(340\) 3.50058 0.189846
\(341\) 0.194849 0.0105516
\(342\) 14.5681 0.787750
\(343\) 2.80446 0.151427
\(344\) −11.9263 −0.643024
\(345\) −6.70044 −0.360740
\(346\) −6.91163 −0.371572
\(347\) 10.0841 0.541341 0.270670 0.962672i \(-0.412755\pi\)
0.270670 + 0.962672i \(0.412755\pi\)
\(348\) −5.89254 −0.315873
\(349\) −1.68331 −0.0901056 −0.0450528 0.998985i \(-0.514346\pi\)
−0.0450528 + 0.998985i \(0.514346\pi\)
\(350\) 14.3718 0.768208
\(351\) −72.7885 −3.88516
\(352\) −0.103454 −0.00551410
\(353\) 29.5254 1.57148 0.785738 0.618559i \(-0.212283\pi\)
0.785738 + 0.618559i \(0.212283\pi\)
\(354\) −21.9317 −1.16566
\(355\) −13.4123 −0.711853
\(356\) 0.195299 0.0103508
\(357\) 40.8229 2.16058
\(358\) −14.6092 −0.772121
\(359\) −10.9526 −0.578058 −0.289029 0.957320i \(-0.593332\pi\)
−0.289029 + 0.957320i \(0.593332\pi\)
\(360\) 9.62524 0.507295
\(361\) −16.1241 −0.848636
\(362\) −0.464401 −0.0244084
\(363\) 37.4127 1.96366
\(364\) 14.6785 0.769361
\(365\) 10.4912 0.549137
\(366\) 38.7697 2.02652
\(367\) 16.3364 0.852752 0.426376 0.904546i \(-0.359790\pi\)
0.426376 + 0.904546i \(0.359790\pi\)
\(368\) −1.75653 −0.0915656
\(369\) −12.4108 −0.646078
\(370\) 5.67666 0.295115
\(371\) −2.13562 −0.110876
\(372\) −6.41211 −0.332453
\(373\) 38.1215 1.97386 0.986929 0.161157i \(-0.0515226\pi\)
0.986929 + 0.161157i \(0.0515226\pi\)
\(374\) 0.323213 0.0167129
\(375\) −33.3569 −1.72254
\(376\) 1.12399 0.0579652
\(377\) 6.61945 0.340919
\(378\) 73.0475 3.75716
\(379\) 7.40020 0.380123 0.190061 0.981772i \(-0.439131\pi\)
0.190061 + 0.981772i \(0.439131\pi\)
\(380\) 1.90014 0.0974750
\(381\) −42.6079 −2.18287
\(382\) −0.0538546 −0.00275544
\(383\) 2.61367 0.133552 0.0667760 0.997768i \(-0.478729\pi\)
0.0667760 + 0.997768i \(0.478729\pi\)
\(384\) 3.40447 0.173734
\(385\) −0.444892 −0.0226738
\(386\) −7.36228 −0.374730
\(387\) 102.452 5.20793
\(388\) −11.2817 −0.572741
\(389\) 2.92045 0.148073 0.0740363 0.997256i \(-0.476412\pi\)
0.0740363 + 0.997256i \(0.476412\pi\)
\(390\) −14.5887 −0.738727
\(391\) 5.48781 0.277530
\(392\) −7.73070 −0.390459
\(393\) 57.6137 2.90623
\(394\) −19.1876 −0.966655
\(395\) 4.67590 0.235270
\(396\) 0.888709 0.0446593
\(397\) 17.4895 0.877774 0.438887 0.898542i \(-0.355373\pi\)
0.438887 + 0.898542i \(0.355373\pi\)
\(398\) 10.0373 0.503123
\(399\) 22.1589 1.10933
\(400\) −3.74456 −0.187228
\(401\) 0.619684 0.0309455 0.0154728 0.999880i \(-0.495075\pi\)
0.0154728 + 0.999880i \(0.495075\pi\)
\(402\) 49.6299 2.47532
\(403\) 7.20313 0.358813
\(404\) −16.3651 −0.814192
\(405\) −43.7249 −2.17271
\(406\) −6.64300 −0.329687
\(407\) 0.524132 0.0259803
\(408\) −10.6363 −0.526577
\(409\) −17.8248 −0.881379 −0.440689 0.897660i \(-0.645266\pi\)
−0.440689 + 0.897660i \(0.645266\pi\)
\(410\) −1.61876 −0.0799447
\(411\) −49.8623 −2.45952
\(412\) −2.72133 −0.134070
\(413\) −24.7249 −1.21663
\(414\) 15.0894 0.741601
\(415\) −10.5467 −0.517717
\(416\) −3.82445 −0.187509
\(417\) −62.7499 −3.07288
\(418\) 0.175442 0.00858114
\(419\) 19.7361 0.964172 0.482086 0.876124i \(-0.339879\pi\)
0.482086 + 0.876124i \(0.339879\pi\)
\(420\) 14.6406 0.714388
\(421\) 7.14855 0.348399 0.174200 0.984710i \(-0.444266\pi\)
0.174200 + 0.984710i \(0.444266\pi\)
\(422\) −0.217298 −0.0105779
\(423\) −9.65550 −0.469467
\(424\) 0.556433 0.0270228
\(425\) 11.6989 0.567478
\(426\) 40.7527 1.97447
\(427\) 43.7074 2.11515
\(428\) −0.571223 −0.0276111
\(429\) −1.34699 −0.0650333
\(430\) 13.3630 0.644421
\(431\) −28.3249 −1.36436 −0.682181 0.731183i \(-0.738968\pi\)
−0.682181 + 0.731183i \(0.738968\pi\)
\(432\) −19.0324 −0.915696
\(433\) −1.41383 −0.0679443 −0.0339721 0.999423i \(-0.510816\pi\)
−0.0339721 + 0.999423i \(0.510816\pi\)
\(434\) −7.22875 −0.346991
\(435\) 6.60237 0.316559
\(436\) 1.32179 0.0633024
\(437\) 2.97882 0.142496
\(438\) −31.8771 −1.52315
\(439\) −0.221097 −0.0105524 −0.00527618 0.999986i \(-0.501679\pi\)
−0.00527618 + 0.999986i \(0.501679\pi\)
\(440\) 0.115916 0.00552608
\(441\) 66.4099 3.16238
\(442\) 11.9485 0.568330
\(443\) −29.8839 −1.41983 −0.709914 0.704289i \(-0.751266\pi\)
−0.709914 + 0.704289i \(0.751266\pi\)
\(444\) −17.2482 −0.818565
\(445\) −0.218825 −0.0103733
\(446\) −8.46482 −0.400821
\(447\) 28.4644 1.34632
\(448\) 3.83806 0.181331
\(449\) −19.5468 −0.922469 −0.461234 0.887278i \(-0.652593\pi\)
−0.461234 + 0.887278i \(0.652593\pi\)
\(450\) 32.1673 1.51638
\(451\) −0.149462 −0.00703787
\(452\) −4.40607 −0.207244
\(453\) 39.9706 1.87798
\(454\) 13.6199 0.639214
\(455\) −16.4467 −0.771033
\(456\) −5.77347 −0.270368
\(457\) −16.4176 −0.767985 −0.383992 0.923336i \(-0.625451\pi\)
−0.383992 + 0.923336i \(0.625451\pi\)
\(458\) 16.8844 0.788956
\(459\) 59.4615 2.77543
\(460\) 1.96813 0.0917646
\(461\) −25.8489 −1.20390 −0.601951 0.798533i \(-0.705610\pi\)
−0.601951 + 0.798533i \(0.705610\pi\)
\(462\) 1.35178 0.0628906
\(463\) 18.2560 0.848428 0.424214 0.905562i \(-0.360550\pi\)
0.424214 + 0.905562i \(0.360550\pi\)
\(464\) 1.73082 0.0803515
\(465\) 7.18454 0.333175
\(466\) 10.1780 0.471487
\(467\) −13.4379 −0.621834 −0.310917 0.950437i \(-0.600636\pi\)
−0.310917 + 0.950437i \(0.600636\pi\)
\(468\) 32.8536 1.51866
\(469\) 55.9507 2.58357
\(470\) −1.25939 −0.0580911
\(471\) −18.9838 −0.874726
\(472\) 6.44203 0.296518
\(473\) 1.23382 0.0567311
\(474\) −14.2075 −0.652571
\(475\) 6.35022 0.291368
\(476\) −11.9910 −0.549605
\(477\) −4.77999 −0.218861
\(478\) −5.56786 −0.254668
\(479\) 31.0748 1.41984 0.709921 0.704281i \(-0.248731\pi\)
0.709921 + 0.704281i \(0.248731\pi\)
\(480\) −3.81458 −0.174111
\(481\) 19.3760 0.883470
\(482\) −17.7321 −0.807677
\(483\) 22.9518 1.04435
\(484\) −10.9893 −0.499514
\(485\) 12.6407 0.573986
\(486\) 75.7587 3.43649
\(487\) −6.65137 −0.301402 −0.150701 0.988579i \(-0.548153\pi\)
−0.150701 + 0.988579i \(0.548153\pi\)
\(488\) −11.3879 −0.515505
\(489\) −2.34746 −0.106156
\(490\) 8.66196 0.391308
\(491\) −1.68704 −0.0761349 −0.0380675 0.999275i \(-0.512120\pi\)
−0.0380675 + 0.999275i \(0.512120\pi\)
\(492\) 4.91851 0.221743
\(493\) −5.40748 −0.243541
\(494\) 6.48570 0.291805
\(495\) −0.995766 −0.0447564
\(496\) 1.88344 0.0845689
\(497\) 45.9429 2.06082
\(498\) 32.0456 1.43600
\(499\) −20.7511 −0.928947 −0.464474 0.885587i \(-0.653756\pi\)
−0.464474 + 0.885587i \(0.653756\pi\)
\(500\) 9.79796 0.438178
\(501\) −22.3461 −0.998350
\(502\) −7.39420 −0.330019
\(503\) −21.2123 −0.945809 −0.472904 0.881114i \(-0.656794\pi\)
−0.472904 + 0.881114i \(0.656794\pi\)
\(504\) −32.9705 −1.46862
\(505\) 18.3365 0.815961
\(506\) 0.181720 0.00807843
\(507\) −5.53715 −0.245914
\(508\) 12.5153 0.555276
\(509\) 17.2262 0.763539 0.381770 0.924258i \(-0.375315\pi\)
0.381770 + 0.924258i \(0.375315\pi\)
\(510\) 11.9176 0.527721
\(511\) −35.9369 −1.58976
\(512\) −1.00000 −0.0441942
\(513\) 32.2761 1.42502
\(514\) 16.0060 0.705995
\(515\) 3.04915 0.134362
\(516\) −40.6028 −1.78744
\(517\) −0.116280 −0.00511401
\(518\) −19.4450 −0.854362
\(519\) −23.5304 −1.03287
\(520\) 4.28516 0.187917
\(521\) −19.8601 −0.870088 −0.435044 0.900409i \(-0.643267\pi\)
−0.435044 + 0.900409i \(0.643267\pi\)
\(522\) −14.8685 −0.650776
\(523\) −0.834827 −0.0365044 −0.0182522 0.999833i \(-0.505810\pi\)
−0.0182522 + 0.999833i \(0.505810\pi\)
\(524\) −16.9230 −0.739283
\(525\) 48.9285 2.13542
\(526\) −15.5834 −0.679470
\(527\) −5.88429 −0.256324
\(528\) −0.352205 −0.0153277
\(529\) −19.9146 −0.865852
\(530\) −0.623463 −0.0270815
\(531\) −55.3397 −2.40154
\(532\) −6.50877 −0.282191
\(533\) −5.52527 −0.239326
\(534\) 0.664889 0.0287726
\(535\) 0.640034 0.0276711
\(536\) −14.5779 −0.629668
\(537\) −49.7367 −2.14630
\(538\) −15.9836 −0.689100
\(539\) 0.799769 0.0344485
\(540\) 21.3251 0.917686
\(541\) −12.0615 −0.518564 −0.259282 0.965802i \(-0.583486\pi\)
−0.259282 + 0.965802i \(0.583486\pi\)
\(542\) 12.1165 0.520447
\(543\) −1.58104 −0.0678489
\(544\) 3.12423 0.133950
\(545\) −1.48102 −0.0634400
\(546\) 49.9724 2.13862
\(547\) 20.8571 0.891786 0.445893 0.895086i \(-0.352886\pi\)
0.445893 + 0.895086i \(0.352886\pi\)
\(548\) 14.6461 0.625651
\(549\) 97.8266 4.17514
\(550\) 0.387388 0.0165183
\(551\) −2.93522 −0.125044
\(552\) −5.98007 −0.254528
\(553\) −16.0169 −0.681109
\(554\) 17.9231 0.761479
\(555\) 19.3260 0.820344
\(556\) 18.4316 0.781675
\(557\) 12.8057 0.542596 0.271298 0.962495i \(-0.412547\pi\)
0.271298 + 0.962495i \(0.412547\pi\)
\(558\) −16.1795 −0.684934
\(559\) 45.6116 1.92917
\(560\) −4.30040 −0.181725
\(561\) 1.10037 0.0464575
\(562\) −20.3334 −0.857714
\(563\) −29.0983 −1.22635 −0.613173 0.789949i \(-0.710107\pi\)
−0.613173 + 0.789949i \(0.710107\pi\)
\(564\) 3.82658 0.161128
\(565\) 4.93684 0.207695
\(566\) −1.61413 −0.0678472
\(567\) 149.776 6.29001
\(568\) −11.9703 −0.502264
\(569\) 0.149402 0.00626327 0.00313164 0.999995i \(-0.499003\pi\)
0.00313164 + 0.999995i \(0.499003\pi\)
\(570\) 6.46896 0.270955
\(571\) 20.9906 0.878428 0.439214 0.898382i \(-0.355257\pi\)
0.439214 + 0.898382i \(0.355257\pi\)
\(572\) 0.395653 0.0165431
\(573\) −0.183346 −0.00765940
\(574\) 5.54492 0.231441
\(575\) 6.57745 0.274299
\(576\) 8.59041 0.357934
\(577\) −35.1608 −1.46377 −0.731883 0.681431i \(-0.761358\pi\)
−0.731883 + 0.681431i \(0.761358\pi\)
\(578\) 7.23921 0.301111
\(579\) −25.0647 −1.04165
\(580\) −1.93932 −0.0805261
\(581\) 36.1269 1.49879
\(582\) −38.4082 −1.59207
\(583\) −0.0575650 −0.00238410
\(584\) 9.36331 0.387456
\(585\) −36.8113 −1.52196
\(586\) −0.643565 −0.0265854
\(587\) 36.5805 1.50984 0.754919 0.655818i \(-0.227676\pi\)
0.754919 + 0.655818i \(0.227676\pi\)
\(588\) −26.3189 −1.08537
\(589\) −3.19403 −0.131608
\(590\) −7.21806 −0.297163
\(591\) −65.3234 −2.68705
\(592\) 5.06635 0.208226
\(593\) 22.3199 0.916570 0.458285 0.888805i \(-0.348464\pi\)
0.458285 + 0.888805i \(0.348464\pi\)
\(594\) 1.96897 0.0807878
\(595\) 13.4354 0.550799
\(596\) −8.36090 −0.342476
\(597\) 34.1716 1.39855
\(598\) 6.71778 0.274710
\(599\) −13.1602 −0.537710 −0.268855 0.963181i \(-0.586645\pi\)
−0.268855 + 0.963181i \(0.586645\pi\)
\(600\) −12.7482 −0.520445
\(601\) −42.2678 −1.72414 −0.862070 0.506789i \(-0.830832\pi\)
−0.862070 + 0.506789i \(0.830832\pi\)
\(602\) −45.7739 −1.86561
\(603\) 125.230 5.09976
\(604\) −11.7406 −0.477720
\(605\) 12.3131 0.500599
\(606\) −55.7144 −2.26324
\(607\) 43.6465 1.77156 0.885778 0.464109i \(-0.153625\pi\)
0.885778 + 0.464109i \(0.153625\pi\)
\(608\) 1.69585 0.0687758
\(609\) −22.6159 −0.916442
\(610\) 12.7597 0.516625
\(611\) −4.29863 −0.173904
\(612\) −26.8384 −1.08488
\(613\) −36.0549 −1.45625 −0.728123 0.685447i \(-0.759607\pi\)
−0.728123 + 0.685447i \(0.759607\pi\)
\(614\) −5.29202 −0.213568
\(615\) −5.51101 −0.222225
\(616\) −0.397061 −0.0159980
\(617\) −43.8146 −1.76391 −0.881955 0.471334i \(-0.843773\pi\)
−0.881955 + 0.471334i \(0.843773\pi\)
\(618\) −9.26468 −0.372680
\(619\) −1.64726 −0.0662091 −0.0331045 0.999452i \(-0.510539\pi\)
−0.0331045 + 0.999452i \(0.510539\pi\)
\(620\) −2.11033 −0.0847527
\(621\) 33.4310 1.34154
\(622\) −13.1005 −0.525283
\(623\) 0.749568 0.0300308
\(624\) −13.0202 −0.521226
\(625\) 7.74455 0.309782
\(626\) 10.9173 0.436341
\(627\) 0.597286 0.0238533
\(628\) 5.57613 0.222512
\(629\) −15.8284 −0.631121
\(630\) 36.9423 1.47181
\(631\) 12.9588 0.515881 0.257941 0.966161i \(-0.416956\pi\)
0.257941 + 0.966161i \(0.416956\pi\)
\(632\) 4.17319 0.166000
\(633\) −0.739786 −0.0294039
\(634\) 26.7093 1.06076
\(635\) −14.0229 −0.556483
\(636\) 1.89436 0.0751162
\(637\) 29.5657 1.17144
\(638\) −0.179060 −0.00708905
\(639\) 102.830 4.06790
\(640\) 1.12046 0.0442902
\(641\) 17.5748 0.694162 0.347081 0.937835i \(-0.387173\pi\)
0.347081 + 0.937835i \(0.387173\pi\)
\(642\) −1.94471 −0.0767516
\(643\) −25.3767 −1.00076 −0.500380 0.865806i \(-0.666806\pi\)
−0.500380 + 0.865806i \(0.666806\pi\)
\(644\) −6.74168 −0.265659
\(645\) 45.4939 1.79132
\(646\) −5.29822 −0.208456
\(647\) 6.83324 0.268642 0.134321 0.990938i \(-0.457115\pi\)
0.134321 + 0.990938i \(0.457115\pi\)
\(648\) −39.0240 −1.53301
\(649\) −0.666451 −0.0261605
\(650\) 14.3209 0.561712
\(651\) −24.6101 −0.964545
\(652\) 0.689524 0.0270038
\(653\) 20.4040 0.798469 0.399235 0.916849i \(-0.369276\pi\)
0.399235 + 0.916849i \(0.369276\pi\)
\(654\) 4.50001 0.175964
\(655\) 18.9616 0.740890
\(656\) −1.44472 −0.0564069
\(657\) −80.4347 −3.13806
\(658\) 4.31392 0.168174
\(659\) 36.2105 1.41056 0.705280 0.708929i \(-0.250821\pi\)
0.705280 + 0.708929i \(0.250821\pi\)
\(660\) 0.394632 0.0153610
\(661\) 36.3919 1.41548 0.707740 0.706473i \(-0.249715\pi\)
0.707740 + 0.706473i \(0.249715\pi\)
\(662\) 17.9560 0.697878
\(663\) 40.6782 1.57981
\(664\) −9.41280 −0.365287
\(665\) 7.29284 0.282804
\(666\) −43.5220 −1.68644
\(667\) −3.04025 −0.117719
\(668\) 6.56375 0.253959
\(669\) −28.8182 −1.11418
\(670\) 16.3340 0.631037
\(671\) 1.17812 0.0454807
\(672\) 13.0666 0.504053
\(673\) −10.8815 −0.419450 −0.209725 0.977760i \(-0.567257\pi\)
−0.209725 + 0.977760i \(0.567257\pi\)
\(674\) −17.0461 −0.656593
\(675\) 71.2680 2.74311
\(676\) 1.62644 0.0625552
\(677\) −2.38205 −0.0915496 −0.0457748 0.998952i \(-0.514576\pi\)
−0.0457748 + 0.998952i \(0.514576\pi\)
\(678\) −15.0003 −0.576085
\(679\) −43.2998 −1.66169
\(680\) −3.50058 −0.134241
\(681\) 46.3686 1.77685
\(682\) −0.194849 −0.00746114
\(683\) 15.6160 0.597528 0.298764 0.954327i \(-0.403426\pi\)
0.298764 + 0.954327i \(0.403426\pi\)
\(684\) −14.5681 −0.557023
\(685\) −16.4104 −0.627011
\(686\) −2.80446 −0.107075
\(687\) 57.4824 2.19309
\(688\) 11.9263 0.454687
\(689\) −2.12805 −0.0810723
\(690\) 6.70044 0.255082
\(691\) 11.2577 0.428262 0.214131 0.976805i \(-0.431308\pi\)
0.214131 + 0.976805i \(0.431308\pi\)
\(692\) 6.91163 0.262741
\(693\) 3.41092 0.129570
\(694\) −10.0841 −0.382786
\(695\) −20.6520 −0.783374
\(696\) 5.89254 0.223356
\(697\) 4.51364 0.170966
\(698\) 1.68331 0.0637143
\(699\) 34.6507 1.31061
\(700\) −14.3718 −0.543205
\(701\) 22.3718 0.844971 0.422486 0.906370i \(-0.361158\pi\)
0.422486 + 0.906370i \(0.361158\pi\)
\(702\) 72.7885 2.74722
\(703\) −8.59177 −0.324045
\(704\) 0.103454 0.00389905
\(705\) −4.28754 −0.161478
\(706\) −29.5254 −1.11120
\(707\) −62.8101 −2.36222
\(708\) 21.9317 0.824244
\(709\) 52.1103 1.95704 0.978522 0.206141i \(-0.0660905\pi\)
0.978522 + 0.206141i \(0.0660905\pi\)
\(710\) 13.4123 0.503356
\(711\) −35.8494 −1.34446
\(712\) −0.195299 −0.00731913
\(713\) −3.30833 −0.123898
\(714\) −40.8229 −1.52776
\(715\) −0.443315 −0.0165790
\(716\) 14.6092 0.545972
\(717\) −18.9556 −0.707910
\(718\) 10.9526 0.408749
\(719\) 33.7289 1.25788 0.628938 0.777456i \(-0.283490\pi\)
0.628938 + 0.777456i \(0.283490\pi\)
\(720\) −9.62524 −0.358712
\(721\) −10.4446 −0.388978
\(722\) 16.1241 0.600077
\(723\) −60.3685 −2.24513
\(724\) 0.464401 0.0172593
\(725\) −6.48117 −0.240705
\(726\) −37.4127 −1.38852
\(727\) 48.2376 1.78903 0.894517 0.447033i \(-0.147519\pi\)
0.894517 + 0.447033i \(0.147519\pi\)
\(728\) −14.6785 −0.544020
\(729\) 140.846 5.21653
\(730\) −10.4912 −0.388298
\(731\) −37.2605 −1.37813
\(732\) −38.7697 −1.43297
\(733\) 30.7900 1.13725 0.568626 0.822596i \(-0.307475\pi\)
0.568626 + 0.822596i \(0.307475\pi\)
\(734\) −16.3364 −0.602987
\(735\) 29.4894 1.08773
\(736\) 1.75653 0.0647467
\(737\) 1.50813 0.0555528
\(738\) 12.4108 0.456846
\(739\) 26.1911 0.963454 0.481727 0.876321i \(-0.340010\pi\)
0.481727 + 0.876321i \(0.340010\pi\)
\(740\) −5.67666 −0.208678
\(741\) 22.0804 0.811142
\(742\) 2.13562 0.0784011
\(743\) −8.62158 −0.316295 −0.158148 0.987415i \(-0.550552\pi\)
−0.158148 + 0.987415i \(0.550552\pi\)
\(744\) 6.41211 0.235079
\(745\) 9.36808 0.343220
\(746\) −38.1215 −1.39573
\(747\) 80.8598 2.95851
\(748\) −0.323213 −0.0118178
\(749\) −2.19239 −0.0801081
\(750\) 33.3569 1.21802
\(751\) −7.22212 −0.263539 −0.131769 0.991280i \(-0.542066\pi\)
−0.131769 + 0.991280i \(0.542066\pi\)
\(752\) −1.12399 −0.0409876
\(753\) −25.1733 −0.917367
\(754\) −6.61945 −0.241066
\(755\) 13.1550 0.478758
\(756\) −73.0475 −2.65671
\(757\) −14.4122 −0.523819 −0.261910 0.965092i \(-0.584352\pi\)
−0.261910 + 0.965092i \(0.584352\pi\)
\(758\) −7.40020 −0.268787
\(759\) 0.618659 0.0224559
\(760\) −1.90014 −0.0689253
\(761\) −24.9852 −0.905713 −0.452857 0.891583i \(-0.649595\pi\)
−0.452857 + 0.891583i \(0.649595\pi\)
\(762\) 42.6079 1.54352
\(763\) 5.07312 0.183659
\(764\) 0.0538546 0.00194839
\(765\) 30.0714 1.08724
\(766\) −2.61367 −0.0944356
\(767\) −24.6372 −0.889599
\(768\) −3.40447 −0.122848
\(769\) 50.8227 1.83272 0.916358 0.400361i \(-0.131115\pi\)
0.916358 + 0.400361i \(0.131115\pi\)
\(770\) 0.444892 0.0160328
\(771\) 54.4920 1.96248
\(772\) 7.36228 0.264974
\(773\) 35.3377 1.27101 0.635505 0.772097i \(-0.280792\pi\)
0.635505 + 0.772097i \(0.280792\pi\)
\(774\) −102.452 −3.68256
\(775\) −7.05266 −0.253339
\(776\) 11.2817 0.404989
\(777\) −66.1997 −2.37490
\(778\) −2.92045 −0.104703
\(779\) 2.45003 0.0877814
\(780\) 14.5887 0.522359
\(781\) 1.23838 0.0443126
\(782\) −5.48781 −0.196244
\(783\) −32.9417 −1.17724
\(784\) 7.73070 0.276096
\(785\) −6.24785 −0.222995
\(786\) −57.6137 −2.05501
\(787\) −19.8830 −0.708752 −0.354376 0.935103i \(-0.615307\pi\)
−0.354376 + 0.935103i \(0.615307\pi\)
\(788\) 19.1876 0.683528
\(789\) −53.0534 −1.88875
\(790\) −4.67590 −0.166361
\(791\) −16.9108 −0.601278
\(792\) −0.888709 −0.0315789
\(793\) 43.5524 1.54659
\(794\) −17.4895 −0.620680
\(795\) −2.12256 −0.0752794
\(796\) −10.0373 −0.355761
\(797\) −25.7452 −0.911943 −0.455971 0.889994i \(-0.650708\pi\)
−0.455971 + 0.889994i \(0.650708\pi\)
\(798\) −22.1589 −0.784417
\(799\) 3.51159 0.124231
\(800\) 3.74456 0.132390
\(801\) 1.67770 0.0592785
\(802\) −0.619684 −0.0218818
\(803\) −0.968668 −0.0341835
\(804\) −49.6299 −1.75031
\(805\) 7.55381 0.266237
\(806\) −7.20313 −0.253719
\(807\) −54.4155 −1.91552
\(808\) 16.3651 0.575721
\(809\) 10.2074 0.358873 0.179437 0.983770i \(-0.442572\pi\)
0.179437 + 0.983770i \(0.442572\pi\)
\(810\) 43.7249 1.53634
\(811\) −6.72203 −0.236042 −0.118021 0.993011i \(-0.537655\pi\)
−0.118021 + 0.993011i \(0.537655\pi\)
\(812\) 6.64300 0.233124
\(813\) 41.2501 1.44671
\(814\) −0.524132 −0.0183708
\(815\) −0.772586 −0.0270625
\(816\) 10.6363 0.372346
\(817\) −20.2252 −0.707592
\(818\) 17.8248 0.623229
\(819\) 126.094 4.40609
\(820\) 1.61876 0.0565294
\(821\) −38.4075 −1.34043 −0.670216 0.742167i \(-0.733798\pi\)
−0.670216 + 0.742167i \(0.733798\pi\)
\(822\) 49.8623 1.73915
\(823\) −5.44865 −0.189928 −0.0949640 0.995481i \(-0.530274\pi\)
−0.0949640 + 0.995481i \(0.530274\pi\)
\(824\) 2.72133 0.0948020
\(825\) 1.31885 0.0459165
\(826\) 24.7249 0.860289
\(827\) 27.7143 0.963720 0.481860 0.876248i \(-0.339961\pi\)
0.481860 + 0.876248i \(0.339961\pi\)
\(828\) −15.0894 −0.524391
\(829\) 4.61777 0.160382 0.0801909 0.996780i \(-0.474447\pi\)
0.0801909 + 0.996780i \(0.474447\pi\)
\(830\) 10.5467 0.366081
\(831\) 61.0186 2.11671
\(832\) 3.82445 0.132589
\(833\) −24.1525 −0.836833
\(834\) 62.7499 2.17285
\(835\) −7.35444 −0.254511
\(836\) −0.175442 −0.00606778
\(837\) −35.8464 −1.23903
\(838\) −19.7361 −0.681772
\(839\) −14.2444 −0.491770 −0.245885 0.969299i \(-0.579079\pi\)
−0.245885 + 0.969299i \(0.579079\pi\)
\(840\) −14.6406 −0.505149
\(841\) −26.0043 −0.896698
\(842\) −7.14855 −0.246355
\(843\) −69.2245 −2.38422
\(844\) 0.217298 0.00747972
\(845\) −1.82236 −0.0626912
\(846\) 9.65550 0.331963
\(847\) −42.1776 −1.44924
\(848\) −0.556433 −0.0191080
\(849\) −5.49527 −0.188597
\(850\) −11.6989 −0.401268
\(851\) −8.89921 −0.305061
\(852\) −40.7527 −1.39616
\(853\) 34.2844 1.17388 0.586938 0.809632i \(-0.300333\pi\)
0.586938 + 0.809632i \(0.300333\pi\)
\(854\) −43.7074 −1.49563
\(855\) 16.3230 0.558234
\(856\) 0.571223 0.0195240
\(857\) 4.90205 0.167451 0.0837253 0.996489i \(-0.473318\pi\)
0.0837253 + 0.996489i \(0.473318\pi\)
\(858\) 1.34699 0.0459855
\(859\) 48.6695 1.66058 0.830292 0.557329i \(-0.188174\pi\)
0.830292 + 0.557329i \(0.188174\pi\)
\(860\) −13.3630 −0.455675
\(861\) 18.8775 0.643344
\(862\) 28.3249 0.964750
\(863\) −15.3208 −0.521526 −0.260763 0.965403i \(-0.583974\pi\)
−0.260763 + 0.965403i \(0.583974\pi\)
\(864\) 19.0324 0.647495
\(865\) −7.74423 −0.263312
\(866\) 1.41383 0.0480438
\(867\) 24.6457 0.837011
\(868\) 7.22875 0.245360
\(869\) −0.431731 −0.0146455
\(870\) −6.60237 −0.223841
\(871\) 55.7524 1.88910
\(872\) −1.32179 −0.0447616
\(873\) −96.9144 −3.28006
\(874\) −2.97882 −0.100760
\(875\) 37.6052 1.27129
\(876\) 31.8771 1.07703
\(877\) 37.8015 1.27646 0.638232 0.769844i \(-0.279666\pi\)
0.638232 + 0.769844i \(0.279666\pi\)
\(878\) 0.221097 0.00746165
\(879\) −2.19100 −0.0739005
\(880\) −0.115916 −0.00390753
\(881\) −44.4516 −1.49761 −0.748806 0.662789i \(-0.769373\pi\)
−0.748806 + 0.662789i \(0.769373\pi\)
\(882\) −66.4099 −2.23614
\(883\) 30.9777 1.04248 0.521241 0.853409i \(-0.325469\pi\)
0.521241 + 0.853409i \(0.325469\pi\)
\(884\) −11.9485 −0.401870
\(885\) −24.5737 −0.826035
\(886\) 29.8839 1.00397
\(887\) 33.2633 1.11687 0.558436 0.829547i \(-0.311401\pi\)
0.558436 + 0.829547i \(0.311401\pi\)
\(888\) 17.2482 0.578813
\(889\) 48.0344 1.61102
\(890\) 0.218825 0.00733504
\(891\) 4.03717 0.135250
\(892\) 8.46482 0.283423
\(893\) 1.90611 0.0637856
\(894\) −28.4644 −0.951992
\(895\) −16.3691 −0.547159
\(896\) −3.83806 −0.128221
\(897\) 22.8705 0.763623
\(898\) 19.5468 0.652284
\(899\) 3.25990 0.108724
\(900\) −32.1673 −1.07224
\(901\) 1.73842 0.0579152
\(902\) 0.149462 0.00497653
\(903\) −155.836 −5.18589
\(904\) 4.40607 0.146544
\(905\) −0.520345 −0.0172968
\(906\) −39.9706 −1.32794
\(907\) 10.9486 0.363542 0.181771 0.983341i \(-0.441817\pi\)
0.181771 + 0.983341i \(0.441817\pi\)
\(908\) −13.6199 −0.451993
\(909\) −140.583 −4.66283
\(910\) 16.4467 0.545203
\(911\) 33.2020 1.10003 0.550015 0.835155i \(-0.314622\pi\)
0.550015 + 0.835155i \(0.314622\pi\)
\(912\) 5.77347 0.191179
\(913\) 0.973788 0.0322277
\(914\) 16.4176 0.543047
\(915\) 43.4400 1.43608
\(916\) −16.8844 −0.557876
\(917\) −64.9514 −2.14488
\(918\) −59.4615 −1.96252
\(919\) −18.8565 −0.622017 −0.311009 0.950407i \(-0.600667\pi\)
−0.311009 + 0.950407i \(0.600667\pi\)
\(920\) −1.96813 −0.0648874
\(921\) −18.0165 −0.593664
\(922\) 25.8489 0.851288
\(923\) 45.7800 1.50687
\(924\) −1.35178 −0.0444704
\(925\) −18.9713 −0.623771
\(926\) −18.2560 −0.599929
\(927\) −23.3773 −0.767812
\(928\) −1.73082 −0.0568171
\(929\) −18.9793 −0.622690 −0.311345 0.950297i \(-0.600780\pi\)
−0.311345 + 0.950297i \(0.600780\pi\)
\(930\) −7.18454 −0.235590
\(931\) −13.1101 −0.429666
\(932\) −10.1780 −0.333392
\(933\) −44.6003 −1.46015
\(934\) 13.4379 0.439703
\(935\) 0.362148 0.0118435
\(936\) −32.8536 −1.07385
\(937\) −6.18280 −0.201983 −0.100992 0.994887i \(-0.532202\pi\)
−0.100992 + 0.994887i \(0.532202\pi\)
\(938\) −55.9507 −1.82686
\(939\) 37.1675 1.21291
\(940\) 1.25939 0.0410766
\(941\) 9.39988 0.306427 0.153214 0.988193i \(-0.451038\pi\)
0.153214 + 0.988193i \(0.451038\pi\)
\(942\) 18.9838 0.618525
\(943\) 2.53770 0.0826389
\(944\) −6.44203 −0.209670
\(945\) 81.8470 2.66248
\(946\) −1.23382 −0.0401150
\(947\) 50.3046 1.63468 0.817341 0.576155i \(-0.195447\pi\)
0.817341 + 0.576155i \(0.195447\pi\)
\(948\) 14.2075 0.461438
\(949\) −35.8095 −1.16243
\(950\) −6.35022 −0.206028
\(951\) 90.9311 2.94864
\(952\) 11.9910 0.388629
\(953\) 21.2584 0.688628 0.344314 0.938855i \(-0.388112\pi\)
0.344314 + 0.938855i \(0.388112\pi\)
\(954\) 4.77999 0.154758
\(955\) −0.0603421 −0.00195262
\(956\) 5.56786 0.180077
\(957\) −0.609604 −0.0197057
\(958\) −31.0748 −1.00398
\(959\) 56.2127 1.81520
\(960\) 3.81458 0.123115
\(961\) −27.4527 −0.885570
\(962\) −19.3760 −0.624708
\(963\) −4.90704 −0.158127
\(964\) 17.7321 0.571114
\(965\) −8.24917 −0.265550
\(966\) −22.9518 −0.738463
\(967\) −27.1321 −0.872509 −0.436254 0.899823i \(-0.643695\pi\)
−0.436254 + 0.899823i \(0.643695\pi\)
\(968\) 10.9893 0.353209
\(969\) −18.0376 −0.579452
\(970\) −12.6407 −0.405869
\(971\) 12.3740 0.397100 0.198550 0.980091i \(-0.436377\pi\)
0.198550 + 0.980091i \(0.436377\pi\)
\(972\) −75.7587 −2.42996
\(973\) 70.7417 2.26787
\(974\) 6.65137 0.213124
\(975\) 48.7551 1.56141
\(976\) 11.3879 0.364517
\(977\) −29.3625 −0.939388 −0.469694 0.882829i \(-0.655636\pi\)
−0.469694 + 0.882829i \(0.655636\pi\)
\(978\) 2.34746 0.0750636
\(979\) 0.0202044 0.000645734 0
\(980\) −8.66196 −0.276696
\(981\) 11.3548 0.362529
\(982\) 1.68704 0.0538355
\(983\) 58.2021 1.85636 0.928180 0.372132i \(-0.121373\pi\)
0.928180 + 0.372132i \(0.121373\pi\)
\(984\) −4.91851 −0.156796
\(985\) −21.4990 −0.685014
\(986\) 5.40748 0.172209
\(987\) 14.6866 0.467480
\(988\) −6.48570 −0.206338
\(989\) −20.9490 −0.666139
\(990\) 0.995766 0.0316475
\(991\) 36.4659 1.15838 0.579189 0.815193i \(-0.303369\pi\)
0.579189 + 0.815193i \(0.303369\pi\)
\(992\) −1.88344 −0.0597993
\(993\) 61.1305 1.93992
\(994\) −45.9429 −1.45722
\(995\) 11.2464 0.356535
\(996\) −32.0456 −1.01540
\(997\) 27.1476 0.859772 0.429886 0.902883i \(-0.358554\pi\)
0.429886 + 0.902883i \(0.358554\pi\)
\(998\) 20.7511 0.656865
\(999\) −96.4248 −3.05074
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 \(a_p\))