Properties

Label 8015.2.a.l.1.17
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.44897 q^{2}\) \(-0.334420 q^{3}\) \(+0.0995284 q^{4}\) \(-1.00000 q^{5}\) \(+0.484566 q^{6}\) \(-1.00000 q^{7}\) \(+2.75374 q^{8}\) \(-2.88816 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.44897 q^{2}\) \(-0.334420 q^{3}\) \(+0.0995284 q^{4}\) \(-1.00000 q^{5}\) \(+0.484566 q^{6}\) \(-1.00000 q^{7}\) \(+2.75374 q^{8}\) \(-2.88816 q^{9}\) \(+1.44897 q^{10}\) \(+1.28070 q^{11}\) \(-0.0332843 q^{12}\) \(-2.76676 q^{13}\) \(+1.44897 q^{14}\) \(+0.334420 q^{15}\) \(-4.18915 q^{16}\) \(-5.48093 q^{17}\) \(+4.18488 q^{18}\) \(+2.60890 q^{19}\) \(-0.0995284 q^{20}\) \(+0.334420 q^{21}\) \(-1.85570 q^{22}\) \(-6.54731 q^{23}\) \(-0.920905 q^{24}\) \(+1.00000 q^{25}\) \(+4.00896 q^{26}\) \(+1.96912 q^{27}\) \(-0.0995284 q^{28}\) \(-7.08572 q^{29}\) \(-0.484566 q^{30}\) \(-9.08612 q^{31}\) \(+0.562503 q^{32}\) \(-0.428292 q^{33}\) \(+7.94173 q^{34}\) \(+1.00000 q^{35}\) \(-0.287454 q^{36}\) \(-5.27324 q^{37}\) \(-3.78024 q^{38}\) \(+0.925260 q^{39}\) \(-2.75374 q^{40}\) \(-3.98210 q^{41}\) \(-0.484566 q^{42}\) \(+4.75514 q^{43}\) \(+0.127466 q^{44}\) \(+2.88816 q^{45}\) \(+9.48688 q^{46}\) \(+10.9570 q^{47}\) \(+1.40094 q^{48}\) \(+1.00000 q^{49}\) \(-1.44897 q^{50}\) \(+1.83293 q^{51}\) \(-0.275371 q^{52}\) \(-11.4309 q^{53}\) \(-2.85321 q^{54}\) \(-1.28070 q^{55}\) \(-2.75374 q^{56}\) \(-0.872470 q^{57}\) \(+10.2670 q^{58}\) \(-8.15041 q^{59}\) \(+0.0332843 q^{60}\) \(-14.6321 q^{61}\) \(+13.1656 q^{62}\) \(+2.88816 q^{63}\) \(+7.56325 q^{64}\) \(+2.76676 q^{65}\) \(+0.620585 q^{66}\) \(+1.19958 q^{67}\) \(-0.545508 q^{68}\) \(+2.18955 q^{69}\) \(-1.44897 q^{70}\) \(+8.09731 q^{71}\) \(-7.95324 q^{72}\) \(+14.8891 q^{73}\) \(+7.64079 q^{74}\) \(-0.334420 q^{75}\) \(+0.259660 q^{76}\) \(-1.28070 q^{77}\) \(-1.34068 q^{78}\) \(-11.2918 q^{79}\) \(+4.18915 q^{80}\) \(+8.00598 q^{81}\) \(+5.76996 q^{82}\) \(-14.2236 q^{83}\) \(+0.0332843 q^{84}\) \(+5.48093 q^{85}\) \(-6.89008 q^{86}\) \(+2.36961 q^{87}\) \(+3.52671 q^{88}\) \(+7.10603 q^{89}\) \(-4.18488 q^{90}\) \(+2.76676 q^{91}\) \(-0.651643 q^{92}\) \(+3.03858 q^{93}\) \(-15.8764 q^{94}\) \(-2.60890 q^{95}\) \(-0.188112 q^{96}\) \(-9.93147 q^{97}\) \(-1.44897 q^{98}\) \(-3.69887 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44897 −1.02458 −0.512290 0.858813i \(-0.671203\pi\)
−0.512290 + 0.858813i \(0.671203\pi\)
\(3\) −0.334420 −0.193078 −0.0965388 0.995329i \(-0.530777\pi\)
−0.0965388 + 0.995329i \(0.530777\pi\)
\(4\) 0.0995284 0.0497642
\(5\) −1.00000 −0.447214
\(6\) 0.484566 0.197823
\(7\) −1.00000 −0.377964
\(8\) 2.75374 0.973593
\(9\) −2.88816 −0.962721
\(10\) 1.44897 0.458206
\(11\) 1.28070 0.386146 0.193073 0.981184i \(-0.438155\pi\)
0.193073 + 0.981184i \(0.438155\pi\)
\(12\) −0.0332843 −0.00960835
\(13\) −2.76676 −0.767361 −0.383680 0.923466i \(-0.625344\pi\)
−0.383680 + 0.923466i \(0.625344\pi\)
\(14\) 1.44897 0.387255
\(15\) 0.334420 0.0863469
\(16\) −4.18915 −1.04729
\(17\) −5.48093 −1.32932 −0.664660 0.747146i \(-0.731424\pi\)
−0.664660 + 0.747146i \(0.731424\pi\)
\(18\) 4.18488 0.986385
\(19\) 2.60890 0.598523 0.299262 0.954171i \(-0.403260\pi\)
0.299262 + 0.954171i \(0.403260\pi\)
\(20\) −0.0995284 −0.0222552
\(21\) 0.334420 0.0729765
\(22\) −1.85570 −0.395637
\(23\) −6.54731 −1.36521 −0.682604 0.730789i \(-0.739153\pi\)
−0.682604 + 0.730789i \(0.739153\pi\)
\(24\) −0.920905 −0.187979
\(25\) 1.00000 0.200000
\(26\) 4.00896 0.786222
\(27\) 1.96912 0.378957
\(28\) −0.0995284 −0.0188091
\(29\) −7.08572 −1.31579 −0.657893 0.753112i \(-0.728552\pi\)
−0.657893 + 0.753112i \(0.728552\pi\)
\(30\) −0.484566 −0.0884693
\(31\) −9.08612 −1.63192 −0.815958 0.578112i \(-0.803790\pi\)
−0.815958 + 0.578112i \(0.803790\pi\)
\(32\) 0.562503 0.0994374
\(33\) −0.428292 −0.0745561
\(34\) 7.94173 1.36200
\(35\) 1.00000 0.169031
\(36\) −0.287454 −0.0479090
\(37\) −5.27324 −0.866915 −0.433458 0.901174i \(-0.642707\pi\)
−0.433458 + 0.901174i \(0.642707\pi\)
\(38\) −3.78024 −0.613235
\(39\) 0.925260 0.148160
\(40\) −2.75374 −0.435404
\(41\) −3.98210 −0.621899 −0.310950 0.950426i \(-0.600647\pi\)
−0.310950 + 0.950426i \(0.600647\pi\)
\(42\) −0.484566 −0.0747702
\(43\) 4.75514 0.725152 0.362576 0.931954i \(-0.381897\pi\)
0.362576 + 0.931954i \(0.381897\pi\)
\(44\) 0.127466 0.0192162
\(45\) 2.88816 0.430542
\(46\) 9.48688 1.39876
\(47\) 10.9570 1.59825 0.799123 0.601168i \(-0.205298\pi\)
0.799123 + 0.601168i \(0.205298\pi\)
\(48\) 1.40094 0.202208
\(49\) 1.00000 0.142857
\(50\) −1.44897 −0.204916
\(51\) 1.83293 0.256662
\(52\) −0.275371 −0.0381871
\(53\) −11.4309 −1.57016 −0.785078 0.619396i \(-0.787377\pi\)
−0.785078 + 0.619396i \(0.787377\pi\)
\(54\) −2.85321 −0.388272
\(55\) −1.28070 −0.172690
\(56\) −2.75374 −0.367983
\(57\) −0.872470 −0.115561
\(58\) 10.2670 1.34813
\(59\) −8.15041 −1.06109 −0.530547 0.847656i \(-0.678013\pi\)
−0.530547 + 0.847656i \(0.678013\pi\)
\(60\) 0.0332843 0.00429698
\(61\) −14.6321 −1.87345 −0.936726 0.350063i \(-0.886160\pi\)
−0.936726 + 0.350063i \(0.886160\pi\)
\(62\) 13.1656 1.67203
\(63\) 2.88816 0.363874
\(64\) 7.56325 0.945406
\(65\) 2.76676 0.343174
\(66\) 0.620585 0.0763887
\(67\) 1.19958 0.146551 0.0732757 0.997312i \(-0.476655\pi\)
0.0732757 + 0.997312i \(0.476655\pi\)
\(68\) −0.545508 −0.0661526
\(69\) 2.18955 0.263591
\(70\) −1.44897 −0.173186
\(71\) 8.09731 0.960974 0.480487 0.877002i \(-0.340460\pi\)
0.480487 + 0.877002i \(0.340460\pi\)
\(72\) −7.95324 −0.937298
\(73\) 14.8891 1.74264 0.871320 0.490715i \(-0.163264\pi\)
0.871320 + 0.490715i \(0.163264\pi\)
\(74\) 7.64079 0.888224
\(75\) −0.334420 −0.0386155
\(76\) 0.259660 0.0297850
\(77\) −1.28070 −0.145949
\(78\) −1.34068 −0.151802
\(79\) −11.2918 −1.27043 −0.635216 0.772334i \(-0.719089\pi\)
−0.635216 + 0.772334i \(0.719089\pi\)
\(80\) 4.18915 0.468361
\(81\) 8.00598 0.889553
\(82\) 5.76996 0.637185
\(83\) −14.2236 −1.56125 −0.780623 0.625002i \(-0.785098\pi\)
−0.780623 + 0.625002i \(0.785098\pi\)
\(84\) 0.0332843 0.00363161
\(85\) 5.48093 0.594490
\(86\) −6.89008 −0.742977
\(87\) 2.36961 0.254049
\(88\) 3.52671 0.375949
\(89\) 7.10603 0.753237 0.376619 0.926368i \(-0.377087\pi\)
0.376619 + 0.926368i \(0.377087\pi\)
\(90\) −4.18488 −0.441125
\(91\) 2.76676 0.290035
\(92\) −0.651643 −0.0679385
\(93\) 3.03858 0.315086
\(94\) −15.8764 −1.63753
\(95\) −2.60890 −0.267668
\(96\) −0.188112 −0.0191991
\(97\) −9.93147 −1.00839 −0.504194 0.863590i \(-0.668210\pi\)
−0.504194 + 0.863590i \(0.668210\pi\)
\(98\) −1.44897 −0.146369
\(99\) −3.69887 −0.371751
\(100\) 0.0995284 0.00995284
\(101\) −7.35364 −0.731714 −0.365857 0.930671i \(-0.619224\pi\)
−0.365857 + 0.930671i \(0.619224\pi\)
\(102\) −2.65587 −0.262971
\(103\) 3.52525 0.347353 0.173676 0.984803i \(-0.444435\pi\)
0.173676 + 0.984803i \(0.444435\pi\)
\(104\) −7.61892 −0.747097
\(105\) −0.334420 −0.0326361
\(106\) 16.5631 1.60875
\(107\) −17.2285 −1.66554 −0.832770 0.553619i \(-0.813246\pi\)
−0.832770 + 0.553619i \(0.813246\pi\)
\(108\) 0.195983 0.0188585
\(109\) −4.63683 −0.444128 −0.222064 0.975032i \(-0.571279\pi\)
−0.222064 + 0.975032i \(0.571279\pi\)
\(110\) 1.85570 0.176934
\(111\) 1.76348 0.167382
\(112\) 4.18915 0.395838
\(113\) 13.9686 1.31406 0.657029 0.753865i \(-0.271813\pi\)
0.657029 + 0.753865i \(0.271813\pi\)
\(114\) 1.26419 0.118402
\(115\) 6.54731 0.610540
\(116\) −0.705230 −0.0654790
\(117\) 7.99085 0.738754
\(118\) 11.8097 1.08717
\(119\) 5.48093 0.502436
\(120\) 0.920905 0.0840667
\(121\) −9.35980 −0.850891
\(122\) 21.2016 1.91950
\(123\) 1.33169 0.120075
\(124\) −0.904327 −0.0812109
\(125\) −1.00000 −0.0894427
\(126\) −4.18488 −0.372818
\(127\) −3.23631 −0.287176 −0.143588 0.989638i \(-0.545864\pi\)
−0.143588 + 0.989638i \(0.545864\pi\)
\(128\) −12.0840 −1.06808
\(129\) −1.59022 −0.140011
\(130\) −4.00896 −0.351609
\(131\) −0.438322 −0.0382964 −0.0191482 0.999817i \(-0.506095\pi\)
−0.0191482 + 0.999817i \(0.506095\pi\)
\(132\) −0.0426272 −0.00371023
\(133\) −2.60890 −0.226221
\(134\) −1.73815 −0.150154
\(135\) −1.96912 −0.169475
\(136\) −15.0930 −1.29422
\(137\) −19.0566 −1.62812 −0.814059 0.580782i \(-0.802747\pi\)
−0.814059 + 0.580782i \(0.802747\pi\)
\(138\) −3.17261 −0.270070
\(139\) 7.63665 0.647732 0.323866 0.946103i \(-0.395017\pi\)
0.323866 + 0.946103i \(0.395017\pi\)
\(140\) 0.0995284 0.00841168
\(141\) −3.66425 −0.308585
\(142\) −11.7328 −0.984595
\(143\) −3.54339 −0.296313
\(144\) 12.0990 1.00825
\(145\) 7.08572 0.588437
\(146\) −21.5740 −1.78547
\(147\) −0.334420 −0.0275825
\(148\) −0.524837 −0.0431413
\(149\) −3.89493 −0.319085 −0.159542 0.987191i \(-0.551002\pi\)
−0.159542 + 0.987191i \(0.551002\pi\)
\(150\) 0.484566 0.0395647
\(151\) −16.0726 −1.30797 −0.653985 0.756507i \(-0.726904\pi\)
−0.653985 + 0.756507i \(0.726904\pi\)
\(152\) 7.18423 0.582718
\(153\) 15.8298 1.27977
\(154\) 1.85570 0.149537
\(155\) 9.08612 0.729815
\(156\) 0.0920896 0.00737307
\(157\) −15.0373 −1.20011 −0.600053 0.799960i \(-0.704854\pi\)
−0.600053 + 0.799960i \(0.704854\pi\)
\(158\) 16.3616 1.30166
\(159\) 3.82273 0.303162
\(160\) −0.562503 −0.0444698
\(161\) 6.54731 0.516000
\(162\) −11.6005 −0.911418
\(163\) 23.2829 1.82366 0.911830 0.410568i \(-0.134670\pi\)
0.911830 + 0.410568i \(0.134670\pi\)
\(164\) −0.396332 −0.0309483
\(165\) 0.428292 0.0333425
\(166\) 20.6097 1.59962
\(167\) 0.502309 0.0388698 0.0194349 0.999811i \(-0.493813\pi\)
0.0194349 + 0.999811i \(0.493813\pi\)
\(168\) 0.920905 0.0710493
\(169\) −5.34505 −0.411157
\(170\) −7.94173 −0.609103
\(171\) −7.53494 −0.576211
\(172\) 0.473272 0.0360866
\(173\) −25.0670 −1.90581 −0.952905 0.303269i \(-0.901922\pi\)
−0.952905 + 0.303269i \(0.901922\pi\)
\(174\) −3.43350 −0.260293
\(175\) −1.00000 −0.0755929
\(176\) −5.36505 −0.404406
\(177\) 2.72566 0.204873
\(178\) −10.2965 −0.771752
\(179\) 22.5898 1.68844 0.844222 0.535993i \(-0.180063\pi\)
0.844222 + 0.535993i \(0.180063\pi\)
\(180\) 0.287454 0.0214256
\(181\) −15.7216 −1.16858 −0.584289 0.811546i \(-0.698627\pi\)
−0.584289 + 0.811546i \(0.698627\pi\)
\(182\) −4.00896 −0.297164
\(183\) 4.89328 0.361722
\(184\) −18.0296 −1.32916
\(185\) 5.27324 0.387696
\(186\) −4.40283 −0.322831
\(187\) −7.01943 −0.513312
\(188\) 1.09053 0.0795354
\(189\) −1.96912 −0.143232
\(190\) 3.78024 0.274247
\(191\) 10.9594 0.792991 0.396496 0.918037i \(-0.370226\pi\)
0.396496 + 0.918037i \(0.370226\pi\)
\(192\) −2.52930 −0.182537
\(193\) −13.0071 −0.936272 −0.468136 0.883656i \(-0.655074\pi\)
−0.468136 + 0.883656i \(0.655074\pi\)
\(194\) 14.3905 1.03317
\(195\) −0.925260 −0.0662592
\(196\) 0.0995284 0.00710917
\(197\) 8.24681 0.587561 0.293780 0.955873i \(-0.405087\pi\)
0.293780 + 0.955873i \(0.405087\pi\)
\(198\) 5.35958 0.380888
\(199\) 0.954882 0.0676898 0.0338449 0.999427i \(-0.489225\pi\)
0.0338449 + 0.999427i \(0.489225\pi\)
\(200\) 2.75374 0.194719
\(201\) −0.401162 −0.0282958
\(202\) 10.6552 0.749700
\(203\) 7.08572 0.497320
\(204\) 0.182429 0.0127726
\(205\) 3.98210 0.278122
\(206\) −5.10799 −0.355891
\(207\) 18.9097 1.31431
\(208\) 11.5904 0.803647
\(209\) 3.34123 0.231117
\(210\) 0.484566 0.0334383
\(211\) −10.5900 −0.729045 −0.364522 0.931195i \(-0.618768\pi\)
−0.364522 + 0.931195i \(0.618768\pi\)
\(212\) −1.13770 −0.0781376
\(213\) −2.70790 −0.185543
\(214\) 24.9636 1.70648
\(215\) −4.75514 −0.324298
\(216\) 5.42244 0.368950
\(217\) 9.08612 0.616806
\(218\) 6.71865 0.455045
\(219\) −4.97922 −0.336465
\(220\) −0.127466 −0.00859376
\(221\) 15.1644 1.02007
\(222\) −2.55523 −0.171496
\(223\) 21.5634 1.44399 0.721997 0.691897i \(-0.243225\pi\)
0.721997 + 0.691897i \(0.243225\pi\)
\(224\) −0.562503 −0.0375838
\(225\) −2.88816 −0.192544
\(226\) −20.2402 −1.34636
\(227\) 2.83245 0.187996 0.0939982 0.995572i \(-0.470035\pi\)
0.0939982 + 0.995572i \(0.470035\pi\)
\(228\) −0.0868355 −0.00575082
\(229\) 1.00000 0.0660819
\(230\) −9.48688 −0.625547
\(231\) 0.428292 0.0281796
\(232\) −19.5122 −1.28104
\(233\) 4.36674 0.286075 0.143037 0.989717i \(-0.454313\pi\)
0.143037 + 0.989717i \(0.454313\pi\)
\(234\) −11.5785 −0.756913
\(235\) −10.9570 −0.714757
\(236\) −0.811197 −0.0528044
\(237\) 3.77622 0.245292
\(238\) −7.94173 −0.514786
\(239\) −7.43132 −0.480692 −0.240346 0.970687i \(-0.577261\pi\)
−0.240346 + 0.970687i \(0.577261\pi\)
\(240\) −1.40094 −0.0904301
\(241\) −30.3116 −1.95254 −0.976270 0.216556i \(-0.930518\pi\)
−0.976270 + 0.216556i \(0.930518\pi\)
\(242\) 13.5621 0.871806
\(243\) −8.58472 −0.550710
\(244\) −1.45631 −0.0932308
\(245\) −1.00000 −0.0638877
\(246\) −1.92959 −0.123026
\(247\) −7.21821 −0.459283
\(248\) −25.0208 −1.58882
\(249\) 4.75667 0.301442
\(250\) 1.44897 0.0916412
\(251\) 7.54658 0.476336 0.238168 0.971224i \(-0.423453\pi\)
0.238168 + 0.971224i \(0.423453\pi\)
\(252\) 0.287454 0.0181079
\(253\) −8.38514 −0.527170
\(254\) 4.68933 0.294234
\(255\) −1.83293 −0.114783
\(256\) 2.38286 0.148929
\(257\) −25.5149 −1.59158 −0.795788 0.605576i \(-0.792943\pi\)
−0.795788 + 0.605576i \(0.792943\pi\)
\(258\) 2.30418 0.143452
\(259\) 5.27324 0.327663
\(260\) 0.275371 0.0170778
\(261\) 20.4647 1.26673
\(262\) 0.635118 0.0392377
\(263\) 0.118886 0.00733085 0.00366542 0.999993i \(-0.498833\pi\)
0.00366542 + 0.999993i \(0.498833\pi\)
\(264\) −1.17940 −0.0725873
\(265\) 11.4309 0.702196
\(266\) 3.78024 0.231781
\(267\) −2.37640 −0.145433
\(268\) 0.119392 0.00729301
\(269\) −17.7563 −1.08262 −0.541311 0.840822i \(-0.682072\pi\)
−0.541311 + 0.840822i \(0.682072\pi\)
\(270\) 2.85321 0.173641
\(271\) −28.5012 −1.73133 −0.865663 0.500627i \(-0.833103\pi\)
−0.865663 + 0.500627i \(0.833103\pi\)
\(272\) 22.9604 1.39218
\(273\) −0.925260 −0.0559993
\(274\) 27.6126 1.66814
\(275\) 1.28070 0.0772292
\(276\) 0.217923 0.0131174
\(277\) −6.13518 −0.368627 −0.184313 0.982868i \(-0.559006\pi\)
−0.184313 + 0.982868i \(0.559006\pi\)
\(278\) −11.0653 −0.663654
\(279\) 26.2422 1.57108
\(280\) 2.75374 0.164567
\(281\) −2.81507 −0.167933 −0.0839664 0.996469i \(-0.526759\pi\)
−0.0839664 + 0.996469i \(0.526759\pi\)
\(282\) 5.30940 0.316170
\(283\) 21.6921 1.28946 0.644732 0.764409i \(-0.276969\pi\)
0.644732 + 0.764409i \(0.276969\pi\)
\(284\) 0.805912 0.0478221
\(285\) 0.872470 0.0516807
\(286\) 5.13428 0.303597
\(287\) 3.98210 0.235056
\(288\) −1.62460 −0.0957305
\(289\) 13.0406 0.767094
\(290\) −10.2670 −0.602901
\(291\) 3.32129 0.194697
\(292\) 1.48189 0.0867211
\(293\) 7.53736 0.440337 0.220169 0.975462i \(-0.429339\pi\)
0.220169 + 0.975462i \(0.429339\pi\)
\(294\) 0.484566 0.0282605
\(295\) 8.15041 0.474535
\(296\) −14.5211 −0.844022
\(297\) 2.52186 0.146333
\(298\) 5.64365 0.326928
\(299\) 18.1148 1.04761
\(300\) −0.0332843 −0.00192167
\(301\) −4.75514 −0.274082
\(302\) 23.2888 1.34012
\(303\) 2.45920 0.141278
\(304\) −10.9291 −0.626826
\(305\) 14.6321 0.837833
\(306\) −22.9370 −1.31122
\(307\) 22.5849 1.28899 0.644495 0.764608i \(-0.277067\pi\)
0.644495 + 0.764608i \(0.277067\pi\)
\(308\) −0.127466 −0.00726306
\(309\) −1.17891 −0.0670660
\(310\) −13.1656 −0.747753
\(311\) 20.1645 1.14342 0.571712 0.820454i \(-0.306279\pi\)
0.571712 + 0.820454i \(0.306279\pi\)
\(312\) 2.54792 0.144248
\(313\) 24.1799 1.36673 0.683364 0.730078i \(-0.260516\pi\)
0.683364 + 0.730078i \(0.260516\pi\)
\(314\) 21.7887 1.22961
\(315\) −2.88816 −0.162730
\(316\) −1.12386 −0.0632220
\(317\) −32.1807 −1.80745 −0.903725 0.428113i \(-0.859178\pi\)
−0.903725 + 0.428113i \(0.859178\pi\)
\(318\) −5.53904 −0.310614
\(319\) −9.07469 −0.508085
\(320\) −7.56325 −0.422798
\(321\) 5.76155 0.321578
\(322\) −9.48688 −0.528683
\(323\) −14.2992 −0.795630
\(324\) 0.796822 0.0442679
\(325\) −2.76676 −0.153472
\(326\) −33.7364 −1.86849
\(327\) 1.55065 0.0857512
\(328\) −10.9656 −0.605476
\(329\) −10.9570 −0.604080
\(330\) −0.620585 −0.0341621
\(331\) 17.1037 0.940106 0.470053 0.882638i \(-0.344235\pi\)
0.470053 + 0.882638i \(0.344235\pi\)
\(332\) −1.41566 −0.0776942
\(333\) 15.2300 0.834597
\(334\) −0.727833 −0.0398253
\(335\) −1.19958 −0.0655398
\(336\) −1.40094 −0.0764274
\(337\) 12.9189 0.703739 0.351869 0.936049i \(-0.385546\pi\)
0.351869 + 0.936049i \(0.385546\pi\)
\(338\) 7.74484 0.421264
\(339\) −4.67139 −0.253715
\(340\) 0.545508 0.0295843
\(341\) −11.6366 −0.630157
\(342\) 10.9179 0.590374
\(343\) −1.00000 −0.0539949
\(344\) 13.0944 0.706003
\(345\) −2.18955 −0.117881
\(346\) 36.3215 1.95265
\(347\) −16.4850 −0.884959 −0.442480 0.896779i \(-0.645901\pi\)
−0.442480 + 0.896779i \(0.645901\pi\)
\(348\) 0.235843 0.0126425
\(349\) 18.1603 0.972098 0.486049 0.873931i \(-0.338438\pi\)
0.486049 + 0.873931i \(0.338438\pi\)
\(350\) 1.44897 0.0774510
\(351\) −5.44808 −0.290797
\(352\) 0.720398 0.0383974
\(353\) 8.01974 0.426847 0.213424 0.976960i \(-0.431539\pi\)
0.213424 + 0.976960i \(0.431539\pi\)
\(354\) −3.94942 −0.209909
\(355\) −8.09731 −0.429761
\(356\) 0.707251 0.0374842
\(357\) −1.83293 −0.0970091
\(358\) −32.7321 −1.72995
\(359\) −18.2538 −0.963399 −0.481700 0.876336i \(-0.659980\pi\)
−0.481700 + 0.876336i \(0.659980\pi\)
\(360\) 7.95324 0.419172
\(361\) −12.1936 −0.641770
\(362\) 22.7802 1.19730
\(363\) 3.13011 0.164288
\(364\) 0.275371 0.0144334
\(365\) −14.8891 −0.779333
\(366\) −7.09024 −0.370613
\(367\) −3.17942 −0.165964 −0.0829822 0.996551i \(-0.526444\pi\)
−0.0829822 + 0.996551i \(0.526444\pi\)
\(368\) 27.4277 1.42977
\(369\) 11.5009 0.598715
\(370\) −7.64079 −0.397226
\(371\) 11.4309 0.593464
\(372\) 0.302425 0.0156800
\(373\) 13.1734 0.682094 0.341047 0.940046i \(-0.389218\pi\)
0.341047 + 0.940046i \(0.389218\pi\)
\(374\) 10.1710 0.525929
\(375\) 0.334420 0.0172694
\(376\) 30.1727 1.55604
\(377\) 19.6045 1.00968
\(378\) 2.85321 0.146753
\(379\) 22.2542 1.14312 0.571560 0.820560i \(-0.306338\pi\)
0.571560 + 0.820560i \(0.306338\pi\)
\(380\) −0.259660 −0.0133203
\(381\) 1.08229 0.0554472
\(382\) −15.8798 −0.812483
\(383\) −4.89810 −0.250281 −0.125141 0.992139i \(-0.539938\pi\)
−0.125141 + 0.992139i \(0.539938\pi\)
\(384\) 4.04112 0.206223
\(385\) 1.28070 0.0652706
\(386\) 18.8470 0.959285
\(387\) −13.7336 −0.698119
\(388\) −0.988464 −0.0501816
\(389\) −31.6877 −1.60663 −0.803315 0.595554i \(-0.796932\pi\)
−0.803315 + 0.595554i \(0.796932\pi\)
\(390\) 1.34068 0.0678879
\(391\) 35.8853 1.81480
\(392\) 2.75374 0.139085
\(393\) 0.146584 0.00739417
\(394\) −11.9494 −0.602003
\(395\) 11.2918 0.568155
\(396\) −0.368143 −0.0184999
\(397\) −9.98880 −0.501324 −0.250662 0.968075i \(-0.580648\pi\)
−0.250662 + 0.968075i \(0.580648\pi\)
\(398\) −1.38360 −0.0693536
\(399\) 0.872470 0.0436781
\(400\) −4.18915 −0.209458
\(401\) −20.9647 −1.04693 −0.523464 0.852048i \(-0.675360\pi\)
−0.523464 + 0.852048i \(0.675360\pi\)
\(402\) 0.581274 0.0289913
\(403\) 25.1391 1.25227
\(404\) −0.731896 −0.0364132
\(405\) −8.00598 −0.397820
\(406\) −10.2670 −0.509544
\(407\) −6.75344 −0.334756
\(408\) 5.04741 0.249884
\(409\) −4.47431 −0.221240 −0.110620 0.993863i \(-0.535284\pi\)
−0.110620 + 0.993863i \(0.535284\pi\)
\(410\) −5.76996 −0.284958
\(411\) 6.37292 0.314353
\(412\) 0.350862 0.0172857
\(413\) 8.15041 0.401055
\(414\) −27.3997 −1.34662
\(415\) 14.2236 0.698211
\(416\) −1.55631 −0.0763044
\(417\) −2.55385 −0.125063
\(418\) −4.84135 −0.236798
\(419\) 15.1396 0.739620 0.369810 0.929107i \(-0.379423\pi\)
0.369810 + 0.929107i \(0.379423\pi\)
\(420\) −0.0332843 −0.00162411
\(421\) −26.8311 −1.30767 −0.653833 0.756639i \(-0.726840\pi\)
−0.653833 + 0.756639i \(0.726840\pi\)
\(422\) 15.3446 0.746965
\(423\) −31.6457 −1.53866
\(424\) −31.4777 −1.52869
\(425\) −5.48093 −0.265864
\(426\) 3.92368 0.190103
\(427\) 14.6321 0.708098
\(428\) −1.71472 −0.0828842
\(429\) 1.18498 0.0572114
\(430\) 6.89008 0.332269
\(431\) 16.9811 0.817953 0.408976 0.912545i \(-0.365886\pi\)
0.408976 + 0.912545i \(0.365886\pi\)
\(432\) −8.24894 −0.396877
\(433\) −7.70046 −0.370060 −0.185030 0.982733i \(-0.559238\pi\)
−0.185030 + 0.982733i \(0.559238\pi\)
\(434\) −13.1656 −0.631967
\(435\) −2.36961 −0.113614
\(436\) −0.461496 −0.0221017
\(437\) −17.0813 −0.817109
\(438\) 7.21477 0.344735
\(439\) 11.5626 0.551852 0.275926 0.961179i \(-0.411015\pi\)
0.275926 + 0.961179i \(0.411015\pi\)
\(440\) −3.52671 −0.168129
\(441\) −2.88816 −0.137532
\(442\) −21.9728 −1.04514
\(443\) 4.60378 0.218732 0.109366 0.994002i \(-0.465118\pi\)
0.109366 + 0.994002i \(0.465118\pi\)
\(444\) 0.175516 0.00832962
\(445\) −7.10603 −0.336858
\(446\) −31.2448 −1.47949
\(447\) 1.30254 0.0616081
\(448\) −7.56325 −0.357330
\(449\) 31.4977 1.48647 0.743233 0.669032i \(-0.233291\pi\)
0.743233 + 0.669032i \(0.233291\pi\)
\(450\) 4.18488 0.197277
\(451\) −5.09988 −0.240144
\(452\) 1.39027 0.0653930
\(453\) 5.37501 0.252540
\(454\) −4.10415 −0.192617
\(455\) −2.76676 −0.129708
\(456\) −2.40255 −0.112510
\(457\) −22.3912 −1.04741 −0.523707 0.851898i \(-0.675451\pi\)
−0.523707 + 0.851898i \(0.675451\pi\)
\(458\) −1.44897 −0.0677062
\(459\) −10.7926 −0.503756
\(460\) 0.651643 0.0303830
\(461\) −35.3570 −1.64674 −0.823369 0.567507i \(-0.807908\pi\)
−0.823369 + 0.567507i \(0.807908\pi\)
\(462\) −0.620585 −0.0288722
\(463\) −3.68681 −0.171341 −0.0856703 0.996324i \(-0.527303\pi\)
−0.0856703 + 0.996324i \(0.527303\pi\)
\(464\) 29.6831 1.37801
\(465\) −3.03858 −0.140911
\(466\) −6.32730 −0.293106
\(467\) −1.28493 −0.0594594 −0.0297297 0.999558i \(-0.509465\pi\)
−0.0297297 + 0.999558i \(0.509465\pi\)
\(468\) 0.795316 0.0367635
\(469\) −1.19958 −0.0553912
\(470\) 15.8764 0.732326
\(471\) 5.02877 0.231714
\(472\) −22.4441 −1.03307
\(473\) 6.08992 0.280015
\(474\) −5.47165 −0.251321
\(475\) 2.60890 0.119705
\(476\) 0.545508 0.0250033
\(477\) 33.0143 1.51162
\(478\) 10.7678 0.492508
\(479\) −23.0059 −1.05117 −0.525583 0.850743i \(-0.676153\pi\)
−0.525583 + 0.850743i \(0.676153\pi\)
\(480\) 0.188112 0.00858612
\(481\) 14.5898 0.665237
\(482\) 43.9207 2.00053
\(483\) −2.18955 −0.0996280
\(484\) −0.931566 −0.0423439
\(485\) 9.93147 0.450965
\(486\) 12.4390 0.564247
\(487\) 43.2864 1.96149 0.980747 0.195283i \(-0.0625624\pi\)
0.980747 + 0.195283i \(0.0625624\pi\)
\(488\) −40.2930 −1.82398
\(489\) −7.78628 −0.352108
\(490\) 1.44897 0.0654580
\(491\) 1.40108 0.0632296 0.0316148 0.999500i \(-0.489935\pi\)
0.0316148 + 0.999500i \(0.489935\pi\)
\(492\) 0.132541 0.00597542
\(493\) 38.8363 1.74910
\(494\) 10.4590 0.470573
\(495\) 3.69887 0.166252
\(496\) 38.0631 1.70908
\(497\) −8.09731 −0.363214
\(498\) −6.89230 −0.308851
\(499\) 12.8905 0.577057 0.288529 0.957471i \(-0.406834\pi\)
0.288529 + 0.957471i \(0.406834\pi\)
\(500\) −0.0995284 −0.00445104
\(501\) −0.167982 −0.00750490
\(502\) −10.9348 −0.488044
\(503\) 32.8478 1.46461 0.732305 0.680977i \(-0.238445\pi\)
0.732305 + 0.680977i \(0.238445\pi\)
\(504\) 7.95324 0.354265
\(505\) 7.35364 0.327233
\(506\) 12.1499 0.540127
\(507\) 1.78749 0.0793853
\(508\) −0.322104 −0.0142911
\(509\) 28.5619 1.26599 0.632993 0.774157i \(-0.281826\pi\)
0.632993 + 0.774157i \(0.281826\pi\)
\(510\) 2.65587 0.117604
\(511\) −14.8891 −0.658656
\(512\) 20.7152 0.915492
\(513\) 5.13724 0.226815
\(514\) 36.9704 1.63070
\(515\) −3.52525 −0.155341
\(516\) −0.158272 −0.00696752
\(517\) 14.0327 0.617156
\(518\) −7.64079 −0.335717
\(519\) 8.38292 0.367969
\(520\) 7.61892 0.334112
\(521\) 23.1733 1.01524 0.507620 0.861581i \(-0.330525\pi\)
0.507620 + 0.861581i \(0.330525\pi\)
\(522\) −29.6529 −1.29787
\(523\) 13.0566 0.570925 0.285463 0.958390i \(-0.407853\pi\)
0.285463 + 0.958390i \(0.407853\pi\)
\(524\) −0.0436255 −0.00190579
\(525\) 0.334420 0.0145953
\(526\) −0.172263 −0.00751104
\(527\) 49.8004 2.16934
\(528\) 1.79418 0.0780817
\(529\) 19.8672 0.863793
\(530\) −16.5631 −0.719456
\(531\) 23.5397 1.02154
\(532\) −0.259660 −0.0112577
\(533\) 11.0175 0.477221
\(534\) 3.44334 0.149008
\(535\) 17.2285 0.744852
\(536\) 3.30331 0.142681
\(537\) −7.55450 −0.326001
\(538\) 25.7285 1.10923
\(539\) 1.28070 0.0551637
\(540\) −0.195983 −0.00843378
\(541\) 13.0025 0.559022 0.279511 0.960143i \(-0.409828\pi\)
0.279511 + 0.960143i \(0.409828\pi\)
\(542\) 41.2976 1.77388
\(543\) 5.25762 0.225626
\(544\) −3.08304 −0.132184
\(545\) 4.63683 0.198620
\(546\) 1.34068 0.0573757
\(547\) −16.6444 −0.711661 −0.355831 0.934551i \(-0.615802\pi\)
−0.355831 + 0.934551i \(0.615802\pi\)
\(548\) −1.89668 −0.0810220
\(549\) 42.2600 1.80361
\(550\) −1.85570 −0.0791275
\(551\) −18.4860 −0.787528
\(552\) 6.02945 0.256630
\(553\) 11.2918 0.480178
\(554\) 8.88972 0.377688
\(555\) −1.76348 −0.0748554
\(556\) 0.760063 0.0322339
\(557\) 12.0159 0.509130 0.254565 0.967056i \(-0.418068\pi\)
0.254565 + 0.967056i \(0.418068\pi\)
\(558\) −38.0243 −1.60970
\(559\) −13.1563 −0.556453
\(560\) −4.18915 −0.177024
\(561\) 2.34744 0.0991090
\(562\) 4.07896 0.172061
\(563\) 21.4417 0.903659 0.451830 0.892104i \(-0.350771\pi\)
0.451830 + 0.892104i \(0.350771\pi\)
\(564\) −0.364697 −0.0153565
\(565\) −13.9686 −0.587664
\(566\) −31.4314 −1.32116
\(567\) −8.00598 −0.336219
\(568\) 22.2979 0.935597
\(569\) −40.7414 −1.70797 −0.853985 0.520298i \(-0.825821\pi\)
−0.853985 + 0.520298i \(0.825821\pi\)
\(570\) −1.26419 −0.0529510
\(571\) −31.7372 −1.32816 −0.664081 0.747661i \(-0.731177\pi\)
−0.664081 + 0.747661i \(0.731177\pi\)
\(572\) −0.352668 −0.0147458
\(573\) −3.66503 −0.153109
\(574\) −5.76996 −0.240833
\(575\) −6.54731 −0.273042
\(576\) −21.8439 −0.910162
\(577\) 31.9765 1.33120 0.665600 0.746309i \(-0.268176\pi\)
0.665600 + 0.746309i \(0.268176\pi\)
\(578\) −18.8955 −0.785949
\(579\) 4.34984 0.180773
\(580\) 0.705230 0.0292831
\(581\) 14.2236 0.590096
\(582\) −4.81246 −0.199483
\(583\) −14.6396 −0.606310
\(584\) 41.0007 1.69662
\(585\) −7.99085 −0.330381
\(586\) −10.9214 −0.451161
\(587\) −0.889352 −0.0367075 −0.0183538 0.999832i \(-0.505843\pi\)
−0.0183538 + 0.999832i \(0.505843\pi\)
\(588\) −0.0332843 −0.00137262
\(589\) −23.7048 −0.976739
\(590\) −11.8097 −0.486199
\(591\) −2.75790 −0.113445
\(592\) 22.0904 0.907910
\(593\) 7.77931 0.319458 0.159729 0.987161i \(-0.448938\pi\)
0.159729 + 0.987161i \(0.448938\pi\)
\(594\) −3.65410 −0.149930
\(595\) −5.48093 −0.224696
\(596\) −0.387656 −0.0158790
\(597\) −0.319332 −0.0130694
\(598\) −26.2479 −1.07336
\(599\) 41.6102 1.70015 0.850073 0.526665i \(-0.176558\pi\)
0.850073 + 0.526665i \(0.176558\pi\)
\(600\) −0.920905 −0.0375958
\(601\) 25.6159 1.04489 0.522446 0.852672i \(-0.325019\pi\)
0.522446 + 0.852672i \(0.325019\pi\)
\(602\) 6.89008 0.280819
\(603\) −3.46457 −0.141088
\(604\) −1.59968 −0.0650901
\(605\) 9.35980 0.380530
\(606\) −3.56333 −0.144750
\(607\) 20.6682 0.838895 0.419448 0.907780i \(-0.362224\pi\)
0.419448 + 0.907780i \(0.362224\pi\)
\(608\) 1.46752 0.0595156
\(609\) −2.36961 −0.0960213
\(610\) −21.2016 −0.858427
\(611\) −30.3154 −1.22643
\(612\) 1.57552 0.0636865
\(613\) −28.9050 −1.16746 −0.583730 0.811948i \(-0.698407\pi\)
−0.583730 + 0.811948i \(0.698407\pi\)
\(614\) −32.7250 −1.32067
\(615\) −1.33169 −0.0536991
\(616\) −3.52671 −0.142095
\(617\) 35.2831 1.42044 0.710221 0.703978i \(-0.248595\pi\)
0.710221 + 0.703978i \(0.248595\pi\)
\(618\) 1.70822 0.0687145
\(619\) −47.3886 −1.90471 −0.952355 0.304991i \(-0.901347\pi\)
−0.952355 + 0.304991i \(0.901347\pi\)
\(620\) 0.904327 0.0363186
\(621\) −12.8924 −0.517356
\(622\) −29.2179 −1.17153
\(623\) −7.10603 −0.284697
\(624\) −3.87605 −0.155166
\(625\) 1.00000 0.0400000
\(626\) −35.0360 −1.40032
\(627\) −1.11737 −0.0446236
\(628\) −1.49664 −0.0597223
\(629\) 28.9023 1.15241
\(630\) 4.18488 0.166729
\(631\) −43.5288 −1.73285 −0.866427 0.499303i \(-0.833589\pi\)
−0.866427 + 0.499303i \(0.833589\pi\)
\(632\) −31.0948 −1.23688
\(633\) 3.54150 0.140762
\(634\) 46.6291 1.85188
\(635\) 3.23631 0.128429
\(636\) 0.380470 0.0150866
\(637\) −2.76676 −0.109623
\(638\) 13.1490 0.520574
\(639\) −23.3864 −0.925150
\(640\) 12.0840 0.477661
\(641\) −8.95842 −0.353836 −0.176918 0.984226i \(-0.556613\pi\)
−0.176918 + 0.984226i \(0.556613\pi\)
\(642\) −8.34834 −0.329483
\(643\) −2.62887 −0.103672 −0.0518362 0.998656i \(-0.516507\pi\)
−0.0518362 + 0.998656i \(0.516507\pi\)
\(644\) 0.651643 0.0256783
\(645\) 1.59022 0.0626147
\(646\) 20.7192 0.815186
\(647\) −19.5396 −0.768180 −0.384090 0.923296i \(-0.625485\pi\)
−0.384090 + 0.923296i \(0.625485\pi\)
\(648\) 22.0463 0.866062
\(649\) −10.4382 −0.409737
\(650\) 4.00896 0.157244
\(651\) −3.03858 −0.119091
\(652\) 2.31731 0.0907529
\(653\) 32.0258 1.25327 0.626633 0.779315i \(-0.284433\pi\)
0.626633 + 0.779315i \(0.284433\pi\)
\(654\) −2.24685 −0.0878589
\(655\) 0.438322 0.0171267
\(656\) 16.6816 0.651307
\(657\) −43.0022 −1.67768
\(658\) 15.8764 0.618928
\(659\) 7.48380 0.291527 0.145764 0.989319i \(-0.453436\pi\)
0.145764 + 0.989319i \(0.453436\pi\)
\(660\) 0.0426272 0.00165926
\(661\) 42.4287 1.65028 0.825142 0.564926i \(-0.191095\pi\)
0.825142 + 0.564926i \(0.191095\pi\)
\(662\) −24.7829 −0.963214
\(663\) −5.07128 −0.196952
\(664\) −39.1681 −1.52002
\(665\) 2.60890 0.101169
\(666\) −22.0679 −0.855112
\(667\) 46.3924 1.79632
\(668\) 0.0499940 0.00193433
\(669\) −7.21124 −0.278803
\(670\) 1.73815 0.0671508
\(671\) −18.7394 −0.723426
\(672\) 0.188112 0.00725659
\(673\) 42.2405 1.62825 0.814126 0.580688i \(-0.197216\pi\)
0.814126 + 0.580688i \(0.197216\pi\)
\(674\) −18.7192 −0.721037
\(675\) 1.96912 0.0757915
\(676\) −0.531984 −0.0204609
\(677\) 0.714895 0.0274757 0.0137378 0.999906i \(-0.495627\pi\)
0.0137378 + 0.999906i \(0.495627\pi\)
\(678\) 6.76873 0.259951
\(679\) 9.93147 0.381135
\(680\) 15.0930 0.578791
\(681\) −0.947229 −0.0362979
\(682\) 16.8611 0.645647
\(683\) −22.9528 −0.878263 −0.439132 0.898423i \(-0.644714\pi\)
−0.439132 + 0.898423i \(0.644714\pi\)
\(684\) −0.749940 −0.0286747
\(685\) 19.0566 0.728117
\(686\) 1.44897 0.0553221
\(687\) −0.334420 −0.0127589
\(688\) −19.9200 −0.759443
\(689\) 31.6266 1.20488
\(690\) 3.17261 0.120779
\(691\) 19.0997 0.726588 0.363294 0.931675i \(-0.381652\pi\)
0.363294 + 0.931675i \(0.381652\pi\)
\(692\) −2.49488 −0.0948411
\(693\) 3.69887 0.140509
\(694\) 23.8863 0.906712
\(695\) −7.63665 −0.289675
\(696\) 6.52527 0.247340
\(697\) 21.8256 0.826703
\(698\) −26.3138 −0.995993
\(699\) −1.46033 −0.0552346
\(700\) −0.0995284 −0.00376182
\(701\) −29.7326 −1.12298 −0.561492 0.827482i \(-0.689772\pi\)
−0.561492 + 0.827482i \(0.689772\pi\)
\(702\) 7.89413 0.297945
\(703\) −13.7574 −0.518869
\(704\) 9.68626 0.365065
\(705\) 3.66425 0.138004
\(706\) −11.6204 −0.437339
\(707\) 7.35364 0.276562
\(708\) 0.271281 0.0101954
\(709\) −28.0817 −1.05463 −0.527315 0.849670i \(-0.676801\pi\)
−0.527315 + 0.849670i \(0.676801\pi\)
\(710\) 11.7328 0.440324
\(711\) 32.6127 1.22307
\(712\) 19.5681 0.733346
\(713\) 59.4896 2.22790
\(714\) 2.65587 0.0993936
\(715\) 3.54339 0.132515
\(716\) 2.24833 0.0840241
\(717\) 2.48518 0.0928109
\(718\) 26.4493 0.987080
\(719\) −24.3876 −0.909503 −0.454751 0.890618i \(-0.650272\pi\)
−0.454751 + 0.890618i \(0.650272\pi\)
\(720\) −12.0990 −0.450901
\(721\) −3.52525 −0.131287
\(722\) 17.6683 0.657544
\(723\) 10.1368 0.376992
\(724\) −1.56475 −0.0581533
\(725\) −7.08572 −0.263157
\(726\) −4.53545 −0.168326
\(727\) −12.8921 −0.478143 −0.239071 0.971002i \(-0.576843\pi\)
−0.239071 + 0.971002i \(0.576843\pi\)
\(728\) 7.61892 0.282376
\(729\) −21.1470 −0.783223
\(730\) 21.5740 0.798489
\(731\) −26.0626 −0.963960
\(732\) 0.487020 0.0180008
\(733\) 6.65434 0.245784 0.122892 0.992420i \(-0.460783\pi\)
0.122892 + 0.992420i \(0.460783\pi\)
\(734\) 4.60690 0.170044
\(735\) 0.334420 0.0123353
\(736\) −3.68288 −0.135753
\(737\) 1.53630 0.0565903
\(738\) −16.6646 −0.613432
\(739\) −4.80076 −0.176599 −0.0882995 0.996094i \(-0.528143\pi\)
−0.0882995 + 0.996094i \(0.528143\pi\)
\(740\) 0.524837 0.0192934
\(741\) 2.41391 0.0886773
\(742\) −16.5631 −0.608051
\(743\) −6.04337 −0.221710 −0.110855 0.993837i \(-0.535359\pi\)
−0.110855 + 0.993837i \(0.535359\pi\)
\(744\) 8.36745 0.306766
\(745\) 3.89493 0.142699
\(746\) −19.0880 −0.698860
\(747\) 41.0802 1.50305
\(748\) −0.698633 −0.0255445
\(749\) 17.2285 0.629515
\(750\) −0.484566 −0.0176939
\(751\) −17.1640 −0.626322 −0.313161 0.949700i \(-0.601388\pi\)
−0.313161 + 0.949700i \(0.601388\pi\)
\(752\) −45.9006 −1.67382
\(753\) −2.52373 −0.0919697
\(754\) −28.4064 −1.03450
\(755\) 16.0726 0.584942
\(756\) −0.195983 −0.00712785
\(757\) 28.1755 1.02406 0.512028 0.858969i \(-0.328894\pi\)
0.512028 + 0.858969i \(0.328894\pi\)
\(758\) −32.2458 −1.17122
\(759\) 2.80416 0.101785
\(760\) −7.18423 −0.260599
\(761\) −47.6650 −1.72786 −0.863928 0.503615i \(-0.832003\pi\)
−0.863928 + 0.503615i \(0.832003\pi\)
\(762\) −1.56820 −0.0568101
\(763\) 4.63683 0.167865
\(764\) 1.09077 0.0394626
\(765\) −15.8298 −0.572328
\(766\) 7.09723 0.256433
\(767\) 22.5502 0.814241
\(768\) −0.796878 −0.0287548
\(769\) 16.4901 0.594649 0.297324 0.954777i \(-0.403906\pi\)
0.297324 + 0.954777i \(0.403906\pi\)
\(770\) −1.85570 −0.0668749
\(771\) 8.53270 0.307298
\(772\) −1.29458 −0.0465928
\(773\) −17.6275 −0.634017 −0.317008 0.948423i \(-0.602678\pi\)
−0.317008 + 0.948423i \(0.602678\pi\)
\(774\) 19.8997 0.715279
\(775\) −9.08612 −0.326383
\(776\) −27.3487 −0.981760
\(777\) −1.76348 −0.0632644
\(778\) 45.9147 1.64612
\(779\) −10.3889 −0.372221
\(780\) −0.0920896 −0.00329734
\(781\) 10.3702 0.371076
\(782\) −51.9969 −1.85941
\(783\) −13.9526 −0.498627
\(784\) −4.18915 −0.149613
\(785\) 15.0373 0.536704
\(786\) −0.212396 −0.00757592
\(787\) −1.84529 −0.0657774 −0.0328887 0.999459i \(-0.510471\pi\)
−0.0328887 + 0.999459i \(0.510471\pi\)
\(788\) 0.820792 0.0292395
\(789\) −0.0397580 −0.00141542
\(790\) −16.3616 −0.582120
\(791\) −13.9686 −0.496667
\(792\) −10.1857 −0.361934
\(793\) 40.4836 1.43761
\(794\) 14.4735 0.513646
\(795\) −3.82273 −0.135578
\(796\) 0.0950379 0.00336853
\(797\) 7.61111 0.269599 0.134800 0.990873i \(-0.456961\pi\)
0.134800 + 0.990873i \(0.456961\pi\)
\(798\) −1.26419 −0.0447517
\(799\) −60.0547 −2.12458
\(800\) 0.562503 0.0198875
\(801\) −20.5234 −0.725158
\(802\) 30.3773 1.07266
\(803\) 19.0685 0.672914
\(804\) −0.0399270 −0.00140812
\(805\) −6.54731 −0.230762
\(806\) −36.4259 −1.28305
\(807\) 5.93808 0.209030
\(808\) −20.2500 −0.712392
\(809\) −5.68837 −0.199992 −0.0999961 0.994988i \(-0.531883\pi\)
−0.0999961 + 0.994988i \(0.531883\pi\)
\(810\) 11.6005 0.407599
\(811\) 43.8866 1.54107 0.770533 0.637401i \(-0.219990\pi\)
0.770533 + 0.637401i \(0.219990\pi\)
\(812\) 0.705230 0.0247487
\(813\) 9.53138 0.334280
\(814\) 9.78557 0.342984
\(815\) −23.2829 −0.815565
\(816\) −7.67844 −0.268799
\(817\) 12.4057 0.434021
\(818\) 6.48316 0.226679
\(819\) −7.99085 −0.279223
\(820\) 0.396332 0.0138405
\(821\) 4.31248 0.150507 0.0752533 0.997164i \(-0.476023\pi\)
0.0752533 + 0.997164i \(0.476023\pi\)
\(822\) −9.23421 −0.322080
\(823\) 22.5449 0.785865 0.392932 0.919567i \(-0.371461\pi\)
0.392932 + 0.919567i \(0.371461\pi\)
\(824\) 9.70760 0.338180
\(825\) −0.428292 −0.0149112
\(826\) −11.8097 −0.410913
\(827\) −16.8185 −0.584836 −0.292418 0.956291i \(-0.594460\pi\)
−0.292418 + 0.956291i \(0.594460\pi\)
\(828\) 1.88205 0.0654058
\(829\) −29.7592 −1.03358 −0.516790 0.856112i \(-0.672873\pi\)
−0.516790 + 0.856112i \(0.672873\pi\)
\(830\) −20.6097 −0.715373
\(831\) 2.05173 0.0711736
\(832\) −20.9257 −0.725468
\(833\) −5.48093 −0.189903
\(834\) 3.70046 0.128137
\(835\) −0.502309 −0.0173831
\(836\) 0.332547 0.0115014
\(837\) −17.8917 −0.618426
\(838\) −21.9370 −0.757800
\(839\) −22.8086 −0.787439 −0.393720 0.919231i \(-0.628812\pi\)
−0.393720 + 0.919231i \(0.628812\pi\)
\(840\) −0.920905 −0.0317742
\(841\) 21.2074 0.731290
\(842\) 38.8775 1.33981
\(843\) 0.941416 0.0324241
\(844\) −1.05400 −0.0362803
\(845\) 5.34505 0.183875
\(846\) 45.8538 1.57649
\(847\) 9.35980 0.321607
\(848\) 47.8858 1.64441
\(849\) −7.25429 −0.248967
\(850\) 7.94173 0.272399
\(851\) 34.5255 1.18352
\(852\) −0.269513 −0.00923337
\(853\) 18.8903 0.646790 0.323395 0.946264i \(-0.395176\pi\)
0.323395 + 0.946264i \(0.395176\pi\)
\(854\) −21.2016 −0.725504
\(855\) 7.53494 0.257689
\(856\) −47.4427 −1.62156
\(857\) 26.6372 0.909909 0.454955 0.890515i \(-0.349655\pi\)
0.454955 + 0.890515i \(0.349655\pi\)
\(858\) −1.71701 −0.0586177
\(859\) 6.02854 0.205691 0.102845 0.994697i \(-0.467205\pi\)
0.102845 + 0.994697i \(0.467205\pi\)
\(860\) −0.473272 −0.0161384
\(861\) −1.33169 −0.0453840
\(862\) −24.6052 −0.838058
\(863\) 27.4201 0.933391 0.466695 0.884418i \(-0.345444\pi\)
0.466695 + 0.884418i \(0.345444\pi\)
\(864\) 1.10764 0.0376826
\(865\) 25.0670 0.852304
\(866\) 11.1578 0.379157
\(867\) −4.36104 −0.148109
\(868\) 0.904327 0.0306948
\(869\) −14.4615 −0.490572
\(870\) 3.43350 0.116407
\(871\) −3.31894 −0.112458
\(872\) −12.7686 −0.432400
\(873\) 28.6837 0.970797
\(874\) 24.7504 0.837193
\(875\) 1.00000 0.0338062
\(876\) −0.495574 −0.0167439
\(877\) −23.0021 −0.776725 −0.388363 0.921507i \(-0.626959\pi\)
−0.388363 + 0.921507i \(0.626959\pi\)
\(878\) −16.7539 −0.565417
\(879\) −2.52065 −0.0850193
\(880\) 5.36505 0.180856
\(881\) −12.7993 −0.431219 −0.215610 0.976480i \(-0.569174\pi\)
−0.215610 + 0.976480i \(0.569174\pi\)
\(882\) 4.18488 0.140912
\(883\) −27.4825 −0.924861 −0.462431 0.886655i \(-0.653023\pi\)
−0.462431 + 0.886655i \(0.653023\pi\)
\(884\) 1.50929 0.0507629
\(885\) −2.72566 −0.0916221
\(886\) −6.67076 −0.224109
\(887\) 24.0207 0.806535 0.403268 0.915082i \(-0.367874\pi\)
0.403268 + 0.915082i \(0.367874\pi\)
\(888\) 4.85615 0.162962
\(889\) 3.23631 0.108542
\(890\) 10.2965 0.345138
\(891\) 10.2533 0.343497
\(892\) 2.14617 0.0718591
\(893\) 28.5858 0.956588
\(894\) −1.88735 −0.0631225
\(895\) −22.5898 −0.755095
\(896\) 12.0840 0.403697
\(897\) −6.05796 −0.202269
\(898\) −45.6393 −1.52300
\(899\) 64.3817 2.14725
\(900\) −0.287454 −0.00958181
\(901\) 62.6520 2.08724
\(902\) 7.38959 0.246047
\(903\) 1.59022 0.0529191
\(904\) 38.4659 1.27936
\(905\) 15.7216 0.522604
\(906\) −7.78825 −0.258747
\(907\) 26.1891 0.869595 0.434797 0.900528i \(-0.356820\pi\)
0.434797 + 0.900528i \(0.356820\pi\)
\(908\) 0.281909 0.00935549
\(909\) 21.2385 0.704437
\(910\) 4.00896 0.132896
\(911\) −29.6976 −0.983924 −0.491962 0.870617i \(-0.663720\pi\)
−0.491962 + 0.870617i \(0.663720\pi\)
\(912\) 3.65491 0.121026
\(913\) −18.2162 −0.602869
\(914\) 32.4442 1.07316
\(915\) −4.89328 −0.161767
\(916\) 0.0995284 0.00328851
\(917\) 0.438322 0.0144747
\(918\) 15.6382 0.516138
\(919\) −30.8884 −1.01892 −0.509458 0.860496i \(-0.670154\pi\)
−0.509458 + 0.860496i \(0.670154\pi\)
\(920\) 18.0296 0.594417
\(921\) −7.55286 −0.248875
\(922\) 51.2313 1.68721
\(923\) −22.4033 −0.737414
\(924\) 0.0426272 0.00140233
\(925\) −5.27324 −0.173383
\(926\) 5.34209 0.175552
\(927\) −10.1815 −0.334404
\(928\) −3.98574 −0.130838
\(929\) −34.1081 −1.11905 −0.559526 0.828813i \(-0.689017\pi\)
−0.559526 + 0.828813i \(0.689017\pi\)
\(930\) 4.40283 0.144374
\(931\) 2.60890 0.0855033
\(932\) 0.434614 0.0142363
\(933\) −6.74342 −0.220770
\(934\) 1.86183 0.0609210
\(935\) 7.01943 0.229560
\(936\) 22.0047 0.719246
\(937\) −38.9570 −1.27267 −0.636334 0.771413i \(-0.719550\pi\)
−0.636334 + 0.771413i \(0.719550\pi\)
\(938\) 1.73815 0.0567528
\(939\) −8.08624 −0.263885
\(940\) −1.09053 −0.0355693
\(941\) 7.17550 0.233914 0.116957 0.993137i \(-0.462686\pi\)
0.116957 + 0.993137i \(0.462686\pi\)
\(942\) −7.28657 −0.237409
\(943\) 26.0720 0.849021
\(944\) 34.1433 1.11127
\(945\) 1.96912 0.0640555
\(946\) −8.82414 −0.286897
\(947\) −20.8186 −0.676515 −0.338257 0.941054i \(-0.609837\pi\)
−0.338257 + 0.941054i \(0.609837\pi\)
\(948\) 0.375841 0.0122068
\(949\) −41.1946 −1.33723
\(950\) −3.78024 −0.122647
\(951\) 10.7619 0.348978
\(952\) 15.0930 0.489168
\(953\) −21.8539 −0.707916 −0.353958 0.935261i \(-0.615164\pi\)
−0.353958 + 0.935261i \(0.615164\pi\)
\(954\) −47.8370 −1.54878
\(955\) −10.9594 −0.354636
\(956\) −0.739627 −0.0239213
\(957\) 3.03476 0.0980998
\(958\) 33.3349 1.07700
\(959\) 19.0566 0.615371
\(960\) 2.52930 0.0816329
\(961\) 51.5576 1.66315
\(962\) −21.1402 −0.681588
\(963\) 49.7587 1.60345
\(964\) −3.01686 −0.0971666
\(965\) 13.0071 0.418714
\(966\) 3.17261 0.102077
\(967\) 20.3076 0.653048 0.326524 0.945189i \(-0.394123\pi\)
0.326524 + 0.945189i \(0.394123\pi\)
\(968\) −25.7744 −0.828421
\(969\) 4.78195 0.153618
\(970\) −14.3905 −0.462050
\(971\) 7.00744 0.224880 0.112440 0.993659i \(-0.464133\pi\)
0.112440 + 0.993659i \(0.464133\pi\)
\(972\) −0.854423 −0.0274056
\(973\) −7.63665 −0.244820
\(974\) −62.7209 −2.00971
\(975\) 0.925260 0.0296320
\(976\) 61.2962 1.96204
\(977\) −22.9913 −0.735558 −0.367779 0.929913i \(-0.619882\pi\)
−0.367779 + 0.929913i \(0.619882\pi\)
\(978\) 11.2821 0.360763
\(979\) 9.10070 0.290860
\(980\) −0.0995284 −0.00317932
\(981\) 13.3919 0.427571
\(982\) −2.03012 −0.0647838
\(983\) −44.9190 −1.43269 −0.716346 0.697745i \(-0.754187\pi\)
−0.716346 + 0.697745i \(0.754187\pi\)
\(984\) 3.66713 0.116904
\(985\) −8.24681 −0.262765
\(986\) −56.2729 −1.79209
\(987\) 3.66425 0.116634
\(988\) −0.718416 −0.0228559
\(989\) −31.1334 −0.989984
\(990\) −5.35958 −0.170339
\(991\) 52.8419 1.67858 0.839290 0.543685i \(-0.182971\pi\)
0.839290 + 0.543685i \(0.182971\pi\)
\(992\) −5.11097 −0.162273
\(993\) −5.71983 −0.181513
\(994\) 11.7328 0.372142
\(995\) −0.954882 −0.0302718
\(996\) 0.473424 0.0150010
\(997\) 40.5194 1.28326 0.641632 0.767013i \(-0.278258\pi\)
0.641632 + 0.767013i \(0.278258\pi\)
\(998\) −18.6780 −0.591241
\(999\) −10.3836 −0.328524
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 \(a_p\))