Properties

Label 8042.2.a.a.1.16
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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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: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.98933 q^{3}\) \(+1.00000 q^{4}\) \(+4.18312 q^{5}\) \(-1.98933 q^{6}\) \(-0.474573 q^{7}\) \(+1.00000 q^{8}\) \(+0.957423 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.98933 q^{3}\) \(+1.00000 q^{4}\) \(+4.18312 q^{5}\) \(-1.98933 q^{6}\) \(-0.474573 q^{7}\) \(+1.00000 q^{8}\) \(+0.957423 q^{9}\) \(+4.18312 q^{10}\) \(-1.64498 q^{11}\) \(-1.98933 q^{12}\) \(-2.31472 q^{13}\) \(-0.474573 q^{14}\) \(-8.32159 q^{15}\) \(+1.00000 q^{16}\) \(-2.88362 q^{17}\) \(+0.957423 q^{18}\) \(-6.87657 q^{19}\) \(+4.18312 q^{20}\) \(+0.944080 q^{21}\) \(-1.64498 q^{22}\) \(+3.42193 q^{23}\) \(-1.98933 q^{24}\) \(+12.4985 q^{25}\) \(-2.31472 q^{26}\) \(+4.06335 q^{27}\) \(-0.474573 q^{28}\) \(-9.60384 q^{29}\) \(-8.32159 q^{30}\) \(+4.42024 q^{31}\) \(+1.00000 q^{32}\) \(+3.27241 q^{33}\) \(-2.88362 q^{34}\) \(-1.98519 q^{35}\) \(+0.957423 q^{36}\) \(-1.78331 q^{37}\) \(-6.87657 q^{38}\) \(+4.60474 q^{39}\) \(+4.18312 q^{40}\) \(+1.06121 q^{41}\) \(+0.944080 q^{42}\) \(+7.16539 q^{43}\) \(-1.64498 q^{44}\) \(+4.00501 q^{45}\) \(+3.42193 q^{46}\) \(+10.3673 q^{47}\) \(-1.98933 q^{48}\) \(-6.77478 q^{49}\) \(+12.4985 q^{50}\) \(+5.73647 q^{51}\) \(-2.31472 q^{52}\) \(-8.42623 q^{53}\) \(+4.06335 q^{54}\) \(-6.88116 q^{55}\) \(-0.474573 q^{56}\) \(+13.6797 q^{57}\) \(-9.60384 q^{58}\) \(-10.5518 q^{59}\) \(-8.32159 q^{60}\) \(-0.448317 q^{61}\) \(+4.42024 q^{62}\) \(-0.454366 q^{63}\) \(+1.00000 q^{64}\) \(-9.68275 q^{65}\) \(+3.27241 q^{66}\) \(+3.74413 q^{67}\) \(-2.88362 q^{68}\) \(-6.80734 q^{69}\) \(-1.98519 q^{70}\) \(+5.11142 q^{71}\) \(+0.957423 q^{72}\) \(-7.11511 q^{73}\) \(-1.78331 q^{74}\) \(-24.8635 q^{75}\) \(-6.87657 q^{76}\) \(+0.780664 q^{77}\) \(+4.60474 q^{78}\) \(-3.62629 q^{79}\) \(+4.18312 q^{80}\) \(-10.9556 q^{81}\) \(+1.06121 q^{82}\) \(+1.55571 q^{83}\) \(+0.944080 q^{84}\) \(-12.0625 q^{85}\) \(+7.16539 q^{86}\) \(+19.1052 q^{87}\) \(-1.64498 q^{88}\) \(-5.45327 q^{89}\) \(+4.00501 q^{90}\) \(+1.09850 q^{91}\) \(+3.42193 q^{92}\) \(-8.79331 q^{93}\) \(+10.3673 q^{94}\) \(-28.7655 q^{95}\) \(-1.98933 q^{96}\) \(-17.9809 q^{97}\) \(-6.77478 q^{98}\) \(-1.57494 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.98933 −1.14854 −0.574269 0.818666i \(-0.694714\pi\)
−0.574269 + 0.818666i \(0.694714\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.18312 1.87075 0.935373 0.353662i \(-0.115064\pi\)
0.935373 + 0.353662i \(0.115064\pi\)
\(6\) −1.98933 −0.812139
\(7\) −0.474573 −0.179372 −0.0896858 0.995970i \(-0.528586\pi\)
−0.0896858 + 0.995970i \(0.528586\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.957423 0.319141
\(10\) 4.18312 1.32282
\(11\) −1.64498 −0.495981 −0.247991 0.968762i \(-0.579770\pi\)
−0.247991 + 0.968762i \(0.579770\pi\)
\(12\) −1.98933 −0.574269
\(13\) −2.31472 −0.641988 −0.320994 0.947081i \(-0.604017\pi\)
−0.320994 + 0.947081i \(0.604017\pi\)
\(14\) −0.474573 −0.126835
\(15\) −8.32159 −2.14862
\(16\) 1.00000 0.250000
\(17\) −2.88362 −0.699382 −0.349691 0.936865i \(-0.613713\pi\)
−0.349691 + 0.936865i \(0.613713\pi\)
\(18\) 0.957423 0.225667
\(19\) −6.87657 −1.57759 −0.788796 0.614655i \(-0.789295\pi\)
−0.788796 + 0.614655i \(0.789295\pi\)
\(20\) 4.18312 0.935373
\(21\) 0.944080 0.206015
\(22\) −1.64498 −0.350712
\(23\) 3.42193 0.713522 0.356761 0.934196i \(-0.383881\pi\)
0.356761 + 0.934196i \(0.383881\pi\)
\(24\) −1.98933 −0.406070
\(25\) 12.4985 2.49969
\(26\) −2.31472 −0.453954
\(27\) 4.06335 0.781993
\(28\) −0.474573 −0.0896858
\(29\) −9.60384 −1.78339 −0.891694 0.452638i \(-0.850483\pi\)
−0.891694 + 0.452638i \(0.850483\pi\)
\(30\) −8.32159 −1.51931
\(31\) 4.42024 0.793899 0.396949 0.917840i \(-0.370069\pi\)
0.396949 + 0.917840i \(0.370069\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.27241 0.569654
\(34\) −2.88362 −0.494538
\(35\) −1.98519 −0.335559
\(36\) 0.957423 0.159570
\(37\) −1.78331 −0.293174 −0.146587 0.989198i \(-0.546829\pi\)
−0.146587 + 0.989198i \(0.546829\pi\)
\(38\) −6.87657 −1.11553
\(39\) 4.60474 0.737348
\(40\) 4.18312 0.661409
\(41\) 1.06121 0.165733 0.0828664 0.996561i \(-0.473593\pi\)
0.0828664 + 0.996561i \(0.473593\pi\)
\(42\) 0.944080 0.145675
\(43\) 7.16539 1.09271 0.546356 0.837553i \(-0.316015\pi\)
0.546356 + 0.837553i \(0.316015\pi\)
\(44\) −1.64498 −0.247991
\(45\) 4.00501 0.597032
\(46\) 3.42193 0.504536
\(47\) 10.3673 1.51223 0.756113 0.654441i \(-0.227096\pi\)
0.756113 + 0.654441i \(0.227096\pi\)
\(48\) −1.98933 −0.287135
\(49\) −6.77478 −0.967826
\(50\) 12.4985 1.76755
\(51\) 5.73647 0.803267
\(52\) −2.31472 −0.320994
\(53\) −8.42623 −1.15743 −0.578716 0.815529i \(-0.696446\pi\)
−0.578716 + 0.815529i \(0.696446\pi\)
\(54\) 4.06335 0.552953
\(55\) −6.88116 −0.927856
\(56\) −0.474573 −0.0634174
\(57\) 13.6797 1.81193
\(58\) −9.60384 −1.26105
\(59\) −10.5518 −1.37373 −0.686866 0.726784i \(-0.741014\pi\)
−0.686866 + 0.726784i \(0.741014\pi\)
\(60\) −8.32159 −1.07431
\(61\) −0.448317 −0.0574012 −0.0287006 0.999588i \(-0.509137\pi\)
−0.0287006 + 0.999588i \(0.509137\pi\)
\(62\) 4.42024 0.561371
\(63\) −0.454366 −0.0572448
\(64\) 1.00000 0.125000
\(65\) −9.68275 −1.20100
\(66\) 3.27241 0.402806
\(67\) 3.74413 0.457418 0.228709 0.973495i \(-0.426550\pi\)
0.228709 + 0.973495i \(0.426550\pi\)
\(68\) −2.88362 −0.349691
\(69\) −6.80734 −0.819507
\(70\) −1.98519 −0.237276
\(71\) 5.11142 0.606614 0.303307 0.952893i \(-0.401909\pi\)
0.303307 + 0.952893i \(0.401909\pi\)
\(72\) 0.957423 0.112833
\(73\) −7.11511 −0.832761 −0.416380 0.909191i \(-0.636702\pi\)
−0.416380 + 0.909191i \(0.636702\pi\)
\(74\) −1.78331 −0.207305
\(75\) −24.8635 −2.87099
\(76\) −6.87657 −0.788796
\(77\) 0.780664 0.0889650
\(78\) 4.60474 0.521384
\(79\) −3.62629 −0.407990 −0.203995 0.978972i \(-0.565393\pi\)
−0.203995 + 0.978972i \(0.565393\pi\)
\(80\) 4.18312 0.467687
\(81\) −10.9556 −1.21729
\(82\) 1.06121 0.117191
\(83\) 1.55571 0.170762 0.0853808 0.996348i \(-0.472789\pi\)
0.0853808 + 0.996348i \(0.472789\pi\)
\(84\) 0.944080 0.103008
\(85\) −12.0625 −1.30837
\(86\) 7.16539 0.772664
\(87\) 19.1052 2.04829
\(88\) −1.64498 −0.175356
\(89\) −5.45327 −0.578046 −0.289023 0.957322i \(-0.593330\pi\)
−0.289023 + 0.957322i \(0.593330\pi\)
\(90\) 4.00501 0.422165
\(91\) 1.09850 0.115154
\(92\) 3.42193 0.356761
\(93\) −8.79331 −0.911823
\(94\) 10.3673 1.06931
\(95\) −28.7655 −2.95128
\(96\) −1.98933 −0.203035
\(97\) −17.9809 −1.82569 −0.912843 0.408311i \(-0.866118\pi\)
−0.912843 + 0.408311i \(0.866118\pi\)
\(98\) −6.77478 −0.684356
\(99\) −1.57494 −0.158288
\(100\) 12.4985 1.24985
\(101\) −1.45358 −0.144637 −0.0723183 0.997382i \(-0.523040\pi\)
−0.0723183 + 0.997382i \(0.523040\pi\)
\(102\) 5.73647 0.567995
\(103\) −10.3315 −1.01800 −0.508998 0.860768i \(-0.669984\pi\)
−0.508998 + 0.860768i \(0.669984\pi\)
\(104\) −2.31472 −0.226977
\(105\) 3.94920 0.385402
\(106\) −8.42623 −0.818427
\(107\) −13.7672 −1.33093 −0.665464 0.746430i \(-0.731766\pi\)
−0.665464 + 0.746430i \(0.731766\pi\)
\(108\) 4.06335 0.390997
\(109\) −18.1779 −1.74113 −0.870565 0.492054i \(-0.836246\pi\)
−0.870565 + 0.492054i \(0.836246\pi\)
\(110\) −6.88116 −0.656093
\(111\) 3.54758 0.336722
\(112\) −0.474573 −0.0448429
\(113\) 4.19917 0.395025 0.197512 0.980300i \(-0.436714\pi\)
0.197512 + 0.980300i \(0.436714\pi\)
\(114\) 13.6797 1.28122
\(115\) 14.3143 1.33482
\(116\) −9.60384 −0.891694
\(117\) −2.21617 −0.204885
\(118\) −10.5518 −0.971375
\(119\) 1.36849 0.125449
\(120\) −8.32159 −0.759654
\(121\) −8.29403 −0.754002
\(122\) −0.448317 −0.0405888
\(123\) −2.11109 −0.190350
\(124\) 4.42024 0.396949
\(125\) 31.3669 2.80555
\(126\) −0.454366 −0.0404782
\(127\) −17.8711 −1.58581 −0.792904 0.609347i \(-0.791432\pi\)
−0.792904 + 0.609347i \(0.791432\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.2543 −1.25502
\(130\) −9.68275 −0.849233
\(131\) −4.64025 −0.405421 −0.202710 0.979239i \(-0.564975\pi\)
−0.202710 + 0.979239i \(0.564975\pi\)
\(132\) 3.27241 0.284827
\(133\) 3.26343 0.282975
\(134\) 3.74413 0.323443
\(135\) 16.9975 1.46291
\(136\) −2.88362 −0.247269
\(137\) 15.7299 1.34390 0.671950 0.740596i \(-0.265457\pi\)
0.671950 + 0.740596i \(0.265457\pi\)
\(138\) −6.80734 −0.579479
\(139\) 16.6442 1.41174 0.705871 0.708341i \(-0.250556\pi\)
0.705871 + 0.708341i \(0.250556\pi\)
\(140\) −1.98519 −0.167779
\(141\) −20.6240 −1.73685
\(142\) 5.11142 0.428941
\(143\) 3.80768 0.318414
\(144\) 0.957423 0.0797852
\(145\) −40.1740 −3.33627
\(146\) −7.11511 −0.588851
\(147\) 13.4773 1.11159
\(148\) −1.78331 −0.146587
\(149\) 5.33057 0.436697 0.218349 0.975871i \(-0.429933\pi\)
0.218349 + 0.975871i \(0.429933\pi\)
\(150\) −24.8635 −2.03010
\(151\) 17.6667 1.43770 0.718849 0.695166i \(-0.244669\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(152\) −6.87657 −0.557763
\(153\) −2.76085 −0.223201
\(154\) 0.780664 0.0629077
\(155\) 18.4904 1.48518
\(156\) 4.60474 0.368674
\(157\) 16.2883 1.29995 0.649975 0.759955i \(-0.274779\pi\)
0.649975 + 0.759955i \(0.274779\pi\)
\(158\) −3.62629 −0.288492
\(159\) 16.7625 1.32935
\(160\) 4.18312 0.330704
\(161\) −1.62395 −0.127986
\(162\) −10.9556 −0.860754
\(163\) −4.11200 −0.322077 −0.161038 0.986948i \(-0.551484\pi\)
−0.161038 + 0.986948i \(0.551484\pi\)
\(164\) 1.06121 0.0828664
\(165\) 13.6889 1.06568
\(166\) 1.55571 0.120747
\(167\) −22.9167 −1.77335 −0.886673 0.462397i \(-0.846990\pi\)
−0.886673 + 0.462397i \(0.846990\pi\)
\(168\) 0.944080 0.0728374
\(169\) −7.64206 −0.587851
\(170\) −12.0625 −0.925155
\(171\) −6.58378 −0.503474
\(172\) 7.16539 0.546356
\(173\) −13.2232 −1.00534 −0.502671 0.864478i \(-0.667649\pi\)
−0.502671 + 0.864478i \(0.667649\pi\)
\(174\) 19.1052 1.44836
\(175\) −5.93143 −0.448374
\(176\) −1.64498 −0.123995
\(177\) 20.9911 1.57778
\(178\) −5.45327 −0.408740
\(179\) 15.1931 1.13559 0.567794 0.823171i \(-0.307797\pi\)
0.567794 + 0.823171i \(0.307797\pi\)
\(180\) 4.00501 0.298516
\(181\) 12.6131 0.937528 0.468764 0.883323i \(-0.344699\pi\)
0.468764 + 0.883323i \(0.344699\pi\)
\(182\) 1.09850 0.0814265
\(183\) 0.891850 0.0659275
\(184\) 3.42193 0.252268
\(185\) −7.45979 −0.548455
\(186\) −8.79331 −0.644756
\(187\) 4.74352 0.346880
\(188\) 10.3673 0.756113
\(189\) −1.92836 −0.140267
\(190\) −28.7655 −2.08687
\(191\) −14.8350 −1.07342 −0.536710 0.843767i \(-0.680333\pi\)
−0.536710 + 0.843767i \(0.680333\pi\)
\(192\) −1.98933 −0.143567
\(193\) −18.8113 −1.35407 −0.677033 0.735952i \(-0.736735\pi\)
−0.677033 + 0.735952i \(0.736735\pi\)
\(194\) −17.9809 −1.29095
\(195\) 19.2622 1.37939
\(196\) −6.77478 −0.483913
\(197\) 20.2467 1.44252 0.721258 0.692666i \(-0.243564\pi\)
0.721258 + 0.692666i \(0.243564\pi\)
\(198\) −1.57494 −0.111926
\(199\) 13.5938 0.963642 0.481821 0.876270i \(-0.339976\pi\)
0.481821 + 0.876270i \(0.339976\pi\)
\(200\) 12.4985 0.883775
\(201\) −7.44829 −0.525362
\(202\) −1.45358 −0.102274
\(203\) 4.55772 0.319889
\(204\) 5.73647 0.401633
\(205\) 4.43915 0.310044
\(206\) −10.3315 −0.719832
\(207\) 3.27623 0.227714
\(208\) −2.31472 −0.160497
\(209\) 11.3118 0.782456
\(210\) 3.94920 0.272521
\(211\) −13.3638 −0.920003 −0.460001 0.887918i \(-0.652151\pi\)
−0.460001 + 0.887918i \(0.652151\pi\)
\(212\) −8.42623 −0.578716
\(213\) −10.1683 −0.696720
\(214\) −13.7672 −0.941108
\(215\) 29.9737 2.04419
\(216\) 4.06335 0.276476
\(217\) −2.09773 −0.142403
\(218\) −18.1779 −1.23116
\(219\) 14.1543 0.956458
\(220\) −6.88116 −0.463928
\(221\) 6.67479 0.448995
\(222\) 3.54758 0.238098
\(223\) −0.111513 −0.00746748 −0.00373374 0.999993i \(-0.501188\pi\)
−0.00373374 + 0.999993i \(0.501188\pi\)
\(224\) −0.474573 −0.0317087
\(225\) 11.9663 0.797754
\(226\) 4.19917 0.279325
\(227\) −1.85493 −0.123116 −0.0615579 0.998104i \(-0.519607\pi\)
−0.0615579 + 0.998104i \(0.519607\pi\)
\(228\) 13.6797 0.905963
\(229\) −5.21795 −0.344812 −0.172406 0.985026i \(-0.555154\pi\)
−0.172406 + 0.985026i \(0.555154\pi\)
\(230\) 14.3143 0.943859
\(231\) −1.55300 −0.102180
\(232\) −9.60384 −0.630523
\(233\) −0.368052 −0.0241119 −0.0120559 0.999927i \(-0.503838\pi\)
−0.0120559 + 0.999927i \(0.503838\pi\)
\(234\) −2.21617 −0.144875
\(235\) 43.3676 2.82899
\(236\) −10.5518 −0.686866
\(237\) 7.21388 0.468592
\(238\) 1.36849 0.0887060
\(239\) −17.7774 −1.14992 −0.574962 0.818180i \(-0.694983\pi\)
−0.574962 + 0.818180i \(0.694983\pi\)
\(240\) −8.32159 −0.537156
\(241\) −26.0379 −1.67725 −0.838625 0.544710i \(-0.816640\pi\)
−0.838625 + 0.544710i \(0.816640\pi\)
\(242\) −8.29403 −0.533160
\(243\) 9.60423 0.616111
\(244\) −0.448317 −0.0287006
\(245\) −28.3397 −1.81056
\(246\) −2.11109 −0.134598
\(247\) 15.9173 1.01280
\(248\) 4.42024 0.280686
\(249\) −3.09482 −0.196126
\(250\) 31.3669 1.98382
\(251\) −2.18913 −0.138176 −0.0690882 0.997611i \(-0.522009\pi\)
−0.0690882 + 0.997611i \(0.522009\pi\)
\(252\) −0.454366 −0.0286224
\(253\) −5.62902 −0.353894
\(254\) −17.8711 −1.12134
\(255\) 23.9963 1.50271
\(256\) 1.00000 0.0625000
\(257\) −5.34519 −0.333424 −0.166712 0.986006i \(-0.553315\pi\)
−0.166712 + 0.986006i \(0.553315\pi\)
\(258\) −14.2543 −0.887434
\(259\) 0.846309 0.0525871
\(260\) −9.68275 −0.600499
\(261\) −9.19493 −0.569152
\(262\) −4.64025 −0.286676
\(263\) −19.2592 −1.18757 −0.593787 0.804622i \(-0.702368\pi\)
−0.593787 + 0.804622i \(0.702368\pi\)
\(264\) 3.27241 0.201403
\(265\) −35.2479 −2.16526
\(266\) 3.26343 0.200094
\(267\) 10.8483 0.663908
\(268\) 3.74413 0.228709
\(269\) 2.58412 0.157557 0.0787784 0.996892i \(-0.474898\pi\)
0.0787784 + 0.996892i \(0.474898\pi\)
\(270\) 16.9975 1.03443
\(271\) −16.8995 −1.02657 −0.513287 0.858217i \(-0.671572\pi\)
−0.513287 + 0.858217i \(0.671572\pi\)
\(272\) −2.88362 −0.174845
\(273\) −2.18528 −0.132259
\(274\) 15.7299 0.950281
\(275\) −20.5598 −1.23980
\(276\) −6.80734 −0.409754
\(277\) 5.03892 0.302759 0.151380 0.988476i \(-0.451628\pi\)
0.151380 + 0.988476i \(0.451628\pi\)
\(278\) 16.6442 0.998252
\(279\) 4.23204 0.253366
\(280\) −1.98519 −0.118638
\(281\) −12.8954 −0.769273 −0.384636 0.923068i \(-0.625673\pi\)
−0.384636 + 0.923068i \(0.625673\pi\)
\(282\) −20.6240 −1.22814
\(283\) 28.4974 1.69400 0.846998 0.531596i \(-0.178407\pi\)
0.846998 + 0.531596i \(0.178407\pi\)
\(284\) 5.11142 0.303307
\(285\) 57.2239 3.38965
\(286\) 3.80768 0.225153
\(287\) −0.503620 −0.0297278
\(288\) 0.957423 0.0564167
\(289\) −8.68471 −0.510865
\(290\) −40.1740 −2.35910
\(291\) 35.7699 2.09687
\(292\) −7.11511 −0.416380
\(293\) −1.12299 −0.0656059 −0.0328029 0.999462i \(-0.510443\pi\)
−0.0328029 + 0.999462i \(0.510443\pi\)
\(294\) 13.4773 0.786010
\(295\) −44.1396 −2.56990
\(296\) −1.78331 −0.103653
\(297\) −6.68415 −0.387854
\(298\) 5.33057 0.308792
\(299\) −7.92082 −0.458073
\(300\) −24.8635 −1.43550
\(301\) −3.40050 −0.196001
\(302\) 17.6667 1.01661
\(303\) 2.89165 0.166121
\(304\) −6.87657 −0.394398
\(305\) −1.87536 −0.107383
\(306\) −2.76085 −0.157827
\(307\) 19.4889 1.11229 0.556145 0.831085i \(-0.312280\pi\)
0.556145 + 0.831085i \(0.312280\pi\)
\(308\) 0.780664 0.0444825
\(309\) 20.5528 1.16921
\(310\) 18.4904 1.05018
\(311\) −1.97238 −0.111843 −0.0559217 0.998435i \(-0.517810\pi\)
−0.0559217 + 0.998435i \(0.517810\pi\)
\(312\) 4.60474 0.260692
\(313\) −8.70211 −0.491872 −0.245936 0.969286i \(-0.579095\pi\)
−0.245936 + 0.969286i \(0.579095\pi\)
\(314\) 16.2883 0.919204
\(315\) −1.90067 −0.107091
\(316\) −3.62629 −0.203995
\(317\) −7.49906 −0.421189 −0.210595 0.977573i \(-0.567540\pi\)
−0.210595 + 0.977573i \(0.567540\pi\)
\(318\) 16.7625 0.939995
\(319\) 15.7982 0.884527
\(320\) 4.18312 0.233843
\(321\) 27.3875 1.52862
\(322\) −1.62395 −0.0904994
\(323\) 19.8294 1.10334
\(324\) −10.9556 −0.608645
\(325\) −28.9305 −1.60477
\(326\) −4.11200 −0.227742
\(327\) 36.1618 1.99975
\(328\) 1.06121 0.0585954
\(329\) −4.92004 −0.271250
\(330\) 13.6889 0.753548
\(331\) −15.4599 −0.849753 −0.424876 0.905251i \(-0.639682\pi\)
−0.424876 + 0.905251i \(0.639682\pi\)
\(332\) 1.55571 0.0853808
\(333\) −1.70738 −0.0935638
\(334\) −22.9167 −1.25395
\(335\) 15.6621 0.855713
\(336\) 0.944080 0.0515038
\(337\) 22.7842 1.24114 0.620568 0.784153i \(-0.286902\pi\)
0.620568 + 0.784153i \(0.286902\pi\)
\(338\) −7.64206 −0.415673
\(339\) −8.35352 −0.453701
\(340\) −12.0625 −0.654183
\(341\) −7.27123 −0.393759
\(342\) −6.58378 −0.356010
\(343\) 6.53713 0.352972
\(344\) 7.16539 0.386332
\(345\) −28.4759 −1.53309
\(346\) −13.2232 −0.710884
\(347\) 34.3711 1.84514 0.922569 0.385832i \(-0.126085\pi\)
0.922569 + 0.385832i \(0.126085\pi\)
\(348\) 19.1052 1.02415
\(349\) −33.0556 −1.76942 −0.884712 0.466138i \(-0.845645\pi\)
−0.884712 + 0.466138i \(0.845645\pi\)
\(350\) −5.93143 −0.317048
\(351\) −9.40553 −0.502030
\(352\) −1.64498 −0.0876780
\(353\) −8.08837 −0.430500 −0.215250 0.976559i \(-0.569057\pi\)
−0.215250 + 0.976559i \(0.569057\pi\)
\(354\) 20.9911 1.11566
\(355\) 21.3817 1.13482
\(356\) −5.45327 −0.289023
\(357\) −2.72237 −0.144083
\(358\) 15.1931 0.802982
\(359\) 11.5420 0.609161 0.304581 0.952487i \(-0.401484\pi\)
0.304581 + 0.952487i \(0.401484\pi\)
\(360\) 4.00501 0.211083
\(361\) 28.2872 1.48880
\(362\) 12.6131 0.662932
\(363\) 16.4995 0.866001
\(364\) 1.09850 0.0575772
\(365\) −29.7633 −1.55788
\(366\) 0.891850 0.0466177
\(367\) 22.6836 1.18407 0.592037 0.805911i \(-0.298324\pi\)
0.592037 + 0.805911i \(0.298324\pi\)
\(368\) 3.42193 0.178380
\(369\) 1.01602 0.0528921
\(370\) −7.45979 −0.387816
\(371\) 3.99886 0.207610
\(372\) −8.79331 −0.455912
\(373\) −5.55121 −0.287431 −0.143715 0.989619i \(-0.545905\pi\)
−0.143715 + 0.989619i \(0.545905\pi\)
\(374\) 4.74352 0.245281
\(375\) −62.3991 −3.22228
\(376\) 10.3673 0.534653
\(377\) 22.2302 1.14491
\(378\) −1.92836 −0.0991840
\(379\) 23.3873 1.20132 0.600662 0.799503i \(-0.294904\pi\)
0.600662 + 0.799503i \(0.294904\pi\)
\(380\) −28.7655 −1.47564
\(381\) 35.5516 1.82136
\(382\) −14.8350 −0.759023
\(383\) −11.6663 −0.596118 −0.298059 0.954548i \(-0.596339\pi\)
−0.298059 + 0.954548i \(0.596339\pi\)
\(384\) −1.98933 −0.101517
\(385\) 3.26561 0.166431
\(386\) −18.8113 −0.957470
\(387\) 6.86031 0.348729
\(388\) −17.9809 −0.912843
\(389\) 16.0353 0.813022 0.406511 0.913646i \(-0.366745\pi\)
0.406511 + 0.913646i \(0.366745\pi\)
\(390\) 19.2622 0.975377
\(391\) −9.86756 −0.499024
\(392\) −6.77478 −0.342178
\(393\) 9.23098 0.465641
\(394\) 20.2467 1.02001
\(395\) −15.1692 −0.763245
\(396\) −1.57494 −0.0791440
\(397\) 27.3738 1.37385 0.686926 0.726727i \(-0.258960\pi\)
0.686926 + 0.726727i \(0.258960\pi\)
\(398\) 13.5938 0.681398
\(399\) −6.49203 −0.325008
\(400\) 12.4985 0.624923
\(401\) 9.90184 0.494474 0.247237 0.968955i \(-0.420477\pi\)
0.247237 + 0.968955i \(0.420477\pi\)
\(402\) −7.44829 −0.371487
\(403\) −10.2316 −0.509674
\(404\) −1.45358 −0.0723183
\(405\) −45.8286 −2.27724
\(406\) 4.55772 0.226196
\(407\) 2.93351 0.145409
\(408\) 5.73647 0.283998
\(409\) 35.4042 1.75063 0.875313 0.483556i \(-0.160655\pi\)
0.875313 + 0.483556i \(0.160655\pi\)
\(410\) 4.43915 0.219234
\(411\) −31.2920 −1.54352
\(412\) −10.3315 −0.508998
\(413\) 5.00761 0.246409
\(414\) 3.27623 0.161018
\(415\) 6.50773 0.319452
\(416\) −2.31472 −0.113489
\(417\) −33.1107 −1.62144
\(418\) 11.3118 0.553280
\(419\) 6.61810 0.323315 0.161658 0.986847i \(-0.448316\pi\)
0.161658 + 0.986847i \(0.448316\pi\)
\(420\) 3.94920 0.192701
\(421\) −21.5293 −1.04927 −0.524636 0.851326i \(-0.675799\pi\)
−0.524636 + 0.851326i \(0.675799\pi\)
\(422\) −13.3638 −0.650540
\(423\) 9.92589 0.482613
\(424\) −8.42623 −0.409214
\(425\) −36.0409 −1.74824
\(426\) −10.1683 −0.492656
\(427\) 0.212759 0.0102961
\(428\) −13.7672 −0.665464
\(429\) −7.57472 −0.365711
\(430\) 29.9737 1.44546
\(431\) −24.9918 −1.20381 −0.601906 0.798567i \(-0.705592\pi\)
−0.601906 + 0.798567i \(0.705592\pi\)
\(432\) 4.06335 0.195498
\(433\) 17.6771 0.849506 0.424753 0.905309i \(-0.360361\pi\)
0.424753 + 0.905309i \(0.360361\pi\)
\(434\) −2.09773 −0.100694
\(435\) 79.9192 3.83183
\(436\) −18.1779 −0.870565
\(437\) −23.5311 −1.12565
\(438\) 14.1543 0.676318
\(439\) 19.0271 0.908115 0.454058 0.890972i \(-0.349976\pi\)
0.454058 + 0.890972i \(0.349976\pi\)
\(440\) −6.88116 −0.328046
\(441\) −6.48633 −0.308873
\(442\) 6.67479 0.317487
\(443\) 17.8049 0.845938 0.422969 0.906144i \(-0.360988\pi\)
0.422969 + 0.906144i \(0.360988\pi\)
\(444\) 3.54758 0.168361
\(445\) −22.8117 −1.08138
\(446\) −0.111513 −0.00528031
\(447\) −10.6042 −0.501564
\(448\) −0.474573 −0.0224214
\(449\) −29.3336 −1.38434 −0.692169 0.721735i \(-0.743345\pi\)
−0.692169 + 0.721735i \(0.743345\pi\)
\(450\) 11.9663 0.564097
\(451\) −1.74567 −0.0822004
\(452\) 4.19917 0.197512
\(453\) −35.1449 −1.65125
\(454\) −1.85493 −0.0870560
\(455\) 4.59517 0.215425
\(456\) 13.6797 0.640612
\(457\) −23.8034 −1.11348 −0.556738 0.830688i \(-0.687947\pi\)
−0.556738 + 0.830688i \(0.687947\pi\)
\(458\) −5.21795 −0.243819
\(459\) −11.7172 −0.546912
\(460\) 14.3143 0.667409
\(461\) −2.65682 −0.123741 −0.0618703 0.998084i \(-0.519707\pi\)
−0.0618703 + 0.998084i \(0.519707\pi\)
\(462\) −1.55300 −0.0722520
\(463\) −9.37826 −0.435845 −0.217922 0.975966i \(-0.569928\pi\)
−0.217922 + 0.975966i \(0.569928\pi\)
\(464\) −9.60384 −0.445847
\(465\) −36.7834 −1.70579
\(466\) −0.368052 −0.0170497
\(467\) 15.2842 0.707270 0.353635 0.935384i \(-0.384946\pi\)
0.353635 + 0.935384i \(0.384946\pi\)
\(468\) −2.21617 −0.102442
\(469\) −1.77686 −0.0820478
\(470\) 43.3676 2.00040
\(471\) −32.4028 −1.49304
\(472\) −10.5518 −0.485688
\(473\) −11.7870 −0.541965
\(474\) 7.21388 0.331344
\(475\) −85.9465 −3.94350
\(476\) 1.36849 0.0627246
\(477\) −8.06746 −0.369384
\(478\) −17.7774 −0.813119
\(479\) −40.6094 −1.85549 −0.927746 0.373211i \(-0.878257\pi\)
−0.927746 + 0.373211i \(0.878257\pi\)
\(480\) −8.32159 −0.379827
\(481\) 4.12786 0.188214
\(482\) −26.0379 −1.18599
\(483\) 3.23058 0.146996
\(484\) −8.29403 −0.377001
\(485\) −75.2163 −3.41540
\(486\) 9.60423 0.435657
\(487\) −13.7642 −0.623718 −0.311859 0.950128i \(-0.600952\pi\)
−0.311859 + 0.950128i \(0.600952\pi\)
\(488\) −0.448317 −0.0202944
\(489\) 8.18011 0.369917
\(490\) −28.3397 −1.28026
\(491\) −3.16730 −0.142938 −0.0714691 0.997443i \(-0.522769\pi\)
−0.0714691 + 0.997443i \(0.522769\pi\)
\(492\) −2.11109 −0.0951752
\(493\) 27.6939 1.24727
\(494\) 15.9173 0.716155
\(495\) −6.58818 −0.296117
\(496\) 4.42024 0.198475
\(497\) −2.42574 −0.108809
\(498\) −3.09482 −0.138682
\(499\) 8.62864 0.386271 0.193135 0.981172i \(-0.438134\pi\)
0.193135 + 0.981172i \(0.438134\pi\)
\(500\) 31.3669 1.40277
\(501\) 45.5888 2.03676
\(502\) −2.18913 −0.0977054
\(503\) 16.4282 0.732497 0.366248 0.930517i \(-0.380642\pi\)
0.366248 + 0.930517i \(0.380642\pi\)
\(504\) −0.454366 −0.0202391
\(505\) −6.08050 −0.270579
\(506\) −5.62902 −0.250241
\(507\) 15.2026 0.675170
\(508\) −17.8711 −0.792904
\(509\) −16.7018 −0.740296 −0.370148 0.928973i \(-0.620693\pi\)
−0.370148 + 0.928973i \(0.620693\pi\)
\(510\) 23.9963 1.06258
\(511\) 3.37664 0.149374
\(512\) 1.00000 0.0441942
\(513\) −27.9419 −1.23367
\(514\) −5.34519 −0.235766
\(515\) −43.2180 −1.90441
\(516\) −14.2543 −0.627511
\(517\) −17.0540 −0.750036
\(518\) 0.846309 0.0371847
\(519\) 26.3053 1.15467
\(520\) −9.68275 −0.424617
\(521\) 16.0802 0.704485 0.352242 0.935909i \(-0.385419\pi\)
0.352242 + 0.935909i \(0.385419\pi\)
\(522\) −9.19493 −0.402451
\(523\) −9.00341 −0.393692 −0.196846 0.980434i \(-0.563070\pi\)
−0.196846 + 0.980434i \(0.563070\pi\)
\(524\) −4.64025 −0.202710
\(525\) 11.7996 0.514975
\(526\) −19.2592 −0.839742
\(527\) −12.7463 −0.555238
\(528\) 3.27241 0.142413
\(529\) −11.2904 −0.490887
\(530\) −35.2479 −1.53107
\(531\) −10.1026 −0.438414
\(532\) 3.26343 0.141488
\(533\) −2.45640 −0.106398
\(534\) 10.8483 0.469454
\(535\) −57.5899 −2.48983
\(536\) 3.74413 0.161722
\(537\) −30.2241 −1.30427
\(538\) 2.58412 0.111410
\(539\) 11.1444 0.480024
\(540\) 16.9975 0.731455
\(541\) 27.9037 1.19967 0.599837 0.800122i \(-0.295232\pi\)
0.599837 + 0.800122i \(0.295232\pi\)
\(542\) −16.8995 −0.725897
\(543\) −25.0917 −1.07679
\(544\) −2.88362 −0.123634
\(545\) −76.0404 −3.25721
\(546\) −2.18528 −0.0935215
\(547\) −4.01884 −0.171833 −0.0859165 0.996302i \(-0.527382\pi\)
−0.0859165 + 0.996302i \(0.527382\pi\)
\(548\) 15.7299 0.671950
\(549\) −0.429229 −0.0183191
\(550\) −20.5598 −0.876672
\(551\) 66.0414 2.81346
\(552\) −6.80734 −0.289740
\(553\) 1.72094 0.0731817
\(554\) 5.03892 0.214083
\(555\) 14.8400 0.629921
\(556\) 16.6442 0.705871
\(557\) −14.4793 −0.613506 −0.306753 0.951789i \(-0.599243\pi\)
−0.306753 + 0.951789i \(0.599243\pi\)
\(558\) 4.23204 0.179156
\(559\) −16.5859 −0.701508
\(560\) −1.98519 −0.0838897
\(561\) −9.43641 −0.398405
\(562\) −12.8954 −0.543958
\(563\) −5.31302 −0.223917 −0.111959 0.993713i \(-0.535712\pi\)
−0.111959 + 0.993713i \(0.535712\pi\)
\(564\) −20.6240 −0.868425
\(565\) 17.5656 0.738991
\(566\) 28.4974 1.19784
\(567\) 5.19923 0.218347
\(568\) 5.11142 0.214471
\(569\) −11.5685 −0.484977 −0.242488 0.970154i \(-0.577964\pi\)
−0.242488 + 0.970154i \(0.577964\pi\)
\(570\) 57.2239 2.39685
\(571\) 22.6878 0.949453 0.474727 0.880133i \(-0.342547\pi\)
0.474727 + 0.880133i \(0.342547\pi\)
\(572\) 3.80768 0.159207
\(573\) 29.5116 1.23286
\(574\) −0.503620 −0.0210207
\(575\) 42.7689 1.78359
\(576\) 0.957423 0.0398926
\(577\) 34.5170 1.43696 0.718482 0.695546i \(-0.244837\pi\)
0.718482 + 0.695546i \(0.244837\pi\)
\(578\) −8.68471 −0.361236
\(579\) 37.4218 1.55520
\(580\) −40.1740 −1.66813
\(581\) −0.738298 −0.0306298
\(582\) 35.7699 1.48271
\(583\) 13.8610 0.574064
\(584\) −7.11511 −0.294425
\(585\) −9.27048 −0.383287
\(586\) −1.12299 −0.0463904
\(587\) 26.8394 1.10778 0.553891 0.832589i \(-0.313142\pi\)
0.553891 + 0.832589i \(0.313142\pi\)
\(588\) 13.4773 0.555793
\(589\) −30.3961 −1.25245
\(590\) −44.1396 −1.81720
\(591\) −40.2773 −1.65679
\(592\) −1.78331 −0.0732935
\(593\) −45.0683 −1.85074 −0.925368 0.379071i \(-0.876244\pi\)
−0.925368 + 0.379071i \(0.876244\pi\)
\(594\) −6.68415 −0.274254
\(595\) 5.72455 0.234684
\(596\) 5.33057 0.218349
\(597\) −27.0426 −1.10678
\(598\) −7.92082 −0.323906
\(599\) −7.49872 −0.306389 −0.153195 0.988196i \(-0.548956\pi\)
−0.153195 + 0.988196i \(0.548956\pi\)
\(600\) −24.8635 −1.01505
\(601\) −29.5657 −1.20601 −0.603006 0.797737i \(-0.706030\pi\)
−0.603006 + 0.797737i \(0.706030\pi\)
\(602\) −3.40050 −0.138594
\(603\) 3.58471 0.145981
\(604\) 17.6667 0.718849
\(605\) −34.6949 −1.41055
\(606\) 2.89165 0.117465
\(607\) 19.7198 0.800401 0.400201 0.916428i \(-0.368940\pi\)
0.400201 + 0.916428i \(0.368940\pi\)
\(608\) −6.87657 −0.278882
\(609\) −9.06679 −0.367405
\(610\) −1.87536 −0.0759313
\(611\) −23.9974 −0.970832
\(612\) −2.76085 −0.111601
\(613\) 2.56921 0.103770 0.0518848 0.998653i \(-0.483477\pi\)
0.0518848 + 0.998653i \(0.483477\pi\)
\(614\) 19.4889 0.786508
\(615\) −8.83093 −0.356098
\(616\) 0.780664 0.0314539
\(617\) 15.2894 0.615528 0.307764 0.951463i \(-0.400419\pi\)
0.307764 + 0.951463i \(0.400419\pi\)
\(618\) 20.5528 0.826755
\(619\) −23.4825 −0.943843 −0.471922 0.881640i \(-0.656439\pi\)
−0.471922 + 0.881640i \(0.656439\pi\)
\(620\) 18.4904 0.742592
\(621\) 13.9045 0.557969
\(622\) −1.97238 −0.0790853
\(623\) 2.58797 0.103685
\(624\) 4.60474 0.184337
\(625\) 68.7193 2.74877
\(626\) −8.70211 −0.347806
\(627\) −22.5030 −0.898681
\(628\) 16.2883 0.649975
\(629\) 5.14239 0.205041
\(630\) −1.90067 −0.0757244
\(631\) 36.0811 1.43637 0.718183 0.695854i \(-0.244974\pi\)
0.718183 + 0.695854i \(0.244974\pi\)
\(632\) −3.62629 −0.144246
\(633\) 26.5850 1.05666
\(634\) −7.49906 −0.297826
\(635\) −74.7571 −2.96664
\(636\) 16.7625 0.664677
\(637\) 15.6817 0.621333
\(638\) 15.7982 0.625455
\(639\) 4.89379 0.193595
\(640\) 4.18312 0.165352
\(641\) −11.2523 −0.444439 −0.222219 0.974997i \(-0.571330\pi\)
−0.222219 + 0.974997i \(0.571330\pi\)
\(642\) 27.3875 1.08090
\(643\) −30.9620 −1.22102 −0.610510 0.792008i \(-0.709036\pi\)
−0.610510 + 0.792008i \(0.709036\pi\)
\(644\) −1.62395 −0.0639928
\(645\) −59.6274 −2.34783
\(646\) 19.8294 0.780179
\(647\) 4.12008 0.161977 0.0809886 0.996715i \(-0.474192\pi\)
0.0809886 + 0.996715i \(0.474192\pi\)
\(648\) −10.9556 −0.430377
\(649\) 17.3576 0.681346
\(650\) −28.9305 −1.13475
\(651\) 4.17306 0.163555
\(652\) −4.11200 −0.161038
\(653\) 35.9180 1.40558 0.702790 0.711398i \(-0.251937\pi\)
0.702790 + 0.711398i \(0.251937\pi\)
\(654\) 36.1618 1.41404
\(655\) −19.4107 −0.758440
\(656\) 1.06121 0.0414332
\(657\) −6.81217 −0.265768
\(658\) −4.92004 −0.191803
\(659\) −32.7456 −1.27559 −0.637795 0.770206i \(-0.720153\pi\)
−0.637795 + 0.770206i \(0.720153\pi\)
\(660\) 13.6889 0.532839
\(661\) 44.4352 1.72833 0.864164 0.503210i \(-0.167848\pi\)
0.864164 + 0.503210i \(0.167848\pi\)
\(662\) −15.4599 −0.600866
\(663\) −13.2783 −0.515688
\(664\) 1.55571 0.0603734
\(665\) 13.6513 0.529375
\(666\) −1.70738 −0.0661596
\(667\) −32.8637 −1.27249
\(668\) −22.9167 −0.886673
\(669\) 0.221836 0.00857669
\(670\) 15.6621 0.605080
\(671\) 0.737475 0.0284699
\(672\) 0.944080 0.0364187
\(673\) 8.06606 0.310924 0.155462 0.987842i \(-0.450313\pi\)
0.155462 + 0.987842i \(0.450313\pi\)
\(674\) 22.7842 0.877616
\(675\) 50.7857 1.95474
\(676\) −7.64206 −0.293926
\(677\) −26.4165 −1.01527 −0.507634 0.861573i \(-0.669480\pi\)
−0.507634 + 0.861573i \(0.669480\pi\)
\(678\) −8.35352 −0.320815
\(679\) 8.53325 0.327476
\(680\) −12.0625 −0.462577
\(681\) 3.69006 0.141403
\(682\) −7.27123 −0.278430
\(683\) −20.0634 −0.767706 −0.383853 0.923394i \(-0.625403\pi\)
−0.383853 + 0.923394i \(0.625403\pi\)
\(684\) −6.58378 −0.251737
\(685\) 65.8002 2.51410
\(686\) 6.53713 0.249589
\(687\) 10.3802 0.396029
\(688\) 7.16539 0.273178
\(689\) 19.5044 0.743057
\(690\) −28.4759 −1.08406
\(691\) −10.7900 −0.410470 −0.205235 0.978713i \(-0.565796\pi\)
−0.205235 + 0.978713i \(0.565796\pi\)
\(692\) −13.2232 −0.502671
\(693\) 0.747426 0.0283924
\(694\) 34.3711 1.30471
\(695\) 69.6246 2.64101
\(696\) 19.1052 0.724180
\(697\) −3.06012 −0.115910
\(698\) −33.0556 −1.25117
\(699\) 0.732176 0.0276934
\(700\) −5.93143 −0.224187
\(701\) 1.91478 0.0723203 0.0361601 0.999346i \(-0.488487\pi\)
0.0361601 + 0.999346i \(0.488487\pi\)
\(702\) −9.40553 −0.354989
\(703\) 12.2630 0.462509
\(704\) −1.64498 −0.0619977
\(705\) −86.2724 −3.24921
\(706\) −8.08837 −0.304410
\(707\) 0.689830 0.0259437
\(708\) 20.9911 0.788892
\(709\) 8.85290 0.332478 0.166239 0.986086i \(-0.446838\pi\)
0.166239 + 0.986086i \(0.446838\pi\)
\(710\) 21.3817 0.802440
\(711\) −3.47189 −0.130206
\(712\) −5.45327 −0.204370
\(713\) 15.1258 0.566464
\(714\) −2.72237 −0.101882
\(715\) 15.9280 0.595672
\(716\) 15.1931 0.567794
\(717\) 35.3651 1.32073
\(718\) 11.5420 0.430742
\(719\) −48.7524 −1.81816 −0.909078 0.416625i \(-0.863213\pi\)
−0.909078 + 0.416625i \(0.863213\pi\)
\(720\) 4.00501 0.149258
\(721\) 4.90306 0.182600
\(722\) 28.2872 1.05274
\(723\) 51.7979 1.92639
\(724\) 12.6131 0.468764
\(725\) −120.033 −4.45792
\(726\) 16.4995 0.612355
\(727\) −33.9372 −1.25866 −0.629330 0.777138i \(-0.716671\pi\)
−0.629330 + 0.777138i \(0.716671\pi\)
\(728\) 1.09850 0.0407132
\(729\) 13.7609 0.509662
\(730\) −29.7633 −1.10159
\(731\) −20.6623 −0.764223
\(732\) 0.891850 0.0329637
\(733\) 47.8091 1.76587 0.882935 0.469495i \(-0.155564\pi\)
0.882935 + 0.469495i \(0.155564\pi\)
\(734\) 22.6836 0.837267
\(735\) 56.3769 2.07949
\(736\) 3.42193 0.126134
\(737\) −6.15903 −0.226871
\(738\) 1.01602 0.0374004
\(739\) −34.5436 −1.27071 −0.635353 0.772222i \(-0.719146\pi\)
−0.635353 + 0.772222i \(0.719146\pi\)
\(740\) −7.45979 −0.274227
\(741\) −31.6648 −1.16323
\(742\) 3.99886 0.146803
\(743\) 19.7476 0.724470 0.362235 0.932087i \(-0.382014\pi\)
0.362235 + 0.932087i \(0.382014\pi\)
\(744\) −8.79331 −0.322378
\(745\) 22.2984 0.816950
\(746\) −5.55121 −0.203244
\(747\) 1.48947 0.0544970
\(748\) 4.74352 0.173440
\(749\) 6.53355 0.238731
\(750\) −62.3991 −2.27849
\(751\) 50.2282 1.83285 0.916426 0.400205i \(-0.131061\pi\)
0.916426 + 0.400205i \(0.131061\pi\)
\(752\) 10.3673 0.378057
\(753\) 4.35489 0.158701
\(754\) 22.2302 0.809577
\(755\) 73.9020 2.68957
\(756\) −1.92836 −0.0701337
\(757\) −46.2342 −1.68041 −0.840205 0.542268i \(-0.817566\pi\)
−0.840205 + 0.542268i \(0.817566\pi\)
\(758\) 23.3873 0.849464
\(759\) 11.1980 0.406460
\(760\) −28.7655 −1.04343
\(761\) 16.4378 0.595870 0.297935 0.954586i \(-0.403702\pi\)
0.297935 + 0.954586i \(0.403702\pi\)
\(762\) 35.5516 1.28790
\(763\) 8.62675 0.312309
\(764\) −14.8350 −0.536710
\(765\) −11.5489 −0.417553
\(766\) −11.6663 −0.421519
\(767\) 24.4246 0.881920
\(768\) −1.98933 −0.0717837
\(769\) 36.2035 1.30553 0.652766 0.757560i \(-0.273609\pi\)
0.652766 + 0.757560i \(0.273609\pi\)
\(770\) 3.26561 0.117684
\(771\) 10.6333 0.382950
\(772\) −18.8113 −0.677033
\(773\) −5.42466 −0.195111 −0.0975557 0.995230i \(-0.531102\pi\)
−0.0975557 + 0.995230i \(0.531102\pi\)
\(774\) 6.86031 0.246589
\(775\) 55.2462 1.98450
\(776\) −17.9809 −0.645477
\(777\) −1.68359 −0.0603983
\(778\) 16.0353 0.574893
\(779\) −7.29746 −0.261459
\(780\) 19.2622 0.689696
\(781\) −8.40821 −0.300870
\(782\) −9.86756 −0.352863
\(783\) −39.0238 −1.39460
\(784\) −6.77478 −0.241956
\(785\) 68.1360 2.43188
\(786\) 9.23098 0.329258
\(787\) −44.6895 −1.59301 −0.796504 0.604633i \(-0.793320\pi\)
−0.796504 + 0.604633i \(0.793320\pi\)
\(788\) 20.2467 0.721258
\(789\) 38.3129 1.36398
\(790\) −15.1692 −0.539696
\(791\) −1.99281 −0.0708562
\(792\) −1.57494 −0.0559632
\(793\) 1.03773 0.0368509
\(794\) 27.3738 0.971460
\(795\) 70.1196 2.48688
\(796\) 13.5938 0.481821
\(797\) −25.5059 −0.903464 −0.451732 0.892154i \(-0.649194\pi\)
−0.451732 + 0.892154i \(0.649194\pi\)
\(798\) −6.49203 −0.229815
\(799\) −29.8954 −1.05762
\(800\) 12.4985 0.441887
\(801\) −5.22109 −0.184478
\(802\) 9.90184 0.349646
\(803\) 11.7042 0.413034
\(804\) −7.44829 −0.262681
\(805\) −6.79319 −0.239428
\(806\) −10.2316 −0.360394
\(807\) −5.14067 −0.180960
\(808\) −1.45358 −0.0511368
\(809\) −4.20177 −0.147727 −0.0738633 0.997268i \(-0.523533\pi\)
−0.0738633 + 0.997268i \(0.523533\pi\)
\(810\) −45.8286 −1.61025
\(811\) 15.7122 0.551729 0.275865 0.961196i \(-0.411036\pi\)
0.275865 + 0.961196i \(0.411036\pi\)
\(812\) 4.55772 0.159945
\(813\) 33.6187 1.17906
\(814\) 2.93351 0.102820
\(815\) −17.2010 −0.602524
\(816\) 5.73647 0.200817
\(817\) −49.2733 −1.72385
\(818\) 35.4042 1.23788
\(819\) 1.05173 0.0367505
\(820\) 4.43915 0.155022
\(821\) 48.7730 1.70219 0.851094 0.525014i \(-0.175940\pi\)
0.851094 + 0.525014i \(0.175940\pi\)
\(822\) −31.2920 −1.09143
\(823\) −15.7202 −0.547971 −0.273985 0.961734i \(-0.588342\pi\)
−0.273985 + 0.961734i \(0.588342\pi\)
\(824\) −10.3315 −0.359916
\(825\) 40.9001 1.42396
\(826\) 5.00761 0.174237
\(827\) −12.9109 −0.448956 −0.224478 0.974479i \(-0.572068\pi\)
−0.224478 + 0.974479i \(0.572068\pi\)
\(828\) 3.27623 0.113857
\(829\) 8.42570 0.292637 0.146318 0.989238i \(-0.453258\pi\)
0.146318 + 0.989238i \(0.453258\pi\)
\(830\) 6.50773 0.225886
\(831\) −10.0241 −0.347731
\(832\) −2.31472 −0.0802485
\(833\) 19.5359 0.676880
\(834\) −33.1107 −1.14653
\(835\) −95.8632 −3.31748
\(836\) 11.3118 0.391228
\(837\) 17.9610 0.620823
\(838\) 6.61810 0.228619
\(839\) 15.3530 0.530043 0.265022 0.964242i \(-0.414621\pi\)
0.265022 + 0.964242i \(0.414621\pi\)
\(840\) 3.94920 0.136260
\(841\) 63.2337 2.18047
\(842\) −21.5293 −0.741948
\(843\) 25.6531 0.883540
\(844\) −13.3638 −0.460001
\(845\) −31.9676 −1.09972
\(846\) 9.92589 0.341259
\(847\) 3.93612 0.135247
\(848\) −8.42623 −0.289358
\(849\) −56.6907 −1.94562
\(850\) −36.0409 −1.23619
\(851\) −6.10236 −0.209186
\(852\) −10.1683 −0.348360
\(853\) −39.6835 −1.35874 −0.679368 0.733798i \(-0.737746\pi\)
−0.679368 + 0.733798i \(0.737746\pi\)
\(854\) 0.212759 0.00728047
\(855\) −27.5407 −0.941873
\(856\) −13.7672 −0.470554
\(857\) 15.3071 0.522879 0.261440 0.965220i \(-0.415803\pi\)
0.261440 + 0.965220i \(0.415803\pi\)
\(858\) −7.57472 −0.258597
\(859\) 13.8908 0.473948 0.236974 0.971516i \(-0.423844\pi\)
0.236974 + 0.971516i \(0.423844\pi\)
\(860\) 29.9737 1.02209
\(861\) 1.00186 0.0341435
\(862\) −24.9918 −0.851223
\(863\) 28.9141 0.984248 0.492124 0.870525i \(-0.336221\pi\)
0.492124 + 0.870525i \(0.336221\pi\)
\(864\) 4.06335 0.138238
\(865\) −55.3143 −1.88074
\(866\) 17.6771 0.600692
\(867\) 17.2767 0.586748
\(868\) −2.09773 −0.0712014
\(869\) 5.96519 0.202355
\(870\) 79.9192 2.70951
\(871\) −8.66661 −0.293657
\(872\) −18.1779 −0.615582
\(873\) −17.2153 −0.582651
\(874\) −23.5311 −0.795952
\(875\) −14.8859 −0.503235
\(876\) 14.1543 0.478229
\(877\) 25.1673 0.849840 0.424920 0.905231i \(-0.360302\pi\)
0.424920 + 0.905231i \(0.360302\pi\)
\(878\) 19.0271 0.642134
\(879\) 2.23400 0.0753509
\(880\) −6.88116 −0.231964
\(881\) 8.64097 0.291122 0.145561 0.989349i \(-0.453501\pi\)
0.145561 + 0.989349i \(0.453501\pi\)
\(882\) −6.48633 −0.218406
\(883\) 24.0934 0.810808 0.405404 0.914138i \(-0.367131\pi\)
0.405404 + 0.914138i \(0.367131\pi\)
\(884\) 6.67479 0.224497
\(885\) 87.8080 2.95163
\(886\) 17.8049 0.598169
\(887\) −1.47342 −0.0494726 −0.0247363 0.999694i \(-0.507875\pi\)
−0.0247363 + 0.999694i \(0.507875\pi\)
\(888\) 3.54758 0.119049
\(889\) 8.48116 0.284449
\(890\) −22.8117 −0.764649
\(891\) 18.0218 0.603753
\(892\) −0.111513 −0.00373374
\(893\) −71.2914 −2.38568
\(894\) −10.6042 −0.354659
\(895\) 63.5546 2.12440
\(896\) −0.474573 −0.0158544
\(897\) 15.7571 0.526114
\(898\) −29.3336 −0.978875
\(899\) −42.4513 −1.41583
\(900\) 11.9663 0.398877
\(901\) 24.2981 0.809486
\(902\) −1.74567 −0.0581244
\(903\) 6.76470 0.225115
\(904\) 4.19917 0.139662
\(905\) 52.7623 1.75388
\(906\) −35.1449 −1.16761
\(907\) 21.4521 0.712304 0.356152 0.934428i \(-0.384089\pi\)
0.356152 + 0.934428i \(0.384089\pi\)
\(908\) −1.85493 −0.0615579
\(909\) −1.39169 −0.0461595
\(910\) 4.59517 0.152328
\(911\) −38.0964 −1.26219 −0.631095 0.775705i \(-0.717394\pi\)
−0.631095 + 0.775705i \(0.717394\pi\)
\(912\) 13.6797 0.452981
\(913\) −2.55912 −0.0846946
\(914\) −23.8034 −0.787346
\(915\) 3.73071 0.123334
\(916\) −5.21795 −0.172406
\(917\) 2.20214 0.0727210
\(918\) −11.7172 −0.386725
\(919\) −45.4482 −1.49920 −0.749599 0.661892i \(-0.769754\pi\)
−0.749599 + 0.661892i \(0.769754\pi\)
\(920\) 14.3143 0.471930
\(921\) −38.7698 −1.27751
\(922\) −2.65682 −0.0874978
\(923\) −11.8315 −0.389439
\(924\) −1.55300 −0.0510899
\(925\) −22.2886 −0.732845
\(926\) −9.37826 −0.308189
\(927\) −9.89164 −0.324884
\(928\) −9.60384 −0.315261
\(929\) −16.3576 −0.536675 −0.268338 0.963325i \(-0.586474\pi\)
−0.268338 + 0.963325i \(0.586474\pi\)
\(930\) −36.7834 −1.20618
\(931\) 46.5872 1.52683
\(932\) −0.368052 −0.0120559
\(933\) 3.92371 0.128457
\(934\) 15.2842 0.500115
\(935\) 19.8427 0.648925
\(936\) −2.21617 −0.0724377
\(937\) 22.9535 0.749858 0.374929 0.927053i \(-0.377667\pi\)
0.374929 + 0.927053i \(0.377667\pi\)
\(938\) −1.77686 −0.0580165
\(939\) 17.3113 0.564934
\(940\) 43.3676 1.41450
\(941\) 40.6526 1.32524 0.662618 0.748957i \(-0.269445\pi\)
0.662618 + 0.748957i \(0.269445\pi\)
\(942\) −32.4028 −1.05574
\(943\) 3.63138 0.118254
\(944\) −10.5518 −0.343433
\(945\) −8.06654 −0.262405
\(946\) −11.7870 −0.383227
\(947\) −13.3149 −0.432675 −0.216338 0.976319i \(-0.569411\pi\)
−0.216338 + 0.976319i \(0.569411\pi\)
\(948\) 7.21388 0.234296
\(949\) 16.4695 0.534623
\(950\) −85.9465 −2.78847
\(951\) 14.9181 0.483752
\(952\) 1.36849 0.0443530
\(953\) 20.9200 0.677666 0.338833 0.940847i \(-0.389968\pi\)
0.338833 + 0.940847i \(0.389968\pi\)
\(954\) −8.06746 −0.261194
\(955\) −62.0564 −2.00810
\(956\) −17.7774 −0.574962
\(957\) −31.4277 −1.01591
\(958\) −40.6094 −1.31203
\(959\) −7.46500 −0.241057
\(960\) −8.32159 −0.268578
\(961\) −11.4615 −0.369725
\(962\) 4.12786 0.133088
\(963\) −13.1810 −0.424753
\(964\) −26.0379 −0.838625
\(965\) −78.6898 −2.53312
\(966\) 3.23058 0.103942
\(967\) −8.80297 −0.283085 −0.141542 0.989932i \(-0.545206\pi\)
−0.141542 + 0.989932i \(0.545206\pi\)
\(968\) −8.29403 −0.266580
\(969\) −39.4472 −1.26723
\(970\) −75.2163 −2.41505
\(971\) 4.87576 0.156471 0.0782354 0.996935i \(-0.475071\pi\)
0.0782354 + 0.996935i \(0.475071\pi\)
\(972\) 9.60423 0.308056
\(973\) −7.89888 −0.253226
\(974\) −13.7642 −0.441035
\(975\) 57.5522 1.84314
\(976\) −0.448317 −0.0143503
\(977\) −15.2086 −0.486566 −0.243283 0.969955i \(-0.578224\pi\)
−0.243283 + 0.969955i \(0.578224\pi\)
\(978\) 8.18011 0.261571
\(979\) 8.97055 0.286700
\(980\) −28.3397 −0.905278
\(981\) −17.4040 −0.555666
\(982\) −3.16730 −0.101073
\(983\) −26.5822 −0.847842 −0.423921 0.905699i \(-0.639347\pi\)
−0.423921 + 0.905699i \(0.639347\pi\)
\(984\) −2.11109 −0.0672991
\(985\) 84.6942 2.69858
\(986\) 27.6939 0.881953
\(987\) 9.78756 0.311542
\(988\) 15.9173 0.506398
\(989\) 24.5195 0.779674
\(990\) −6.58818 −0.209386
\(991\) −51.7593 −1.64419 −0.822094 0.569352i \(-0.807194\pi\)
−0.822094 + 0.569352i \(0.807194\pi\)
\(992\) 4.42024 0.140343
\(993\) 30.7548 0.975974
\(994\) −2.42574 −0.0769399
\(995\) 56.8646 1.80273
\(996\) −3.09482 −0.0980632
\(997\) −53.7429 −1.70206 −0.851028 0.525120i \(-0.824020\pi\)
−0.851028 + 0.525120i \(0.824020\pi\)
\(998\) 8.62864 0.273135
\(999\) −7.24622 −0.229260
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 \(a_p\))